Controls on the size distributions of shallow landslides.

Rainfall-triggered shallow landslides are destructive hazards and play an important role in landscape processes. A theory explaining the size distributions of such features remains elusive. Prior work connects size distributions to topography, but field-mapped inventories reveal pronounced similarities in the form, mode, and spread of distributions from diverse landscapes. We analyze nearly identical distributions occurring in the Oregon Coast Range and the English Lake District, two regions of strikingly different topography, lithology, and vegetation. Similarity in minimum sizes at these sites is partly explained by theory that accounts for the interplay of mechanical soil strength controls resisting failure. Maximum sizes, however, are not explained by current theory. We develop a generalized framework to account for the entire size distribution by unifying a mechanistic slope stability model with a flexible spatial-statistical description for the variability of hillslope strength. Using hillslope-scale numerical experiments, we find that landslides can occur not only in individual low strength areas but also across multiple smaller patches that coalesce. We show that reproducing observed size distributions requires spatial strength variations to be strongly localized, of large amplitude, and a consequence of multiple interacting factors. Such constraints can act together with the mechanical determinants of landslide initiation to produce size distributions of broadly similar character in widely different landscapes, as found in our examples. We propose that size distributions reflect the systematic scale dependence of the spatially averaged strength. Our results highlight the critical need to constrain the form, amplitude, and wavelength of spatial variability in material strength properties of hillslopes.

A multidimensional stability model for predicting shallow landslide size and shape across landscapes.

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.