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.

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.

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.

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.

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.

A Unified Characteristic Theory for Plastic Plane Stress and Strain Problems

2003 ◽  
Vol 70 (5) ◽  
pp. 649-654 ◽  
Author(s):  
Y.-Q. Zhang ◽  
H. Hao ◽  
M.-H. Yu
Keyword(s):  
Plane Stress ◽  
Yield Criterion ◽  
Strength Criterion ◽  
Rigid Plastic ◽  
Strength Criteria ◽  
Special Cases ◽  
Characteristic Theory ◽  
Characteristic Methods ◽  
Von Mises ◽  
Suitable Characteristic

Based on the unified strength criterion, a characteristic theory for solving the plastic plane stress and plane strain problems of an ideal rigid-plastic body is established in this paper, which can be adapted for a wide variety of materials. Through this new theory, a suitable characteristic method for material of interest can be obtained and the relations among different sorts of characteristic methods can be revealed. Those characteristic methods on the basis of different strength criteria, such as Tresca, von Mises, Mohr-Coulomb, twin shear (TS) and generalized twin shear (GTS), are the special cases (Tresca, Mohr-Coulomb, TS, and GTS) or linear approximation (von Mises) of the proposed theory. Moreover, a series of new characteristic methods can be easily derived from it. Using the proposed theory, the influence of yield criterion on the limit analysis is analyzed. Two examples are given to illustrate the application of this theory.

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 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.

Principal Stress and Principal Strain Response in Thin-Walled Cylinder

2014 ◽  
Vol 518 ◽  
pp. 286-289
Author(s):  
Yun Zhu ◽  
Xue You Zhao
Keyword(s):  
Internal Pressure ◽  
Principal Stress ◽  
Direct Measurement ◽  
Measurement Technique ◽  
Strain Measurement ◽  
Principal Strain ◽  
Strain Response ◽  
Thin Walled ◽  
Walled Cylinder

The thin-walled cylinder internal pressure is common in practice. In the determination of air on the surface of thin-walled cylindrical principal stress and principal strain, and the resistance strain measurement technique was used for the direct measurement. This paper deals with the function relations of principal stress and principal stain of a thin-walled cylinder varying with time, and the relations between the principal stain rate and the thickness of a thin-walled cylinder, as it is subjected to internal pressure.

Study on the Ultimate Pullout Force of Prestressed Cable Based on Triple Shear Unified Yield Criterion

2012 ◽  
Vol 594-597 ◽  
pp. 840-843
Author(s):  
Xiao Yan Luo ◽  
Wei Ping Liu
Keyword(s):  
Principal Stress ◽  
Yield Criterion ◽  
Intermediate Principal Stress ◽  
Stress Effect ◽  
Pullout Force ◽  
Grouting Pressure ◽  
Effect Parameter ◽  
Ultimate Equilibrium ◽  
Intermediate Principal Stress Effect ◽  
Prestressed Cable

Based on the triple shear unified yield criterion and the ultimate equilibrium principle, the ultimate pullout force of prestressed cable is studied. The ultimate pullout force of prestressed cable is related to the rock type, the shapes of rapture surface, grouting pressures and compressive strength of rock, etc. The results show that the intermediate principal stress effect parameter b have influences on the ultimate pullout force of prestressed cable. With the increase of the intermediate principal stress effect parameter b, the ultimate pullout force of prestressed cable increases too. When the grouting pressure increases, the ultimate pullout force of prestressed cable increases also.

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