Coupling a Stochastic Rainfall Generator and a Physically-Based Landslide Triggering Model to Validate the I-D Power-Law Empirical Model

摘要

Knowledge of the rainfall conditions that trigger landslides serves as a fundamental basis for landslide early warning.Empirical models, derived from the analysis of rainfall and landslide historical data, are often used for this purpose.The most extensively-used empirical relationship is the Intensity-Duration power-law model, as proved by the fact that lots of regional empirical thresholds are of this type.In spite of this, the use of such a relationship has not been at this time fully supported by physically-based considerations, and deterministic rainfall thresholds, derived from physically-based hydrological-geomechanical models reveal a relationship between critical intensity and duration that in general deviates from a power-law.Nonetheless, deterministic thresholds are generally derived under the assumption of constant-intensity rainfall (uniform hyetographs), and do not account for the real stochastic nature of rain intensity within events, which constitutes a source of uncertainty, because to a given rain duration and mean intensity may correspond different variable-intensity hyetographs.Another source of uncertainty, of more relevance, is that to a given hyetograph may correspond different initial conditions, due to the aleatory nature of antecedent rainfall.In this study, we adopt a Monte Carlo simulation frame work, that combines a stochastic rainfall generator and a physically-based hydrological and geotechnical model, to study the effect of the two above mentioned aleatory factors on threshold determination, with the aim of validating from a physically-based perspective the I-D power-law model.In particular, we derive optimal power-law thresholds through the optimation of a ROC-index, and contextually we quantify the above-mentioned uncertainty, through Receiver-Operating-Characteristics (ROC) concepts.Application of the approach to the Peloritani Mountains, an area hit by destructive shallow rapidly-moving landslide phenomena, shows that the I-D power-law relationship may have a physically-based justification in cases where soil water pore pressure memory is low, i.e.it is adequate to model the transient part of hillslope response.In other most general cases, where the hillslope has a significant upslope contributing area, the effect of antecedent precipitation should be accounted for, by modifying the I-D model.