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

机译：基于塑性极限分析理论的多种破坏模式的岩质边坡可靠度分析

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摘要

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.
机译：由于参数的随机性和可变性，岩质边坡的可靠性分析通常包含多种破坏模式。传统的方法（例如极限平衡法（LEM）和有限元法（FEM））无法有效地解决此可靠性问题。结合塑性极限分析理论，刚性有限元离散化，数学规划理论和蒙特卡洛方法，提出了一种进行边坡可靠度分析的数值方法。岩石边坡使用刚性有限元离散为岩石块和界面，以建立岩石边坡的静态容许应力场和运动学上容许的速度场。另外，通过将界面的抗剪强度参数设置为随机变量，根据上下定理，建立了用于进行岩质边坡可靠度分析的随机规划模型。然后提出了一种基于蒙特卡洛方法的随机规划模型的数值求解策略。最后，提出了一种基于速度场的单元失效概率估计方法。该方法经过验证，具有较高的精度和效率。

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