Derivation and evaluation of landslide-triggering thresholds by a Monte Carlo approach

摘要

Assessment of landslide-triggering rainfall thresholds is useful for earlywarning in prone areas.In this paper, it is shown how stochastic rainfall models and hydrologicaland slope stability physically based models can be advantageously combined ina Monte Carlo simulation framework to generate virtually unlimited-lengthsynthetic rainfall and related slope stability factor of safety data,exploiting the information contained in observed rainfall records andfield-measurements of soil hydraulic and geotechnical parameters. Thesynthetic data set, dichotomized in triggering and non-triggering rainfallevents, is analyzed by receiver operating characteristics (ROC) analysis toderive stochastic-input physically based thresholds that optimize thetrade-off between correct and wrong predictions. Moreover, the specificmodeling framework implemented in this work, based on hourly analysis,enables one to analyze the uncertainty related to variability of rainfallintensity within events and to past rainfall (antecedent rainfall). Aspecific focus is dedicated to the widely used power-law rainfallintensity–duration (I–D) thresholds.Results indicate that variability of intensity during rainfall eventsinfluences significantly rainfall intensity and duration associated withlandslide triggering. Remarkably, when a time-variable rainfall-rate event isconsidered, the simulated triggering points may be separated with a very goodapproximation from the non-triggering ones by a I–D power-law equation,while a representation of rainfall as constant–intensity hyetographsglobally leads to non-conservative results. This indicates that the I–Dpower-law equation is adequate to represent the triggering part due totransient infiltration produced by rainfall events of variable intensity andthus gives a physically based justification for this widely used thresholdform, which provides results that are valid when landslide occurrence ismostly due to that part. These conditions are more likely to occur inhillslopes of low specific upslope contributing area, relatively highhydraulic conductivity and high critical wetness ratio. Otherwise, rainfalltime history occurring before single rainfall events influences landslidetriggering, determining whether a threshold based only on rainfall intensityand duration may be sufficient or it needs to be improved by the introductionof antecedent rainfall variables. Further analyses show that predictabilityof landslides decreases with soil depth, critical wetness ratio and theincrease of vertical basal drainage (leakage) that occurs in the presence ofa fractured bedrock.