Deltares Coastal Structures Toolbox package contents

Hydraulic

Wave Overtopping

TAW (2002)

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.taw2002.Rc_diml_max_equation(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], q: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]], c3: float, cor3: float = 0.0, c2: float = 0.2, g: float = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the maximum of the dimensionless crest freeboard Rc/Hm0 with the TAW (2002) formula.

The maximum value of the dimensionless crest freeboard Rc/Hm0 (-) is calculated using the TAW (2002) formulas. Here eqs. 23 and 25 from TAW (2002) are implemented.

For more details see TAW (2002), available here (in Dutch): https://open.rijkswaterstaat.nl/open-overheid/onderzoeksrapporten/@97617/technisch-rapport-golfoploop/

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
q (float | npt.NDArray[np.float64]) – Mean wave overtopping discharge (m^3/s/m)
gamma_beta (float | npt.NDArray[np.float64]) – Influence factor for oblique wave incidence (-)
gamma_f (float | npt.NDArray[np.float64]) – Influence factor for surface roughness (-)
c3 (float) – Coefficient in the q max equation (-)
cor3 (float, optional) – Uncertainty accounted for in coefficient c3, by default 0.0
c2 (float, optional) – Coefficient in the q max equation (-), by default 0.2
g (float, optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

The maximum value of the dimensionless crest freeboard of the structure Rc/Hm0 (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.taw2002.calculate_crest_freeboard_Rc(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], q: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, B_berm: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, db: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_b: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, gamma_v: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, sigma: float | ndarray[tuple[Any, ...], dtype[float64]] = 0, g: float = 9.81, use_best_fit: bool = False) → tuple[float | ndarray[tuple[Any, ...], dtype[float64]], bool | ndarray[tuple[Any, ...], dtype[bool]]][source]

Calculate the crest freeboard Rc with the TAW (2002) formula.

The crest freeboard Rc (m) is calculated using the TAW (2002) formulas. Here eqs. 22 and 23 from TAW (2002) are implemented for design calculations and eqs. 24 and 25 for best fit calculations (using the option best_fit=True).

For more details see TAW (2002), available here (in Dutch): https://open.rijkswaterstaat.nl/open-overheid/onderzoeksrapporten/@97617/technisch-rapport-golfoploop/

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
q (float | npt.NDArray[np.float64]) – Mean wave overtopping discharge (m^3/s/m)
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
cot_alpha_down (float | npt.NDArray[np.float64], optional) – Cotangent of the lower part of the front-side slope of the structure (-), by default np.nan
cot_alpha_up (float | npt.NDArray[np.float64], optional) – Cotangent of the upper part of the front-side slope of the structure (-), by default np.nan
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
B_berm (float | npt.NDArray[np.float64], optional) – Berm width of the structure (m), by default 0.0
db (float | npt.NDArray[np.float64], optional) – Berm height of the structure (m), by default 0.0
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_b (float | npt.NDArray[np.float64], optional) – Influence factor for a berm gamma_b (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0
gamma_v (float | npt.NDArray[np.float64], optional) – Influence factor for a crest wall (-), by default 1.0
sigma (float | npt.NDArray[np.float64], optional) – Apply sigma standard deviations to the best fit coefficients, by default 0
g (float, optional) – Gravitational constant (m/s^2), by default 9.81
use_best_fit (bool, optional) – Use the coefficients of the best fit instead of the more conservative design variant, by default False

Returns:

The crest freeboard of the structure Rc (m)

Return type:

tuple[float | npt.NDArray[np.float64], bool | npt.NDArray[np.bool]]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.taw2002.calculate_dimensionless_crest_freeboard(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], q: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, B_berm: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, db: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_b: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, gamma_v: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, sigma: float | ndarray[tuple[Any, ...], dtype[float64]] = 0, g: float = 9.81, use_best_fit: bool = False) → tuple[float | ndarray[tuple[Any, ...], dtype[float64]], bool | ndarray[tuple[Any, ...], dtype[bool]]][source]

Calculate the dimensionless crest freeboard Rc/Hm0 with the TAW (2002) formula.

The dimensionless crest freeboard Rc/Hm0 (-) is calculated using the TAW (2002) formulas. Here eqs. 22 and 23 from TAW (2002) are implemented for design calculations and eqs. 24 and 25 for best fit calculations (using the option best_fit=True).

For more details see TAW (2002), available here (in Dutch): https://open.rijkswaterstaat.nl/open-overheid/onderzoeksrapporten/@97617/technisch-rapport-golfoploop/

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
q (float | npt.NDArray[np.float64]) – Mean wave overtopping discharge (m^3/s/m)
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
cot_alpha_down (float | npt.NDArray[np.float64], optional) – Cotangent of the lower part of the front-side slope of the structure (-), by default np.nan
cot_alpha_up (float | npt.NDArray[np.float64], optional) – Cotangent of the upper part of the front-side slope of the structure (-), by default np.nan
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
B_berm (float | npt.NDArray[np.float64], optional) – Berm width of the structure (m), by default 0.0
db (float | npt.NDArray[np.float64], optional) – Berm height of the structure (m), by default 0.0
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_b (float | npt.NDArray[np.float64], optional) – Influence factor for a berm gamma_b (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0
gamma_v (float | npt.NDArray[np.float64], optional) – Influence factor for a crest wall (-), by default 1.0
sigma (float | npt.NDArray[np.float64], optional) – Apply sigma standard deviations to the best fit coefficients, by default 0
g (float, optional) – Gravitational constant (m/s^2), by default 9.81
use_best_fit (bool, optional) – Use the coefficients of the best fit instead of the more conservative design variant, by default False

Returns:

The dimensionless crest freeboard of the structure Rc/Hm0 (-)

Return type:

tuple[float | npt.NDArray[np.float64], bool | npt.NDArray[np.bool]]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.taw2002.calculate_dimensionless_overtopping_discharge_q(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, B_berm: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, db: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_b: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, gamma_v: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, sigma: float | ndarray[tuple[Any, ...], dtype[float64]] = 0, use_best_fit: bool = False) → tuple[float | ndarray[tuple[Any, ...], dtype[float64]], bool | ndarray[tuple[Any, ...], dtype[bool]]][source]

Calculate the dimensionless mean wave overtopping discharge q with the TAW (2002) formula.

The dimensionless mean wave overtopping discharge q/sqrt(g*Hm0^3) (-) is calculated using the TAW (2002) formulas. Here eqs. 22 and 23 from TAW (2002) are implemented for design calculations and eqs. 24 and 25 for best fit calculations (using the option best_fit=True).

For more details see TAW (2002), available here (in Dutch): https://open.rijkswaterstaat.nl/open-overheid/onderzoeksrapporten/@97617/technisch-rapport-golfoploop/

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
cot_alpha_down (float | npt.NDArray[np.float64], optional) – Cotangent of the lower part of the front-side slope of the structure (-), by default np.nan
cot_alpha_up (float | npt.NDArray[np.float64], optional) – Cotangent of the upper part of the front-side slope of the structure (-), by default np.nan
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
B_berm (float | npt.NDArray[np.float64], optional) – Berm width of the structure (m), by default 0.0
db (float | npt.NDArray[np.float64], optional) – Berm height of the structure (m), by default 0.0
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_b (float | npt.NDArray[np.float64], optional) – Influence factor for a berm gamma_b (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0
gamma_v (float | npt.NDArray[np.float64], optional) – Influence factor for a crest wall (-), by default 1.0
sigma (float | npt.NDArray[np.float64], optional) – Apply sigma standard deviations to the best fit coefficients, by default 0
use_best_fit (bool, optional) – Use the coefficients of the best fit instead of the more conservative design variant, by default False

Returns:

Dimensionless mean wave overtopping discharge q/sqrt(g*Hm0^3) (-) and a boolean indicating whether the maximum value formula was used

Return type:

tuple[float | npt.NDArray[np.float64], bool | npt.NDArray[np.bool]]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.taw2002.calculate_influence_crest_wall_gamma_v(alpha_wall_deg: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the influence factor for crest walls gamma_v

The influence factor for crest walls gamma_v (-) on wave overtopping is calculated using eq. 16 from TAW (2002).

Parameters:: alpha_wall_deg (float | npt.NDArray[np.float64]) – Slope of the (near) vertical crest wall (degrees)
Returns:: The influence factor for a crest wall gamma_v (-)
Return type:: float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.taw2002.calculate_influence_oblique_waves_gamma_beta(beta: float | ndarray[tuple[Any, ...], dtype[float64]], c_gamma_beta: float = 0.0033, max_angle: float = 80.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the influence factor for oblique wave incidence gamma_beta

The influence factor for oblique wave incidence gamma_beta (-) on wave overtopping is calculated using eq. 9 from TAW (2002). Note that this uses the implementation for wave runup, but changes the coefficient to the value used for wave overtopping

Parameters:

beta (float | npt.NDArray[np.float64]) – Angle of wave incidence (degrees)
c_gamma_beta (float, optional) – Coefficient for wave overtopping, by default 0.0033
max_angle (float, optional) – Maximum angle of wave incidence, by default 80.0

Returns:

The influence factor for oblique wave incidence gamma_beta (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.taw2002.calculate_overtopping_discharge_q(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, B_berm: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, db: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_b: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, gamma_v: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, sigma: float | ndarray[tuple[Any, ...], dtype[float64]] = 0, g: float = 9.81, use_best_fit: bool = False) → tuple[float | ndarray[tuple[Any, ...], dtype[float64]], bool | ndarray[tuple[Any, ...], dtype[bool]]][source]

Calculate the mean wave overtopping discharge q with the TAW (2002) formula.

The mean wave overtopping discharge q (m^3/s/m) is calculated using the TAW (2002) formulas. Here eqs. 22 and 23 from TAW (2002) are implemented for design calculations and eqs. 24 and 25 for best fit calculations (using the option best_fit=True).

For more details see TAW (2002), available here (in Dutch): https://open.rijkswaterstaat.nl/open-overheid/onderzoeksrapporten/@97617/technisch-rapport-golfoploop/

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
cot_alpha_down (float | npt.NDArray[np.float64], optional) – Cotangent of the lower part of the front-side slope of the structure (-), by default np.nan
cot_alpha_up (float | npt.NDArray[np.float64], optional) – Cotangent of the upper part of the front-side slope of the structure (-), by default np.nan
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
B_berm (float | npt.NDArray[np.float64], optional) – Berm width of the structure (m), by default 0.0
db (float | npt.NDArray[np.float64], optional) – Berm height of the structure (m), by default 0.0
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_b (float | npt.NDArray[np.float64], optional) – Influence factor for a berm gamma_b (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0
gamma_v (float | npt.NDArray[np.float64], optional) – Influence factor for a crest wall (-), by default 1.0
sigma (float | npt.NDArray[np.float64], optional) – Apply sigma standard deviations to the best fit coefficients, by default 0
g (float, optional) – Gravitational constant (m/s^2), by default 9.81
use_best_fit (bool, optional) – Use the coefficients of the best fit instead of the more conservative design variant, by default False

Returns:

Mean wave overtopping discharge q (m^3/s/m) and a boolean indicating whether the maximum value formula was used

Return type:

tuple[float | npt.NDArray[np.float64], bool | npt.NDArray[np.bool]]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.taw2002.check_validity_range(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_b: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_v: float | ndarray[tuple[Any, ...], dtype[float64]] = nan) → None[source]

Check the parameter values vs the validity range of the TAW (2002) wave overtopping formula

For all parameters supplied, their values are checked versus the range of test conditions specified by TAW (2002) in the table on pages 39-40. When parameters are nan (by default), they are not checked.

For more details see TAW (2002), available here (in Dutch): https://open.rijkswaterstaat.nl/open-overheid/onderzoeksrapporten/@97617/technisch-rapport-golfoploop/

Parameters:

Hm0 (float | npt.NDArray[np.float64], optional) – Spectral significant wave height (m), by default np.nan
Tmm10 (float | npt.NDArray[np.float64], optional) – Spectral wave period Tm-1,0 (s), by default np.nan
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
cot_alpha_down (float | npt.NDArray[np.float64], optional) – Cotangent of the lower part of the front-side slope of the structure (-), by default np.nan
cot_alpha_up (float | npt.NDArray[np.float64], optional) – Cotangent of the upper part of the front-side slope of the structure (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default np.nan
gamma_b (float | npt.NDArray[np.float64], optional) – Influence factor for a berm, by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_v (float | npt.NDArray[np.float64], optional) – Influence factor for a crest wall (-), by default np.nan

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.taw2002.q_diml_max_equation(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]], c3: float, cor3: float = 0.0, c2: float = 0.2) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the maximum wave overtopping discharge q with the TAW (2002) formula.

The maximum wave overtopping discharge q (m^3/s/m) is calculated using the TAW (2002) formulas. Here eqs. 23 and 25 from TAW (2002) are implemented.

For more details see TAW (2002), available here (in Dutch): https://open.rijkswaterstaat.nl/open-overheid/onderzoeksrapporten/@97617/technisch-rapport-golfoploop/

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
gamma_beta (float | npt.NDArray[np.float64]) – Influence factor for oblique wave incidence (-)
gamma_f (float | npt.NDArray[np.float64]) – Influence factor for surface roughness (-)
c3 (float) – Coefficient in the q max equation (-)
cor3 (float, optional) – Uncertainty accounted for in coefficient c3, by default 0.0
c2 (float, optional) – Coefficient in the q max equation (-), by default 0.2

Returns:

Maximum value for the dimensionless mean wave overtopping discharge q/sqrt(g*Hm0^3) (-)

Return type:

float | npt.NDArray[np.float64]

Van Gent (2002)

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.vangent2002_velocity.calculate_maximum_wave_overtopping_velocity_uXp(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], zXp: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], Bc: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f_Crest: float | ndarray[tuple[Any, ...], dtype[float64]], cu1: float = 1.7, cu2: float = 0.1, g: float = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the maximum wave overtopping velocity following Van Gent (2002).

For a given wave runup height with an exceedance probability, the maximum wave overtopping velocity with the same exceedance probability is calculated.

For more details see Van Gent (2002), available here: https://doi.org/10.1142/9789812791306_0185 or here: https://www.researchgate.net/publication/259260272_Wave_overtopping_events_at_dikes

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
zXp (float | npt.NDArray[np.float64]) – The wave runup height z (m)
Rc (float | npt.NDArray[np.float64]) – Freeboard of the structure (m)
Bc (float | npt.NDArray[np.float64]) – Width of the crest of the structure (m)
gamma_f (float | npt.NDArray[np.float64]) – Influence factor for surface roughness (-)
gamma_f_Crest (float | npt.NDArray[np.float64]) – Influence factor for surface roughness on the crest of the structure (-)
cu1 (float, optional) – Coefficient, by default 1.7
cu2 (float, optional) – Coefficient, by default 0.1
g (float, optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

The maximum wave overtopping velocity u (m/s)

Return type:

float | npt.NDArray[np.float64]

Van Gent et al. (2007)

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.vangent2007.write_input_file_NN_Overtopping(beta: float | ndarray[tuple[Any, ...], dtype[float64]], h: float | ndarray[tuple[Any, ...], dtype[float64]], Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], Bt: float | ndarray[tuple[Any, ...], dtype[float64]], ht: float | ndarray[tuple[Any, ...], dtype[float64]], B_berm: float | ndarray[tuple[Any, ...], dtype[float64]], db: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], Ac: float | ndarray[tuple[Any, ...], dtype[float64]], Gc: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]], tan_alpha_B: float | ndarray[tuple[Any, ...], dtype[float64]], output_dir: str, file_name: str = 'input_NN_Overtopping')[source]

Generate input file for NN Overtopping model described by Van Gent et al. (2007).

This function creates a CSV input file with the necessary parameters for the NN Overtopping model, which predicts the mean wave overtopping discharge q (m^3/s/m) including uncertainties. The model is available as a free web tool at https://www.deltares.nl/en/software-and-data/products/overtopping-neural-network.

The input file can contain up to 200 combinations of input parameters. All input parameters should be (1D) arrays of the same length.

Note that the NN Overtopping model is also available as a downloadable installer here: https://dserie.deltares.nl/NNOvertopping/helppage.aspx

For more details, see Van Gent et al. (2007), which is available here: https://doi.org/10.1016/j.coastaleng.2006.12.001

Parameters:

beta (float | npt.NDArray[np.float64]) – Angle of wave incidence (degrees)
h (float | npt.NDArray[np.float64]) – Water depth at toe of the structure (m)
Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
Bt (float | npt.NDArray[np.float64]) – Toe width of the structure (m)
ht (float | npt.NDArray[np.float64]) – Water depth above the toe of the structure (m)
B_berm (float | npt.NDArray[np.float64]) – Berm width of the structure (m)
db (float | npt.NDArray[np.float64]) – Berm height of the structure (m)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
Ac (float | npt.NDArray[np.float64]) – Armour crest freeboard of the structure (m)
Gc (float | npt.NDArray[np.float64]) – Width of the crest of the structure (m)
cot_alpha_down (float | npt.NDArray[np.float64]) – Cotangent of the lower part of the front-side slope of the structure (-)
cot_alpha_up (float | npt.NDArray[np.float64]) – Cotangent of the lower part of the front-side slope of the structure (-)
gamma_f (float | npt.NDArray[np.float64]) – Influence factor for surface roughness (-)
tan_alpha_B (float | npt.NDArray[np.float64]) – Tangent of the berm slope (-).
output_dir (str) – Directory where the input file will be saved.
file_name (str, optional) – Name of the input file, by default “input_NN_Overtopping”

EurOtop (2007)

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.eurotop2007.calculate_crest_freeboard_Rc_rubble_mound(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], q: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c2: float = 0.2, c3: float = 2.3, use_best_fit: bool = False) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the crest freeboard Rc for simple rubble mound slopes with the EurOtop (2007) formula.

The crest freeboard Rc/Hm0 (-) is calculated using the EurOtop (2007) formulas. Here eq. 6.5 from EurOtop (2007) is implemented for design calculations and eq. 6.6 for best fit calculations (using the option best_fit=True).

For more details see EurOtop (2007), available here: https://www.overtopping-manual.com/assets/downloads/EAK-K073_EurOtop_2007.pdf

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
q (float | npt.NDArray[np.float64]) – Mean wave overtopping discharge (m^3/s/m)
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
c2 (float, optional) – Coefficient in wave overtopping formula (-), by default 0.2
c3 (float, optional) – Coefficient in wave overtopping formula (-), by default 2.3
use_best_fit (bool, optional) – Switch to either use best fit values for the coefficients (true) or the design values (false), by default False

Returns:

The crest freeboard of the structure Rc (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.eurotop2007.calculate_dimensionless_crest_freeboard_rubble_mound(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], q: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c2: float = 0.2, c3: float = 2.3, use_best_fit: bool = False) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the dimensionless crest freeboard Rc/Hm0 for simple rubble mound slopes with the EurOtop (2007) formula.

The dimensionless crest freeboard Rc/Hm0 (-) is calculated using the EurOtop (2007) formulas. Here eq. 6.5 from EurOtop (2007) is implemented for design calculations and eq. 6.6 for best fit calculations (using the option best_fit=True).

For more details see EurOtop (2007), available here: https://www.overtopping-manual.com/assets/downloads/EAK-K073_EurOtop_2007.pdf

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
q (float | npt.NDArray[np.float64]) – Mean wave overtopping discharge (m^3/s/m)
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
c2 (float, optional) – Coefficient in wave overtopping formula (-), by default 0.2
c3 (float, optional) – Coefficient in wave overtopping formula (-), by default 2.3
use_best_fit (bool, optional) – Switch to either use best fit values for the coefficients (true) or the design values (false), by default False

Returns:

The dimensionless crest freeboard of the structure Rc/Hm0 (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.eurotop2007.calculate_dimensionless_overtopping_discharge_q_rubble_mound(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c2: float = 0.2, c3: float = 2.3, use_best_fit: bool = False) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the dimensionless mean wave overtopping discharge q for simple rubble mound slopes with the EurOtop (2007) formula.

The dimensionless mean wave overtopping discharge q/sqrt(g*Hm0^3) (-) is calculated using the EurOtop (2007) formulas. Here eq. 6.5 from EurOtop (2007) is implemented for design calculations and eq. 6.6 for best fit calculations (using the option best_fit=True).

For more details see EurOtop (2007), available here: https://www.overtopping-manual.com/assets/downloads/EAK-K073_EurOtop_2007.pdf

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
c2 (float, optional) – Coefficient in wave overtopping formula (-), by default 0.2
c3 (float, optional) – Coefficient in wave overtopping formula (-), by default 2.3
use_best_fit (bool, optional) – Switch to either use best fit values for the coefficients (true) or the design values (false), by default False

Returns:

The dimensionless mean wave overtopping discharge q/sqrt(g*Hm0^3) (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.eurotop2007.calculate_overtopping_discharge_q_rubble_mound(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c2: float = 0.2, c3: float = 2.3, use_best_fit: bool = False, g: float = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the mean wave overtopping discharge q for simple rubble mound slopes with the EurOtop (2007) formula.

The mean wave overtopping discharge q (m^3/s/m) is calculated using the EurOtop (2007) formulas. Here eq. 6.5 from EurOtop (2007) is implemented for design calculations and eq. 6.6 for best fit calculations (using the option best_fit=True).

For more details see EurOtop (2007), available here: https://www.overtopping-manual.com/assets/downloads/EAK-K073_EurOtop_2007.pdf

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
c2 (float, optional) – Coefficient in wave overtopping formula (-), by default 0.2
c3 (float, optional) – Coefficient in wave overtopping formula (-), by default 2.3
use_best_fit (bool, optional) – Switch to either use best fit values for the coefficients (true) or the design values (false), by default False
g (float, optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

The mean wave overtopping discharge q (m^3/s/m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.eurotop2007.check_best_fit(c2: float, c3: float, use_best_fit: bool) → tuple[float, float][source]

Check whether best fit coefficients need to be used

If so, return the best fit coefficients, otherwise return the input coefficients

Parameters:

c2 (float) – Coefficient in wave overtopping formula (-)
c3 (float) – Coefficient in wave overtopping formula (-)
use_best_fit (bool) – Switch to either use best fit values for the coefficients (true) or the design values (false)

Returns:

Coefficients c2 and c3 in the wave runup formula (-)

Return type:

tuple[float, float]

EurOtop (2018)

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.eurotop2018.Rc_diml_max_equation(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], q: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, gamma_star: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, c2: float = 0.1035, c3: float = 1.35, g: float = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the maximum dimensionless crest freeboard Rc/Hm0 with the EurOtop (2018) formula.

The maximum value of the dimensionless crest freeboard Rc/Hm0 (-) is calculated using the EurOtop (2018) formulas. Here eqs. 5.11 and 5.13 from EurOtop (2018) are implemented.

For more details see EurOtop (2018) and the errata of November 2019, available here: https://www.overtopping-manual.com/assets/downloads/EurOtop_II_2018_Final_version.pdf

https://www.overtopping-manual.com/assets/downloads/Errata_EurOtop_2018_Nov_2019.pdf

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
q (float | npt.NDArray[np.float64]) – Mean wave overtopping discharge (m^3/s/m)
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0
gamma_star (float | npt.NDArray[np.float64], optional) – Influence factor for a promenade or storm wall on slope, by default 1.0
c2 (float, optional) – Coefficient in wave overtopping formula (-), by default 0.1035
c3 (float, optional) – Coefficient in wave overtopping formula (-), by default 1.35
g (float, optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

The maximum value of the dimensionless crest freeboard of the structure Rc/Hm0 (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.eurotop2018.calculate_crest_freeboard_Rc(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], q: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_b: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, gamma_v: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, gamma_star: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, B_berm: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, db: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c1: float = 2.5, c2: float = 0.1035, c3: float = 1.35, c4: float = 0.026, use_best_fit: bool = False, g: float = 9.81) → tuple[float | ndarray[tuple[Any, ...], dtype[float64]], bool | ndarray[tuple[Any, ...], dtype[bool]]][source]

Calculate the crest freeboard Rc with the EurOtop (2018) formula.

The crest freeboard Rc (m) is calculated using the EurOtop (2018) formulas. Here eqs. 5.12 and 5.13 from EurOtop (2018) are implemented for design calculations and eqs. 5.10 and 5.11 for best fit calculations (using the option best_fit=True).

For more details see EurOtop (2018) and the errata of November 2019, available here: https://www.overtopping-manual.com/assets/downloads/EurOtop_II_2018_Final_version.pdf

https://www.overtopping-manual.com/assets/downloads/Errata_EurOtop_2018_Nov_2019.pdf

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
q (float | npt.NDArray[np.float64]) – Mean wave overtopping discharge (m^3/s/m)
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_b (float | npt.NDArray[np.float64], optional) – Influence factor for a berm (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0
gamma_v (float | npt.NDArray[np.float64], optional) – Influence factor for a crest wall (-), by default 1.0
gamma_star (float | npt.NDArray[np.float64], optional) – Influence factor for a promenade or storm wall on slope, by default 1.0
B_berm (float | npt.NDArray[np.float64], optional) – Berm width of the structure (m), by default 0.0
db (float | npt.NDArray[np.float64], optional) – Berm height of the structure (m), by default 0.0
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
cot_alpha_down (float | npt.NDArray[np.float64], optional) – Cotangent of the lower part of the front-side slope of the structure (-), by default np.nan
cot_alpha_up (float | npt.NDArray[np.float64], optional) – Cotangent of the upper part of the front-side slope of the structure (-), by default np.nan
c1 (float, optional) – Coefficient in wave overtopping formula (-), by default 2.5
c2 (float, optional) – Coefficient in wave overtopping formula (-), by default 0.1035
c3 (float, optional) – Coefficient in wave overtopping formula (-), by default 1.35
c4 (float, optional) – Coefficient in wave overtopping formula (-), by default 0.026
use_best_fit (bool, optional) – Switch to either use best fit values for the coefficients (true) or the design values (false), by default False
g (float, optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

The crest freeboard of the structure Rc (m) and a boolean indicating whether the maximum value formula was used

Return type:

tuple[float | npt.NDArray[np.float64], bool | npt.NDArray[np.bool]]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.eurotop2018.calculate_crest_freeboard_Rc_rubble_mound(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], q: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, B_berm: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, db: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c2: float = 0.1035, c3: float = 1.35, use_best_fit: bool = False, g: float = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the crest freeboard Rc/Hm0 with the EurOtop (2018) formula for rubble mound structures.

The crest freeboard Rc/Hm0 (-) for rubble mound structures is calculated using the EurOtop (2018) formulas. Here eq. 6.6 from EurOtop (2018) is implemented for design calculations and eq. 6.5 for best fit calculations (using the option best_fit=True).

For more details see EurOtop (2018) and the errata of November 2019, available here: https://www.overtopping-manual.com/assets/downloads/EurOtop_II_2018_Final_version.pdf

https://www.overtopping-manual.com/assets/downloads/Errata_EurOtop_2018_Nov_2019.pdf

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
q (float | npt.NDArray[np.float64]) – Mean wave overtopping discharge (m^3/s/m)
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0
B_berm (float | npt.NDArray[np.float64], optional) – Berm width of the structure (m), by default 0.0
db (float | npt.NDArray[np.float64], optional) – Berm height of the structure (m), by default 0.0
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
cot_alpha_down (float | npt.NDArray[np.float64], optional) – Cotangent of the lower part of the front-side slope of the structure (-), by default np.nan
cot_alpha_up (float | npt.NDArray[np.float64], optional) – Cotangent of the upper part of the front-side slope of the structure (-), by default np.nan
c2 (float, optional) – Coefficient in wave overtopping formula (-), by default 0.1035
c3 (float, optional) – Coefficient in wave overtopping formula (-), by default 1.35
use_best_fit (bool, optional) – Switch to either use best fit values for the coefficients (true) or the design values (false), by default False
g (float, optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

The crest freeboard of the structure Rc (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.eurotop2018.calculate_dimensionless_crest_freeboard(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], q: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_b: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, gamma_v: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, gamma_star: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, B_berm: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, db: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c1: float = 2.5, c2: float = 0.1035, c3: float = 1.35, c4: float = 0.026, use_best_fit: bool = False, g: float = 9.81) → tuple[float | ndarray[tuple[Any, ...], dtype[float64]], bool | ndarray[tuple[Any, ...], dtype[bool]]][source]

Calculate the dimensionless crest freeboard Rc/Hm0 with the EurOtop (2018) formula.

The dimensionless crest freeboard Rc/Hm0 (-) is calculated using the EurOtop (2018) formulas. Here eqs. 5.12 and 5.13 from EurOtop (2018) are implemented for design calculations and eqs. 5.10 and 5.11 for best fit calculations (using the option best_fit=True).

For more details see EurOtop (2018) and the errata of November 2019, available here: https://www.overtopping-manual.com/assets/downloads/EurOtop_II_2018_Final_version.pdf

https://www.overtopping-manual.com/assets/downloads/Errata_EurOtop_2018_Nov_2019.pdf

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
q (float | npt.NDArray[np.float64]) – Mean wave overtopping discharge (m^3/s/m)
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_b (float | npt.NDArray[np.float64], optional) – Influence factor for a berm (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0
gamma_v (float | npt.NDArray[np.float64], optional) – Influence factor for a crest wall (-), by default 1.0
gamma_star (float | npt.NDArray[np.float64], optional) – Influence factor for a promenade or storm wall on slope, by default 1.0
B_berm (float | npt.NDArray[np.float64], optional) – Berm width of the structure (m), by default 0.0
db (float | npt.NDArray[np.float64], optional) – Berm height of the structure (m), by default 0.0
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
cot_alpha_down (float | npt.NDArray[np.float64], optional) – Cotangent of the lower part of the front-side slope of the structure (-), by default np.nan
cot_alpha_up (float | npt.NDArray[np.float64], optional) – Cotangent of the upper part of the front-side slope of the structure (-), by default np.nan
c1 (float, optional) – Coefficient in wave overtopping formula (-), by default 2.5
c2 (float, optional) – Coefficient in wave overtopping formula (-), by default 0.1035
c3 (float, optional) – Coefficient in wave overtopping formula (-), by default 1.35
c4 (float, optional) – Coefficient in wave overtopping formula (-), by default 0.026
use_best_fit (bool, optional) – Switch to either use best fit values for the coefficients (true) or the design values (false), by default False
g (float, optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

The dimensionless crest freeboard of the structure Rc/Hm0 (-) and a boolean indicating whether the maximum value formula was used

Return type:

tuple[float | npt.NDArray[np.float64], bool | npt.NDArray[np.bool]]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.eurotop2018.calculate_dimensionless_crest_freeboard_rubble_mound(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], q: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, B_berm: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, db: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c2: float = 0.1035, c3: float = 1.35, use_best_fit: bool = False, g: float = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the dimensionless crest freeboard Rc/Hm0 with the EurOtop (2018) formula for rubble mound structures.

The dimensionless crest freeboard Rc/Hm0 (-) for rubble mound structures is calculated using the EurOtop (2018) formulas. Here eq. 6.6 from EurOtop (2018) is implemented for design calculations and eq. 6.5 for best fit calculations (using the option best_fit=True).

For more details see EurOtop (2018) and the errata of November 2019, available here: https://www.overtopping-manual.com/assets/downloads/EurOtop_II_2018_Final_version.pdf

https://www.overtopping-manual.com/assets/downloads/Errata_EurOtop_2018_Nov_2019.pdf

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
q (float | npt.NDArray[np.float64]) – Mean wave overtopping discharge (m^3/s/m)
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0
B_berm (float | npt.NDArray[np.float64], optional) – Berm width of the structure (m), by default 0.0
db (float | npt.NDArray[np.float64], optional) – Berm height of the structure (m), by default 0.0
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
cot_alpha_down (float | npt.NDArray[np.float64], optional) – Cotangent of the lower part of the front-side slope of the structure (-), by default np.nan
cot_alpha_up (float | npt.NDArray[np.float64], optional) – Cotangent of the upper part of the front-side slope of the structure (-), by default np.nan
c2 (float, optional) – Coefficient in wave overtopping formula (-), by default 0.1035
c3 (float, optional) – Coefficient in wave overtopping formula (-), by default 1.35
use_best_fit (bool, optional) – Switch to either use best fit values for the coefficients (true) or the design values (false), by default False
g (float, optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

The dimensionless crest freeboard of the structure Rc/Hm0 (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.eurotop2018.calculate_dimensionless_overtopping_discharge_q(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_b: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, gamma_v: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, gamma_star: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, B_berm: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, db: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c1: float = 2.5, c2: float = 0.1035, c3: float = 1.35, c4: float = 0.026, use_best_fit: bool = False) → tuple[float | ndarray[tuple[Any, ...], dtype[float64]], bool | ndarray[tuple[Any, ...], dtype[bool]]][source]

Calculate the dimensionless mean wave overtopping discharge q with the EurOtop (2018) formula.

The mean wave overtopping discharge q/sqrt(g*Hm0^3) (-) is calculated using the EurOtop (2018) formulas. Here eqs. 5.12 and 5.13 from EurOtop (2018) are implemented for design calculations and eqs. 5.10 and 5.11 for best fit calculations (using the option best_fit=True).

For more details see EurOtop (2018) and the errata of November 2019, available here: https://www.overtopping-manual.com/assets/downloads/EurOtop_II_2018_Final_version.pdf

https://www.overtopping-manual.com/assets/downloads/Errata_EurOtop_2018_Nov_2019.pdf

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_b (float | npt.NDArray[np.float64], optional) – Influence factor for a berm (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0
gamma_v (float | npt.NDArray[np.float64], optional) – Influence factor for a crest wall (-), by default 1.0
gamma_star (float | npt.NDArray[np.float64], optional) – Influence factor for a promenade or storm wall on slope, by default 1.0
B_berm (float | npt.NDArray[np.float64], optional) – Berm width of the structure (m), by default 0.0
db (float | npt.NDArray[np.float64], optional) – Berm height of the structure (m), by default 0.0
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
cot_alpha_down (float | npt.NDArray[np.float64], optional) – Cotangent of the lower part of the front-side slope of the structure (-), by default np.nan
cot_alpha_up (float | npt.NDArray[np.float64], optional) – Cotangent of the upper part of the front-side slope of the structure (-), by default np.nan
c1 (float, optional) – Coefficient in wave overtopping formula (-), by default 2.5
c2 (float, optional) – Coefficient in wave overtopping formula (-), by default 0.1035
c3 (float, optional) – Coefficient in wave overtopping formula (-), by default 1.35
c4 (float, optional) – Coefficient in wave overtopping formula (-), by default 0.026
use_best_fit (bool, optional) – Switch to either use best fit values for the coefficients (true) or the design values (false), by default False

Returns:

Dimensionless mean wave overtopping discharge q/sqrt(g*Hm0^3) (-) and a boolean indicating whether the maximum value formula was used

Return type:

tuple[float | npt.NDArray[np.float64], bool | npt.NDArray[np.bool]]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.eurotop2018.calculate_dimensionless_overtopping_discharge_q_rubble_mound(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, B_berm: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, db: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c2: float = 0.1035, c3: float = 1.35, use_best_fit: bool = False) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the dimensionless mean wave overtopping discharge q with the EurOtop (2018) formula (rubble mound).

The dimensionless mean wave overtopping discharge q/sqrt(g*Hm0^3) (-) for rubble mound structures is calculated using the EurOtop (2018) formulas. Here eq. 6.6 from EurOtop (2018) is implemented for design calculations and eq. 6.5 for best fit calculations (using the option best_fit=True).

For more details see EurOtop (2018) and the errata of November 2019, available here: https://www.overtopping-manual.com/assets/downloads/EurOtop_II_2018_Final_version.pdf

https://www.overtopping-manual.com/assets/downloads/Errata_EurOtop_2018_Nov_2019.pdf

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0
B_berm (float | npt.NDArray[np.float64], optional) – Berm width of the structure (m), by default 0.0
db (float | npt.NDArray[np.float64], optional) – Berm height of the structure (m), by default 0.0
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
cot_alpha_down (float | npt.NDArray[np.float64], optional) – Cotangent of the lower part of the front-side slope of the structure (-), by default np.nan
cot_alpha_up (float | npt.NDArray[np.float64], optional) – Cotangent of the upper part of the front-side slope of the structure (-), by default np.nan
c2 (float, optional) – Coefficient in wave overtopping formula (-), by default 0.1035
c3 (float, optional) – Coefficient in wave overtopping formula (-), by default 1.35
use_best_fit (bool, optional) – Switch to either use best fit values for the coefficients (true) or the design values (false), by default False

Returns:

Dimensionless mean wave overtopping discharge q/sqrt(g*Hm0^3) (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.eurotop2018.calculate_influence_oblique_waves_gamma_beta(beta: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f_crit: float = 0.6, c_gamma_beta_smooth: float = 0.0033, c_gamma_beta_rough: float = 0.0063, max_angle: float = 80.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the influence factor for oblique wave incidence gamma_beta

The influence factor gamma_beta is determined using the EurOtop (2018) eq. 5.29 for smooth slopes and eq. 6.9 for rough slopes.

