A multiscale framework for the simulation of the anisotropic mechanical behavior of shale

TL;DR

This paper develops a multiscale micromechanical framework using LDPM to simulate the anisotropic mechanical behavior of shale, capturing heterogeneity, anisotropy, and bedding effects, and upscaling to predict macroscopic properties.

Contribution

It introduces a novel multiscale LDPM-based model that explicitly incorporates shale's internal structure and anisotropy, calibrated with experimental data, and includes a homogenization approach for upscaling.

Findings

The model accurately predicts elastic properties, tensile and compressive strengths across orientations.

The dependence of mechanical behavior on loading orientation is successfully captured.

Upscaling provides insights into macroscopic properties from mesoscale parameters.

Abstract

Shale, like many other sedimentary rocks, is typically heterogeneous, anisotropic, and is characterized by partial alignment of anisotropic clay minerals and naturally formed bedding planes. In this study, a micromechanical framework based on the Lattice Discrete Particle Model (LDPM) is formulated to capture these features. Material anisotropy is introduced through an approximated geometric description of shale internal structure, which includes representation of material property variation with orientation and explicit modeling of parallel lamination. The model is calibrated by carrying out numerical simulations to match various experimental data, including the ones relevant to elastic properties, Brazilian tensile strength, and unconfined compressive strength. Furthermore, parametric study is performed to investigate the relationship between the mesoscale parameters and the macroscopic properties. It is shown that the dependence of the elastic stiffness, strength, and failure mode on loading orientation can be captured successfully. Finally, a homogenization approach based on the asymptotic expansion of field variables is applied to upscale the proposed micromechanical model, and the properties of the homogenized model are analyzed.