scholarly journals Solution of Strain-Softening Surrounding Rock in Deep Tunnel Incorporating 3D Hoek-Brown Failure Criterion and Flow Rule

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Jin-feng Zou ◽  
Song-qing Zuo ◽  
Yuan Xu
Keyword(s):  
Principal Stress ◽  
Failure Criterion ◽  
Strain Softening ◽  
Numerical Procedure ◽  
Intermediate Principal Stress ◽  
Surrounding Rock ◽  
Flow Rule ◽  
Stress Equilibrium ◽  
Novel Approach ◽  
Dilatancy Effect

In order to investigate the influence of the intermediate principal stress on the stress and displacement of surrounding rock, a novel approach based on 3D Hoek-Brown (H-B) failure criterion was proposed. Taking the strain-softening characteristic of rock mass into account, the potential plastic zone is subdivided into a finite number of concentric annulus and a numerical procedure for calculating the stress and displacement of each annulus was presented. Strains were obtained based on the nonassociated and associated flow rule and 3D plastic potential function. Stresses were achieved by the stress equilibrium equation and generalized Hoek-Brown failure criterion. Using the proposed approach, we can get the solutions of the stress and displacement of the surrounding rock considering the intermediate principal stress. Moreover, the proposed approach was validated with the published results. Compared with the results based on generalized Hoek-Brown failure criterion, it is shown that the plastic radius calculated by 3D Hoek-Brown failure criterion is smaller than those solved by generalized H-B failure criterion, and the influences of dilatancy effect on the results based on the generalized H-B failure criterion are greater than those based on 3D H-B failure criterion. The displacements considering the nonassociated flow rule are smaller than those considering associated flow rules.

scholarly journals A Numerical Approach for the Quasi-Plane Strain-Softening Problem of Cylindrical Cavity Expansion Based on the Hoek-Brown Failure Criterion

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Jin-feng Zou ◽  
Jia-min Du
Keyword(s):  
Plastic Strain ◽  
Plane Strain ◽  
Principal Stress ◽  
Failure Criterion ◽  
Strain Softening ◽  
Axial Direction ◽  
Intermediate Principal Stress ◽  
Surrounding Rock ◽  
Cavity Expansion ◽  
Cylindrical Cavity Expansion

This paper focuses on a novel approach for the quasi-plane strain-softening problem of the cylindrical cavity expansion based on generalized Hoek-Brown failure criterion. Because the intermediate principal stress is deformation-dependent, the quasi-plane strain problem is defined to implement the numerical solution of the intermediate principal stress. This approach assumes that the initial total strain in axial direction is a nonzero constant (ε0) and the plastic strain in axial direction is not zero. Based on 3D failure criterion, the numerical solution of plastic strain is given. Solution of the intermediate principal stress can be derived by Hooke’s law. The radial and circumferential stress and strain considering the intermediate principal stress are obtained by the proposed approach of the intermediate principal stress, stress equilibrium equation, and generalized H-B failure criterion. The numerical results can be used for the solution of strain-softening surrounding rock. In additional, the validity and accuracy of the proposed approach are verified with the published results. At last, parametric studies are carried out using MATLAB programming to highlight the influences of the out-of-plane stress on the stress and displacement of surrounding rock.

scholarly journals A Proposed Algorithm to Compute the Stress-Strain Plastic Region and Displacement of a Deep-Lying Tunnel Considering Intermediate Stress and Strain-Softening Behavior

2021 ◽  
Vol 12 (1) ◽  
pp. 85
Author(s):  
Jinwang Li ◽  
Xiufeng He ◽  
Caihua Shen ◽  
Xiangtian Zheng
Keyword(s):  
Principal Stress ◽  
Radial Displacement ◽  
Strain Softening ◽  
Plastic Region ◽  
Intermediate Principal Stress ◽  
Surrounding Rock ◽  
Parameter Analysis ◽  
Flow Rule ◽  
Stress Strain ◽  
Softening Behavior

Past studies on deep-lying tunnels under the assumption of plane strain have generally neglected the influence of intermediate principal stress even though this affects the surrounding rocks in the plastic zone. This study proposes a finite difference method to compute the stress strain plastic region and displacement of a tunnel based on the Drucker–Prager (D–P) yield criterion and non-associated flow rule and considering the influences of intermediate principal stress and the strain-softening behavior of surrounding rock. The computed results were compared with those of other well-known solutions and the accuracy and validity of the method were confirmed through some examples. Parameter analysis was conducted to investigate the effects of intermediate principal stress on stress-strain, the plastic region, the ground response curve, and the dilatability of surrounding rock. The results showed that the plastic radius , the residual radius , and radial displacement of surrounding rock first decreased and then increased with increasing intermediate principal stress coefficient b from 0 to 1, with the minimums occurring at b = 0.75. On the contrary, the peak and rate of variation of the dilatancy coefficient first increased and then decreased with increasing b and the dilatancy coefficient gradually transitioned from nonlinear to linear variation. Meanwhile, the inhibition of the plastic radius and radial displacement gradually weakened with increasing support pressure, whereas the dilatancy coefficient of the tunnel opening gradually increased.

