Theoretical analysis and optimization of frame protection to control shallow slope stability and soil erosion

The frame protection is widely used for highways or railways to prevent the subgrade slope from shallow instability. However, the frame structure's design is empirical, and the theoretical analysis of the soil-structure interaction is scarce at present. By analyzing the critical stability conditions of soil particles of the shallow slope under rainfall infiltration, the paper discusses the shielding effect of the frame structure against erosion, together with the stabilization impact and the bearing behavior of frame protection. Under the unfavorable seepage condition, the equation of anti-erosion safety factor and the shallow stability analysis method, as well as the strength examination method of the frame structure, are established. On this basis, an mathematical optimization model is established, which takes the geometric parameters as decision variables, and anti-erosion stability, shallow stability, and safety of frame structure as constraints, and the minimum masonry quantity and shortest construction axis under unit protection area as objective functions. Finally, a case study involving numerical investigation and validation is implemented based on the mathematical optimization model, and the recommended optimal geometric parameters of the frame structure are given, considering the requirement of structural safety and cost-efficiency. The theoretical method and optimization model proposed in this paper can guide the frame structure's design in practical engineering.