Damage Constitutive Model Of Rock Research Articles

Creep damage constitutive model of rock based on the mechanisms of crack-initiated damage and extended damage

Since the classical element model cannot describe the nonlinear characteristics of rock during the entire compressive creep process, nonlinear elements and creep damage are generally introduced in the model to resolve this issue. However, several previous studies have reckoned that creep damage in rock only occurs in the accelerated creep stage and is only described by the Weibull distribution. Nevertheless, the creep damage mechanism of rocks is still not clearly understood. In this study, a reasonable representation of the damage variables of solid materials is presented. Specifically, based on the Gurson damage model, the damage state functions reflecting the constant creep stage and accelerated creep stage of rock are established. Further, the one-dimensional and three-dimensional creep damage constitutive equations of rock are derived by modifying the Nishihara model. Finally, the creep-acoustic emission tests of phyllite under different confining pressures are conducted to examine the creep damage characteristics of phyllite. And the proposed constitutive model is verified by analyzing the results of creep tests performed on saturated phyllite. Overall, this study reveals the relationship between the creep characteristics of rocks and the corresponding damage evolution pattern, which bridges the gap between the traditional theory and the quantitative analysis of rock creep and its damage pattern.

Compaction elastoplastic damage constitutive model of rock under hydro-mechanical coupling: A heuristic modeling method based on internal state variables theory

Based on the internal state variables (ISV) theory, this paper employs a heuristic modeling approach to investigate the compaction elastoplastic damage constitutive model of rocks under hydro-mechanical coupling. The heuristic modeling method demonstrated herein can seamlessly integrate with existing constitutive theories, facilitating a broader spectrum of research on hydro-mechanical coupling constitutive models. Furthermore, a numerical solution was conducted in the principal axes via stress spectrum decomposition, which can well reflect the distinct characteristics of compaction deformation and the influence of water pressure on rock stress distribution. Utilizing the classic Drucker-Prager (D-P) criterion, the modeling method and numerical algorithm were implemented to derive a hydro-mechanical coupling compaction elastic–plastic damage constitutive model. This contribution expands the application domain of the classic D-P criterion within the context of hydro-mechanical coupling environments. The rationality of the model was confirmed through compression test data under various water pressures and confining pressures. Water pressure increases nonlinear compaction deformation by changing the opening degree of microcracks under low confining pressure, which has not been paid enough attention in existing research. This study thoroughly considers the influence of water pressure on compaction deformation. The developed process of “heuristic modeling method-numerical method-model application” is helpful for enriching the constitutive theory of rock under hydro-mechanical coupling.

Damage constitutive model of rock and application based on strength theory

Abstract Extending the one-dimensional damage constitutive model of rock materials to 3 dimensions using classical methods fails to capture the significant differences in tensile, compressive, and shear strengths exhibited by the rock materials. Consequently, it is necessary to revise the existing damage constitutive model to describe the damage evolution law and constitutive relationship of rock materials more accurately and provide a theoretical basis for the safety and stability analysis of underground engineering more scientifically, thus ensuring the sustainable development of underground engineering. By introducing the Weibull distribution function and building upon strength theory, a correction function was established. This correction function adjusted the equivalent strain, enabling the development of a 3-dimensional damage constitutive model that accounted for the varying tensile, compressive, and shear strengths of rock materials. The impact of various parameters on the model's fitting effectiveness was evaluated, and a comparative analysis was conducted against pertinent experimental results. Using the theory of neutral axis deviation, the relationship between bending moment and damage variables in a purely bending rock beam was derived. The study revealed that all parameters of the damage constitutive model could be derived from the uniaxial stress-strain curve, and its theoretical findings exhibited strong agreement with experimental results obtained from rock and rock-like materials under uniaxial tension, compression and triaxial compression. Based on the examined cases, it was concluded that, when considering both tensile and compressive damage, the ultimate bending moment of a rock beam was approximately one-third of its elastic limit bending moment in an undamaged state. The results have verified the feasibility of the damage constitutive model.

