Abstract This study aimed to investigate the stability of multi-stage drained and undrained slopes considering the spatial variability in soil properties. A bivariate random field was adopted to characterize the spatial randomness in soil strength parameters of each stage of soil slopes. The random field was then incorporated with the finite element method to obtain the factor of safety (FS) and evaluate the slope failure mechanism. Monte Carlo simulations were conducted for slopes with random soils, resulting in histograms of the FS. The results indicated that around 65%–75% cases of a random slope under the drained condition had an FS being less than that of a uniform slope, and this comparison value reached about 92.6% under the undrained condition. As such, the deterministic analysis of a multi-stage slope may result in an overestimated value of the FS. Moreover, the influence of cross-correlation between cohesive strength and friction angle on the stability of drained slopes was also investigated. The findings demonstrated that the failure probability of multi-stage slope increases as the correlation coefficient increases.

中文翻译：

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双变量随机场和有限元方法对多级土坡进行概率稳定性分析

摘要 本研究旨在考虑土壤性质的空间变异性，研究多级排水和不排水边坡的稳定性。采用二元随机场表征土坡各阶段土体强度参数的空间随机性。然后将随机场与有限元方法结合以获得安全系数 (FS) 并评估边坡破坏机制。对具有随机土壤的斜坡进行了蒙特卡罗模拟，得到了 FS 的直方图。结果表明，在排水条件下，随机坡度约65%～75%的情况下FS小于均匀坡度，不排水条件下该比较值达到约92.6%。因此，多阶段斜率的确定性分析可能会导致 FS 值被高估。此外，还研究了粘结强度和摩擦角之间的互相关对排水边坡稳定性的影响。研究结果表明，随着相关系数的增加，多级斜坡的破坏概率增加。