基于非局部Mohr-Coulomb模型的土体渐进破坏分析

Progressive failure of soils based on non-local Mohr-Coulomb models

软化塑性模型的常规有限元数值分析结果严重依赖网格尺寸,而非局部塑性模型是解决这一问题的有效方法。但现有非局部模型仅能用于von Mises准则,无法用来进行一般软化土体渐进破坏分析。提出了一种改进的针对非局部模型的全隐式应力回代迭代计算方法,该方法具有在迭代计算过程中逐步确定弹塑性点的特点,克服了现有算法误差较大及不稳定的缺点。将非局部理论推广到Mohr-Coulomb塑性模型中,使其能用来分析土体稳定性问题。采用局部和非局部模型对两个土体稳定问题,包括条形基础承载力问题和三角形荷载下边坡稳定问题进行渐进破坏分析,数值计算结果表明该方法可以消除软化塑性有限元计算的网格敏感性,起到了正则化的效果。

The numerical solutions of softening plasticity model using the ordinary finite element method seriously depend on mesh size. The non-local theory is an effective way to solve this problem. But the existing non-local theory can only be applied in von Mises plasticity model and cannot be used to analyze the progressive failure of softening soils. An improved full implicit stress return iterative algorithm for non-local models is proposed. This algorithm, which can assure whether a Gauss point be plastic state after loading or not, overcomes inaccuracy and instability of the existing algorithms. The non-local theory is extended to the Mohr-Coulomb plasticity model, so that it can be used to analyze geotechnical problems. The numerical solutions of the strip foundation bearing and stability problems of slopes subjected to triangle loads using both the local and non-local models demonstrate that the proposed approach can regularly control the equation and eliminate dependence on mesh size of finite element solutions of softening plasticity.