Limits on the Validity of the Infinite Slope Stability Model

Abstract:

Mechanistic models of landslides at any scale larger than an individual hillslope rely almost exclusively on the infinite slope stability model. The model’s central assumption that landslides are infinitely long (down slope) and wide (across slope) is usually considered valid since most natural slides are shallow and planar. However, this is rarely justified, because the critical length/depth (L/H) and width/depth (W/H) ratios below which edge effects become important are poorly constrained. We identify the critical L/H and W/H ratios by benchmarking infinite slope stability predictions against finite element predictions for a set of synthetic two‐ and three-dimensional slopes. In each case we assume that the difference between the predictions is due to error in the infinite slope method. We use a 10-noded tetrahedral finite element mesh in PLAXIS 3D and examine ~4000 models across the range of geometric and geotechnical conditions found on natural slopes. We find that: L/H ratios of >12 lead to <10% error in FS and of >25 lead to <5% error in factor of safety for 95% of parameter combinations, consistent with previous studies. Critical W/H ratios are shorter, with ratios of 10 and 20 leading to <10% and <5% error respectively. To put these results in context we compare critical L/H and W/H ratios with measured ratios at ~300 shallow landslides from six separate inventories across a range of landscapes. Although critical W/H is narrower than critical L/H for any given error threshold, more landslides fail the width than length criteria because most landslides are narrower than they are long.