基于SMP破坏准则的柱形孔扩张问题理论分析

Theoretical analysis of expansion of cylindrical cavity based on SMP criterion

考虑土的应变软化特性,采用应力跌落的简化应力-应变模型,并用简化的体积应变vε与大主应变1ε及小主应变3ε与1ε之间的相互关系反映土的剪胀特性,利用空间准滑动面(SM P)理论和平面应变轴对称问题的柱形孔扩张基本方程,通过推导确定了无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,探讨了土的剪胀性和软化特性对孔扩张问题的影响.通过与基于M ohr-Cou lom b破坏准则的解答进行对比分析,探讨了孔扩张问题中的中主应力效应.计算与分析表明,土的剪胀性和软化特性及中主应力对孔扩张(极限扩孔压力与塑性区半径)具有显著影响,基于M ohr-Cou lom b破坏准则的解答往往偏于保守.

In order to incorporate the strain-softening and shear dilatancy behavior of geomaterials in the analysis, a strain-softening stress-strain model with a stress-dropping and a simplified model which is related to volumetric strain e, and principal strain el and major component e1 and minor component ε3 of principal strains are adopted. Based on the spatial mobilization plane （SMP） theory and the governing equations of axial symmetry in the plane strain condition, the partial differential equations for the boundary-value problem of cavity expansion in cohesionless soils are established and the closed-form solutions of stresses, strains, displacements in the elastic and plastic regions are obtained. Consequently, the problems for the maximum radius of plastic region and ultimate cavity pressure are solved for cylindrical cavity expansion. On the basis of the computed numerical results, both effects of the strain-softening rate and the soil dilatancy on expansion of cylindrical cavity are examined. Meanwhile, a comparative study is made for the present results and current solutions based on Mohr-Coulomb criterion and the effect of intermediate principal stress on the cavity expansion behavior is observed. The results indicate that the strain-softening, the shear dilatancy and the intermediate principal stress will play an important role in the cavity expansion behavior including both ultimate pressure of cavity expansion and radius of plastic region surrounding the cavity, the solution based on Mohr-Coulomb criterion is often conservative.