scholarly journals The Elastoplastic Solutions of Deep Buried Roadway Based on the Generalized 3D Hoek-Brown Strength Criterion considering Strain-Softening Properties

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Rui Wang ◽  
Jian-biao Bai ◽  
Shuai Yan ◽  
Zhi-guo Chang ◽  
Yuan-ba Song ◽  
...  
Keyword(s):  
Strain Softening ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Strength Criterion ◽  
Surrounding Rock ◽  
Theoretical Research ◽  
Flow Rule ◽  
Softening Behavior ◽  
Deep Underground ◽  
Elastoplastic Solutions

The deep underground roadways are widely used in the mining industries at present, but the relevant theoretical bases are not fully understood. In this paper, the numerical solutions for strain-softening surrounding rock under the generalized three-dimensional (3D) Hoek-Brown (GZZ) strength criterion are developed incorporating the confinement-dependent characteristics of ψ and η ∗ and their influences on the stress and displacement of equivalent circular roadway. On the basic of a finite difference, method for the strain-softening model is proposed to consider the variation of ψ and η ∗ in analyzing the strain-softening behavior of rock masses. Combining the equilibrium equation and strength criterion, the stress conditions for each annulus are calculated analytically. The displacement for each step is obtained analytically by solving the differential equation through invoking flow rule and Hooke’s law. The accuracy of the proposed method is verified through the comparison between the results and the previous studies. The effect of intermediate principal stress of GZZ strength criterion is considered; the rationality of the proposed method is verified by two aspects. First, by comparing with the two-dimensional narrow and generalized H-B strength criterion, the advantage of GZZ strength criterion that considers the effect intermediate main stress is highlighted. On the other hand, compared with the three-dimensional linear D-P criterion, the advantage of GZZ strength criterion in the theoretical research of deep underground roadway in coal mine is highlighted. The results show that the strain-softening of the surrounding rock in the plastic zone of the roadway can reduce the pressure of the surrounding rock, but it will greatly increase its deformation. In the high field stress areas, the strain-softening of surrounding rock is the key reason for the destruction of the roadway. It is suggested that in the design and calculation of the support system of the roadway, the strain-softening characteristics of the surrounding rock should be considered, which is very important to avoid large deformation and damage of roadway.

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 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.

scholarly journals Semianalytical Solution for Large Deformation of Salt Cavern with Strain-Softening Behavior

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Lina Ran ◽  
Huabin Zhang ◽  
Qingqing Zhang
Keyword(s):  
Plastic Zone ◽  
Large Deformation ◽  
Strain Softening ◽  
Structural Characteristics ◽  
Strength Criterion ◽  
Geological Strength Index ◽  
Salt Rock ◽  
Salt Cavern ◽  
Softening Behavior ◽  
The Impact

A semianalytical solution of stress and displacement in the strain-softening and plastic flow zones of a salt cavern is presented. The solution is derived by adopting the large deformation theory, considering the nonlinear Hoek–Brown (H-B) strength criterion. The Romberg method is used to carry out numerical calculation, and then, the large deformation law of displacement is analyzed. The results are compared with those obtained by former numerical methods, and the solutions are validated. The results indicate that the displacement of the plastic zone decreases with the increase in distance away from the salt cavern. Similarly, it decreases with an increase in the geological strength index or running pressure, with the running pressure having a more significant effect on the displacement. It increases with the dilation angle, and the impact degree gradually increases. Compared with the softening parameter, h, of the plastic zone, the flow parameter, f, has little impact on the displacement. The displacement of the plastic zone obviously increased when considering the strain-softening of salt rock. When considering the shear dilation and softening behaviors of salt rock, the analytical solution obtained by employing the experiential regression Hoek–Brown (H-B) criterion, which considers many factors such as the structural characteristics of the salt formation and the rock mass quality, is safer and closer to the actual situation. This study can provide reference for many applications, including but not confined to analyzing the deformation of the surrounding rock of an underground salt cavern storage facility during construction.

