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 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 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 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 Investigation into the gas adsorption-loading coupling damage constitutive model of coal rock

2021 ◽  
Vol 14 (15) ◽  
Author(s):  
Zhongzhong Liu ◽  
Hanpeng Wang ◽  
Su Wang ◽  
Yang Xue ◽  
Chong Zhang
Keyword(s):  
Constitutive Model ◽  
Gas Adsorption ◽  
Damage Constitutive Model ◽  
Coal Rock

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.

CYCLIC DAMAGE IN STEEL EXPERIENCING SEISMIC LOADING

2010 ◽  
Vol 24 (15n16) ◽  
pp. 2478-2483 ◽  
Author(s):  
C. K. SEAL ◽  
M. A. HODGSON ◽  
W. G. FERGUSON
Keyword(s):  
Failure Modes ◽  
Strain Curve ◽  
Field Analysis ◽  
Test Results ◽  
Steel Members ◽  
Growing Crack ◽  
Load Regime ◽  
Remaining Capacity ◽  
Accumulation Of Damage ◽  
Cyclic Damage

During the mid 1990s earthquakes in Northridge, California, and Kobe, Japan, illustrated a lack of understanding of the behaviour of structural steels exposed to seismic loads. Under this type of load regime, structural steel members are subjected to fully plastic load cycles and unexpectedly brittle failures may result. A method for determining the accumulation of damage through cyclic pre-straining is proposed. Toughness, as defined by the area under the true stress strain curve, is used as an indicator of the level of damage that the steel has suffered and from this some idea of its remaining capacity to further deform can be determined. Observations during the testing of these samples have indicated that there is a transition in the failure mode from a fatigue type failure, with a progressively growing crack, to an overload failure, in which the steel fails due to a lack of ability to further deform. Similar transitions have been noted by other researchers in the field. Analysis of the test results seems to show differences in the damage accumulation behaviour that may be used to identify when this transition in failure modes may occur.

The Studies of Rock Damage Softening Statistical Constitutive Model under True Triaxial Stress State

2014 ◽  
Vol 580-583 ◽  
pp. 312-315
Author(s):  
Hui Mei Zhang ◽  
Xiang Miao Xie ◽  
Geng She Yang
Keyword(s):  
Constitutive Model ◽  
Strain Curve ◽  
Stress Path ◽  
Complex Stress ◽  
Model Parameters ◽  
Stress Strain ◽  
Deformation And Failure ◽  
True Triaxial ◽  
Complex Stress Path ◽  
The Impact

From the feature of rock micro-unit failure obeys Poisson random distribution, the damage softening statistical constitutive of was established under true triaxial confinement based on D-P criterion, so the impact of the intermediate principal stress on rock deformation and failure was considered in theory, and the actual engineering rock complex stress path evolution was reflected more realistically. Furthermore, according to the geometrical conditions of stress-strain relationship, the theoretical relationship between constitutive model parameters and the stress-strain curve characteristic parameters during the process of rock softening and deforming, which enhance the adaptability of the model. Finally, the rationality of the model verified by the measured data.

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