Based on cnoidal wave theory and expanding Biot consolidation theory

the mathematical solutions to the problems of oblique incidence shallow water wave reflected by vertical breakwater resting on permeable elastic seabed are given

and accordingly the analytical solutions to the shallow wave-induced seepage pressure are derived by applying the eigenfunction expansion approach. Then the wave-induced uplift force and overturning moment caused by the seepage pressure on the bottom of vertical breakwater are accordingly evaluated and compared with horizontal wave force and moment. The evaluating results demonstrate that in certain condition

the wave-induced seepage loads may have same order of magnitude as the direct wave loads. The variation of incident wave angle

sea water and seepage condition

and structure geometry condition may have some influence on wave-induced seepage loads

especially on wave-induced seepage overturning moment. The cnoidal wave-induced seepage loads are obviously larger than those predicted by Airy wave theory for shallow water

it denotes that the cnoidal wave theory can reflect wave nonlinear effects.