Abstract:

In the framework of finite deformation theory, a theoretical model of poroviscoelasticity is proposed which is based on logarithmic strain and Kelvin rheological model. The model is obtained by assuming a linear relationship between Kirchhoff stress and pore pressure and logarithmic strain and the variation of Lagrangian porosity, and then directly replacing the infinitesimal strain in the linear pore viscoelastic model with the logarithmic strain. As a verification, the theoretical model is used to study the classic Terzaghi's one-dimensional consolidation problem. By comparing with the numerical results of the poroelastic finite deformation model, the results show that the viscoelastic response and elastic response curves of the pore solid skeleton are almost identical in the early stage of consolidation, but with the passage of time, the viscous response of the pore solid skeleton gradually dominates the deformation of the skeleton and affects the final result of consolidation. In addition, the viscous response of the skeleton delays the diffusion of pore pressure. In addition, by setting the viscosity contribution coefficient ζ=0.001, the poroviscoelastic response is numerically "degraded" to the poroelastic response, which verifies the correctness of the model to a certain extent.

Key words: poroviscoelasticity, logarithmic strain, finite deformation, finite elements, rheological model