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

2021 ◽  
Vol 11 (20) ◽  
pp. 9431
Author(s):  
Youliang Chen ◽  
Peng Xiao ◽  
Xi Du ◽  
Suran Wang ◽  
Tomas Manuel Fernandez-Steeger ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Damage Evolution ◽  
Damage Mechanics ◽  
Triaxial Compression ◽  
Confining Pressure ◽  
Model Parameters ◽  
Theoretical Derivation ◽  
Freeze Thaw ◽  
Peak Point ◽  
Damage Constitutive Model

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.

scholarly journals Study on Damage Constitutive Model of High-Concentration Cemented Backfill in Coal Mine

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Baogui Yang ◽  
Haigang Yang
Keyword(s):  
Constitutive Model ◽  
Coal Mine ◽  
Damage Evolution ◽  
Triaxial Compression ◽  
Failure Process ◽  
Model Parameters ◽  
High Concentration ◽  
Deformation And Failure ◽  
Cemented Backfill ◽  
Damage Constitutive Model

In order to construct the damage constitutive model (DCM) of high-concentration cemented backfill (HCCB) in coal mine, the generalized Hoek-Brown strength criterion was used as the failure criterion. For the difference of theoretical derivation of constitutive relation, a new DCM based on residual strength was proposed. Combined with the conventional triaxial compression test, the correctness and rationality of the DCM were verified. The damage evolution characteristics of HCCB were analyzed, and the physical meaning of model parameters was clarified. The results show that (a) the theoretical curves of stress-strain relation are in good agreement with its experimental curves, which means DCM can simulate the deformation and failure process of HCCB. (b) The damage evolution curve of HCCB is S -shaped. To some extent, the confining pressure can inhibit the development of damage. (c) The parameter F 0 reflects the position of the peak point of the DCM, and parameter n is the slope of the straight line segment in the postpeak strain softening stage, which are, respectively, used to characterize the strength level and brittleness of HCCB. The establishment of DCM of HCCB is helpful to reveal its deformation and failure mechanism and provides theoretical basis for its strength design.

scholarly journals Statistical Damage Constitutive Model for Cemented Sand considering the Residual Strength and Initial Compaction Phase

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Cai Tan ◽  
Ming-dao Yuan ◽  
Yong-sheng Shi ◽  
Bing-sheng Zhou ◽  
Hao Li
Keyword(s):  
Constitutive Model ◽  
Residual Strength ◽  
Damage Mechanics ◽  
Triaxial Compression ◽  
Triaxial Stress ◽  
Cemented Sand ◽  
Damage Constitutive Model ◽  
Statistical Damage Constitutive Model ◽  
Initial Compaction ◽  
Statistical Damage

Based on continuum damage mechanics and the assumption of volume invariance, a damage constitutive model of cemented sand under triaxial stress was established while considering residual strength. Statistical theory was then introduced into this model. Assuming that the microunit strength of cemented sand obeys a Weibull random distribution, an expression of microunit strength based on the Mohr–Coulomb criterion was derived. Additionally, a damage evolution equation and a statistical damage constitutive model of cemented sand under triaxial stress were established. In order to consider the nonlinear deformation and volume change in the initial pore compaction stage, the critical point reflecting the completion of the initial compaction stage was determined. This was done by applying the volume invariance assumption to the linear portion of the stress and strain curve and performing a coordinate transformation. The nonlinearity of the initial compaction stage was fitted by a quadratic function. A triaxial compression test of cemented sand was then carried out to verify this proposed method. The results show that the calculated values by the damage constitutive model fit well with the actual experimental values and that the calculated results can reflect the stress softening, residual strength, and initial compaction characteristics of cemented sand, which shows the rationality and feasibility of the model.

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

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Lingjie Zhu ◽  
Xiaoli Xu ◽  
Xiaojian Cao ◽  
Shaoyong Chen
Keyword(s):  
Constitutive Model ◽  
Residual Strength ◽  
Damage Evolution ◽  
Damage Mechanics ◽  
Thermal Damage ◽  
Peak Stress ◽  
Confining Pressure ◽  
Evolution Rate ◽  
Correction Coefficient ◽  
Initial Compaction

From the theory of damage mechanics, based on the Hoek-Brown strength criterion and Weibull distribution law of rock microelement strength, a statistical constitutive model of rock thermal damage is established by using equivalent strain hypothesis, and the theoretical model is modified by considering the compression coefficient and residual strength correction coefficient. The rationality of the modified model is verified by experimental data. The results show that the stress-strain curves of rock can be divided into four stages: initial compaction, stable damage propagation, damage strengthening expansion, and damage failure according to the characteristics of rock damage evolution. The peak stress of rock increases exponentially with the increase of confining pressure, and the maximum damage evolution rate decreases exponentially with the increase of confining pressure, which indicates that confining pressure delays the development of cumulative damage. The peak stress and maximum damage evolution rate of rock decrease exponentially with the increase of temperature, which accelerates the damage of rock. The initial damage of rock is thermal damage caused by temperature, and the damage value increases with the increase of temperature. The revised theoretical curve reflects the characteristics of rock compaction stage and residual strength and improves the coincidence with the experimental curve. The research results provide a reference for the establishment of thermal damage constitutive model of rock in deep engineering.

