scholarly journals A Statistical Constitutive Model considering Deterioration for Brittle Rocks under a Coupled Thermal-Mechanical Condition

Geofluids ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Meiben Gao ◽  
Tianbin Li ◽  
Tao Wei ◽  
Lubo Meng
Keyword(s):  
Constitutive Model ◽  
Model Performance ◽  
Strain Curve ◽  
Geological Structure ◽  
Underground Engineering ◽  
Mechanical Coupling ◽  
Brittle Rocks ◽  
Damage Constitutive Model ◽  
The Stability

Due to active actions of groundwater and geothermal, the stability of underground engineering is important during geological structure active area. The damage mechanical theory and statistical mesoscopic strength theory based on Weibull distribution are widely used to discuss constitutive behaviors of rocks. In these theories, a statistical method is used to capture mesoscopic properties of rocks in order to generate a realistic behavior at a macroscopic scale. Based on the above theories, this paper aims at establishing a constitutive relation of brittle rocks under thermal-mechanical coupling conditions. First, a statistical damage constitutive model was established by considering the thermal effects and crack initiation strength. Subsequently, the parameters of the model were determined and expressed according to the characteristics of stress-strain curve. Third, the model was verified by conventional triaxial experiments under thermal-mechanical actions, and the experimental data and theoretical results were compared and analyzed in the case study. Finally, the physical meaning of the parameters and their effects on the model performance were discussed.

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.

Research on strain softening constitutive model of coal-rock combined body with damage threshold

2021 ◽  
pp. 105678952110190
Author(s):  
Tuo Wang ◽  
Zhanguo Ma
Keyword(s):  
Constitutive Model ◽  
Failure Modes ◽  
Strain Softening ◽  
Strain Curve ◽  
Model Parameters ◽  
Test Results ◽  
Underground Engineering ◽  
Rock Stratum ◽  
Damage Constitutive Model ◽  
Coal Rock

The coal seam and the roof of the roadway bear loads together in the underground engineering of coal mine. Especially for the roadway driven along the roof, its deformation is completely different from that arranged in the complete rock stratum. Accurately knowing the mechanical mechanism of coal-rock combined body can help understand the deformation and failure modes of such roadways. This article started with tests of coal-rock combined samples with different height ratios, based on the test results, a strain softening damage constitutive model of coal-rock combined body and a method for solving the parameters of the model were proposed, and the influence of the model parameters was discussed. The test results show that the stress peak value and residual strength of the coal-rock combined samples are negatively correlated with the proportion of coal in the coal-rock combined samples, and have a positive correlation with the confining pressure. The damage constitutive model fitted the test curve well. The model can accurately describe the stress-strain curve of coal-rock combined samples, and can reflect the influence of different height ratios of coal and rock samples and confining pressures. The effects of model parameters were discussed based on the damage constitutive model, which are expected to be widely used in underground engineering.

scholarly journals A Thermal Damage Constitutive Model for Oil Shale Based on Weibull Statistical Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Guijie Zhao ◽  
Chen Chen ◽  
Huan Yan
Keyword(s):  
High Temperature ◽  
Constitutive Model ◽  
Oil Shale ◽  
Thermal Damage ◽  
Triaxial Compression ◽  
Strain Curve ◽  
Practical Significance ◽  
Compression Tests ◽  
Different Temperatures ◽  
Damage Constitutive Model

In this work, we first studied the thermal damage to typical rocks, assuming that the strength of thermally damaged rock microelements obeys a Weibull distribution and considering the influence of temperature on rock mechanical parameters; under the condition that microelement failure conforms to the Drucker–Prager criterion, the statistical thermal damage constitutive model of rocks after high-temperature exposure was established. On this basis, conventional triaxial compression tests were carried out on oil shale specimens heated to different temperatures, and according to the results of these tests, the relationship between the temperature and parameters in the statistical thermal damage constitutive model was determined, and the thermal damage constitutive model for oil shale was established. The results show that the thermal damage in oil shale increases with the increase of temperature; the damage variable is largest at 700°C, reaching 0.636; from room temperature to 700°C, the elastic modulus and Poisson’s ratio decrease by 62.66% and 64.57%, respectively; the theoretical stress-strain curve obtained from the model is in good agreement with the measured curves; the maximum difference between the two curves before peak strength is only 5 × 10−4; the model accurately reflects the deformation characteristics of oil shale at high temperature. The research results are of practical significance to the underground in situ thermal processing of oil shale.

