基于广义SMP破坏准则的柱形孔扩张问题理论分析

›› 2006, Vol. 27 ›› Issue (12): 2105-2110.

基于广义SMP破坏准则的柱形孔扩张问题理论分析

栾茂田^{1, 2}，李波^{1, 2, 3}

1. 大连理工大学海岸和近海工程国家重点实验室，大连 116024；2. 大连理工大学土木水利学院岩土工程研究所，大连 116024； 3. 沈阳农业大学水利学院，沈阳 110161

收稿日期:2005-01-26 出版日期:2006-12-11 发布日期:2013-12-09
作者简介:栾茂田，男，1962年生，教授，博士，博士生导师，主要从事岩土力学基本理论与数值分析、海洋土力学理论与实验技术、非线性土动力学理论与计算等方面的科研与教学工作
基金资助:
国家自然科学基金资助项目(No. 50179006)与教育部跨世纪优秀人才培养计划研究基金资助项目(教技函[1998]2号)及中国科学院武汉岩土力学研究所前沿领域基础研究基金项目资助(No. Q110305)

Theoretical analysis of cylindrical cavity expansion based on extended SMP criterion

LUAN Mao-tian ^{1, 2}, LI Bo^{1, 2, 3}

1. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China; 2. School of Civil and Hydraulic Engineering, Dalian University of Technology, Dalian 116024, China; 3. College of Water Resources, Shenyang Agricultural University, Shenyang 110161, China

Received:2005-01-26 Online:2006-12-11 Published:2013-12-09

摘要/Abstract

摘要： 采用应力跌落的简化应力-应变模型考虑土的应变软化特性，同时采用简化的体积应变?v与大主应变?1及大主应变?1与小主应变?3之间的相互关系反映土的剪胀特性，根据空间准滑动面(SMP)理论和平面应变轴对称问题的柱形孔扩张基本方程，推导并给出一般黏性土中柱形孔扩张问题的应力场、应变场、位移场、塑性区半径和孔扩张压力。通过算例分析，探讨了土的剪胀因素、软化特性对孔扩张问题的影响程度。为了反映中主应力的影响，将本文解与基于Mohr-Coulomb破坏准则的解答进行了比较。计算结果表明，土的剪胀性和软化特性及中主应力对孔扩张问题的影响是显著的，基于Mohr－Coulomb破坏准则的孔扩张解答往往偏于保守。

关键词: 剪胀, 应变软化, 推广的空间准滑动面理论, 柱形孔扩张, 弹塑性分析

Abstract: In order to incorporate the strain-softening and shear dilatation behavior of geomaterials in the analysis, a strain-softening stress-strain model with stress-dropping and a simplified model of ?v-?1 and ?1-?3 are adopted. Based on the extended spatial mobilization plane (SMP) theory, the governing equations of axisymmetric problem in the plane strain condition, the partial differential equations for the boundary-value problem of cavity expansion in cohesive soils are established; and the closed-form solutions of stresses, strains, displacements in the elastic and plastic regions are obtained. Consequently, the maximum radius of plastic region and ultimate cavity pressure are solved for cylindrical cavity expansion. Based on numerical results, the strain-softening rate and the effects of soil dilatancy on expansion of cylindrical cavity are examined. Also a comparative study is made for the present solution and current solution based on Mohr-Coulomb criterion in order to display the effect of intermediate principal stress. The results indicate that soil strain-softening and shear dilatancy as well as the intermediate stress have considerable effect on both ultimate cavity pressure and maximum radius of plastic region in the cylindrical cavity expansion.

Key words: shear dilatancy, strain softening, extended spatial mobilization plane criterion (SMP), expansion of cylindrical cavity, elastoplastic analysis

中图分类号:

TU 43

栾茂田，李波，. 基于广义SMP破坏准则的柱形孔扩张问题理论分析[J]. , 2006, 27(12): 2105-2110.

LUAN Mao-tian ， LI Bo，. Theoretical analysis of cylindrical cavity expansion based on extended SMP criterion[J]. , 2006, 27(12): 2105-2110.

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