The final time of existence (critical time) of acoustic waves is a characteristic feature of nonlinear hyperbolic models. We consider such a problem for poroelastic saturated materials whose material properties are described by Signorini-type constitutive relations for stresses in the skeleton and whose material parameters depend on the current porosity. In the one-dimensional case under considerations the governing set of equations describes changes of an extension of the skeleton, a 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.