scholarly journals A Statistical Damage Constitutive Model of Anisotropic Rock: Development and Validation

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Tenglong Rong ◽  
Can Guan ◽  
Keliu Liu ◽  
Shuai Heng ◽  
Wenlong Shen ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Damage Evolution ◽  
Stress Conditions ◽  
Anisotropic Damage ◽  
Anisotropic Rock ◽  
Stress Strain ◽  
True Triaxial ◽  
Damage Constitutive Model ◽  
Statistical Damage Constitutive Model ◽  
Statistical Damage

The damage constitutive model is of great significance to research the stress-strain relationship and damage evolution of rock under loading in engineering. In order to investigate the effect of anisotropic characteristic on the stress-strain relationship and damage evolution, a statistical damage constitutive model of anisotropic rock under true triaxial condition was developed. In this study, the plane which existed perpendicular to the coordinate axis was extracted from representative volume element (RVE) of rock. The extracted plane was assumed to be composed of abundant mesoscopic elements whose failure strength satisfied the Weibull distribution. According to the number of failure elements on the plane in each direction under loading, the anisotropic damage variable was established based on the proposed concept of areal damage. A statistical damage constitutive model of anisotropic rock was developed by using strain equivalent hypothesis and generalized Hooke constitutive model. Subsequently, the parameters in the anisotropic damage constitutive model were determined by the method of total differential. Thus, the damage evolution of anisotropic rock under various stress conditions can be conveniently evaluated by the anisotropic damage model. The model was validated based on the tests of rocks under the stress conditions of conventional triaxial and true triaxial, respectively. Moreover, for the purpose of studying the influence of parameters on the model, sensitivity analyses of mechanical parameters and model parameters were carried out. The results of statistical damage constitutive clearly demonstrate the stress-strain and damage evolution of anisotropic rock under various stress conditions.

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.

scholarly journals Mechanical Properties and Statistical Damage Constitutive Model of Rock under a Coupled Chemical-Mechanical Condition

Geofluids ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Yun Lin ◽  
Feng Gao ◽  
Keping Zhou ◽  
Rugao Gao ◽  
Hongquan Guo
Keyword(s):  
Mechanical Properties ◽  
Constitutive Model ◽  
Weibull Distribution ◽  
Damage Evolution ◽  
Chemical Corrosion ◽  
Mechanical Condition ◽  
Confining Pressures ◽  
Damage Constitutive Model ◽  
Statistical Damage Constitutive Model ◽  
Statistical Damage

Chemical corrosion has a significant impact on the damage evolution behavior of rock. To investigate the mechanical damage evolution process of rock under a coupled chemical-mechanical (CM) condition, an improved statistical damage constitutive model was established using the Drucker-Prager (D-P) strength criterion and two-parameter Weibull distribution. The damage variable correction coefficient and chemical damage variable which was determined by porosity were also considered in the model. Moreover, a series of conventional triaxial compressive tests were carried out to investigate the mechanical properties of sandstone specimens under the effect of chemical corrosion. The relationship between rock mechanics properties and confining pressure was also explored to determine Weibull distribution parameters, including the shape parameter m and scale parameter F0. Then, the reliability of the damage constitutive model was verified based on experimental data. The results of this study are as follows: (i) the porosity of sandstone increased and the mechanical properties degraded after chemical corrosion; (ii) the relationships among the compressive strength, the peak axial strain, and confining pressures were linear, while the relationships among the elastic modulus, the residual strength, and confining pressures were exponential functions; and (iii) the improved statistical damage constitutive model was in good agreement with the testing curves with R2>0.98. It is hoped that the study can provide an alternative method to analyze the damage constitutive behavior of rock under a coupled chemical-mechanical condition.

scholarly journals A Nonlinear Statistical Damage Constitutive Model for Porous Rocks

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Yue Pan ◽  
Zhiming Zhao ◽  
Liu He ◽  
Guang Wu
Keyword(s):  
Constitutive Model ◽  
Solid Skeleton ◽  
Porous Rocks ◽  
Different Types ◽  
Confining Pressures ◽  
Damage Constitutive Model ◽  
Statistical Damage Constitutive Model ◽  
Energy Theory ◽  
Water Contents ◽  
Statistical Damage

In the current paper, the deformation behaviours of rocks during compression are studied by testing 10 groups of sandstone samples with different porosity characteristics. According to the energy theory, the rock material was divided into two parts: solid skeleton and voids. A statistical damage-based approach was adopted to establish a nonlinear statistical damage constitutive model. The validity of the statistical damage constitutive model is verified by the test data. The statistical damage constitutive model performs well in each stage of rock compression before failure. For different types of rocks, different confining pressures, and different water contents, the statistical damage constitutive model fits well. This model can be applied to most types of rocks and in most engineering environments.

A statistical damage constitutive model considering whole joint shear deformation

2020 ◽  
Vol 29 (6) ◽  
pp. 988-1008 ◽  
Author(s):  
Shijie Xie ◽  
Hang Lin ◽  
Yixian Wang ◽  
Yifan Chen ◽  
Wei Xiong ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Damage Evolution ◽  
Shear Stiffness ◽  
Rock Joints ◽  
Residual Phase ◽  
Proposed Model ◽  
Damage Constitutive Model ◽  
Damage Theory ◽  
Joint Shear ◽  
Statistical Damage

The whole shear deformation of rock joints significantly affects the long-term behavior and safety of engineering projects. In this paper, a new damage constitutive model related to the Weibull distribution and statistical damage theory is proposed. This model considers the shear stiffness degradation, post-peak softening, and residual phase of rock joints in the whole shearing process. Main works include the three following aspects: First, the phase of initial damage is determined on the assumption that the joint shear failure is regarded as a result of damage evolution, according to the typical joint shear curve and the three-parameter Weibull distribution. Then, a statistical damage evolution model for the whole joint shearing process is introduced to make this model be capable of describing the residual phase of rock joints. Finally, a statistical constitutive model for the whole joint shearing process is proposed by statistical damage theory, and the calculated results of the models are compared to the experimental results. The results indicate that the proposed model shows a good agreement with the experimental examples, and the proposed model can distinctly reflect the effects of residual stress, peak stress, and shear stiffness. In addition, the model parameters can be mathematically confirmed and have distinct physical meanings.

Statistical Damage Constitutive Model for Concrete under Biaxial Tension

2013 ◽  
Vol 438-439 ◽  
pp. 183-186
Author(s):  
Wei Feng Bai ◽  
Jun Hong Zhang ◽  
Jun Feng Guan ◽  
Ying Cui
Keyword(s):  
Constitutive Model ◽  
Biaxial Tension ◽  
Damage Model ◽  
Damage Mechanism ◽  
Deformation Properties ◽  
Damage Constitutive Model ◽  
Strength And Deformation ◽  
Statistical Damage Constitutive Model ◽  
Damage Theory ◽  
Statistical Damage

Based on the statistical damage theory and the experimental phenomena, the statistical damage constitutive model for concrete under biaxial tension is proposed. The two meso-scale damage modes, rupture and yield are considered, and the whole damage evolution process is driven by the principal tensile damage strain. The results show that the proposed statistical damage model can accurately predict the constitutive behavior in the uniform damage phase for concrete under biaxial tension. The damage mechanism is discussed in the view point of biaxial strength and deformation properties.

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.

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