Parameters:

beta (float | npt.NDArray[np.float64]) – Angle of wave incidence (degrees)
gamma_f (float | npt.NDArray[np.float64]) – Influence factor for surface roughness (-)
gamma_f_crit (float, optional) – Critical value for the influence factor dividing smooth (higher) and rough (lower) slopes, by default 0.6
c_gamma_beta_smooth (float, optional) – Coefficient for wave runup on smooth slopes, by default 0.0022
c_gamma_beta_rough (float, optional) – Coefficient for wave runup on rough slopes, by default 0.0063
max_angle (float, optional) – Maximum angle of wave incidence, by default 80.0

Returns:

The influence factor for oblique wave incidence gamma_beta (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.eurotop2018.calculate_overtopping_discharge_q(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_b: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, gamma_v: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, gamma_star: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, B_berm: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, db: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c1: float = 2.5, c2: float = 0.1035, c3: float = 1.35, c4: float = 0.026, use_best_fit: bool = False, g: float = 9.81) → tuple[float | ndarray[tuple[Any, ...], dtype[float64]], bool | ndarray[tuple[Any, ...], dtype[bool]]][source]

Calculate the mean wave overtopping discharge q with the EurOtop (2018) formula.

The mean wave overtopping discharge q (m^3/s/m) is calculated using the EurOtop (2018) formulas. Here eqs. 5.12 and 5.13 from EurOtop (2018) are implemented for design calculations and eqs. 5.10 and 5.11 for best fit calculations (using the option best_fit=True).

For more details see EurOtop (2018) and the errata of November 2019, available here: https://www.overtopping-manual.com/assets/downloads/EurOtop_II_2018_Final_version.pdf

https://www.overtopping-manual.com/assets/downloads/Errata_EurOtop_2018_Nov_2019.pdf

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_b (float | npt.NDArray[np.float64], optional) – Influence factor for a berm (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0
gamma_v (float | npt.NDArray[np.float64], optional) – Influence factor for a crest wall (-), by default 1.0
gamma_star (float | npt.NDArray[np.float64], optional) – Influence factor for a promenade or storm wall on slope, by default 1.0
B_berm (float | npt.NDArray[np.float64], optional) – Berm width of the structure (m), by default 0.0
db (float | npt.NDArray[np.float64], optional) – Berm height of the structure (m), by default 0.0
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
cot_alpha_down (float | npt.NDArray[np.float64], optional) – Cotangent of the lower part of the front-side slope of the structure (-), by default np.nan
cot_alpha_up (float | npt.NDArray[np.float64], optional) – Cotangent of the upper part of the front-side slope of the structure (-), by default np.nan
c1 (float, optional) – Coefficient in wave overtopping formula (-), by default 2.5
c2 (float, optional) – Coefficient in wave overtopping formula (-), by default 0.1035
c3 (float, optional) – Coefficient in wave overtopping formula (-), by default 1.35
c4 (float, optional) – Coefficient in wave overtopping formula (-), by default 0.026
use_best_fit (bool, optional) – Switch to either use best fit values for the coefficients (true) or the design values (false), by default False
g (float, optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

Mean wave overtopping discharge q (m^3/s/m) and a boolean indicating whether the maximum value formula was used

Return type:

tuple[float | npt.NDArray[np.float64], bool | npt.NDArray[np.bool]]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.eurotop2018.calculate_overtopping_discharge_q_rubble_mound(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, B_berm: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, db: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c2: float = 0.1035, c3: float = 1.35, use_best_fit: bool = False, g: float = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the mean wave overtopping discharge q with the EurOtop (2018) formula (rubble mound).

The mean wave overtopping discharge q/sqrt(g*Hm0^3) (-) for rubble mound structures is calculated using the EurOtop (2018) formulas. Here eq. 6.6 from EurOtop (2018) is implemented for design calculations and eq. 6.5 for best fit calculations (using the option best_fit=True).

For more details see EurOtop (2018) and the errata of November 2019, available here: https://www.overtopping-manual.com/assets/downloads/EurOtop_II_2018_Final_version.pdf

https://www.overtopping-manual.com/assets/downloads/Errata_EurOtop_2018_Nov_2019.pdf

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0
B_berm (float | npt.NDArray[np.float64], optional) – Berm width of the structure (m), by default 0.0
db (float | npt.NDArray[np.float64], optional) – Berm height of the structure (m), by default 0.0
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
cot_alpha_down (float | npt.NDArray[np.float64], optional) – Cotangent of the lower part of the front-side slope of the structure (-), by default np.nan
cot_alpha_up (float | npt.NDArray[np.float64], optional) – Cotangent of the upper part of the front-side slope of the structure (-), by default np.nan
c2 (float, optional) – Coefficient in wave overtopping formula (-), by default 0.1035
c3 (float, optional) – Coefficient in wave overtopping formula (-), by default 1.35
use_best_fit (bool, optional) – Switch to either use best fit values for the coefficients (true) or the design values (false), by default False
g (float, optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

Mean wave overtopping discharge q (m^3/s/m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.eurotop2018.check_best_fit(c1: float, c2: float, c3: float, c4: float, use_best_fit: bool) → tuple[float, float, float, float][source]

Check whether best fit coefficients need to be used

If so, return the best fit coefficients, otherwise return the input coefficients

Parameters:

c1 (float) – Coefficient in wave overtopping formula (-)
c2 (float) – Coefficient in wave overtopping formula (-)
c3 (float) – Coefficient in wave overtopping formula (-)
c4 (float) – Coefficient in wave overtopping formula (-)
use_best_fit (bool) – Switch to either use best fit values for the coefficients (true) or the design values (false)

Returns:

Coefficients c1, c2, c3 and c4 in the wave runup formula (-)

Return type:

tuple[float, float, float, float]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.eurotop2018.check_validity_range_rubble_mound(cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan) → None[source]

Check the parameter values vs the validity range of the EurOtop (2018) manual for rubble mound structures.

For all parameters supplied, their values are checked versus the range of test conditions specified by EurOtop (2018) . When parameters are nan (by default), they are not checked.

For more details see EurOtop (2018) and the errata of November 2019, available here: https://www.overtopping-manual.com/assets/downloads/EurOtop_II_2018_Final_version.pdf

https://www.overtopping-manual.com/assets/downloads/Errata_EurOtop_2018_Nov_2019.pdf

Parameters:: cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.eurotop2018.q_diml_max_equation(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, gamma_star: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, c2: float = 0.1035, c3: float = 1.35) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the maximum dimensionless mean wave overtopping discharge q with the EurOtop (2018) formula.

The maximum value of the dimensionless mean wave overtopping discharge q/sqrt(g*Hm0^3) (-) is calculated using the EurOtop (2018) formulas. Here eqs. 5.11 and 5.13 from EurOtop (2018) are implemented.

For more details see EurOtop (2018) and the errata of November 2019, available here: https://www.overtopping-manual.com/assets/downloads/EurOtop_II_2018_Final_version.pdf

https://www.overtopping-manual.com/assets/downloads/Errata_EurOtop_2018_Nov_2019.pdf

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0
gamma_star (float | npt.NDArray[np.float64], optional) – Influence factor for a promenade or storm wall on slope, by default 1.0
c2 (float, optional) – Coefficient in wave overtopping formula (-), by default 0.1035
c3 (float, optional) – Coefficient in wave overtopping formula (-), by default 1.35

Returns:

Maximum value for the dimensionless mean wave overtopping discharge q/sqrt(g*Hm0^3) (-)

Return type:

float | npt.NDArray[np.float64]

Den Bieman et al. (2021)

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.denbieman2021.write_input_file_XGB_Overtopping(beta: float | ndarray[tuple[Any, ...], dtype[float64]], h: float | ndarray[tuple[Any, ...], dtype[float64]], Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], Bt: float | ndarray[tuple[Any, ...], dtype[float64]], ht: float | ndarray[tuple[Any, ...], dtype[float64]], B_berm: float | ndarray[tuple[Any, ...], dtype[float64]], db: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], Ac: float | ndarray[tuple[Any, ...], dtype[float64]], Gc: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f_down: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f_up: float | ndarray[tuple[Any, ...], dtype[float64]], tan_alpha_f: float | ndarray[tuple[Any, ...], dtype[float64]], output_dir: str, file_name: str = 'input_XGB_Overtopping')[source]

Generate input file for XGB Overtopping model described by Den Bieman et al. (2021).

This function creates a CSV input file with the necessary parameters for the XGB Overtopping model, which predicts the mean wave overtopping discharge q (m^3/s/m) including uncertainties. The model is available as a free web tool at https://www.deltares.nl/en/software-and-data/products/overtopping-xgb.

The input file can contain up to 200 combinations of input parameters. All input parameters should be (1D) arrays of the same length.

For more details, see Den Bieman et al. (2021), which is available here: https://doi.org/10.1016/j.coastaleng.2020.103830 or here: https://www.researchgate.net/publication/346963461_Wave_overtopping_predictions_using_an_advanced_machine_learning_technique

Parameters:

beta (float | npt.NDArray[np.float64]) – Angle of wave incidence (degrees)
h (float | npt.NDArray[np.float64]) – Water depth at toe of the structure (m)
Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
Bt (float | npt.NDArray[np.float64]) – Toe width of the structure (m)
ht (float | npt.NDArray[np.float64]) – Water depth above the toe of the structure (m)
B_berm (float | npt.NDArray[np.float64]) – Berm width of the structure (m)
db (float | npt.NDArray[np.float64]) – Berm height of the structure (m)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
Ac (float | npt.NDArray[np.float64]) – Armour crest freeboard of the structure (m)
Gc (float | npt.NDArray[np.float64]) – Width of the crest of the structure (m)
cot_alpha_down (float | npt.NDArray[np.float64]) – Cotangent of the lower part of the front-side slope of the structure (-)
cot_alpha_up (float | npt.NDArray[np.float64]) – Cotangent of the lower part of the front-side slope of the structure (-)
gamma_f_down (float | npt.NDArray[np.float64]) – Influence factor for surface roughness of the lower part of the structure (-)
gamma_f_up (float | npt.NDArray[np.float64]) – Influence factor for surface roughness of the upper part of the structure (-)
tan_alpha_f (float | npt.NDArray[np.float64]) – Tangent of the foreshore slope (-)
output_dir (str) – Directory where the input file will be saved.
file_name (str, optional) – Name of the input file, by default “input_XGB_Overtopping”

Van Gent (2021)

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.vangent2021_caisson.calculate_crest_freeboard_Rc(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], q: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Hm0_swell: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c: float = 1.0, c_swell: float = 0.4, short_crested_waves: bool = True, crossing_seas: bool = False, parapet: bool = False, g: float = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the crest freeboard Rc for caisson breakwaters with the Van Gent (2021) formula.

The crest freeboard Rc (m) of a caisson breakwater is calculated using the Van Gent (2021) formula. Here, eq. 11 from Van Gent (2021) is implemented.

For more details, see: https://doi.org/10.1016/j.coastaleng.2020.103834

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
q (float | npt.NDArray[np.float64]) – Mean wave overtopping discharge (m^3/s/m)
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
Hm0_swell (float | npt.NDArray[np.float64], optional) – Spectral significant wave height of swell or infragravity waves in case of a second wave field (m), by default np.nan
c (float, optional) – Exponent in the wave overtopping formula, by default 1.0
c_swell (float, optional) – Coefficient for the effective freeboard reduction due to swell (only active for crossing_seas = True), by default 0.4
short_crested_waves (bool, optional) – Use coefficient for short-crested waves (else long-crested), by default True
crossing_seas (bool, optional) – Calculation for crossing seas where Hm0_swell has an influence, by default False
parapet (bool, optional) – Indicate the presence of a recurved parapet / bullnose / recurved wave return wall, by default False
g (float, optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

The crest freeboard of the structure Rc (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.vangent2021_caisson.calculate_dimensionless_crest_freeboard(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], q: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Hm0_swell: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c: float = 1.0, c_swell: float = 0.4, short_crested_waves: bool = True, crossing_seas: bool = False, parapet: bool = False, g: float = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the dimensionless crest freeboard Rc/Hm0 for caisson breakwaters with the Van Gent (2021) formula.

The dimensionless crest freeboard Rc/Hm0 (-) of a caisson breakwater is calculated using the Van Gent (2021) formula. Here, eq. 11 from Van Gent (2021) is implemented.

For more details, see: https://doi.org/10.1016/j.coastaleng.2020.103834

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
q (float | npt.NDArray[np.float64]) – Mean wave overtopping discharge (m^3/s/m)
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
Hm0_swell (float | npt.NDArray[np.float64], optional) – Spectral significant wave height of swell or infragravity waves in case of a second wave field (m), by default np.nan
c (float, optional) – Exponent in the wave overtopping formula, by default 1.0
c_swell (float, optional) – Coefficient for the effective freeboard reduction due to swell (only active for crossing_seas = True), by default 0.4
short_crested_waves (bool, optional) – Use coefficient for short-crested waves (else long-crested), by default True
crossing_seas (bool, optional) – Calculation for crossing seas where Hm0_swell has an influence, by default False
parapet (bool, optional) – Indicate the presence of a recurved parapet / bullnose / recurved wave return wall, by default False
g (float, optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

The dimensionless crest freeboard of the structure Rc/Hm0 (-)

Return type:

float | npt.NDArray[np.float64]

Raises:

ValueError – When Hm0_swell is not provided in the case of crossing seas.

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.vangent2021_caisson.calculate_dimensionless_overtopping_discharge_q(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Hm0_swell: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c: float = 1.0, c_swell: float = 0.4, short_crested_waves: bool = True, crossing_seas: bool = False, parapet: bool = False) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the dimensionless mean wave overtopping discharge q for caisson breakwaters with the Van Gent (2021) formula.

The dimensionless mean wave overtopping discharge q (m^3/s/m) for caisson breakwaters is calculated using the Van Gent (2021) formula. Here, eq. 11 from Van Gent (2021) is implemented.

For more details, see: https://doi.org/10.1016/j.coastaleng.2020.103834

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
Hm0_swell (float | npt.NDArray[np.float64], optional) – Spectral significant wave height of swell or infragravity waves in case of a second wave field (m), by default np.nan
c (float, optional) – Exponent in the wave overtopping formula, by default 1.0
c_swell (float, optional) – Coefficient for the effective freeboard reduction due to swell (only active for crossing_seas = True), by default 0.4
short_crested_waves (bool, optional) – Use coefficient for short-crested waves (else long-crested), by default True
crossing_seas (bool, optional) – Calculation for crossing seas where Hm0_swell has an influence, by default False
parapet (bool, optional) – Indicate the presence of a recurved parapet / bullnose / recurved wave return wall, by default False

Returns:

The dimensionless mean wave overtopping discharge q/sqrt(g*Hm0^3)

Return type:

float | npt.NDArray[np.float64]

Raises:

ValueError – When Hm0_swell is not provided in the case of crossing seas.

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.vangent2021_caisson.calculate_influence_oblique_waves_gamma_beta(beta: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_p: float, c_beta: float) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the influence factor for oblique wave incidence gamma_beta

The influence factor gamma_beta is determined using Van Gent (2021) eq. 10

For more details, see: https://doi.org/10.1016/j.coastaleng.2020.103834

Parameters:

beta (float | npt.NDArray[np.float64]) – Angle of wave incidence (degrees)
gamma_p (float) – Influence factor for a recurved parapet / bullnose / recurved wave return wall (-)
c_beta (float) – Coefficient in the gamma_beta formula

Returns:

The influence factor for oblique wave incidence gamma_beta (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.vangent2021_caisson.calculate_overtopping_discharge_q(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Hm0_swell: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c: float = 1.0, c_swell: float = 0.4, short_crested_waves: bool = True, crossing_seas: bool = False, parapet: bool = False, g: float = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the mean wave overtopping discharge q for caisson breakwaters with the Van Gent (2021) formula.

The mean wave overtopping discharge q (m^3/s/m) for caisson breakwaters is calculated using the Van Gent (2021) formula. Here, eq. 11 from Van Gent (2021) is implemented.

For more details, see: https://doi.org/10.1016/j.coastaleng.2020.103834

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
Hm0_swell (float | npt.NDArray[np.float64], optional) – Spectral significant wave height of swell or infragravity waves in case of a second wave field (m), by default np.nan
c (float, optional) – Exponent in the wave overtopping formula, by default 1.0
c_swell (float, optional) – Coefficient for the effective freeboard reduction due to swell (only active for crossing_seas = True), by default 0.4
short_crested_waves (bool, optional) – Use coefficient for short-crested waves (else long-crested), by default True
crossing_seas (bool, optional) – Calculation for crossing seas where Hm0_swell has an influence, by default False
parapet (bool, optional) – Indicate the presence of a recurved parapet / bullnose / recurved wave return wall, by default False
g (float, optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

The mean wave overtopping discharge q (m^3/s/m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.vangent2021_caisson.check_validity_range(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Rc: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, q_diml: float | ndarray[tuple[Any, ...], dtype[float64]] = nan) → None[source]

Check the parameter values vs the validity range of the Van Gent (2021) formula.

For all parameters supplied, their values are checked versus the range of test conditions specified in Table 2 in Van Gent (2021). When parameters are nan (by default), they are not checked.

For more details, see: https://doi.org/10.1016/j.coastaleng.2020.103834

Parameters:

Hm0 (float | npt.NDArray[np.float64], optional) – Spectral significant wave height (m), by default np.nan
Tmm10 (float | npt.NDArray[np.float64], optional) – Spectral wave period Tm-1,0 (s), by default np.nan
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
Rc (float | npt.NDArray[np.float64], optional) – Crest freeboard of the structure (m), by default np.nan
q_diml (float | npt.NDArray[np.float64], optional) – Dimensionless mean wave overtopping discharge q/sqrt(g*Hm0^3) (-), by default np.nan

De Ridder et al. (2024)

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.deridder2024.calculate_crest_freeboard_discharge_q_eq24(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], smm10_HF: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]], q: float | ndarray[tuple[Any, ...], dtype[float64]], g: float = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the crest freeboard given a q for a rubble mound breakwater following equation 24 in De Ridder et al. (2024).

For more details see De Ridder et al. (2024), available here https://doi.org/10.1016/j.coastaleng.2024.104626

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Significant spectral wave height (m)
smm10_HF (float | npt.NDArray[np.float64]) – Wave steepness sm-1,0 based on the deep water wave length corresponding to the high frequency spectral wave period Tm-1,0,HF(-)
gamma_f (float | npt.NDArray[np.float64]) – Reduction factor for wave overtopping due to friction (-)
q (float | npt.NDArray[np.float64]) – Mean wave overtopping discharge (m^3/s/m)
g (float, optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

Crest freeboard Rc (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.deridder2024.calculate_crest_freeboard_discharge_q_eq26(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], smm10_HF: float | ndarray[tuple[Any, ...], dtype[float64]], Hm0_LF: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]], q: float | ndarray[tuple[Any, ...], dtype[float64]], g: float = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the crest freeboard given a q for a rubble mound breakwater following equation 26 in De Ridder et al. (2024).

For more details see De Ridder et al. (2024), available here https://doi.org/10.1016/j.coastaleng.2024.104626

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Significant spectral wave height (m)
smm10_HF (float | npt.NDArray[np.float64]) – Wave steepness sm-1,0 based on the deep water wave length corresponding to the high frequency spectral wave period Tm-1,0,HF(-)
Hm0_LF (float | npt.NDArray[np.float64]) – Low-frequency wave height (m)
gamma_f (float | npt.NDArray[np.float64]) – Reduction factor for wave overtopping due to friction (-)
q (float | npt.NDArray[np.float64]) – Mean wave overtopping discharge (m^3/s/m)
g (float, optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

Crest freeboard Rc (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.deridder2024.calculate_dimensionless_crest_freeboard_discharge_q_eq24(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], smm10_HF: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]], q: float | ndarray[tuple[Any, ...], dtype[float64]], g: float = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the dimensionless crest freeboard given a q for a rubble mound breakwater following equation 24 in De Ridder et al. (2024).

For more details see De Ridder et al. (2024), available here https://doi.org/10.1016/j.coastaleng.2024.104626

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Significant spectral wave height (m)
smm10_HF (float | npt.NDArray[np.float64]) – Wave steepness sm-1,0 based on the deep water wave length corresponding to the high frequency spectral wave period Tm-1,0,HF(-)
gamma_f (float | npt.NDArray[np.float64]) – Reduction factor for wave overtopping due to friction (-)
q (float | npt.NDArray[np.float64]) – Mean wave overtopping discharge (m^3/s/m)
g (float, optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

Dimensionless crest freeboard Rc (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.deridder2024.calculate_dimensionless_overtopping_discharge_eq24(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], smm10_HF: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the dimensionless mean wave overtopping discharge q for a rubble mound breakwater following De Ridder et al. (2024) using equation 24.

For more details see De Ridder et al. (2024), available here https://doi.org/10.1016/j.coastaleng.2024.104626

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Significant spectral wave height (m)
smm10_HF (float | npt.NDArray[np.float64]) – Wave steepness sm-1,0 based on the deep water wave length corresponding to the high frequency spectral wave period Tm-1,0,HF(-)
gamma_f (float | npt.NDArray[np.float64]) – Reduction factor for wave overtopping due to friction (-)
Rc (float | npt.NDArray[np.float64]) – Freeboard of the structure (m)

Returns:

Dimensionless mean wave overtopping discharge q/sqrt(g*Hm0^3) (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.deridder2024.calculate_dimensionless_overtopping_discharge_eq26(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], smm10_HF: float | ndarray[tuple[Any, ...], dtype[float64]], Hm0_LF: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the dimensionless mean wave overtopping discharge q for a rubble mound breakwater following De Ridder et al. (2024) using equation 26.

For more details see De Ridder et al. (2024), available here https://doi.org/10.1016/j.coastaleng.2024.104626

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Significant spectral wave height (m)
smm10_HF (float | npt.NDArray[np.float64]) – Wave steepness sm-1,0 based on the deep water wave length corresponding to the high frequency spectral wave period Tm-1,0,HF(-)
Hm0_LF (float | npt.NDArray[np.float64]) – Low-frequency wave height (m)
gamma_f (float | npt.NDArray[np.float64]) – Reduction factor for wave overtopping due to friction (-)
Rc (float | npt.NDArray[np.float64]) – Freeboard of the structure (m)

Returns:

Dimensionless mean wave overtopping discharge q/sqrt(g*Hm0^3) (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.deridder2024.calculate_overtopping_discharge_q_eq24(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], smm10_HF: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], g: float = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the mean wave overtopping discharge q for a rubble mound breakwater following equation 24 in: De Ridder et al. (2024).

For more details see De Ridder et al. (2024), available here https://doi.org/10.1016/j.coastaleng.2024.104626

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Significant spectral wave height (m)
smm10_HF (float | npt.NDArray[np.float64]) – Wave steepness sm-1,0 based on the deep water wave length corresponding to the high frequency spectral wave period Tm-1,0,HF(-)
gamma_f (float | npt.NDArray[np.float64]) – Reduction factor for wave overtopping due to friction (-)
Rc (float | npt.NDArray[np.float64]) – Freeboard of the structure (m)
g (float, optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

Mean wave overtopping discharge q (m^3/s/m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.deridder2024.calculate_overtopping_discharge_q_eq26(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], smm10_HF: float | ndarray[tuple[Any, ...], dtype[float64]], Hm0_LF: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], g: float = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the mean wave overtopping discharge q for a rubble mound breakwater following equation 26 in: De Ridder et al. (2024).

For more details see De Ridder et al. (2024), available here https://doi.org/10.1016/j.coastaleng.2024.104626

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Significant spectral wave height (m)
smm10_HF (float | npt.NDArray[np.float64]) – Wave steepness sm-1,0 based on the deep water wave length corresponding to the high frequency spectral wave period Tm-1,0,HF(-)
Hm0_LF (float | npt.NDArray[np.float64]) – Low-frequency wave height (m)
gamma_f (float | npt.NDArray[np.float64]) – Reduction factor for wave overtopping due to friction (-)
Rc (float | npt.NDArray[np.float64]) – Freeboard of the structure (m)
g (float, optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

Mean wave overtopping discharge q (m^3/s/m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.deridder2024.check_validity_range(h: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Hm0: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Hm0_HF: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Hm0_LF: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Tmm10_HF: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Rc: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, m_foreshore_slope: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan) → None[source]

Check the parameter values vs the validity range as defined in De Ridder et al. (2024).

For all parameters supplied, their values are checked versus the range of test conditions specified in Table 3 (De Ridder et al., 2024). When parameters are nan (by default), they are not checked.

For more details see De Ridder et al. (2024), available here https://doi.org/10.1016/j.coastaleng.2024.104626

Parameters:

h (float | npt.NDArray[np.float64], optional) – Water depth at the toe of the structure (m), by default np.nan
Hm0 (float | npt.NDArray[np.float64], optional) – Significant spectral wave height (m), by default np.nan
Hm0_HF (float | npt.NDArray[np.float64], optional) – High frequency significant spectral wave height (m), by default np.nan
Hm0_LF (float | npt.NDArray[np.float64], optional) – Low frequency significant spectral wave height (m), by default np.nan
Tmm10 (float | npt.NDArray[np.float64], optional) – Spectral wave period Tm-1,0 (s), by default np.nan
Tmm10_HF (float | npt.NDArray[np.float64], optional) – High frequency spectral wave period Tm-1,0 (s), by default np.nan
Rc (float | npt.NDArray[np.float64], optional) – Freeboard of the structure (m), by default np.nan
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
m_foreshore_slope (float | npt.NDArray[np.float64], optional) – (Tangent of the) slope of the foreshore (-), by default np.nan
Dn50 (float | npt.NDArray[np.float64], optional) – Median nominal rock diameter (m), by default np.nan

Van Gent et al. (2025)

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.vangent2025.Rc_diml_max_equation(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Hm0_swell: float | ndarray[tuple[Any, ...], dtype[float64]], q: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], ksi_mm10: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_b: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_v: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]], c2: float = 0.8, c3: float = -2.5, g: float = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the maximum dimensionless crest freeboard Rc/Hm0 with the Van Gent et al. (2025) formula.

The maximum value for the dimensionless crest freeboard Rc/Hm0 (-) is calculated using the Van Gent et al. (2025) formula. Here, eq. B2 from Van Gent et al. (2025) is implemented.

For more details, see: https://doi.org/10.59490/jchs.2025.0048

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Hm0_swell (float | npt.NDArray[np.float64]) – Spectral significant wave height of swell or infragravity waves in case of a second wave field (m)
q (float | npt.NDArray[np.float64]) – Mean wave overtopping discharge (m^3/s/m)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
ksi_mm10 (float | npt.NDArray[np.float64]) – _description_
gamma_f (float | npt.NDArray[np.float64]) – Influence factor for surface roughness (-)
gamma_b (float | npt.NDArray[np.float64]) – Influence factor for a berm (-)
gamma_v (float | npt.NDArray[np.float64]) – Influence factor for a crest wall (-)
gamma_beta (float | npt.NDArray[np.float64]) – Influence factor for oblique wave incidence (-)
c2 (float, optional) – _description_, by default 0.8
c3 (float, optional) – _description_, by default -2.5
g (float, optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

The maximum value of the dimensionless crest freeboard of the structure Rc/Hm0 (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.vangent2025.calculate_crest_freeboard_Rc(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Hm0_swell: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], q: float | ndarray[tuple[Any, ...], dtype[float64]], Ac: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, B_berm: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, db: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_b: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_v: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, design_calculation: bool = True, include_influence_wind: bool = False) → tuple[float | ndarray[tuple[Any, ...], dtype[float64]], bool | ndarray[tuple[Any, ...], dtype[bool]]][source]

Calculate the crest freeboard Rc with the Van Gent et al. (2025) formula.

The crest freeboard Rc (m) is calculated using the Van Gent et al. (2025) formula. Here, eq. B1 from Van Gent et al. (2025) is implemented.

For more details, see: https://doi.org/10.59490/jchs.2025.0048

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Hm0_swell (float | npt.NDArray[np.float64]) – Spectral significant wave height of swell or infragravity waves in case of a second wave field (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
q (float | npt.NDArray[np.float64]) – Mean wave overtopping discharge (m^3/s/m)
Ac (float | npt.NDArray[np.float64]) – Armour crest freeboard of the structure (m)
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
B_berm (float | npt.NDArray[np.float64], optional) – Berm width of the structure (m), by default 0.0
db (float | npt.NDArray[np.float64], optional) – Berm height of the structure (m), by default 0.0
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal rock diameter (m), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default np.nan
gamma_b (float | npt.NDArray[np.float64], optional) – Influence factor for a berm (-), by default np.nan
gamma_v (float | npt.NDArray[np.float64], optional) – Influence factor for a crest wall (-), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
design_calculation (bool, optional) – Use the 95% confidence level for design calculations, by default True
include_influence_wind (bool, optional) – Include influence of wind on wave overtopping, by default False

Returns:

The crest freeboard of the structure Rc (m) and a boolean indicating whether the maximum value formula was used

Return type:

tuple[float | npt.NDArray[np.float64], bool | npt.NDArray[np.bool]]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.vangent2025.calculate_dimensionless_crest_freeboard(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Hm0_swell: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], q: float | ndarray[tuple[Any, ...], dtype[float64]], Ac: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, B_berm: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, db: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_b: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_v: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, g: float = 9.81, design_calculation: bool = True, include_influence_wind: bool = False, max_iter: int = 1000, tolerance: float = 1e-05) → tuple[float | ndarray[tuple[Any, ...], dtype[float64]], bool | ndarray[tuple[Any, ...], dtype[bool]]][source]

Calculate the dimensionless crest freeboard Rc/Hm0 with the Van Gent et al. (2025) formula.

The dimensionless crest freeboard Rc/Hm0 (-) is calculated using the Van Gent et al. (2025) formula. Here, eq. B1 from Van Gent et al. (2025) is implemented.

For more details, see: https://doi.org/10.59490/jchs.2025.0048

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Hm0_swell (float | npt.NDArray[np.float64]) – Spectral significant wave height of swell or infragravity waves in case of a second wave field (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
q (float | npt.NDArray[np.float64]) – Mean wave overtopping discharge (m^3/s/m)
Ac (float | npt.NDArray[np.float64]) – Armour crest freeboard of the structure (m)
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
B_berm (float | npt.NDArray[np.float64], optional) – Berm width of the structure (m), by default 0.0
db (float | npt.NDArray[np.float64], optional) – Berm height of the structure (m), by default 0.0
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal rock diameter (m), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default np.nan
gamma_b (float | npt.NDArray[np.float64], optional) – Influence factor for a berm (-), by default np.nan
gamma_v (float | npt.NDArray[np.float64], optional) – Influence factor for a crest wall (-), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
g (float, optional) – Gravitational constant (m/s^2), by default 9.81
design_calculation (bool, optional) – Use the 95% confidence level for design calculations, by default True
include_influence_wind (bool, optional) – Include influence of wind on wave overtopping, by default False
max_iter (int, optional) – Maximum number of iterations, by default 1000
tolerance (float, optional) – Tolerance for convergence of the iterative solution, by default 1e-5

Returns:

The dimensionless crest freeboard of the structure Rc/Hm0 (-) and a boolean indicating whether the maximum value formula was used

Return type:

tuple[float | npt.NDArray[np.float64], bool | npt.NDArray[np.bool]]

Raises:

ValueError – Raise an error if gamma_f is not provided and Dn50 is not provided so it cannot be calculated.

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.vangent2025.calculate_dimensionless_overtopping_discharge_q(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Hm0_swell: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], Ac: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, B_berm: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, db: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_b: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_v: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, design_calculation: bool = True, include_influence_wind: bool = False) → tuple[float | ndarray[tuple[Any, ...], dtype[float64]], bool | ndarray[tuple[Any, ...], dtype[bool]]][source]

Calculate the dimensionless mean wave overtopping discharge q with the Van Gent et al. (2025) formula.

The dimensionless mean wave overtopping discharge q/sqrt(g*Hm0^3) (-) is calculated using the Van Gent et al. (2025) formula. Here, eq. B1 from Van Gent et al. (2025) is implemented.

For more details, see: https://doi.org/10.59490/jchs.2025.0048

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Hm0_swell (float | npt.NDArray[np.float64]) – Spectral significant wave height of swell or infragravity waves in case of a second wave field (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
Ac (float | npt.NDArray[np.float64]) – Armour crest freeboard of the structure (m)
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
B_berm (float | npt.NDArray[np.float64], optional) – Berm width of the structure (m), by default 0.0
db (float | npt.NDArray[np.float64], optional) – Berm height of the structure (m), by default 0.0
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal rock diameter (m), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default np.nan
gamma_b (float | npt.NDArray[np.float64], optional) – Influence factor for a berm (-), by default np.nan
gamma_v (float | npt.NDArray[np.float64], optional) – Influence factor for a crest wall (-), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
design_calculation (bool, optional) – Use the 95% confidence level for design calculations, by default True
include_influence_wind (bool, optional) – Include influence of wind on wave overtopping, by default False

Returns:

Dimensionless mean wave overtopping discharge q/sqrt(g*Hm0^3) (-) and a boolean indicating whether the maximum value formula was used

Return type:

tuple[float | npt.NDArray[np.float64], bool | npt.NDArray[np.bool]]

Raises:

ValueError – Raise an error if gamma_f is not provided and Dn50 is not provided so it cannot be calculated.

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.vangent2025.calculate_influence_berm_gamma_b(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], smm10: float | ndarray[tuple[Any, ...], dtype[float64]], Ac: float | ndarray[tuple[Any, ...], dtype[float64]], B_berm: float | ndarray[tuple[Any, ...], dtype[float64]], BL: float | ndarray[tuple[Any, ...], dtype[float64]], c_b1: float = 18.0, c_b2: float = 1.3, c_b3: float = 0.34, c_b4: float = 0.2) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate influence factor for a berm gamma_b

The influence factor gamma_b is determined using Van Gent et al. (2025) eq. B4.

For more details, see: https://doi.org/10.59490/jchs.2025.0048

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
smm10 (float | npt.NDArray[np.float64]) – The deep water wave steepness based on the spectral wave period Tm-1,0 (-)
Ac (float | npt.NDArray[np.float64]) – Armour crest freeboard of the structure (m)
B_berm (float | npt.NDArray[np.float64]) – Berm width of the structure (m)
BL (float | npt.NDArray[np.float64]) – Vertical distance of the berm relative to the crest of the armour Ac (m)
c_b1 (float, optional) – Coefficient in the gamma_b formula, by default 18.0
c_b2 (float, optional) – Coefficient in the gamma_b formula, by default 1.3
c_b3 (float, optional) – Coefficient in the gamma_b formula, by default 0.34
c_b4 (float, optional) – Coefficient in the gamma_b formula, by default 0.2

Returns:

The influence factor for a berm gamma_b (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.vangent2025.calculate_influence_crest_wall_gamma_v(cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], Ac: float | ndarray[tuple[Any, ...], dtype[float64]], c_v: float = 0.45) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the influence factor for a crest wall gamma_v

The influence factor gamma_v is determined using Van Gent et al. (2025) eq. B5a for cot_alpha <= 4.0 and B5b for cot_alpha > 4.0.

