Three-field model for wave propagation in porous media based on mixture theories

Abstract

Simulations of wave propagation in porous media are important to the understanding of various phenomena, such as seismic effects and non-destructive testing. The derivation and implementation of finite element analysis for a fully dynamic three-field deformable porous media model based on the de la Cruz and Spanos (dCS) theory [1] is presented. The dCS theory accounts for the fluid viscous dissipation mechanism and nonreciprocal solid-fluid interactions, which are neglected in Biot theory [2]. While the Biot theory is based on experimental data, the dCS theory is derived from mixture theories associated with the volume fraction concept and representing the connection between micro and macro pore scales. dCS results presented build upon recent FE model for quasi-static analysis [3]. Here, for the fully dynamic case incorporating both fluid and solid inertia, the accuracy and robustness of the FEA model is verified by wave propagation examples in one and two dimensions. Time integration scheme utilized and the changes in convergence rates according to how strongly coupled is the system will be discussed. The required element approximation order for all variables to ensure numerical stability will be demonstrated. The presented model is compared with the results from Biot theory, allowing one to observe the differences between the two theories and their relevance. The solutions in the time and frequency domain are also discussed, where the analysis of the correspondent eigenproblem leads to important information regarding wave velocity and attenuation.

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