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Effects of 3D deformation and nonlinear stress–strain relationship on the Brazilian test for a transversely isotropic rock

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Journal of Rock Mechanics and Geotechnical Engineering 2023年第12期15卷 3221-3229页

作者： Juhyi Yim Yoonsung Lee Seungki Hong Ki-Bok Min R&D Center Hyundai Engineering and Construction75Yulgok-roJongno-guSeoulRepublic of Korea Department of Energy Systems Engineering and Research Institute of Energy and Resources Seoul National University1Gwanak-roGwanak-guSeoul08826Republic of Korea

To improve the accuracy of indirect tensile strength for a transversely isotropic rock in the Brazilian test, this study considered the three-dimensional (3D) deformation and the nonlinear stress–strain relationship. A parametric study of a numerical Brazilian test was performed for a general range of elastic constants, revealing that the 3D modeling evaluated the indirect tensile strength up to 40% higher than the plane stress modeling. For the actual Asan gneiss, the 3D model evaluated the indirect tensile strength up to 10% higher and slightly enhanced the accuracy of deformation estimation compared with the plane stress model. The nonlinearity in stress–strain curve of Asan gneiss under uniaxial compression was then considered, such that the evaluated indirect tensile strength was affected by up to 10% and its anisotropy agreed well with the physical intuition. The estimation of deformation was significantly enhanced. The further validation on the nonlinear model is expected as future research.

关键词： Anisotropy transversely isotropy Brazilian test Indirect tensile strength Nonlinearity 3D modeling

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Closed form stress distribution in 2D elasticity for all boundary conditions

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Applied Mathematics and Mechanics(English Edition) 2007年第12期28卷 1629-1642页

作者：梁以德郑建军 Department of Building and Construction City University of Hong Kong

This paper applies a Hamiltonian method to study analytically the stress distributions of orthotropic two-dimensional elasticity in （x. z） plane for arbitrary boundary conditions without beam assumptions. It is a method of separable variables for partial differential equations using displacements and their conjugate stresses as unknowns. Since coordinates （x, z） can not be easily separated, an alternative symplectic expansion is used. Similar to the Hamiltonian formulation in classical dynamics, we treat the x coordinate as time variable so that z becomes the only independent coordinate in the Hamiltonian matrix differential operator. The exponential of the Hamiltonian matrix is symplectic. There are homogenous solutions with constants to be determined by the boundary conditions and particular integrals satisfying the loading conditions. The homogenous solutions consist of the eigen-solutions of the derogatory zero eigenvalues （zero eigen-solutions） and that of the well-behaved nonzero eigenvalues （nonzero eigen-solutions）. The Jordan chains at zerO eigenvalues give the classical Saint-Venant solutions associated with aver- aged global behaviors such as rigid-body translation, rigid-body rotation or bending. On the other hand, the nonzero eigen-solutions describe the exponentially decaying localized solutions usually ignored by Saint-Venant＇s principle. Completed numerical examples are newly given to compare with established results.

关键词： transversely isotropy eigenfunctions symplectic expansion

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STRESS IN transversely ISOTROPIC HALF-SPACE WITH TYPICAL LOADS ACTING ON ITS SURFACE

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Applied Mathematics and Mechanics(English Edition) 2000年第8期21卷 901-908页

作者：吴世明梁剑胡亚元 Department of Geotechnical Engineering Tongji University P R China Department of Mechanics Zhejiang University Hangzhou P R China Department of Civil Engineering Zhejiang University Hangzhou P R China

Based on the results of Hu and Lekhnitskii, the united solution of additional vertical stress coefficient for both transversely isotropic and isotropic half-space was obtained. Five typical load cases, namely, vertical circular uniform load, rectangular uniform load, linearly distributed rectangular load, uniform linear and strip loads are studied in detail. The final solutions are expressed in terms of elementary functions. Numerical results show that there are anisotropic effects on the variation of additional vertical stress coefficients.

关键词： transversely isotropy half-space additional stress coefficients

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POINT FORCE SOLUTION FOR A transversely ISOTROPIC ELASTIC LAYER

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Applied Mathematics and Mechanics(English Edition) 1996年第4期17卷 309-318页

作者：丁皓江梁剑王耘 Department of Mechanics Zhejiang University Hangzhou P. R. China Department of Engineering Mechanics Qinghua University Beijing P. R. China

By introduction of transmitting matrices'technique for layered structure,mixed equations with stresses and displacements are derived from the basic equations of transversely isotropic ***,using Fourier transformation and the general solutions in Zhou et al.[7],the point force solution for transversely isotropic elastic layer is obtained and it can be degenerated to the corresponding solution of isotropic medium. In this paper,all equations are derived by the use of computer algebra software.

关键词： transversely isotropy elastic layer point force solution Fourier Transformation

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