scholarly journals The Analysis of Anchoring Mechanism of Rock Slope in Two Layers Based on the Nonlinear Twin-Shear Strength Criterion

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
X. B. Gu ◽  
Y. H. Wang ◽  
X. J. Ji ◽  
Y. H. Zhu
Keyword(s):  
Principal Stress ◽  
Inclination Angle ◽  
Rock Slope ◽  
Great Influence ◽  
Strength Criterion ◽  
Intermediate Principal Stress ◽  
Characteristic Model ◽  
Force Increase ◽  
Surcharge Load ◽  
Influential Parameters

The nonlinear strength criterion is introduced into the paper firstly, and then the geometric anchoring characteristic model of rock slope separated from two layers according to rock type with the fracture surface of log-spiral curve considering nonlinear twin-shear criterion subjected to seismic loads is established. Finally, some correlated influential parameters are analyzed, and the conclusions are drawn, showing that the intermediate principal stress has great influence on the total anchoring force of bolt P, so when different criteria are selected, the influence of intermediate principal stress should not be omitted. The effects of thickness ratio h1/h2 on total anchoring force increase gradually with the increase of inclination angle ϕ . The total anchoring force P decreases gradually with the increase of inclination angle ϕ and surcharge load q. The total anchoring force increases gradually with the increase of horizontal seismic acceleration coefficients kh and geometric coefficients mi and GSI.

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.

scholarly journals Three dimensional statistical damage constitutive model of rock based on Griffith strength criterion

2021 ◽  
Author(s):  
Song Chen ◽  
Xiuling Cao ◽  
Zhao Yang
Keyword(s):  
Constitutive Model ◽  
Principal Stress ◽  
Damage Mechanics ◽  
Brittle Materials ◽  
Strength Criterion ◽  
Intermediate Principal Stress ◽  
True Triaxial ◽  
Damage Constitutive Model ◽  
Two Parameters ◽  
The Relationship

Abstract According to the damage mechanics theory and Lemaitre strain equivalence theory, because most rock materials are brittle materials, Griffith strength criterion has good applicability to describe the fracture failure of brittle materials from the perspective of energy. Using a new method to describe the rock micro-element strength based on Griffith strength criterion, and assuming the micro-element strength obeys the Weibull distribution, a true triaxial constitutive model of damage softening reflecting the whole process of rock failure is established. On this basis, the influence of the two parameters in the model on the curve of the constitutive model is analyzed, and the relationship between the two parameters and the intermediate principal stress in the model is established, and the model is revised reasonably. Finally, a true triaxial damage constitutive model of rock is established. The results are in good agreement with the experimental curve, which verifies its validity and rationality. At the same time, the relationship between the damage evolution and the strain and stress is discussed, and the influence of the size of the intermediate principal stress on the relationship is analyzed in detail.

scholarly journals An Extension Failure Criterion for Brittle Rock

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Aizhong Lu ◽  
Ning Zhang ◽  
Guisen Zeng
Keyword(s):  
Principal Stress ◽  
Poisson’S Ratio ◽  
Compressive Strain ◽  
Strength Criterion ◽  
Maximum Principal Stress ◽  
Intermediate Principal Stress ◽  
Brittle Rock ◽  
Poisson's Ratio ◽  
Triaxial Tests ◽  
True Triaxial

Under the triaxial compressive state, the compressive strain is supposed to happen in the direction of the maximum principal stress, but tensile strain happens in the direction of the minimum principal stress. Moreover, as the intermediate principal stress is not too high, the corresponding strain can also be tensile. If the brittle rock is assumed as linear elastic in the prefailure stage, a new strength criterion based on the sum of the two tensile strains was presented. The new criterion considers the differences in mechanical parameters (i.e., elastic modulus and Poisson’s ratio) under tension and compression. The parameters of the criterion only include Poisson’s ratio and uniaxial strength. And the effect of the intermediate principal stress σ 2 can be reflected. Certain featured failure phenomenon of rock material can be explained well by the proposed criterion. The results of conventional and true triaxial tests can verify the criterion well. Finally, the criterion is compared with the Mohr–Coulomb and Drucker–Prager criteria.

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.