Numerical solutions for strain-softening surrounding rock under three-dimensional principal stress condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sheng Yu-ming ◽  
Li Chao ◽  
Xia Ming-yao ◽  
Zou Jin-feng
Keyword(s):  
Finite Element ◽  
Principal Stress ◽  
Stress Condition ◽  
Strain Softening ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Strength Criterion ◽  
Surrounding Rock ◽  
Flow Rule ◽  
Finite Element Software

Abstract In this study, elastoplastic model for the surrounding rock of axisymmetric circular tunnel is investigated under three-dimensional (3D) principal stress states. Novel numerical solutions for strain-softening surrounding rock were first proposed based on the modified 3D Hoek–Brown criterion and the associated flow rule. Under a 3D axisymmetric coordinate system, the distributions for stresses and displacement can be effectively determined on the basis of the redeveloped stress increment approach. The modified 3D Hoek–Brown strength criterion is also embedded into finite element software to characterize the yielding state of surrounding rock based on the modified yield surface and stress renewal algorithm. The Euler implicit constitutive integral algorithm and the consistent tangent stiffness matrix are reconstructed in terms of the 3D Hoek–Brown strength criterion. Therefore, the numerical solutions and finite element method (FEM) models for the deep buried tunnel under 3D principal stress condition are presented, so that the stability analysis of surrounding rock can be conducted in a direct and convenient way. The reliability of the proposed solutions was verified by comparison of the principal stresses obtained by the developed numerical approach and FEM model. From a practical point of view, the proposed approach can also be applied for the determination of ground response curve of the tunnel, which shows a satisfying accuracy compared with the measuring data.

scholarly journals Three-Dimensional Numerical Analysis of the Tunnel for Polyaxial State of Stress

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Wenge Qiu ◽  
Chao Kong ◽  
Kai Liu
Keyword(s):  
Numerical Simulation ◽  
Mechanical Behavior ◽  
Principal Stress ◽  
Failure Criterion ◽  
Rock Strength ◽  
Strength Criterion ◽  
Intermediate Principal Stress ◽  
State Of Stress ◽  
Coulomb Failure ◽  
Coulomb Failure Criterion

The aim of this study is to have a comprehensive understanding of the mechanical behavior of rock masses around excavation under different value of intermediate principal stress. Numerical simulation was performed to investigate the influence of intermediate principal stress using a new polyaxial strength criterion which takes polyaxial state of stress into account. In order to equivalently substitute polyaxial failure criterion with Mohr-Coulomb failure criterion, a mathematical relationship was established between these two failure criteria. The influence of intermediate principal stress had been analyzed when Mohr-Coulomb strength criterion and polyaxial strength criterion were applied in the numerical simulation, respectively. Results indicate that intermediate principal stress has great influence on the mechanical behavior of rock masses; rock strength enhanced by intermediate principal stress is significant based on polyaxial strength criterion; the results of numerical simulation under Mohr-Coulomb failure criterion show that it does not exert a significant influence on rock strength. Results also indicate that when intermediate principal stress is relatively small, polyaxial strength criterion is not applicable.

A General Criterion for Complex Rocks and Soils and its Application

2014 ◽  
Vol 580-583 ◽  
pp. 243-249
Author(s):  
Huai Ning Ruan ◽  
Man Lu Luo ◽  
Di Wang ◽  
J. W. Ju
Keyword(s):  
Principal Stress ◽  
Failure Criterion ◽  
General Model ◽  
Engineering Application ◽  
Nonlinear Behavior ◽  
Failure Criteria ◽  
Intermediate Principal Stress ◽  
General Criterion ◽  
Special Cases

A failure criterion is proposed for complex rocks and soils. Their anisotropic and nonlinear behavior is analyzed theoretically and experimentally. The influence of the intermediate principal stress is taken into account. The nonhomogeneous strength and the effect of geological temperature are also discussed. Many classical failure criteria are special cases of the proposed condition. The criterion is applied in the analysis of the bedrock of Ankang Dam in China. The case study illustrates the potential of the proposed general model in engineering application.

