基于二阶锥规划的边坡稳定上限有限元分析

Upper Bound Finite Element Limit Analysis of Slope Stability Using Second-order Cone Programming

边坡稳定上限极限分析通常采用三节点三角形单元,并对屈服准则线性化,因而其计算精度较低。针对此问题,基于六节点三角形单元和二阶锥规划,假设材料严格满足Mohr-Coulomb屈服准则并考虑孔隙水压力与地震荷载的作用,发展了一种应用于边坡稳定性分析的上限有限元法,扩大了上限极限分析的应用范围。根据上限定理,在满足屈服条件、流动法则、功能平衡以及相应的边界条件的基础上,将边坡稳定的上限分析形成二阶锥规划数学模型,并用先进的内点法进行求解。通过2个算例的计算分析,并与已有计算方法进行对比,验证了本文方法的正确性与可行性,并表明该方法的计算结果并不明显依赖于有限元网格的密度,且材料内摩擦角较大时,仍具有较高的计算精度。

Three-node triangular elements together with the linearized yield criterion are commonly used in the finite element upper bound limit analysis. Therefore,the method is of low calculation precision. Aiming at this problem,a method of upper bound limit analysis using six-node triangular elements and second-order cone programming is developed to investigate the slope stability subjected to pore water pressure and earthquake loads. The proposed method formulates the slope stability problem as a second- order cone programming with constraints based on the yield criterion,flow rule,boundary conditions,and the energy-work balance equation. The optimization problem is solved by a state-of-the-art interior-point method,and the strict upper bound solutions can be obtained. Finally,the results of two numerical examples are compared with published solutions,which demonstrate the validity of the proposed method. The results also indicate that the mesh-dependence phenomenon is overcome and the calculation precision is improved even for large internal friction angel of materials.