基于塑性极限分析上限法理论的土质边坡可靠度分析

将极限分析的上限定理、有限元离散思想、随机规划理论和蒙特卡洛方法这四者结合起来，提出了一种土质边坡可靠度分析的上限数值方法。首先采用三节点有限单元离散土质边坡，然后将土体的抗剪参数设为随机变量，根据上限定理构建同时满足三角形单元的塑性流动约束条件、单元公共边的塑性流动约束条件和单元速度边界条件的机动许可速度场，并根据内功功率等于外功功率条件建立目标函数，构建土质边坡可靠度分析的上限法随机规划模型。采用蒙特卡洛方法求解上限法随机规划模型，同时提出了一种基于上限法速度场的边坡失效风险系数估算方法，该方法特别适用于具有多种失效模式的边坡风险分析。对2个经典算例进行了深入分析，验证了方法的正确性。

Reliability analysis of soil slope based on upper bound method of limit analysis

The upper bound numerical method for reliability analysis of soil slopes is proposed, by combining the theory of upper bound limit analysis, finite element discretization, stochastic programming theory and Monte Carlo method. Firstly, three-node finite element is used to discrete the soil slope, and then shear strength parameters of soil are set as random variable. According to the upper bound theorem, kinematically admissible velocity fields are established to satisfy the plastic flow constraint conditions of triangular finite elements, the plastic flow constraint conditions of velocity discontinuities and the velocity boundary conditions. The objective function is established based on the internal and the energy-work balance equation. Then the upper bound limit method stochastic programming model of soil slope reliability analysis are established. The Monte Carlo method is used to solve the upper bound stochastic programming model. At the same time, an estimation method for coefficient of slope failure risk based on velocity field of upper bound method is proposed, it is especially suitable for slope risk analysis with multiple failure modes. Finally, two examples of soil slope are selected, and the results prove the correctness of the method.