A novel hyper-spherical ring-augmented method for slope reliability analysis accounting for high-dimensional random fields

Traditional probabilistic slope stability analysis with random variable model cannot effectively accommodate this uncertainty and particularly provides less reliable results. To cope with this, this study presents a novel hyper-spherical ring-augmented method for slope reliability analysis considering soil spatial variability, where Karhunen-Loève (K-L) expansion is employed for random field discretization. However, high-dimensional issues may emerge when discretizing random fields using K-L expansion, as the number of truncated terms required to achieve comparable accuracy can vary significantly between different autocorrelation functions. In this study, the weighted low discrepancy simulation (WLDS) is augmented by the hyper-spherical coordinate transformation, allowing it to effectively deal with the curse of dimensionality involved in random fields. Moreover, the judgment-based strength reduction strategy is adopted, which simplifies the process by merely determining whether the slope is stable or unstable without calculating the exact factor of safety. Three illustrative examples including different slopes are analyzed to demonstrate the validity of the proposed method. The results demonstrate that the proposed method can accurately estimate failure probabilities with considerably less computational cost than traditional methods for both low- and high-dimensional random fields. Finally, given a specific target reliability index, the relationship between the total sample size and dimensions is discussed.