Study on mechanical characteristics and damage model of layered sandstone after high temperature action

Rock engineering, which includes slopes, tunnels, and mines, often encounters stratified rocks. These projects are also frequently exposed to special environments of high temperatures, such as deep underground or fire-related conditions. It is of significant importance to conduct research on the damage characteristics and constitutive models of stratified rocks under high-temperature conditions to accurately reflect the influences of rock structure characteristics, geological conditions, and load effects on the damage and deformation characteristics of rock engineering. Under five temperature conditions (20, 200, 400, 600, 800 ℃), the intact sandstone rock samples and the layered sandstone samples are subjected to high-temperature treatment, followed by triaxial compression tests. Based on existing research on statistical damage constitutive models for rocks, a high-temperature layered rock statistical damage constitutive model is established by introducing the Weibull distribution function and high-temperature, bedding, and load coupling damage variables, under the condition that the microelement strength follows the Drucker-Prager (D-P) criterion. The results indicate that the peak strength, damage threshold, elastic modulus, and longitudinal wave velocity show a "U"-shaped trend with an increasing bedding angle, with an opening upwards. As the temperature increases, the anisotropy of the rock initially increases and then decreases, with obvious ductile characteristics after the temperature reaches 600 ℃. The analysis of damage threshold, stress-strain curve, and macroscopic failure morphology shows that the 60° dipping angle sandstone is prone to undergo compressive-shear failure along the weak plane of bedding, exhibiting low toughness mechanical characteristics. Theoretical curves of the statistical damage constitutive model for high-temperature rock are in good agreement with the Triaxial shear test curve of sandstone, which indicates that the constitutive model can reflect the stress-strain process of layered sandstone after high-temperature action, and verifies the applicability of the model. This model does not include unconventional mechanical parameters and can reflect the ductility, brittleness, and strength characteristics with clear physical meanings. The findings of the study can offer theoretical support for computing and numerically modeling rock mechanics after high-temperature action.

The time-dependent deformation and damage constitutive model of rock based on dynamic disturbance tests

Abstract In the deep rock excavation process, the rock will produce deformation and damage under multiple dynamic disturbances, while there is also unrecoverable time-dependent deformation. In order to research this deformation characteristic, a sine wave disturbance triaxial loading test was carried out on red sandstone to simulate the failure process of deep underground rock mass under dynamic disturbance loads with low confining pressure. Based on the results that the deformation of the rock increases suddenly during dynamic disturbances and varies with the number of disturbances, a novel disturbance damage model relating the number of disturbances to the deformation of the disturbances is created to describe the deformation and damage accumulation of the rock under multiple disturbances and an operator is developed to ensure that the model works. In order to describe the time-dependent deformation of rocks, the elasticity model in the traditional Bingham model was improved to a nonlinear elasticity model that varies with time, and its viscous and plasticity models were retained. The time-dependent deformation and damage constitutive model is obtained by combining the improved Bingham model with the disturbance damage model. The model parameters were identified according to the test data, and the finite-element calculation of the model was realized with the secondary development program. The results show the strain of rock increases suddenly under multiple disturbances, and the main reason for rock damage is the action of dynamic disturbances. The fitted curves and finite-element results are consistent with the experimental results. The time-dependent deformation and damage constitutive model of rock not only reflects the decaying rheological and steady-state rheological properties of rock under static loading but describes the characteristics of strain surge and disturbance damage accumulation caused by dynamic disturbances. This article contributes to the characteristics of the deformation of deep rock mass.

Anisotropic time-dependent deformation and damage constitutive model of rock under true triaxial compression

Anisotropic time-dependent deformation and damage constitutive model of rock under true triaxial compression

Mechanical properties investigation and damage constitutive models of red sandstone subjected to freeze-thaw cycles

The mechanical properties of rock can be degraded by long-term freeze-thaw cycles (FTCs). However, the damage constitutive model of rock subjected to FTCs for simulating the whole deformation process is still lacking. In this paper, uniaxial compression tests for red sandstones were carried out under different numbers of FTCs, and the relationships between the mechanical parameters and the number of FTCs were established. The method for determining the fully compacted point was firstly proposed, and a random exponential function of strain difference during compaction stage and linear elastic stage was constructed. Then, a novel damage constitutive model simulating the whole deformation process of rock subjected to FTCs was proposed. The proposed model and three existing models were compared with experimental data, and their model performances were evaluated. The proposed model with the consideration of the initial compaction stage was found to be more consistent with the experimental data, while the two existing models can be improved to be more versatile. The finding enriches the research of rock in constitutive modelling in cold regions.

