Damage Evolution Constitutive Behavior of Rock in Thermo-mechanical Coupling Processes

For thermal and loaded rock in engineering structures for some projects, triple-shear Drucker–Prager yield criteria, compaction coefficient K, damage variable correction factor δ, and thermal damage variable DT are introduced in a new thermomechanical (TM) constitutive model for the entire process. The compaction stage of rock in uniaxial compression test and the strain softening of rock caused by thermal attack are considered in this article. The damage evolution of rocks is described by a damage variable and a constitutive equation, which are in agreement with the actual thermal experimental breakage. The uniaxial compressive strength of granite subjected to a TM coupling effect can be predicted properly by this new unified constitutive model. The new TM unified constitutive model considering the compaction stage and post-failure stage is in good agreement with the test curves throughout the entire process. The coupling effect of heat and load in the total damage of rock has obvious nonlinear properties, but the coupling effect significantly weakens the specimens. By using the new TM unified constitutive model, the whole process of changes in rock damage with strain after high temperature can be calculated. Meanwhile, the model well represents the stress–strain curve at the post-failure stage. It is expected that this model can provide references for studying the mechanical response of the rock damage propagation characteristics in the future.

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Three-Dimensional Reconstruction and Numerical Simulation Analysis of Acid-Corroded Sandstone Based on CT

Shock and Vibration ◽

10.1155/2021/5582781 ◽

2021 ◽

Vol 2021 ◽

pp. 1-14

Author(s):

Zizhen Miao ◽

Shuguang Li ◽

Jiangsheng Xie ◽

Runke Huo ◽

Fan Ding ◽

...

Keyword(s):

Numerical Simulation ◽

Uniaxial Compression ◽

Damage Evolution ◽

Simulation Analysis ◽

Acid Corrosion ◽

Three Dimensional ◽

Strain Curve ◽

Uniaxial Compression Test ◽

Evolution Law ◽

Simulation Results

Due to its unique technological characteristics, coal mining and production often encounter an acid corrosion environment caused by acid gases. Acid erosion and a series of chemical reactions caused by it often led to the deterioration of coal, rock, support structure, etc. and induced serious safety accidents. To further explore the macro-mesoscopic damage evolution law and failure mechanisms of rock masses under corrosion conditions through numerical simulation, a zonal refined numerical model that can reflect the acid corrosion characteristics of sandstone is established based on CT and digital image processing (DIP). The uniaxial compression test of corroded sandstone is simulated by ABAQUS software. Comparing the numerical simulation results with the physical experiment results, we found that the three-dimensional finite element model based on CT scanning technology can genuinely reflect sandstone’s corrosion characteristic. The numerical simulation results of the stress-strain curve and macroscopic failure mode of the acid-corroded sandstone are in good agreement with the experimental results, which provides a useful method for further studying the damage evolution mechanism of the acid-corroded rock mass. Furthermore, the deformation and damage evolution law of the corroded sandstone under uniaxial compression is qualitatively analyzed based on the numerical simulation. The results show that the rock sample’s axial displacement decreases gradually from top to bottom under the axial load, and the vertical variation is relatively uniform. In contrast, the rock sample’s removal gradually increases with the increase of axial pressure, and the growth presents a certain degree of nonuniformity in the vertical. The acid-etched rock sample’s damage starts from both the end and the middle; it first appears in the corroded area. Moreover, with the displacement load increase, it gradually develops and is merged in the middle of the rock sample and forms macroscopic damage.

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Numerical Study of Rock Fragmentation Process and Acoustic Emission by FDEM Based on Heterogeneous Model

Mathematical Problems in Engineering ◽

10.1155/2020/2109584 ◽

2020 ◽

Vol 2020 ◽

pp. 1-13

Author(s):

Qi Liu ◽

Penghai Deng

Keyword(s):

Acoustic Emission ◽

Mechanical Response ◽

Numerical Study ◽

High Energy ◽

Uniaxial Compression Test ◽

Rock Damage ◽

Heterogeneous Model ◽

Damage And Fracture ◽

Heterogeneous Rock ◽

Rock Model

Rock has the characteristics of natural heterogeneity and discontinuity. Its failure phenomenon induced by external force involves complex processes, including the microcrack initiation, propagation, coalescence, and the macrocrack formation. In this study, the Weibull random distribution based on the rock microstructure characteristics is introduced into the combined finite-discrete element method (FDEM) to establish the heterogeneous rock model, and the mechanical response and damage evolution of rock samples in uniaxial compression test are simulated. The results show that FDEM simulation with loaded heterogeneous rock model can reflect the progressive development of rock damage, fracture, and acoustic emission (AE) activity in real rock well. Meanwhile, the statistical analysis indicates that the number and energy evolution of AE events with different fracture modes in the model are consistent with the macroscopic failure mode of rock. The change of b-value also agrees with the increasing trend of high-energy events in the loading process. This method provides a new tool for the analysis of rock damage and fracture evolution.

