Growth and decay of acceleration waves in incompressible saturated poroelastic solids

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 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.