Multiscale modeling of compaction bands in saturated high-porosity sandstones

Abstract

We propose a hierarchical multiscale modeling approach to simulate the hydro-mechanical coupling behavior in saturated high-porosity sandstone, with a particular focus on the occurrence and transition of compaction bands. In this multiscale approach, we use the finite element method (FEM) to solve the global boundary value problem for a sandstone, and the discrete element method (DEM) to solve the local representative volume elements (RVEs) embedded at the Gauss integration points of the FE mesh to provide the effective material constitutive responses required for FEM. The global governing equations for a coupled hydro-mechanical problem are solved with the standard u–p formulation, where the total stress is decomposed into the pore pressure and the effective stress which is directly derivable from the DEM solution of the RVEs, according to the seminal Terzaghi's effective stress principle. By choosing proper RVEs to represent the typical microstructure of high-porosity sandstone, we perform both drained and undrained simulations on saturated sandstone specimens to examine localized compactive failures developed therein. We identify that both mean effective stress and porosity control critically the initiation and development of failure modes in sandstone. Under undrained shear, our simulations show that a sandstone specimen may first develop a compaction band followed by a gradual transition to a shear-enhanced compaction band and even shear band, with the build-up of excessive pore pressure and hence drop of mean effective stress. In the specimen, regions experiencing localized volumetric contraction show relatively higher pore pressure than other regions and act as the source of flux flow. The Darcy flux peaks during the formation of compaction band and decreases gradually in the following stages. To distinguish the different failure stages with distinct physical attributes, the ratio of deviatoric strain to volumetric strain is adopted as a useful indicator signifying the underlying microstructural mechanisms for different deformation bands. This study signifies the importance of considering pore pressure and mean effective stress in fluid-involved engineering operations, e.g. aquifer management, hydrocarbon extraction and CO2 geological sequestration.