Time-dependent reliability analysis of rainfall-induced shallow landslides considering spatial variability of soil permeability

The rainfall-induced earth slope instability is time-dependent as a result of the infiltration process. In order to cater for the uncertainty of geo-material parameters, we conduct a time-dependent reliability analysis of the rainfall-induced landslide, which incorporates discretizing the stochastic process of rainfall infiltration, assigning instantaneous landslide limit state functions at discrete time instants, and calculating the time-dependent slope reliability index within the forecast time as a series system reliability problem. Via the widely used numerical package Python, we adopt a simplified Hasofer-Lind-Rackwitz-Fiessler (HLRF) algorithm to calculate the first-order reliability indices, and the numerical calculations extended to slope reliability analysis are easily implemented. In addition, we account for the spatial variability of soil's permeability in the water infiltration model, which for simplicity is based on the Karhunen-Lo'eve (KL) expansion technique. At last, we present extensive parametric studies of an example earth slope using the proposed method, revealing the potential influences of various sources of uncertainties and spatial variability when probabilistically modelling the water infiltration process and the slope instability mechanism, which may be used further for rainfall-induced landslide forecast.