A Rational Probabilistic Method for Spatially Distributed Landslide Hazard Assessment

First-order, second-moment (FOSM) approximations of limit equilibrium slope stability equations can be combined with digital elevation models to perform spatially distributed probabilistic landslide hazard analyses. This is most easily accomplished using the infinite slope idealization, which is the basis of many published reconnaissance-level slope stability assessments. Comparisons of FOSM and Monte Carlo results show that FOSM approximations yield accurate results when input distributions are symmetric, or nearly symmetric, probability density functions. Contrary to the assumptions of previous authors, however, the Monte Carlo results suggest that factors of safety may be better represented by log-normal distributions than by normal distributions. A 3-3 2km area near Wheeling, West Virginia, covered by a pre-existing landslide hazard map was used to illustrate the application of the spatially distributed FOSM approach. This area was chosen specifically because it includes active translational landslides as well as several map units that likely violate the infinite slope idealization to one degree or another: large dormant landslides, actively moving cove landforms, and areas deemed susceptible to sliding by virtue of underlying bedrock lithology. Using a 50 percent probability of sliding threshold to delineate unstable areas, the FOSM model predicted 74 percent of the mapped active landslide area to be unstable and 77 percent of the area without mapped slope hazards to be stable (both on a raster-by-raster basis). The overall degree of correspondence for all hazard map units was 54 percent if dormant landslides were considered to be unstable and 65 percent if considered to be stable. The degree of correspondence varies as a function of the threshold probability but is similar to values reported for pairs of landslide inventory maps prepared by different geologists.