scholarly journals Study of Damage Constitutive Model of Brittle Rocks considering Stress Dropping Characteristics

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Fei Li ◽  
Shuang You ◽  
Hongguang Ji ◽  
Hao Wang
Keyword(s):  
Constitutive Model ◽  
Triaxial Compression ◽  
Strain Curve ◽  
Brittle Rock ◽  
Model Parameters ◽  
Deformation And Failure ◽  
Brittle Rocks ◽  
Whole Process ◽  
Confining Pressures ◽  
Damage Constitutive Model

Deep brittle rock exhibits characteristics of rapid stress dropping rate and large stress dropping degree after peak failure. To simulate the whole process of deformation and failure of the deep brittle rock under load, the Lemaitre strain equivalent theory is modified to make the damaged part of the rock has residual stress. Based on the damage constitutive model considering residual strength characteristics, a correction factor reflecting stress dropping rate is added, the Weibull distribution is used to describe the inhomogeneity of rock materials, and Drucker–Prager criterion is used to quantitatively describe the influence of stress on damage; a damage constitutive model of deep brittle rock considering stress dropping characteristics is established. According to the geometric features of the rock stress-strain curve, the theoretical expressions of model parameters are derived. To verify the rationality of the model, triaxial compression experiments of deep brittle rock under different confining pressures are conducted. And the influence of model parameters on rock mechanical behaviour is analysed. The results show that the model reflects the stress dropping characteristics of deep brittle rock and the theoretical curve is in good agreement with the experimental results, which indicates that the proposed constitutive model is scientific and feasible.

Statistical damage model with strain softening and hardening for rocks under the influence of voids and volume changes

2010 ◽  
Vol 47 (8) ◽  
pp. 857-871 ◽  
Author(s):  
Wen-Gui Cao ◽  
Heng Zhao ◽  
Xiang Li ◽  
Yong-Jie Zhang
Keyword(s):  
Constitutive Model ◽  
Strain Softening ◽  
Triaxial Compression ◽  
Damage Model ◽  
Damage Threshold ◽  
Model Parameters ◽  
Volume Changes ◽  
Conventional Triaxial Compression ◽  
Damage Constitutive Model ◽  
Statistical Damage

With regards to the composition of natural rocks including voids or pores, deformation behavior is strongly affected by variation in porosity. By using a statistical damage-based approach, the characteristics of strain softening and hardening under the influence of voids and volume changes are investigated in the present paper. Suppose that a rock consists of three parts: voids, a damaged part, and an undamaged part. The effects of voids and volume changes on rock behavior are first analyzed through determination of the porosity and an associated damage model is then developed. Later, a statistical evolution equation describing the influence of the damage threshold on the propagation condition of rock damage is formulated based on measurement of the mesoscopic element strength. A statistical damage constitutive model reflecting strain softening and hardening behavior for rocks loaded in conventional triaxial compression is further developed and a corresponding method for determining the model parameters is also provided. Theoretical results of this proposed model are then compared with those observed experimentally. Finally, several aspects of the present constitutive model, which affect the relevant behavior of rocks, are particularly discussed.

scholarly journals Study on Damage Statistical Constitutive Model of Triaxial Compression of Acid-Etched Rock under Coupling Effect of Temperature and Confining Pressure

Materials ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7414
Author(s):  
Youliang Chen ◽  
Peng Xiao ◽  
Xi Du ◽  
Suran Wang ◽  
Zhoulin Wang ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Coupling Effect ◽  
Triaxial Compression ◽  
Strain Curve ◽  
Confining Pressure ◽  
Effect Of Temperature ◽  
Acid Etching ◽  
Model Parameters ◽  
Stress Strain Curve ◽  
Stress Strain

Based on Lemaitre’s strain equivalence hypothesis theory, it is assumed that the strength of acid-etching rock microelements under the coupling effect of temperature and confining pressure follows the Weibull distribution. Under the hypothesis that micro-element damage meets the D-P criterion and based on continuum damage mechanics and statistical theory, chemical damage variables, thermal damage variables and mechanical damage variables were introduced in the construction of damage evolution equations and constitutive models for acid-etching rocks considering the coupled effects of temperature and confining pressure. The required model parameters were obtained by theoretical derivation, and the model was verified based on the triaxial compression test data of granite. Comparing the experimental stress-strain curve with the theoretical stress-strain curve, the results show that they were in good agreement. By selecting reasonable model parameters, the damage statistical constitutive model can accurately reflect the stress-strain curve characteristics of rock in the process of triaxial compression. The comparison between the experimental and theoretical results also verifies the reasonableness and reliability of the model. This model provides a new rock damage statistical constitutive equation for the study of rock mechanics and its application in engineering, and has certain reference significance for rock underground engineering.

