Mountainous rainfall exhibits strong spatial heterogeneity associated with topographic effects. Understanding modulating patterns and non-linear responses of rainfall to terrain factors supports mountain storm-disaster mitigation. Taking the Yanshan Mountains in Huairou (Beijing) as the study area, we divided the region by watershed divides into northern and southern zones. Elevation, slope, and sine-cosine transformed aspect served as independent variables, while annual, flood-season, maximum-daily, and maximum-3-day extreme rainfall were dependent variables. We applied Kriging interpolation, quadratic-polynomial ordinary least-squares (OLS), multiscale geographically weighted regression (MGWR), and XGBoost-SHAP to characterize terrain-rainfall statistical associations from global-linear, spatial-non-stationary, and non-linear empirical transition perspectives. Elevation and slope dominated rainfall spatial patterns, whereas aspect exerted minor local modulation. Southern rainfall generally corresponds to higher values with rising elevation, while northern rainfall presented a U-shaped non-linear elevation response. Extreme rainfall was more sensitive to slope than routine rainfall; empirical transition-response features lie at 700–800 m elevation and 20° slope. Multi-model coupling mitigated single-model limitations and provides references for extreme-precipitation understanding and geohazard risk assessment in the North China Yanshan Mountains.

The deformation prediction of large-span variable-section foundation pit excavations in water-rich soft soils and silty fine sand strata remains challenging. Therefore, the deformation characteristics of a large-span variable-section foundation pit were investigated by considering seepage-induced changes in the mechanical properties of silty fine sand and the creep behaviour of mucky silty clay. Based on a large-span variable-section foundation pit project located in the Yangtze River floodplain area, the characteristics of the upper muddy soil and underlying silty fine sand composite strata, together with the “L-shaped” construction method, were considered. A combination of laboratory tests and numerical simulations was adopted to investigate the soil saturation state, seepage characteristics and deformation behaviour of the retaining structure during the dewatering process. The results showed that the seepage conditions within the composite strata were significantly altered by dewatering, and the shear strength of the silty fine sand was exponentially reduced under seepage conditions. The results showed that accounting for seepage-induced changes in soil mechanical properties, together with soil creep, altered the location of the maximum deformation of the retaining structure and increased its deformation. Specifically, incorporating the modified mechanical properties of the silty fine sand increased the maximum horizontal displacement by up to 5.7% compared with the analysis considering soil creep alone. The influence of seepage within the silty fine sand layer on the deep deformation of the retaining structure was found to be significant. The seepage-induced displacement increment was mainly concentrated within the silty fine sand layer, with a maximum increase of 7.44 mm, and was jointly governed by creep duration, excavation depth and seepage conditions. Field monitoring results demonstrated that the numerical model incorporating the weakening effect of seepage on silty fine sand was capable of better reproducing the deformation evolution of the retaining structure during construction, thereby improving the accuracy of deformation prediction.