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 Triaxial Compressive Failure Characteristics and Constitutive Model Study of Jurassic-Cretaceous Weakly Cemented Sandstone

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Jinlong Cai ◽  
Wei Zou
Keyword(s):  
Constitutive Model ◽  
Residual Strength ◽  
Triaxial Compression ◽  
Volumetric Strain ◽  
Ductile Failure ◽  
Mathematical Expression ◽  
Confining Pressure ◽  
Mining Area ◽  
Peak Strength ◽  
Correction Coefficient

A conventional triaxial compression test of Jurassic-Cretaceous typical weakly consolidated sandstone from a mining area in Ordos, China, was conducted using an MTS816 tester. Results showed that, before the peak, the rock had a distinct yield stage. When the specimen reached its peak strength, the strength decreased rapidly and showed an obvious brittle failure. When the confining pressure was increased to 15 MPa, the decrease of strength was slow and the rock tended toward ductile failure. With the increase of confining pressure, the cyclic strain initially increased slightly, whereas the volumetric strain increased greatly and the rock sample was in a compression state. When the load reached a critical value, the curve was reversely bent, resulting in volume expansion, whereas the peak strength, residual strength, and elastic modulus increased with confining pressure, and Poisson’s ratio decreased with the confining pressure. In the model based on macroscopic failure rock, the expression of the relationship between fracture angle and confining pressure provided a solid theoretical basis for the direction and failure mode of the macroscopic crack. Based on the rock strength theory and Weibull random distribution assumption of rock element strength, the damage variable correction coefficient was introduced when the residual strength was considered. Then, the mathematical expression of the 3D damage statistical constitutive model was established. Finally, the theoretical curve of the established constitutive model was compared with the triaxial test curve, which showed a high degree of coincidence.

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.

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 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 the Damage Evolution Process and Fractal of Quartz-Filled Shale under Thermal-Mechanical Coupling

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zhonghu Wu ◽  
Huailei Song ◽  
Liping Li ◽  
Zongqing Zhou ◽  
Yujun Zuo ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Critical Temperature ◽  
Failure Mode ◽  
Damage Evolution ◽  
Damage Mechanics ◽  
Thermal Damage ◽  
Failure Modes ◽  
Factors Affecting ◽  
Mechanical Coupling ◽  
Theory Of Damage

Filling of brittle minerals such as quartz is one of the main factors affecting the initiation and propagation of reservoir fractures in shale fracturing, in order to explore the failure mode and thermal damage characteristics of quartz-filled shale under thermal-mechanical coupling. Combining the theory of damage mechanics and thermoelasticity, RFPA2D-Thermal is used to establish a numerical model that can reflect the damage evolution of shale under thermal-solid coupling, and the compression test under thermal-mechanical coupling is performed. The test results show that during the temperature loading process, there is a temperature critical value between 60°C and 75°C. When the temperature is less than the critical temperature, the test piece unit does not appear obvious damage. When the temperature is greater than the critical temperature, the specimen unit will experience obvious thermal damage, and the higher the temperature, the more serious the cracking. Under the thermal-mechanical coupling of shale, the tensile strength and elastic modulus of shale show a decreasing trend with the increase of temperature. The failure modes of shale under thermal-solid coupling can be roughly divided into three categories: “V”-shaped failure (30°C, 45°C, and 75°C), “M”-shaped failure (60°C), and inverted “λ”-shaped failure (90°C). The larger the fractal dimension, the more complex the failure mode of the specimen. The maximum fractal dimension is 1.262 when the temperature is 60°C, and the corresponding failure mode is the most complex “M” shape. The fractal dimension is between 1.071 and 1.189, and the corresponding failure mode is “V” shape. The fractal dimension is 1.231, and the corresponding failure mode is inverted “λ” shape.

Development of “Material Specific” Creep Continuum Damage Mechanics-Based Constitutive Equations

2020 ◽  
Author(s):  
Ricardo Vega ◽  
Jaime A. Cano ◽  
Calvin M. Stewart
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Creep Strain ◽  
Creep Deformation ◽  
Damage Evolution ◽  
Damage Mechanics ◽  
Constitutive Models ◽  
Continuum Damage Mechanics ◽  
Creep Strain Rate ◽  
Continuum Damage

Abstract The objective of this study is to introduce a method for creating “material specific” creep continuum damage mechanics-based constitutive models. Herein, material specific is defined as a constitutive model based on the mechanism-informed minimum creep strain rate (MCSR) equations found in deformation mechanism maps and calibrated to available material data. The material specific models are created by finding the best MCSR model for a dataset. Once the best MCSR model is found, the Monkman Grant inverse relationship between the MCSR and rupture time is employed to derive a rupture equation. The equations are substituted into continuum damage mechanics-based creep strain rate and damage evolution equations to furnish predictions of creep deformation and damage. Material specific modeling allows for the derivation of creep constitutive models that can better the material behavior specific to the available data of a material. The material specific framework is also advantageous since it has a systematic framework that moves from finding the best MCSR model, to rupture time, to damage evolution and, creep strain rate. Data for Alloy P91 was evaluated and a material specific constitutive model derived. The material specific model was able to accurately predict the MCSR, creep deformation, damage, and rupture of alloy P91.

