A multi-dimensional stability model for predicting shallow 1 landslide size and shape across landscapes 2

16 The size of a shallow landslide is a fundamental control on both its hazard and geomorphic 17 importance. Existing models are either unable to predict landslide size or are computationally intensive such 18 that they cannot practically be applied across landscapes. We derive a model appropriate for natural slopes 19 that is capable of predicting shallow landslide size but simple enough to be applied over entire watersheds. It 20 accounts for lateral resistance by representing the forces acting on each margin of potential landslides using 21 earth pressure theory, and by representing root reinforcement as an exponential function of soil depth. We 22 test our model’s ability to predict failure of an observed landslide where the relevant parameters are well 23 constrained by field data. The model predicts failure for the observed scar geometry and finds that larger or 24 smaller conformal shapes are more stable. Numerical experiments demonstrate that friction on the 25 boundaries of a potential landslide increases considerably the magnitude of lateral reinforcement, relative to 26 that due to root cohesion alone. We find that there is a critical depth in both cohesive and cohesionless soils, 27 resulting in a minimum size for failure, which is consistent with observed size frequency distributions. 28 Furthermore, the differential resistance on the boundaries of a potential landslide is responsible for a critical 29 landslide shape which is longer than it is wide, consistent with observed aspect ratios. Finally, our results 30 show that minimum size increases as approximately the square of failure surface depth, consistent with 31 observed landslide depth-area data. 32