Random-Field Modelling of Cohesion and Friction Angle for Reliability Assessment of Soil-Nailed Slopes

Soil spatial variability is the primary source of uncertainty governing the reliability of geotechnical slopes. This paper presents a random field (RF) framework for characterising cohesion (c′) and friction angle (φ′) as spatially correlated Gaussian fields, discretised via the Karhunen–Loève expansion and propagated through a Monte Carlo Simulation (MCS) and Adaptive Radial Based Importance Sampling (ARBIS) reliability loop applied to a soil-nailed slope. Five random field realisations demonstrate that non-negligible failure probabilities (7–46%) persist even when the mean factor of safety significantly exceeds unity—an outcome attributable to localised weak zones within spatially heterogeneous soil. Failure surfaces exhibit both linear and non-linear geometries, revealing failure pathways invisible to deterministic approaches.