Modeling elastic wave propagation through a partially saturated poroviscoelastic interlayer by fractional order derivatives

Abstract

The reflection and transmission problems of elastic waves through a partially saturated porous interlayer sandwiched between two elastic solid half-spaces are investigated. The partially saturated porous interlayer contains solid phase, gas phase and liquid phase. The solid frame is modeled by the fractional Zener model where the fractional order derivatives are used to describe the complex history-dependent viscoelastic behavior. Due to the coupled effects of the multiple fields, there exist three longitudinal waves and one transverse wave in the porous medium. The numerical results of reflection and transmission coefficients and the energy dissipation ratios are provided and shown graphically. The effects of the gas saturation, the interlayer thickness and the viscoelasticity of the solid frame are discussed based upon the numerical results. It is observed that the reflection and transmission coefficients and the energy dissipation ratios are affected noticeably by the gas saturation, the interlayer thickness and the viscoelasticity of the solid frame. In particular, there exists the characteristic gas saturation where the energy dissipation increases drastically.