For more details, see: https://doi.org/10.59490/jchs.2025.0048

Parameters:

cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
Ac (float | npt.NDArray[np.float64]) – Armour crest freeboard of the structure (m)
c_v (float, optional) – Coefficient in the gamma_v formula, by default 0.45

Returns:

The influence factor for a crest wall gamma_v (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.vangent2025.calculate_influence_friction_gamma_f(Dn50: float | ndarray[tuple[Any, ...], dtype[float64]], Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], smm10: float | ndarray[tuple[Any, ...], dtype[float64]], c_f1: float = 0.7, c_f2: float = 0.05, smm10_lim: float = 0.012) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate influence factor for surface roughness gamma_f

The influence factor gamma_f is determined using Van Gent et al. (2025) eq. B3a for sm-1,0 >= smm10__lim: (0.012 by default) and eq. B3b for sm-1,0 < smm10__lim.

For more details, see: https://doi.org/10.59490/jchs.2025.0048

Parameters:

Dn50 (float | npt.NDArray[np.float64]) – Nominal rock diameter (m)
Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
smm10 (float | npt.NDArray[np.float64]) – Deep water wave steepness based on the spectral wave period Tm-1,0 (-)
c_f1 (float, optional) – Coefficient in the gamma_f formula, by default 0.70
c_f2 (float, optional) – Coefficient in the gamma_f formula, by default 0.05
smm10_lim (float, optional) – Limit for the deep water wave steepness (-), by default 0.012

Returns:

The influence factor for surface roughness gamma_f (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.vangent2025.calculate_influence_oblique_waves_gamma_beta(beta: float | ndarray[tuple[Any, ...], dtype[float64]], c_beta: float = 0.35) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the influence factor for oblique wave incidence gamma_beta

The influence factor gamma_beta is determined using Van Gent et al. (2025) eq. B6

For more details, see: https://doi.org/10.59490/jchs.2025.0048

Parameters:

beta (float | npt.NDArray[np.float64]) – Angle of wave incidence (degrees)
c_beta (float, optional) – Coefficient in the gamma_beta formula, by default 0.35

Returns:

The influence factor for oblique wave incidence gamma_beta (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.vangent2025.calculate_influence_wind_gamma_w(Rc: float | ndarray[tuple[Any, ...], dtype[float64]], Ac: float | ndarray[tuple[Any, ...], dtype[float64]], Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], q_diml: float | ndarray[tuple[Any, ...], dtype[float64]], c_w1: float = 0.075, c_w2: float = -0.3) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the influence factor for wind gamma_w

The influence factor gamma_w is determined using Van Gent et al. (2025) eq. B7

For more details, see: https://doi.org/10.59490/jchs.2025.0048

Parameters:

hc (float | npt.NDArray[np.float64]) – protruding part of a crest wall, hc = Rc - Ac (m)
Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
q_diml (float | npt.NDArray[np.float64]) – Dimensionless mean wave overtopping discharge q/sqrt(g*Hm0^3) (-)

Returns:

The influence factor for wind gamma_w (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.vangent2025.calculate_overtopping_discharge_q(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Hm0_swell: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], Ac: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, B_berm: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, db: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_b: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_v: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, g: float = 9.81, design_calculation: bool = True, include_influence_wind: bool = False) → tuple[float | ndarray[tuple[Any, ...], dtype[float64]], bool | ndarray[tuple[Any, ...], dtype[bool]]][source]

Calculate the mean wave overtopping discharge q with the Van Gent et al. (2025) formula.

The mean wave overtopping discharge q (m^3/s/m) is calculated using the Van Gent et al. (2025) formula. Here, eq. B1 from Van Gent et al. (2025) is implemented.

For more details, see: https://doi.org/10.59490/jchs.2025.0048

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Hm0_swell (float | npt.NDArray[np.float64]) – Spectral significant wave height of swell or infragravity waves in case of a second wave field (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
Ac (float | npt.NDArray[np.float64]) – Armour crest freeboard of the structure (m)
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
B_berm (float | npt.NDArray[np.float64], optional) – Berm width of the structure (m), by default 0.0
db (float | npt.NDArray[np.float64], optional) – Berm height of the structure (m), by default 0.0
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal rock diameter (m), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default np.nan
gamma_b (float | npt.NDArray[np.float64], optional) – Influence factor for a berm (-), by default np.nan
gamma_v (float | npt.NDArray[np.float64], optional) – Influence factor for a crest wall (-), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
g (float, optional) – Gravitational constant (m/s^2), by default 9.81
design_calculation (bool, optional) – Use the 95% confidence level for design calculations, by default True
include_influence_wind (bool, optional) – Include influence of wind on wave overtopping, by default False

Returns:

Mean wave overtopping discharge q (m^3/s/m) and a boolean indicating whether the maximum value formula was used

Return type:

tuple[float | npt.NDArray[np.float64], bool | npt.NDArray[np.bool]]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.vangent2025.check_validity_range(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Hm0_deep: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, h: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Rc: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Ac: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Gc: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, B_berm: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, db: float | ndarray[tuple[Any, ...], dtype[float64]] = nan) → None[source]

Check the parameter values vs the validity range of the Van Gent et al. (2025) formula.

For all parameters supplied, their values are checked versus the validity range. Not that this range is wider than that specified in Table 1 (Van Gent et al., 2025), since that does not describe the entire data set the formula is derived from. When parameters are nan (by default), they are not checked.

For more details, see: https://doi.org/10.59490/jchs.2025.0048

Parameters:

Hm0 (float | npt.NDArray[np.float64], optional) – Spectral significant wave height (m), by default np.nan
Hm0_deep (float | npt.NDArray[np.float64], optional) – Spectral significant wave height on deep water (m), by default np.nan
Tmm10 (float | npt.NDArray[np.float64], optional) – Spectral wave period Tm-1,0 (s), by default np.nan
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
h (float | npt.NDArray[np.float64], optional) – Water depth at toe of the structure (m), by default np.nan
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal rock diameter (m), by default np.nan
Rc (float | npt.NDArray[np.float64], optional) – Crest freeboard of the structure (m), by default np.nan
Ac (float | npt.NDArray[np.float64], optional) – Armour crest freeboard of the structure (m), by default np.nan
Gc (float | npt.NDArray[np.float64], optional) – Width of the crest of the structure (m), by default np.nan
B_berm (float | npt.NDArray[np.float64], optional) – Berm width of the structure (m), by default np.nan
db (float | npt.NDArray[np.float64], optional) – Berm height of the structure (m), by default np.nan

deltares_coastal_structures_toolbox.functions.hydraulic.wave_overtopping.vangent2025.q_diml_max_equation(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Hm0_swell: float | ndarray[tuple[Any, ...], dtype[float64]], ksi_mm10: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_b: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_v: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]], c2: float = 0.8, c3: float = -2.5) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the maximum dimensionless mean wave overtopping discharge q with the Van Gent et al. (2025) formula.

The maximum value for the dimensionless mean wave overtopping discharge q/sqrt(g*Hm0^3) (-) is calculated using the Van Gent et al. (2025) formula. Here, eq. B2 from Van Gent et al. (2025) is implemented.

For more details, see: https://doi.org/10.59490/jchs.2025.0048

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Hm0_swell (float | npt.NDArray[np.float64]) – Spectral significant wave height of swell or infragravity waves in case of a second wave field (m)
ksi_mm10 (float | npt.NDArray[np.float64]) – The Iribarren number based on the spectral wave period Tm-1,0 (-)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
gamma_f (float | npt.NDArray[np.float64]) – Influence factor for surface roughness (-)
gamma_b (float | npt.NDArray[np.float64]) – Influence factor for a berm (-)
gamma_v (float | npt.NDArray[np.float64]) – Influence factor for a crest wall (-)
gamma_beta (float | npt.NDArray[np.float64]) – Influence factor for oblique wave incidence (-)
c2 (float, optional) – Coefficient in wave overtopping formula (-), by default 0.8
c3 (float, optional) – Coefficient in wave overtopping formula (-), by default -2.5

Returns:

Maximum value of the dimensionless mean wave overtopping discharge q/sqrt(g*Hm0^3) (-)

Return type:

float | npt.NDArray[np.float64]

Wave Runup

Van Gent (2001)

deltares_coastal_structures_toolbox.functions.hydraulic.wave_runup.vangent2001.calculate_wave_runup_height_z10p(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], gamma: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], c0: float = 1.1, c1: float = 4.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the wave runup height with a 10% probability of exceedance z10% with the Van Gent (2001) formula.

The wave runup height is calculated using the Van Gent (2001) formula. Van Gent (2001) provides the coefficients to calculate the z2%, and Van Gent (2007) lists coefficients for the z1% and z10%.

For more details see Van Gent (2001), available here: https://doi.org/10.1061/(ASCE)0733-950X(2001)127:5(254) or here: https://www.researchgate.net/publication/245293002_Wave_Run-Up_on_Dikes_with_Shallow_Foreshores

And Van Gent (2007), available here: https://doi.org/10.1142/9789814282024_0002 or here: https://www.researchgate.net/publication/259258925_REAR-SIDE_STABILITY_OF_RUBBLE_MOUND_STRUCTURES_WITH_CREST_ELEMENTS

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
gamma (float | npt.NDArray[np.float64]) – Reduction factor gamma = gamma_f * gamma_beta (-)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
c0 (float, optional) – Coefficient in wave runup formula (-), by default 1.1
c1 (float, optional) – Coefficient in wave runup formula (-), by default 4.0

Returns:

The 10% exceedance wave runup height z10% (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_runup.vangent2001.calculate_wave_runup_height_z1p(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], gamma: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], c0: float = 1.45, c1: float = 5.1) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the wave runup height with a 1% probability of exceedance z1% with the Van Gent (2001) formula.

The wave runup height is calculated using the Van Gent (2001) formula. Van Gent (2001) provides the coefficients to calculate the z2%, and Van Gent (2007) lists coefficients for the z1% and z10%.

For more details see Van Gent (2001), available here: https://doi.org/10.1061/(ASCE)0733-950X(2001)127:5(254) or here: https://www.researchgate.net/publication/245293002_Wave_Run-Up_on_Dikes_with_Shallow_Foreshores

And Van Gent (2007), available here: https://doi.org/10.1142/9789814282024_0002 or here: https://www.researchgate.net/publication/259258925_REAR-SIDE_STABILITY_OF_RUBBLE_MOUND_STRUCTURES_WITH_CREST_ELEMENTS

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
gamma (float | npt.NDArray[np.float64]) – Reduction factor gamma = gamma_f * gamma_beta (-)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
c0 (float, optional) – Coefficient in wave runup formula (-), by default 1.45
c1 (float, optional) – Coefficient in wave runup formula (-), by default 5.1

Returns:

The 1% exceedance wave runup height z1% (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_runup.vangent2001.calculate_wave_runup_height_z2p(Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], gamma: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], Hm0: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c0: float = 1.35, c1: float = 4.7) → float[source]

Calculate the wave runup height with a 2% probability of exceedance z2% with the Van Gent (2001) formula.

The wave runup height is calculated using the Van Gent (2001) formula. Van Gent (2001) provides the coefficients to calculate the z2%, and Van Gent (2007) lists coefficients for the z1% and z10%.

For more details see Van Gent (2001), available here: https://doi.org/10.1061/(ASCE)0733-950X(2001)127:5(254) or here: https://www.researchgate.net/publication/245293002_Wave_Run-Up_on_Dikes_with_Shallow_Foreshores

And Van Gent (2007), available here: https://doi.org/10.1142/9789814282024_0002 or here: https://www.researchgate.net/publication/259258925_REAR-SIDE_STABILITY_OF_RUBBLE_MOUND_STRUCTURES_WITH_CREST_ELEMENTS

Note that in Van Gent (2001) various values for the coefficients c0 and c1 are given for different wave height metrics (Hm0 and Hs), and including or excluding long waves. Here, only the coefficients including long waves are implemented. This function can be called supplying either Hm0 or Hs.

Parameters:

Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
gamma (float | npt.NDArray[np.float64]) – Reduction factor gamma = gamma_f * gamma_beta (-)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
Hm0 (float | npt.NDArray[np.float64], optional) – Spectral significant wave height (m), by default np.nan
Hs (float | npt.NDArray[np.float64], optional) – Significant wave height (m), by default np.nan
c0 (float, optional) – Coefficient in wave runup formula (-), by default 1.35
c1 (float, optional) – Coefficient in wave runup formula (-), by default 4.7

Returns:

The 2% exceedance wave runup height z2% (m)

Return type:

float | npt.NDArray[np.float64]

Raises:

ValueError – Raise an error when both or neither Hm0 and Hs are provided.

deltares_coastal_structures_toolbox.functions.hydraulic.wave_runup.vangent2001.calculate_wave_runup_height_zXp(H: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], gamma: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], c0: float, c1: float) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the wave runup height with the Van Gent (2001) formula.

The wave runup height is calculated using the Van Gent (2001) formula. Van Gent (2001) provides the coefficients to calculate the z2%, and Van Gent (2007) lists coefficients for the z1% and z10%.

For more details see Van Gent (2001), available here: https://doi.org/10.1061/(ASCE)0733-950X(2001)127:5(254) or here: https://www.researchgate.net/publication/245293002_Wave_Run-Up_on_Dikes_with_Shallow_Foreshores

And Van Gent (2007), available here: https://doi.org/10.1142/9789814282024_0002 or here: https://www.researchgate.net/publication/259258925_REAR-SIDE_STABILITY_OF_RUBBLE_MOUND_STRUCTURES_WITH_CREST_ELEMENTS

Parameters:

H (float | npt.NDArray[np.float64]) – Wave height, either the Hs or the Hm0 depending on the coefficients used (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
gamma (float | npt.NDArray[np.float64]) – Reduction factor gamma = gamma_f * gamma_beta (-)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
c0 (float) – Coefficient in wave runup formula (-)
c1 (float) – Coefficient in wave runup formula (-)

Returns:

The wave runup height z (m)

Return type:

float | npt.NDArray[np.float64]

TAW (2002)

deltares_coastal_structures_toolbox.functions.hydraulic.wave_runup.taw2002.calculate_adjusted_influence_roughness_gamma_f(gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_b: float | ndarray[tuple[Any, ...], dtype[float64]], ksi_mm10: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate adjusted influence factor for surface roughness gamma_f

In case of longer waves, slope roughness has a smaller effect on the wave runup height. This is reflected in an adjusted value of the influence factor, as described in the last paragraph of Section 2.7 in TAW (2002).

Parameters:

gamma_f (float | npt.NDArray[np.float64]) – Influence factor for surface roughness (-)
gamma_b (float | npt.NDArray[np.float64]) – Influence factor for a berm
ksi_mm10 (float | npt.NDArray[np.float64]) – The Iribarren number based on the spectral wave period Tm-1,0 (-)

Returns:

The adjusted influence factor for surface roughness gamma_f (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_runup.taw2002.calculate_berm_length(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], B_berm: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]] = nan) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the berm length of the structure

Calculate the berm length of the structure L_berm (m) as is needed for the determination of the influence factor for berms in eq. 11 (TAW, 2002)

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
B_berm (float | npt.NDArray[np.float64]) – Berm width of the structure (m)
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
cot_alpha_down (float | npt.NDArray[np.float64], optional) – Cotangent of the lower part of the front-side slope of the structure (-), by default np.nan
cot_alpha_up (float | npt.NDArray[np.float64], optional) – Cotangent of the upper part of the front-side slope of the structure (-), by default np.nan

Returns:

Berm length of the structure L_berm (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_runup.taw2002.calculate_dimensionless_wave_runup_height_z2p(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_b: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, B_berm: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, db: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c1: float = 1.75, c2: float = 4.3, c3: float = 1.6, c4: float = 1.0, use_best_fit: bool = False) → tuple[float | ndarray[tuple[Any, ...], dtype[float64]], bool | ndarray[tuple[Any, ...], dtype[bool]]][source]

Calculate the dimensionless wave runup height with a 2% probability of exceedance z2%/Hm0 with the TAW (2002) formula.

The dimensionless 2% exceedance wave runup height z2%/Hm0 (-) is calculated using the TAW (2002) formulas. Here eqs. 3a and 3b from TAW (2002) are implemented for design calculations and eqs. 5a and 5b for best fit calculations (using the option best_fit=True).

For more details see TAW (2002), available here (in Dutch): https://open.rijkswaterstaat.nl/open-overheid/onderzoeksrapporten/@97617/technisch-rapport-golfoploop/

The TAW (2002) formulas are also included in the EurOtop (2007) manual, available here (in English): https://www.overtopping-manual.com/assets/downloads/EAK-K073_EurOtop_2007.pdf

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_b (float | npt.NDArray[np.float64], optional) – Influence factor for a berm (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0
B_berm (float | npt.NDArray[np.float64], optional) – Berm width of the structure (m), by default 0.0
db (float | npt.NDArray[np.float64], optional) – Berm height of the structure (m), by default 0.0
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
cot_alpha_down (float | npt.NDArray[np.float64], optional) – Cotangent of the lower part of the front-side slope of the structure (-), by default np.nan
cot_alpha_up (float | npt.NDArray[np.float64], optional) – Cotangent of the upper part of the front-side slope of the structure (-), by default np.nan
c1 (float, optional) – Coefficient in wave runup formula (-), by default 1.75
c2 (float, optional) – Coefficient in wave runup formula (-), by default 4.3
c3 (float, optional) – Coefficient in wave runup formula (-), by default 1.6
c4 (float, optional) – Coefficient in wave runup formula (-), by default 1.0
use_best_fit (bool, optional) – Switch to either use best fit values for the coefficients (true) or the design values (false), by default False

Returns:

The dimensionless 2% exceedance wave runup height z2%/Hm0 (-) and a boolean indicating whether the maximum value formula was used

Return type:

tuple[float | npt.NDArray[np.float64], bool | npt.NDArray[np.bool]]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_runup.taw2002.calculate_influence_berm_gamma_b(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], z2p: float | ndarray[tuple[Any, ...], dtype[float64]], db: float | ndarray[tuple[Any, ...], dtype[float64]], B_berm: float | ndarray[tuple[Any, ...], dtype[float64]], L_berm: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the influence factor for a berm gamma_b

The influence factor for a berm gamma_b (-) on wave runup is calculated using eqs. 10, 11, 12 and 13 from TAW (2002).

Note that the actual the recommended procedure to determine gamma_b is iterative and implemented in iteration_procedure_gamma_b()

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
z2p (float | npt.NDArray[np.float64]) – Wave runup height exceeded by 2% of waves z2% (m)
db (float | npt.NDArray[np.float64]) – Berm height of the structure (m)
B_berm (float | npt.NDArray[np.float64]) – Berm width of the structure (m)
L_berm (float | npt.NDArray[np.float64]) – Berm length of the structure (m)

Returns:

The influence factor for a berm gamma_b (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_runup.taw2002.calculate_influence_oblique_waves_gamma_beta(beta: float | ndarray[tuple[Any, ...], dtype[float64]], c_gamma_beta: float = 0.0022, max_angle: float = 80.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the influence factor for oblique wave incidence gamma_beta

The influence factor for oblique wave incidence gamma_beta (-) on wave runup is calculated using eq. 8 from TAW (2002). Note that this implementation can also be used for wave overtopping by changing the c_gamma_beta to 0.0033

Parameters:

beta (float | npt.NDArray[np.float64]) – Angle of wave incidence (degrees)
c_gamma_beta (float, optional) – Coefficient for wave runup, by default 0.0022
max_angle (float, optional) – Maximum angle of wave incidence, by default 80.0

Returns:

The influence factor for oblique wave incidence gamma_beta (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_runup.taw2002.calculate_wave_runup_height_z2p(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_b: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, B_berm: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, db: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c1: float = 1.75, c2: float = 4.3, c3: float = 1.6, c4: float = 1.0, use_best_fit: bool = False) → tuple[float | ndarray[tuple[Any, ...], dtype[float64]], bool | ndarray[tuple[Any, ...], dtype[bool]]][source]

Calculate the wave runup height with a 2% probability of exceedance z2% with the TAW (2002) formula.

The 2% exceedance wave runup height z2% (m) is calculated using the TAW (2002) formulas. Here eqs. 3a and 3b from TAW (2002) are implemented for design calculations and eqs. 5a and 5b for best fit calculations (using the option best_fit=True).

For more details see TAW (2002), available here (in Dutch): https://open.rijkswaterstaat.nl/open-overheid/onderzoeksrapporten/@97617/technisch-rapport-golfoploop/

The TAW (2002) formulas are also included in the EurOtop (2007) manual, available here (in English): https://www.overtopping-manual.com/assets/downloads/EAK-K073_EurOtop_2007.pdf

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_b (float | npt.NDArray[np.float64], optional) – Influence factor for a berm (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0
B_berm (float | npt.NDArray[np.float64], optional) – Berm width of the structure (m), by default 0.0
db (float | npt.NDArray[np.float64], optional) – Berm height of the structure (m), by default 0.0
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
cot_alpha_down (float | npt.NDArray[np.float64], optional) – Cotangent of the lower part of the front-side slope of the structure (-), by default np.nan
cot_alpha_up (float | npt.NDArray[np.float64], optional) – Cotangent of the upper part of the front-side slope of the structure (-), by default np.nan
c1 (float, optional) – Coefficient in wave runup formula (-), by default 1.75
c2 (float, optional) – Coefficient in wave runup formula (-), by default 4.3
c3 (float, optional) – Coefficient in wave runup formula (-), by default 1.6
c4 (float, optional) – Coefficient in wave runup formula (-), by default 1.0
use_best_fit (bool, optional) – Switch to either use best fit values for the coefficients (true) or the design values (false), by default False

Returns:

The 2% exceedance wave runup height z2% (m) and a boolean indicating whether the maximum value formula was used

Return type:

tuple[float | npt.NDArray[np.float64], bool | npt.NDArray[np.bool]]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_runup.taw2002.check_calculate_gamma_beta(beta: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]]) → bool[source]

Check whether the influence factor for oblique wave incidence gamma_beta should be calculated

If the angle of wave incidence (beta) is provided, the influence factor for oblique wave incidence gamma_beta is calculated. If the influence factor for oblique wave incidence gamma_beta is provided directly, that value is used. I neither of the two values is provided, an error is raised.

Parameters:

beta (float | npt.NDArray[np.float64]) – Angle of wave incidence (degrees)
gamma_beta (float | npt.NDArray[np.float64]) – Influence factor for oblique wave incidence (-)

Returns:

Indicates whether gamma_beta need to be calculated (True) or not (False)

Return type:

bool

Raises:

ValueError – Raise an error when neither beta nor gamma_beta is provided

deltares_coastal_structures_toolbox.functions.hydraulic.wave_runup.taw2002.check_composite_slope(cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]] = nan) → bool[source]

Check whether the structure has a composite slope

This function checks whether the structure has a composite slope, i.e. the lower and upper part of the front-side of the structure have different slopes. If so, it returns true, if not it returns false.

Parameters:

cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
cot_alpha_down (float | npt.NDArray[np.float64], optional) – Cotangent of the lower part of the front-side slope of the structure (-), by default np.nan
cot_alpha_up (float | npt.NDArray[np.float64], optional) – Cotangent of the upper part of the front-side slope of the structure (-), by default np.nan

Returns:

True if the structure has a composite slope, false if upper and lower slopes are equal

Return type:

bool

Raises:

ValueError – Raise error when no slopes are provided

deltares_coastal_structures_toolbox.functions.hydraulic.wave_runup.taw2002.check_validity_range(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_b: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan) → None[source]

Check the parameter values vs the validity range of the TAW (2002) wave runup formula

For all parameters supplied, their values are checked versus the range of test conditions specified by TAW (2002) in the table on pages 39-40. When parameters are nan (by default), they are not checked.

For more details see TAW (2002), available here (in Dutch): https://open.rijkswaterstaat.nl/open-overheid/onderzoeksrapporten/@97617/technisch-rapport-golfoploop/

The TAW (2002) formulas are also included in the EurOtop (2007) manual, available here (in English): https://www.overtopping-manual.com/assets/downloads/EAK-K073_EurOtop_2007.pdf

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m), by default np.nan
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s), by default np.nan
gamma_f (float | npt.NDArray[np.float64]) – Influence factor for surface roughness (-), by default np.nan
gamma_b (float | npt.NDArray[np.float64]) – Influence factor for a berm, by default np.nan
gamma_beta (float | npt.NDArray[np.float64]) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_v (float | npt.NDArray[np.float64]) – Influence factor for a crest wall (-), by default np.nan
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-), by default np.nan

deltares_coastal_structures_toolbox.functions.hydraulic.wave_runup.taw2002.determine_average_slope(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], z2p: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]], B_berm: float | ndarray[tuple[Any, ...], dtype[float64]], db: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Determine the average slope of the front-side of the structure in case of composite slopes

For structures with composite slopes (i.e. the lower and upper part of the front-side of the structure have different slopes), the average slope of the front-side of the structure is determined. This is done following the iterative procedure described in Section 2.3 of TAW (2002).

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
z2p (float | npt.NDArray[np.float64]) – The 2% exceedance wave runup height z2% (m)
cot_alpha_down (float | npt.NDArray[np.float64]) – Cotangent of the lower part of the front-side slope of the structure (-)
cot_alpha_up (float | npt.NDArray[np.float64]) – Cotangent of the upper part of the front-side slope of the structure (-)
B_berm (float | npt.NDArray[np.float64]) – Berm width of the structure (m)
db (float | npt.NDArray[np.float64]) – Berm height of the structure (m)

Returns:

Average cotangent of the front-side slope of the structure cot_alpha_average (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_runup.taw2002.iteration_procedure_gamma_b(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha_average: float | ndarray[tuple[Any, ...], dtype[float64]], B_berm: float | ndarray[tuple[Any, ...], dtype[float64]], L_berm: float | ndarray[tuple[Any, ...], dtype[float64]], db: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]], c1: float = 1.75, c2: float = 4.3, c3: float = 1.6, c4: float = 1.0, use_best_fit: bool = False, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Iterative procedure to determine the influence factor for a berm gamma_b

Iteratively determine the influence factor for a berm gamma_b (-) (TAW, 2002), as in some cases the value of gamma_b is dependant on the z2%.

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
cot_alpha_average (float | npt.NDArray[np.float64]) – Cotangent of the average front-side slope of the structure (-)
B_berm (float | npt.NDArray[np.float64]) – Berm width of the structure (m)
L_berm (float | npt.NDArray[np.float64]) – Berm length of the structure (m)
db (float | npt.NDArray[np.float64]) – Berm height of the structure (m)
gamma_beta (float | npt.NDArray[np.float64]) – Influence factor for oblique wave incidence (-)
c1 (float, optional) – Coefficient in wave runup formula (-), by default 1.75
c2 (float, optional) – Coefficient in wave runup formula (-), by default 4.3
c3 (float, optional) – Coefficient in wave runup formula (-), by default 1.6
c4 (float, optional) – Coefficient in wave runup formula (-), by default 1.0
use_best_fit (bool, optional) – Switch to either use best fit values for the coefficients (true) or the design values (false), by default False
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0

Returns:

The influence factor for a berm gamma_b (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_runup.taw2002.iteration_procedure_z2p(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]], B_berm: float | ndarray[tuple[Any, ...], dtype[float64]], db: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]], c1: float = 1.75, c2: float = 4.3, c3: float = 1.6, c4: float = 1.0, use_best_fit: bool = False, tolerance: float = 0.0001, max_iter: int = 1000) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Iterative procedure to determine the 2% exceedance wave runup height z2%

This iterative procedure to determine the 2% exceedance wave runup height z2% (m) is used in the determination of the average slope of the front-side of the structure in case of composite slopes.

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
cot_alpha_down (float | npt.NDArray[np.float64]) – Cotangent of the lower part of the front-side slope of the structure (-)
cot_alpha_up (float | npt.NDArray[np.float64]) – Cotangent of the upper part of the front-side slope of the structure (-)
B_berm (float | npt.NDArray[np.float64]) – Berm width of the structure (m)
db (float | npt.NDArray[np.float64]) – Berm height of the structure (m)
gamma_f (float | npt.NDArray[np.float64]) – Influence factor for surface roughness (-)
gamma_beta (float | npt.NDArray[np.float64]) – Influence factor for oblique wave incidence (-)
c1 (float, optional) – Coefficient in wave runup formula (-), by default 1.75
c2 (float, optional) – Coefficient in wave runup formula (-), by default 4.3
c3 (float, optional) – Coefficient in wave runup formula (-), by default 1.6
c4 (float, optional) – Coefficient in wave runup formula (-), by default 1.0
use_best_fit (bool, optional) – Switch to either use best fit values for the coefficients (true) or the design values (false), by default False
tolerance (float, optional) – Maximum allowable tolerance for the z2% iterative procedure, by default 1e-4
max_iter (int, optional) – Maximum number of iterations in the z2% iterative procedure, by default 1000

Returns:

The 2% exceedance wave runup height z2% (m)

Return type:

float | npt.NDArray[np.float64]

EurOtop (2018)

deltares_coastal_structures_toolbox.functions.hydraulic.wave_runup.eurotop2018.calculate_dimensionless_wave_runup_height_z2p(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_b: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, B_berm: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, db: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c1: float = 1.75, c2: float = 4.3, c3: float = 1.5, c4: float = 1.07, use_best_fit: bool = False) → tuple[float | ndarray[tuple[Any, ...], dtype[float64]], bool | ndarray[tuple[Any, ...], dtype[bool]]][source]

Calculate the dimensionless wave runup height with a 2% probability of exceedance z2%/Hm0 with the EurOtop (2018) formula.

The dimensionless 2% exceedance wave runup height z2%/Hm0 (-) is calculated using the EurOtop (2018) formulas. Here eqs. 5.4 and 5.5 from EurOtop (2018) are implemented for design calculations and eqs. 5.1 and 5.2 for best fit calculations (using the option best_fit=True). Note that an erratat has been published regarding eqs. 5.2 and 5.5.

For more details see EurOtop (2018) and the errata of November 2019, available here: https://www.overtopping-manual.com/assets/downloads/EurOtop_II_2018_Final_version.pdf

https://www.overtopping-manual.com/assets/downloads/Errata_EurOtop_2018_Nov_2019.pdf

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_b (float | npt.NDArray[np.float64], optional) – Influence factor for a berm (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0
B_berm (float | npt.NDArray[np.float64], optional) – Berm width of the structure (m), by default 0.0
db (float | npt.NDArray[np.float64], optional) – Berm height of the structure (m), by default 0.0
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
cot_alpha_down (float | npt.NDArray[np.float64], optional) – Cotangent of the lower part of the front-side slope of the structure (-), by default np.nan
cot_alpha_up (float | npt.NDArray[np.float64], optional) – Cotangent of the upper part of the front-side slope of the structure (-), by default np.nan
c1 (float, optional) – Coefficient in wave runup formula (-), by default 1.75
c2 (float, optional) – Coefficient in wave runup formula (-), by default 4.3
c3 (float, optional) – Coefficient in wave runup formula (-), by default 1.5
c4 (float, optional) – Coefficient in wave runup formula (-), by default 1.07
use_best_fit (bool, optional) – Switch to either use best fit values for the coefficients (true) or the design values (false), by default False

Returns:

The 2% exceedance wave runup height z2% (m) and a boolean indicating whether the maximum value formula was used

Return type:

tuple[float | npt.NDArray[np.float64], bool | npt.NDArray[np.bool]]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_runup.eurotop2018.calculate_influence_oblique_waves_gamma_beta(beta: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f_crit: float = 0.6, c_gamma_beta_smooth: float = 0.0022, c_gamma_beta_rough: float = 0.0063, max_angle: float = 80.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the influence factor for oblique wave incidence gamma_beta

The influence factor gamma_beta is determined using the EurOtop (2018) eq. 5.28 for smooth slopes and eq. 6.9 for rough slopes.

Parameters:

beta (float | npt.NDArray[np.float64]) – Angle of wave incidence (degrees)
gamma_f (float | npt.NDArray[np.float64]) – Influence factor for surface roughness (-)
gamma_f_crit (float, optional) – Critical value for the influence factor dividing smooth (higher) and rough (lower) slopes, by default 0.6
c_gamma_beta_smooth (float, optional) – Coefficient for wave runup on smooth slopes, by default 0.0022
c_gamma_beta_rough (float, optional) – Coefficient for wave runup on rough slopes, by default 0.0063
max_angle (float, optional) – Maximum angle of wave incidence, by default 80.0

Returns:

The influence factor for oblique wave incidence gamma_beta (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_runup.eurotop2018.calculate_wave_runup_height_z2p(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_b: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, B_berm: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, db: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.0, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c1: float = 1.75, c2: float = 4.3, c3: float = 1.5, c4: float = 1.07, use_best_fit: bool = False) → tuple[float | ndarray[tuple[Any, ...], dtype[float64]], bool | ndarray[tuple[Any, ...], dtype[bool]]][source]

Calculate the wave runup height with a 2% probability of exceedance z2% with the EurOtop (2018) formula.

The 2% exceedance wave runup height z2% (m) is calculated using the EurOtop (2018) formulas. Here eqs. 5.4 and 5.5 from EurOtop (2018) are implemented for design calculations and eqs. 5.1 and 5.2 for best fit calculations (using the option best_fit=True). Note that an erratat has been published regarding eqs. 5.2 and 5.5.

For more details see EurOtop (2018) and the errata of November 2019, available here: https://www.overtopping-manual.com/assets/downloads/EurOtop_II_2018_Final_version.pdf

https://www.overtopping-manual.com/assets/downloads/Errata_EurOtop_2018_Nov_2019.pdf

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default np.nan
gamma_b (float | npt.NDArray[np.float64], optional) – Influence factor for a berm (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0
B_berm (float | npt.NDArray[np.float64], optional) – Berm width of the structure (m), by default 0.0
db (float | npt.NDArray[np.float64], optional) – Berm height of the structure (m), by default 0.0
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
cot_alpha_down (float | npt.NDArray[np.float64], optional) – Cotangent of the lower part of the front-side slope of the structure (-), by default np.nan
cot_alpha_up (float | npt.NDArray[np.float64], optional) – Cotangent of the upper part of the front-side slope of the structure (-), by default np.nan
c1 (float, optional) – Coefficient in wave runup formula (-), by default 1.75
c2 (float, optional) – Coefficient in wave runup formula (-), by default 4.3
c3 (float, optional) – Coefficient in wave runup formula (-), by default 1.5
c4 (float, optional) – Coefficient in wave runup formula (-), by default 1.07
use_best_fit (bool, optional) – Switch to either use best fit values for the coefficients (true) or the design values (false), by default False

Returns:

The 2% exceedance wave runup height z2% (m) and a boolean indicating whether the maximum value formula was used

Return type:

tuple[float | npt.NDArray[np.float64], bool | npt.NDArray[np.bool]]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_runup.eurotop2018.check_best_fit(c1: float, c2: float, c3: float, c4: float, use_best_fit: bool) → tuple[float, float, float, float][source]

Check whether best fit coefficients need to be used

If so, return the best fit coefficients, otherwise return the input coefficients

Parameters:

c1 (float) – Coefficient in wave runup formula (-)
c2 (float) – Coefficient in wave runup formula (-)
c3 (float) – Coefficient in wave runup formula (-)
c4 (float) – Coefficient in wave runup formula (-)
use_best_fit (bool) – Switch to either use best fit values for the coefficients (true) or the design values (false)

Returns:

Coefficients c1, c2, c3 and c4 in the wave runup formula (-)

Return type:

tuple[float, float, float, float]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_runup.eurotop2018.iteration_procedure_gamma_b(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha_average: float | ndarray[tuple[Any, ...], dtype[float64]], B_berm: float | ndarray[tuple[Any, ...], dtype[float64]], L_berm: float | ndarray[tuple[Any, ...], dtype[float64]], db: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]], c1: float = 1.75, c2: float = 4.3, c3: float = 1.5, c4: float = 1.07, use_best_fit: bool = False, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Iterative procedure to determine the influence factor for a berm gamma_b

Iteratively determine the influence factor for a berm gamma_b (-), as in some cases the value of gamma_b is dependant on the z2%. This is a wrapper function around the TAW (2002) implementation, using the EurOtop (2018) coefficients.

