MODELING THE SPATIAL DISTRIBUTION OF SHALLOW RAINFALL-INDUCED LANDSLIDES

Mathematical modeling commonly represents shallow landslides, typically less than 3 or 4 meters thick, in digital landscapes as uniform slabs using the one-dimensional (1-D) infinite-slope stability analysis. This approach neglects the effects of irregular topography, variable thickness of slope deposits, and other conditions that violate the assumption of laterally constant stress. Model accuracy also decreases as the ratio of slab depth to length increases, as in the case of models based on digital, high-resolution (< 10-m cell spacing) topography, so that many isolated, small landslides are incorrectly predicted (Fig. 1A). These effects of variable geometry and depth-to-length ratio contribute to the over-prediction of unstable areas by distributed 1-D slope stability models.

Use of 3-D methods of slope stability analysis with gridded elevation models accounts for interaction between grid cells and improves the accuracy of predictions of landslide location, size, and shape. Whereas distributed 1-D methods compute factor of safety, F, cell by cell, 3-D methods compute composite F values for 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 supported by adjacent stable cells: 3-D methods correctly predict F>1 in most of these non-landslide areas. Further, 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. Using 3-D analyses to predict landslide size and location reduces spurious clusters of unstable cells and improves accuracy (Fig. 1B).  For example, receiver operator characteristics analysis shows that simple 3-D analysis improves prediction of landslide points (true positives) with only a slight increase in the number of false positives (Fig. 2).

Figure 1.  Landslide susceptibility maps of a study area north of Seattle, Washington based on 1.8-m topographic data, (A) Factor of safety computed cell-by-cell using the infinite slope analysis (1-D), and (B) Factor of safety computed for a moving circle using a simplified 3-D method of columns 

Figure 2.  Receiver operator characteristics (ROC) plot comparing results of 1-D and 3-D factor-of-safety computations depicted in Figure 1.