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

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Hang Lin ◽  
Linyuan Liang ◽  
Yifan Chen ◽  
Rihong Cao
Keyword(s):  
Mechanical Properties ◽  
Constitutive Model ◽  
Lognormal Distribution ◽  
Constitutive Models ◽  
Strain Curve ◽  
Statistical Distribution ◽  
Freeze Thaw ◽  
Accurate Quantitative Analysis ◽  
Distribution Parameters ◽  
Damage Constitutive Model

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.

scholarly journals Uniaxial Compression Behavior of Cement Mortar and Its Damage-Constitutive Model Based on Energy Theory

Materials ◽  
2019 ◽  
Vol 12 (8) ◽  
pp. 1309 ◽  
Author(s):  
Yunliang Tan ◽  
Qingheng Gu ◽  
Jianguo Ning ◽  
Xuesheng Liu ◽  
Zhichuang Jia ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Uniaxial Compression ◽  
Loading Rate ◽  
Cement Mortar ◽  
Axial Stress ◽  
Great Influence ◽  
Strain Curve ◽  
Compression Tests ◽  
Whole Process ◽  
Damage Constitutive Model

The mechanical properties of mortar materials in construction are influenced both by their own proportions and external loads. The trend of the stress–strain curve in cracks compaction stage has great influence on the relationship between the strength and deformation of cement mortar. Uniaxial compression tests of mortar specimens with different cement–sand ratios and loading rates were carried out, and the stored and dissipated energies were calculated. Results indicated that the elastic modulus and strength of mortar specimens increase with the cement–sand ratio and loading rate. The energy dissipation shows good consistency with the damage evolution. When the loading rate is less than 1.0 mm/min, most of the constitutive energy at the peak point is stored in the specimen and it increase with cement–sand ratio. A simple representation method of axial stress in cracks compaction stage was proposed and an energy-based damage constitutive model—which can describe well the whole process of cement mortar under uniaxial compression—was developed and verified.

scholarly journals Damage Strengthening Constitutive Model of Cemented Paste Backfill

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Kangli Cheng ◽  
Bingbing Tu ◽  
Lang Liu ◽  
Bo Zhang ◽  
Huafu Qiu
Keyword(s):  
Constitutive Model ◽  
Uniaxial Compression ◽  
Strain Curve ◽  
Cemented Paste Backfill ◽  
Test Results ◽  
Stress Strain ◽  
Filling Materials ◽  
Paste Backfill ◽  
Damage Constitutive Model ◽  
Ucs Test

In order to consider the influence of mesoscopic characteristics of materials on the constitutive model of cemented paste backfill (CPB), the uniaxial compression variables and the damage constitutive model, considering the influence of porosity and pore size of filling materials, were derived based on the strain equivalence principle and Weibull probability distribution function. The nuclear magnetic resonance (NMR) tests and unconfined compression strength (UCS) tests were carried out on 8 groups of CPB specimens with different slurry concentrations and cement-tailings ratios. Then, the expression of damage strengthening coefficient is determined, and the stress-strain curves measured by the theoretical model were compared with the experimental ones. The results show that the uniaxial compression constitutive model proposed is in good agreement with UCS test results and can effectively describe the damage evolution law and the development process of stress-strain curve of CPB under uniaxial compression. The 28-day compressive strength of CPB can reach 8 MPa, the residual strength is about 1∼2 MPa, the elastic modulus is about 200∼2000 MPa, and the porosity is about 3∼5%. The CPB with slurry concentration of 74% and 76% and cement-tailings ratio of 1 : 4 and 1 : 6 is more reasonable, and the relevant mechanical parameters are more stable.

scholarly journals Damage constitutive model of stratified cemented backfill based on coupling macroscopic and mesoscopic deformations

2020 ◽  
Vol 194 ◽  
pp. 05024
Author(s):  
Yanan Tang ◽  
Weidong Song ◽  
Jianxin Fu
Keyword(s):  
Mechanical Properties ◽  
Constitutive Model ◽  
Compressive Load ◽  
Strain Curve ◽  
Strength Distribution ◽  
Stress Strain ◽  
Strain Relationship ◽  
Damage Constitutive Model ◽  
Stratified Structure ◽  
Relationship Of

The mechanical properties and stress-strain relationship of cemented backfills with different stratified structure have a direct effect on the mining-filling cycle and the mining of adjacent pillars. To obtain the stress-strain evolution curves, the uniaxial compressive strength tests were performed on backfills with stratified numbers of 0, 1, 2 and 3. The deformation of stratified backfill under the compressive load is regarded as a compound of closed deformation of the macroscopic stratified structure and elastic deformation of material. The damage constitutive model of cemented backfills with different stratified structure are established by considering the influence of compacted section. Comparative analysis reveals that the calculated curve based on the established sectional damage constitutive model conforms well to the trial curve. The maximum closed strain of the structural plane has a more significant effect on the mechanical properties of backfill. In the Weibull distribution, with the increase of the parameter m, the peak strength of backfill gradually increases and then reaches to a certain value, and the stress-strain curve gradually becomes steeper, which shows that m is a reflection of the concentration level of micro-unit strength distribution in the backfill..

