Analytical solutions and application analysis of transient seepage of water in the unsaturated vegetated soil under a time-varying rainfall condition

Aiming at the issue of transient seepage of water in the unsaturated vegetated soil under a time-varying rainfall condition, based on several assumptions, the corresponding analytical solutions are obtained by using methods such as variable substitution, Green's function operation, and Fourier series transformation. The analytical solutions also consider two types of typical bottom boundaries and the arbitrary initial water content distribution form. Furthermore, the expressions of analytical solution under several common rainfall patterns are provided. On this basis, the developed analytical solutions'reliability is verified through comparisons in two aspects. Eventually, taking a class of vegetation cover of landfill as the research object, the analytical solutions are applied to analyze the impacts of several factors on its bottom water leakage. The results show that when the total rainfall is the same, overall, the cumulative leakage amount CQb is larger under the rainfall pattern with a larger rainfall rate in the early stage. For different forms of water content distribution with the equal initial total water storage, the form with a larger bottom water content leads to a larger CQb, and its impact mainly occurs in the early stage of rainfall infiltration. Among four typical root shapes considered, the vegetation cover with a uniform root shape has the best effect in blocking the bottom water leakage, and the exponential root shape has the worst effect, but the effect of root shape is relatively small. An increase in the transpiration rate can obviously reduce the CQb, and this effect will gradually become more significant as the rainfall infiltration process proceeds. Generally, the obtained analytical solution and the relevant application analysis are helpful for guiding the engineering practices related to the seepage of water in unsaturated vegetated soils.