Analytical Solutions for Water Infiltration in an Infinite Vegetated Slope under Heavy Rainfall and Its Shallow Stability

Abstract

Heavy rainfall is a common natural phenomenon. Regarding the issue of water infiltration in an infinite vegetated slope (consisting of rooted and unrooted layers) under the heavy rainfall condition, the infiltration process is divided into two stages— before and after the slope surface reaches saturation—and the corresponding analytical solutions are acquired through several mathematical approaches. Then the proposed solutions are effectively verified by two comparisons. Finally, based on the factor of safety ( F s ), the effects of key factors on the slope’s shallow stability are quantitatively investigated, and some novel findings are obtained. For example, an increased heavy rainfall rate reduces the F s , but this effect exhibits a tendency of increasing and then decreasing. An increase in transpiration rate enhances the infinite vegetated slope’s whole stability, while its influence will be declined after the heavy rainfall infiltration. The increased root tensile strength improves the F s within the rooted layer, but does not affect the unrooted layer’s stability. Moreover, compared with the “exponential” root shape, the F s within the unrooted layer is slightly lower in the case of the “uniform” root shape. Overall, the findings provide useful insights into infiltration mechanisms and shallow stability of infinite vegetated slopes under heavy rainfalls.