Quantitative research on the delayed effects of landslide displacement based on DLNMs: a case study of the Outang landslide in the Three Gorges Reservoir Area

Landslides often exhibit significant delayed responses to various triggering factors; however, quantitative research on this phenomenon remains limited. Advances in automatic monitoring technologies have greatly improved real-time landslide observation, providing a robust data foundation for quantitative analysis. Taking the Outang landslide in the Three Gorges Reservoir Area (TGRA) as a typical case, this study first introduces a distributed lag non-linear model (DLNM) to elucidate the spatio-temporal relationships between rainfall, reservoir water level and landslide surface displacement. The results indicate that reservoir water-level fluctuations, especially during drawdown, predominantly impact the frontal zone of the landslide, whereas rainfall mainly affects the middle and rear zones. As elevation (natural ground level at monitoring points, AMSL) increases, the impact of rainfall on landslide surface displacement gradually intensifies, although the duration of its effect shortens. This model effectively incorporates both delayed effects of exposure factors and the non-linear relationships between exposure and response, thus facilitating quantitative analysis of landslide-related delayed effects.