On nonlinear Biot's consolidation models

Abstract

The propagation of elastic waves in a fluid-saturated porous solid is generally set within the framework of Biot’s mechanics. Its modelling is motivated by many applications such as the study of poroelastic behavior of rocks for engineering reservoir models [4] or the detection of buried objects [18]. The general theory of linear poroelasticity was first developed by Biot [5–8] and its interest for soil mechanics was first observed by Terzaghi [16]. The propagation is governed by a system of coupled equations which reads as follows: ⎪⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎪⎩ (x) 2u t2 −∇ ( ∗(x) t div u ) −∇(( (x)+ (x))div u)− div( (x)∇u) + ∇p = f(t, x),