A nonlinear constitutive model for whole stress–strain behaviors of compressed rocks incorporating crack closure effect

Abstract

This paper is devoted to establishing a nonlinear constitutive model incorporating crack closure effect for capturing the whole process of rock deformation and failure behavior under compression. The model formulated in the framework of irreversible thermodynamics is based on the additive decomposition of the total strain into crack closure strain, elastic, and plastic parts. New specific criteria are proposed for the description of crack closure strain and plastic strain evolution. Notably, analytical solutions of the model under conventional triaxial compression loading conditions are derived. For application, a robust semi‐implicit return mapping (SRM) algorithm with a crack closure strain correction and a plastic strain correction is developed. The analytical solutions, herein, are subtly used to calibrate model parameters and as reference results for assessing the accuracy and robustness of the SRM algorithm. Validation of the model conducted by comparing with experimental data from the literature shows that the model can properly describe the nonlinear mechanical behaviors of rocks, including crack closure effect, strain hardening/softening, peak and residual strength, as well as volumetric compaction/dilation transition. In addition, a nonlocal formulation is introduced as an extension of the model to remedy the mesh dependency problem.

Micro‐Thermomechanical Modeling of Rocks With Temperature‐Dependent Friction and Damage Laws

“…Prior researches mainly focus on the room temperature conditions and take into account the influence of mesocracking evolution on the damage resistance, with appreciable success achieved in modeling hardening/weakening behaviors of quasi‐brittle rocks (Q. Z. Zhu et al., 2016; Zhao, Shao, & Zhu, 2018; Ren et al., 2023; C. X. Zhao, Liu, et al., 2023).…”

“…Among them, the temperature dependence of fundamental mechanical properties of quasi‐brittle rocks, including peak strength, plastic deformation, damage evolution, and strain hardening/softening, was typically characterized by employing empirical equations. Note that some of these models have been further modified to describe the mechanical response of geologic materials under hydro‐thermal‐mechanical (Long, 2021), thermal‐creep (Geng et al., 2018), and freeze‐thaw cyclic loading (Ren et al., 2023; Zhao et al., 2020). These macroscopic models explicitly present stress‐strain relationships and short‐ and long‐term strength criteria, which facilitate analysis of specific rock and mining engineering using finite element (Long, 2021), discrete element (Fan et al., 2021), phase field method (J. Liu, Ji, et al., 2020).…”