In the present paper the evolution of the amplitudes of acceleration waves in incompressible saturated poroelastic solids within the framework of the geometrically linear theory is examined. The incompressible porous media model by Bowen is adopted to describe the mechanical behaviour of an incompressible two‐phase system. The underlying assumption made is that the amplitudes do not change tangentially to the wave fronts. The differential equations governing the amplitudes of acceleration waves are derived and the explicit solutions are obtained. The results indicate that the amplitudes of acceleration waves may either decay to vanish or grow to infinity in finite time, which depends on the geometrical property of the initial shapes of the wave fronts and the diffusion effect between the two phases. In particular, the longitudinal acceleration waves in the liquid are completely carried by the solid skeleton. The behaviour of acceleration waves in the porous medium is similar to that in isotropic elastic non‐porous solids.

SUMMARYIn this study, the prediction model proposed by Sassa et al. (Geotechnique 2001; 51(10):847-857) for the wave-induced progressive liquefaction in marine sediment, based on two-layered inviscid fluid system, is re-examined. An alternative approach with a similar framework of Sassa et al. (Geotechnique 2001; 51(10):847-857) is developed to correct the inappropriate mechanism of wave components used. Then, a two-layered wave model which includes viscous effects is established and applied to describe the progressive nature of wave-induced liquefaction. A comprehensive comparison shows that Sassa's model overestimates the maximum liquefaction depth. It is found that the viscosity of liquefied soil cannot be ignored and the solution for an infinite seabed is not suitable for liquefaction analysis of shallow seabed. A parametric study demonstrates the significant influence of numerous wave and soil characteristics on the liquefaction depth.