New strength formulae for rock surrounding a circular opening

2013 ◽  
Vol 50 (7) ◽  
pp. 735-743 ◽  
Author(s):  
Wen Fan ◽  
Mao-hong Yu ◽  
Long-sheng Deng ◽  
Xianglin Peng ◽  
Li-wei Chen
Keyword(s):  
Plastic Material ◽  
Strength Criterion ◽  
Surrounding Rock ◽  
Strength Theory ◽  
Unified Strength Theory ◽  
Special Cases ◽  
Elastic Plastic Material ◽  
Strength Models ◽  
Strength Formula ◽  
Strain Model

In this paper, the unified strength theory proposed by Yu Mao-hong in 1991 is used to develop new strength formulae for rock surrounding a tunnel. The new formulae can be applied to an elastic–plastic material. The formulae have a series of expressions with the unified parameter, especially variations such as the well-known Kastner and Airy formulae, which are widely used in rock mechanics and engineering. These formulae are derived on the basis of the Mohr–Coulomb strength criterion. For the strength-weakening (plastic-softening) of geomaterials, the analytical solutions for the radius of the plastic residual zones, radius of the plastic-softening zones, and displacement around the opening are presented according to the elastoplastic-softening – residual plastic, tri-linear stress–strain model. In addition, the derivation for the stress state in the surrounding rock is given. The Kastner formula, Airy formula, and available solutions can be considered as special cases in the new strength formula. The influence of softening, shear dilatancy, and different strength models on the results is analyzed. The results presented in this paper are useful for analyzing surrounding rock with various stress conditions and reinforcement of caves.

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.

Maximum Reduction in Thickness in a Single Sheet Forming Pass Based on Unified Strength Theory

2012 ◽  
Vol 159 ◽  
pp. 151-155 ◽  
Author(s):  
Xiao Wei Li ◽  
Jun Hai Zhao ◽  
Qi Yao Wang
Keyword(s):  
Compression Ratio ◽  
Yield Criterion ◽  
Sheet Forming ◽  
Strength Theory ◽  
Unified Strength Theory ◽  
Maximum Reduction ◽  
Special Cases ◽  
Wide Range ◽  
Tension And Compression ◽  
Single Sheet

Based on unified strength theory, the equation for estimating the maximum reduction in thickness in a single sheet forming pass is obtained. Included the contribution of both intermediate principal shear stress and varying tension-compression-ratio to material mechanical property, the equation developed by this paper can reasonably apply to a wide range of material. It can be proved that the equation for estimating the maximum reduction based on unified strength theory becomes that based on unified yield criterion, when material has equal strength in tension and compression, i.e., the tension-compression-ratio of material is equal to units; and, that the values of the maximum reduction obtained previously based on Mises, or Tresca criterion, are all just special cases of those based on unified yield criterion. In addition, the maximum reduction in thickness for sheet drawing and extrusion is equal to one another.

Study on the Bearing Capacity of Slime Friction Pile Based on the Double-Sheared Theory

2013 ◽  
Vol 353-356 ◽  
pp. 1005-1010
Author(s):  
Xiang Qiu Wang ◽  
Wen Tao Yang
Keyword(s):  
Bearing Capacity ◽  
Strength Criterion ◽  
Intermediate Principal Stress ◽  
Resistance Force ◽  
Strength Theory ◽  
Unified Strength Theory ◽  
Friction Resistance ◽  
Double Shear ◽  
Friction Pile ◽  
Lateral Friction

The bearing capacity of slime friction pile based on the Mohr-Coulombs strength criterion couldnt make full use of the potential strengths ability of rock-soil. But the double shear unified strength theory can depict really the bearing characteristics of rock-soil because it can consider the effect of intermediate principal stress comprehensively. On this condition, based on the Mindlins displacement solution and the double shear unified strength theory, a calculated formula of bearing capacity was proposed for the slime friction pile, and then the distribution regularities of lateral friction-resistance force for the slime friction pile were discussed.

Upper Bound Solution for Ultimate Bearing Capacity of Foundation Based on Unified Strength Theory

2012 ◽  
Vol 446-449 ◽  
pp. 1751-1754
Author(s):  
Yao Tang ◽  
Ping Tang
Keyword(s):  
Bearing Capacity ◽  
Upper Bound ◽  
Strength Theory ◽  
Unified Strength Theory ◽  
Positive Effects ◽  
Bound Solution ◽  
Upper Bound Solution ◽  
Potential Capacity ◽  
Special Cases ◽  
Foundation Base

Based on unified strength theory, an upper bound solution for bearing capacity of foundation is established considering the strength of soil above the basement by using Prandtl slip model. The proposed method could be degenerated to classical slip-line method in some certain situations. A series of results could be presented by means of changing the parameters of unified strength theory. The results obtained by this proposed method are greater than those by Terzaghi method, which is mainly because the positive effects of soil strength above foundation base. Since unified strength theory could be simplified to Mohr-Coulomb strength theory in a certain situation, the results are close to those obtained by Meyerhof method. This proposed solution can consider the effects of intermediate principal stress so that we can make full use of the potential capacity of soil, which is a rigorous upper-bound solution. Other solutions are special cases of this proposed solution.

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.

Unification of Hoek-Brown Criterion on the Basis of United Strength Theory

2014 ◽  
Vol 501-504 ◽  
pp. 415-418
Author(s):  
Yuan Li ◽  
Qi Liang Liu ◽  
Qing Chi Cai
Keyword(s):  
Rock Mass ◽  
Rock Strength ◽  
Hard Rock ◽  
Strength Criterion ◽  
Strength Reduction ◽  
Strength Theory ◽  
Unified Strength Theory ◽  
Rock Mass Strength ◽  
Decomposition Formula ◽  
Theory Formula

Based on twin failure mechanism of fracture and shear , the bilinear transitional strength decomposition formula reflecting the nonlinear strength of rock material is proposed,.The decomposed brittle shear formula is integrated and finally the unified strength theory formula characterized by nonlinearity of Hoek-Brown criterion is established. It makes the unified strength theory characterized by nonlinearity of empirical strength criterion, rock mass strength reduction, etc. Besides, it contributes to promote the accuracy and applicability of unified strength theory in rock strength and rock mass strength,especially for the hard rock failure analysis.

scholarly journals Plastic Failure Analysis of Roadway Floor Surrounding Rocks Based on Unified Strength Theory

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Wenxiang Zheng ◽  
Qingwei Bu ◽  
Yaoqing Hu
Keyword(s):  
Spatial Relationship ◽  
Mining Area ◽  
Surrounding Rock ◽  
Strength Theory ◽  
Rock Body ◽  
Unified Strength Theory ◽  
Plastic Failure ◽  
In Situ Stresses ◽  
The Stability

Taking the whole surrounding rock of an excavation roadway as the research object, the elastoplastic failure mechanics analysis of the surrounding rock body of the excavated roadway under three-directional in situ stresses is carried out by using the knowledge of generalized plane strain problems and unified strength theory, and the equations are derived for the elastic-plastic zone stress together with the plastic fracture range of the roadway floor surrounding rock under three-directional in situ stresses. At the same time, by means of the conclusion of mechanical analysis and the results of in situ detection of in situ stress in the Changcun mining area, the stability of the roadway floor surrounding rock was analyzed. The analysis reveals the influence on the stability of the roadway floor surrounding rock between the spatial relationship with the different in situ stresses and the roadway layout; meanwhile, it calculates the range of the plastic failure zone and the stress value of the #1 roadway floor in the S6 mining area of Changcun mine, which provides a reliable theoretical mechanical reference for research on roadway floor heave control technology.

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