Abstract
The size of a shallow landslide is a fundamental control on both its hazard and geomorphic importance. Existing models are either unable to predict landslide size or are computationally intensive such that they cannot practically be applied across landscapes. We derive a model appropriate for natural slopes that is capable of predicting shallow landslide size but simple enough to be applied over entire watersheds. It accounts for lateral resistance by representing the forces acting on each margin of potential landslides using earth pressure theory and by representing root reinforcement as an exponential function of soil depth. We test our model's ability to predict failure of an observed landslide where the relevant parameters are well constrained by field data. The model predicts failure for the observed scar geometry and finds that larger or smaller conformal shapes are more stable. Numerical experiments demonstrate that friction on the boundaries of a potential landslide increases considerably the magnitude of lateral reinforcement, relative to that due to root cohesion alone. We find that there is a critical depth in both cohesive and cohesionless soils, resulting in a minimum size for failure, which is consistent with observed size-frequency distributions. Furthermore, the differential resistance on the boundaries of a potential landslide is responsible for a critical landslide shape which is longer than it is wide, consistent with observed aspect ratios. Finally, our results show that minimum size increases as approximately the square of failure surface depth, consistent with observed landslide depth-area data.
Highlights
Shallow landslides usually involve only the colluvial soil mantle and are generally translational, failing along a quasi-planar surface
We suggest that our model is an alternative explanation of the observed landslide depth-area scaling to that of Klar et al [2011], both based on limit equilibrium slope stability models
In this paper we derive MD-STAB, a new multidimensional shallow slope stability model, which predicts that observed shallow landslide depth-area scaling in both cohesive and cohesionless soils arises from depthvarying friction on the margins of a potential landslide
Summary
Shallow landslides usually involve only the colluvial soil mantle and are generally translational, failing along a quasi-planar surface. They are important as agents of landscape-scale sediment transfer and erosion as well as potential hazards to life and infrastructure [Spiker and Gori, 2003]. Field mapped inventories of shallow landslides (Figure 1) [Rice et al, 1969; Montgomery, 1991; Morgan et al, 1997; Gabet and Dunne, 2002; Paudel et al, 2003; Warburton et al, 2008; Larsen et al, 2010] show that their scar size varies across several orders of magnitude in volume (100–105 m3) and area (101–104 m2). Landslide depth appears to scale as a power function of surface area both for some individual inventories (Figure 1d) and for global compilations of soil and bedrock landslides, albeit with almost 2 orders of magnitude of scatter in the global compilation [Guzzetti et al, 2009; Larsen et al, 2010]
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