INFLUENCE OF THREE-DIMENSIONAL GEOMETRY ON PREDICTED SHALLOW LANDSLIDE SIZE AND SHAPE

Shallow landslides are often modeled in digital landscapes as uniform slabs using the one-dimensional (1-D) infinite-slope stability analysis. Although this is an acceptable first approximation in many cases, irregular topography, variable thickness of slope deposits, and other conditions violate the assumption of laterally constant stress and complicate the prediction of landslide shapes. Accuracy also decreases as the ratio of slab depth to length increases. These effects of variable geometry contribute to the over-prediction of unstable areas by distributed 1-D slope stability models.

We compare 1-D factor-of-safety computations distributed over gridded elevation models comprising square grid cells with 2-D and 3-D computations and with observed landslide dimensions to illustrate the influence of geometry on the predicted shapes and sizes of shallow landslides. Whereas 1-D methods compute factor of safety, F, cell by cell, 2-D and 3-D methods compute composite F values for rows (2-D) or contiguous groups (3-D) of cells. Although 1-D analyses commonly identify clusters of unstable grid cells (F<1) that roughly coincide with mapped shallow landslides, these analyses also identify isolated unstable cells and scattered small groups of unstable cells away from mapped slides. Many of these isolated cells and scattered groups are incorrect because they are adjacent to stable cells: 2-D and 3-D methods correctly predict F>1. Further, 2-D and 3-D analyses correctly predict larger landslides in observed landslide areas where 1-D analysis predicts unstable cells interspersed with stable, low F (<1.3) cells. Shallow landslides modeled in 2-D and 3-D are preferentially found within areas of concave profile (hollows). These predicted landslides cannot cross into adjacent convex areas, because the line of thrust must remain within a modeled landslide mass to prevent interslice tension and numerical instability. Physically, tension would cause the mass to separate. However, once a landslide has begun moving, it might contribute to instability of adjacent areas. Consequently, source areas of shallow landslides and debris flows computed using 2-D or 3-D methods are likely to be confined to individual concavities whereas observed source areas may be much larger as a result of simultaneous or progressive failure.