scholarly journals A Study of Coupled Creep Damaged Constitutive Model of Artificial Frozen Soil

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Dongwei Li ◽  
Junhao Chen ◽  
Yan Zhou
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Damage Mechanics ◽  
Yield Criterion ◽  
Creep Damage ◽  
Confining Pressure ◽  
Frozen Soil ◽  
Finite Element Program ◽  
Finite Element Software ◽  
Frozen Clay

Artificial frozen soil is a kind of typical creep material, and the frozen clay under the unloading stress paths of high-confining pressure conforms to the improved the Zienkiewicz–Pande parabola-type yield criterion, and the Mohr–Coulomb yield function can describe the shear yield surface of artificial frozen clay under low-confining pressure. Based on the results of triaxial creep and shear tests for artificial frozen soil, the viscoplastic damage variable and evolution rule of artificial frozen clay were obtained by using the theory of viscoelastic-plastic mechanics and damage mechanics. An improved Zienkiewicz–Pande parabola-type yield criterion was used instead of a linear Newton body to obtain a coupled constitutive model of viscoelastic-plastic damage in the frozen soil under the unloading stress paths and to derive the coupling flexibility matrix for viscoelastic and viscoplastic damage. A finite element program of artificial frozen soil considering creep damage was written in the Visual Fortran 6.6A environment and embedded into the nonlinear finite element software ADINA as a user subroutine. The results of numerical simulation and laboratory testing were identical, with a maximum error of no more than 4.8%. This work shows that it is reasonable to describe the creep constitutive model of frozen soil with the viscoelastic-plastic-coupled constitutive model.

Application and Analysis of Plane Woven C/SiC Composites Based on Continuum Damage Mechanics

2012 ◽  
Vol 490-495 ◽  
pp. 3916-3919 ◽  
Author(s):  
Yan Jun Chang ◽  
Ke Shi Zhang ◽  
Gui Qiong Jiao ◽  
Jian Yun Chen
Keyword(s):  
Constitutive Model ◽  
Damage Evolution ◽  
Damage Mechanics ◽  
Kinematic Hardening ◽  
Ceramic Matrix Composites ◽  
Shear Loading ◽  
Internal Variables ◽  
Anisotropic Damage ◽  
Initial Modulus ◽  
Sic Composites

The aim of this article was to propose a macroscopic damage model, which describes the nonlinear behavior observed on woven C/SiC ceramic matrix composites. The model was built within a thermodynamic framework with internal variables. The anisotropic damage evolution processes of the material were described by nonlinear damage isotropic and kinematic hardening functions in this model. The anisotropic damage and damage coupling were considered with a damage yield function including anisotropic coefficients. Using the principle of energy equivalence, the damage variables were defined by the unloading modulus and initial modulus. The damage variable and the irrecoverable strain induced by micro-crack propagation were deduced by thermodynamics. The constants of constitutive model were identified and the damage evolution processes under tensile and shear loading. Uniaxial tension and shear tests had been used to valid the constitutive model to C/SiC composites.

scholarly journals Elastoplastic constitutive behavior and strain localization of a low-porosity sandstone during brittle fracturing

2021 ◽  
Author(s):  
Shihuai Zhang ◽  
Pei Guo ◽  
Shunchuan Wu
Keyword(s):  
Constitutive Model ◽  
Yield Surface ◽  
Strain Localization ◽  
Pure Shear ◽  
Failure Process ◽  
Frictional Coefficient ◽  
Peak Stress ◽  
Confining Pressure ◽  
Elastoplastic Behavior ◽  
Confining Pressures

We investigated the elastoplastic behavior and strain localization of the Zigong sandstone (porosity: 6.5%) during brittle fracturing based on two series of axisymmetric compression experiments. The experiments were conducted under various confining pressures (σ3 = 0 ~ 80 MPa). For each confining pressure, the sandstone specimens were deformed under constant axial and circumferential strain rates, respectively. When σ3 < 60 MPa, the sandstone first undergoes stable deformation in the post-peak stage and then loses its stability. Before the emergence of instability, the mechanical behavior is hardly affected by the controlling method. When the confining is larger, the sandstone manifests a stable failure process during the whole loading stage. The observed elastoplastic behavior was described by a two-yield surface constitutive model established in the framework of generalized plastic mechanics. The proposed constitutive model incorporates two quadratic yield functions, as well as two linearly independent plastic potential functions, to honor the shear yield and volumetric dilatancy, respectively. Via the return mapping algorithm, the proposed constitutive model was verified by comparing the numerical results with experimental results. In addition, the two-yield surface constitutive model, which is equivalent to the model proposed by Rudnicki and Rice,1 was applied to localization analysis. Assuming that the onset of localization occurs at peak stress, frictional coefficient μ and dilatancy factor β were determined from experimental data. The variations of both plastic parameters predict the transition of localization mode from pure dilation bands under uniaxial compression to pure shear bands at high confining pressures, which is consistent with the experimental observations.

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