A Mechanical Explanation for the Shape of Landslides on Maps

Landslides in rock or consolidated sediments commonly have roughly elliptical shapes in map view and a width: length ratio between 0.5 and 1. A fracture mechanics analysis that treats the landslide slip surface as a shear fracture (slip patch) provides an explanation for these observations. The slip patch is parallel to the surface of an elastic half-space, simulating sliding at depth along a pre-existing weakness (e.g., a geologic contact or bedding plane). The slip patch propagation tendency is inferred from the fracture energy release rate G at its perimeter; G is essentially a measure of the energy available to drive propagation a unit distance. The energy consumed per unit amount of patch advance (G*) is considered as a constant around the patch perimeter. The tendency for a slip patch to propagate in plane is inferred to be greatest where G is highest. A "preferred" patch shape is assumed to occur if G is uniform around the fracture perimeter. For a slip patch with a length that is small relative to its depth (i.e., during slip nucleation) a uniform value of G is obtained for elliptical patches with width: length ratios of 1, ∼0.75 and ∼0.5 for Poisson's ratios of 0, 0.25 and 0.5, respectively. Boundary element analyses reveal that as a slip patch spreads in a material with a Poisson's ratio of 0.25, the patch would tend to maintain a width: length ratio between 0.5 and 1. I interpret these results as predicting that the distribution of width: length ratios for a large sample of landslides would peak between 0.5 and 1. Data from about 350 landslides in Hokkaido, Japan (Yamagishi and Ito, 1994) show that ∼ 60% of the slides have a ratio between 0.4 and 1, consistent with the prediction. The presence of landslides with width: length ratios less than 0.5 or greater than 1 indicates that factors other than the fracture energy release rate come into play in real slopes. Structural, stratigraphic, topographic, and hydrologic heterogeneity probably account for some of this variation, as could variation in the energy required for patch propagation (G*) as a function of position on the patch perimeter. Nonetheless, the consistency of the model predictions with the observations suggests that the simple model here captures at least some of the essential physics of the sliding process.