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.