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
cot_alpha_average (float | npt.NDArray[np.float64]) – Cotangent of the average front-side slope of the structure (-)
B_berm (float | npt.NDArray[np.float64]) – Berm width of the structure (m)
L_berm (float | npt.NDArray[np.float64]) – Berm length of the structure (m)
db (float | npt.NDArray[np.float64]) – Berm height of the structure (m)
gamma_beta (float | npt.NDArray[np.float64]) – Influence factor for oblique wave incidence (-)
c1 (float, optional) – Coefficient in wave runup formula (-), by default 1.75
c2 (float, optional) – Coefficient in wave runup formula (-), by default 4.3
c3 (float, optional) – Coefficient in wave runup formula (-), by default 1.5
c4 (float, optional) – Coefficient in wave runup formula (-), by default 1.07
use_best_fit (bool, optional) – Switch to either use best fit values for the coefficients (true) or the design values (false), by default False
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 1.0

Returns:

The influence factor for a berm gamma_b (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_runup.eurotop2018.iteration_procedure_z2p(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha_down: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha_up: float | ndarray[tuple[Any, ...], dtype[float64]], B_berm: float | ndarray[tuple[Any, ...], dtype[float64]], db: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]], c1: float = 1.75, c2: float = 4.3, c3: float = 1.5, c4: float = 1.07, use_best_fit: bool = False, tolerance: float = 0.0001, max_iter: int = 1000) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Iterative procedure to determine the 2% exceedance wave runup height z2%

This iterative procedure to determine the 2% exceedance wave runup height z2% (m) is used in the determination of the average slope of the front-side of the structure in case of composite slopes. This is a wrapper function around the TAW (2002) implementation, using the EurOtop (2018) coefficients.

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
cot_alpha_down (float | npt.NDArray[np.float64]) – Cotangent of the lower part of the front-side slope of the structure (-)
cot_alpha_up (float | npt.NDArray[np.float64]) – Cotangent of the upper part of the front-side slope of the structure (-)
B_berm (float | npt.NDArray[np.float64]) – Berm width of the structure (m)
db (float | npt.NDArray[np.float64]) – Berm height of the structure (m)
gamma_f (float | npt.NDArray[np.float64]) – Influence factor for surface roughness (-)
gamma_beta (float | npt.NDArray[np.float64]) – Influence factor for oblique wave incidence (-)
c1 (float, optional) – Coefficient in wave runup formula (-), by default 1.75
c2 (float, optional) – Coefficient in wave runup formula (-), by default 4.3
c3 (float, optional) – Coefficient in wave runup formula (-), by default 1.5
c4 (float, optional) – Coefficient in wave runup formula (-), by default 1.07
use_best_fit (bool, optional) – Switch to either use best fit values for the coefficients (true) or the design values (false), by default False
tolerance (float, optional) – Maximum allowable tolerance for the z2% iterative procedure, by default 1e-4
max_iter (int, optional) – Maximum number of iterations in the z2% iterative procedure, by default 1000

Returns:

The 2% exceedance wave runup height z2% (m)

Return type:

float | npt.NDArray[np.float64]

Wave Transmission

Goda et al. (1967)

deltares_coastal_structures_toolbox.functions.hydraulic.wave_transmission.goda1967_caisson.calculate_wave_transmission_Kt(Hsi: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], alpha_1: float | ndarray[tuple[Any, ...], dtype[float64]] = 2.2, beta_1: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.4) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate wave transmission coefficient Kt using Goda et al (1967) for caisson structures

For caisson structures Y., Takeda, H. and Moriya, Y. (1967). Laboratory investigation of wave transmission

over breakwaters. Rep. port and Harbour Res. Inst., 13 (from Seelig 1979).

Parameters:

Hsi (float | npt.NDArray[np.float64]) – Incident significant wave height (m)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard, vertical distance from SWL to crest of structure
alpha_1 (float | npt.NDArray[np.float64], optional) – coefficient depending on structure type, by default 2.2 vertical (caisson) breakwater: 2.2 vertical wall (no crest width): 1.8
beta_1 (float | npt.NDArray[np.float64], optional) – coefficient depending on structure type, by default 0.4 vertical (caisson) breakwater: 0.4 vertical wall (no crest width): 0.1

Returns:

Kt – Wave Transmission Coefficient (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_transmission.goda1967_caisson.check_validity()[source]: No range provided

D’Angremond et al. (1996)

deltares_coastal_structures_toolbox.functions.hydraulic.wave_transmission.dangremond1996.calculate_wave_transmission_Kt_impermeable(Hsi: float | ndarray[tuple[Any, ...], dtype[float64]], Tpi: float | ndarray[tuple[Any, ...], dtype[float64]], h: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], B: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], C1: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.8) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate wave transmission coefficient Kt using D’Angremond et al 1996

For impermeable structures

Background: d’Angremond, K.; van der Meer, J.W.; de Jong, R.J.Wave Transmission at Low-Crested Structures.: In Coastal Engineering 1996; American Society of Civil Engineers: New York, NY, USA, 1997; pp. 2418–2427.

https://doi.org/10.9753/icce.v25.%p

Parameters:

Hsi (float | npt.NDArray[np.float64]) – Incident significant wave height (m)
Tpi (float | npt.NDArray[np.float64]) – Incident peak wave period (s)
h (float | npt.NDArray[np.float64]) – Water level in front of the structure
Rc (float | npt.NDArray[np.float64]) – Crest freeboard, vertical distance from SWL to top of crest
B (float | npt.NDArray[np.float64]) – Width of structure at crest level
cot_alpha (float | npt.NDArray[np.float64]) – Slope of front slope
C1 (float | npt.NDArray[np.float64], optional) – Constant (calibration) value, by default 0.80

Returns:

Kt – Wave Transmission Coefficient (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_transmission.dangremond1996.calculate_wave_transmission_Kt_permeable(Hsi: float | ndarray[tuple[Any, ...], dtype[float64]], Tpi: float | ndarray[tuple[Any, ...], dtype[float64]], h: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], B: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], C1: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.64, do_validity_check: bool = True) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate wave transmission coefficient Kt using D’Angremond et al 1996

For permeable structures

Background: d’Angremond, K.; van der Meer, J.W.; de Jong, R.J.Wave Transmission at Low-Crested Structures.: In Coastal Engineering 1996; American Society of Civil Engineers: New York, NY, USA, 1997; pp. 2418–2427.

https://doi.org/10.9753/icce.v25.%p

Parameters:

Hsi (float | npt.NDArray[np.float64]) – Incident significant wave height (m)
Tpi (float | npt.NDArray[np.float64]) – Incident peak wave period (s)
h (float | npt.NDArray[np.float64]) – Water level in front of the structure
Rc (float | npt.NDArray[np.float64]) – Crest freeboard, vertical distance from SWL to top of crest
B (float | npt.NDArray[np.float64]) – Width of structure at crest level
cot_alpha (float | npt.NDArray[np.float64]) – Slope of front slope
C1 (float | npt.NDArray[np.float64], optional) – Constant (calibration) value, by default 0.64

Returns:

Kt – Wave Transmission Coefficient (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_transmission.dangremond1996.check_validity(Kt: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, s0p: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Hsi_over_h: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Rc_over_Hsi: float | ndarray[tuple[Any, ...], dtype[float64]] = nan)[source]

Check the parameter values vs the validity range as defined in D’Angremond et al. (1996).

For all parameters supplied, their values are checked versus the range of validity specified by D’Angremond et al. (1996). When parameters are nan (by default), they are not checked.

Background: d’Angremond, K.; van der Meer, J.W.; de Jong, R.J.Wave Transmission at Low-Crested Structures.: In Coastal Engineering 1996; American Society of Civil Engineers: New York, NY, USA, 1997; pp. 2418–2427.

https://doi.org/10.9753/icce.v25.%p

Parameters:

Kt (float | npt.NDArray[np.float64], optional) – Wave Transmission Coefficient (-), by default np.nan
s0p (float | npt.NDArray[np.float64], optional) – Wave steepness (-), by default np.nan
Hsi_over_h (float | npt.NDArray[np.float64], optional) – Relative water depth Hsi/h (-), by default np.nan
Rc_over_Hsi (float | npt.NDArray[np.float64], optional) – Relative crest level Rc/Hsi (-), by default np.nan

Briganti et al. (2003)

deltares_coastal_structures_toolbox.functions.hydraulic.wave_transmission.briganti2003.calculate_wave_transmission_Kt(Hsi: float | ndarray[tuple[Any, ...], dtype[float64]], Tpi: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], B: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate wave transmission coefficient Kt using Briganti (2003)

For permeable structures

See: Briganti, R.,J.W. Van der Meer, M. Buccino and M.Calabrese (2003),’Wave transmission: behind low-crested structures’. Proceedings of Coastal Structures 2003, Portland, USA, p. 580-592

http://dx.doi.org/10.1061/40733(147)48

Note that for structures with B/Hsi < 10 this approach is equal to D’Angremond (1996)

Parameters:

Hsi (float | npt.NDArray[np.float64]) – Incident significant wave height (m)
Tpi (float | npt.NDArray[np.float64]) – Incident peak wave period (s)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard, vertical distance from SWL to top of crest
B (float | npt.NDArray[np.float64]) – Width of structure at crest level
cot_alpha (float | npt.NDArray[np.float64]) – Slope of front slope

Returns:

Kt – Wave Transmission Coefficient (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_transmission.briganti2003.check_validity(s0p: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, ksi_0p: float | ndarray[tuple[Any, ...], dtype[float64]] = nan)[source]

Check the parameter values vs the validity range as defined in Briganti (2003).

For all parameters supplied, their values are checked versus the range of validity specified by Briganti (2003). When parameters are nan (by default), they are not checked.

See: Briganti, R.,J.W. Van der Meer, M. Buccino and M.Calabrese (2003),’Wave transmission: behind low-crested structures’. Proceedings of Coastal Structures 2003, Portland, USA, p. 580-592

http://dx.doi.org/10.1061/40733(147)48

Parameters:

s0p (float | npt.NDArray[np.float64], optional) – Wave steepness s0p (-), by default np.nan
ksi_0p (float | npt.NDArray[np.float64], optional) – Iribarren number ksi_0p (-), by default np.nan

Van Gent et al. (2023)

deltares_coastal_structures_toolbox.functions.hydraulic.wave_transmission.vangent2023.calculate_wave_transmission_Kt(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], B: float | ndarray[tuple[Any, ...], dtype[float64]], structure_type: str = 'permeable') → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the wave transmission coefficient with the Van Gent et al. (2023) formula.

Here, eq. 6 from Van Gent et al. (2023) is implemented. The coefficients in this formula depend on the type of structure, as listed in Table 1 of Van Gent et al. (2023). The possible structure types are:

impermeable

permeable

perforated

perforated_with_screen

perforated_with_perforated_screen

For more details, see: https://doi.org/10.1016/j.coastaleng.2023.104344

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
B (float | npt.NDArray[np.float64]) – Crest width of the structure (m)
structure_type (str, optional) – Type of structure, by default “permeable”

Returns:

Wave transmission coefficient Kt (-)

Return type:

float | npt.NDArray[np.float64]

Raises:

ValueError – If a non-valid structure type is provided.

deltares_coastal_structures_toolbox.functions.hydraulic.wave_transmission.vangent2023.check_validity_range(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Rc: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, B: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, structure_type: str = nan) → None[source]

Check the parameter values vs the validity range of the Van Gent et al. (2023) formula.

For all parameters supplied, their values are checked versus the range of test conditions specified in the conclusions of Van Gent et al. (2023). When parameters are nan (by default), they are not checked.

For more details, see: https://doi.org/10.1016/j.coastaleng.2023.104344

Parameters:

Hm0 (float | npt.NDArray[np.float64], optional) – Spectral significant wave height (m), by default np.nan
Tmm10 (float | npt.NDArray[np.float64], optional) – Spectral wave period Tm-1,0 (s), by default np.nan
Rc (float | npt.NDArray[np.float64], optional) – Crest freeboard of the structure (m), by default np.nan
B (float | npt.NDArray[np.float64], optional) – Crest width of the structure (m), by default np.nan
structure_type (str, optional) – Type of structure, by default np.nan

Van Gent (2024)

deltares_coastal_structures_toolbox.functions.hydraulic.wave_transmission.vangent2024_setup.calculate_dimensionless_structure_induced_setup_impermeable(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the dimensionless structure-induced setup delta/Hm0 for an impermeable submerged structure following Van Gent (2024).

Here, eq. 2 from Van Gent (2024) is implemented.

For more details, see: https://doi.org/10.59490/jchs.2024.0033

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)

Returns:

The dimensionless structure-induced setup delta/Hm0 (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_transmission.vangent2024_setup.calculate_dimensionless_structure_induced_setup_permeable(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], hc: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the dimensionless structure-induced setup delta/Hm0 for a permeable submerged structure following Van Gent (2024).

Here, eq. 3 from Van Gent (2024) is implemented.

For more details, see: https://doi.org/10.59490/jchs.2024.0033

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
hc (float | npt.NDArray[np.float64]) – Submerged structure height (m)

Returns:

The dimensionless structure-induced setup delta/Hm0 (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_transmission.vangent2024_setup.calculate_structure_induced_setup_delta_impermeable(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the structure-induced setup delta for an impermeable submerged structure following Van Gent (2024).

Here, eq. 2 from Van Gent (2024) is implemented.

For more details, see: https://doi.org/10.59490/jchs.2024.0033

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)

Returns:

The structure-induced setup delta (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_transmission.vangent2024_setup.calculate_structure_induced_setup_delta_permeable(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], hc: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the structure-induced setup delta for a permeable submerged structure following Van Gent (2024).

Here, eq. 3 from Van Gent (2024) is implemented.

For more details, see: https://doi.org/10.59490/jchs.2024.0033

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
hc (float | npt.NDArray[np.float64]) – Submerged structure height (m)

Returns:

The structure-induced setup delta (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.hydraulic.wave_transmission.vangent2024_setup.check_validity_range(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Rc: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, B: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, hc: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, structure_type: str = 'impermeable') → None[source]

Check the parameter values vs the validity range of the Van Gent (2024) formula.

For all parameters supplied, their values are checked versus the range of test conditions specified in of Van Gent (2024). When parameters are nan (by default), they are not checked.

Note that the validity ranges differ between impermeable and permeable submerged structures.

For more details, see: https://doi.org/10.59490/jchs.2024.0033

Parameters:

Hm0 (float | npt.NDArray[np.float64], optional) – Spectral significant wave height (m), by default np.nan
Tmm10 (float | npt.NDArray[np.float64], optional) – Spectral wave period Tm-1,0 (s), by default np.nan
Rc (float | npt.NDArray[np.float64], optional) – Crest freeboard of the structure (m), by default np.nan
B (float | npt.NDArray[np.float64], optional) – Submerged structure crest width (m), by default np.nan
hc (float | npt.NDArray[np.float64], optional) – Submerged structure height (m), by default np.nan
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal rock diameter (m), by default np.nan
structure_type (str, optional) – Impermeable or permeable submerged structure, by default “impermeable”

Structural

Forces Caisson

Goda (1985)

deltares_coastal_structures_toolbox.functions.structural.forces_caisson.goda1985.calculate_Wup(hacc: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], Bup: float | ndarray[tuple[Any, ...], dtype[float64]], rho_fill_below_SWL: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_fill_above_SWL: float | ndarray[tuple[Any, ...], dtype[float64]], g: float | ndarray[tuple[Any, ...], dtype[float64]] = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate weight of upright section

Parameters:

hacc (float | npt.NDArray[np.float64]) – height of caisson below water level
Rc (float | npt.NDArray[np.float64]) – crest freeboard distance top caisson to water level
Bup (float | npt.NDArray[np.float64]) – Width of upright section
rho_fill_below_SWL (float | npt.NDArray[np.float64]) – Density of fill placed below water level
rho_water (float | npt.NDArray[np.float64]) – Density of water
rho_fill_above_SWL (float | npt.NDArray[np.float64]) – Density of fill placed above water level
g (float | npt.NDArray[np.float64], optional) – Gravitational acceleration, by default 9.81

Returns:

Wup – Weight of upright section of caisson

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.forces_caisson.goda1985.calculate_bearing_pressures(Wup: float | ndarray[tuple[Any, ...], dtype[float64]], tup: float | ndarray[tuple[Any, ...], dtype[float64]], MH: float | ndarray[tuple[Any, ...], dtype[float64]], MU: float | ndarray[tuple[Any, ...], dtype[float64]], FU: float | ndarray[tuple[Any, ...], dtype[float64]], Bup: float | ndarray[tuple[Any, ...], dtype[float64]]) → tuple[float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]]][source]

Calculate pressures on foundation using results from other functions

Calculation of forces, moments and reactions of waves on caisson structures according to Goda (1985, 2000) See: Goda, Y., 1985. “Random seas and design of maritime structures.” University of Tokyo Press.,

Japan. ISBN 0-86008-369-1.

or Goda, Y., 2000. “Random seas and design of maritime structures.” In P.L. Liu (ed) Advanced

Series on Ocean Engineering, Vol. 15, World Scientific, Singapore, 444 pp. (2nd ed.).

Note that this set of equations is valid for not impulsively breaking waves

Parameters:

Wup (float | npt.NDArray[np.float64]) – Weight of upright section of caisson
tup (float | npt.NDArray[np.float64]) – Horizontal distance from heel of caisson to center of gravity
MH (float | npt.NDArray[np.float64]) – Moment as result of horizontal forces
MU (float | npt.NDArray[np.float64]) – Moment as result of uplift forces
FU (float | npt.NDArray[np.float64]) – Uplift force
Bup (float | npt.NDArray[np.float64]) – Width of upright section of caisson

Returns:

pe (float | npt.NDArray[np.float64]) – Bearing pressure at heel
Me (float | npt.NDArray[np.float64]) – Eccentricity moment
We (float | npt.NDArray[np.float64]) – Effective weight of caisson
te (float | npt.NDArray[np.float64]) – Effective arm

deltares_coastal_structures_toolbox.functions.structural.forces_caisson.goda1985.calculate_forces_and_reactions(HD: float | ndarray[tuple[Any, ...], dtype[float64]], Hsi: float | ndarray[tuple[Any, ...], dtype[float64]], Tmax: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]], h_s: float | ndarray[tuple[Any, ...], dtype[float64]], d: float | ndarray[tuple[Any, ...], dtype[float64]], B1: float | ndarray[tuple[Any, ...], dtype[float64]], cota_seabed: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], hacc: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], Bup: float | ndarray[tuple[Any, ...], dtype[float64]], rho_fill_above_SWL: float | ndarray[tuple[Any, ...], dtype[float64]] = 2400, rho_fill_below_SWL: float | ndarray[tuple[Any, ...], dtype[float64]] = 2100, offshore_wave_steepness: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, muf: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.6, tup_over_Bup: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.5, g: float | ndarray[tuple[Any, ...], dtype[float64]] = 9.81, return_dict: bool = False) → tuple[float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]]] | dict[source]

Calculate wave induced pressures and forces on caisson and its reaction forces

Calculation of forces, moments and reactions of waves on caisson structures according to Goda (1985, 2000) See: Goda, Y., 1985. “Random seas and design of maritime structures.” University of Tokyo Press.,

Japan. ISBN 0-86008-369-1.

or Goda, Y., 2000. “Random seas and design of maritime structures.” In P.L. Liu (ed) Advanced

Series on Ocean Engineering, Vol. 15, World Scientific, Singapore, 444 pp. (2nd ed.).

Note that this set of equations is valid for not impulsively breaking waves

Parameters:

HD (float | npt.NDArray[np.float64]) – design wave height (Hmax) (m)
Hsi (float | npt.NDArray[np.float64]) – incident wave height (Hs) (m)
Tmax (float | npt.NDArray[np.float64]) – Maximum wave period (s)
beta (float | npt.NDArray[np.float64]) – Angle of wave incidence (degrees)
h_s (float | npt.NDArray[np.float64]) – water depth at site (m)
d (float | npt.NDArray[np.float64]) – water depth above toe berm (m)
B1 (float | npt.NDArray[np.float64]) – Width of toe berm (top of toe berm) (m)
cota_seabed (float | npt.NDArray[np.float64]) – Slope of seabed approaching caisson (-)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
hacc (float | npt.NDArray[np.float64]) – Distance between lowest part of caisson to water level (m)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard (m)
Bup (float | npt.NDArray[np.float64]) – Width of upright section of caisson (m)
rho_fill_above_SWL – Density of fill material above water level, by default 2400 (example by Goda) (kg/m^3)
rho_fill_below_SWL – Density of fill material above water level, by default 2100 (example by Goda) (kg/m^3)
offshore_wave_steepness – Offshore wave steepness, used for impulse breaking check (-)
muf – Friction factor of bottom caisson with rubble mound (-)
tup_over_Bup – Ratio between width of caisson and centre of mass caisson, by default 0.5 (= caisson middle) (-)
g (float | npt.NDArray[np.float64]) – Gravitational acceleration, by default 9.81 (m/s^2)
return_dict (bool) – Return a dictionary with all results

Return type:

FH, FU, MH, MU, p1, pe, pu, SF_sliding, SF_overturning

FHfloat | npt.NDArray[np.float64]

Wave induced horizontal force (N/m1)

FUfloat | npt.NDArray[np.float64]

Wave induced uplift force (N/m1)

MHfloat | npt.NDArray[np.float64]

Wave induced horizontal moment (N*m/m1)

MUfloat | npt.NDArray[np.float64]

Wave induced uplift moment (N*m/m1)

p1float | npt.NDArray[np.float64]

Wave induced pressure around still water level (N/m^2)

pefloat | npt.NDArray[np.float64]

Bearing pressure at heel of caisson (N/m^2)

pufloat | npt.NDArray[np.float64]

Wave induced uplift pressure (N/m^2)

impulsive_breakingfloat | npt.NDArray[np.float64]

Result of impulsive breaking check. Goda formula is NOT applicable for impulsive breaking waves

SF_sliding

Safety factor for sliding

SF_overturning

Safety factor for overturning

OR

all_resultsdict

All inputs, results and intermediate results

deltares_coastal_structures_toolbox.functions.structural.forces_caisson.goda1985.calculate_pressures_and_forces(HD: float | ndarray[tuple[Any, ...], dtype[float64]], Hsi: float | ndarray[tuple[Any, ...], dtype[float64]], Tmax: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]], h_s: float | ndarray[tuple[Any, ...], dtype[float64]], d: float | ndarray[tuple[Any, ...], dtype[float64]], B1: float | ndarray[tuple[Any, ...], dtype[float64]], cota_seabed: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], hacc: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], Bup: float | ndarray[tuple[Any, ...], dtype[float64]], offshore_wave_steepness: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, g: float | ndarray[tuple[Any, ...], dtype[float64]] = 9.81, return_dict: bool = False) → tuple[float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]], bool | ndarray[tuple[Any, ...], dtype[float64]]] | dict[source]

Calculate wave induced pressures and forces on caisson

Calculation of forces, moments and reactions of waves on caisson structures according to Goda (1985, 2000) See: Goda, Y., 1985. “Random seas and design of maritime structures.” University of Tokyo Press.,

Japan. ISBN 0-86008-369-1.

or Goda, Y., 2000. “Random seas and design of maritime structures.” In P.L. Liu (ed) Advanced

Series on Ocean Engineering, Vol. 15, World Scientific, Singapore, 444 pp. (2nd ed.).

Note that this set of equations is valid for not impulsively breaking waves

Parameters:

HD (float | npt.NDArray[np.float64]) – design wave height (Hmax) (m)
Hsi (float | npt.NDArray[np.float64]) – incident wave height (Hs) (m)
Tmax (float | npt.NDArray[np.float64]) – Maximum wave period (s)
beta (float | npt.NDArray[np.float64]) – Angle of wave incidence (degrees)
h_s (float | npt.NDArray[np.float64]) – water depth at site (m)
d (float | npt.NDArray[np.float64]) – water depth above toe berm (m)
B1 (float | npt.NDArray[np.float64]) – Width of toe berm (top of toe berm) (m)
cota_seabed (float | npt.NDArray[np.float64]) – Slope of seabed approaching caisson (-)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
hacc (float | npt.NDArray[np.float64]) – Distance between lowest part of caisson to water level (m)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard (m)
Bup (float | npt.NDArray[np.float64]) – Width of upright section of caisson (m)
g (float | npt.NDArray[np.float64]) – Gravitational acceleration, by default 9.81 (m/s^2)
return_dict (bool) – Return a dictionary with all results

Returns:

Wup (float | npt.NDArray[np.float64]) – Weight of upright section of caisson (N)
FH (float | npt.NDArray[np.float64]) – Wave induced horizontal force (N/m1)
FU (float | npt.NDArray[np.float64]) – Wave induced uplift force (N/m1)
MH (float | npt.NDArray[np.float64]) – Wave induced horizontal moment (N*m/m1)
MU (float | npt.NDArray[np.float64]) – Wave induced uplift moment (N*m/m1)
p1 (float | npt.NDArray[np.float64]) – Wave induced pressure around still water level (N/m^2)
p2 (float | npt.NDArray[np.float64]) – Wave induced pressure at seafloor (N/m^2)
p3 (float | npt.NDArray[np.float64]) – Wave induced pressure at bottom of caisson(N/m^2)
p4 (float | npt.NDArray[np.float64]) – Wave induced pressure at top of caisson (N/m^2)
hstar_c (float | npt.NDArray[np.float64]) – Wave induced pressure (N/m^2)
pu (float | npt.NDArray[np.float64]) – Wave induced uplift pressure (N/m^2)
h_5Hs (float | npt.NDArray[np.float64]) – Water depth at distance of 5 Hs from caisson (m)
etastar (float | npt.NDArray[np.float64]) – Elevation to which the pressure is exerted (m)
L (float | npt.NDArray[np.float64]) – Local wave length
alpha_1 (float | npt.NDArray[np.float64]) – Alpha factor
alpha_2 (float | npt.NDArray[np.float64]) – Alpha factor
alpha_3 (float | npt.NDArray[np.float64]) – Alpha factor
impulsive_breaking (float | npt.NDArray[np.float64]) – Result of impulsive breaking check. Goda formula is NOT applicable for impulsive breaking waves

OR
all_results (dict) – All inputs, results and intermediate results

deltares_coastal_structures_toolbox.functions.structural.forces_caisson.goda1985.calculate_safety_factors(FU: float | ndarray[tuple[Any, ...], dtype[float64]], FH: float | ndarray[tuple[Any, ...], dtype[float64]], Wup: float | ndarray[tuple[Any, ...], dtype[float64]], muf: float | ndarray[tuple[Any, ...], dtype[float64]], tup: float | ndarray[tuple[Any, ...], dtype[float64]], MH: float | ndarray[tuple[Any, ...], dtype[float64]], MU: float | ndarray[tuple[Any, ...], dtype[float64]]) → tuple[float | ndarray[tuple[Any, ...], dtype[float64]], float | ndarray[tuple[Any, ...], dtype[float64]]][source]

Calculate safety factors based on pre-calculated forces and moments

Calculation of forces, moments and reactions of waves on caisson structures according to Goda (1985, 2000) See: Goda, Y., 1985. “Random seas and design of maritime structures.” University of Tokyo Press.,

Japan. ISBN 0-86008-369-1.

or Goda, Y., 2000. “Random seas and design of maritime structures.” In P.L. Liu (ed) Advanced

Series on Ocean Engineering, Vol. 15, World Scientific, Singapore, 444 pp. (2nd ed.).

Note that this set of equations is valid for not impulsively breaking waves

Parameters:

FU (float | npt.NDArray[np.float64]) – Uplift force
FH (float | npt.NDArray[np.float64]) – Horizontal force
Wup (float | npt.NDArray[np.float64]) – Weight of upright section of caisson
muf (float | npt.NDArray[np.float64]) – Friction factor between caisson and underlayer
tup (float | npt.NDArray[np.float64]) – Distance center of gravity and heel of caisson
MH (float | npt.NDArray[np.float64]) – Moment due to horizontal wave pressure
MU (float | npt.NDArray[np.float64]) – Moment due to uplift pressure

Returns:

Safety factors for sliding and overturning

Return type:

tuple[ float | npt.NDArray[np.float64], float | npt.NDArray[np.float64], ]

deltares_coastal_structures_toolbox.functions.structural.forces_caisson.goda1985.check_impulsive_breaking(beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, B1: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, L: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cota_seabed: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, offshore_wave_steepness: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Rc: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Hsi: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, d: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, h_s: float | ndarray[tuple[Any, ...], dtype[float64]] = nan) → bool[source]

Check whether impulsive breaking occurs

Parameters:

beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
B1 (float | npt.NDArray[np.float64], optional) – Width of the toe berm (m), by default np.nan
L (float | npt.NDArray[np.float64], optional) – Local wave length (m), by default np.nan
cota_seabed (float | npt.NDArray[np.float64], optional) – Cotangent of the sea bed slope (-), by default np.nan
offshore_wave_steepness (float | npt.NDArray[np.float64], optional) – Offshore wave steepness (-), by default np.nan
Rc (float | npt.NDArray[np.float64], optional) – Crest freeboard of the structure (m), by default np.nan
Hsi (float | npt.NDArray[np.float64], optional) – Incident significant wave height (m), by default np.nan
d (float | npt.NDArray[np.float64], optional) – Water depth above the toe berm (m), by default np.nan
h_s (float | npt.NDArray[np.float64], optional) – Water depth (m), by default np.nan

Returns:

Boolean indicating whether impulsive breaking occurs

Return type:

bool

deltares_coastal_structures_toolbox.functions.structural.forces_caisson.goda1985.check_validity_range(beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cota_seabed: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Tmax: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, tup: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Bup: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, h_s: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, B1: float | ndarray[tuple[Any, ...], dtype[float64]] = nan)[source]

Check the parameter values vs the validity range as defined in Goda (1985).

For all parameters supplied, their values are checked versus the range of validity specified by Goda (1985). When parameters are nan (by default), they are not checked.

Parameters:

beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan
cota_seabed (float | npt.NDArray[np.float64], optional) – Cotangent of the sea bed slope (-), by default np.nan
Tmax (float | npt.NDArray[np.float64], optional) – Maximum wave period (s), by default np.nan
tup (float | npt.NDArray[np.float64], optional) – Di, by default np.nan
Bup (float | npt.NDArray[np.float64], optional) – Width of upright section of caisson (m), by default np.nan
h_s (float | npt.NDArray[np.float64], optional) – Water depth at site (m), by default np.nan
B1 (float | npt.NDArray[np.float64], optional) – Width of toe berm (top of toe berm) (m), by default np.nan

Forces Crest Wall

Van Gent & Van der Werf (2019)

deltares_coastal_structures_toolbox.functions.structural.forces_crestwall.vangentvanderwerf2019.calculate_FH01p_perpendicular(FH2p: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the 0.1% exceedance horizontal force on the crest wall with the Van Gent & van der Werf (2019) method.

The 0.1% exceedence horizontal force on a crest wall of a rubble mound breakwater for perpendicular wave attack is calculated using the Van Gent & Van der Werf (2019) method.

For more details, see Van Gent & Van der Werf (2019), available here: https://www.researchgate.net/publication/336170265_Prediction_method_for_wave_overtopping_and_forces_on_rubble_mound_breakwater_crest_walls

Parameters:: FH2p (float | npt.NDArray[np.float64]) – The 2% exceedance horizontal force on the crest wall (N/m)
Returns:: The 0.1% exceedance horizontal force on the crest wall FH01% (N/m)
Return type:: float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.forces_crestwall.vangentvanderwerf2019.calculate_FH2p_oblique(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], Ac: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], Hwall: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.45, c0: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.45, c1: float | ndarray[tuple[Any, ...], dtype[float64]] = 5.0, cFH: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, rho_water: float | ndarray[tuple[Any, ...], dtype[float64]] = 1025.0, g: float | ndarray[tuple[Any, ...], dtype[float64]] = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the 2% exceedance horizontal force on the crest wall with the Van Gent & van der Werf (2019) method.

The 2% exceedence horizontal force on a crest wall of a rubble mound breakwater for oblique wave attack is calculated using the Van Gent & Van der Werf (2019) method. Here, eq. 13, 14 and 15 from Van Gent & Van der Werf (2019) are implemented and the 2% exceedance wave runup height is calculated using Van Gent (2001), see hydraulic.wave_runup.vangent2001.py.

For more details, see Van Gent & Van der Werf (2019), available here: https://doi.org/10.1016/j.coastaleng.2019.04.001

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
beta (float | npt.NDArray[np.float64]) – Angle of wave incidence (degrees)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
Ac (float | npt.NDArray[np.float64]) – Armour crest freeboard of the structure (m)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
Hwall (float | npt.NDArray[np.float64]) – Height of the crest wall (m)
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default 1.0
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 0.45
c0 (float | npt.NDArray[np.float64], optional) – Coefficient in wave runup formula (-), by default 1.45
c1 (float | npt.NDArray[np.float64], optional) – Coefficient in wave runup formula (-), by default 5.0
cFH (float | npt.NDArray[np.float64], optional) – Coefficient in horizontal force formula (-), by default 1.0
rho_water (float | npt.NDArray[np.float64], optional) – Water density (kg/m^3), by default 1025.0
g (float | npt.NDArray[np.float64], optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

The 2% exceedance horizontal force on the crest wall FH2% (N/m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.forces_crestwall.vangentvanderwerf2019.calculate_FH2p_perpendicular(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], Ac: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], Hwall: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.45, c0: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.45, c1: float | ndarray[tuple[Any, ...], dtype[float64]] = 5.0, rho_water: float | ndarray[tuple[Any, ...], dtype[float64]] = 1025.0, g: float | ndarray[tuple[Any, ...], dtype[float64]] = 9.81, cFH: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the 2% exceedance horizontal force on the crest wall with the Van Gent & van der Werf (2019) method.

The 2% exceedence horizontal force on a crest wall of a rubble mound breakwater for perpendicular wave attack is calculated using the Van Gent & Van der Werf (2019) method. Here, eq. 13 from Van Gent & Van der Werf (2019) is implemented and the 2% exceedance wave runup height is calculated using Van Gent (2001), see hydraulic.wave_runup.vangent2001.py.

For more details, see Van Gent & Van der Werf (2019), available here: https://doi.org/10.1016/j.coastaleng.2019.04.001

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
Ac (float | npt.NDArray[np.float64]) – Armour crest freeboard of the structure (m)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
Hwall (float | npt.NDArray[np.float64]) – Height of the crest wall (m)
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default 1.0
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 0.45
c0 (float | npt.NDArray[np.float64], optional) – Coefficient in wave runup formula (-), by default 1.45
c1 (float | npt.NDArray[np.float64], optional) – Coefficient in wave runup formula (-), by default 5.0
rho_water (float | npt.NDArray[np.float64], optional) – Water density (kg/m^3), by default 1025.0
g (float | npt.NDArray[np.float64], optional) – Gravitational constant (m/s^2), by default 9.81
cFH (float | npt.NDArray[np.float64], optional) – Coefficient in horizontal force formula (-), by default 1.0

Returns:

The 2% exceedance horizontal force on the crest wall FH2% (N/m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.forces_crestwall.vangentvanderwerf2019.calculate_FH2p_perpendicular_from_z2p(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], z2p: float | ndarray[tuple[Any, ...], dtype[float64]], Ac: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], Hwall: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]] = 1025.0, g: float | ndarray[tuple[Any, ...], dtype[float64]] = 9.81, cFH: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the 2% exceedance horizontal force on the crest wall with the Van Gent & van der Werf (2019) method.

The 2% exceedence horizontal force on a crest wall of a rubble mound breakwater for perpendicular wave attack is calculated using the Van Gent & Van der Werf (2019) method. Here, eq. 13 from Van Gent & Van der Werf (2019) is implemented.

For more details, see Van Gent & Van der Werf (2019), available here: https://doi.org/10.1016/j.coastaleng.2019.04.001

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
z2p (float | npt.NDArray[np.float64]) – The 2% exceedance wave runup height (m)
Ac (float | npt.NDArray[np.float64]) – Armour crest freeboard of the structure (m)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
Hwall (float | npt.NDArray[np.float64]) – Height of the crest wall (m)
rho_water (float | npt.NDArray[np.float64], optional) – Water density (kg/m^3), by default 1025.0
g (float | npt.NDArray[np.float64], optional) – Gravitational constant (m/s^2), by default 9.81
cFH (float | npt.NDArray[np.float64], optional) – Coefficient in horizontal force formula (-), by default 1.0

Returns:

The 2% exceedance horizontal force on the crest wall FH2% (N/m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.forces_crestwall.vangentvanderwerf2019.calculate_FV01p_perpendicular(FV2p: float | ndarray[tuple[Any, ...], dtype[float64]], s0p: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the 0.1% exceedance vertical force on the crest wall with the Van Gent & van der Werf (2019) method.

