Application Assessments of Using Scarp Boundary-Fitted, Volume Constrained, Smooth Minimal Surfaces as Failure Interfaces of Deep-Seated Landslides

More than 9,000 potential deep-seated landslide sites in the mountain ranges of Taiwan have been identified by a series of renewed governmental hazard mitigation initiatives after the 2009 Morakot typhoon. Among these sites, 186 sites have protection targets where thorough mitigation strategies are to be implemented. One of the important tasks in the hazard mitigation initiative is to estimate the volume, failure interface and related quantities of each landslide site. In addition, with this number of sites, an automated tool is needed to generate predictions at low operational costs. We propose to use volume-constrained smooth minimal surfaces to approximate the landslide failure interfaces. A volume-constrained smooth minimal surface in the current context is defined as a differentiable surface that encloses a given landslide volume with the minimal surface area. Although the stratigraphy and geological structures are omitted, the smooth minimal surface method is verified with 24 known landslides and is shown to be able to generate acceptable, approximated failure interfaces. A collection of assessment indices is employed to measure the fitness of the predictions. Finally, the prediction fitness vs. the landslide scarp geometry is investigated.