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 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 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. A larger initial effective saturation of the cover S leads to a larger value of CQ during the rainfall

and at the same time

the value of CQ increases linearly with an increasing S.