The 0.1% exceedence vertical force on a crest wall of a rubble mound breakwater for perpendicular wave attack is calculated using the Van Gent & Van der Werf (2019) method.

For more details, see Van Gent & Van der Werf (2019), available here: https://www.researchgate.net/publication/336170265_Prediction_method_for_wave_overtopping_and_forces_on_rubble_mound_breakwater_crest_walls

Parameters:

FV2p (float | npt.NDArray[np.float64]) – The 2% exceedance vertical force on the crest wall (N/m)
s0p (float | npt.NDArray[np.float64]) – Deep water wave steepness (-)

Returns:

The 0.1% exceedance vertical force on the crest wall FH01% (N/m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.forces_crestwall.vangentvanderwerf2019.calculate_FV2p_oblique(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], Ac: float | ndarray[tuple[Any, ...], dtype[float64]], Bwall: float | ndarray[tuple[Any, ...], dtype[float64]], Fb: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.45, c0: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.45, c1: float | ndarray[tuple[Any, ...], dtype[float64]] = 5.0, cFV: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.4, cFb: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.5, rho_water: float | ndarray[tuple[Any, ...], dtype[float64]] = 1025.0, g: float | ndarray[tuple[Any, ...], dtype[float64]] = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the 2% exceedance vertical force on the crest wall with the Van Gent & van der Werf (2019) method.

The 2% exceedence vertical force on a crest wall of a rubble mound breakwater for oblique wave attack is calculated using the Van Gent & Van der Werf (2019) method. Here, eq. 16, 17 and 18 from Van Gent & Van der Werf (2019) is implemented and the 2% exceedance wave runup height is calculated using Van Gent (2001), see hydraulic.wave_runup.vangent2001.py.

For more details, see Van Gent & Van der Werf (2019), available here: https://doi.org/10.1016/j.coastaleng.2019.04.001

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
beta (float | npt.NDArray[np.float64]) – Angle of wave incidence (degrees)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
Ac (float | npt.NDArray[np.float64]) – Armour crest freeboard of the structure (m)
Bwall (float | npt.NDArray[np.float64]) – Width of the crest wall (m)
Fb (float | npt.NDArray[np.float64]) – Level of the base plate of the crest wall w.r.t. still water level (m)
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default 1.0
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 0.45
c0 (float | npt.NDArray[np.float64], optional) – Coefficient in wave runup formula (-), by default 1.45
c1 (float | npt.NDArray[np.float64], optional) – Coefficient in wave runup formula (-), by default 5.0
cFV (float | npt.NDArray[np.float64], optional) – Coefficient in vertical force formula (-), by default 0.4
cFb (float | npt.NDArray[np.float64], optional) – Coefficient in vertical force formula (-), by default 0.5
rho_water (float | npt.NDArray[np.float64], optional) – Water density (kg/m^3), by default 1025.0
g (float | npt.NDArray[np.float64], optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

The 2% exceedance vertical force on the crest wall FV2% (N/m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.forces_crestwall.vangentvanderwerf2019.calculate_FV2p_perpendicular(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], Ac: float | ndarray[tuple[Any, ...], dtype[float64]], Bwall: float | ndarray[tuple[Any, ...], dtype[float64]], Fb: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.45, c0: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.45, c1: float | ndarray[tuple[Any, ...], dtype[float64]] = 5.0, cFV: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.4, cFb: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.5, rho_water: float | ndarray[tuple[Any, ...], dtype[float64]] = 1025.0, g: float | ndarray[tuple[Any, ...], dtype[float64]] = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the 2% exceedance vertical force on the crest wall with the Van Gent & van der Werf (2019) method.

The 2% exceedence vertical force on a crest wall of a rubble mound breakwater for perpendicular wave attack is calculated using the Van Gent & Van der Werf (2019) method. Here, eq. 16 from Van Gent & Van der Werf (2019) is implemented and the 2% exceedance wave runup height is calculated using Van Gent (2001), see hydraulic.wave_runup.vangent2001.py.

For more details, see Van Gent & Van der Werf (2019), available here: https://doi.org/10.1016/j.coastaleng.2019.04.001

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Spectral significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
Ac (float | npt.NDArray[np.float64]) – Armour crest freeboard of the structure (m)
Bwall (float | npt.NDArray[np.float64]) – Width of the crest wall (m)
Fb (float | npt.NDArray[np.float64]) – Level of the base plate of the crest wall w.r.t. still water level (m)
gamma_beta (float | npt.NDArray[np.float64], optional) – Influence factor for oblique wave incidence (-), by default 1.0
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default 0.45
c0 (float | npt.NDArray[np.float64], optional) – Coefficient in wave runup formula (-), by default 1.45
c1 (float | npt.NDArray[np.float64], optional) – Coefficient in wave runup formula (-), by default 5.0
cFV (float | npt.NDArray[np.float64], optional) – Coefficient in vertical force formula (-), by default 0.4
cFb (float | npt.NDArray[np.float64], optional) – Coefficient in vertical force formula (-), by default 0.5
rho_water (float | npt.NDArray[np.float64], optional) – Water density (kg/m^3), by default 1025.0
g (float | npt.NDArray[np.float64], optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

The 2% exceedance vertical force on the crest wall FV2% (N/m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.forces_crestwall.vangentvanderwerf2019.calculate_FV2p_perpendicular_from_z2p(z2p: float | ndarray[tuple[Any, ...], dtype[float64]], Ac: float | ndarray[tuple[Any, ...], dtype[float64]], Bwall: float | ndarray[tuple[Any, ...], dtype[float64]], Fb: float | ndarray[tuple[Any, ...], dtype[float64]], cFV: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.4, cFb: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.5, rho_water: float | ndarray[tuple[Any, ...], dtype[float64]] = 1025.0, g: float | ndarray[tuple[Any, ...], dtype[float64]] = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the 2% exceedance vertical force on the crest wall with the Van Gent & van der Werf (2019) method.

The 2% exceedence vertical force on a crest wall of a rubble mound breakwater for perpendicular wave attack is calculated using the Van Gent & Van der Werf (2019) method. Here, eq. 16 from Van Gent & Van der Werf (2019) is implemented.

For more details, see Van Gent & Van der Werf (2019), available here: https://doi.org/10.1016/j.coastaleng.2019.04.001

Parameters:

z2p (float | npt.NDArray[np.float64]) – The 2% exceedance wave runup height (m)
Ac (float | npt.NDArray[np.float64]) – Armour crest freeboard of the structure (m)
Bwall (float | npt.NDArray[np.float64]) – Width of the crest wall (m)
Fb (float | npt.NDArray[np.float64]) – Level of the base plate of the crest wall w.r.t. still water level (m)
cFV (float | npt.NDArray[np.float64], optional) – Coefficient in vertical force formula (-), by default 0.4
cFb (float | npt.NDArray[np.float64], optional) – Coefficient in vertical force formula (-), by default 0.5
rho_water (float | npt.NDArray[np.float64], optional) – Water density (kg/m^3), by default 1025.0
g (float | npt.NDArray[np.float64], optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

The 2% exceedance vertical force on the crest wall FV2% (N/m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.forces_crestwall.vangentvanderwerf2019.calculate_influence_oblique_waves_force_gamma_F_beta(z2p: float | ndarray[tuple[Any, ...], dtype[float64]], Ac: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_A: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the influence factor on wave forces for oblique wave attack on a crest wall

The influence factor on wave forces for oblique wave attack on a crest wall of a rubble mound breakwater is calculated using the Van Gent & Van der Werf (2019) method. Here, eq. 20 from Van Gent & Van der Werf (2019) is implemented.

For more details, see Van Gent & Van der Werf (2019), available here: https://doi.org/10.1016/j.coastaleng.2019.04.001

Parameters:

z2p (float | npt.NDArray[np.float64]) – The 2% exceedance wave runup height (m)
Ac (float | npt.NDArray[np.float64]) – Armour crest freeboard of the structure (m)
beta (float | npt.NDArray[np.float64]) – Angle of wave incidence (degrees)
gamma_A (float | npt.NDArray[np.float64]) – Coefficient for either horizontal or vertical force (-)

Returns:

Influence factor on wave forces on a crest wall for oblique wave attack gamma_F_beta (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.forces_crestwall.vangentvanderwerf2019.calculate_influence_oblique_waves_gamma_beta(beta: float | ndarray[tuple[Any, ...], dtype[float64]], c_beta: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.5) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculates influence factor for oblique incident waves on wave runup level

Parameters:

beta (float | npt.NDArray[np.float64]) – Angle of wave incidence (degrees)
c_beta (float | npt.NDArray[np.float64]) – Coefficient, 0.5 default

Returns:

influence factor for wave runup gamma_beta

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.forces_crestwall.vangentvanderwerf2019.calculate_influence_oblique_waves_horizontal_force_gamma_FH_beta(z2p: float | ndarray[tuple[Any, ...], dtype[float64]], Ac: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_A: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the influence factor on horizontal wave forces for oblique wave attack on a crest wall

The influence factor on horizontal wave forces for oblique wave attack on a crest wall of a rubble mound breakwater is calculated using the Van Gent & Van der Werf (2019) method. Here, eq. 14 from Van Gent & Van der Werf (2019) is implemented.

For more details, see Van Gent & Van der Werf (2019), available here: https://doi.org/10.1016/j.coastaleng.2019.04.001

Parameters:

z2p (float | npt.NDArray[np.float64]) – The 2% exceedance wave runup height (m)
Ac (float | npt.NDArray[np.float64]) – Armour crest freeboard of the structure (m)
beta (float | npt.NDArray[np.float64]) – Angle of wave incidence (degrees)
gamma_A (float | npt.NDArray[np.float64], optional) – Coefficient for horizontal force (-), by default 1.0

Returns:

Influence factor on horizontal wave forces on a crest wall for oblique wave attack gamma_FH_beta (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.forces_crestwall.vangentvanderwerf2019.calculate_influence_oblique_waves_vertical_force_gamma_FV_beta(z2p: float | ndarray[tuple[Any, ...], dtype[float64]], Ac: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_A: float | ndarray[tuple[Any, ...], dtype[float64]] = 0.75) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the influence factor on vertical wave forces for oblique wave attack on a crest wall

The influence factor on vertical wave forces for oblique wave attack on a crest wall of a rubble mound breakwater is calculated using the Van Gent & Van der Werf (2019) method. Here, eq. 17 from Van Gent & Van der Werf (2019) is implemented.

For more details, see Van Gent & Van der Werf (2019), available here: https://doi.org/10.1016/j.coastaleng.2019.04.001

Parameters:

z2p (float | npt.NDArray[np.float64]) – The 2% exceedance wave runup height (m)
Ac (float | npt.NDArray[np.float64]) – Armour crest freeboard of the structure (m)
beta (float | npt.NDArray[np.float64]) – Angle of wave incidence (degrees)
gamma_A (float | npt.NDArray[np.float64], optional) – Coefficient for vertical force (-), by default 0.75

Returns:

Influence factor on horizontal wave forces on a crest wall for oblique wave attack gamma_FV_beta (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.forces_crestwall.vangentvanderwerf2019.check_validity(Rc: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Ac: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Hm0: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Fb: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, beta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan) → None[source]

Check the parameter values vs the validity range as defined in Van Gent & Van der Werf (2019).

For all parameters supplied, their values are checked versus the range of test conditions specified in Table 2 (Van Gent & Van der Werf, 2019). When parameters are nan (by default), they are not checked.

For more details, see Van Gent & Van der Werf (2019), available here: https://doi.org/10.1016/j.coastaleng.2019.04.001

Parameters:

Rc (float | npt.NDArray[np.float64], optional) – Crest freeboard of the structure (m), by default np.nan
Ac (float | npt.NDArray[np.float64], optional) – Armour crest freeboard of the structure (m), by default np.nan
Hm0 (float | npt.NDArray[np.float64], optional) – Spectral significant wave height (m), by default np.nan
Fb (float | npt.NDArray[np.float64], optional) – Level of the base plate of the crest wall w.r.t. still water level (m), by default np.nan
beta (float | npt.NDArray[np.float64], optional) – Angle of wave incidence (degrees), by default np.nan

Stability Concrete Armour

Cubes (double layer) Hudson (1959)

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.cubes_double_layer_hudson1959.calculate_significant_wave_height_Hs(M: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], KD: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], alpha_Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Determine significant wave height Hs based on M for doubles layer cubes, using Hudson 1959

For more details see: Hudson 1959 and Rock Manual: Hudson 1959, available here: https://doi.org/10.1061/JWHEAU.0000142 (or google) or more information in the Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 591

For more properties, see also unit_properties

Parameters:

M (float | npt.NDArray[np.float64]) – Unit mass M (kg)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
KD (float | npt.NDArray[np.float64]) – trunk_non_breaking: 7.5 trunk_breaking: 6.5 head_non_breaking: 5.0
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
alpha_Hs (float | npt.NDArray[np.float64], optional) – Factor between Hs and H used according to Rock Manual by default 1.0 for concrete armour units

Returns:

Hs – Significant wave height (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.cubes_double_layer_hudson1959.calculate_unit_mass_M(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], KD: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], alpha_Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Determine required unit mass M based on Hs for double layer cubes, using Hudson 1959

For more details see: Hudson 1959 and Rock Manual: Hudson 1959, available here: https://doi.org/10.1061/JWHEAU.0000142 (or google) or more information in the Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 591

For more properties, see also unit_properties

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
KD (float | npt.NDArray[np.float64]) – trunk_non_breaking: 7.5 trunk_breaking: 6.5 head_non_breaking: 5.0
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
alpha_Hs (float | npt.NDArray[np.float64], optional) – Factor between Hs and H used according to Rock Manual by default 1.0 for concrete armour units

Returns:

M – Unit mass M (kg)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.cubes_double_layer_hudson1959.check_validity_range()[source]: No validity ranges provided

Cubes (double layer) Van der Meer (1988)

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.cubes_double_layer_vandermeer1988.calculate_damage_Nod_vanDerMeer1988(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], Dn: float | ndarray[tuple[Any, ...], dtype[float64]], s0m: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Determine required nominal diameter Hs based on Dn and Nod for double layer cubes, using van der Meer 1988

For more details see: van der Meer 1988 (PhD thesis) and Rock Manual: van der Meer 1988, available here: https://repository.tudelft.nl/record/uuid:67e5692c-0905-4ddd-8487-37fdda9af6b4 or more information in the Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 591

For more properties, see also unit_properties

Parameters:

Dn (float | npt.NDArray[np.float64]) – Nominal block diameter, or equivalent cube size (m)
s0m (float | npt.NDArray[np.float64]) – Fictitious wave steepness for mean period wave (-)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
N_waves (float | npt.NDArray[np.float64]) – Number of waves
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-) Formula only valid for 1.5, otherwise a warning is raised
Nod (float | npt.NDArray[np.float64], optional) – Damage number, the number of displaced units per width Dn across armour face (-)

Returns:

Hs – Significant wave height (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.cubes_double_layer_vandermeer1988.calculate_nominal_diameter_Dn_vanDerMeer1988(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], Tm: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], Nod: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Determine required nominal diameter Dn based on Hs and Nod for double layer cubes, using van der Meer 1988

For more details see: van der Meer 1988 (PhD thesis) and Rock Manual: van der Meer 1988, available here: https://repository.tudelft.nl/record/uuid:67e5692c-0905-4ddd-8487-37fdda9af6b4 or more information in the Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 591

For more properties, see also unit_properties

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
Tm (float | npt.NDArray[np.float64]) – Mean wave period (s)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
N_waves (float | npt.NDArray[np.float64]) – Number of waves
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-) Formula only valid for 1.5, otherwise a warning is raised
Nod (float | npt.NDArray[np.float64], optional) – Damage number, the number of displaced units per width Dn across armour face (-)

Returns:

Dn – Nominal block diameter, or equivalent cube size (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.cubes_double_layer_vandermeer1988.calculate_wave_height_Hs_vanDerMeer1988(Dn: float | ndarray[tuple[Any, ...], dtype[float64]], s0m: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], Nod: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Determine required nominal diameter Hs based on Dn and Nod for double layer cubes, using van der Meer 1988

For more details see: van der Meer 1988 (PhD thesis) and Rock Manual: van der Meer 1988, available here: https://repository.tudelft.nl/record/uuid:67e5692c-0905-4ddd-8487-37fdda9af6b4 or more information in the Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 591

For more properties, see also unit_properties

Parameters:

Dn (float | npt.NDArray[np.float64]) – Nominal block diameter, or equivalent cube size (m)
s0m (float | npt.NDArray[np.float64]) – Fictitious wave steepness for mean period wave (-)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
N_waves (float | npt.NDArray[np.float64]) – Number of waves
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-) Formula only valid for 1.5, otherwise a warning is raised
Nod (float | npt.NDArray[np.float64], optional) – Damage number, the number of displaced units per width Dn across armour face (-)

Returns:

Hs – Significant wave height (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.cubes_double_layer_vandermeer1988.check_validity_range(Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Tm: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, N_waves: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan)[source]

Check the parameter values vs the validity range as defined in Van der Meer (1988).

For all parameters supplied, their values are checked versus the range of test conditions specified in Van der Meer (1988). When parameters are nan (by default), they are not checked.

For more details see: van der Meer 1988 (PhD thesis) and Rock Manual: van der Meer 1988, available here: https://repository.tudelft.nl/record/uuid:67e5692c-0905-4ddd-8487-37fdda9af6b4 or more information in the Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 591

Parameters:

Hs (float | npt.NDArray[np.float64], optional) – Significant wave height (m), by default np.nan
Tm (float | npt.NDArray[np.float64], optional) – Mean wave period (s), by default np.nan
rho_armour (float | npt.NDArray[np.float64], optional) – Armour rock density (kg/m^3), by default np.nan
N_waves (float | npt.NDArray[np.float64], optional) – Number of waves (-), by default np.nan
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan

Cubes (single layer) Van Gent (2002)

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.cubes_single_layer_vangent2002.calculate_significant_wave_height_Hs_failure(M: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], Ns: float | ndarray[tuple[Any, ...], dtype[float64]] = 3.5) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate wave height Hs for failure using van Gent (2002)

For more details see Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 594 And van Gent (2002) with DOI: https://doi.org/10.1680/bcsac.30428.0026

Note that it is recommended to use a safety factor due to the small difference between start of damage and failure. Start of damage is determined as an Nod of 0.0 Failure is determined as an Nod of 0.2

Parameters:

M (float | npt.NDArray[np.float64]) – Unit mass M (kg)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
Ns (float | npt.NDArray[np.float64], optional) – Stability number, by default 3.5 Recommended range for start of damage (see van Gent (2002)) 3.5 - 3.75

Returns:

Hs – Significant wave height (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.cubes_single_layer_vangent2002.calculate_significant_wave_height_Hs_start_of_damage(M: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], Ns: float | ndarray[tuple[Any, ...], dtype[float64]] = 2.9) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate wave height Hs for start of damage using van Gent (2002)

For more details see Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 594 And van Gent (2002) with DOI: https://doi.org/10.1680/bcsac.30428.0026

Note that it is recommended to use a safety factor due to the small difference between start of damage and failure. Start of damage is determined as an Nod of 0.0 Failure is determined as an Nod of 0.2

Parameters:

M (float | npt.NDArray[np.float64]) – Unit mass M (kg)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
Ns (float | npt.NDArray[np.float64], optional) – Stability number, by default 2.9 Recommended range for start of damage (see van Gent (2002)) 2.9 - 3.0

Returns:

Hs – Significant wave height (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.cubes_single_layer_vangent2002.calculate_unit_mass_M_failure(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], Ns: float | ndarray[tuple[Any, ...], dtype[float64]] = 3.5) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate required unit mass M for failure using van Gent (2002)

For more details see Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 594 And van Gent (2002) with DOI: https://doi.org/10.1680/bcsac.30428.0026

Note that it is recommended to use a safety factor due to the small difference between start of damage and failure. Start of damage is determined as an Nod of 0.0 Failure is determined as an Nod of 0.2

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
Ns (float | npt.NDArray[np.float64], optional) – Stability number, by default 3.5 Recommended range for start of damage (see van Gent (2002)) 3.5 - 3.75

Returns:

M – Unit mass M (kg)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.cubes_single_layer_vangent2002.calculate_unit_mass_M_start_of_damage(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], Ns: float | ndarray[tuple[Any, ...], dtype[float64]] = 2.9) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate required unit mass M for start of damage using van Gent (2002)

For more details see Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 594 And van Gent (2002) with DOI: https://doi.org/10.1680/bcsac.30428.0026

Note that it is recommended to use a safety factor due to the small difference between start of damage and failure. Start of damage is determined as an Nod of 0.0 Failure is determined as an Nod of 0.2

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
Ns (float | npt.NDArray[np.float64], optional) – Stability number, by default 2.9 Recommended range for start of damage (see van Gent (2002)) 2.9 - 3.0

Returns:

M – Unit mass M (kg)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.cubes_single_layer_vangent2002.check_validity_range()[source]: No validity ranges provided

Accropode

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.accropode_hudson1959.calculate_KD_breaking_trunk_from_seabed_slope(seabed_slope_perc: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Returns the KD value based on the seabed slope. Only to be applied for breaking condition at the trunk

For more information, see Concrete Layer Innovations: https://www.concretelayer.com/en/solutions/technologies/accropode

This value is an interpretation of graphical information in the design table (design table 2012, retrieved in march-2025)

Parameters:: seabed_slope_perc (float | npt.NDArray[np.float64]) – slope of seabed (%)
Returns:: KD value
Return type:: float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.accropode_hudson1959.calculate_KD_nonbreaking_trunk_from_seabed_slope() → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Returns the KD value based on the seabed slope. Only to be applied for nonbreaking condition at the trunk. This value is fixed at 15, similar to 1% trunk breaking waves value

For more information, see Concrete Layer Innovations: https://www.concretelayer.com/en/solutions/technologies/accropode

This value is an interpretation of graphical information in the design table (design table 2012, retrieved in march-2025)

Returns:: KD value
Return type:: float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.accropode_hudson1959.calculate_significant_wave_height_Hs(M: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], KD: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.33, alpha_Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Determine significant wave height Hs based on M for Accropodes, using Hudson 1959

For more details see: Hudson 1959 and Rock Manual: Hudson 1959, available here: https://doi.org/10.1061/JWHEAU.0000142 (or google) or more information in the Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 591 Information in this set of functions is also based on the design manual (design table 2012, retrieved in march-2025)

For more properties, see also unit_properties

More information is available at the Accropode website and from the concrete layer innovations (CLI) team https://www.concretelayer.com/en/solutions/technologies/accropode

A calculator is also available on the CLI website

Parameters:

M (float | npt.NDArray[np.float64]) – Unit mass M (kg)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
KD (float | npt.NDArray[np.float64]) – trunk_non_breaking: 15 trunk_breaking: 12 head_non_breaking: 11.5 head_breaking: 9.5 see also functions to calculate KD from seabed slope
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-) Note that 1.33 is recommended, and shallower then 1.5
alpha_Hs (float | npt.NDArray[np.float64], optional) – Factor between Hs and H used according to Rock Manual by default 1.0 for concrete armour units

Returns:

Hs – Significant wave height (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.accropode_hudson1959.calculate_unit_mass_M(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], KD: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.33, alpha_Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Determine required unit mass M based on Hs for Accropodes, using Hudson 1959

For more details see: Hudson 1959 and Rock Manual: Hudson 1959, available here: https://doi.org/10.1061/JWHEAU.0000142 (or google) or more information in the Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 591 Information in this set of functions is also based on the design manual (design table 2012, retrieved in march-2025)

For more properties, see also unit_properties

More information is available at the Accropode website and from the concrete layer innovations (CLI) team https://www.concretelayer.com/en/solutions/technologies/accropode

A calculator is also available on the CLI website

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
KD (float | npt.NDArray[np.float64]) – trunk_non_breaking: 15 trunk_breaking: 12 head_non_breaking: 11.5 head_breaking: 9.5 see also functions to calculate KD from seabed slope
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-) Note that 1.33 is recommended, and shallower then 1.5
alpha_Hs (float | npt.NDArray[np.float64], optional) – Factor between Hs and H used according to Rock Manual by default 1.0 for concrete armour units

Returns:

M – Unit mass M (kg)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.accropode_hudson1959.check_validity_range(cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, seabed_slope_perc: float | ndarray[tuple[Any, ...], dtype[float64]] = nan)[source]

Check the parameter values vs the validity range for Accropode

For all parameters supplied, their values are checked versus the range of validity. When parameters are nan (by default), they are not checked.

For more details see: Hudson 1959 and Rock Manual: Hudson 1959, available here: https://doi.org/10.1061/JWHEAU.0000142 (or google) or more information in the Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 591 Information in this set of functions is also based on the design manual (design table 2012, retrieved in march-2025)

Parameters:

cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
seabed_slope_perc (float | npt.NDArray[np.float64], optional) – Seabed slope in percentage, by default np.nan

Accropode II

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.accropode2_hudson1959.calculate_KD_breaking_trunk_from_seabed_slope(seabed_slope_perc: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Returns the KD value based on the seabed slope. Only to be applied for breaking condition at the trunk

For more information, see Concrete Layer Innovations: https://www.concretelayer.com/en/solutions/technologies/accropode-2

This value is an interpretation of graphical information in the design table (design table 2012, retrieved march-2025)

Parameters:: seabed_slope_perc (float | npt.NDArray[np.float64]) – slope of seabed (%)
Returns:: KD value
Return type:: float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.accropode2_hudson1959.calculate_KD_nonbreaking_trunk_from_seabed_slope() → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Returns the KD value based on the seabed slope. Only to be applied for nonbreaking condition at the trunk. This value is fixed at 16, similar to 1% trunk breaking waves value

For more information, see Concrete Layer Innovations: https://www.concretelayer.com/en/solutions/technologies/accropode-2

This value is an interpretation of graphical information in the design table (design table 2012, retrieved march-2025)

Returns:: KD value
Return type:: float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.accropode2_hudson1959.calculate_significant_wave_height_Hs(M: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], KD: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.33, alpha_Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Determine significant wave height Hs based on M for Accropode II, using Hudson 1959

For more details see: Hudson 1959 and Rock Manual: Hudson 1959, available here: https://doi.org/10.1061/JWHEAU.0000142 (or google) or more information in the Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 591 Information in this set of functions is also based on the design manual (design table 2012, retrieved in march-2025)

For more properties, see also unit_properties

More information is available at the Accropode website and from the concrete layer innovations (CLI) team https://www.concretelayer.com/en/solutions/technologies/accropode-2

A calculator is also available on the CLI website

Parameters:

M (float | npt.NDArray[np.float64]) – Unit mass M (kg)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
KD (float | npt.NDArray[np.float64]) – trunk: 16 see also functions to calculate KD from seabed slope
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-) Note that 1.33 is recommended, and shallower then 1.5
alpha_Hs (float | npt.NDArray[np.float64], optional) – Factor between Hs and H used according to Rock Manual by default 1.0 for concrete armour units

Returns:

Hs – Significant wave height (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.accropode2_hudson1959.calculate_unit_mass_M(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], KD: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.33, alpha_Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Determine required unit mass M based on Hs for Accropode II, using Hudson 1959

For more details see: Hudson 1959 and Rock Manual: Hudson 1959, available here: https://doi.org/10.1061/JWHEAU.0000142 (or google) or more information in the Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 591 Information in this set of functions is also based on the design manual (design table 2012, retrieved in march-2025)

For more properties, see also unit_properties

More information is available at the Accropode website and from the concrete layer innovations (CLI) team https://www.concretelayer.com/en/solutions/technologies/accropode-2

A calculator is also available on the CLI website

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
KD (float | npt.NDArray[np.float64]) – trunk: 16 see also functions to calculate KD from seabed slope
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-) Note that 1.33 is recommended, and shallower then 1.5
alpha_Hs (float | npt.NDArray[np.float64], optional) – Factor between Hs and H used according to Rock Manual by default 1.0 for concrete armour units

Returns:

M – Unit mass M (kg)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.accropode2_hudson1959.check_validity_range(cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, seabed_slope_perc: float | ndarray[tuple[Any, ...], dtype[float64]] = nan)[source]

Check the parameter values vs the validity range for Accropode II

For all parameters supplied, their values are checked versus the range of validity. When parameters are nan (by default), they are not checked.

For more details see: Hudson 1959 and Rock Manual: Hudson 1959, available here: https://doi.org/10.1061/JWHEAU.0000142 (or google) or more information in the Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 591 Information in this set of functions is also based on the design manual (design table 2012, retrieved in march-2025)

For more properties, see also unit_properties

More information is available at the Accropode website and from the concrete layer innovations (CLI) team https://www.concretelayer.com/en/solutions/technologies/accropode-2

A calculator is also available on the CLI website

Parameters:

cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
seabed_slope_perc (float | npt.NDArray[np.float64], optional) – Seabed slope in percentage, by default np.nan

Core Loc

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.core_loc_hudson1959.calculate_KD_breaking_trunk_from_seabed_slope(seabed_slope_perc: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Returns the KD value based on the seabed slope. Only to be applied for breaking condition at the trunk

For more information, see Concrete Layer Innovations: https://www.concretelayer.com/en/solutions/technologies/core-loc

This value is an interpretation of graphical information in the design table (design table 2012, retrieved march-2025)

Parameters:: seabed_slope_perc (float | npt.NDArray[np.float64]) – slope of seabed (%)
Returns:: KD value
Return type:: float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.core_loc_hudson1959.calculate_KD_nonbreaking_trunk_from_seabed_slope() → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Returns the KD value based on the seabed slope. Only to be applied for nonbreaking condition at the trunk. This value is fixed at 16, similar to 1% trunk breaking waves value

For more information, see Concrete Layer Innovations: https://www.concretelayer.com/en/solutions/technologies/core-loc

This value is an interpretation of graphical information in the design table (design table 2012, retrieved march-2025)

Returns:: KD value
Return type:: float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.core_loc_hudson1959.calculate_significant_wave_height_Hs(M: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], KD: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.33, alpha_Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Determine significant wave height Hs based on M for Coreloc, using Hudson 1959

For more details see: Hudson 1959 and Rock Manual: Hudson 1959, available here: https://doi.org/10.1061/JWHEAU.0000142 (or google) or more information in the Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 591 Information in this set of functions is also based on the design manual (design table 2012, retrieved in march-2025)

For more properties, see also unit_properties

More information is available at the Coreloc website and from the concrete layer innovations (CLI) team https://www.concretelayer.com/en/solutions/technologies/core-loc

A calculator is also available on the CLI website

Parameters:

M (float | npt.NDArray[np.float64]) – Unit mass M (kg)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
KD (float | npt.NDArray[np.float64]) – trunk: 16 head: 13 see also functions to calculate KD from seabed slope
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-) Note that 1.33 is recommended, and shallower then 1.5
alpha_Hs (float | npt.NDArray[np.float64], optional) – Factor between Hs and H used according to Rock Manual by default 1.0 for concrete armour units

Returns:

Hs – Significant wave height (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.core_loc_hudson1959.calculate_unit_mass_M(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], KD: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.33, alpha_Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Determine required unit mass M based on Hs for Coreloc, using Hudson 1959

For more details see: Hudson 1959 and Rock Manual: Hudson 1959, available here: https://doi.org/10.1061/JWHEAU.0000142 (or google) or more information in the Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 591 Information in this set of functions is also based on the design manual (design table 2012, retrieved in march-2025)

For more properties, see also unit_properties

More information is available at the Coreloc website and from the concrete layer innovations (CLI) team https://www.concretelayer.com/en/solutions/technologies/core-loc

A calculator is also available on the CLI website

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
KD (float | npt.NDArray[np.float64]) – trunk: 16 head: 13 see also functions to calculate KD from seabed slope
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-) Note that 1.33 is recommended, and shallower then 1.5
alpha_Hs (float | npt.NDArray[np.float64], optional) – Factor between Hs and H used according to Rock Manual by default 1.0 for concrete armour units

Returns:

M – Unit mass M (kg)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.core_loc_hudson1959.check_validity_range(cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, seabed_slope_perc: float | ndarray[tuple[Any, ...], dtype[float64]] = nan)[source]

Check the parameter values vs the validity range for Core Loc

For all parameters supplied, their values are checked versus the range of validity. When parameters are nan (by default), they are not checked.

For more details see: Hudson 1959 and Rock Manual: Hudson 1959, available here: https://doi.org/10.1061/JWHEAU.0000142 (or google) or more information in the Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 591 Information in this set of functions is also based on the design manual (design table 2012, retrieved in march-2025)

Parameters:

cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
seabed_slope_perc (float | npt.NDArray[np.float64], optional) – Seabed slope in percentage, by default np.nan

Cubipod

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.cubipod_hudson1959.calculate_significant_wave_height_Hs(M: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], KD: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.33, alpha_Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Determine significant wave height Hs based on M for Cubipod unit, using Hudson 1959

For more details see: Hudson 1959 and Rock Manual: Hudson 1959, available here: https://doi.org/10.1061/JWHEAU.0000142 (or google) or more information in the Cubidpod Manual (2016) (retrieved march 2025): https://www.cubipod.com/

A calculator is also available on the cupipod website

Parameters:

M (float | npt.NDArray[np.float64]) – Unit mass M (kg)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
KD (float | npt.NDArray[np.float64]) – trunk_double_layer: 28 trunk_single_layer: 12 head_double_layer: 7 head_single_layer: 5
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-) Note that 1.33 is recommended, and shallower then 1.5
alpha_Hs (float | npt.NDArray[np.float64], optional) – Factor between Hs and H used according to Rock Manual by default 1.0 for concrete armour units

Returns:

Hs – Significant wave height (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.cubipod_hudson1959.calculate_unit_mass_M(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], KD: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.33, alpha_Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Determine required unit mass M based on Hs for Cubipod unit, using Hudson 1959

For more details see: Hudson 1959 and Rock Manual: Hudson 1959, available here: https://doi.org/10.1061/JWHEAU.0000142 (or google) or more information in the Cubidpod Manual (2016) (retrieved march 2025): https://www.cubipod.com/

A calculator is also available on the cupipod website

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
KD (float | npt.NDArray[np.float64]) – trunk_double_layer: 28 trunk_single_layer: 12 head_double_layer: 7 head_single_layer: 5
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
alpha_Hs (float | npt.NDArray[np.float64], optional) – Factor between Hs and H used according to Rock Manual by default 1.0 for concrete armour units

Returns:

M – Unit mass M (kg)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.cubipod_hudson1959.check_validity_range()[source]: No validity ranges provided

Tetrapod

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.tetrapod_hudson1959.calculate_significant_wave_height_Hs(M: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], KD: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], alpha_Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Determine significant wave height Hs based on M for Tetrapods, using Hudson 1959

For more details see: Hudson 1959 and Rock Manual: Hudson 1959, available here: https://doi.org/10.1061/JWHEAU.0000142 (or google) or more information in the Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 591

For more properties, see also unit_properties

Parameters:

M (float | npt.NDArray[np.float64]) – Unit mass M (kg)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
KD (float | npt.NDArray[np.float64]) – trunk_non_breaking: 8.0 trunk_breaking: 7.0 head_non_breaking: 5.5 head_breaking: 4.5
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
alpha_Hs (float | npt.NDArray[np.float64], optional) – Factor between Hs and H used according to Rock Manual by default 1.0 for concrete armour units

Returns:

Hs – Significant wave height (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.tetrapod_hudson1959.calculate_unit_mass_M(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], KD: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], alpha_Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Determine required unit mass M based on Hs for Tetrapods, using Hudson 1959

For more details see: Hudson 1959 and Rock Manual: Hudson 1959, available here: https://doi.org/10.1061/JWHEAU.0000142 (or google) or more information in the Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 591

For more properties, see also unit_properties

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
KD (float | npt.NDArray[np.float64]) – trunk_non_breaking: 8.0 trunk_breaking: 7.0 head_non_breaking: 5.5 head_breaking: 4.5
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
alpha_Hs (float | npt.NDArray[np.float64], optional) – Factor between Hs and H used according to Rock Manual by default 1.0 for concrete armour units

Returns:

M – Unit mass M (kg)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.tetrapod_hudson1959.check_validity_range()[source]: No validity ranges provided

Xbloc

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.xbloc.calculate_correctionfactor_unit_mass_M_by_cotalpha_seabed(cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate correction factor based on seabed slope

A steep foreshore can lead to adverse wave impact against the armour layer

The design manual states on correction factors: “It should be noted that the factors presented should be used with care as these are based more on project specific model test experience rather than on vast research programs. For the detailed design, physical model tests are always recommended.”

