Mohr-Coulomb Strength Criterion Research Articles

Determination of mine fault activation degree and the division of tectonic stress hazard zones

This article conducts a comprehensive study on the activation characteristics of faults in the mine and analyzes the distribution patterns of the original rock stress field. Through quantitative research and analysis, we determine the partitioning characteristics of tectonic stress in the mine field under the dual effects of fault activation and original rock stress. The study also reveals the significant impact of different fault activation characteristics and different tectonic stress partitions on the stability of roadway surrounding rock. Using the Mohr–Coulomb strength criterion as a foundation, we investigate the mechanisms of fault activation and establish a mathematical model for fuzzy comprehensive evaluation. This model enables us to determine the strength level of fault activation in coal seam 9 of the Limin coal mine and construct a geological structure model. It has realized the transformation of fault activation degree from qualitative evaluation to quantitative evaluation. The stress state analysis software is used to draw the division of tectonic stress dangerous areas under the synergistic effect of fault activation and original rock stress. We then analyze the impact on the stability of roadway surrounding rock in these different hazardous areas. Utilizing the fuzzy comprehensive evaluation method, we take into account the impact of faults on the distribution characteristics of stress fields and the stability of roadway surrounding rock. This approach enables us to more accurately and comprehensively determine the hazardous areas of tectonic stress in the mine field under the dual effects of faults and original rock stress.

Rock strength weakening subject to principal stress rotation: Experimental and numerical investigations

During the construction and operation of gas storage reservoirs, changes in the principal stress direction can induce fracture propagation under conditions of lower differential stress, potentially leading to failure in the surrounding rock. However, the weakening of strength due to pure stress rotation has not yet been investigated. Based on fracture mechanics, an enhanced Mohr-Coulomb strength criterion considering stress rotation is proposed and verified with experimental and numerical simulations. The micro-damage state and the evolution of the rock under the pure stress-rotation condition are analyzed. The findings indicate that differential stress exceeding the crack initiation stress is a prerequisite for stress rotation to promote the development of rock damage. As the differential stress increases, stress rotation is more likely to induce rock damage, leading to a transition from brittle to plastic failure, characterized by wider fractures and a more complex fracture network. Overall, a negative exponential relationship exists between the stress rotation angle required for rock failure and the differential stress. The feasibility of applying the enhanced criterion to practical engineering is discussed using monitoring data obtained from a mine-by tunnel. This study introduces new concepts for understanding the damage evolution of the surrounding rock under complex stress paths and offers a new theoretical basis for predicting the damage of gas storage reservoirs.

Experimental study on the physical and mechanical properties of carbonatite rocks under high confining pressure after thermal treatment

AbstractOil and gas exploration studies have been increasingly moving deeper into the earth. The rocks in deep and ultra‐deep reservoirs are exposed to a complex environment of high temperatures and large geo‐stresses. The Tarim oilfield in the Xinjiang Uygur Autonomous Region (Xinjiang for short), China, has achieved a breakthrough in the exploration of deep hydrocarbon reservoirs at a depth of over 9000 m. The mechanical properties of deep rocks are significantly different from those of shallow rocks. In this study, triaxial compression tests were conducted on heat‐treated carbonatite rocks to explore the evolution of the mechanical properties of carbonatite rocks under high confining pressure after thermal treatment. The rocks for the tests were collected from reservoirs in the Tarim oilfield, Xinjiang, China. The experiments were performed at confining pressures ranging from atmospheric to 120 MPa and temperatures ranging from 25 to 500°C. The results show that the critical confining pressure of the brittle–ductile transition increases with increasing temperature. Young's modulus is negatively correlated with the temperature and positively correlated with the confining pressure. As the confining pressure increases, the failure mode of the specimens gradually transforms from shear fracture failure into “V”‐type failure and finally into bulging failure (multiple shear fractures). With increasing temperature, the failure angle tends to decrease. In addition, an improved version of the Mohr‒Coulomb strength criterion with a temperature‐dependent power function was proposed to describe the failure strength of carbonatite rocks after exposure to high temperature and high confining pressure. The surface of the strength envelope of this criterion is temperature dependent, which could reflect the strength evolution of rock under high confining pressures after thermal treatment. Compared with other strength criteria, this criterion is more capable of replicating physical processes.

