Probabilistic analysis of slopes designed by the partial material factor approach considering Gaussian copula-based cross-correlated random fields

TY - JOUR

T1 - Probabilistic analysis of slopes designed by the partial material factor approach considering Gaussian copula-based cross-correlated random fields

AU - Li, Yuting

AU - Chen, Xiaobin

AU - Wang, Yinsheng

AU - He, Pengpeng

AU - Wu, Honggang

N1 - Publisher Copyright: © 2026

PY - 2026/3/2

Y1 - 2026/3/2

N2 - Conventional slope design using a single factor of safety often results in different levels of reliability for the same factor of safety due to soil spatial variability. This limitation also applies to the partial factor design method. In addition, cross-correlations between soil properties (e.g., cohesion and friction angle) are often neglected in conventional practice. To address these limitations, this study combines copula theory with the Random Finite Element Method within the framework of the partial factor design method to construct cross-correlated random fields that capture nonlinear dependencies between soil parameters. A drained slope is used as an example to explore the influence of spatial variability and the cross-correlation between c ′ and ϕ ′ on the probabilistic slope design. The results show that the calibrated design slope height follows an approximately lognormal distribution, with stronger negative cross-correlation leading to reduced dispersion but increased bias in design outcomes. The failure probability and calibrated design height are both more sensitive to nonlinear cross-correlation than to spatial variability alone. For an intermediate ρ c ′,ϕ ′ =-0.4 and ν ϕ ′ =0.10, the partial material factor required to satisfy the tolerable failure probability of 10 -3 is 1.55. Compared with conventional Pearson correlation assumptions, the Gaussian copula-based dependence structure results in consistently higher partial factor-based design requirements (e.g., failure probabilities up to two orders of magnitude higher for ρ c ′,ϕ ′ =-0.8). This highlights the risk of unconservative designs when nonlinear dependence is neglected.

AB - Conventional slope design using a single factor of safety often results in different levels of reliability for the same factor of safety due to soil spatial variability. This limitation also applies to the partial factor design method. In addition, cross-correlations between soil properties (e.g., cohesion and friction angle) are often neglected in conventional practice. To address these limitations, this study combines copula theory with the Random Finite Element Method within the framework of the partial factor design method to construct cross-correlated random fields that capture nonlinear dependencies between soil parameters. A drained slope is used as an example to explore the influence of spatial variability and the cross-correlation between c ′ and ϕ ′ on the probabilistic slope design. The results show that the calibrated design slope height follows an approximately lognormal distribution, with stronger negative cross-correlation leading to reduced dispersion but increased bias in design outcomes. The failure probability and calibrated design height are both more sensitive to nonlinear cross-correlation than to spatial variability alone. For an intermediate ρ c ′,ϕ ′ =-0.4 and ν ϕ ′ =0.10, the partial material factor required to satisfy the tolerable failure probability of 10 -3 is 1.55. Compared with conventional Pearson correlation assumptions, the Gaussian copula-based dependence structure results in consistently higher partial factor-based design requirements (e.g., failure probabilities up to two orders of magnitude higher for ρ c ′,ϕ ′ =-0.8). This highlights the risk of unconservative designs when nonlinear dependence is neglected.

KW - Slope stability

KW - Gaussian copula

KW - Partial factor design

KW - Random finite element method

KW - Cross correlation

UR - https://www.scopus.com/pages/publications/105031621468

U2 - 10.1016/j.compgeo.2026.108038

DO - 10.1016/j.compgeo.2026.108038

M3 - Article

SN - 0266-352X

VL - 194

JO - Computers and Geotechnics

JF - Computers and Geotechnics

M1 - 108038

ER -