Study on the Coupled Mechanism of Seepage–Stress–Damage and Damage Constitutive Model of Rock after Freezing and Thawing

Study on the Coupled Mechanism of Seepage–Stress–Damage and Damage Constitutive Model of Rock after Freezing and Thawing

An Improved Statistical Damage Constitutive Model for Rock Considering the Temperature Effect

An Improved Statistical Damage Constitutive Model for Rock Considering the Temperature Effect

A statistical thermal damage constitutive model for rock considering characteristics of the void compaction stage based on normal distribution

A statistical thermal damage constitutive model for rock considering characteristics of the void compaction stage based on normal distribution

Tunnel Slotting-Blasting Numerical Modeling Using Rock Tension-Compression Coupling Damage Algorithm

Slotting-blasting is the most critical technology in the construction of rock tunnels using the drilling and blasting method. At present, there is no effective method to simulate the effect of slotting-blasting. In this paper, we proposed that the weight coefficient of tension damage or compression damage is calculated by the proportion relation of current principal stresses, and the damage properties of rock were denoted by the tension-compression weighted damage variable. The blasting damage constitutive model of rock was established by coupling the tension-compression weighted damage variable and the classical PLASTIC_KINEMATIC model. The proposed method was used to simulate tunnel slotting-blasting and investigate the rock damage evolution law in slotting-blasting construction. The numerical simulation of the explosive blasting test shows that the proposed method may effectively simulate the slot cavity formation process, the blasting damage law and the dynamic response characteristics of surrounding rock in slotting-blasting construction. The findings in this paper could be significant for the slotting-blasting design of rock tunnels.

Investigation on the Expression Ability of a Developed Constitutive Model for Rocks Based on Statistical Damage Theory

Abstract The three-parameter Weibull distribution has a strong ability to fit many kinds of experimental data, which provides a solution for using a unified expression to characterize the elastic-brittle, strain softening, elastic-plasticity, and other constitutive behaviors of rocks. Therefore, a statistical damage constitutive model based on three-parameter Weibull distribution was constructed through theoretical analysis and derivation. Its expression ability was verified by combining with the conventional triaxial compression test data of marble. Meanwhile, the application effect of this statistical damage constitutive model on granite and sandstone was analyzed. The results show that the statistical damage constitutive model of rock based on three-parameter Weibull distribution can well express elastic-brittle, elastic-plastic, strain softening behaviors of rock by setting reasonable constitutive parameters, which lays a theoretical foundation for constructing a unified rock constitutive model. Conventional triaxial tests of marble show that with the increasing of confining pressure (σ3= 5, 15, 25, 35 MPa), the plastic deformation increases and the failure mode gradually changes from brittle tensile failure to shear failure, showing brittle-ductile and brittle-plastic transition characteristics. And its constitutive behaviors are characterized by elastic-brittleness, strain softening, and elastic-plasticity, which can be well expressed by the statistical damage constitutive model. When σ3 is 25 and 35 MPa, sandstone samples show elastic-brittle behavior. And for granite samples, they show strain softening behavior when σ3 is 5 MPa. The statistical damage constitutive model is also suitable for describing both sandstone elastic-brittle behavior and granite strain softening behavior. It is concluded that the three-parameter Weibull distribution provides a useful approach to characterize various constitutive behaviors of rock, and the model has a wide potential in numerical simulation for mining engineering, geoengineering, and other rock engineering.

Thermal Damage Constitutive Model and Brittleness Index Based on Energy Dissipation for Deep Rock

In deep underground engineering, rock usually encounters a high temperature problem. The stress–strain relationship of rock under high temperatures is the basis of engineering excavation. Based on the Lemaitre’s equivalent strain hypothesis and energy dissipation theory, the thermal damage constitutive model of rock is established. The results show that the peak stress, ultimate elastic energy and dissipated energy at the peak all decrease with the increase of temperature in a logistic function, which indicates that the increase of temperature aggravates the deterioration of rock’s mechanical properties. Compared with rock’s constitutive model that is established on strength criterion, the thermal damage constitutive model based on energy dissipation better reflects the phenomenon of stress drop after the peak and well describes the whole stress-strain curve of rock failure, which verifies the rationality of the model. The damage model further improves the theoretical system of the rock damage constitutive model and makes up for the defect in that the traditional damage model cannot reasonably explain the nature of rock failure. The brittleness index, defined based on the energy drop coefficient, shows a logistic function with the increase of temperature, which has good physical meaning. Analyzing the phenomenon of the rock stress drop from the perspective of energy is of great significance for deeply understanding the brittle fracture mechanism of rock.

