Unified Triple-Shear Solution for Unsaturated Soil Pressure on Backfill Surface Inclination Under Rainfall Infiltration

To refine the theoretical framework of earth pressure calculation and enrich its practical applications, a theoretical analysis of unsaturated Rankine’s earth pressure was conducted. Based on the triple-shear unified solution for unsaturated soil shear strength, the stress circle graphical method was employed to establish the triple-shear unified solution for unsaturated earth pressure on backfill surface inclination under rainfall infiltration. The derived formula was subsequently validated through degeneration analysis and example validation. Furthermore, the effects of rainfall infiltration, backfill surface angle θ, soil unsaturation, and the intermediate principal stress parameter b on earth pressure were investigated. The results demonstrate that the formulas proposed in this study can be reduced to or approximate various existing formulae, making them applicable to earth pressure calculations under different working conditions. Both active earth pressure pa and passive earth pressure pp increase linearly with the depth of rainfall infiltration z. With increasing duration of rainfall infiltration t,pa initially decrease and then increase, pp first increase and then decrease, ultimately all stabilizing over time. With an increase in the backfill surface angle θ,pa increases nonlinearly, while pp decreases nonlinearly, and the trends become more pronounced as θ grows larger. Moreover, a larger θ leads to a greater influence of the unsaturated characteristic parameters α and n on both pa and pp. Additionally, pa decreases with an increase in b, whereas pp increases with an increase in b. This study provides a theoretical basis for earth pressure analysis and optimal design of retaining walls, with practical implications for future research and engineering applications.