Transient Dynamic Analysis of Gradient-Saturated Viscoelastic Porous Media

Abstract

In the present work, by considering the inhomogeneity, solid skeleton viscosity, and compressibility of solid particles and fluid, the calculation formulations of reverberation ray matrix method (RRMM) is established for transient response of viscoelastic porous medium. The derivation process of the formulas and calculation method is described in detail herein. Feasibility and efficiency of the present approach are validated by comparing the solutions with those obtained from other methods. As numerical examples, by assuming that the material properties of the saturated poroviscoelastic media have an exponential law distribution along the thickness coordinate, the transient response, in terms of displacement of solid skeleton, total stress, and pore fluid pressure, are examined by using numerical inverse Laplace transform. The effects of inhomogeneity on transient response of gradient saturated poroviscoelastic media are demonstrated and discussed. The results show that there are significant effects of inhomogeneity on compressive wave propagation and that RRMM is an effective way for solving the partial differential equations with variable coefficients in a mathematic model of saturated porous media with gradient-variation properties.