Abstract: The seepage phenomenon of water in multi-layered unsaturated soils is ubiquitous in natural environments and engineering practices. To accurately describe the one-dimensional transient seepage behavior of water in the two-layered unsaturated soil under a time-varying rainfall scenario, based on the exponential soil-water characteristic curve and permeability coefficient function, the corresponding analytical solutions are derived for the first time via the approach of variable substitution, separation variable, and Fourier series transformation. The solutions also account for the arbitrary initial water content distribution and two types of bottom boundary. On this basis, the correctness of the proposed analytical solutions is validated by comparing them with existing two analytical solutions and corresponding numerical solutions. Finally, taking the simplified two-layered soil cover as an example, the one-dimensional transient seepage laws of water in the two-layered unsaturated soil are analyzed. The results indicate that, for the same total rainfall, water storage in the cover is smaller and cumulative leakage CQ_b is larger under the “previous-peak” rainfall pattern, while the opposite occur under the “post-peak” pattern. Compared to the case where the soil cover with a smaller saturated permeability coefficient is located above the two-layered cover, the corresponding water storage is larger and the value CQ_b is smaller when it is located below. When the initial total water storage is the same, the larger volumetric water content at the bottom zone, the smaller water storage in the cover after a period of rainfall, and the larger value of CQ_b. A larger initial effective saturation of the cover S_ini leads to a larger value of CQ_b during the rainfall, and at the same time, the value of CQ_b increases linearly with an increasing S_ini.

Key words: two-layered unsaturated soil, transient seepage, time-varying rainfall, analytical solution, initial water content distribution, bottom boundary type