scholarly journals Stability Analysis of Surrounding Rock in Circular Tunnels Based on Critical Support Pressure

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Hao Fan ◽  
Lianguo Wang ◽  
Kai Wang
Keyword(s):  
Principal Stress ◽  
Strain Softening ◽  
Damage Zone ◽  
Intermediate Principal Stress ◽  
Damage Variable ◽  
Support Pressure ◽  
Initial Field ◽  
Tunnel Stability ◽  
Stress Coefficient ◽  
Softening Coefficient

Accurate calculation for the critical support pressure of tunnels plays an important role in tunnel stability evaluation and support design. In this study, a mechanical model for circular tunnels is developed. Considering the intermediate principal stress and strain-softening characteristic of rock mass, the critical support pressure when the plastic zone and damage zone begin to occur is determined based on the unified strength criterion and strain-softening model. Through the example study, the critical support pressure under different intermediate principal stress coefficient is solved. Furthermore, the effect of initial field stress, softening coefficient, and maximum damage variable on the critical support pressure are also discussed. The results show that the critical support pressure and radii of plastic and damage zones all decrease with the increase of the intermediate principal stress coefficient. The larger the initial field stress, the larger the critical support pressure. The softening coefficient and maximum damage variable of rock mass has no influence on the critical support pressure when the plastic zone begins to form, but has a significant effect on the critical support pressure when the damage zone begins to form. As softening coefficient increases and maximum damage variable decreases, the critical support pressure when the damage zone which begins to form increases. Data presented in this contribution provide significant theoretical insights into evaluating tunnel stability and support system reliability.

Slope Stability Analysis Using Unified Strength Theory

2011 ◽  
Vol 137 ◽  
pp. 59-64
Author(s):  
Zong Yuan Ma ◽  
Hong Jian Liao ◽  
Mao Hong Yu
Keyword(s):  
Slope Stability ◽  
Plane Strain ◽  
Principal Stress ◽  
Stability Problem ◽  
Factor Of Safety ◽  
Intermediate Principal Stress ◽  
Flow Rule ◽  
Problem Analysis ◽  
Strength Theory ◽  
Unified Strength Theory

Numerical computations using finite difference method and unified strength theory are reported to analyze the slope stability problem. The Factor of safety of plane strain and axisymmetric slopes was calculated by strength reducing method, and the influences of intermediate principal stress on slope stability problem was analyzed. The associative and non-associative flow rule was taking into account in plane strain slope problem analysis. The intermediate principal stress has equivalent influences on slope stability problem under associative and non-associative flow rule. The Factor of safety of plane strain slope is lower than the axisymmetric situation. The influence of intermediate principal stress on slope stability under plane strain condition is heavier than axisymmetry.

scholarly journals The Plastic Zone of Tunnel Surrounding Rock under Unequal Stress in Two Directions Based on the Unified Strength Theory

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Zongshan Zou ◽  
Jun Yang ◽  
Zhongming Wang ◽  
Hongyan Liu
Keyword(s):  
Plastic Zone ◽  
Principal Stress ◽  
Interaction Mechanism ◽  
Strength Criterion ◽  
Intermediate Principal Stress ◽  
Surrounding Rock ◽  
Elastic Displacement ◽  
Strength Theory ◽  
Support Structure ◽  
Unified Strength Theory

For the deficiencies that the existing calculation theory for the Plastic Zone of Tunnel Surrounding Rock (PZTSR) does not consider the effect of the intermediate principal stress σ2 and interaction between the surrounding rock and support structure on the PZTSR under unequal stress, the Unified Strength Theory (UST) for the rock is adopted to replace the often used Mohr-Coulomb (M-C) strength criterion to consider the effect of σ2 on the PZTSR. Meanwhile, the interaction mechanism between the surrounding rock and support structure is also considered in the proposed model. Finally, the effect of the initial elastic displacement of the surrounding rock, stiffness of the support structure, and the coefficient b of the intermediate principal stress on the plastic zone is discussed. The results show that the PZTSR will increase nonlinearly with increasing the initial elastic displacement of the surrounding rock, and when it increases to a certain value, its increase extent will be much obvious. With increasing the stiffness of the support structure, the PZTSR will gradually decrease nonlinearly, but the decrease extent is not very much. With increasing b, the PZTSR will decrease; namely, σ2 can improve the stress condition of the surrounding rock and reduce the PZTSR.

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