Are real-world shallow landslides reproducible by physically-based models? Four test cases in the Laternser valley, Vorarlberg (Austria)

Original Paper Landslides DOI 10.1007/s10346-017-0840-9 Received: 18 January 2017 Accepted: 5 May 2017 © The Author(s) 2017 This article is an open access publication Thomas Zieher I Barbara Schneider-Muntau I Martin Mergili Are real-world shallow landslides reproducible by physically-based models? Four test cases in the Laternser valley, Vorarlberg (Austria) Abstract In contrast to the complex nature of slope failures, physically-based slope stability models rely on simplified representations of landslide geometry. Depending on the modelling approach, landslide geometry is reduced to a slope-parallel layer of infinite length and width (e.g., the infinite slope stability model), a concatenation of rigid bodies (e.g., Janbu’s model), or a 3D representation of the slope failure (e.g., Hovland’s model). In this paper, the applicability of four slope stability models is tested at four shallow landslide sites where information on soil material and landslide geometry is available. Soil samples were collected in the field for conducting respective laboratory tests. Landslide geometry was extracted from pre- and post-event digital terrain models derived from airborne laser scanning. Results for fully saturated conditions suggest that a more complex representation of landslide geometry leads to increasingly stable conditions as predicted by the respective models. Using the maximum landslide depth and the median slope angle of the sliding surfaces, the infinite slope stability model correctly predicts slope failures for all test sites. Applying a 2D model for the slope failures, only two test sites are predicted to fail while the two other remain stable. Based on 3D models, none of the slope failures are predicted correctly. The differing results may be explained by the stabilizing effects of cohesion in shallower parts of the landslides. These parts are better represented in models which include a more detailed landslide geometry. Hence, comparing the results of the applied models, the infinite slope stability model generally yields a lower factor of safety due to the overestimation of landslide depth and volume. This simple approach is considered feasible for computing a regional overview of slope stability. For the local scale, more detailed studies including comprehensive material sampling and testing as well as regolith depth measurements are necessary. Keywords Slope failure . Landslide geometry . Infinite slope stability model . Janbu’s model . r.slope.stability . Differential digital terrain model Introduction Landslides are a common geomorphological feature in mountain regions often putting lives and infrastructure at risk. The term Bshallow landslides^ typically refers to translational sliding movements of soil material (earth and/or debris), characterized by a pre-defined, planar sliding surface in a depth of up to 2.0 m (e.g., Cruden and Varnes 1996; Hungr et al. 2014). In the past decades, the Laternser valley (Vorarlberg, Austria) was repeatedly affected by rainfall-triggered shallow landslides (Andrecs et al. 2002; Markart et al. 2007). Since the 1950s, more than 800 shallow landslides have been documented in a comprehensive shallow landslide inventory (Zieher et al. 2016). To be aware of the associated risks, it is necessary to assess shallow landslide susceptibility, hazard, and risk areawide. Various techniques have been proposed for landslide susceptibility modelling/mapping (i.e., heuristic, statistically-, and physically-based). Amongst them, physically-based landslide susceptibility models employ physical laws to assess slope stability. They typically rely on the limit equilibrium concept relating stabilizing to destabilizing forces. The proposed techniques differ in the complexity of the considered landslide geometry (shape of the potential sliding surface) in two (e.g., Bishop 1955; Fellenius 1927; Janbu 1954; Morgenstern and Price 1965) and three dimensions (e.g., Hovland 1977; Hungr 1987; Lam and Fredlund 1993; Mergili et al. 2014). While slope failures show complex geometrical shapes in nature, their representation in physically-based slope stability models is simplified. Shallow landslides are approximated by either a slope-parallel layer of infinite length and width (e.g., the infinite slope stability model, ISSM), a concatenation of rigid bodies of infinite width (e.g., Janbu’s model), or a representation of discrete, 3D units (columns on the basis of raster cells; e.g., the r.slope.stability model, RSS). Consequently, the considered sliding surfaces are either planar (ISSM), an irregular 2D polyline (2D models) or an irregular 3D surface (3D models). Furthermore, some of these approaches include inter-slice forces between the geometrical subunits (e.g., Janbu 1954) while others assume them to cancel each other out (e.g., Fellenius 1927). The result of physically-based slope stability models based on the limit equilibrium concept is a dimensionless factor of safety (FOS) which is a quantitative measure of slope stability. Slope failures are predicted, if the FOS falls below 1. In engineering, these models are usually applied at local scale to evaluate the stability of a single slope unit in the context of a specific engineering task. For the assessment of slope stability at catchment scale, the ISSM has proven feasible in combination with geographical information systems (GIS). Most spatially distributed physically-based shallow landslide susceptibility models include the infinite slope approach, often combined with an infiltration model (e.g., Baum et al. 2008; Dietrich et al. 1995). Recently, models including a more complex landslide geometry (e.g., ellipsoidal and truncated sliding surfaces) have been implemented in GIS (Mergili et al. 2014; Xie et al. 2006). For all these physically-based slope stability models, the result is a FOS map which is a spatially distributed quantitative measure of slope stability. Besides geotechnical input parameters characterizing the involved material, physically-based models require data on topography (e.g., slope angle) and depth of the pre-defined sliding surface. Topographic data are usually derived from digital terrain models (DTMs), which have become readily available. The depth of the pre-defined sliding surface is more difficult to obtain. It can be assessed by (i) direct measurements (Andrecs et al. 2002; Wiegand et al. 2013), (ii) means of geophysics (Davis and Annan 1989; Sass 2007), or modelling (Dietrich et al. 1995; Catani et al. 2010). Moreover, depth and volume of past landslides can be Landslides Original Paper assessed efficiently with the help of multi-temporal remotely sensed elevation data (Zieher et al. 2016). Numerous studies have focussed on the area-wide assessment of slope stability at catchment scale by applying physically-based slope stability models which include the infinite slope approach (e.g., Baum et al. 2005; Gioia et al. 2016; Montrasio et al. 2011). In such studies, littl (...truncated)