Diagram Loads on Caisson Breakwaters by Slightly Breaking Waves (Goda Method)

Shown are the results of the method of Goda to determine the pressure loads of a Caisson breakwater by slightly breaking waves without consideration of pressure impact.
The formulae for the calculated parameters are shown in the lower part of the page for the purpose of clarity.

The lever arm of the horizontal force \( s_z \) and the lever arm of the uplift force \( s_x \) result from a geometrical approach.

Formulae for the method of Goda:

Theoretical maximum height of the pressure figure above SWL \( \eta^* = 0.75 \cdot \left( 1 + \cos( \theta ) \right) \cdot H_D \),
Actual maximum height of the pressure figure above SWL \( R_C^* = \min \left\{ \eta^* ; R_C \right\} \),
Coefficient \( \alpha_1 = 0.6 + \frac{1}{2} \cdot \left( \frac{4 \pi \cdot h_s / L}{\sinh \left(4 \pi \cdot h_s / L \right)} \right)^2 \),
Coefficient \( \alpha_2 = \min \left( \frac{h_D - d}{3 \cdot h_D} \cdot \left( \frac{H_D}{d} \right)^2 ; \frac{2 \cdot d}{H_D} \right) \),
Coefficient \( \alpha_3 = 1 - \frac{h'}{h_s} \cdot \left( 1 - \frac{1}{\cosh \left( 2 \pi \cdot h_s / L \right)} \right) \),
Wave pressure ordinate \( p_1 = \frac{1}{2} \cdot \left( 1 + \cos \theta \right) \cdot \left( \alpha_1 + \alpha_2 \cdot \cos^2 \theta \right) \cdot \rho_w \cdot g \cdot H_D \),
Wave pressure ordinate \( p_2 = \frac{p_1}{\cosh \left( 2 \pi \cdot h_s / L \right)} \),
Wave pressure ordinate \( p_3 = \alpha_3 \cdot p_1 \),
Wave pressure ordinate \( p_4 = \begin{cases} p_1 \cdot \left( 1 - R_C / \eta^* \right) & \text{ for } \eta^* > R_C \\ 0 & \text{ for } \eta^* \leq R_C \end{cases} \),
Uplift pressure ordinate \( p_u = \frac{1}{2} \cdot \left( 1 + \cos \theta \right) \cdot \alpha_1 \cdot \alpha_3 \cdot \rho_w \cdot g \cdot H_D \),
Horizontal force \( F_h = \frac{1}{2} \cdot \left( p_1 + p_3 \right) \cdot h' + \frac{1}{2} \cdot \left( p_1 + p_4 \right) \cdot R_C^* \),
Uplift force \( F_u = \frac{1}{2} \cdot p_u \cdot B_C \),
Torsional moment around the back edge of the Caisson due to the horizontal force \( M_{F_h} = \frac{1}{6} \cdot \left( 2 \cdot p_1 + p_3 \right) \cdot h'^2 + \frac{1}{2} \cdot \left( p_1 + p_4 \right) \cdot h' \cdot R_C^* + \frac{1}{6} \cdot \left( p_1 + 2 \cdot p_4 \right) \cdot {R_C^*}^2 \),
Torsional moment around the back edge of the caisson due to the uplift force \( M_{F_u} = \frac{2}{3} \cdot F_u \cdot B_C \).

The following also applies: Sea water density \( \rho_w = 1025 \frac{kg}{m^3} \), and acceleration due to gravity \( g = 9.81 \frac{m}{s^2} \).

The field of Loads on Structures is part of the module Coastal Dynamics and Engineering Design within the specialization Coastal and Ocean Engineering of the master programmes Civil and Environmental Engineering.