Upper Bound Stability Analysis of Soil-Nailed Slopes with a Discretized Technique in Layered Ground

Abstract

Soils in the site are usually layered due to natural sedimentation, which causes nonuniformity along the depth. Conventional upper bound limit analysis is no longer suitable for analyzing such slope stability issues; hence, an alternative approach is required. To account for varying soil properties, including internal friction angle, cohesion, unit weight, and limit bonding strength at the soil–nail interface among different soil layers, the discretized technique was introduced to generate a potential failure mechanism. Considering the influence of soil parameters within the depth on the failure mechanism, three failure modes were employed to carry out the upper bound limit analysis of soil-nailed slope stability, including toe failure mode, intermediate failure mode, and bellow-toe failure mode. The upper bound solutions of the factor of safety and failure surface were determined by the strength reduction technique in combination with the particle swarm optimization algorithm. A finite-element limit analysis model of soil-nailed slopes in a layered ground by Optum G2 (version 2023 2.3.7) was established to verify the proposed upper bound limit analysis method. The results of the discretized technique were compared with those from the conventional upper bound analysis, the shear strength reduction finite-element method and limit equilibrium method in previous literature, and the finite-element limit analysis by Optum G2. To better estimate the influences of the soil nail inclination angle and soil thickness ratio H1/H on the factor of safety and critical failure surface, a parametric study was performed under two cases: a hard soil layer or a soft soil layer in the upper part of the ground. To evaluate the contribution of soil nails to slope stability, a dimensionless parameter η, meaning the ratio of the energy dissipation rate of soil nails to the total energy dissipation rate, was proposed and discussed in the parametric analysis. The results showed that the proposed discretized method agrees well with the shear strength reduction finite-element method, limit equilibrium method, and finite-element limit analysis (FELA). The simplified approach with weighted average parameters has a relative error greater than 10% and is not appropriate for stability analysis in the layered ground compared with the proposed discretized method and FELA.