Asymptotic Determination of the Liquefaction Depth for Short and Long Water Waves

In this work, an analytical solution that models the dynamic response of a poroelastic soil, induced by the action of water waves in a stratified fluid, is obtained. We propose a reduction of the generalized governing equations for the limit when the horizontal displacements of the porous soil are very small compared with the vertical displacements. The results obtained are similar to those calculated with the governing equations in their complete form. We consider that the instantaneous liquefaction depth is unknown; therefore, the boundary value problem is solved as an eigenvalue problem. The instantaneous liquefaction depth is calculated for a wide range of wave frequencies, from long waves to short waves. It is found that liquefaction depth increases with increasing wavelength. For large values of soil shear modulus, the liquefaction depth increases because the pore pressure magnitude is larger than for the case of soils with low shear modulus. This work can be used as a benchmark to identify the effects that the physical parameters of a poroelastic soil have on the liquefaction depth.