Role of rainfall temporal distribution on effective infiltration in the loess slope and prediction model

Rainfall is one of the main causes of landslides, particularly in the Loess Plateau. When rainfall occurs, rainfall thresholds can be used to predict whether it will cause landslides in monitoring and early-warning system. However, most rainfall thresholds are established based on constant rainfall processes. Therefore, this study takes the temporal distribution of rainfall into account in rainfall threshold studies and proposes four well-delineated temporal distribution types and an innovative three-step model. Rainfall thresholds are derived from 45 months of rainfall data and slope moisture data obtained through in-situ monitoring of the loess slope in Yan'an city, northwest China. Our analysis focuses on effective rainfall infiltration rather than shallow landslides as the monitoring index for thresholds. The results revealed a total of 189 rainfall events over the course of 45 months. Among these, 167 were classified as ineffective rainfall events with an infiltration depth of <10 cm, while 22 were categorized as effective rainfall events with an infiltration depth exceeding 10 cm, accounting for only 11.6% of the total. In this study, the temporal distribution of rainfall was classified into four types: transitory, constant, unimodal, and multimodal. Analysis of the monitoring data showed that transitory rainfall events were all effective, constant rainfall events were mostly effective (> 76%), unimodal rainfall events were 86.7% effective, and all multimodal rainfall events were effective, with the deepest infiltration depth. A three-step method was employed to establish thresholds for different types of rainfall. Firstly, cumulative rainfall exceeding 34 mm at a single time point was considered the most effective rainfall. Secondly, multimodal or constant rainfall with a constant value of Ac > 3.5 mm/3 h and a peak value of Ap > 9.5 mm/3 h was deemed the most effective rainfall. Lastly, a temperature difference Tr during rainfall below 7.7 °C was indicative of mostly ineffective rainfall. The model demonstrated an accuracy of 96%, as validated by existing monitoring data in the nearby loess area. This model has been demonstrated to be superior to previous model and is currently suitable for application in loess regions of China.