Multi-objective optimization design of pile-anchor structures for slopes based on reliability theory considering the spatial variability of soil properties

Pile-anchor structures (PAS) are emerging as a promising tool for slope stabilization and landslide mitigation. However, the optimized design of PAS is an essential yet challenging issue. In particular, there is an irreconcilable contradiction between the safety and cost-efficiency in PAS design, and a coordinated balance between these two factors is critical for safe and practical applications. Previous optimization design studies rarely considered the uncertainty of PAS-reinforced slope systems while the spatial variability of soil properties has a significant impact on the optimization design. This study, therefore, proposes a framework for the multi-objective optimization design of PAS in slopes based on reliability theory and in consideration of the spatial variability of soil properties. The study is automated by coupling a multi-objective optimization design using Pareto optimality theory and PAS-reinforced slope simulations using Monte Carlo simulations to consider the spatial variability of soil properties. An illustrative example of the PAS design for a two-layer slope is provided to demonstrate the proposed framework. The results suggest that the optimal PAS design achieved meets the minimum failure probability and has the lowest total cost. This study aims to motivate the subsequent development of optimization design for slope engineering.