Abstract: 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.

Key words: soil slope, reliability, risk analysis, upper bound method, finite element discretization, linear programming