Reliability analysis of a rock slope based on plastic limit analysis theory with multiple failure modes

Due to the randomness and variability of parameters, reliability analysis of rock slopes generally contains multiple failure modes. This reliability problem cannot be effectively treated by traditional methods, such as limit equilibrium method (LEM) and finite element method (FEM). A numerical method for performing reliability analysis of rock slope is proposed by combining the plastic limit analysis theory, rigid finite element discretization, mathematical programming theory and Monte Carlo method. The rock slope is discretized into rock blocks and interfaces using rigid finite elements to establish static admissible stress fields and kinematically admissible velocity fields for the rock slope. Additionally, stochastic programming models for performing reliability analysis of rock slopes are established according to the lower and upper bound theorems by setting the shear strength parameters of the interfaces to random variables. A numerical solution strategy is then proposed for stochastic programming models based on the Monte Carlo method at the same time. Finally, an estimation method for the failure probability of element is proposed based on the velocity fields. The proposed method is validated, and it has high precision and efficiency.