考虑参数空间变异性的非饱和土坡可靠度分析

在考虑多个土体参数空间变异性的基础上，提出了基于拉丁超立方抽样的非饱和土坡稳定可靠度分析的非侵入式随机有限元法。利用Hermite随机多项式展开拟合边坡安全系数与输入参数间的隐式函数关系，采用拉丁超立方抽样技术产生输入参数样本点，通过Karhunen-Loève展开方法离散土体渗透系数、有效黏聚力和内摩擦角随机场，并编写了计算程序NISFEM-KL-LHS。研究了该方法在稳定渗流条件下非饱和土坡可靠度分析中的应用。结果表明：非侵入式随机有限元法为考虑多个土体参数空间变异性的非饱和土坡可靠度问题提供了一种有效的分析工具。土体渗透系数空间变异性和坡面降雨强度对边坡地下水位和最危险滑动面位置均有明显的影响。当降雨强度与饱和渗透系数的比值大于0.01时，边坡失效概率急剧增加。当土体参数变异性或者参数间负相关性较大时，忽略土体参数空间变异性会明显高估边坡失效概率。

Reliability analysis of unsaturated slope considering spatial variability

A non-intrusive stochastic finite element method (NISFEM) based on Latin hypercube sampling (LHS) for reliability analysis of unsaturated slope considering the spatial variability of multiple soil parameters is proposed. The safety factor is explicitly expressed as a function of uncertain input parameters using the Hermite polynomial chaos expansion, the Latin hypercube sample points are selected as the collocation points for calculating the unknown coefficients of polynomial chaos expansion. The Karhunen-Loève (K-L) expansion method is used to discretize the random fields of soil hydraulic conductivity, effective cohesion and internal friction angle. A computer program named NISFEM-KL-LHS is developed. An example of reliability analysis of unsaturated slope stability under the steady-state seepage condition is presented to demonstrate the validity and capability of the proposed method. The results indicate that the proposed NISFEM can effectively evaluate the reliability of unsaturated slope considering the spatial variability of multiple soil parameters. Both the spatial variability of the soil hydraulic conductivity and the rainfall intensity have significant effects on the location of the groundwater table and the critical slip surface of slope. The probability of slope failure increases obviously when the ratio of the rainfall intensity to the saturated hydraulic conductivity is more than 0.01. In addition, if the spatial variability of soil properties is ignored, the probability of slope failure will be overestimated significantly when the coefficients of variation or the negative cross-correlation of soil parameters become larger.