Deterministic Parameter Variation Versus Random-Field Reliability Assessment in Soil-Nailed Slope Stability

Geotechnical reliability analysis of slopes traditionally relies on deterministic parameter variation using the First Order Reliability Method (FORM), which treats soil cohesion and friction angle as fixed, bounded scalars. This paper contrasts that conventional approach (Case 1) with a spatially resolved Monte Carlo Simulation (MCS) and Adaptive Radial Based Importance Sampling (ARBIS) framework grounded in random field theory (Case 2), applied to a soil-nailed slope. Results demonstrate that while FORM with set-varied parameters yields smooth, monotonically improving factors of safety as soil strength increases, random field realizations reveal non-negligible probabilities of failure even when the mean factor of safety exceeds unity a phenomenon attributable to localised weak zones created by spatial variability of cohesion and friction angle. Anchoring consistently improves the minimum factor of safety in both approaches. The random field framework better captures the physical heterogeneity of soil, supports identification of critical non-linear failure surfaces, and provides a more economically calibrated reliability-based design.