Hysteresis modelling of rainfall-induced deformation of mudstone sandstone slopes

The lag effect between rainfall infiltration and slope deformation is critical for enhancing the timeliness and reliability of early warning systems against rainfall-induced landslides. However, most existing prediction models rely on remote sensing data with insufficient spatiotemporal precision, thus failing to achieve high-accuracy forecasting based on in-situ monitoring data. This study focuses on a deep-cut graben slope segment (chainage DK224 + 720–DK225 + 260) along the Bei’an–Heihe Railway, which is characterized by interbedded mudstone and sandstone strata. Based on continuous field monitoring data, we systematically analyzed the coupled lag relationships among rainfall, groundwater level (GWL), and slope deformation, and developed a tailored distributed lag model (DLM). Key findings are as follows: (1) Rainfall is the dominant trigger for stepwise slope displacement, and shows a significant positive correlation with the displacement rate. (2) By analyzing the morphological characteristics of deep displacement curves from typical cross-sections, slope deformation can be categorized into three distinct patterns: “T-type” dominated by shallow shear failure, “S-type” induced by deep creep, and “V-type” caused by localized strain softening. (3) The DLM quantitatively delineates the response sequence of the slope system to rainfall, with daily deformation exhibiting a 3-day lag. Rigorously validated through Granger causality tests, stationarity tests, and synchronous monitoring data, the model demonstrates strong applicability for short-term slope stability warning. It thereby offers a data-driven method for slope risk prevention and control in complex geological settings.