Evolution mechanism of water-conducting fractures in overburden under the influence of water-rich fault in underground coal mining

Based on the 7618 working face in Yaoqiao coal mine of Datun mining area, the activation mechanism of water-rich faults and the development characteristics of water-conducting fractures in overlying strata under the influence of faults are studied by theoretical analysis, numerical simulation and field measurement in this paper. The research results show that Anderson model and Mohr–Coulomb strength criterion are combined to establish the fault failure mechanical model, and the fault activation criterion under the influence of mining is obtained. FLAC3D numerical simulation results show that with the advance of the working face, the fault begins to be affected by the mining effect of the working face at the distance of 20 ~ 30 m from the fault. Meanwhile, with the advance of the working face, the overburden shear failure range also expands, and the fault fracture gradually expands from top to bottom. The failure zone of the working face roof is connected with the fault fracture zone. Then the fault is "activated" and causes the fault to become a water gushing channel, and finally the water gushing disaster occurs. Through numerical simulation and comparative analysis, the development height of water-conducting fracture is 73.2 m in the absence of fault, and 73.7 m in the presence of fault, indicating that the fault has little influence on the maximum development height of water-conducting fracture. The actual development height of the water-conducting fracture zone in the 7618 working face is 73.97 m and the fracture production ratio is 13.7. The research results can provide theoretical reference for the safe mining of similar working faces across faults.

Validation of a damage constitutive model based on logistic model dedicated to the mechanical behavior of the rock

The establishment of mechanical models of rocks can provide crucial guidance to the surrounding rocks stability analysis in the rock engineering. According to statistical damage theory and Mohr–Coulomb strength criterion, the Logistic model is used to yield the damage evolution equation and further establish statistical damage constitutive model for describing the whole failure process of rocks. Then, the rationality of the proposed damage model is proved by comparing with the different test curves, and damage evolution laws are summarized into four stages, including: slow-growth stage, rapid-growth stage, constant-speed-similar growth stage and speed-reducing growth stage. Physical meanings of model parameters r′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${r}{\\prime}$$\\end{document} and m\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m$$\\end{document} are also discussed. Finally, to verify the application of this proposed model, this damage constitutive model is developed and implemented to simulate the tunnel excavation and analyze the stability of surrounding rocks by using Fortran, python and Abaqus. The displacement data on site is used to prove the superiority of proposed damage constitutive model compared with the existing ones in Abaqus. The research outcomes presented in this paper can also provide useful references for the theory and application of rock mechanics.

Experimental study on the shear mechanical behavior of ice-rich debris–rock interface: effects of temperature, stress, and ice content

Glacier collapses can occur due to shear failure at the ice-rich debris–rock interface (IDRI). To examine the shear behavior of IDRI, shear tests were conducted on artificial IDRI specimens with varying ice contents (40%, 65%, and 90%), normal stresses (150, 250, 350, 450, and 550 kPa), and temperatures (−1, −3, −5, −7, and −9 °C). Our findings reveal that temperature has the most significant impact on both peak and residual shear strength, followed by normal stress and ice content. As the temperature increases from −9 to −1 °C, the peak and residual shear stress decreased by 62.5%–78%. Notably, for IDRI with the lowest ice content (40%), the residual shear stress is highly influenced by normal stress. We have developed an improved Mohr–Coulomb strength criterion of IDRI in which the cohesion and internal friction angle are determined by ice content and temperature. Furthermore, we propose a novel constitutive model, based on the disturbed state concept, to describe the shear behavior of IDRI. This model combines a spring model and a hyperbolic model. We also discuss the mechanisms through which ice content and temperature influence the shear deformation modes and shear strength of IDRI.

