A Statistical Damage Constitutive Model of Anisotropic Rock: Development and Validation

Abstract

The damage constitutive model is of great significance to research the stress-strain relationship and damage evolution of rock under loading in engineering. In order to investigate the effect of anisotropic characteristic on the stress-strain relationship and damage evolution, a statistical damage constitutive model of anisotropic rock under true triaxial condition was developed. In this study, the plane which existed perpendicular to the coordinate axis was extracted from representative volume element (RVE) of rock. The extracted plane was assumed to be composed of abundant mesoscopic elements whose failure strength satisfied the Weibull distribution. According to the number of failure elements on the plane in each direction under loading, the anisotropic damage variable was established based on the proposed concept of areal damage. A statistical damage constitutive model of anisotropic rock was developed by using strain equivalent hypothesis and generalized Hooke constitutive model. Subsequently, the parameters in the anisotropic damage constitutive model were determined by the method of total differential. Thus, the damage evolution of anisotropic rock under various stress conditions can be conveniently evaluated by the anisotropic damage model. The model was validated based on the tests of rocks under the stress conditions of conventional triaxial and true triaxial, respectively. Moreover, for the purpose of studying the influence of parameters on the model, sensitivity analyses of mechanical parameters and model parameters were carried out. The results of statistical damage constitutive clearly demonstrate the stress-strain and damage evolution of anisotropic rock under various stress conditions.

Experimental and damage model study of layered shale under different moisture contents

“…This structure can result in strong anisotropy in the shale. The impact of the anisotropy of bedding on rock has been analyzed and studied by many scholars (Chandler et al, 2016;Chen et al, 2014;Geng et al, 2016;Heng et al, 2015;Ma et al, 2021;Rong et al, 2021). A statistical damage constitutive model for true triaxial conditions has been developed by Rong et al (2021), which revealed that the elastic modulus has a greater impact on strain in the same direction compared to other directions.…”

“…The impact of the anisotropy of bedding on rock has been analyzed and studied by many scholars (Chandler et al, 2016;Chen et al, 2014;Geng et al, 2016;Heng et al, 2015;Ma et al, 2021;Rong et al, 2021). A statistical damage constitutive model for true triaxial conditions has been developed by Rong et al (2021), which revealed that the elastic modulus has a greater impact on strain in the same direction compared to other directions. In a separate study, Ma et al (2021) conducted triaxial tests on Longmaxi shale with varying bedding angles, revealing that the shale strength decreased initially but gradually increased with the increase of loading direction.…”

Anisotropic Hypoplastic Model Considering the Relation between Fabric Tensor and Anisotropic Parameters

“…Numerous anisotropic plastic models and damage models have been used to predict the mechanical response of anisotropic soil and rock [1][2][3][4][5][6]. Based on the framework of critical state soil mechanics (CSSM) for the triaxial space, Dafalias et al [1] have presented an anisotropic clay plasticity constitutive model.…”

“…An anisotropic elastoplastic model for soft clays has been established by Sivasithamparam and Castro [4] based on an existing model called S-CLAY1S, which is a Cam clay type model that accounts for anisotropy and destructuration. Rong et al [6] have developed a statistical damage constitutive model for anisotropic rock and accurately predicted the mechanical state and deformation of rock for geotechnical, coal mining, shale gas exploitation, etc. However, these models are described by complex formulation and parameters.…”