考虑参数空间变异性的边坡可靠度分析非侵入式 随机有限元法

提出了考虑土体参数空间变异性的边坡可靠度分析的非侵入式随机有限元法。采用Karhunen-Loeve级数展开方法表征土体抗剪强度参数空间变异性，其中通过wavelet-Galerkin技术求解Fredholm积分方程得到相关函数的特征解。基于有限元滑面应力法计算边坡安全系数，采用随机多项式展开将隐式函数表达的安全系数替换为显式函数表达的安全系数，并编写了计算程序NISFEM。研究了所提方法在考虑土体参数空间变异性的边坡稳定可靠度分析中的应用。结果表明：提出的非侵入式随机有限元法极大地提高了考虑土体参数空间变异性的边坡可靠度分析的计算效率，为解决复杂边坡稳定可靠度问题提供了一条有效的途径。考虑抗剪强度参数空间变异性的边坡可靠度分析存在临界变异系数，其随边坡安全系数的增加而增大。当抗剪强度参数的变异系数小于临界变异系数时，忽略土体参数空间变异性将会高估边坡失效概率。当边坡安全系数小于1时，边坡失效概率并不总是随着抗剪强度变异系数的增加而增大。此外，土体黏聚力和内摩擦角随机场间相关性对边坡失效概率具有十分明显的影响。

Reliability analysis of slopes considering spatial variability of soil parameters using non-intrusive stochastic finite element method

A non-intrusive stochastic finite element method (NISFEM) is proposed for the reliability analysis of slope stability considering spatial variability of soil parameters. Firstly, the Karhunen-Loeve (K-L) expansion method is used to characterize the spatial variability of shear strength parameters, where the wavelet-Galerkin technique is employed to numerically solve the eigenvalue problem of the Fredholm integral equation. Thereafter, the finite element method is used for slope stability analysis, the factor of safety is explicitly expressed using the Hermite polynomial chaos expansion (PCE), and the flow chart of procedure is also presented. Finally, the proposed NISFEM is studied by application to the reliability analysis of a homogeneous slope. The results indicate that the proposed method can greatly improve the calculation efficiency for slope reliability analysis considering spatial variability of soil parameters, and that it provides on effective way for solving complex slope reliability problems. There exists a critical coefficient of variation for slope reliability analysis, which increases as the factor of safety increases. If the spatial variability of soil properties is ignored, it will lead to overestimating the probability of failure when the coefficient of variation of shear strength parameters is less than the critical value. The probability of failure does not always increase with the coefficient of variation when the factor of safety is less than 1.0. In addition, the correlation between the random fields of effective cohesion and internal friction angle has a very significant effect on the