Thermo-mechanical coupling damage constitutive model of rock based on the Hoek–Brown strength criterion

Abstract

Studying the thermal damage constitutive model of rock using statistical theory can better reflect the damage evolution process and the stress–strain relationship of rock under temperature and loading, which is one of the key problems especially in deep rock mechanics. The thermal-mechanical coupling damage constitutive model of rock is established using the Hoek–Brown strength criterion, based on the Weibull distribution and the continuous damage theory. The rationality of the model is also verified by experiments. The main conclusions are as follows. The stress–strain curves of rock can be divided into four stages according to the damage evolution characteristics, including the non-damage of loading, damage stability expansion, damage intensification expansion, and damage stability expansion to saturation, and the method of determining the demarcation points of each stage is given clearly. The initial damage point of the rock is about 25% of the peak stress, the damage value is about 0.3 when the rock reaches the peak stress and about 0.6 when reaches the residual stress. Both the damage value and the strain energy release rate of the rock corresponding to the peak stress show exponential growth with the increase in confining pressure. The maximum damage evolution rate of the rock shows exponential decay as the confining pressure rises, indicating that the confining pressure can delay the development of cumulative damage. The modified damage constitutive model considering compaction coefficient is in good agreement with the test curves in the stage of compaction, linear elasticity, yield, and pre-peak strength. It is hoped that through the research of this paper, it can provide references for studying the macroscopic mechanical response from the damage propagation characteristics of the rock in the future.

Statistical Constitutive Model of Thermal Damage for Deep Rock considering Initial Compaction Stage and Residual Strength

“…Rock has compaction characteristics in the early stage of loading, and the theoretical model derived from (17) does not agree with the actual situation in the initial stage of loading. Therefore, the compaction coefficient K is defined as the ratio of slope to elastic modulus of rock stress-strain curve, and the ratio increases logarithmically with strain, which can be expressed as [24]…”

“…Wen et al [16] established the damage constitutive model based on rock strain analysis and proposed the damage evolution equation reflecting the initial damage of rock and the determination method of each parameter of the model. Xu et al [17] established the constitutive model of rock thermal damage, but the influence of residual strength was not considered.…”

Damage Ratio Based on Statistical Damage Constitutive Model for Rock

“…In these studies, they believed that it was a good attempt to combine the physical basis of mesomechanics model with macroscopic continuity theory, for the development of microcracks could be described by the theory of mesostructure and was the only phenomenon on the macroscale. 3The damage theory of rock is studied based on the microscopic phenomenological theory and the damage variable is assumed to be a kind of distribution (e.g., Krajcinovic et al [12], Cao et al [13][14][15][16], Wang et al [17], Deng and Gu [18], Zhao et al [19], Xu et al [20,21], Wang et al [22], Chen et al [23], and Bian et al [24]). Statistical damage theory was introduced in these studies.…”

Mechanical Properties and Statistical Damage Constitutive Model of Rock under a Coupled Chemical-Mechanical Condition

“…A reasonable constitutive model is a useful method to investigate the damage evolution behavior of materials [24][25][26]. In recent years, many damage constitutive models have been established based on various strength theories or criterions, such as rock strain strength theory [27][28][29], Drucker-Prager (D-P) criterion [30][31][32][33], Mohr-Coulomb (M-C) criterion [34][35][36][37], and Hoek-Brown (H-B) criterion [38,39]. However, the strength of microelements, which is affected by many factors, cannot be calculated accurately using the strain strength theory [39].…”

“…As known, the model parameters in the constitutive models are highly affected by some mechanical properties, such as peak strength, peak axial strain, and elastic modulus [36,37,39]. In general, the values of these mechanical properties are obtained by conventional mechanical tests.…”