基于Chebyshev-Galerkin-KL展开的土质边坡稳定可靠度分析

Reliability analysis of soil slope stability based on Chebyshev-Galerkin-KL expansion

提出了一种基于Chebyshev-Galerkin-KL(Karhunen-Loève)展开的新型随机场离散方法,推导了该方法的理论公式,并研发了基于Python语言的边坡滑体体积计算及其失效模式自动识别的高效程序。采用一个水位上涨时的非饱和土坡算例验证了方法的有效性。结果表明:所提随机场生成方法为求解第二类Fredholm积分方程提供了一种新思路,可准确表征岩土体参数的空间变异性。基于Python提出的边坡风险评估程序,与随机有限元计算过程不耦合,极大地提升了开展边坡风险评估的效率,从而增强预测滑坡致灾风险的时效性。此外,研究中非饱和土坡算例可靠度分析结果表明:水位上涨速度越慢,最大水位高度越高,该边坡的安全程度将越低。岩土体参数的竖向空间变异性对该算例边坡安全系数的影响甚微,但对滑体体积的影响较为显著。在对水位上升条件下的边坡开展可靠度分析时,应关注抗剪强度参数间的负相关性,否则将会低估边坡的安全程度。

A novel method is put forward for the random field discretization based on the Chebyshev-Galerkin-KL(Karhunen-Loève)expansion,followed by the derivation of equations for the proposed method.By means of Python language,an efficient program is exploited for automatically calculating the slope sliding volume and identifying the slope failure mode.The proposed method is validated through an unsaturated slope example subjected to water rising.The results indicate that the proposed method for the random field generation provides a new way to solve the Fredholm integral equation of the second kind,which can accurately characterize the spatial variability of geotechnical parameters.The Python-based program for risk estimation is decoupled from the random finite element calculations,which ensures the slope risk estimation with sufficient efficiency and promotes the reduction of the required time to predict the landslide risk.In addition,the obtained results from the unsaturated slope example show that a lower water rising velocity and a greater maximum water level will lead to the decrease of slope stability.The vertical spatial variability of geotechnical parameters has marginal effects on the safety factor of slopes.However,the sliding volume may be significantly affected.Attention should be paid to the negative cross-correlation between shear strength parameters when conducting reliability analysis of slope stability under water rising.Otherwise,the slope stability will be underestimated.