Threshold to liquefaction in granular materials as a formation of strong wave discontinuity in poroelastic media

We consider a one-dimensional problem of propagation of acoustic waves in a nonlinear poroelastic saurated material. Stress-strain relations in the skeleton are described by Signorini-type constitutitve equations. Material parameters depend on the current porosity. The governing set of equations describes changes of extension of the skeleton, and of the mass density of the fluid, partial velocities of the skeleton and of the fluid and a porosity. We rely on a second order approximation. Relations of the critical time to an initial porosity and to an initial amplitude are discussed. The connection to the threshold of liquefaction in granular materials is indicated.