Forces exerted on the crown wall

Fuerza Sobre El Espaldon

The following equation is used when designing the parapet for a Cubipod breakwater. It is obtained from specific laboratory tests, conducted to estimate the maximum horizontal force (Fh) and the vertical force (sub-pressures) for the wave that has generated the maximum horizontal force (Fv(Fh)). Although these actions occur separately in time, they are given at the same time (to be on the safe side).

Fh = ρw * g * hf2 * 0.5 * ( -1.25 + 1.80 *
γf * Ru Rc
+ 0.82 * (
Rc - Ac hf
) + 0.16 * √ L01 / Ba ) 2
Fv (Fh) = ρw * g * hf * Be * 0.5 * ( -0.6 + 0.40 *
γf * Ru Rc
+ 0.27 * (
Rc - Ac hf
) + 0.16 * √ L01 / Ba - 1.03 *
wc hf
) 2
2.48Hs > Ru = Ru0.1% = {
1.12 Hs ξm          ξm <=1.5 1.34 Hs ξm0.55   ξm >1.5
with ξm = tan α / √ Hs / L01

Where Rc is the freeboard of the structure, Ac is the freeboard of the upper berm armor, Yf is the roughness factor (0.46 for single-layer Cubipods and 0.44 for double-layer Cubipods), Ba is the upper berm width, Hs is the significant wave height at the breakwater toe, tanα is the slope gradient, wc is the parapet foundation elevation, Be is the width of the parapet base, hf is the parapet height, ρw is the seawater density (in kg/m3 for N/m and dimensions in metres), g is the gravitational acceleration and L01 = (gT012/2π)•tanh(2πhs/L01)

The validity ranges for the variables in the above equations are:

  • 0.30<γf(Ru/Rc)<0.96

  • 0.066<(Rc-Ac)/hf<0.589

  • 0.0127<wc/hf<0.266

  • 3.13<(L01/Ba)0.5<6.59

Where the armor for conventional double-layer cubes is concerned, Cubipod armor significantly reduces the forces exerted on the crown wall, thereby making it possible to reduce the weight of the crown wall to withstand sliding (the most frequent cause of failure).