Elastic–Brittle–Plastic Analysis of Double-Layered Combined Thick-Walled Cylinder Under Internal Pressure

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Qian Zhu ◽  
Junhai Zhao ◽  
Changguang Zhang ◽  
Yan Li ◽  
Su Wang
Keyword(s):  
Internal Pressure ◽  
Principal Stress ◽  
Yield Criterion ◽  
Engineering Application ◽  
Strength Criterion ◽  
Intermediate Principal Stress ◽  
Material Behavior ◽  
Strength Theory ◽  
Special Cases ◽  
Walled Cylinder

The elastic–brittle–plastic unified solutions of limit internal pressure are presented for double-layered combined thick-walled cylinder by the triple-shear unified strength criterion. The unified solutions obtained in this paper are especially versatile that can take into account of material brittle softening and intermediate principal stress quantitatively. The conventional existing elastic-perfectly plastic solutions, based on the Tresca yield criterion, Mises yield criterion, or twin-shear strength theory, can be categorized as special cases of the present unified solutions which can overcome their shortages. Parametric studies were carried out to evaluate the influences of various factors such as brittle softening parameter, strength theory parameter, cohesion, internal friction angle, and intermediate principal stress coefficient on the unified solutions. It is shown that proper choices of failure criterion, material behavior model, and brittle softening are significant in combined cylinder design. The new solutions can be naturally degraded to the existing formula and agree well with the results of the prevailing failure criteria. It is concluded that the unified solutions have an important practical value for the optimum design and engineering application of combined thick-walled cylinder.

Finite Element Analysis of Dongjusi Railway Tunnel within Hard Rock Mass Based on the Unified Rock Mass Strength Criterion

2007 ◽  
Vol 353-358 ◽  
pp. 2994-2997
Author(s):  
Yuan Hua ◽  
Tai Quan Zhou ◽  
Guo Liang Dai
Keyword(s):  
Rock Mass ◽  
Principal Stress ◽  
Hard Rock ◽  
Plastic Material ◽  
Strength Criterion ◽  
Intermediate Principal Stress ◽  
Stress Effect ◽  
Railway Tunnel ◽  
Rock Mass Strength ◽  
Intermediate Principal Stress Effect

The twin shear strength criterion has been proposed to consider the intermediate principal stress effect on the rock mass strength. The unified rock mass strength criterion could consider the intermediate principal stress effect on the rock mass strength. The unified rock mass elasto-plastic material model is implemented in ABAQUS user interface. As a case for study, the stability analysis of Dongjusi railway tunnel within hard rock mass is studied using the unified rock mass strength material. For comparison, the Hoek-Brown empirical strength criterion is also chosen for the rock mass material modeling. The computation results show that the plastic zone calculated using the unified rock mass strength criterion is smaller than that using the Hoek-Brown empirical strength criterion. The railway tunnel lining structure is designed according to the unified rock mass strength criterion and greatly makes use of the rock mass potential strength, which decreases engineering cost.

scholarly journals Bifurcation analysis of shear band in sand under true triaxial conditions with hypoplasticity

2021 ◽  
Author(s):  
Jun Liu ◽  
shun wang ◽  
Yang Wu ◽  
Wei Wu
Keyword(s):  
Shear Band ◽  
Principal Stress ◽  
Stress Ratio ◽  
Strength Criterion ◽  
Intermediate Principal Stress ◽  
True Triaxial ◽  
Acoustic Tensor ◽  
Strain Relationship ◽  
Bifurcation Behaviour ◽  
Hypoplastic Constitutive Model

Predicting the onset of shear band is of significance in understanding the failureof geomaterials. The prediction accuracy is dictated by the constitutive modelused for the description of the pre-bifurcation behaviour. In this study, we firstmodify a recently proposed hypoplastic constitutive model by incorporating ageneral strength criterion and a stiffness function. We proceed to consider theonset of shear band in sand under true triaxial conditions. We demonstrate thatour analyses capture the pre-bifurcation stress–strain relationship at differentvalues of intermediate principal stress and predict fairly well the onset ofshear band. The acoustic tensor criterion generally adopted in elastoplasticapproaches is inadequate for hypoplastic approaches. No special non-coaxialtreatment is required for the present approach to yield a reasonable variationtrend of bifurcation strain with intermediate principal stress ratio 𝑏.

scholarly journals Failure Probability Model considering the Effect of Intermediate Principal Stress on Rock Strength

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Yonglai Zheng ◽  
Shuxin Deng
Keyword(s):  
Principal Stress ◽  
Failure Probability ◽  
Rock Strength ◽  
Probability Model ◽  
Strength Criterion ◽  
Intermediate Principal Stress ◽  
Stress Effect ◽  
New Model ◽  
Uniformity Coefficient ◽  
Intermediate Principal Stress Effect

A failure probability model is developed to describe the effect of the intermediate principal stress on rock strength. Each shear plane in rock samples is considered as a micro-unit. The strengths of these micro-units are assumed to match Weibull distribution. The macro strength of rock sample is a synthetic consideration of all directions’ probabilities. New model reproduces the typical phenomenon of intermediate principal stress effect that occurs in some true triaxial experiments. Based on the new model, a strength criterion is proposed and it can be regarded as a modified Mohr-Coulomb criterion with a uniformity coefficient. New strength criterion can quantitatively reflect the intermediate principal stress effect on rock strength and matches previously published experimental results better than common strength criteria.

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.

Sign in / Sign up

Export Citation Format

Share Document