基于非线性破坏准则的土坡稳定有限元上限分析

材料的非线性破坏准则是指材料的强度与应力相关，因此描述材料强度的前提是应力已知。现有土坡稳定的上限极限分析方法由于无法确定土坡内的应力分布而无法采用非线性强度准则。论文基于Mohr-Coulomb屈服准则和有限单元法，将边坡稳定上限极限分析形成标准二次锥规划数学模型，并转化为对偶问题的“静力形式”进行求解，从而可以确定边坡内部的应力分布，进而使用迭代的方法确定材料在非线性破坏准则下的等效剪切强度，最终得到问题的上限解。通过两个算例的计算分析，并与已有计算方法进行对比，验证了所提出方法的正确性，得到的上限解也更为严格、精确。

Upper bound FEM analysis of slope stability using a nonlinear failure criterion

The upper bound finite element (FE) limit analysis is applied to stability problems of slopes using a nonlinear criterion. Generally speaking, the equivalent shear strength parameters of materials with a nonlinear failure criterion are expressed in terms of stress, which cannot be obtained directly by the upper bound method. Based on the Mohr-Coulomb criterion and FEM, the corresponding dual second-order cone programming (SOCP) problem of the upper bound limit analysis, which is considered as a static form, is formulated. By solving the dual problem, the distribution of stress of slopes can be obtained. Then, the equivalent shear strength parameters of materials can be determined iteratively so that the analysis of slope stability with a nonlinear failure criterion is able to be transformed into the traditional upper bound method. Finally, the results of two numerical examples are compared with the published solutions and demonstrate the accuracy and validity of the proposed method, by which the nonlinear failure criterion can be represented exactly.