Tension-shear extension criteria used in PFC2D to reveal a brittle failure of rock bridges in rock slopes with stepped joints

Stepped failure is a typical mode in alpine valleys and usually manifests as brittle fractures determined by joints. Tension-shear extension criteria were proposed to reflect the intrinsic mechanism of this failure mode. These criteria combined the theory of linear elastic fracture mechanics and the Mohr-Coulomb (M−C) strength criterion, including propagation trends and fracture conditions, and reflected the fracture behavior of rock bridges determined by joints. The proposed extension criteria were numerically applied in the 2D Particle Flow Code (PFC2D). The mesoscopic strength parameters were calibrated according to a mathematical relationship, which could satisfy the relationship between stress and strength with the proposed criteria. For massive rock slopes dominated by stepped joints, it is determined through theoretical and experimental analysis that rock bridges undergo tensile failure under low normal stress levels, which gives a reasonable explanation of why rock bridges observed in situ generally undergo tensile fracture. The internal mechanism of rock bridge failure is revealed through mechanical analysis of fracture behavior, which is considered in the numerical method. Taking the Xiaowan Hydropower Station as an example, it is confirmed that the simulation results truly reproduce the mesoscopic mechanism of the stepped failure of the slope.

An improved numerical manifold method for crack propagation of concrete gravity dams under seismic loads

In the safety analysis of concrete gravity dams it is necessary to consider the external load and internal load of the dam body within a reasonable range, in which the influence of strong earthquake can not be ignored. The modified Mohr-Coulomb strength criterion is introduced into the numerical manifold method (NMM), meanwhile, the calculation mechanism of dynamic load is introduced, and the calculation part considering the Hydro-Mechanical coupling principle is added to the NMM. The effectiveness and accuracy of the improved NMM are verified by the displacement of the central point of the circular arch under dynamic load containing an analytical solution. Based on the improved NMM, the crack propagation of concrete gravity dam is predicted and analyzed. The crack propagation of Koyna concrete gravity dam under seismic conditions is analyzed, and the results are compared with XFEM and experimental results. The influence of adding Hydro-Mechanical coupling module on crack propagation and seismic response of concrete gravity dam is discussed and it is proved that the improved NMM can accurately predict the crack propagation of concrete gravity dams under dynamic load and the advantage of NMM in dealing with continuous-discontinuous problems.

Numerical simulation of interaction bored pile and soil mass with taking into account the dilatancy of the soil

Pile testing is a necessary and mandatory process of construction buildings and structures erected on pile foundations. There is a need for a correct assessment of the interaction of the elements of the "foundation-pile" system for the reliable and effective design of pile foundations.
 The use of soil parameters provided in reports on engineering and geological investigations, without their clarification, leads to a significant discrepancy in the results of numerical modeling of the interaction of piles with the foundation and data from real observations of their settlement as a result of loads. Therefore, there is a need to identify the calculated parameters of the adopted soil model in order to match the simulation results with the results of experimental studies in a wide range of loads.
 In this paper, a model of ideal elastic-plastic behavior of the soil environment using the Mohr-Coulomb strength criterion was chosen to describe the interaction behavior of the elements of the "foundation-pile" system. When using this model, it is necessary to take into account a number of its inherent shortcomings, for example, not taking into account the change of the young`s modulus depending the change of the stress-strain state. Additionally, this work examines the influence of the dilatancy effect of sandy soil.
 At the initial stage of loads up to 15% of the total settlement of the pile (displacement resulting from potential pile failure), the value of the young`s modulus (E) makes a significant contribution to its operation. At the later stages of loading, significant plastic shear deformations occur in the soil, and accordingly, the leading parameters are the soil strength parameters, in this case, the specific cohesion (c) and the friction angle(φ). Since in this work the drill pile passes through sandy soil for a considerable length, it is also important to take into account the effect of soil dilatation(ψ).
 The results of a comparison field test of the bored pile with large-diameter and their numerical simulation of interaction with sandy soils are presented, and the calculation parameters of the soil environment model are identified in order to match the simulation results with experimental data at the corresponding specified loads.
 A convergence of up to 5% was achieved in a wide range of loads on the bored pile.

Calculation Method for Determining the Wall Displacement and Primary Support Bearing Capacity of Tunnels

The primary support structure of a tunnel often needs various support methods, such as bolts, steel arch frames, and shotcrete. It is of great significance to quickly calculate the displacement of tunnel walls and the bearing capacity of primary supports for guiding construction and ensuring construction safety. In order to solve the above problems, this paper constructs a mechanical model of primary support and analyzes the displacement of a tunnel wall at different construction stages of primary support; based on the Mohr–Coulomb strength criterion, the displacement of the tunnel wall at different stages of the primary support is derived, and the calculation method and process for calculating the bearing capacity of the primary support are given. The accuracy of the proposed method is then verified by an example. Compared with previous methods, the method proposed in this paper considers the support effects of bolts, steel arches, and shotcrete separately and calculates the corresponding displacement of the tunnel wall, which is closer to the actual construction situation. In addition, the bearing capacity of the primary support can be calculated and analyzed. By comparing with the numerical simulation results, it has been proven that the proposed method has a relatively small calculation error. Compared with the numerical simulation results and previous analytical methods, the method proposed in this paper is simpler and faster in calculation; thus, it can quickly assist in the design of tunnel support structures.

