The prediction of failure load factor and stress distribution at limit state plays an important role in geo-technical engineering design. This paper develops a pseudo-lower bound numerical procedure for adaptive limit analysis of geo-mechanics problems governed by the Mohr–Coulomb failure criterion. Equilibrium equations for the residual stress are enforced in a weak manner, allowing the use of displacement-based elements within the static limit analysis framework. The method does not require the construction of stress-based elements, but the stress fields at limit state can still be obtained. Non-linear failure criterion is cast in the form of a standard conic constraint, enabling the use of the highly efficient second-order cone based solvers. A refinement indicator based on Mohr–Coulomb yield function values is proposed, and adaptive mesh refinement is performed to speed up the computational progress. The proposed method is applied to various soil engineering problems, providing accurate bearing capacity together with stress distribution at limit state.

极限状态下破坏载荷因子和应力分布的预测在岩土工程设计中具有重要作用。本文开发了一种伪下界数值程序，用于对受 Mohr-Coulomb 破坏准则控制的地质力学问题进行自适应极限分析。残余应力的平衡方程以较弱的方式强制执行，允许在静态极限分析框架内使用基于位移的元素。该方法不需要构建基于应力的单元，但仍然可以获得极限状态的应力场。非线性失效准则以标准圆锥约束的形式投射，从而能够使用基于二阶圆锥的高效求解器。提出了基于 Mohr-Coulomb 屈服函数值的细化指标，并执行自适应网格细化以加快计算进度。所提出的方法应用于各种土壤工程问题，提供准确的承载力以及极限状态下的应力分布。