Parameters:: cot_alpha (float | npt.NDArray[np.float64]) – Seabed slope (-)
Returns:: Correction factor applied on volume or mass
Return type:: correction_factor = float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.xbloc.calculate_correctionfactor_unit_mass_M_by_percslope_seabed(perc_slope: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate correction factor based on seabed slope in percentage

A steep foreshore can lead to adverse wave impact against the armour layer

The design manual states on correction factors: “It should be noted that the factors presented should be used with care as these are based more on project specific model test experience rather than on vast research programs. For the detailed design, physical model tests are always recommended.”

Parameters:: perc_slope (float | npt.NDArray[np.float64]) – Seabed slope (%)
Returns:: Correction factor applied on volume or mass
Return type:: correction_factor = float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.xbloc.calculate_correctionfactor_unit_mass_M_by_rel_depth(rel_depth: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate correction factor by relative depth

Parameters:: rel_depth (float | npt.NDArray[np.float64]) – the depth in front of the structure divided by the design wave height (-)
Returns:: Correction factor applied on volume or mass
Return type:: correction_factor = float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.xbloc.calculate_correctionfactor_unit_mass_M_by_relative_freeboard(rel_freeboard: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate correction factor by relative freeboard

Parameters:: rel_freeboard (float | npt.NDArray[np.float64]) – the freeboard divided by the design wave height (-)
Returns:: Correction factor applied on volume or mass
Return type:: correction_factor = float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.xbloc.calculate_correctionfactor_unit_mass_M_by_structure_slope(cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]])[source]

Calculate correction factor for structure slope different then 1:1.33

Parameters:: cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
Returns:: Correction factor applied on volume or mass
Return type:: correction_factor = float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.xbloc.calculate_unit_mass_M(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], total_correction_factor: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate Xbloc unit volume V

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
total_correction_factor (float | npt.NDArray[np.float64], optional) – Total correction factor (starting point: maximum of calculated factors), by default 1.0 The design manual states on correction factors: “It should be noted that the factors presented should be used with care as these are based more on project specific model test experience rather than on vast research programs. For the detailed design, physical model tests are always recommended.”

Returns:

M – Mass of unit (kg)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.xbloc.calculate_unit_volume_V(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], total_correction_factor: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate Xbloc unit volume V

For more information see Xbloc website and team at https://www.xbloc.com/ and the design manual The information in this approach is based on the design manual from 2024, (retrieved march 2025). This approach is limited to a slope of 1:1.33 (or 4:3), expandable by correction factors

A calculator is also available at the xbloc website.

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
total_correction_factor (float | npt.NDArray[np.float64], optional) – Total correction factor (starting point: maximum of calculated factors), by default 1.0 The design manual states on correction factors: “It should be noted that the factors presented should be used with care as these are based more on project specific model test experience rather than on vast research programs. For the detailed design, physical model tests are always recommended.”

Returns:

V – Volume of unit (m3)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.xbloc.calculate_wave_height_Hs_from_M(M: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], total_correction_factor: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate applicable Hs from Xbloc mass M

For more information see Xbloc website and team at https://www.xbloc.com/ and the design manual The information in this approach is based on the design manual from 2024, (retrieved march 2025). This approach is limited to a slope of 1:1.33 (or 4:3), expandable by correction factors

A calculator is also available at the xbloc website.

Parameters:

M (float | npt.NDArray[np.float64]) – Mass of unit (kg)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
total_correction_factor (float | npt.NDArray[np.float64]) – Total correction factor (all correction factors multiplied), by default 1.0

Returns:

Hs – Significant wave height (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.xbloc.calculate_wave_height_Hs_from_V(V: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], total_correction_factor: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate applicable Hs from Xbloc Volume V

For more information see Xbloc website and team at https://www.xbloc.com/ and the design manual Information in this approach is based on the design manual from 2024, (retrieved march 2025)

Parameters:

V (float | npt.NDArray[np.float64]) – Volume of unit (m3)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
total_correction_factor (float | npt.NDArray[np.float64]) – Total correction factor (all correction factors multiplied) by default 1.0

Returns:

Hs – Significant wave height (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.xbloc.check_validity_range()[source]: No validity ranges provided

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.xbloc.switch_correction_factor_unit_mass_M_near_design_event_frequency(design_event_occurs_frequently: bool = False) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Switch for correction factor by near design event frequency

Parameters:: design_event_occurs_frequently (bool, optional) – switch true/false. True in case there is frequently a near-design wave height during the lifetime of the structure, by default False
Returns:: Correction factor applied on volume or mass
Return type:: correction_factor = float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.xbloc.switch_correctionfactor_unit_mass_M_by_core_permeability(low_core_permeability: bool = False, core_impermeable: bool = False)[source]

Switch for correction factor by low or impermeable core

Parameters:

low_core_permeability (bool, optional) – For core with low permeability, by default False
core_impermeable (bool, optional) – For impermeable core, by default False

Returns:

Correction factor applied on volume or mass

Return type:

correction_factor = float | npt.NDArray[np.float64]

XblocPlus

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.xblocplus.calculate_correctionfactor_unit_mass_M_by_cotalpha_seabed(cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate correction factor based on seabed slope

A steep foreshore can lead to adverse wave impact against the armour layer

The design manual states on correction factors: “It should be noted that the factors presented should be used with care as these are based more on project specific model test experience rather than on vast research programs. For the detailed design, physical model tests are always recommended.”

Parameters:: cot_alpha (float | npt.NDArray[np.float64]) – Seabed slope (-)
Returns:: Correction factor applied on volume or mass
Return type:: correction_factor = float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.xblocplus.calculate_correctionfactor_unit_mass_M_by_percslope_seabed(perc_slope: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate correction factor based on seabed slope in percentage

A steep foreshore can lead to adverse wave impact against the armour layer

The design manual states on correction factors: “It should be noted that the factors presented should be used with care as these are based more on project specific model test experience rather than on vast research programs. For the detailed design, physical model tests are always recommended.”

Parameters:: perc_slope (float | npt.NDArray[np.float64]) – Seabed slope (%)
Returns:: Correction factor applied on volume or mass
Return type:: correction_factor = float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.xblocplus.calculate_correctionfactor_unit_mass_M_by_relative_freeboard(rel_freeboard: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate correction factor by relative freeboard

Parameters:: rel_freeboard (float | npt.NDArray[np.float64]) – the freeboard divided by the design wave height (-)
Returns:: Correction factor applied on volume or mass
Return type:: correction_factor = float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.xblocplus.calculate_unit_mass_M(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], total_correction_factor: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate XblocPlus unit volume V

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
total_correction_factor (float | npt.NDArray[np.float64], optional) – Total correction factor (starting point: maximum of calculated factors), by default 1.0 The design manual states on correction factors: “It should be noted that the factors presented should be used with care as these are based more on project specific model test experience rather than on vast research programs. For the detailed design, physical model tests are always recommended.”

Returns:

M – Mass of unit (kg)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.xblocplus.calculate_unit_volume_V(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], total_correction_factor: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate XblocPlusunit volume V

For more information see Xbloc website and team at https://www.xbloc.com/ and the design manual The information in this approach is based on the design manual from 2024, (retrieved march 2025). This approach is limited to a slope of 1:1.33 (or 4:3), expandable by correction factors

A calculator is also available at the xbloc website.

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
total_correction_factor (float | npt.NDArray[np.float64], optional) – Total correction factor (starting point: maximum of calculated factors), by default 1.0 The design manual states on correction factors: “It should be noted that the factors presented should be used with care as these are based more on project specific model test experience rather than on vast research programs. For the detailed design, physical model tests are always recommended.”

Returns:

V – Volume of unit (m3)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.xblocplus.calculate_wave_height_Hs_from_M(M: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], total_correction_factor: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate applicable Hs from XblocPlus mass M

For more information see Xbloc website and team at https://www.xbloc.com/ and the design manual The information in this approach is based on the design manual from 2024, (retrieved march 2025). This approach is limited to a slope of 1:1.33 (or 4:3), expandable by correction factors

A calculator is also available at the xbloc website.

Parameters:

M (float | npt.NDArray[np.float64]) – Mass of unit (kg)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
total_correction_factor (float | npt.NDArray[np.float64]) – Total correction factor (all correction factors multiplied), by default 1.0

Returns:

Hs – Significant wave height (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.xblocplus.calculate_wave_height_Hs_from_V(V: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], total_correction_factor: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate applicable Hs from XblocPlus Volume V

For more information see Xbloc website and team at https://www.xbloc.com/ and the design manual Information in this approach is based on the design manual from 2024, (retrieved march 2025)

Parameters:

V (float | npt.NDArray[np.float64]) – Volume of unit (m3)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour density (kg/m^3)
total_correction_factor (float | npt.NDArray[np.float64]) – Total correction factor (all correction factors multiplied) by default 1.0

Returns:

Hs – Significant wave height (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.xblocplus.check_validity_range()[source]: No validity ranges provided

deltares_coastal_structures_toolbox.functions.structural.stability_concrete_armour.xblocplus.switch_correctionfactor_unit_mass_M_by_core_permeability(low_core_permeability: bool = False, core_impermeable: bool = False)[source]

Switch for correction factor by low or impermeable core

Parameters:

low_core_permeability (bool, optional) – For core with low permeability, by default False
core_impermeable (bool, optional) – For impermeable core, by default False

Returns:

Correction factor applied on volume or mass

Return type:

correction_factor = float | npt.NDArray[np.float64]

Stability Rock Armour

Hudson (1959)

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.hudson1959.calculate_median_rock_mass_M50(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], KD: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], damage_percentage: float | ndarray[tuple[Any, ...], dtype[float64]], rock_type: str = 'rough', alpha_Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.27) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the required M50 based on Hs using the Hudson 1959 approach, including damage percentage

For more details see: Hudson 1959 and Rock Manual: Hudson 1959, available here: https://doi.org/10.1061/JWHEAU.0000142 (or google) or more information in the Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 564

Note: no limits to the formula have been provided in the paper

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour rock density (kg/m^3)
KD (float | npt.NDArray[np.float64]) – Stability coefficient, Hudson formula Hints (Rock Manual, 2007) for use with H10Percent: - KD = 2.0 for breaking waves - KD = 4.0 for non-breaking waves Breaking waves relate to breaking on foreshore, not to breaking on structure
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
damage_percentage (float | npt.NDArray[np.float64]) – Percentage of displaced units
alpha_Hs (float | npt.NDArray[np.float64], optional) – Factor between Hs and H10Percent according to SPM, by default 1.27 (as per Hudson approach since Shore Protection Manual 1984)

Returns:

M50 – Median rock mass (kg)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.hudson1959.calculate_median_rock_mass_M50_no_damage(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], KD: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], alpha_Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.27) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the required (no-damage) M50 using the Hudson 1959 approach

For more details see: Hudson 1959 and Rock Manual: Hudson 1959, available here: https://doi.org/10.1061/JWHEAU.0000142 (or google) or more information in the Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 564

Note: no limits to the formula have been provided in the paper

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour rock density (kg/m^3)
KD (float | npt.NDArray[np.float64]) – Stability coefficient, Hudson formula Hints (Rock Manual, 2007) for use with H10Percent: - KD = 2.0 for breaking waves - KD = 4.0 for non-breaking waves Breaking waves relate to breaking on foreshore, not to breaking on structure
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
alpha_Hs (float | npt.NDArray[np.float64], optional) – Factor between Hs and H10Percent according to SPM, by default 1.27 (as per Hudson approach since Shore Protection Manual 1984)

Returns:

M50 – Median rock mass (kg)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.hudson1959.calculate_significant_wave_height_Hs(M50: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], KD: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], damage_percentage: float | ndarray[tuple[Any, ...], dtype[float64]], rock_type: str = 'rough', alpha_Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.27) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the Hs based on M50 using the Hudson 1959 approach, including damage percentage

For more details see: Hudson 1959 and Rock Manual: Hudson 1959, available here: https://doi.org/10.1061/JWHEAU.0000142 (or google) or more information in the Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/BWchapter%205.pdf page 564

Note: no limits to the formula have been provided in the paper

Parameters:

M50 (float | npt.NDArray[np.float64]) – Median rock mass (kg)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour rock density (kg/m^3)
KD (float | npt.NDArray[np.float64]) – Stability coefficient, Hudson formula Hints (Rock Manual, 2007) for use with H10Percent: - KD = 2.0 for breaking waves - KD = 4.0 for non-breaking waves Breaking waves relate to breaking on foreshore, not to breaking on structure
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
damage_percentage (float | npt.NDArray[np.float64]) – Percentage of displaced units
alpha_Hs (float | npt.NDArray[np.float64], optional) – Factor between Hs and H10Percent according to SPM, by default 1.27 (as per Hudson approach since Shore Protection Manual 1984)

Returns:

Hs – Significant wave height (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.hudson1959.calculate_significant_wave_height_Hs_no_damage(M50: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], KD: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], alpha_Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = 1.27) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the required (no-damage) Hs using the Hudson 1959 approach

For more details see: Hudson 1959 and Rock Manual: Hudson 1959, available here: https://doi.org/10.1061/JWHEAU.0000142 (or google) or more information in the Rock Manual (2007 / 2012): https://kennisbank-waterbouw.nl/DesignCodes/rockmanual/ page 564

Note: no limits to the formula have been provided in the paper

Parameters:

M50 (float | npt.NDArray[np.float64]) – Median rock mass (kg)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)
rho_armour (float | npt.NDArray[np.float64]) – Armour rock density (kg/m^3)
KD (float | npt.NDArray[np.float64]) – Stability coefficient, Hudson formula Hints (Rock Manual, 2007) for use with H10Percent: - KD = 2.0 for breaking waves - KD = 4.0 for non-breaking waves Breaking waves relate to breaking on foreshore, not to breaking on structure
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
alpha_Hs (float | npt.NDArray[np.float64], optional) – Factor between Hs and H10Percent according to SPM, by default 1.27 (as per Hudson approach since Shore Protection Manual 1984)

Returns:

Hs – Significant wave height (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.hudson1959.check_validity_range()[source]: No validity ranges provided

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.hudson1959.lookup_table_damage_factors(damage_percentage: float | ndarray[tuple[Any, ...], dtype[float64]], rock_type: str = 'rough') → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Returns the multiplication value for the 0-damage value of the hudson formula, according to SPM1984 and Rock Manual 2007/2012

Parameters:

damage_percentage (float | npt.NDArray[np.float64]) – Percentage of damage required
rock_type (str, optional) – Type of rock, either “smooth” or “rough”, by default “rough”

Returns:

Multiplication factor

Return type:

float | npt.NDArray[np.float64]

Raises:

ValueError – Unknown rock_type

Van der Meer (1988)

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.vandermeer1988.calculate_correction_term_gamma_N(N_waves: int | ndarray[tuple[Any, ...], dtype[int32]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the correction term gamma_N for the number of waves for rock armour layers with the Van der Meer (1988) formula.

For more details see Van der Meer (1988), available here https://resolver.tudelft.nl/uuid:67e5692c-0905-4ddd-8487-37fdda9af6b4

Parameters:: N_waves (int | npt.NDArray[np.int32]) – Number of waves (-)
Returns:: The correction term for the number of waves gamma_N (-)
Return type:: float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.vandermeer1988.calculate_damage_number_S(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], H2p: float | ndarray[tuple[Any, ...], dtype[float64]], Tm: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], P: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, M50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c_pl: float = 8.7, c_s: float = 1.4, rho_water: float = 1025.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the damage number S for rock armour layers with the Van der Meer (1988) formula.

For more details see Van der Meer (1988), available here https://resolver.tudelft.nl/uuid:67e5692c-0905-4ddd-8487-37fdda9af6b4

Note that for cot_alpha >= 4.0, the formula for plunging waves is used as mentioned in Van der Meer (1993), available here (see Section 4.2): https://resolver.tudelft.nl/uuid:5a09837f-65b3-4ecf-92f1-aa3e6dc56d47

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
H2p (float | npt.NDArray[np.float64]) – Wave height exceeded by 2% of waves H2% (m)
Tm (float | npt.NDArray[np.float64]) – Mean wave period (s)
N_waves (float | npt.NDArray[np.float64]) – Number of waves (-)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
P (float | npt.NDArray[np.float64]) – Notional permeability coefficient (-)
rho_armour (float | npt.NDArray[np.float64]) – Armour rock density (kg/m^3)
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal rock diameter (m), by default np.nan
M50 (float | npt.NDArray[np.float64], optional) – Median rock mass (kg), by default np.nan
c_pl (float, optional) – Coefficient for plunging waves (-), by default 8.7
c_s (float, optional) – Coefficient for surging waves (-), by default 1.4
rho_water (float, optional) – Water density (kg/m^3), by default 1025.0

Returns:

The damage number S (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.vandermeer1988.calculate_nominal_rock_diameter_Dn50(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], H2p: float | ndarray[tuple[Any, ...], dtype[float64]], Tm: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], P: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], S: float | ndarray[tuple[Any, ...], dtype[float64]], c_pl: float = 8.7, c_s: float = 1.4, rho_water: float = 1025.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the nominal rock diameter Dn50 for rock armour layers with the Van der Meer (1988) formula.

For more details see Van der Meer (1988), available here https://resolver.tudelft.nl/uuid:67e5692c-0905-4ddd-8487-37fdda9af6b4

Note that for cot_alpha >= 4.0, the formula for plunging waves is used as mentioned in Van der Meer (1993), available here (see Section 4.2): https://resolver.tudelft.nl/uuid:5a09837f-65b3-4ecf-92f1-aa3e6dc56d47

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
H2p (float | npt.NDArray[np.float64]) – Wave height exceeded by 2% of waves H2% (m)
Tm (float | npt.NDArray[np.float64]) – Mean wave period (s)
N_waves (float | npt.NDArray[np.float64]) – Number of waves (-)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
P (float | npt.NDArray[np.float64]) – Notional permeability coefficient (-)
rho_armour (float | npt.NDArray[np.float64]) – Armour rock density (kg/m^3)
S (float | npt.NDArray[np.float64]) – Damage number (-)
c_pl (float, optional) – Coefficient for plunging waves (-), by default 8.7
c_s (float, optional) – Coefficient for surging waves (-), by default 1.4
rho_water (float, optional) – Water density (kg/m^3), by default 1025.0

Returns:

The nominal rock diameter Dn50 (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.vandermeer1988.calculate_significant_wave_height_Hs(ratio_H2p_Hs: float | ndarray[tuple[Any, ...], dtype[float64]], Tm: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], P: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], S: float | ndarray[tuple[Any, ...], dtype[float64]], Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, M50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c_pl: float = 8.7, c_s: float = 1.4, g: float = 9.81, rho_water: float = 1025.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the maximum significant wave height Hs for rock armour layers with the Van der Meer (1988) formula.

For more details see Van der Meer (1988), available here https://resolver.tudelft.nl/uuid:67e5692c-0905-4ddd-8487-37fdda9af6b4

Note that for cot_alpha >= 4.0, the formula for plunging waves is used as mentioned in Van der Meer (1993), available here (see Section 4.2): https://resolver.tudelft.nl/uuid:5a09837f-65b3-4ecf-92f1-aa3e6dc56d47

Parameters:

ratio_H2p_Hs (float | npt.NDArray[np.float64]) – Ratio between the Wave height exceeded by 2% of waves H2% and the significant wave height Hs, H2% / Hs (-)
Tm (float | npt.NDArray[np.float64]) – Mean wave period (s)
N_waves (float | npt.NDArray[np.float64]) – Number of waves (-)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
P (float | npt.NDArray[np.float64]) – Notional permeability coefficient (-)
rho_armour (float | npt.NDArray[np.float64]) – Armour rock density (kg/m^3)
S (float | npt.NDArray[np.float64]) – Damage number (-)
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal rock diameter (m), by default np.nan
M50 (float | npt.NDArray[np.float64], optional) – Median rock mass (kg), by default np.nan
c_pl (float, optional) – Coefficient for plunging waves (-), by default 8.7
c_s (float, optional) – Coefficient for surging waves (-), by default 1.4
g (float, optional) – Gravitational constant (m/s^2), by default 9.81
rho_water (float, optional) – Water density (kg/m^3), by default 1025.0

Returns:

The significant wave height Hs (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.vandermeer1988.check_validity_range(Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, H2p: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Tp: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, N_waves: int | ndarray[tuple[Any, ...], dtype[int32]] = nan, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, P: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]] = nan) → None[source]

Check the parameter values vs the validity range of the Van der Meer (1988) formula

For all parameters supplied, their values are checked versus the range of test conditions specified by Van der Meer (1988). When parameters are nan (by default), they are not checked.

For more details see Van der Meer (1988), available here https://resolver.tudelft.nl/uuid:67e5692c-0905-4ddd-8487-37fdda9af6b4

Parameters:

Hs (float | npt.NDArray[np.float64], optional) – Significant wave height (m), by default np.nan
H2p (float | npt.NDArray[np.float64], optional) – Wave height exceeded by 2% of waves H2% (m), by default np.nan
Tp (float | npt.NDArray[np.float64], optional) – Peak wave period (s), by default np.nan
N_waves (int | npt.NDArray[np.int32], optional) – Number of waves (-), by default np.nan
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
P (float | npt.NDArray[np.float64], optional) – Notional permeability coefficient (-), by default np.nan
rho_armour (float | npt.NDArray[np.float64], optional) – Armour rock density (kg/m^3), by default np.nan

modified Van der Meer (Van Gent et al., 2003)

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.vandermeer1988_modified.calculate_damage_number_S(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], H2p: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], P: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, M50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c_pl: float = 8.4, c_s: float = 1.3, rho_water: float = 1025.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the damage number S for rock armour layers with the Modified Van der Meer formula by Van Gent et al. (2003).

For more details see Van Gent et al. (2003), available here https://doi.org/10.1061/40733(147)9 or here https://www.researchgate.net/publication/259258688_Stability_of_Rock_Slopes_with_Shallow_Foreshores

Note that for cot_alpha >= 4.0, the formula for plunging waves is used as mentioned in Van der Meer (1993), available here (see Section 4.2): https://resolver.tudelft.nl/uuid:5a09837f-65b3-4ecf-92f1-aa3e6dc56d47

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
H2p (float | npt.NDArray[np.float64]) – Wave height exceeded by 2% of waves H2% (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
N_waves (float | npt.NDArray[np.float64]) – Number of waves (-)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
P (float | npt.NDArray[np.float64]) – Notional permeability coefficient (-)
rho_armour (float | npt.NDArray[np.float64]) – Armour rock density (kg/m^3)
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal rock diameter (m), by default np.nan
M50 (float | npt.NDArray[np.float64], optional) – Median rock mass (kg), by default np.nan
c_pl (float, optional) – Coefficient for plunging waves (-), by default 8.4
c_s (float, optional) – Coefficient for surging waves (-), by default 1.3
rho_water (float, optional) – Water density (kg/m^3), by default 1025.0

Returns:

The damage number S (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.vandermeer1988_modified.calculate_nominal_rock_diameter_Dn50(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], H2p: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], P: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], S: float | ndarray[tuple[Any, ...], dtype[float64]], c_pl: float = 8.4, c_s: float = 1.3, rho_water: float = 1025.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the nominal rock diameter Dn50 for rock armour layers with the Modified Van der Meer formula by Van Gent et al. (2003).

For more details see Van Gent et al. (2003), available here https://doi.org/10.1061/40733(147)9 or here https://www.researchgate.net/publication/259258688_Stability_of_Rock_Slopes_with_Shallow_Foreshores

Note that for cot_alpha >= 4.0, the formula for plunging waves is used as mentioned in Van der Meer (1993), available here (see Section 4.2): https://resolver.tudelft.nl/uuid:5a09837f-65b3-4ecf-92f1-aa3e6dc56d47

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
H2p (float | npt.NDArray[np.float64]) – Wave height exceeded by 2% of waves H2% (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
N_waves (float | npt.NDArray[np.float64]) – Number of waves (-)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
P (float | npt.NDArray[np.float64]) – Notional permeability coefficient (-)
rho_armour (float | npt.NDArray[np.float64]) – Armour rock density (kg/m^3)
S (float | npt.NDArray[np.float64]) – Damage number (-)
c_pl (float, optional) – Coefficient for plunging waves (-), by default 8.4
c_s (float, optional) – Coefficient for surging waves (-), by default 1.3
rho_water (float, optional) – Water density (kg/m^3), by default 1025.0

Returns:

The nominal rock diameter Dn50 (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.vandermeer1988_modified.calculate_significant_wave_height_Hs(ratio_H2p_Hs: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], P: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], S: float | ndarray[tuple[Any, ...], dtype[float64]], Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, M50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c_pl: float = 8.4, c_s: float = 1.3, g: float = 9.81, rho_water: float = 1025.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the maximum significant wave height Hs for rock armour layers with the Modified Van der Meer formula by Van Gent et al. (2003).

For more details see Van Gent et al. (2003), available here https://doi.org/10.1061/40733(147)9 or here https://www.researchgate.net/publication/259258688_Stability_of_Rock_Slopes_with_Shallow_Foreshores

Note that for cot_alpha >= 4.0, the formula for plunging waves is used as mentioned in Van der Meer (1993), available here (see Section 4.2): https://resolver.tudelft.nl/uuid:5a09837f-65b3-4ecf-92f1-aa3e6dc56d47

Parameters:

ratio_H2p_Hs (float | npt.NDArray[np.float64]) – Ratio between the Wave height exceeded by 2% of waves H2% and the significant wave height Hs, H2% / Hs (-)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
N_waves (float | npt.NDArray[np.float64]) – Number of waves (-)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
P (float | npt.NDArray[np.float64]) – Notional permeability coefficient (-)
rho_armour (float | npt.NDArray[np.float64]) – Armour rock density (kg/m^3)
S (float | npt.NDArray[np.float64]) – Damage number (-)
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal rock diameter (m), by default np.nan
M50 (float | npt.NDArray[np.float64], optional) – Median rock mass (kg), by default np.nan
c_pl (float, optional) – Coefficient for plunging waves (-), by default 8.4
c_s (float, optional) – Coefficient for surging waves (-), by default 1.3
g (float, optional) – Gravitational constant (m/s^2), by default 9.81
rho_water (float, optional) – Water density (kg/m^3), by default 1025.0

Returns:

The significant wave height Hs (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.vandermeer1988_modified.check_validity_range(Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, H2p: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, N_waves: int | ndarray[tuple[Any, ...], dtype[int32]] = nan, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, P: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, rho_water: float = 1025.0) → None[source]

Check the parameter values vs the validity range of the Modified Van der Meer formula as defined in Van Gent et al. (2003).

For all parameters supplied, their values are checked versus the range of test conditions specified in (Van Gent et al., 2003). When parameters are nan (by default), they are not checked.

For more details see Van Gent et al. (2003), available here https://doi.org/10.1061/40733(147)9 or here https://www.researchgate.net/publication/259258688_Stability_of_Rock_Slopes_with_Shallow_Foreshores

Parameters:

Hs (float | npt.NDArray[np.float64], optional) – Significant wave height (m), by default np.nan
H2p (float | npt.NDArray[np.float64], optional) – Wave height exceeded by 2% of waves H2% (m), by default np.nan
Tmm10 (float | npt.NDArray[np.float64], optional) – Spectral wave period Tm-1,0 (s), by default np.nan
N_waves (int | npt.NDArray[np.int32], optional) – Number of waves (-), by default np.nan
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
P (float | npt.NDArray[np.float64], optional) – Notional permeability coefficient (-), by default np.nan
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal rock diameter (m), by default np.nan
rho_armour (float | npt.NDArray[np.float64], optional) – Armour rock density (kg/m^3), by default np.nan
rho_water (float, optional) – Water density (kg/m^3), by default 1025.0

Kramer & Burcharth (2004)

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.kramerburcharth2004_lowcrested.calculate_crest_freeboard_Rc(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, M50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Rc_Dn50_init: float = -1.0, max_iter: int = 1000, tolerance: float = 1e-05) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the crest freeboard Rc for low-crested structures with the Kramer & Burcharth (2004) formula.

Here, eq. 4 from Kramer & Burcharth (2004) is implemented.

For more details see Kramer & Burcharth (2004), available here: https://doi.org/10.1061/40733(147)12

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
rho_armour (float | npt.NDArray[np.float64]) – Armour rock density (kg/m^3)
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal rock diameter (m), by default np.nan
M50 (float | npt.NDArray[np.float64], optional) – Median rock mass (kg), by default np.nan
Rc_Dn50_init (float, optional) – Initial relative crest height Rc/Dn50 for the iterative solution, by default -1.0
max_iter (int, optional) – Maximum number of iterations, by default 1000
tolerance (float, optional) – Tolerance for convergence of the iterative solution, by default 1e-5

Returns:

The crest freeboard of the structure (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.kramerburcharth2004_lowcrested.calculate_nominal_rock_diameter_Dn50(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], Ns_init: float = 2.0, max_iter: int = 1000, tolerance: float = 1e-05) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the nominal rock diameter Dn50 for low-crested structures with the Kramer & Burcharth (2004) formula.

Here, eq. 4 from Kramer & Burcharth (2004) is implemented.

For more details see Kramer & Burcharth (2004), available here: https://doi.org/10.1061/40733(147)12

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
rho_armour (float | npt.NDArray[np.float64]) – Armour rock density (kg/m^3)
Ns_init (float, optional) – Initial stability number Ns (-) for the iterative solution, by default 2.0
max_iter (int, optional) – Maximum number of iterations, by default 1000
tolerance (float, optional) – Tolerance for convergence of the iterative solution, by default 1e-5

Returns:

The nominal rock diameter Dn50 (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.kramerburcharth2004_lowcrested.calculate_significant_wave_height_Hs(Rc: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, M50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the maximum significant wave height Hs for low-crested structures with the Kramer & Burcharth (2004) formula.

Here, eq. 4 from Kramer & Burcharth (2004) is implemented.

For more details see Kramer & Burcharth (2004), available here: https://doi.org/10.1061/40733(147)12

Parameters:

Rc (float | npt.NDArray[np.float64]) – Crest freeboard of the structure (m)
rho_armour (float | npt.NDArray[np.float64]) – Armour rock density (kg/m^3)
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal rock diameter (m), by default np.nan
M50 (float | npt.NDArray[np.float64], optional) – Median rock mass (kg), by default np.nan

Returns:

The significant wave height Hs (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.kramerburcharth2004_lowcrested.check_validity_range(Rc: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan) → None[source]

Check the parameter values vs the validity range of the Kramer & Burcharth (2004) formula.

For all parameters supplied, their values are checked versus the range of test conditions specified in the conclusions of Kramer & Burcharth (2004). When parameters are nan (by default), they are not checked.

For more details see Kramer & Burcharth (2004), available here: https://doi.org/10.1061/40733(147)12

Parameters:

Rc (float | npt.NDArray[np.float64], optional) – Crest freeboard of the structure (m), by default np.nan
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal rock diameter (m), by default np.nan

Etemad-Shahidi et al. (2020)

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.etemadshahidi2020.calculate_damage_number_S(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, M50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Dn50_core: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, M50_core: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, rho_core: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, rho_water: float = 1025.0, m: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, use_depth_limited_version: bool = False) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the damage number S for rock armour layers with the Etemad-Shahidi et al. (2020) formula.

Here, eqs. 17a & 17b from Etemad-Shahidi et al. (2020) are implemented. The user can also choose to use the depth limited version of the formula (eqs. 12a & 12b) by enabling that option and providing the foreshore slope.

For more details, see: https://doi.org/10.1016/j.coastaleng.2020.103655 and the corresponding corrigendum: https://doi.org/10.1016/j.coastaleng.2022.104142

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
N_waves (float | npt.NDArray[np.float64]) – Number of waves (-)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
rho_armour (float | npt.NDArray[np.float64]) – Armour rock density (kg/m^3)
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal rock diameter (m), by default np.nan
M50 (float | npt.NDArray[np.float64], optional) – Median rock mass (kg), by default np.nan
Dn50_core (float | npt.NDArray[np.float64], optional) – Nominal rock diameter of the core material (m), by default np.nan
M50_core (float | npt.NDArray[np.float64], optional) – Median rock mass of the core material (kg), by default np.nan
rho_core (float | npt.NDArray[np.float64], optional) – Core rock density (kg/m^3), by default np.nan
rho_water (float, optional) – Water density (kg/m^3), by default 1025.0
m (float | npt.NDArray[np.float64], optional) – Tangent of the foreshore slope (-), by default np.nan
use_depth_limited_version (bool, optional) – Use depth limited version of the formula, by default False

Returns:

The damage number S (-)

Return type:

float | npt.NDArray[np.float64]

Raises:

ValueError – If depth limited version is used and m is not provided.

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.etemadshahidi2020.calculate_nominal_rock_diameter_Dn50(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], S: float | ndarray[tuple[Any, ...], dtype[float64]], Dn50_core: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, M50_core: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, rho_core: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, m: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, use_depth_limited_version: bool = False, Cp_init: float = 0.5, max_iter: int = 1000, tolerance: float = 1e-05) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the nominal rock diameter Dn50 for rock armour layers with the Etemad-Shahidi et al. (2020) formula.

Here, eqs. 10a & 10b from Etemad-Shahidi et al. (2020) are implemented. The user can also choose to use the depth limited version of the formula (eqs. 12a & 12b) by enabling that option and providing the foreshore slope.

Note that, due to the dependency of Cp on Dn50, an iterative solution is necessary.

For more details, see: https://doi.org/10.1016/j.coastaleng.2020.103655 and the corresponding corrigendum: https://doi.org/10.1016/j.coastaleng.2022.104142

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
N_waves (float | npt.NDArray[np.float64]) – Number of waves (-)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
rho_armour (float | npt.NDArray[np.float64]) – Armour rock density (kg/m^3)
S (float | npt.NDArray[np.float64]) – Damage number (-)
Dn50_core (float | npt.NDArray[np.float64], optional) – Nominal rock diameter of the core material (m), by default np.nan
M50_core (float | npt.NDArray[np.float64], optional) – Median rock mass of the core material (kg), by default np.nan
rho_core (float | npt.NDArray[np.float64], optional) – Core rock density (kg/m^3), by default np.nan
m (float | npt.NDArray[np.float64], optional) – Tangent of the foreshore slope (-), by default np.nan
use_depth_limited_version (bool, optional) – Use depth limited version of the formula, by default False
Cp_init (float, optional) – Initial coefficient of permeability Cp (-) for the iterative solution, by default 0.5
max_iter (int, optional) – Maximum number of iterations, by default 1000
tolerance (float, optional) – Tolerance for convergence of the iterative solution, by default 1e-5

Returns:

The nominal rock diameter Dn50 (m)

Return type:

float | npt.NDArray[np.float64]

Raises:

ValueError – If depth limited version is used and m is not provided.

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.etemadshahidi2020.calculate_permeability_coefficient_Cp(Dn50: float | ndarray[tuple[Any, ...], dtype[float64]], Dn50_core: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the coefficient of permeability Cp following Etemad-Shahidi et al. (2020).

Here, eq. 11 from Etemad-Shahidi et al. (2020) is implemented.

For more details, see: https://doi.org/10.1016/j.coastaleng.2020.103655 and the corresponding corrigendum: https://doi.org/10.1016/j.coastaleng.2022.104142

Parameters:

Dn50 (float | npt.NDArray[np.float64]) – Nominal rock diameter (m)
Dn50_core (float | npt.NDArray[np.float64]) – Nominal rock diameter of the core material (m)

Returns:

The coefficient of permeability Cp (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.etemadshahidi2020.calculate_significant_wave_height_Hs(Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], S: float | ndarray[tuple[Any, ...], dtype[float64]], Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, M50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Dn50_core: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, M50_core: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, rho_core: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, m: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, use_depth_limited_version: bool = False, g: float = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the maximum significant wave height Hs for rock armour layers with the Etemad-Shahidi et al. (2020) formula.

Here, eqs. 18a & 18b from Etemad-Shahidi et al. (2020) are implemented. The user can also choose to use the depth limited version of the formula (eqs. 12a & 12b) by enabling that option and providing the foreshore slope.