Effect of Soil Creep on the Bearing Characteristics of Soil Slope Reinforced with CFRP and Anti-Slide Piles

In order to research the displacement characteristics and stability of a soil slope reinforced with carbon-fiber-reinforced plastic (CFRP) and anti-slide piles, the displacement composition, aging deformation and failure mode of a soil mass were analyzed. According to the Mohr–Coulomb strength criterion, a new nonlinear, accelerated creep model of soil mass was founded with the addition of a self-building M-C plastic element. Furthermore, a viscoplastic strain analytical formula of an M-C plastic element was obtained, and the tensile deformation characteristics of a CFRP sheet were also discovered under a landslide thrust creep load. According to the environmental conditions of the anti-slide pile, the CFRP was arranged along the load-bearing side of the pile to control deformation. Combining the calculation example, it is shown that the horizontal displacement of the soil slope’s composite structure decreases by approximately 40% with CFRP reinforcement. Furthermore, for the first two calculation conditions, after one year, the maximum horizontal displacement decreased by 50% and increased by 10%, respectively. Simultaneously, the overall safety factor increased by 31.3% without soil creep properties. On the contrary, the overall safety factor was reduced, and the slope has a tendency toward unstable failure. Moreover, there is no through plastic zone in the slope. The stability of the reinforced slope and the bearing capacity of the pile are related to the CFRP method. Simultaneously, the structure can reduce the costs and construction difficulty of anti-slide piles in a complex environment surrounded by the soil creep effect.

Bearing characteristics of mono-column composite bucket foundation in sand for offshore wind turbines

Using a new steel compartment structure, the mono-column composite bucket foundation applied in the South China Sea deep-water project for the first time is based on the optimization of the steel-concrete composite bucket and is suitable for wind farms with a water depth of more than 30m. However, at this stage, there are few studies on large-diameter mono-tube multi-compartment bucket foundations, especially those related to the bearing characteristics of mono-column composite bucket foundations after long-term service. In this study, a cyclic load test is carried out on a mono-column composite bucket foundation in sand, and the influence of cyclic load factors on the cumulative rotation angle, cyclic stiffness, and ultimate bearing capacity after cyclic loading of the foundation is analyzed, and the bearing characteristics of the foundation are analyzed by finite element analysis. The results show that after the cyclic loading, the bearing capacity and stiffness have a certain increase compared with before the cyclic loading in sand. The ultimate bearing capacity calculation formula based on the Mohr-Coulomb strength criterion derived from the limit state of the foundation failure has higher reliability compared with the test results and can be used to predict the bearing capacity of the mono-column composite bucket foundation.

Construction Method of Honeycomb Gas Flow Network Channel: Structure-Based and Engineering Response on Plastic Zone Distribution Form

The plastic zone of the surrounding rock of the borehole is a high-quality channel for gas flow. Studying the distribution form of the plastic zone in the surrounding rock of the boreholes and the characteristics of the extended connection network is essential for the optimal layout of the gas drainage boreholes. Considering gas pressure parameters based on the modified Terzaghi effective stress principle and Mohr–Coulomb strength criterion. The implicit equation of the plastic zone boundary of the surrounding rock of the borehole is derived. The influence of two-way confining pressure ratio, coal body strength, gas pressure and hole diameter on the distribution of the surrounding plastic rock zone and the permeability-increasing circle is analyzed, and a honeycomb gas flow network channel structure based on the distribution of plastic zones is constructed. The gas flow and enrichment zone of the coal seam are connected, and the gas drainage rate is improved.

