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.

在本文中，我们开发了一个三维本构模型来描述流体饱和多孔固体的线性粘弹性行为。所提出的模型基于平衡和非平衡部分的固体自由能表示。分别推导出可压缩固体基质/相和不可压缩固体基质/相对应的本构方程。为了说明，然后将该理论应用于经典的 Terzaghi 问题。为了显示粘性对孔隙压力扩散和固体位移响应的影响，数值结果与多孔弹性响应得到的结果进行了比较。除了发生二次固结外，还发现粘性应变的演变可能导致孔隙压力的增加，