For more details, see: https://doi.org/10.1016/j.coastaleng.2020.103655 and the corresponding corrigendum: https://doi.org/10.1016/j.coastaleng.2022.104142

Parameters:

Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
N_waves (float | npt.NDArray[np.float64]) – Number of waves (-)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
rho_armour (float | npt.NDArray[np.float64]) – Armour rock density (kg/m^3)
S (float | npt.NDArray[np.float64]) – Damage number (-)
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal rock diameter (m), by default np.nan
M50 (float | npt.NDArray[np.float64], optional) – Median rock mass (kg), by default np.nan
Dn50_core (float | npt.NDArray[np.float64], optional) – Nominal rock diameter of the core material (m), by default np.nan
M50_core (float | npt.NDArray[np.float64], optional) – Median rock mass of the core material (kg), by default np.nan
rho_core (float | npt.NDArray[np.float64], optional) – Core rock density (kg/m^3), by default np.nan
m (float | npt.NDArray[np.float64], optional) – Tangent of the foreshore slope (-), by default np.nan
use_depth_limited_version (bool, optional) – Use depth limited version of the formula, by default False
g (float, optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

The significant wave height Hs (m)

Return type:

float | npt.NDArray[np.float64]

Raises:

ValueError – If depth limited version is used and m is not provided.

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.etemadshahidi2020.check_validity_range(Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, N_waves: int | ndarray[tuple[Any, ...], dtype[int32]] = nan, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, P: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, S: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Dn50_core: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, rho_water: float = 1025.0) → None[source]

Check the parameter values vs the validity range of the Etemad-Shahidi et al. (2020) formula.

For all parameters supplied, their values are checked versus the range of test conditions specified in Table 1 of Etemad-Shahidi et al. (2020). When parameters are nan (by default), they are not checked.

For more details, see: https://doi.org/10.1016/j.coastaleng.2020.103655 and the corresponding corrigendum: https://doi.org/10.1016/j.coastaleng.2022.104142

Parameters:

Hs (float | npt.NDArray[np.float64], optional) – Significant wave height (m), by default np.nan
Tmm10 (float | npt.NDArray[np.float64], optional) – Spectral wave period Tm-1,0 (s), by default np.nan
N_waves (int | npt.NDArray[np.int32], optional) – Number of waves (-), by default np.nan
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
P (float | npt.NDArray[np.float64], optional) – Notional permeability coefficient (-), by default np.nan
S (float | npt.NDArray[np.float64], optional) – Damage number (-), by default np.nan
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal rock diameter (m), by default np.nan
Dn50_core (float | npt.NDArray[np.float64], optional) – Nominal rock diameter of the core material (m), by default np.nan
rho_armour (float | npt.NDArray[np.float64], optional) – Armour rock density (kg/m^3), by default np.nan
rho_water (float, optional) – Water density (kg/m^3), by default 1025.0

Van der Meer (2021)

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.vandermeer2021.calculate_damage_number_S(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], P: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, M50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c_pl: float = 6.49, c_s: float = 0.97, c_pl_mult: float = 1.0, c_s_mult: float = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the damage number S for rock armour layers with the Van der Meer (2021) formula.

For more details see Van der Meer (2021), available here https://doi.org/10.48438/jchs.2021.0008

Note that code-wise this comes down to the same as the Modified Van der Meer (1988) formula with different coefficients and without the H2%/Hs term, hence the chosen implementation.

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
N_waves (float | npt.NDArray[np.float64]) – Number of waves (-)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
P (float | npt.NDArray[np.float64]) – Notional permeability coefficient (-)
rho_armour (float | npt.NDArray[np.float64]) – Armour rock density (kg/m^3)
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal rock diameter (m), by default np.nan
M50 (float | npt.NDArray[np.float64], optional) – Median rock mass (kg), by default np.nan
c_pl (float, optional) – Coefficient for plunging waves (-), by default 6.49
c_s (float, optional) – Coefficient for surging waves (-), by default 0.97
c_pl_mult (float, optional) – Multiplication factor on the coefficient for plunging waves (-), by default 1.0
c_s_mult (float, optional) – Multiplication factor on the coefficient for surging waves (-), by default 1.0

Returns:

The damage number S (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.vandermeer2021.calculate_nominal_rock_diameter_Dn50(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], P: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], S: float | ndarray[tuple[Any, ...], dtype[float64]], c_pl: float = 6.49, c_s: float = 0.97, c_pl_mult: float = 1.0, c_s_mult: float = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the nominal rock diameter Dn50 for rock armour layers with the Van der Meer (2021) formula.

For more details see Van der Meer (2021), available here https://doi.org/10.48438/jchs.2021.0008

Note that code-wise this comes down to the same as the Modified Van der Meer (1988) formula with different coefficients and without the H2%/Hs term, hence the chosen implementation.

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
N_waves (float | npt.NDArray[np.float64]) – Number of waves (-)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
P (float | npt.NDArray[np.float64]) – Notional permeability coefficient (-)
rho_armour (float | npt.NDArray[np.float64]) – Armour rock density (kg/m^3)
S (float | npt.NDArray[np.float64]) – Damage number (-)
c_pl (float, optional) – Coefficient for plunging waves (-), by default 6.49
c_s (float, optional) – Coefficient for surging waves (-), by default 0.97
c_pl_mult (float, optional) – Multiplication factor on the coefficient for plunging waves (-), by default 1.0
c_s_mult (float, optional) – Multiplication factor on the coefficient for surging waves (-), by default 1.0

Returns:

The nominal rock diameter Dn50 (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.vandermeer2021.calculate_significant_wave_height_Hs(Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], P: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], S: float | ndarray[tuple[Any, ...], dtype[float64]], Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, M50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c_pl: float = 6.49, c_s: float = 0.97, c_pl_mult: float = 1.0, c_s_mult: float = 1.0, g: float = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the maximum significant wave height Hs for rock armour layers with the Van der Meer (2021) formula.

For more details see Van der Meer (2021), available here https://doi.org/10.48438/jchs.2021.0008

Note that code-wise this comes down to the same as the Modified Van der Meer (1988) formula with different coefficients and without the H2%/Hs term, hence the chosen implementation.

Parameters:

Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
N_waves (float | npt.NDArray[np.float64]) – Number of waves (-)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
P (float | npt.NDArray[np.float64]) – Notional permeability coefficient (-)
rho_armour (float | npt.NDArray[np.float64]) – Armour rock density (kg/m^3)
S (float | npt.NDArray[np.float64]) – Damage number (-)
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal rock diameter (m), by default np.nan
M50 (float | npt.NDArray[np.float64], optional) – Median rock mass (kg), by default np.nan
c_pl (float, optional) – Coefficient for plunging waves (-), by default 6.49
c_s (float, optional) – Coefficient for surging waves (-), by default 0.97
c_pl_mult (float, optional) – Multiplication factor on the coefficient for plunging waves (-), by default 1.0
c_s_mult (float, optional) – Multiplication factor on the coefficient for surging waves (-), by default 1.0
g (float, optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

The significant wave height Hs (m)

Return type:

float | npt.NDArray[np.float64]

Scaravaglione et al. (2025)

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.scaravaglione2025.calculate_damage_number_S(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], rho_core: float | ndarray[tuple[Any, ...], dtype[float64]], Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Dn50_core: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, M50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, M50_core: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c_VGnew: float = 3.3, rho_water: float = 1025.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the damage number S for rock armour layers in shallow water with the Scaravaglione et al. (2025) formula.

For more details see Scaravaglione et al. (2025), available here https://doi.org/10.1016/j.coastaleng.2024.104657

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Significant spectral wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
N_waves (float | npt.NDArray[np.float64]) – Number of waves (-)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
rho_armour (float | npt.NDArray[np.float64]) – Armour rock density (kg/m^3)
rho_core (float | npt.NDArray[np.float64]) – Core rock density (kg/m^3)
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal (armour) rock diameter (m), by default np.nan
Dn50_core (float | npt.NDArray[np.float64], optional) – Nominal core rock diameter (m), by default np.nan
M50 (float | npt.NDArray[np.float64], optional) – Median (armour) rock mass (kg), by default np.nan
M50_core (float | npt.NDArray[np.float64], optional) – Median core rock mass (kg), by default np.nan
c_VGnew (float, optional) – Coefficient (-), by default 3.3
rho_water (float, optional) – Water density (kg/m^3), by default 1025.0

Returns:

The damage number S (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.scaravaglione2025.calculate_nominal_rock_diameter_Dn50(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], rho_core: float | ndarray[tuple[Any, ...], dtype[float64]], S: float | ndarray[tuple[Any, ...], dtype[float64]], Dn50_core: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, M50_core: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c_VGnew: float = 3.3, rho_water: float = 1025.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the nominal rock diameter Dn50 for rock armour layers in shallow water with the Scaravaglione et al. (2025) formula.

For more details see Scaravaglione et al. (2025), available here https://doi.org/10.1016/j.coastaleng.2024.104657

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Significant spectral wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
N_waves (float | npt.NDArray[np.float64]) – Number of waves (-)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
rho_armour (float | npt.NDArray[np.float64]) – Armour rock density (kg/m^3)
rho_core (float | npt.NDArray[np.float64]) – Core rock density (kg/m^3)
S (float | npt.NDArray[np.float64]) – Damage number (-)
Dn50_core (float | npt.NDArray[np.float64], optional) – Nominal core rock diameter (m), by default np.nan
M50_core (float | npt.NDArray[np.float64], optional) – Median core rock mass (kg), by default np.nan
c_VGnew (float, optional) – Coefficient (-), by default 3.3
rho_water (float, optional) – Water density (kg/m^3), by default 1025.0

Returns:

The nominal rock diameter Dn50 (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.scaravaglione2025.calculate_significant_wave_height_Hm0(Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]], rho_core: float | ndarray[tuple[Any, ...], dtype[float64]], S: float | ndarray[tuple[Any, ...], dtype[float64]], Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Dn50_core: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, M50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, M50_core: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, c_VGnew: float = 3.3, g: float = 9.81, rho_water: float = 1025.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the maximum significant spectral wave height Hm0 for rock armour layers in shallow water with the Scaravaglione et al. (2025) formula.

For more details see Scaravaglione et al. (2025), available here https://doi.org/10.1016/j.coastaleng.2024.104657

Parameters:

Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
N_waves (float | npt.NDArray[np.float64]) – Number of waves (-)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
rho_armour (float | npt.NDArray[np.float64]) – Armour rock density (kg/m^3)
rho_core (float | npt.NDArray[np.float64]) – Core rock density (kg/m^3)
S (float | npt.NDArray[np.float64]) – Damage number (-)
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal (armour) rock diameter (m), by default np.nan
Dn50_core (float | npt.NDArray[np.float64], optional) – Nominal core rock diameter (m), by default np.nan
M50 (float | npt.NDArray[np.float64], optional) – Median (armour) rock mass (kg), by default np.nan
M50_core (float | npt.NDArray[np.float64], optional) – Median core rock mass (kg), by default np.nan
c_VGnew (float, optional) – Coefficient (-), by default 3.3
g (float, optional) – Gravitational constant (m/s^2), by default 9.81
rho_water (float, optional) – Water density (kg/m^3), by default 1025.0

Returns:

The significant spectral wave height Hm0 (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_armour.scaravaglione2025.check_validity_range(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, N_waves: int | ndarray[tuple[Any, ...], dtype[int32]] = nan, cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, P: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Dn50_core: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, rho_water: float = 1025.0) → None[source]

Check the parameter values vs the validity range of the stability formula as defined in Scaravaglione et al. (2025).

For all parameters supplied, their values are checked versus the range of test conditions specified in Scaravaglione et al. (2025). When parameters are nan (by default), they are not checked.

For more details see Scaravaglione et al. (2025), available here https://doi.org/10.1016/j.coastaleng.2024.104657

Parameters:

Hm0 (float | npt.NDArray[np.float64], optional) – Significant spectral wave height (m), by default np.nan
Tmm10 (float | npt.NDArray[np.float64], optional) – Spectral wave period Tm-1,0 (s), by default np.nan
N_waves (int | npt.NDArray[np.int32], optional) – Number of waves (-), by default np.nan
cot_alpha (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side slope of the structure (-), by default np.nan
P (float | npt.NDArray[np.float64], optional) – Notional permeability coefficient (-), by default np.nan
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal (armour) rock diameter (m), by default np.nan
Dn50_core (float | npt.NDArray[np.float64], optional) – Nominal core rock diameter (m), by default np.nan
rho_armour (float | npt.NDArray[np.float64], optional) – Armour rock density (kg/m^3), by default np.nan
rho_water (float, optional) – Water density (kg/m^3), by default 1025.0

Stability Rock Rear

Van Gent & Pozueta (2004)

deltares_coastal_structures_toolbox.functions.structural.stability_rock_rear.vangentpozueta2004.calculate_damage_number_S(cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], cot_phi: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f_Crest: float | ndarray[tuple[Any, ...], dtype[float64]], Hs: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], Rc_rear: float | ndarray[tuple[Any, ...], dtype[float64]], Bc: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: int | ndarray[tuple[Any, ...], dtype[int32]], Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, M50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, rho_water: float = 1025.0, cs: float = np.float64(2.62144e-13)) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the damage number S for rock at the rear side of a rubble mound structure following Van Gent & Pozueta (2004).

For more details see Van Gent & Pozueta (2004), available here https://doi.org/10.1142/9789812701916_0281 or here: https://www.researchgate.net/publication/259260766_REAR-SIDE_STABILITY_OF_RUBBLE_MOUND_STRUCTURES

Parameters:

cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
cot_phi (float | npt.NDArray[np.float64]) – Cotangent of the rear-side slope of the structure (-)
gamma_f (float | npt.NDArray[np.float64]) – Influence factor for surface roughness (-)
gamma_f_Crest (float | npt.NDArray[np.float64]) – Influence factor for surface roughness on the crest of the structure (-)
Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
Rc (float | npt.NDArray[np.float64]) – Freeboard of the structure (m)
Rc_rear (float | npt.NDArray[np.float64]) – Vertical distance between still-water level and the crest at the rear side (m)
Bc (float | npt.NDArray[np.float64]) – Width of the crest of the structure (m)
N_waves (int | npt.NDArray[np.int32]) – Number of waves (-)
Dn50 (float | npt.NDArray[np.float64], optional) – Median nominal rock diameter (m), by default np.nan
M50 (float | npt.NDArray[np.float64], optional) – Median rock mass (kg), by default np.nan
rho_rock (float | npt.NDArray[np.float64], optional) – Rock density (kg/m^3), by default np.nan
rho_water (float, optional) – Water density (kg/m^3), by default 1025.0
cs (float, optional) – Coefficient, by default np.power(0.008, 6.0)

Returns:

The damage number S (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_rear.vangentpozueta2004.calculate_maximum_significant_wave_height_Hs(cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], cot_phi: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f_Crest: float | ndarray[tuple[Any, ...], dtype[float64]], S: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], Rc_rear: float | ndarray[tuple[Any, ...], dtype[float64]], Bc: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: int | ndarray[tuple[Any, ...], dtype[int32]], Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, M50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, rho_water: float = 1025.0, cs: float = np.float64(2.62144e-13), tolerance: float = 0.0001, max_iterations: int = 10000) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the maximum allowable Hs for armour at the rear side of a rubble mound structure following Van Gent & Pozueta (2004).

For more details see Van Gent & Pozueta (2004), available here https://doi.org/10.1142/9789812701916_0281 or here: https://www.researchgate.net/publication/259260766_REAR-SIDE_STABILITY_OF_RUBBLE_MOUND_STRUCTURES

Parameters:

cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
cot_phi (float | npt.NDArray[np.float64]) – Cotangent of the rear-side slope of the structure (-)
gamma_f (float | npt.NDArray[np.float64]) – Influence factor for surface roughness (-)
gamma_f_Crest (float | npt.NDArray[np.float64]) – Influence factor for surface roughness on the crest of the structure (-)
S (float | npt.NDArray[np.float64]) – Damage number (-)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
Rc (float | npt.NDArray[np.float64]) – Freeboard of the structure (m)
Rc_rear (float | npt.NDArray[np.float64]) – Vertical distance between still-water level and the crest at the rear side (m)
Bc (float | npt.NDArray[np.float64]) – Width of the crest of the structure (m)
N_waves (int | npt.NDArray[np.int32]) – Number of waves (-)
Dn50 (float | npt.NDArray[np.float64], optional) – Median nominal rock diameter (m), by default np.nan
M50 (float | npt.NDArray[np.float64], optional) – Median rock mass (kg), by default np.nan
rho_rock (float | npt.NDArray[np.float64], optional) – Rock density (kg/m^3), by default np.nan
rho_water (float, optional) – Water density (kg/m^3), by default 1025.0
cs (float, optional) – Coefficient, by default np.power(0.008, 6.0)
tolerance (float, optional) – Tolerance in the iteration to Hs (m), by default 1e-4
max_iterations (int, optional) – Maximum number of iterations, by default 10000

Returns:

The maximum allowable significant wave height Hs (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_rear.vangentpozueta2004.calculate_nominal_rock_diameter_Dn50(cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], cot_phi: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]], gamma_f_Crest: float | ndarray[tuple[Any, ...], dtype[float64]], S: float | ndarray[tuple[Any, ...], dtype[float64]], Hs: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], Rc_rear: float | ndarray[tuple[Any, ...], dtype[float64]], Bc: float | ndarray[tuple[Any, ...], dtype[float64]], rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: int | ndarray[tuple[Any, ...], dtype[int32]], rho_water: float = 1025.0, cs: float = np.float64(2.62144e-13)) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the minimum Dn50 for armour at the rear side of a rubble mound structure following Van Gent & Pozueta (2004).

For more details see Van Gent & Pozueta (2004), available here https://doi.org/10.1142/9789812701916_0281 or here: https://www.researchgate.net/publication/259260766_REAR-SIDE_STABILITY_OF_RUBBLE_MOUND_STRUCTURES

Parameters:

cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
cot_phi (float | npt.NDArray[np.float64]) – Cotangent of the rear-side slope of the structure (-)
gamma_f (float | npt.NDArray[np.float64]) – Influence factor for surface roughness (-)
gamma_f_Crest (float | npt.NDArray[np.float64]) – Influence factor for surface roughness on the crest of the structure (-)
S (float | npt.NDArray[np.float64]) – Damage number (-)
Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
Rc (float | npt.NDArray[np.float64]) – Freeboard of the structure (m)
Rc_rear (float | npt.NDArray[np.float64]) – Vertical distance between still-water level and the crest at the rear side (m)
Bc (float | npt.NDArray[np.float64]) – Width of the crest of the structure (m)
rho_rock (float | npt.NDArray[np.float64]) – Rock density (kg/m^3)
N_waves (int | npt.NDArray[np.int32]) – Number of waves (-)
rho_water (float, optional) – Water density (kg/m^3), by default 1025.0
cs (float, optional) – Coefficient, by default np.power(0.008, 6.0)

Returns:

The median nominal rock diameter Dn50 (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_rear.vangentpozueta2004.check_validity_range(Rc: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Rc_rear: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_phi: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, gamma_f: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, rho_water: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Bc: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, z1p: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, S: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, N_waves: int | ndarray[tuple[Any, ...], dtype[int32]] = nan) → None[source]

Check the parameter values vs the validity range as defined in Van Gent & Pozueta (2004).

For all parameters supplied, their values are checked versus the range of test conditions specified in Table 2 (Van Gent & Pozueta, 2004). When parameters are nan (by default), they are not checked.

For more details see Van Gent & Pozueta (2004), available here https://doi.org/10.1142/9789812701916_0281 or here: https://www.researchgate.net/publication/259260766_REAR-SIDE_STABILITY_OF_RUBBLE_MOUND_STRUCTURES

Parameters:

Rc (float | npt.NDArray[np.float64], optional) – Freeboard of the structure (m), by default np.nan
Rc_rear (float | npt.NDArray[np.float64], optional) – Vertical distance between still-water level and the crest at the rear side (m), by default np.nan
cot_phi (float | npt.NDArray[np.float64], optional) – Cotangent of the rear-side slope of the structure (-), by default np.nan
gamma_f (float | npt.NDArray[np.float64], optional) – Influence factor for surface roughness (-), by default np.nan
Dn50 (float | npt.NDArray[np.float64], optional) – Median nominal rock diameter (m), by default np.nan
rho_rock (float | npt.NDArray[np.float64], optional) – Rock density (kg/m^3), by default np.nan
rho_water (float | npt.NDArray[np.float64], optional) – Water density (kg/m^3), by default np.nan
Bc (float | npt.NDArray[np.float64], optional) – Width of the crest of the structure (m), by default np.nan
Hs (float | npt.NDArray[np.float64], optional) – Significant wave height (m), by default np.nan
Tmm10 (float | npt.NDArray[np.float64], optional) – Spectral wave period Tm-1,0 (s), by default np.nan
z1p (float | npt.NDArray[np.float64], optional) – _description_, by default np.nan
S (float | npt.NDArray[np.float64], optional) – Damage number (-), by default np.nan
N_waves (int | npt.NDArray[np.int32], optional) – Number of waves (-), by default np.nan

Van Gent (2007)

deltares_coastal_structures_toolbox.functions.structural.stability_rock_rear.vangent2007.calculate_damage_number_S(cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], cot_phi: float | ndarray[tuple[Any, ...], dtype[float64]], gamma: float | ndarray[tuple[Any, ...], dtype[float64]], Hs: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], Rc2_front: float | ndarray[tuple[Any, ...], dtype[float64]], Rc2_rear: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: int | ndarray[tuple[Any, ...], dtype[int32]], Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, M50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]] = nan) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the damage number S for rock at the rear side of a rubble mound structure with a crest element following Van Gent (2007).

For more details see Van Gent (2007), available here https://doi.org/10.1142/9789814282024_0002 or here https://www.researchgate.net/publication/259258925_REAR-SIDE_STABILITY_OF_RUBBLE_MOUND_STRUCTURES_WITH_CREST_ELEMENTS

Parameters:

cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
cot_phi (float | npt.NDArray[np.float64]) – Cotangent of the rear-side slope of the structure (-)
gamma (float | npt.NDArray[np.float64]) – Reduction factor for the wave runup (-)
Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
Rc (float | npt.NDArray[np.float64]) – Freeboard of the structure (m)
Rc2_front (float | npt.NDArray[np.float64]) – Vertical distance between top of rock material at the crest and the top of the crest element (m)
Rc2_rear (float | npt.NDArray[np.float64]) – Vertical distance between still-water level and the lowest point of the crest element at the rear side (m)
N_waves (int | npt.NDArray[np.int32]) – Number of waves (-)
Dn50 (float | npt.NDArray[np.float64], optional) – Median nominal rock diameter (m), by default np.nan
M50 (float | npt.NDArray[np.float64], optional) – Median rock mass (kg), by default np.nan
rho_rock (float | npt.NDArray[np.float64], optional) – Rock density (kg/m^3), by default np.nan

Returns:

The damage number S (-)

Return type:

float | npt.NDArray[np.float64]

Raises:

ValueError – Raises an error when neither Dn50 nor M50 is provided

deltares_coastal_structures_toolbox.functions.structural.stability_rock_rear.vangent2007.calculate_maximum_significant_wave_height_Hs(cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], cot_phi: float | ndarray[tuple[Any, ...], dtype[float64]], gamma: float | ndarray[tuple[Any, ...], dtype[float64]], S: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], Rc2_front: float | ndarray[tuple[Any, ...], dtype[float64]], Rc2_rear: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: int | ndarray[tuple[Any, ...], dtype[int32]], Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, M50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, tolerance: float = 0.0001, max_iterations: int = 10000) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the maximum allowable Hs for armour at the rear side of a rubble mound structure following Van Gent (2007).

For more details see Van Gent (2007), available here https://doi.org/10.1142/9789814282024_0002 or here https://www.researchgate.net/publication/259258925_REAR-SIDE_STABILITY_OF_RUBBLE_MOUND_STRUCTURES_WITH_CREST_ELEMENTS

Parameters:

cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
cot_phi (float | npt.NDArray[np.float64]) – Cotangent of the rear-side slope of the structure (-)
gamma (float | npt.NDArray[np.float64]) – Reduction factor for the wave runup (-)
S (float | npt.NDArray[np.float64]) – Damage number (-)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
Rc (float | npt.NDArray[np.float64]) – Freeboard of the structure (m)
Rc2_front (float | npt.NDArray[np.float64]) – Vertical distance between top of rock material at the crest and the top of the crest element (m)
Rc2_rear (float | npt.NDArray[np.float64]) – Vertical distance between still-water level and the lowest point of the crest element at the rear side (m)
N_waves (int | npt.NDArray[np.int32]) – Number of waves (-)
Dn50 (float | npt.NDArray[np.float64], optional) – Median nominal rock diameter (m), by default np.nan
M50 (float | npt.NDArray[np.float64], optional) – Median rock mass (kg), by default np.nan
rho_rock (float | npt.NDArray[np.float64], optional) – Rock density (kg/m^3), by default np.nan
tolerance (float, optional) – Tolerance in the iteration to Hs (m), by default 1e-4
max_iterations (int, optional) – Maximum number of iterations, by default 10000

Returns:

The maximum allowable significant wave height Hs (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_rear.vangent2007.calculate_nominal_rock_diameter_Dn50(cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]], cot_phi: float | ndarray[tuple[Any, ...], dtype[float64]], gamma: float | ndarray[tuple[Any, ...], dtype[float64]], S: float | ndarray[tuple[Any, ...], dtype[float64]], Hs: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], Rc: float | ndarray[tuple[Any, ...], dtype[float64]], Rc2_front: float | ndarray[tuple[Any, ...], dtype[float64]], Rc2_rear: float | ndarray[tuple[Any, ...], dtype[float64]], N_waves: int | ndarray[tuple[Any, ...], dtype[int32]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the minimum Dn50 for armour at the rear side of a rubble mound structure with a crest element following Van Gent (2007).

For more details see Van Gent (2007), available here https://doi.org/10.1142/9789814282024_0002 or here https://www.researchgate.net/publication/259258925_REAR-SIDE_STABILITY_OF_RUBBLE_MOUND_STRUCTURES_WITH_CREST_ELEMENTS

Parameters:

cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)
cot_phi (float | npt.NDArray[np.float64]) – Cotangent of the rear-side slope of the structure (-)
gamma (float | npt.NDArray[np.float64]) – Reduction factor for the wave runup (-)
S (float | npt.NDArray[np.float64]) – Damage number (-)
Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
Rc (float | npt.NDArray[np.float64]) – Freeboard of the structure (m)
Rc2_front (float | npt.NDArray[np.float64]) – Vertical distance between top of rock material at the crest and the top of the crest element (m)
Rc2_rear (float | npt.NDArray[np.float64]) – Vertical distance between still-water level and the lowest point of the crest element at the rear side (m)
N_waves (int | npt.NDArray[np.int32]) – Number of waves (-)

Returns:

The median nominal rock diameter Dn50 (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_rock_rear.vangent2007.check_validity_range(Rc: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Rc2_front: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Rc2_rear: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Gc: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, B_element: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, h: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, z1p: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, S: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, N_waves: int | ndarray[tuple[Any, ...], dtype[int32]] = nan) → None[source]

Check the parameter values vs the validity range as defined in Van Gent (2007).

For all parameters supplied, their values are checked versus the range of test conditions specified in Table 3 (Van Gent, 2007). When parameters are nan (by default), they are not checked.

For more details see Van Gent (2007), available here https://doi.org/10.1142/9789814282024_0002 or here https://www.researchgate.net/publication/259258925_REAR-SIDE_STABILITY_OF_RUBBLE_MOUND_STRUCTURES_WITH_CREST_ELEMENTS

Parameters:

Rc (float | npt.NDArray[np.float64], optional) – Freeboard of the structure (m), by default np.nan
Rc2_front (float | npt.NDArray[np.float64], optional) – Vertical distance between top of rock material at the crest and the top of the crest element (m), by default np.nan
Rc2_rear (float | npt.NDArray[np.float64], optional) – Vertical distance between still-water level and the lowest point of the crest element at the rear side (m), by default np.nan
Gc (float | npt.NDArray[np.float64], optional) – Width of the crest in front of crest element (m), by default np.nan
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal rock diameter (m), by default np.nan
B_element (float | npt.NDArray[np.float64], optional) – Width of the crest element (m), by default np.nan
h (float | npt.NDArray[np.float64], optional) – Water depth at the toe of the structure (m), by default np.nan
Hs (float | npt.NDArray[np.float64], optional) – Significant wave height (m), by default np.nan
Tmm10 (float | npt.NDArray[np.float64], optional) – Spectral wave period Tm-1,0 (s), by default np.nan
z1p (float | npt.NDArray[np.float64], optional) – Wave runup height exceeded by 1% of waves, by default np.nan
S (float | npt.NDArray[np.float64], optional) – Damage number (-), by default np.nan
N_waves (int | npt.NDArray[np.int32], optional) – Number of waves (-), by default np.nan

Stability Toe Berm

Takahashi et al. (1990)

deltares_coastal_structures_toolbox.functions.structural.stability_toe_berm.takahashi1990_caisson.calculate_nominal_diameter_Dn50(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], Tp: float | ndarray[tuple[Any, ...], dtype[float64]], hacc: float | ndarray[tuple[Any, ...], dtype[float64]], Bt: float | ndarray[tuple[Any, ...], dtype[float64]], rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]], g: float | ndarray[tuple[Any, ...], dtype[float64]] = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

calculate nominal diameter Dn50 for toe structure of caisson using Takahashi eta al 1990

For more information, please refer to: Takahashi, S., K. Tanimoto and K. Shimosako, 1990. “Wave and block forces on a caisson

covered with wave dissipating blocks.” Report of Port and Harbour Research Institute, Vol. 30, No.4, Yokosuka, Japan, p. 3-34.

AND

Tanimoto, K., T. Yagyu and Y. Goda, 1983. “Irregular wave tests for composite breakwater: foundations.” In proc. 18th int. conf. on Coastal Engineering, 14-19 Nov. 1982, Vol.III, ASCE, New York, p. 2144-2163

Parameters:

Hs (float | npt.NDArray[np.float64]) – Incident wave height near the toe (m)
Tp (float | npt.NDArray[np.float64]) – Wave period at the peak of the spectrum (s)
ht (float | npt.NDArray[np.float64]) – Water depth above the toe (m)
Bt (float | npt.NDArray[np.float64]) – Width of toe structure (m)
rho_rock (float | npt.NDArray[np.float64]) – Density of rock material (kg/m^3)
rho_water (float | npt.NDArray[np.float64]) –
Density of water (kg/m^3) g : float | npt.NDArray[np.float64], optional

Gravitational acceleration, by default 9.81

Returns:

Dn50 – Nominal diameter of toe armour (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_toe_berm.takahashi1990_caisson.calculate_significant_depth_above_toe_hacc(Dn50: float | ndarray[tuple[Any, ...], dtype[float64]], Tp: float | ndarray[tuple[Any, ...], dtype[float64]], Hs: float | ndarray[tuple[Any, ...], dtype[float64]], Bt: float | ndarray[tuple[Any, ...], dtype[float64]], rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]], g: float | ndarray[tuple[Any, ...], dtype[float64]] = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

calculate water level above toe structure of caisson using Takahashi et al 1990

For more information, please refer to: Takahashi, S., K. Tanimoto and K. Shimosako, 1990. “Wave and block forces on a caisson

covered with wave dissipating blocks.” Report of Port and Harbour Research Institute, Vol. 30, No.4, Yokosuka, Japan, p. 3-34.

AND

Tanimoto, K., T. Yagyu and Y. Goda, 1983. “Irregular wave tests for composite breakwater: foundations.” In proc. 18th int. conf. on Coastal Engineering, 14-19 Nov. 1982, Vol.III, ASCE, New York, p. 2144-2163

For this method an iterative method is used

Parameters:

Dn50 (float | npt.NDArray[np.float64]) – Nominal diameter of toe armour (m)
Tp (float | npt.NDArray[np.float64]) – Mean energy wave period or spectral wave period (s)
Hs (float | npt.NDArray[np.float64]) – Incident wave height near the toe (m)
Bt (float | npt.NDArray[np.float64]) – Width of toe structure (m)
rho_rock (float | npt.NDArray[np.float64]) – Density of rock material (kg/m^3)
rho_water (float | npt.NDArray[np.float64]) –
Density of water (kg/m^3) g : float | npt.NDArray[np.float64], optional

Gravitational acceleration, by default 9.81

Returns:

ht – Water depth above the toe (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_toe_berm.takahashi1990_caisson.calculate_significant_wave_height_Hs(Dn50: float | ndarray[tuple[Any, ...], dtype[float64]], Tp: float | ndarray[tuple[Any, ...], dtype[float64]], hacc: float | ndarray[tuple[Any, ...], dtype[float64]], Bt: float | ndarray[tuple[Any, ...], dtype[float64]], rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]], g: float | ndarray[tuple[Any, ...], dtype[float64]] = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

calculate significant wave height Hs for toe structure of caisson using Takahashi eta al 1990

For more information, please refer to: Takahashi, S., K. Tanimoto and K. Shimosako, 1990. “Wave and block forces on a caisson

covered with wave dissipating blocks.” Report of Port and Harbour Research Institute, Vol. 30, No.4, Yokosuka, Japan, p. 3-34.

AND

Tanimoto, K., T. Yagyu and Y. Goda, 1983. “Irregular wave tests for composite breakwater: foundations.” In proc. 18th int. conf. on Coastal Engineering, 14-19 Nov. 1982, Vol.III, ASCE, New York, p. 2144-2163

For this method an iterative method is used

Parameters:

Dn50 (float | npt.NDArray[np.float64]) – Nominal diameter of toe armour (m)
Tp (float | npt.NDArray[np.float64]) – Mean energy wave period or spectral wave period (s)
ht (float | npt.NDArray[np.float64]) – Water depth above the toe (m)
Bt (float | npt.NDArray[np.float64]) – Width of toe structure (m)
rho_rock (float | npt.NDArray[np.float64]) – Density of rock material (kg/m^3)
rho_water (float | npt.NDArray[np.float64]) –
Density of water (kg/m^3) g : float | npt.NDArray[np.float64], optional

Gravitational acceleration, by default 9.81

Returns:

Hs – Incident wave height near the toe (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_toe_berm.takahashi1990_caisson.calculate_stability_number_Ns(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], Tp: float | ndarray[tuple[Any, ...], dtype[float64]], hacc: float | ndarray[tuple[Any, ...], dtype[float64]], Bt: float | ndarray[tuple[Any, ...], dtype[float64]], beta: float | ndarray[tuple[Any, ...], dtype[float64]], g: float | ndarray[tuple[Any, ...], dtype[float64]] = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

calculate stability number Ns for for toe structure of caisson using Takahashi eta al 1990

For more information, please refer to: Takahashi, S., K. Tanimoto and K. Shimosako, 1990. “Wave and block forces on a caisson

covered with wave dissipating blocks.” Report of Port and Harbour Research Institute, Vol. 30, No.4, Yokosuka, Japan, p. 3-34.

AND

Tanimoto, K., T. Yagyu and Y. Goda, 1983. “Irregular wave tests for composite breakwater: foundations.” In proc. 18th int. conf. on Coastal Engineering, 14-19 Nov. 1982, Vol.III, ASCE, New York, p. 2144-2163

DOI: https://doi.org/10.9753/icce.v18.128

Parameters:

Hs (float | npt.NDArray[np.float64]) – Incident wave height near the toe (m)
Tmm10 (float | npt.NDArray[np.float64]) – Mean energy wave period or spectral wave period (s)
ht (float | npt.NDArray[np.float64]) – Water depth above the toe (m)
Bt (float | npt.NDArray[np.float64]) – Width of toe structure (m)
g (float | npt.NDArray[np.float64], optional) – Gravitational acceleration, by default 9.81

Returns:

Ns – Stability number Hs/Delta*Dn (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_toe_berm.takahashi1990_caisson.check_validity(Ns: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Bt: float | ndarray[tuple[Any, ...], dtype[float64]] = nan)[source]

Check the parameter values vs the validity range

For all parameters supplied, their values are checked versus the range of validity. When parameters are nan (by default), they are not checked.

