Dino Bellugi

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 models 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.

A spectral clustering search algorithm for predicting shallow landslide size and location

The potential hazard and geomorphic significance of shallow landslides depend on their location and size. Commonly applied one-dimensional stability models do not include lateral resistances and cannot predict landslide size. Multidimensional models must be applied to specific geometries, which are not known a priori, and testing all possible geometries is computationally prohibitive. We present an efficient deterministic search algorithm based on spectral graph theory and couple it with a multidimensional stability model to predict discrete landslides in applications at scales broader than a single hillslope using gridded spatial data. The algorithm is general, assuming only that instability results when driving forces acting on a cluster of cells exceed the resisting forces on its margins and that clusters behave as rigid blocks with a failure plane at the soil-bedrock interface. This algorithm recovers predefined clusters of unstable cells of varying shape and size on a synthetic landscape, predicts the size, location, and shape of an observed shallow landslide using field-measured physical parameters, and is robust to modest changes in input parameters. The search algorithm identifies patches of potential instability within large areas of stable landscape. Within these patches will be many different combinations of cells with a Factor of Safety less than one, suggesting that subtle variations in local conditions (e.g., pore pressure and root strength) may determine the ultimate form and exact location at a specific site. Nonetheless, the tests presented here suggest that the search algorithm enables the prediction of shallow landslide size as well as location across landscapes.

Predicting shallow landslide size and location across a natural landscape: Application of a spectral clustering search algorithm

Predicting shallow landslide size and location across landscapes is important for understanding landscape form and evolution and for hazard identification. We test a recently developed model that couples a search algorithm with 3-D slope stability analysis that predicts these two key attributes in an intensively studied landscape with a 10 year landslide inventory. We use process-based submodels to estimate soil depth, root strength, and pore pressure for a sequence of landslide-triggering rainstorms. We parameterize submodels with field measurements independently of the slope stability model, without calibrating predictions to observations. The model generally reproduces observed landslide size and location distributions, overlaps 65% of observed landslides, and of these predicts size to within factors of 2 and 1.5 in 55% and 28% of cases, respectively. Five percent of the landscape is predicted unstable, compared to 2% recorded landslide area. Missed landslides are not due to the search algorithm but to the formulation and parameterization of the slope stability model and inaccuracy of observed landslide maps. Our model does not improve location prediction relative to infinite-slope methods but predicts landslide size, improves process representation, and reduces reliance on effective parameters. Increasing rainfall intensity or root cohesion generally increases landslide size and shifts locations down hollow axes, while increasing cohesion restricts unstable locations to areas with deepest soils. Our findings suggest that shallow landslide abundance, location, and size are ultimately controlled by covarying topographic, material, and hydrologic properties. Estimating the spatiotemporal patterns of root strength, pore pressure, and soil depth across a landscape may be the greatest remaining challenge.