An Associative and Non-Associative Anisotropic Bounding Surface Model for Clay

2012 ◽  
Vol 79 (3) ◽  
Author(s):  
Jianhong Jiang ◽  
Hoe I. Ling ◽  
Victor N. Kaliakin
Keyword(s):  
Mechanical Behavior ◽  
Strain Hardening ◽  
Strain Softening ◽  
Surface Model ◽  
Flow Rule ◽  
Reasonable Accuracy ◽  
Bounding Surface ◽  
Softening Behavior ◽  
Different Types ◽  
Undrained Behavior

An anisotropic elastoplastic bounding surface model with non-associative flow rule is developed for simulating the mechanical behavior of different types of clays. The non-associative flow rule allows for the simulation of not only strain-hardening but also strain-softening response. The theoretical framework of the model is given, followed by the verification of the model as applied to the experimental results of a strain-hardening Kaolin tested under different undrained stress paths. The undrained behavior of Boston Blue clay, which exhibits a strain-softening behavior, is also simulated. It is shown that the non-associative nature of the model gives more accurate results than those of the same model employing an associative flow rule, especially for normally consolidated Kaolin specimens. The results show that the model is also capable of simulating the strain-softening behavior of Boston blue clay with reasonable accuracy.

scholarly journals An Innovative Elastoplastic Analysis for Soft Surrounding Rock considering Supporting Opportunity Based on Drucker-Prager Strength Criterion

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Rui Wang ◽  
Xu-dong Liu ◽  
Jian-biao Bai ◽  
Shuai Yan ◽  
Jun Xu
Keyword(s):  
Strength Criterion ◽  
Homogenization Method ◽  
Surrounding Rock ◽  
Theoretical Research ◽  
Underground Engineering ◽  
Support Design ◽  
Interval Distance ◽  
Space Effect ◽  
The Stability ◽  
Supporting Condition

In order to study the mechanism of excavation and supporting process of equivalent circular roadway, the model of soft roadway was established firstly. The elastoplastic solutions in excavation process were deduced based on Drucker-Prager strength criterion. Then, the elastoplastic solution under supporting condition was obtained based on homogenization method under the condition of rockbolts and liner supporting. Lastly, an example was analyzed to study the effect of different factors such as “space effect,” supporting opportunity, stresses, surrounding displacement, and the radius of plastic zone. Based on theoretical research case, the change rules of considering the “space effect” and the supporting opportunity when calculating the subarea of the roadway were discussed, the control of interval distance of rockbolts on the displacement of surrounding rock mainly reflecting in the plastic residual zone and the “space effect” in excavation, and the supporting time to control the displacement of surrounding rock not being ignored are revealed. The results can provide an important theoretical basis for the stability evaluation and quantitative support design of roadway surrounding rock. Therefore, the “space effect” and the supporting time to control the displacement and stresses of surrounding rock can not being ignored in underground engineering.

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.

Constitutive Model of Strain Softening for Soft Rock

2011 ◽  
Vol 250-253 ◽  
pp. 1932-1935
Author(s):  
Song Li ◽  
Hong Jian Liao ◽  
Hang Zhou Li
Keyword(s):  
Constitutive Model ◽  
Strain Softening ◽  
Three Dimensional ◽  
Soft Rock ◽  
Unified Strength Theory ◽  
Softening Behavior ◽  
Proposed Model ◽  
Deviatoric Plane ◽  
Modified Equation ◽  
Rock Specimens

This paper aims to study the strain softening behavior of soft rock. A modified equation of unified strength theory is proposed that is convenient to be applied in geotechnical engineering where compression is customarily taken as positive. And also the limit line on deviatoric plane of this modified equation is derived and introduced into the three dimensional (3D) elastic viscoplastic constitutive model of Yin and Graham. Parameters of the model are determined from experiments of the diatom soft rock specimens. Numerical simulations are performed to compare the strain softening behavior predicted in this paper and triaxial experimental results. Simulation results show that the proposed model can accurately describe the strain softening of soft rock.

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