Spatially distributed three-dimensional slope stability modelling in a raster GIS

Abstract We present a GRASS GIS implementation of a three-dimensional slope stability model capable of dealing with shallow and deep-seated slope failures, r.rotstab . It exploits a modified version of the revised Hovland method and evaluates the slope stability over a large number of randomly selected slip surfaces, ellipsoidal or truncated in shape. For each raster cell in the modelling domain, the factor of safety is taken from the most critical slip surface. This results in an overview of potentially unstable regions without showing the individual sliding areas. Furthermore, the model produces a susceptibility index for each cell, based on the proportion of slip surfaces with a low factor of safety. We test the model in the Collazzone area, Umbria, central Italy where detailed information on shallow and deep-seated landslides, morphology and lithology is available. The rate of true predictions (landslide plus non-landslide) ranges from 54.7 to 81.2% for shallow landslides and from 58.5 to 87.4% for deep-seated landslides, depending on the adjustment of the uncertain geotechnical parameters. In the same order, the rate of true landslide predictions decreases from 80.2 to 19.9% (shallow) and from 64.3 to 3.6% (deep-seated) so that an increase of the true landslide prediction rate can only be achieved at the cost of a significant increase of the false alarm rate. The results for shallow landslides are very similar to those yielded with the infinite slope stability model in terms of the minimum factor of safety, but differ substantially in terms of the spatial patterns. The evaluation of the landslide susceptibility index yields areas under the ROC curves of 0.68–0.70 (shallow landslides, r.rotstab ), 0.61–0.65 (shallow landslides, infinite slope stability model) and 0.59–0.63 (deep-seated landslides). We conclude that the r.rotstab model outperforms the infinite slope stability model.