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Modeling interaction between loading-induced and creep strains of rockfill materials using a hardening elastoplastic constitutive model

Canadian Geotechnical Journal ◽

10.1139/cgj-2018-0435 ◽

2019 ◽

Vol 56 (10) ◽

pp. 1380-1394 ◽

Cited By ~ 2

Author(s):

Zhongzhi Fu ◽

Shengshui Chen ◽

Qiming Zhong ◽

Yijiang Zhang

Keyword(s):

Constitutive Model ◽

Mechanical Response ◽

Coupling Effect ◽

Reduced Form ◽

Model Parameters ◽

Plastic Strains ◽

Rockfill Materials ◽

Elastoplastic Constitutive Model ◽

Stress Dependent ◽

Creep Strains

An elastoplastic constitutive model that takes into account the stress–strain relationship and creep-induced hardening behavior of rockfill materials is proposed in light of previous experimental observations. It is assumed that the mechanical response during loading and the final amounts of creep strains under a constant stress state are independent of the strain rate. The focus of the proposed model is the coupling effect between loading and creep, including the influence of loading history on subsequent creep strains and the influence of creep history on subsequent loading behavior. An extended yield function, which allows flexible control over the shape of yield surfaces, is used not only to distinguish among loading, unloading, and neutral loading, but also to manipulate the creep-induced hardening using a plastic strains–based hardening parameter. A stress-dependent dilatancy equation is used, instead of a plastic potential function, to define the directions of plastic strains during loading. The hardening law is established based on three different types of experimental results. Only routine experiments are required for calibration of model parameters, and the model can be used in a reduced form according to the available test results. The model is verified using typical experimental data and is found to be capable of capturing important behavior of rockfill materials, such as pressure-dependent strength, shear contraction and dilation, and creep-induced stiffening.

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A constitutive model for frozen soil based on rate-dependent damage evolution

International Journal of Damage Mechanics ◽

10.1177/1056789517741339 ◽

2017 ◽

Vol 27 (10) ◽

pp. 1589-1600 ◽

Cited By ~ 2

Author(s):

Chenxu Cao ◽

Zhiwu Zhu ◽

Tiantian Fu ◽

Zhijie Liu

Keyword(s):

Constitutive Model ◽

Damage Evolution ◽

Mechanical Response ◽

Split Hopkinson Pressure Bar ◽

Frozen Soil ◽

Experimental Results ◽

Strain Rates ◽

Hopkinson Pressure Bar ◽

Dynamic Mechanical ◽

Rate Dependent

The deformation of frozen soil under impact loading is usually accompanied by the evolution of internal defects and microdamage. By taking the strain and strain rates into account, a rate-dependent damage evolution law is proposed in this study, under the assumption of equivalent strain. Subsequently, a damage-modified rate-dependent constitutive model is proposed to describe the dynamic mechanical properties of frozen soil. A split Hopkinson pressure bar is utilized to test the dynamic mechanical response of frozen soil at different temperatures and high strain rates. The experimental results show that frozen soil produces obvious strain rate and temperature effects, and that there is a linear relationship between the peak stress and temperature. The theoretical results of the proposed constitutive model agree well with the experimental results, verifying the applicability of the model.

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Application of RPC Constitutive Model in FEA

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.578-579.25 ◽

2014 ◽

Vol 578-579 ◽

pp. 25-30

Author(s):

Ke Jia Yang ◽

Zi Ling Xie ◽

Wei Li

Keyword(s):

Constitutive Model ◽

Evolution Equation ◽

Constitutive Relation ◽

Damage Evolution ◽

Damage Index ◽

Strain Curve ◽

Plasticity Model ◽

Damage Evolution Equation ◽

Concrete Damaged Plasticity ◽

Compression Member

The damage evolution equation of RPC is established based on 2-parameter Weibull distribution. The constitutive relation of RPC is then calculated based on the damage evolution equation. The constitutive model of RPC is optimized by comparing experimental constitutive curve to models corresponding to different threshold strain. Based on the definition of damage index in ABAQUS, the damaged evolution equation in ABAQUS is recalculated based on the optimized constitutive relation. the concrete damaged plasticity model in ABAQUS is obtained using the aforementioned method. And the concrete damaged plasticity model is applied to three compression member and three simply supported beams with different reinforcements. The calculated stress-strain curve and deformation of three compression member and three beams is in accordance with the deformation characteristics of experiments, which verified the effectiveness of the proposed concrete damaged plasticity model of RPC.

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

Materials ◽

10.3390/ma14237414 ◽

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.

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

International Journal of Damage Mechanics ◽

10.1177/1056789517726838 ◽

2017 ◽

Vol 27 (8) ◽

pp. 1213-1230 ◽

Cited By ~ 17

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.