A Statistical Damage Constitutive Model for Brittle Rocks Based on the Lade-Duncan Failure Criterion

2014 ◽  
Vol 919-921 ◽  
pp. 632-636 ◽  
Author(s):  
Zhen Yuan Tian ◽  
Wei Wang ◽  
Xue Hao Li ◽  
Wei Ya Xu
Keyword(s):  
Constitutive Model ◽  
Failure Criterion ◽  
Elastic Characteristic ◽  
Damage Threshold ◽  
Model Parameters ◽  
Brittle Rocks ◽  
Good Accord ◽  
Damage Constitutive Model ◽  
Statistical Damage Constitutive Model ◽  
Statistical Damage

Micro-unit strength of rock is randomly distributed based on Lemaitres strain equivalence assumptions. The paper presents a method for measuring micro-unit strength taking into account the damage threshold. Assuming that the micro-unit strength obeys the Weibull distribution, combined with the Lade-Duncan failure criterion, a new statistical damage constitutive model for brittle rocks is established and the model parameters m and F0 are determined. The model can simulate the stress-strain relation of full process of rock failure well, especially reflects the influence of different stress on damage threshold and the linear elastic characteristic under low stress for rock. The good accord verifies the validity and feasibility of the new model.

scholarly journals Damage Model and Experimental Study of a Sand Grouting-Reinforced Body in a Seawater Environment

Water ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 2495
Author(s):  
Hongbo Wang ◽  
Quanwei Liu ◽  
Shangqu Sun ◽  
Qingsong Zhang ◽  
Zhipeng Li ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Underground Structure ◽  
Damage Model ◽  
Strain Curve ◽  
Sand Layer ◽  
Stress Strain Curve ◽  
Underground Engineering ◽  
Stress Strain ◽  
Seawater Environment

A water-rich sand layer is a common stratum in marine underground engineering. Grouting is a technology for soil or rock sealing, a method to solve the water seepage problem, and can be used to solve geological challenges in water-rich sand layers. A grouting-reinforced body deteriorates by the long-term erosion of seawater, resulting in attenuation of the performance of the solid. Obtaining the decay law of the performance of the grouting-reinforced body can guarantee the safe operation of the underground structure over a long life cycle. To this end, by describing the solid damage after seawater erosion, the stress–strain curve and the relationship between the damage variable and the internal micro-cracks and pores in the grouting-reinforced body were analyzed. Then, a constitutive model of the solid damage in the seawater environment was established. The stress–strain curve of added solid after deterioration was obtained by designing an indoor grouting reinforcement test and an accelerated deterioration test. Finally, the constitutive model of the sand layer plus solid deterioration in a seawater environment was determined. This research is of great importance for improving the deterioration theory under a seawater environment and ensuring the long term safety of tunnel operations.

scholarly journals An Improved Statistical Damage Constitutive Model for Granite under Impact Loading

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Zhenwei Zhao ◽  
Bo Wu ◽  
Xin Yang ◽  
Zhenya Zhang ◽  
Zhantao Li
Keyword(s):  
Constitutive Model ◽  
Elasticity Modulus ◽  
Strain Curve ◽  
Peak Strength ◽  
Peak Strain ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Damage Constitutive Model ◽  
Statistical Damage Constitutive Model ◽  
Statistical Damage

To study the impact properties of granite, the parameters (including the stress-strain curve, elasticity modulus, peak strength, and peak strain) of the test pieces in each group were determined via standard split-Hopkinson pressure bar tests. The results revealed that the prepeak stress-strain curves are approximately linear; the postpeak stress-strain curve declined sharply and exhibited the characteristics of brittle material failure after the stress exceeded the peak strength. In terms of the specimen form following failure, for increasing strain rate, the granite specimen became increasingly fragmented after failure. In addition, the single-parameter statistical damage constitutive model was improved, and a double-parameter statistical damage constitutive model for describing the total stress-strain curve of granite under the action of impact loading was proposed. The parameters of the statistical damage model, m and a, were obtained via fitting. The results revealed that the parameter m decreases with increasing elasticity modulus, whereas the parameter a increases. Similarly, the peak strength and the peak strain increased (in general) with increasing strain rate.

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