Finite element implementation of coupled hydro-mechanical modeling of transversely isotropic porous media in DEAL.II

In geotechnical engineering, modeling geo-structures is challenging, particularly in cases where the interaction between the structures and soil or rock is complex. Most well-known commercial modeling software is based on homogenous and isotropic materials. However, soil and rock are often modeled in heterogeneous and anisotropic media because of the inherent anisotropy of sedimentary rock masses and their stratified structure. In recent decades, coupled hydro-mechanical (HM) interactions in isotropic porous media have been studied; however, the behavior of transversely isotropic porous media is rarely considered. In addition, it is difficult for commercial software such as Plaxis and Flac3D to express complex rock formation where the anisotropy of the material and the associated cracks and fractures could be assembled into a single model. In this study, a finite element implementation using Differential Equation Analysis Library (DEAL.II), an open-source library of finite element codes, was developed to model the fully coupled HM behavior of transversely isotropic porous media. The proposed implementation can be applied to both isotropic and transversely isotropic porous media based on Biot's theory. The developed code can be used to model poroelastic media with (1) equations of linear elasticity for the solid matrix and (2) diffusion equations for fluid flow based on mass and linear-momentum conservation laws. We verified the performance and accuracy of the code through two examples, i.e., Mandel's problem with a compared analytical solution and a tunnel excavation process with the Flac3D software. On the basis of these numerical applications, we present the code to model the behavior of various geo-structures such as tunnels and pile-soil interactions with anisotropic materials.