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Study on Bending Damage Constitutive Model and Mechanical Properties of Limestone Based on Acoustic Emission

Advances in Civil Engineering ◽

10.1155/2019/2031520 ◽

2019 ◽

Vol 2019 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Yuanshuai Zhang ◽

Shuangying Zuo ◽

Bo Yu ◽

Shiwan Chen ◽

Jienan Jia

Keyword(s):

Acoustic Emission ◽

Constitutive Model ◽

Damage Evolution ◽

Damage Variable ◽

Bending Test ◽

Neutral Layer ◽

Three Point Bending ◽

Bending Process ◽

Damage Constitutive Model ◽

Bending Fracture

To reveal the mechanical characteristics and damage evolution mechanism of limestone in the bending process, the cumulative acoustic emission (AE) hits were used to define the damage variable, and the rock microbody hypothesis and the Weibull distribution function were applied to further improve the damage variable. Meanwhile, the bending damage constitutive model of limestone under three-point bending was developed based on the Lemaitre strain equivalence principle and the continuum damage theory. Then, the three-point bending test with acoustic emission monitoring was carried out to verify the rationality and validity of the model. Results showed that the modified damage variable D had an exponential distribution with the strain ε, and the damage was mainly concentrated in the macrocrack propagation stage. Moreover, the bending neutral layer moved towards the compressive zone in the bending damage process. The bending neutral layer, furthermore, moved slowly a small distance at the initial stage of bending fracture but moved fast a long distance at the end stage of bending fracture. In addition, the bending damage constitutive model could be quantitatively expressed by the cumulative AE hits Np, the stress σ, the strain ε, and Young’s modulus E. The theoretical stress-strain model curves agreed well with experimental results, which demonstrated that the proposed model could capture the damage evolution of limestone reasonably in the bending process.

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Studies on Related ms Magnitude Rate Models in Triangular Wave Unloading Section of Calcium Medium-Fine Sandstone

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.152-153.164 ◽

2010 ◽

Vol 152-153 ◽

pp. 164-170

Author(s):

Jie Liu ◽

Jian Lin Li ◽

Ying Xia Li ◽

Shan Shan Yang ◽

Ji Fang Zhou ◽

...

Keyword(s):

Mechanical Response ◽

Strain Curve ◽

Experimental System ◽

Constant Term ◽

Lag Time ◽

Vertical Force ◽

Time Segment ◽

Triangular Wave ◽

Apparent Modulus ◽

The Impact

Specific to the improvement in the present research of mechanical response under cyclic loading, this paper, taking the calcareous middle- coarse sandstone as the research subject and the RMT-150C experimental system in which data is recoded by ms magnitude as the platform, develops several related models concerning the unloading rate of triangle waves. The unloading process is divided into lag time segment and non-lag time segment, with criterions and related parameters provided as well. The term apparent elastic modulus is defined. The test data analysis shows that there exist a linear relationship between the apparent modulus and instant vertical force before load damage in non-lag time segment. On the preceding basis, a rate-dependent model of triangular wave un-installation section in non-lag time segment is established. Due to the inability of the loading equipment to accurately input the triangle wave, the average loading rate is amended and a constant term is added into it. The model is proved to be reliable, as the predicted value of the deformation rate and the stress strain curve coincides with measured value. At the same time, the impact of the lag time is pointed out quantitatively and a predication model of lag time segment is set up.

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Study on mechanical properties and damage evolution of carbonaceous shale under triaxial compression with acoustic emission

International Journal of Damage Mechanics ◽

10.1177/1056789521991193 ◽

2021 ◽

pp. 105678952199119

Author(s):

Kai Yang ◽

Qixiang Yan ◽

Chuan Zhang ◽

Wang Wu ◽

Fei Wan

Keyword(s):

Mechanical Properties ◽

Acoustic Emission ◽

Water Content ◽

Damage Evolution ◽

Damage Assessment ◽

Triaxial Compression ◽

Confining Pressure ◽

Damage Variable ◽

Natural State ◽

Carbonaceous Shale

To explore the mechanical properties and damage evolution characteristics of carbonaceous shale with different confining pressures and water-bearing conditions, triaxial compression tests accompanied by simultaneous acoustic emission (AE) monitoring were conducted on carbonaceous shale rock specimens. The AE characteristics of carbonaceous shale were investigated, a damage assessment method based on Shannon entropy of AE was further proposed. The results suggest that the mechanical properties of carbonaceous shale intensify with increasing confining pressure and degrade with increasing water content. Moisture in rocks does not only weaken the cohesion but also reduce the internal friction angle of carbonaceous shale. It is observed that AE activities mainly occur in the post-peak stage and the strong AE activities of saturated carbonaceous shale specimens appear at a lower normalized stress level than that of natural-state specimens. The maximum AE counts and AE energy increase with water content while decrease with confining pressure. Both confining pressure and water content induce changes in the proportions of AE dominant frequency bands, but the changes caused by confining pressure are more significant than those caused by water content. The results also indicate that AE entropy can serve as an applicable index for rock damage assessment. The damage evolution process of carbonaceous shale can be divided into two main stages, including the stable damage development stage and the damage acceleration stage. The damage variable increases slowly accompanied by a few AE activities at the first stage, which is followed by a rapid growth along with intense acoustic emission activities at the damage acceleration stage. Moreover, there is a sharp rise in the damage evolution curve for the natural-state specimen at the damage acceleration stage, while the damage variable develops slowly for the saturated-state specimen.

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