On constitutive modelling of linear poroviscoelastic solids

Abstract

In this paper we develop a three-dimensional constitutive model to describe the linear viscoelastic behavior of fluid-saturated porous solids. The proposed model is based on a representation of the solid free energy by equilibrium and non-equilibrium parts. Constitutive equations corresponding to a compressible solid matrix/phase and an incompressible solid matrix/phase are derived separately. For illustration, the theory is then applied to the classical Terzaghi's problem. To show the viscous effective on the diffusion of pore pressure and on the response of solid displacement, numerical results are compared with those obtained for the poroelastic response. Aside from the occurrence of secondary consolidation, it is also found that the evolution of viscous strains may induce an increase in pore pressure, which arises from viscous strain rates playing the role of a nonuniform source term in the equation governing the pore pressure diffusion.