scholarly journals Failure criterion for soft rocks considering intermediate principal stress

2021 ◽  
Author(s):  
Zhongwei Wang ◽  
Quansheng Liu
Keyword(s):  
Principal Stress ◽  
Failure Criterion ◽  
Intermediate Principal Stress ◽  
Soft Rocks

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 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 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.

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.

Axisymmetric Punching Capacity Analysis for Concrete Slabs

2012 ◽  
Vol 446-449 ◽  
pp. 463-470
Author(s):  
Xiao Rong Hu ◽  
Xiao Mei Fan
Keyword(s):  
Principal Stress ◽  
Failure Criterion ◽  
Three Dimensional ◽  
Intermediate Principal Stress ◽  
Concrete Slabs ◽  
Stress Effects ◽  
Coulomb Failure ◽  
Failure Properties ◽  
Stress States ◽  
Coulomb Failure Criterion

The axisymmetric punching analysis for concrete slabs is researched with the triple-shear unified failure criterion, which can explain the failure properties rationally for concrete under the three dimensional stress states, especially the failure properties of the intermediate principal stress effects. Moreover, a new intermediate principal stress parameter is proposed to interpret the different stress states in failure zones for different concrete. It is shown that the coefficients of b and m, which interprets the effects and the magnitudes of the intermediate principal stress have significant impacts on the axisymmetric punching capacity of concrete slabs. For a given thickness of the concrete slabs, the bearing capacity increases with the b and reaches its maximum value approximately when m=1. Using the Mohr-Coulomb failure criterion to analyze the problem of axisymmetric punching of concrete slabs often underestimate the actual ultimate punching capacity significantly.

Stresses Around Wellbores in Nonlinear Rock

1968 ◽  
Vol 8 (03) ◽  
pp. 304-312 ◽  
Author(s):  
M.A. Mahtab ◽  
R.E. Goodman
Keyword(s):  
Finite Element Analysis ◽  
Principal Stress ◽  
Intermediate Principal Stress ◽  
The State ◽  
Initial Stresses ◽  
Stress Strain ◽  
Element Analysis ◽  
Deviator Stress ◽  
State Of Stress ◽  
Strain Data

ABSTRACT The state of stress around a vertical wellbore in rock following nonlinear stress-strain laws is examined by means of finite element analysis. The wellbore is considered an axisymmetric body with axisymmetric loading. The initial vertical and horizontal stresses are "locked" in the rock elements around the wellbore and a new state of stress is generated by the displacements which occur around the borehole. A point-wise variation of the elastic moduli is made on the basis of the new stress state and the triaxial data. The initial stresses are now reintroduced along with the changed moduli and original boundary constraints. This procedure is repeated until convergent stresses are reached. The effect of nonlinearity on stresses is examined for a 6,000-ft wellbore in a schistose gneiss and Berea sandstone using results of laboratory triaxial compression tests. The results show that the effect is restricted to one well radius from the bottom periphery of the hole. Beyond a distance of one-quarter radius, the effect of nonlinearity on stresses is almost always less than 5 percent for the cases considered. The consideration of a static pressure inside the well does not magnify the effect of nonlinearity on borehole stresses. INTRODUCTION The terms "wellbore" and "borehole" here designate cylindrical openings in the ground with vertical axis and a circular cross-section. A knowledge of the stress redistribution that occurs on excavating a wellbore is important in understanding the behavior of the lined or unlined hole, hydraulic fracture response, and the effect of stress redistribution on drillability; also it is important in predicting initial stresses in the virgin ground, and in analyzing the response of measuring instruments placed in the borehole. Our knowledge of the state of stress around a wellbore has been restricted to homogeneous, isotropic, elastic material and derives chiefly from the analysis by Miles and Topping1 and the photoelastic work of Galle and Wilhoit2 and Word and Wilhoit.3 In this investigation the state of stress is examined for a nonlinear elastic material by means of finite element analysis. Many rocks possess stress-strain curves that depart notably from straight lines in their initial or final portions. While the literature contains abundant stress-strain data from triaxial tests (axisymmetric loading) on cylindrical rock specimens, there is little information on rock deformability under nonaxisymmetric loading conditions such as occur at each point around the bottom of a wellbore. Although there is some knowledge of the effect of intermediate principal stress on rock strength, there is virtually nothing known about its effect on rock deformability; therefore, we have assumed here that the effect of intermediate principal stress can be ignored. A schistose gneiss4 and Berea sandstone5 were selected as representative rocks for this analysis. The traditional graphs of deviator stress (s1-s3) vs axial strain were reworked to give the tangent modulus as a function of the deviator stress for varying values of the minor principal stress. The result is a nesting family of skewed, bell-shaped curves for the gneiss (Fig. 1A) and the sandstone (Fig. 2A). A similar replotting of the lateral strain data defines the variation of Poisson's ratio (?) with the deviator stress and confining pressure. These curves, shown in Fig. 1B for the gneiss and in Fig. 2B for the sandstone, are not so well ordered as the tangent modulus curves. However, all of these display an increase of ? with deviator stress application, but the rate of increase diminishes with confinement. The ET and ? curves for the two rock types are tabulated in Tables 1A and 1B for use in a digital computer so that material properties corresponding to a given state of stress can be assigned by interpolation.

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