A statistical damage constitutive model for rock based on modified Mohr–Coulomb strength criterion

A statistical damage constitutive model for rock based on modified Mohr–Coulomb strength criterion

Study on Damage Constitutive Model of Rock under Freeze-Thaw-Confining Pressure-Acid Erosion

Aiming at the acid-etched freeze-thaw rock for geotechnical engineering in cold regions, chemical damage variables, freeze-thaw damage variables, and force damage variables were introduced to define the degree of degradation of rock materials, the law of damage evolution, the total damage variable of acid-corroded rock under the coupling action of freeze-thaw and confining pressure was deduced. The continuous damage mechanics theory was adopted to derive the damage evolution equation and constitutive model of acid-eroded rock under the coupling action of freeze-thaw and confining pressure. The theoretical derivation method was used to obtain the required model parameter expressions. Finally, the model’s rationality and accuracy were verified by the triaxial compression test data of frozen-thawed rocks. Comparing the test curve’s peak point with the peak point of the model theoretical curve, the results show that the two are in suitable agreement. The damage constitutive model can better reflect the stress-strain peak characteristics of rock during triaxial compression, verifying the rationality and reliability of the model and the method for determining the model parameters. The model extends the damage model of rock under the coupling action of freeze-thaw and confining pressure in the chemical environment and further reveals the damage mechanism and failure law of acid-corroded rock under the coupling action of freeze-thaw and confining pressure.

Study on the Damage Process and Numerical Simulation of Tunnel Excavation in Water-Rich Soft Rock

The weakening effect is one of the most important causes triggering large deformation and failure of soft-rock engineering; however, few studies paid attention to damage evolution and constitutive relationship of rock in tensile damage in the excavation unloading and water-weakening process, not to mention the coupling process of unloading and water-weakening. In this paper, the mechanism and engineering characteristics of unloading softening and water-softening of water-rich soft rock are analyzed and summarized. Then with the aid of the strain equivalent principle, the damage of surrounding rock caused by unloading softening and water-softening is coupled, and the compression shear damage and the tensile damage of surrounding rock under the unloading process are analyzed. A damage constitutive model of rock subjected to excavation unloading and water-weakening is proposed considering the influence of water immersion time, and the proposed model is applied in a newly established finite element simulation method, which is suitable for excavation in the water-rich soft rock. Based on the mechanical-hydraulic-damage coupled method, the progressive failure process of surrounding rock under the dual softening effects can be reflected by the deteriorated parameters of damage elements. Finally, the field monitoring data of a typical section in the Xujiadi tunnel is used to verify the applicability and accuracy of the proposed dual softening model and simulation method.

A Damage Constitutive Model of Rock Subjected to Freeze-Thaw Cycles Based on Lognormal Distribution

The constitutive model of rock is closely connected with the mechanical properties of rock. To achieve a more accurate quantitative analysis of the mechanical properties of rock after the action of freeze-thaw cycles, it is necessary to establish the constitutive models of rock subjected to freeze-thaw cycles from the view of rock damage. Based on the assumption of rock couple damage, this study established a statistical damage constitutive model of rock subjected to freeze-thaw cycles by combining the lognormal distribution, which is commonly used in engineering reliability analysis, and the strain strength theory. Then, the coordinates and derivative at the peak of the stress-strain curve of the rock after the action of freeze-thaw cycles were obtained through experiments to solve the statistical distribution parameters με and S of the model, whereafter, the theoretical curves by the established model were compared with the experimental curves to verify the validity of it, which shows a great agreement. Finally, the sensitivity analysis of the statistical distribution parameters was implemented. The results indicate that με reflects the strength of the rock, which shows a positive relation, and S stands for the brittleness of the rock, which shows a negative relation.

Three Dimensional Statistical Damage Constitutive Model of Rock Based on Griffith Strength Criterion

According to the damage mechanics theory and Lemaitre strain equivalence theory, because most rock materials are brittle materials, Griffith strength criterion has good applicability to describe the fracture failure of brittle materials from the perspective of energy. Using a new method to describe the rock micro-element strength based on Griffith strength criterion, and assuming the micro-element strength obeys the Weibull distribution, a true triaxial constitutive model of damage softening reflecting the whole process of rock failure is established. On this basis, the influence of the two parameters in the model on the curve of the constitutive model is analyzed, and the relationship between the two parameters and the intermediate principal stress in the model is established, and the model is revised reasonably. Finally, a true triaxial damage constitutive model of rock is established. The results are in good agreement with the experimental curve, which verifies its validity and rationality. At the same time, the relationship between the damage evolution and the strain and stress is discussed, and the influence of the size of the intermediate principal stress on the relationship is analyzed in detail.

Simulation of subway tunnel construction process based on fi-nite element analysis

Simulation of subway tunnel construction process based on fi-nite element analysis

Application of constitutive model in simulation analysis of tunnel construction

Application of constitutive model in simulation analysis of tunnel construction