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.

scholarly journals Unified Analytical Solutions of Circular Tunnel Excavated in an Elastic-Brittle-Plastic Rock Mass considering Blast-Induced Damage and Dead Weight Loading

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Yue Cao ◽  
Liang Chen ◽  
Jinhai Xu ◽  
Chong Li ◽  
Wei Zhang
Keyword(s):  
Rock Mass ◽  
Principal Stress ◽  
Support System ◽  
Fracture Zone ◽  
Damage Zone ◽  
Intermediate Principal Stress ◽  
Circular Tunnel ◽  
Tunnel Stability ◽  
Stress And Deformation ◽  
Zone Radius

Stress and deformation around circular tunnel are crucial for optimizing the support system and evaluating the tunnel stability. The damage zone induced by blasting or mechanical excavation can dramatically influence the support design and methods because the self-weight of broken rock mass at the roof of the tunnel can exert a high pressure on the support system, leading to the support system instability due to the overload. This paper presents a new closed-form solution for analyzing the stress and deformation of deep circular tunnel excavated in elastic-brittle rock mass with the consideration of the rock gravity and damage zone by using the unified strength criterion. A new modified equilibrium equation in the fracture zone is used to determine the stress and the radius of fracture zone. The correctness of the solution is also verified by comparison with the numerical simulation results. The results illustrate that the rock gravity, damage zone radius, and intermediate principal stress have an extremely important influence on the ground response. The tunnel surface convergence and damage zone radius with the consideration of the gravity are obviously larger than those without consideration of the gravity. The rock gravity effect under the high intermediate principal stress gradually weakens, illustrating that the intermediate principal stress is beneficial to tunnel stability. Large deformation instability of the tunnel is dependent on the extension of damage zone. The larger the radius of damage zone, the larger both fracture range and tunnel surface deformation. The proposed solution in this study is novel and can be used to assess the ground convergence for different scenarios and to optimize the support system during the early design stage of the tunnel.

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 Analysis of Three-Dimensional Damage Constitutive Model of Frozen Sand Based on the Influence of Intermediate Principal Stress and Temperature

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Shilong Ma ◽  
Zhaoming Yao ◽  
Shuang Liu ◽  
Xuan Pan
Keyword(s):  
Constitutive Model ◽  
Weibull Distribution ◽  
Principal Stress ◽  
Three Dimensional ◽  
Intermediate Principal Stress ◽  
Frozen Soil ◽  
Stress Coefficient ◽  
Frozen Sand ◽  
Distribution Parameters ◽  
Damage Constitutive Model

To study the mechanical properties of frozen soil, it is necessary to understand the damage characteristics of frozen soil. Four types of three-dimensional indoor tests of frozen sand were carried out at −5°C, −10°C, and −15°C to study the mechanical damage properties. These include different stress path tests with the principal stress coefficients of 0, 0.25, 0.5, and 0.75 while analyzing the entire failure process. First, the three-dimensional compression test of frozen sand was studied to analyze the influence of temperature and intermediate principal stress coefficient on the large principal stress of frozen soil. The damage cost of frozen sand under the influence of different temperatures and intermediate principal stress coefficients was also established. Second, using the characteristics of discreteness and randomness of the distribution of the microelements inside the frozen soil and assuming that the failure of the microelement of the frozen soil obeys the Weibull distribution, the Drucker–Prager strength criterion was used as the statistical distribution variable of the microelement of the frozen soil based on the strain equivalence hypothesis, statistical theory, and continuous damage mechanics. This allows for a constitutive model of frozen sand damage under the three-dimensional stress state to be established. Finally, the model parameter values through low-temperature three-dimensional test data were able to be determined. This model allows for the physical meaning of Weibull distribution parameters F0 and m to be analyzed, and the distribution parameters with temperature and intermediate principal stress coefficient can be modified to obtain a modified frozen sand damage constitutive model. The results show that the modified damage constitutive model can simulate the entire process curve of the large principal stress-strain of frozen sand. It shows that the large principal stress of frozen sand increases with the increase of temperature and intermediate principal stress coefficient. Concurrently, the frozen sand damage constitutive model proposed in this paper can describe the deformation behavior of frozen soil under different temperature and stress paths and can be adapted to various other sediment types.

The Changing Rule of Rock Strength under True Triaxial Condition

2014 ◽  
Vol 522-524 ◽  
pp. 1410-1413
Author(s):  
Ze Kang Wen ◽  
Ke Min Wei ◽  
Jia Quan Hu ◽  
You Ling Fang
Keyword(s):  
Principal Stress ◽  
Rock Strength ◽  
Quadratic Function ◽  
Intermediate Principal Stress ◽  
Stress Effect ◽  
True Triaxial Test ◽  
True Triaxial ◽  
Minimum Principal Stress ◽  
Stress Coefficient ◽  
Intermediate Principal Stress Effect

The intermediate principal stress effect of the rock has been demonstrated. By analyzing true triaxial test results of Dunham dolomite and Mizuho trachyte, we studied relationship between minimum principal stress and the rock strength under the same intermediate principal stress coefficient, and the relationship between intermediate principal stress and the rock strength under the same minimum principal stress condition. Research shows that the minimum principal stress has a linear relation with the rock strength, the intermediate principal stress coefficient of a quadratic function relation with the rock strength. And the mathematic expression of the intermediate principal stress effect function was calculated.

scholarly journals Experimental Study on Noncoaxial Characteristics of Saturated Remolded Loess

