基于广义SMP破坏准则的柱形孔扩张问题理论分析

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。

Theoretical analysis of cylindrical cavity expansion based on extended SMP criterion

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.