Although vegetation is increasingly used to mitigate landslide risks, how vegetation roots affect the landslide threshold of slope has rarely been explored, particularly in the case of lateral runoff. In this study, we established a two-dimensional saturated-unsaturated infiltration equation considering the hydraulic effects of vegetation roots. The analytical solution for the shallow unsaturated two-dimensional coupled infiltration of vegetated slope (VS) was obtained by a Fourier transform technique. The numerical method was used to evaluate the stability of VS caused by four root architectures, the rainfall amount, and the rainfall duration. Subsequently, the transformation law in runoff, vegetation evaporation, and landslide threshold was analyzed. The results indicate that the factor of safety (FOS) increases with increasing drying time and decreases with increasing depth; the minimum FOS is at the junction of the root-rootless zone. Runoff and vegetation evaporation are favorable for the shallow stability of VS. The time of the safe area is 35 h for rainfall amount 500 m in the uniformly root clay slope. Moreover, four landslide threshold curves that reflected the root architecture, rainfall amount, and rainfall duration are developed, which are more realistic than those created using one-dimensional instability modeling.

中文翻译：

---

植被根系对降雨径流引起的边坡不稳定阈值的影响

尽管植被越来越多地用于减轻滑坡风险，但很少探索植被根系如何影响斜坡的滑坡阈值，特别是在横向径流的情况下。在本研究中，我们建立了考虑植被根系水力效应的二维饱和-非饱和入渗方程。利用傅里叶变换技术得到了植被坡度(VS)浅层非饱和二维耦合入渗的解析解。数值方法用于评估四种根系结构、降雨量和降雨持续时间引起的VS稳定性。随后，分析了径流、植被蒸发和滑坡阈值的转化规律。结果表明，安全系数（FOS）随着干燥时间的增加而增加，随着深度的增加而降低；最小 FOS 位于无根区的交界处。径流和植被蒸发有利于VS的浅层稳定性。均匀根系粘土边坡降雨量为500 m时，安全区时间为35 h。此外，还开发了四个反映根结构、降雨量和降雨持续时间的滑坡阈值曲线，比使用一维不稳定模型创建的曲线更真实。