一种求解应变软化岩体中球腔问题的数值方法

均匀地应力场中球形洞室开挖问题可以简化为空间轴对称问题，为分析和评价球形洞室开挖的稳定性，采用有限差分方法对平衡方程与变形协调方程进行离散，将洞室围岩潜在塑性区划分为一系列的球壳，并考虑岩体的应变软化行为，可以得到满足线性Mohr-Coulomb（H-C）准则和非线性Hoek-Brown（H-B）屈服准则的围岩体塑性区范围及相应的应力与变形分布。计算结果表明，随着离散步的增加，数值解逐渐收敛，文中解与已有文献的结果完全吻合，且计算效率更高。对一组强度参数遵循CWFS（黏聚力弱化与摩擦角强化）规律的围岩体内塑性区范围、变形与应力的分布进行了分析，并与常规的应变软化模型的计算结果进行了对比，CWFS模型的结果更合理一些。

A numerical method for analyzing problems of a spherical cavity in strain-softening rock mass

Excavation of a spherical cavity in an infinite isotropic rock mass subject to a hydrostatic stress field can be regarded as an axisymmetric problem. In order to analyze and evaluate the stability of the excavation of 3D spherical cavity, by invoking the finite difference approximation of the equilibrium and compatibility equations, the distributions of displacement and stress in the potential plastic zone which is divided into a series of spherical shell can be obtained from the outmost shell for which the boundary is known to innermost of the spherical cavity in a successive manner. Linear strain-softening behavior is taken into account, and linear Mohr-Coulomb(H-C) criterion and nonlinear Hoek-Brown(H-B) yield criterion are employed respectively in the procedure. With the increment of the number of the spherical shell, a convergent numerical solution is gotten, and the presented procedure is validated through case studies. On the basis of it, a set of strength parameters which obey cohesion weakening and frictional strengthening law(CWFS model) is studied and the corresponding solution is analyzed. Comparisons of the results from CWFS model and the normal strain-softening model are made and the results from CWFS model seem more reasonable.