An integrated experimental and numerical study of size effect on the mode I fracture toughness of rock

Rock is a typical quasi-brittle and heterogeneous material that shows the apparent size effect of mode I fracture toughness (KIc). To further explore the mechanism of the size effect on the KIc of rocks, a novel experimental procedure, i.e., combining a semi-circular bend test with a small-scale direct tension test, is conducted to determine the KIc and fracture process zone (FPZ) length of rock specimens of various sizes. Meanwhile, the four-dimensional lattice spring model (4D-LSM), incorporating a cohesive zone model (CZM) and the modified Mohr–Coulomb strength criterion for bond fracturing, is adopted to interpret these experimental results. After a detailed comparison between experimental and numerical results, we conclude that the size effect is dominated by the softening zone size of the mesoscale grain bond’s constitutive behaviour, rather than other mechanical parameters of rock, e.g., tensile strength, cohesion, and internal friction angle. Without introducing the size-dependent constitutive model into the discrete numerical model but only using a softening model for the mesoscale grain bond, we have successfully reproduced the change in KIc values and FPZ length of the rock specimens of various sizes with high goodness-of-it for the Bazant size effect curve, which indicates that the discrete numerical model can sufficiently reproduce or interpret the size effect in the KIc of rocks.

Dynamic compressive failure of coal at different burial depths

Dynamic disasters frequently occur in deep coal mines, where coals and rocks are under high in situ stresses. To reveal the failure mechanism of deep burying coals, the specimens were made of buried coals at a depth of about 1 km. An improved Kolsky bar was applied to conduct the dynamic compression experiments subjected to different hydrostatic pressure i.e., 0, 5, 10, 15, and 20 MPa for simulating in situ stresses corresponding to depths of 0, 200, 400, 600, and 800 m. The findings demonstrate that the dynamic compressive strength of coal at a specified depth is rate-dependent. And the dynamic strength is positively correlated with the burial depth at a given loading rate. Moreover, a Mohr–Coulomb strength criterion for coal under dynamic loadings that considers the effect of depth is established, and the model describes the experimental results well.

Simulation of collapse failure process of rock slope based on the smoothed particle hydrodynamics method

The limit equilibrium method (LEM) or finite element method (FEM) for slope problems most frequently focusses on the stability analysis. There are, however, still some problems with the LEM or FEM when considering damage and failure evolution of a rock slope because of the distortion of mesh. In this work, a mesh-free particle approach, named the smoothed particle hydrodynamics (SPH) method, is presented and is improved to analyze the damage and failure process of a rock slope. In order to better describe the cause and mechanism of brittle failure for a rock slope, the plastic factor was suggested and introduced into the SPH algorithm, and the conservation equations of SPH for brittleness characteristics were obtained. Based on the variation of displacement and time, an effective criterion was proposed to define the factor of safety in SPH simulation. The Drucker-Prager Mohr-Coulomb strength criterion was implemented into the SPH algorithm to describe the elastic-plastic behavior. Then, three rock-slope models with different precast cracks were analyzed to illustrate the performance of the proposed method. It is shown that the proposed SPH algorithm can be effectively applied in the prediction of the deformation and failure process of rock slope.

DEM investigation of strength and critical state behaviours of granular materials under true triaxial loadings

This paper investigates the strength and critical state (CS) behaviours of granular materials via DEM simulations of true triaxial drained tests under three different loading modes including constant b (intermediate stress ratio) tests with constant σ1′ (major principal stress), constant p′ (mean pressure) and constant σ3′ (minor principal stress) respectively. To this end, a series of samples are generated with the same particle size distribution, and with the confining stresses ranging from 100 kPa to 900 kPa. The CS is achieved for all samples. Both the macroscopic behaviours and the microscopic behaviours are examined and compared considering different loading modes, confining stresses and intermediate stress ratios (b). The critical state lines (CSLs) are found to be unique and independent of the loading modes, but dependent on the b values. The CSLs with b=0 and b=1 form the two boundaries of CSLs respectively beyond which CSLs under all other b tests cannot go beyond. Six different strength criteria are examined and compared in terms of both peak and CS failures. The Mohr–Coulomb strength criterion is found to be only suitable for axisymmetric loading conditions. The Lade-Duncan criterion is only suitable for describing peak strengths, which is dependent on the loading modes and confining stresses. The Satake criterion and Matsuoka-Nakai criterion are the more appropriate strength criteria for describing CS failures, indicating that the CS values of both the Satake parameter and the Matsuoka-Nakai parameter describe an inherent property that characterizes the CS failure for a given type of soil. The CS mechanical coordination number is fitted by a curved line for a given b value, which is unique regardless of the loading modes. The peak and CS values of both major and minor principal fabric tensors decrease with increasing b values, while they increase with increasing b values for the intermediate principal fabric tensor.

