Reliability analysis of slope stability based on polynomial chaos expansion
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摘要: 利用Mohr-Coulomb屈服准则和塑性力学的上限定理，通过对离散条块边坡体构建机动许可速度场，建立了边坡稳定的虚功方程，其中岩土强度参数为随机变量，虚功方程为非线性随机平衡方程，安全系数成为随机变量的函数。再用多项式混沌展开和随机Galerkin算法对上述方程进行求解，优化得到了边坡临界滑面及其失效概率和稳定系数，得出了基于多项式混沌展开的岩土边坡可靠性的分析方法。数值算例表明该方法能对不确定性参数的岩土边坡稳定性进行有效评估和预测。Abstract: A probabilistic numerical approach for the stability analysis of soil and rock slopes is presented based on the polynomial chaos expansion. The slope is divided into a family of inclined slices. By using the Mohr-Coulomb yield criterion and according to the upper bound theorem in plasticity theory, a work-energy balance equation is proposed for each soil/rock slice with respect to the kinematically-admissible global velocity field of the slope. Geotechnical parameters are modelled as random variables, and the safety factor is treated as a functional of these random parameters. By using the polynomial chaos expansion and a stochastic Galerkin optimization process, the random safety factor and the corresponding critical failure surface are solved. Several numerical examples demonstrate that the proposed method has the advantage of accurately estimating not only the safety factor and the critical failure surface but also the failure probability of the slope.
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