线性软化土体中球孔扩张问题的解析解

Analytical solution to cavity expansion in linear softening soil

采用三折线线性软化模型描述了土体应力-应变关系,以Mohr-Coulomb为屈服准则,同时考虑塑性区弹性变形、土体剪胀以及土体软化的特性,推导了孔扩张后孔周各个区域的应力、应变及位移解析解,讨论了剪胀角、应变软化系数、是否考虑塑性区弹性变形对解答结果的影响.结果表明,最终扩张压力、塑性区半径都随剪胀角的增大而增大;软化系数对塑性区半径影响很小,但对最终扩张压力影响较大,随着软化系数的增大,最终扩张压力增大;考虑塑性区弹性变形对扩张问题解答的影响随扩张半径的增大越趋明显;考虑塑性区的弹性变形,最终扩孔压力偏小.

By using the tri-linear softening model to describe the stress-strain relational expression and supposing the Mohr-Coulomb yield criterion, all the analytical solutions of stress/strain/displacement to the cavity expansion in the soil were induced considering the characteristics of elastic deformation in plastic zone, shear dilation and strain softening of soil. The impacts of softening, shear dilation angle and whether to consider the elastic deformation in the plastic zone on the solution were discussed. Analysis shows that the ultimate pressure and the plastic zone radius increase with increasing shear dilation angle and strain softening, while strain softening has lower impact on the plastic zone radius than on the ultimate pressure; the impact of whether to consider the elastic deformation in the plastic zone on the solution of cavity expansion becomes larger with increasing cavity radius; the ultimate pressure becomes smaller if the elastic deformation in the plastic zone is considered.