基于拉丁超立方抽样的边坡可靠度分析非侵入式随机有限元法

Non-intrusive stochastic finite element method for slope reliability analysis based on Latin hypercube sampling

提出了基于拉丁超立方抽样的边坡可靠度分析非侵入式随机有限元法。采用有限元滑面应力法计算边坡稳定安全系数,通过Hermite随机多项式展开拟合边坡安全系数与输入随机变量间隐式函数关系,采用拉丁超立方抽样技术产生配点计算随机多项式展开系数。研究了该方法在锦屏I级水电站左岸边坡稳定可靠度分析中的应用。结果表明:基于拉丁超立方抽样的非侵入式随机有限元法实现了边坡可靠度分析和边坡稳定有限元分析过程不耦合,该方法计算精度高,为复杂高陡边坡可靠度问题求解提供了一条有效的途径。基于拉丁超立方抽样技术计算随机多项式展开系数,所需样本点数目约等于待定系数数目,其计算效率高于常用的概率配点方法。锦屏I级左岸边坡断层f42-9的内摩擦角敏感性程度最大,它对边坡稳定性具有重要的影响,其次为III2类岩体的内摩擦角,其余变量对边坡稳定性影响不明显。表征输入参数敏感性的Sobol指标为边坡加固方案的制定提供了参考依据。

A non-intrusive stochastic finite element method based on the Latin hypercube sampling for slope reliability analysis is proposed. The finite element method for stress analysis of sliding surface is used to calculate the safety factor of slopes. The safety factor of slopes is explicitly expressed as the input random variables using the Hermite polynomial chaos expansion. The Latin hypercube sampling points are selected as the collocation points to calculate the coefficients of polynomial chaos expansion. An example of reliability analysis of natural slope at the left abutment of Jinping I Hydropower Station is presented to demonstrate the validity and capability of the proposed method. The results indicate the proposed non-intrusive stochastic finite element method based on the Latin hypercube sampling can effectively evaluate the reliability of high-steep rock slopes, which decouples the reliability analysis with finite element analysis of slope stability and produces sufficiently accurate reliability results. The coefficients of polynomial chaos expansion determined by the Latin hypercube sampling are more effective than those by the frequently-used probabilistic collocation method, since the number of sampling points required by the former are only approximately equal to that of unknown coefficients. The internal fiction angle of fault f42-9 at Jinping left abutment slope has a significant effect on the slope stability due to its largest sensitivity, followed by the internal fiction angle of III2 class rock mass, whereas the other variables affect the slope stability slightly. The Sobol's indices used for representing the sensitivities of input uncertain parameters can provide a referential basis for working out the reinforcement schemes.