Probability analysis of rock slope using FORM based on a nonlinear strength criterion

Various uncertainties are frequently encountered in the assessment of landslide stability. However, the uncertainty of parameters in the Mohr–Coulomb strength criterion is a major concern in the studies, neglecting the uncertainty related to the strength criterion itself that is used to describe the strength of geotechnical materials. To assess the reliability of landslides, a new probabilistic analysis method is proposed in this study. According to the traditional limit equilibrium framework, an improved method based on a nonlinear strength criterion is deduced to determine the safety factor of landslides. The local mean value of the random variables on the failure surface is estimated by the analytical method, avoiding random field simulation. The first-order reliability method (FORM) is applied to estimate the failure probability of landslides. An example is analyzed using the proposed probability analysis method, and its effectiveness is primarily verified. The results show that the traditional limit equilibrium method based on the linear Mohr–Coulomb strength criterion estimates the stability and failure probability of landslides inaccurately.

A novel method to retain a waterproof coal pillar near water-conducting fault

AbstractReducing the width of safe coal pillar near geological structures, such as a water-conducting fault, to improve the extraction ratio of coal seam is a major concern that needs to be addressed urgently for mining shallow coal resources in China. To tackle the contradiction between improving the extraction ratio of resources and the disaster caused by reducing the width of the waterproof coal pillar, this study focuses on retaining the coal (rock) pillar near the water-conducting fault and proposes a novel method for calculating the waterproofing of the coal pillar precisely. We consider the different location relationships between the water-conducting fault, confined aquifer and coal seam, and suggest the principle of retaining the waterproofing of the coal pillar. First, we develop a mechanical model describing a waterproof coal pillar near the water-conducting fault by using elastic–plastic mechanics theory and subsequently calculate the length of plastic zone of the coal pillar under water pressure of the fault by using the limit equilibrium method. Furthermore, we use FLAC3D software to simulate the stress distribution of the coal seam roof and floor under fault water pressure. Subsequently, based on the Mohr–Coulomb strength criterion, we propose a method to calculate the width of waterproof coal pillars by combining the plastic zone with the maximum principal stress propagation line. Ultimately, we assess and discuss the accuracy and simplicity of this method by combining it with engineering methods.

A Study of Strength Parameter Evolution and a Statistical Damage Constitutive Model of Cemented Sand and Gravel.

Cemented sand and gravel (CSG) has a wide range of applications in dam construction, and its properties are between rockfill and roller compacted concrete (RCC). A difference in gel content will result in a variance in CSG's structure and mechanical properties. To investigate the intricate structural mechanical properties of CSG, this study conducted a series of laboratory tests and associated discrete element analyses. Accordingly, the evolution law of the strength parameters of CSG is explored and a statistical damage constitutive model suitable for CSG is established. The main contributions of this study are as follows: (1) The failure mechanism of the CSG was described from the microscopic level, and the evolution law of the strength parameter cohesion and friction angle of the CSG was analyzed and summarized. (2) Based on the particle flow model, the energy development law and the spatiotemporal distribution law of acoustic emission (AE) provide illustrations of the strain hardening-softening transition features and the interaction between cohesion and friction of CSG. (3) The evolution function between the strength parameter and the strain softening parameter was built, and the critical strain softening parameter was determined by the microcrack evolution law of the particle flow model. (4) The accuracy of the evolution curve was confirmed by comparing it to experimental results. (5) Based on the relationship between cohesion loss and material damage, a statistical damage constitutive model was developed using the improved Mohr-Coulomb strength criterion as the micro strength function. The constitutive model can accurately describe the stress-strain curves of CSG with different gel content. Furthermore, the model reflects the strain hardening-softening properties of CSG and reveals the relationship between the weakening of cohesion and material damage at the microscopic level. These findings provide valuable guidelines for investigating the damage laws and microcosmic failure features of CSG and other relevant materials.