For more information, please refer to: Takahashi, S., K. Tanimoto and K. Shimosako, 1990. “Wave and block forces on a caisson

covered with wave dissipating blocks.” Report of Port and Harbour Research Institute, Vol. 30, No.4, Yokosuka, Japan, p. 3-34.

AND

Tanimoto, K., T. Yagyu and Y. Goda, 1983. “Irregular wave tests for composite breakwater: foundations.” In proc. 18th int. conf. on Coastal Engineering, 14-19 Nov. 1982, Vol.III, ASCE, New York, p. 2144-2163

Parameters:

Ns (float | npt.NDArray[np.float64], optional) – _description_, by default np.nan
Bt (float | npt.NDArray[np.float64], optional) – _description_, by default np.nan

Gerding (1993)

deltares_coastal_structures_toolbox.functions.structural.stability_toe_berm.gerding1993.calculate_damage_Nod(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], ht: float | ndarray[tuple[Any, ...], dtype[float64]], h: float | ndarray[tuple[Any, ...], dtype[float64]], Dn50: float | ndarray[tuple[Any, ...], dtype[float64]], rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

calculate damage number Nod for toe structures using Gerding 1993

For more information, please refer to: Gerding, E. 1993. Toe structure stability of rubble mound breakwaters, M.Sc. thesis, Delft University of

Technology, Delft and Delft Hydraulics Report H1874, Delft.

https://resolver.tudelft.nl/uuid:51af1788-de9f-4ef3-8115-ffefb2e26f76

Parameters:

Hs (float | npt.NDArray[np.float64]) – Incident wave height near the toe (m)
ht (float | npt.NDArray[np.float64]) – Water depth above the toe (m)
h (float | npt.NDArray[np.float64]) – Water depth in front of the toe (m)
Dn50 (float | npt.NDArray[np.float64]) – Nominal diameter of toe armour (m)
rho_rock (float | npt.NDArray[np.float64]) – Density of rock material (kg/m^3)
rho_water (float | npt.NDArray[np.float64]) – Density of water (kg/m^3)

Returns:

Nod – Damage parameter (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_toe_berm.gerding1993.calculate_depth_above_toe_ht(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], Dn50: float | ndarray[tuple[Any, ...], dtype[float64]], h: float | ndarray[tuple[Any, ...], dtype[float64]], Nod: float | ndarray[tuple[Any, ...], dtype[float64]], rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

calculate depth above toe ht for toe structures using Gerding 1993

For more information, please refer to: Gerding, E. 1993. Toe structure stability of rubble mound breakwaters, M.Sc. thesis, Delft University of

Technology, Delft and Delft Hydraulics Report H1874, Delft.

https://resolver.tudelft.nl/uuid:51af1788-de9f-4ef3-8115-ffefb2e26f76

Parameters:

Hs (float | npt.NDArray[np.float64]) – Incident wave height near the toe (m)
Dn50 (float | npt.NDArray[np.float64]) – Nominal diameter of toe armour (m)
h (float | npt.NDArray[np.float64]) – Water depth in front of the toe (m)
Nod (float | npt.NDArray[np.float64]) – Damage parameter (-)
rho_rock (float | npt.NDArray[np.float64]) – Density of rock material (kg/m^3)
rho_water (float | npt.NDArray[np.float64]) – Density of water (kg/m^3)
g (float | npt.NDArray[np.float64], optional) – Gravitational acceleration, by default 9.81

Returns:

ht – Water depth above the toe (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_toe_berm.gerding1993.calculate_nominal_diameter_Dn50(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], ht: float | ndarray[tuple[Any, ...], dtype[float64]], h: float | ndarray[tuple[Any, ...], dtype[float64]], Nod: float | ndarray[tuple[Any, ...], dtype[float64]], rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

calculate nominal diameter Dn50 for toe structures using Gerding 1993

For more information, please refer to: Gerding, E. 1993. Toe structure stability of rubble mound breakwaters, M.Sc. thesis, Delft University of

Technology, Delft and Delft Hydraulics Report H1874, Delft.

https://resolver.tudelft.nl/uuid:51af1788-de9f-4ef3-8115-ffefb2e26f76

Parameters:

Hs (float | npt.NDArray[np.float64]) – Incident wave height near the toe (m)
ht (float | npt.NDArray[np.float64]) – Water depth above the toe (m)
h (float | npt.NDArray[np.float64]) – Water depth in front of the toe (m)
Nod (float | npt.NDArray[np.float64]) – Damage parameter (-)
rho_rock (float | npt.NDArray[np.float64]) – Density of rock material (kg/m^3)
rho_water (float | npt.NDArray[np.float64]) – Density of water (kg/m^3)
g (float | npt.NDArray[np.float64], optional) – Gravitational acceleration, by default 9.81

Returns:

Dn50 – Nominal diameter of toe armour (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_toe_berm.gerding1993.calculate_wave_height_Hs(Dn50: float | ndarray[tuple[Any, ...], dtype[float64]], ht: float | ndarray[tuple[Any, ...], dtype[float64]], h: float | ndarray[tuple[Any, ...], dtype[float64]], Nod: float | ndarray[tuple[Any, ...], dtype[float64]], rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

calculate wave height Hs for toe structures using Gerding 1993

For more information, please refer to: Gerding, E. 1993. Toe structure stability of rubble mound breakwaters, M.Sc. thesis, Delft University of

Technology, Delft and Delft Hydraulics Report H1874, Delft.

https://resolver.tudelft.nl/uuid:51af1788-de9f-4ef3-8115-ffefb2e26f76

Parameters:

Dn50 (float | npt.NDArray[np.float64]) – Nominal diameter of toe armour (m)
ht (float | npt.NDArray[np.float64]) – Water depth above the toe (m)
h (float | npt.NDArray[np.float64]) – Water depth in front of the toe (m)
Nod (float | npt.NDArray[np.float64]) – Damage parameter (-)
rho_rock (float | npt.NDArray[np.float64]) – Density of rock material (kg/m^3)
rho_water (float | npt.NDArray[np.float64]) – Density of water (kg/m^3)
g (float | npt.NDArray[np.float64], optional) – Gravitational acceleration, by default 9.81

Returns:

Hs – Incident wave height near the toe (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_toe_berm.gerding1993.check_validity(ht: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, h: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan)[source]

Check the parameter values vs the validity range as defined in Gerding (1993).

For all parameters supplied, their values are checked versus the range of validity specified by Gerding (1993). When parameters are nan (by default), they are not checked.

For more information, please refer to: Gerding, E. 1993. Toe structure stability of rubble mound breakwaters, M.Sc. thesis, Delft University of

Technology, Delft and Delft Hydraulics Report H1874, Delft.

https://resolver.tudelft.nl/uuid:51af1788-de9f-4ef3-8115-ffefb2e26f76

Parameters:

ht (float | npt.NDArray[np.float64], optional) – Water depth above the toe (m), by default np.nan
h (float | npt.NDArray[np.float64], optional) – Water depth in front of the toe (m), by default np.nan
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal diameter of toe armour (m), by default np.nan

Van der Meer (1998)

deltares_coastal_structures_toolbox.functions.structural.stability_toe_berm.vandermeer1998.calculate_damage_Nod(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], ht: float | ndarray[tuple[Any, ...], dtype[float64]], h: float | ndarray[tuple[Any, ...], dtype[float64]], Dn50: float | ndarray[tuple[Any, ...], dtype[float64]], rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

calculate damage number Nod for toe structures using van der Meer 1998

For more information, please refer to: WL|Delft Hydraulics (former Deltares), report number H2458/H3051, June, 1997 or Meer, J. Van der, 1998. “Geometrical design of coastal structures.” Infram publication Nr. 2.

Parameters:

Hs (float | npt.NDArray[np.float64]) – Incident significant wave height near the toe (m)
ht (float | npt.NDArray[np.float64]) – Water depth above the toe (m)
h (float | npt.NDArray[np.float64]) – Water depth in front of the toe (m)
Dn50 (float | npt.NDArray[np.float64]) – Nominal diameter of toe armour (m)
rho_rock (float | npt.NDArray[np.float64]) – Density of rock material (kg/m^3)
rho_water (float | npt.NDArray[np.float64]) – Density of water (kg/m^3)

Returns:

Nod – Damage parameter (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_toe_berm.vandermeer1998.calculate_depth_above_toe_ht(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], Dn50: float | ndarray[tuple[Any, ...], dtype[float64]], h: float | ndarray[tuple[Any, ...], dtype[float64]], Nod: float | ndarray[tuple[Any, ...], dtype[float64]], rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

calculate depth above toe ht for toe structures using van der Meer 1998

For more information, please refer to: WL|Delft Hydraulics (former Deltares), report number H2458/H3051, June, 1997 or Meer, J. Van der, 1998. “Geometrical design of coastal structures.” Infram publication Nr. 2.

Parameters:

Hs (float | npt.NDArray[np.float64]) – Incident significant wave height near the toe (m)
Dn50 (float | npt.NDArray[np.float64]) – Nominal diameter of toe armour (m)
h (float | npt.NDArray[np.float64]) – Water depth in front of the toe (m)
Nod (float | npt.NDArray[np.float64]) – Damage parameter (-)
rho_rock (float | npt.NDArray[np.float64]) – Density of rock material (kg/m^3)
rho_water (float | npt.NDArray[np.float64]) – Density of water (kg/m^3)
g (float | npt.NDArray[np.float64], optional) – Gravitational acceleration, by default 9.81

Returns:

ht – Water depth above the toe (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_toe_berm.vandermeer1998.calculate_nominal_diameter_Dn50(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], ht: float | ndarray[tuple[Any, ...], dtype[float64]], h: float | ndarray[tuple[Any, ...], dtype[float64]], Nod: float | ndarray[tuple[Any, ...], dtype[float64]], rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

calculate nominal diameter Dn50 for toe structures using van der Meer 1998

For more information, please refer to: WL|Delft Hydraulics (former Deltares), report number H2458/H3051, June, 1997 or Meer, J. Van der, 1998. “Geometrical design of coastal structures.” Infram publication Nr. 2.

Parameters:

Hs (float | npt.NDArray[np.float64]) – Incident significant wave height near the toe (m)
ht (float | npt.NDArray[np.float64]) – Water depth above the toe (m)
h (float | npt.NDArray[np.float64]) – Water depth in front of the toe (m)
Nod (float | npt.NDArray[np.float64]) – Damage parameter (-)
rho_rock (float | npt.NDArray[np.float64]) – Density of rock material (kg/m^3)
rho_water (float | npt.NDArray[np.float64]) – Density of water (kg/m^3)
g (float | npt.NDArray[np.float64], optional) – Gravitational acceleration, by default 9.81

Returns:

Dn50 – Nominal diameter of toe armour (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_toe_berm.vandermeer1998.calculate_wave_height_Hs(Dn50: float | ndarray[tuple[Any, ...], dtype[float64]], ht: float | ndarray[tuple[Any, ...], dtype[float64]], h: float | ndarray[tuple[Any, ...], dtype[float64]], Nod: float | ndarray[tuple[Any, ...], dtype[float64]], rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

calculate wave height Hs for toe structures using van der Meer 1998

For more information, please refer to: WL|Delft Hydraulics (former Deltares), report number H2458/H3051, June, 1997 or Meer, J. Van der, 1998. “Geometrical design of coastal structures.” Infram publication Nr. 2.

Parameters:

Dn50 (float | npt.NDArray[np.float64]) – Nominal diameter of toe armour (m)
ht (float | npt.NDArray[np.float64]) – Water depth above the toe (m)
h (float | npt.NDArray[np.float64]) – Water depth in front of the toe (m)
Nod (float | npt.NDArray[np.float64]) – Damage parameter (-)
rho_rock (float | npt.NDArray[np.float64]) – Density of rock material (kg/m^3)
rho_water (float | npt.NDArray[np.float64]) – Density of water (kg/m^3)
g (float | npt.NDArray[np.float64], optional) – Gravitational acceleration, by default 9.81

Returns:

Hs – Incident significant wave height near the toe (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_toe_berm.vandermeer1998.check_validity(Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, ht: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, h: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Nod: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Delta: float | ndarray[tuple[Any, ...], dtype[float64]] = nan)[source]

Check the parameter values vs the validity range as defined in Van der Meer (1998).

For all parameters supplied, their values are checked versus the range of validity specified by Van der Meer (1998). When parameters are nan (by default), they are not checked.

For more information, please refer to: WL|Delft Hydraulics (former Deltares), report number H2458/H3051, June, 1997 or Meer, J. Van der, 1998. “Geometrical design of coastal structures.” Infram publication Nr. 2.

Parameters:

Hs (float | npt.NDArray[np.float64], optional) – Incident significant wave height near the toe (m), by default np.nan
ht (float | npt.NDArray[np.float64], optional) – Water depth above the toe (m), by default np.nan
h (float | npt.NDArray[np.float64], optional) – Water depth in front of the toe (m), by default np.nan
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal diameter of toe armour (m), by default np.nan
Nod (float | npt.NDArray[np.float64], optional) – Damage parameter (-), by default np.nan
Delta (float | npt.NDArray[np.float64], optional) – Buoyant density (-), by default np.nan

Van Gent & Van der Werf (2014)

deltares_coastal_structures_toolbox.functions.structural.stability_toe_berm.vangentvanderwerf2014.calculate_damage_Nod(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], ht: float | ndarray[tuple[Any, ...], dtype[float64]], Bt: float | ndarray[tuple[Any, ...], dtype[float64]], tt: float | ndarray[tuple[Any, ...], dtype[float64]], Dn50: float | ndarray[tuple[Any, ...], dtype[float64]], rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha_armour_slope: float | ndarray[tuple[Any, ...], dtype[float64]], g: float = 9.81, c1: float = 0.032, c2: float = 0.3, c3: float = 1.0, c4: float = 3.0, c5: float = 1.0) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

calculate damage number Nod for toe structure using van Gent and van der Werf (2014)

For more information, please refer to: Van Gent, M.R.A. and I.M. van der Werf. 2014. Rock toe stability of rubble mound breakwaters,

Coastal Engineering, Vol. 83, pp. 166-176, Elsevier.

http://dx.doi.org/10.1016/j.coastaleng.2013.10.012

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Incident wave height near the toe (m)
Tmm10 (float | npt.NDArray[np.float64]) – Mean energy wave period or spectral wave period (s)
ht (float | npt.NDArray[np.float64]) – Water depth above the toe (m)
Bt (float | npt.NDArray[np.float64]) – Width of toe structure (m)
tt (float | npt.NDArray[np.float64]) – Height of toe structure (m)
Dn50 (float | npt.NDArray[np.float64]) – Nominal diameter of toe armour (m)
rho_rock (float | npt.NDArray[np.float64]) – Density of rock material (kg/m^3)
rho_water (float | npt.NDArray[np.float64]) – Density of water (kg/m^3)
cot_alpha_armour_slope (float | npt.NDArray[np.float64]) – Slope above structure (not used in formula, only in checks) (-)
g (float, optional) – Gravitational acceleration, by default 9.81
c1 (float, optional) – Coefficient in the toe stability formula, by default 0.032
c2 (float, optional) – Coefficient in the toe stability formula, by default 0.3
c3 (float, optional) – Coefficient in the toe stability formula, by default 1.0
c4 (float, optional) – Coefficient in the toe stability formula, by default 3.0
c5 (float, optional) – Coefficient in the toe stability formula, by default 1.0

Returns:

Nod – Damage parameter (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_toe_berm.vangentvanderwerf2014.calculate_nominal_diameter_Dn50(Hm0: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], ht: float | ndarray[tuple[Any, ...], dtype[float64]], Bt: float | ndarray[tuple[Any, ...], dtype[float64]], tt: float | ndarray[tuple[Any, ...], dtype[float64]], Nod: float | ndarray[tuple[Any, ...], dtype[float64]], rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha_armour_slope: float | ndarray[tuple[Any, ...], dtype[float64]], g: float = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

calculate nominal diameter Dn50 for toe structure using van Gent and van der Werf (2014)

For more information, please refer to: Van Gent, M.R.A. and I.M. van der Werf. 2014. Rock toe stability of rubble mound breakwaters,

Coastal Engineering, Vol. 83, pp. 166-176, Elsevier.

http://dx.doi.org/10.1016/j.coastaleng.2013.10.012

Parameters:

Hm0 (float | npt.NDArray[np.float64]) – Incident wave height near the toe (m)
Tmm10 (float | npt.NDArray[np.float64]) – Mean energy wave period or spectral wave period (s)
ht (float | npt.NDArray[np.float64]) – Water depth above the toe (m)
Bt (float | npt.NDArray[np.float64]) – Width of toe structure (m)
tt (float | npt.NDArray[np.float64]) – Height of toe structure (m)
Nod (float | npt.NDArray[np.float64]) – Damage parameter (-)
rho_rock (float | npt.NDArray[np.float64]) – Density of rock material (kg/m^3)
rho_water (float | npt.NDArray[np.float64]) – Density of water (kg/m^3)
cot_alpha_armour_slope (float | npt.NDArray[np.float64]) – Slope above structure (not used in formula, only in checks) (-)
g (float, optional) – Gravitational acceleration, by default 9.81

Returns:

Dn50 – Nominal diameter of toe armour (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_toe_berm.vangentvanderwerf2014.calculate_velocity_u_delta(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], ht: float | ndarray[tuple[Any, ...], dtype[float64]], g: float = 9.81)[source]

estimate characteristic orbital velocity above the toe structure

Parameters:

Hs (float | npt.NDArray[np.float64]) – Incident wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Wave period determined from spectrum (s)
ht (float | npt.NDArray[np.float64]) – Water depth above the toe structure
g (float, optional) – Gravitational acceleration, by default 9.81

Returns:

u_delta – Characteristic orbital velocity (m/s)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_toe_berm.vangentvanderwerf2014.check_validity(Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, tt: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, ht: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_armour_slope: float | ndarray[tuple[Any, ...], dtype[float64]] = nan)[source]

Check the parameter values vs the validity range as defined in Van Gent & Van der Werf (2014).

For all parameters supplied, their values are checked versus the range of validity specified by Van Gent & Van der Werf (2014). When parameters are nan (by default), they are not checked.

For more information, please refer to: Van Gent, M.R.A. and I.M. van der Werf. 2014. Rock toe stability of rubble mound breakwaters,

Coastal Engineering, Vol. 83, pp. 166-176, Elsevier.

http://dx.doi.org/10.1016/j.coastaleng.2013.10.012

Parameters:

Hs (float | npt.NDArray[np.float64], optional) – Significant wave height (m), by default np.nan
tt (float | npt.NDArray[np.float64], optional) – Height of toe structure (m), by default np.nan
ht (float | npt.NDArray[np.float64], optional) – Water depth above the toe (m), by default np.nan
cot_alpha_armour_slope (float | npt.NDArray[np.float64], optional) – Slope above structure (-), by default np.nan

Etemad-Shahidi et al. (2021)

deltares_coastal_structures_toolbox.functions.structural.stability_toe_berm.etemadshahidi2021.calculate_damage_Nod(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], h: float | ndarray[tuple[Any, ...], dtype[float64]], ht: float | ndarray[tuple[Any, ...], dtype[float64]], Bt: float | ndarray[tuple[Any, ...], dtype[float64]], m: float | ndarray[tuple[Any, ...], dtype[float64]], Dn50: float | ndarray[tuple[Any, ...], dtype[float64]], rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float = 1025.0, g: float = 9.81, c1: float = 1.2, c2: float = 11.2, c3: float = 1.75, c4: float = 0.16666666666666666, c5: float = 0.4, c6: float = -0.1, c7: float = 3.7) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate damage number Nod for toe structure using Etemad-Shahidi et al. (2021)

Here, Eq. 8 of Etemad-Shahidi et al. (2021) is implemented.

For more details see Etemad-Shahidi et al. (2021), available here: https://doi.org/10.1016/j.coastaleng.2020.103835

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
h (float | npt.NDArray[np.float64]) – Water depth (m)
ht (float | npt.NDArray[np.float64]) – Water depth above the toe (m)
Bt (float | npt.NDArray[np.float64]) – Width of toe structure (m)
m (float | npt.NDArray[np.float64]) – Tangent of the foreshore slope
Dn50 (float | npt.NDArray[np.float64]) – Nominal rock diameter (m)
rho_rock (float | npt.NDArray[np.float64]) – Rock density (kg/m^3)
rho_water (float) – Water density (kg/m^3), by default 1025.0
g (float, optional) – Gravitational constant (m/s^2), by default 9.81
c1 (float, optional) – Coefficient in the toe stability formula, by default 1.2
c2 (float, optional) – Coefficient in the toe stability formula, by default 11.2
c3 (float, optional) – Coefficient in the toe stability formula, by default 7.0/4.0
c4 (float, optional) – Coefficient in the toe stability formula, by default 1.0/6.0
c5 (float, optional) – Coefficient in the toe stability formula, by default 2.0/5.0
c6 (float, optional) – Coefficient in the toe stability formula, by default -1.0/10.0
c7 (float, optional) – Coefficient in the toe stability formula, by default 3.7

Returns:

The damage parameter Nod (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_toe_berm.etemadshahidi2021.calculate_nominal_diameter_Dn50(Hs: float | ndarray[tuple[Any, ...], dtype[float64]], Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], h: float | ndarray[tuple[Any, ...], dtype[float64]], ht: float | ndarray[tuple[Any, ...], dtype[float64]], Bt: float | ndarray[tuple[Any, ...], dtype[float64]], Nod: float | ndarray[tuple[Any, ...], dtype[float64]], m: float | ndarray[tuple[Any, ...], dtype[float64]], rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float = 1025.0, g: float = 9.81, c1: float = 1.2, c2: float = 11.2, c3: float = 1.75, c4: float = 0.16666666666666666, c5: float = 0.4, c6: float = -0.1, c7: float = 3.7) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the nominal rock diameter Dn50 for toe stability using Etemad-Shahidi et al. (2021)

Here, Eq. 8 of Etemad-Shahidi et al. (2021) is implemented.

For more details see Etemad-Shahidi et al. (2021), available here: https://doi.org/10.1016/j.coastaleng.2020.103835

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m)
Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
h (float | npt.NDArray[np.float64]) – Water depth (m)
ht (float | npt.NDArray[np.float64]) – Water depth above the toe (m)
Bt (float | npt.NDArray[np.float64]) – Width of toe structure (m)
Nod (float | npt.NDArray[np.float64]) – Damage parameter (-)
m (float | npt.NDArray[np.float64]) – Tangent of the foreshore slope
rho_rock (float | npt.NDArray[np.float64]) – Rock density (kg/m^3)
rho_water (float) – Water density (kg/m^3), by default 1025.0
g (float, optional) – Gravitational constant (m/s^2), by default 9.81
c1 (float, optional) – Coefficient in the toe stability formula, by default 1.2
c2 (float, optional) – Coefficient in the toe stability formula, by default 11.2
c3 (float, optional) – Coefficient in the toe stability formula, by default 7.0/4.0
c4 (float, optional) – Coefficient in the toe stability formula, by default 1.0/6.0
c5 (float, optional) – Coefficient in the toe stability formula, by default 2.0/5.0
c6 (float, optional) – Coefficient in the toe stability formula, by default -1.0/10.0
c7 (float, optional) – Coefficient in the toe stability formula, by default 3.7

Returns:

The nominal rock diameter Dn50 (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_toe_berm.etemadshahidi2021.calculate_significant_wave_height_Hs(Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]], h: float | ndarray[tuple[Any, ...], dtype[float64]], ht: float | ndarray[tuple[Any, ...], dtype[float64]], Bt: float | ndarray[tuple[Any, ...], dtype[float64]], Nod: float | ndarray[tuple[Any, ...], dtype[float64]], m: float | ndarray[tuple[Any, ...], dtype[float64]], Dn50: float | ndarray[tuple[Any, ...], dtype[float64]], rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float = 1025.0, g: float = 9.81, c1: float = 1.2, c2: float = 11.2, c3: float = 1.75, c4: float = 0.16666666666666666, c5: float = 0.4, c6: float = -0.1, c7: float = 3.7, smm10_init: float = 0.03, max_iter: int = 1000) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the maximum significant wave height Hs for toe stability using Etemad-Shahidi et al. (2021)

Here, Eq. 8 of Etemad-Shahidi et al. (2021) is implemented. Note that the Hs needs to be solved iteratively.

For more details see Etemad-Shahidi et al. (2021), available here: https://doi.org/10.1016/j.coastaleng.2020.103835

Parameters:

Tmm10 (float | npt.NDArray[np.float64]) – Spectral wave period Tm-1,0 (s)
h (float | npt.NDArray[np.float64]) – Water depth (m)
ht (float | npt.NDArray[np.float64]) – Water depth above the toe (m)
Bt (float | npt.NDArray[np.float64]) – Width of toe structure (m)
Nod (float | npt.NDArray[np.float64]) – Damage parameter (-)
m (float | npt.NDArray[np.float64]) – Tangent of the foreshore slope
Dn50 (float | npt.NDArray[np.float64]) – Nominal rock diameter (m)
rho_rock (float | npt.NDArray[np.float64]) – Rock density (kg/m^3)
rho_water (float) – Water density (kg/m^3), by default 1025.0
g (float, optional) – Gravitational constant (m/s^2), by default 9.81
c1 (float, optional) – Coefficient in the toe stability formula, by default 1.2
c2 (float, optional) – Coefficient in the toe stability formula, by default 11.2
c3 (float, optional) – Coefficient in the toe stability formula, by default 7.0/4.0
c4 (float, optional) – Coefficient in the toe stability formula, by default 1.0/6.0
c5 (float, optional) – Coefficient in the toe stability formula, by default 2.0/5.0
c6 (float, optional) – Coefficient in the toe stability formula, by default -1.0/10.0
c7 (float, optional) – Coefficient in the toe stability formula, by default 3.7
smm10_init (float, optional) – Initial wave steepness sm-1,0 (-) for the iterative solution, by default 0.03
max_iter (int, optional) – Maximum number of iterations, by default 1000

Returns:

The significant wave height Hs (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.structural.stability_toe_berm.etemadshahidi2021.check_validity(Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Tmm10: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, h: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, ht: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Bt: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Dn50: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, m: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, Nod: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, cot_alpha_armour_slope: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, rho_armour: float | ndarray[tuple[Any, ...], dtype[float64]] = nan, rho_water: float = 1025.0)[source]

Check the parameter values vs the validity range of the Etemad-Shahidi et al. (2021) formula.

For all parameters supplied, their values are checked versus the range of test conditions specified by Etemad-Shahidi et al. (2021) in Table 3. When parameters are nan (by default), they are not checked.

For more details see Etemad-Shahidi et al. (2021), available here: https://doi.org/10.1016/j.coastaleng.2020.103835

Parameters:

Hs (float | npt.NDArray[np.float64], optional) – Significant wave height (m), by default np.nan
Tmm10 (float | npt.NDArray[np.float64], optional) – Spectral wave period Tm-1,0 (s), by default np.nan
h (float | npt.NDArray[np.float64], optional) – Water depth (m), by default np.nan
ht (float | npt.NDArray[np.float64], optional) – Water depth above the toe (m), by default np.nan
Bt (float | npt.NDArray[np.float64], optional) – Width of toe structure (m), by default np.nan
Dn50 (float | npt.NDArray[np.float64], optional) – Nominal rock diameter (m), by default np.nan
m (float | npt.NDArray[np.float64], optional) – Tangent of the foreshore slope, by default np.nan
Nod (float | npt.NDArray[np.float64], optional) – Damage parameter (-), by default np.nan
cot_alpha_armour_slope (float | npt.NDArray[np.float64], optional) – Cotangent of the front-side armour slope of the structure (-), by default np.nan
rho_armour (float | npt.NDArray[np.float64], optional) – Armour rock density (kg/m^3), by default np.nan
rho_water (float, optional) – Water density (kg/m^3), by default 1025.0

General functions

deltares_coastal_structures_toolbox.functions.core_physics.calculate_Dn50_from_M50(M50: float | ndarray[tuple[Any, ...], dtype[float64]], rho_rock: float = 2650) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the nominal rock diameter Dn50 from median rock mass M50

Parameters:

M50 (float | npt.NDArray[np.float64]) – Median rock mass (kg)
rho_rock (float, optional) – Rock density (kg/m^3), by default 2650

Returns:

The nominal rock diameter Dn50 (m)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.core_physics.calculate_Iribarren_number_ksi(H: float | ndarray[tuple[Any, ...], dtype[float64]], T: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the Iribarren number ksi

This function calculates the Iribarren number ksi, which is a dimensionless parameter that characterizes different wave breaking regimes.

Parameters:

H (float | npt.NDArray[np.float64]) – Wave height (m)
T (float | npt.NDArray[np.float64]) – Wave period (s)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)

Returns:

The Iribarren number ksi (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.core_physics.calculate_M50_from_Dn50(Dn50: float | ndarray[tuple[Any, ...], dtype[float64]], rho_rock: float = 2650) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the median rock mass M50 from the nominal rock diameter Dn50

_extended_summary_

Parameters:

Dn50 (float | npt.NDArray[np.float64]) – Nominal rock diameter (m)
rho_rock (float, optional) – Rock density (kg/m^3), by default 2650

Returns:

The median rock mass M50 (kg)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.core_physics.calculate_Nod_from_S(S: float | ndarray[tuple[Any, ...], dtype[float64]], G: float | ndarray[tuple[Any, ...], dtype[float64]], nv: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Estimates Nod value from S value

Estimation of Nod damage value from S damage value according to CEM (2006) and the Rock Manual (2007, 2012)

Parameters:

S (In general the Nod is about half the value of) – Damage value based on eroded cross sectional area
G (float | npt.NDArray[np.float64]) –

Gradation factor depending on armour layer, G = 1 for concrete armour
units and 1.2 - 1.6 for stone armor
nv (float | npt.NDArray[np.float64]) – Porosity depending on armour layer, generally between 0.4 and 0.6
S

Returns:

Nod – Number of displaced units normalized to 1 unit width of structure

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.core_physics.calculate_S_from_Nod(Nod: float | ndarray[tuple[Any, ...], dtype[float64]], G: float | ndarray[tuple[Any, ...], dtype[float64]], nv: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Estimates S value from Nod value

Estimation of S damage value from Nod damage value according to CEM (2006) and the Rock Manual (2007, 2012)

Parameters:

Nod (In general the S is about twice the value of) – Number of displaced units normalized to 1 unit width of structure
G (float | npt.NDArray[np.float64]) –

Gradation factor depending on armour layer, G = 1 for concrete armour
units and 1.2 - 1.6 for stone armor
nv (float | npt.NDArray[np.float64]) – Porosity depending on armour layer, generally between 0.4 and 0.6
Nod

Returns:

S – Damage value based on eroded cross sectional area

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.core_physics.calculate_buoyant_density_Delta(rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate buoyant density

Calculates thebuoyant density of rock material in water.

Parameters:

rho_rock (float | npt.NDArray[np.float64]) – Rock density (kg/m^3)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)

Returns:

The buoyant density Delta (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.core_physics.calculate_critical_Iribarren_number_ksi_mc(c_pl: float | ndarray[tuple[Any, ...], dtype[float64]], c_s: float | ndarray[tuple[Any, ...], dtype[float64]], P: float | ndarray[tuple[Any, ...], dtype[float64]], cot_alpha: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the critical Iribarren number ksi_mc

This function calculates the critical Iribarren number ksi_mc, used in different formulas for rock stability.

Parameters:

c_pl (float | npt.NDArray[np.float64]) – Coefficient for plunging waves (-)
c_s (float | npt.NDArray[np.float64]) – Coefficient for surging waves (-)
P (float | npt.NDArray[np.float64]) – Notional permeability coefficient (-)
cot_alpha (float | npt.NDArray[np.float64]) – Cotangent of the front-side slope of the structure (-)

Returns:

The critical Iribarren number ksi_mc (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.core_physics.calculate_local_wavelength(T: float | ndarray[tuple[Any, ...], dtype[float64]], h: float | ndarray[tuple[Any, ...], dtype[float64]], g: float | ndarray[tuple[Any, ...], dtype[float64]] = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate local wave length for wave with period T at depth h, using approximation of dispersion relation

Parameters:

T (float | npt.NDArray[np.float64]) – Wave period
h (float | npt.NDArray[np.float64]) – Water depth
g (float | npt.NDArray[np.float64], optional) – Gravitational acceleration, by default 9.81

Returns:

L – Wave length at local water depth

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.core_physics.calculate_stability_number_Ns(H: float | ndarray[tuple[Any, ...], dtype[float64]], D: float | ndarray[tuple[Any, ...], dtype[float64]], rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]], rho_water: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate the stability number Ns

The stability number Ns is commonly used in empirical formulas regarding the stability of coastal structures.

Parameters:

H (float | npt.NDArray[np.float64]) – Wave height (m)
D (float | npt.NDArray[np.float64]) – Rock diameter (m)
rho_rock (float | npt.NDArray[np.float64]) – Rock density (kg/m^3)
rho_water (float | npt.NDArray[np.float64]) – Water density (kg/m^3)

Returns:

The stability number Ns (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.core_physics.calculate_wave_steepness_s(H: float | ndarray[tuple[Any, ...], dtype[float64]], T: float | ndarray[tuple[Any, ...], dtype[float64]], g: float = 9.81) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Calculate wave steepness

Determines the wave steepness based on the deep water wave lenght corresponding to the wave period supplied.

Parameters:

H (float | npt.NDArray[np.float64]) – Wave height (m)
T (float | npt.NDArray[np.float64]) – Wave period Tm-1,0 (s)
g (float, optional) – Gravitational constant (m/s^2), by default 9.81

Returns:

Deep water wave steepness s (-)

Return type:

float | npt.NDArray[np.float64]

deltares_coastal_structures_toolbox.functions.core_physics.check_usage_Dn50_or_M50(Dn50: float | ndarray[tuple[Any, ...], dtype[float64]], M50: float | ndarray[tuple[Any, ...], dtype[float64]], rho_rock: float | ndarray[tuple[Any, ...], dtype[float64]]) → float | ndarray[tuple[Any, ...], dtype[float64]][source]

Check usage of Dn50 or M50

This function checks whether Dn50 or M50 is provided. If M50 is provided, it calculates Dn50 from M50.

Parameters:

Dn50 (float | npt.NDArray[np.float64]) – Nominal rock diameter (m)
M50 (float | npt.NDArray[np.float64]) – Median rock mass (kg)
rho_rock (float | npt.NDArray[np.float64]) – Rock density (kg/m^3)

Returns:

The nominal rock diameter Dn50 (m)

Return type:

float | npt.NDArray[np.float64]

Raises:

ValueError – Raise error if neither Dn50 nor M50 is provided

deltares_coastal_structures_toolbox.functions.core_physics.check_usage_stabilitynumber(Hs: float | ndarray[tuple[Any, ...], dtype[float64]] = None, Dn: float | ndarray[tuple[Any, ...], dtype[float64]] = None, Delta: float | ndarray[tuple[Any, ...], dtype[float64]] = None, Ns: float | ndarray[tuple[Any, ...], dtype[float64]] = None) → float | ndarray[tuple[Any, ...], dtype[float64]] | str[source]

Calculates missing value from stability number Ns = Hs / Delta*Dn

Parameter that is None in the input will be calculated

Parameters:

Hs (float | npt.NDArray[np.float64]) – Significant wave height (m), by default None
Dn (float | npt.NDArray[np.float64], optional) – Nomincal diameter (m), by default None
Delta (float | npt.NDArray[np.float64], optional) – Relative buoyant density of material, by default None
Ns (float | npt.NDArray[np.float64], optional) – Stability number, by default None

Returns:

(missing parameter value, missing parameter as calculated)

Return type:

Union[float | npt.NDArray[np.float64], str]

Raises:

ValueError – More then one missing variable
ValueError – No missing variable

deltares_coastal_structures_toolbox.functions.core_utility.check_variable_validity_range(variable_name: str, formula_name: str, values: float, min_value: float, max_value: float) → bool[source]

Check if a variable is within the validity range for a formula and raise a warning if not.

Parameters:

variable_name (str) – Name of the variable to check.
formula_name (str) – Name of the formula for which the validity range is checked.
value (float) – Value of the variable to check.
min_value (float) – Minimum value of the validity range.
max_value (float) – Maximum value of the validity range.

Returns:

A boolean with True if the value is within the validity range, False otherwise.

Return type:

bool