3D Active Earth Pressure of Two-Layer Unsaturated Backfills Under Time-Varying Rainfall Based on Coupled Transient Seepage Framework

Rainfall infiltration can alter matric suction and significantly affect the active earth pressure acting on retaining structures with unsaturated backfills. This effect becomes more complex when hydraulic layering and finite-width failure mechanisms are involved. In this study, a coupled analytical–numerical framework is developed for a vertical retaining wall with a two-layer unsaturated backfill subjected to time-varying rainfall. A one-dimensional transient seepage formulation based on the Gardner-type hydraulic model is combined with a three-dimensional kinematic upper-bound mechanism generated by double-logarithmic-spiral curves. The transient pressure head and effective saturation are converted into a suction-induced resisting contribution and introduced into the work-rate balance. The effects of initial water-content distribution, bottom hydraulic boundary condition, normalized wall width, rainfall intensity, and layer thickness ratio are investigated. The results show that the calculated active earth pressure coefficient is controlled by the coupled influence of transient suction loss, hydraulic contrast between layers, and finite-width confinement. Clay-related profiles are more sensitive to the initial hydraulic state and finite-width effect than sand-dominated profiles. The bottom boundary condition may either increase or decrease the active pressure depending on the hydraulic contrast. For some rainfall intensities, an intermediate layer thickness ratio produces a larger calculated active pressure than the corresponding homogeneous limits. These findings should be interpreted within the assumptions of one-dimensional vertical seepage, hydraulically and mechanically continuous layer interfaces, a smooth wall-back contact, and the adopted admissible three-dimensional failure mechanism.