As is known, limit analysis is a common way to study stability and failure mechanism of geotechnical engineering. This paper presents an upper bound finite element limit analysis (UB-FELA) formulation for non-homogeneous clays using discontinuous quadratic displacement fields and second-order cone programming (SOCP). The details are provided about the application of SOCP to the UB-FELA formulation for non-homogeneous clays. To reduce the calculation error, the analytic expressions are proposed concerning the rate of external work done by body forces and power dissipation caused by the plastic deformation following discontinuous quadratic displacement fields. With SOCP solver MOSEK, large-scale optimization problems of UB-FELA can be achieved in minutes via a desktop computer. The method is then applied to analyzing the stability of an undrained square tunnel and an undrained plane strain heading. The numerical results are compared with those reported in related studies. This method helps to obtain highly precise upper bound solution and clear failure mechanism of the computational domain.

众所周知，极限分析是研究岩土工程稳定性和破坏机理的常用方法。本文介绍了使用不连续二次位移场和二阶锥规划（SOCP）的非均质粘土的上限有限元分析（UB-FELA）公式。提供了有关SOCP在非均质粘土的UB-FELA配方中的应用的详细信息。为了减小计算误差，提出了关于由不连续二次位移场引起的塑性变形引起的体力和功率耗散的外部功率的解析表达式。使用SOCP求解器MOSEK，可以通过台式计算机在几分钟内解决UB-FELA的大规模优化问题。然后将该方法用于分析不排水方形隧道和不排水平面应变方向的稳定性。将数值结果与相关研究报告的结果进行比较。该方法有助于获得高精度的上限解和明确的计算域故障机制。