Diagram Loads on Caisson Breakwaters by Standing Waves (Sainflou Method)

Shown are the results of the method of Sainflou to determine the pressure loads of a Caisson breakwater by standing waves.
The formulae for the calculated parameters are shown in the lower part of the page for the purpose of clarity.

The method of Miche-Rundgren for reflection coefficients \( 0.9 \leq K_r < 1.0 \) is as well taken into account as the increase of the seaward bound horizontal force \( F_{h-} \) according to Oumeraci et al.

The lever arms result from a geometrical approach.

Lernplattform des Leichtweiß-Institut für Wasserbau

h₀ = 0 p₁ = 0 p₂ = 0 p₃ = 0

Landward bound horizontal force F_h+ = 0 kN/m

Seaward bound horizontal force F_h-,d = 0 kN/m
(Note: has been multiplied by the factor 1.3)

Reflection coefficient:

H_d = 1.2 m
(is used instead of H.)

Lever arms of the horizontal forces:
s_Fh+ = 0
s_Fh- = 0

Formulae for the method of Sainflou :

Average water level rise with wave motion \( h_0 = \frac{\pi \cdot H^2}{L} \cdot \coth(\frac{2\pi \cdot d}{L}) \),
Pressure ordinate \( p_1 = \frac{\rho_w \cdot g \cdot H}{\cosh(\frac{2\pi \cdot d}{L})} \),
Pressure ordinate \( p_2 = ( p_1 + \rho_w \cdot g \cdot d ) \cdot \left( \frac{H + h_0}{d + H + h_0} \right) \),
Pressure ordinate \( p_3 = \rho_w \cdot g \cdot ( H - h_0 ) \),
Landward bound horizontal force \( F_{h+} = \frac{1}{2} \cdot \left[ p_2 \cdot ( H + h_0 ) + ( p_2 + p_1) \cdot d \right] \),
Seaward bound horizontal force \( F_{h-} = \frac{1}{2} \cdot \left[ p_3 \cdot ( H - h_0 ) + ( p_3 + p_1 ) \cdot ( d - H + h_0 ) \right] \).

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

Method of Miche-Rundgren :
Design wave height \( H_{d} = \frac{( 1 + K_r ) \cdot H}{2} \)

Increase of the seaward bound horizontal force \( F_{h-} \) according to Oumeraci et al. for relative wave heights \( \frac{H_d}{d} < 0.6 \) :
Seaward bound horizontal force \( F_{h-,d} = F_{h-} \cdot 1.3 \)

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.