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Xuemeng Jiang ◽  
Haoshuang Niu ◽  
Wenpeng Huang ◽  
Xuwen Shang ◽  
Deng Wang
Keyword(s):  
Principal Stress ◽  
Elastic Strain ◽  
Stress Amplitude ◽  
Intermediate Principal Stress ◽  
Deviatoric Stress ◽  
Stress Axis ◽  
Cycle Number ◽  
Stress Coefficient ◽  
Practical Engineering ◽  
Axis Rotation

In practical engineering, if the influence of noncoaxial stress and strain is not considered, part of soil deformation will be ignored, resulting in the structural design which is not safe enough. A series of undrained tests was performed on remolded loess specimens using a hollow cylinder apparatus to examine the coupling between principal stress magnitude and direction in these specimens. First, the elastic parameters of remolded loess were obtained, and these parameters were used as the basis for investigating the noncoaxiality of the soil body under principal stress axis rotation (PSAR). The effects of elastic strain, intermediate principal stress coefficient, and magnitude of the deviatoric stress on the noncoaxiality of remolded loess were also investigated. The results of these experiments show that remolded loess exhibits significant noncoaxial behavior during PSAR. The noncoaxiality angle of remolded loess cyclically fluctuates with increases in the principal stress angle. It was also observed that the noncoaxiality angle will be overestimated if the effects of elastic strain are overlooked. Reversals in the direction of PSAR cause dramatic changes in the noncoaxiality angle. Increases in the intermediate principal stress coefficient are accompanied by increases in the noncoaxiality angle, up to a certain degree; however, these changes do not affect the development of the noncoaxiality angle. In coupled rotational tests with a range of deviatoric stress amplitudes, it was observed that changes in the deviatoric stress amplitude will affect the development of the noncoaxiality angle; increases in the deviatoric stress amplitude cause the noncoaxiality angle versus principle stress angle plot to shift to the left gradually, thus accelerating the trends of the noncoaxiality angle. Increases in the cycle number also increase the noncoaxiality of remolded loess.

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 New Unified Solution for Circular Tunnel Based on a Four-Stage Constitutive Model considering the Intermediate Principal Stress

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Liang Chen ◽  
Xianbiao Mao ◽  
Yanlong Chen ◽  
Ming Li ◽  
Yang Hao ◽  
...  
Keyword(s):  
Strain Softening ◽  
Damage Zone ◽  
Surface Displacement ◽  
Plastic Shear ◽  
Circular Tunnel ◽  
Plastic Model ◽  
Dilation Angle ◽  
Perfectly Plastic ◽  
Plastic Shear Strain ◽  
Softening Coefficient

Based on the triaxial test, the elasto-perfectly plastic strain-softening damage model (EPSDM) is proposed as a new four-stage constitutive model. Compared with traditional models, such as the elasto-brittle-plastic model (EBM), elasto-strain-softening model (ESM), elasto-perfectly plastic model (EPM), and elasto-peak plastic-brittle plastic model (EPBM), this model incorporates both the plastic bearing capacity and strain-softening characteristics of rock mass. Moreover, a new closed-form solution of the circular tunnel is presented for the stress and displacement distribution, and a plastic shear strain increment is introduced to define the critical condition where the strain-softening zone begins to occur. The new analysis solution obtained in this paper is a series of results rather than one specific solution; hence, it is suitable for a wide range of rock masses and engineering structures. The numerical simulation has been used to verify the correctness of the EPSDM. The parametric studies are also conducted to investigate the effects of supporting resistance, residual cohesion, dilation angle, strain-softening coefficient, plastic shear strain increment, and yield parameter on the result. It is shown that when the supporting resistance is fully released, both the post-peak failure radii and surface displacement could be summarized as EBM > EPBM > ESM > EPSDM > EPM; the dilation angle in the damage zone had the highest influence on the surface displacement, whereas the dilation angle in the perfectly plastic zone had the lowest influence; the strain-softening coefficient had the most significant effect on the damage zone radii; the EPSDM is recommended as the optimum model for support design and stability evaluation of the circular tunnel excavated in the perfectly plastic strain-softening rock mass.

Influences of principal stress direction and intermediate principal stress on the stress–strain–strength behaviour of completely decomposed granite

2010 ◽  
Vol 47 (2) ◽  
pp. 164-179 ◽  
Author(s):  
Md. Kumruzzaman ◽  
Jian-Hua Yin
Keyword(s):  
Principal Stress ◽  
Hollow Cylinder ◽  
Friction Angle ◽  
Intermediate Principal Stress ◽  
Principal Stress Direction ◽  
Stress Direction ◽  
Stress Coefficient ◽  
Decomposed Granite ◽  
Shear Condition ◽  
Completely Decomposed Granite

The measurement and study of the stress–strain–strength behaviour of soils in general stress states involving the change of magnitudes and direction of the principal stresses are necessary and important. To investigate the strength behaviour under such conditions, consolidated undrained tests on remoulded hollow cylinder specimens of completely decomposed granite (CDG) were carried out using a hollow cylinder apparatus. Tests were conducted by maintaining a fixed principal stress direction with angle α from the vertical direction together with a fixed value of intermediate principal stress coefficient b. It is observed that the value of the friction angle decreases with an increase in α and the failure surface is anisotropic. There is an increase in friction angle with an increase in b value up to b = 0.25, and the friction angles are almost the same for b > 0.25. In addition, the behaviour of the soil in an undrained simple shear condition was examined. The simple shear condition is very near to the condition of α = 45° and b = 0.25. After having analyzed the test results of all hollow cylinder specimens, it was found that the strength anisotropy is very strong and is dependent on the principal stress direction and intermediate principal stress coefficient.

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.

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