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

2017 ◽  
Vol 27 (8) ◽  
pp. 1213-1230 ◽  
Author(s):  
Xiaoli Xu ◽  
Feng Gao ◽  
Zhizhen Zhang
Keyword(s):  
Constitutive Model ◽  
Damage Evolution ◽  
Mechanical Response ◽  
Peak Stress ◽  
Strength Criterion ◽  
Confining Pressure ◽  
Stress Strain ◽  
Mechanical Coupling ◽  
Damage Stability ◽  
Damage Constitutive Model

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.

scholarly journals Study of statistical damage constitutive model of layered composite rock under triaxial compression

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yong-Sheng Liu ◽  
Zhuan-Zhuan Qiu ◽  
Xue-Cai Zhan ◽  
Hui-Nan Liu ◽  
Hai-Nan Gong
Keyword(s):  
Constitutive Model ◽  
Axial Strain ◽  
Triaxial Compression ◽  
Confining Pressure ◽  
Layered Composite ◽  
Model Parameters ◽  
Compression Tests ◽  
Fitting Method ◽  
Confining Pressures ◽  
Curve Fitting Method

Abstract The layered composite rock was subjected to triaxial compression tests under constant confining pressure and the stress–strain curves under different confining pressures were obtained. Based on the continuous damage theory and statistical strength theory, it is assumed that the strength of rock microelements obeys Weibull distribution by taking the defects such as random micro-cracks in the rock into account. The statistical constitutive model of layered composite rock with damage correction is established by taking the axial strain of rock as a random distribution variable of microelement strength. The model parameters were determined by the curve fitting method and referring to some test parameters. By comparing the experimental data and the constitutive model curve, the rationality and feasibility of the model are verified.

scholarly journals Damage Ratio Based on Statistical Damage Constitutive Model for Rock

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Ying Chen ◽  
Lin Zhang ◽  
Hui Xie ◽  
Jianfeng Liu ◽  
Hong Liu ◽  
...  
Keyword(s):  
Rock Mass ◽  
Constitutive Model ◽  
Damage Mechanics ◽  
Damage Index ◽  
Confining Pressure ◽  
Peak Strain ◽  
Rock Damage ◽  
Damage Degree ◽  
Damage Constitutive Model ◽  
Critical Damage

The study of damage characteristics of rock mass is of great significance to the analysis of rock mass structure. According to the characteristics of the microscopic unit strength of rock with random distribution, the Weibull distribution is widely used as the statistical functions of the strength of the microunit of rock to establish the damage constitutive model. The concepts of damage ratio De and damage index Cc are proposed. Damage ratio is mainly used to describe the law of damage evolution in rock. Damage index can be used to evaluate the damage degree of rock. The influence of confining pressure on distribution parameters and damage ratio is analyzed through uniaxial and triaxial compression tests of sandstone. The results show that damage ratio is an index of structural characteristics of rock damage, which can reflect the evolution characteristics of microcracks in rock under spatial stress. Critical damage ratio refers to the damage ratio corresponding to the peak stress of rock and can be used as a parameter to characterize the strength of rock for corresponding to the peak strain one to one. The critical damage ratio is linearly related to the logarithmic function of confining pressure. Its relationship is as follows: Der=Ccln⁡σ3+b. With the increase of σ3, the increasing trend of Der slows down and gradually tends to a certain value. The larger the damage index is, the more serious the damage of rock is. The smaller the damage index is, the less serious the damage of rock is. Therefore, the damage index can be used to evaluate the damage degree of rock. It will be an important direction of rock damage mechanics research to distinguish the severity of rock damage by using damage index as the limit value.

Constitutive model of rock triaxial damage based on the rock strength statistics

2020 ◽  
Vol 29 (10) ◽  
pp. 1487-1511
Author(s):  
Kai Chen
Keyword(s):  
Constitutive Model ◽  
Rock Strength ◽  
Triaxial Compression ◽  
Confining Pressure ◽  
X Ray Diffraction ◽  
Proposed Model ◽  
Testing Data ◽  
Deformation Behaviors ◽  
Damage Constitutive Model ◽  
Rock Specimens

Firstly, an X-ray diffraction test is carried out to investigate brittle rock specimens’ composition, and a triaxial compression test is conducted to study the deformation behaviors and mechanical properties. Then, assuming that the rock material is able to be divided into the elastic part satisfying the Hooke’s law and the damage part where rock strength follows lognormal distribution, this paper determines a damage variable and establishes a damage constitutive model which effectively reflects the residual strength in the process of rock failure. Meanwhile, testing data are used to validate the reliability of the proposed model in this paper and the dependence of statistic parameters on the confining pressure. Finally, impacts caused by statistic parameters variation on compression strength are analyzed comprehensively, and we also conduct a comparison between this proposed model and other models from other literatures, thereby showing the reliability and rationality of this proposed model. In addition, the research outcomes presented in this paper also can effectively offer significant reference for the development of rock mechanics and rock engineering.

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