Limits on the Validity of Infinite Width and Length Assumptions for Modelling Shallow Landslides

Abstract

Actualmente los mecanismos para el modelamiento de deslizamientos de suelos, cualquiera sea la escala más grande que la de un talud individual, se basan exclusivamente en los modelos de estabilidad infinito (infinity slope stability model), en los que la asunción principal es que el largo y el ancho de los deslizamientos individuales son infinitos. Estas asunciones son por lo general válidos, ya que la mayoría de los deslizamientos de suelos superficiales son planos y paralelos a la superficie de deslizamiento, sin embargo, estas asunciones son raramente justificadas. Para determinar la validez de las asunciones infinitas en longitud y ancho de un deslizamiento individual, se han identificado las longitudes y anchos críticos en los que los efectos de borde son pobremente influyentes. Usando elementos finitos para el cálculo de estabilidad de taludes, se han generado modelos sintéticos de deslizamientos superficiales en dos y tres dimensiones (plaxis 2D & 3D), los que posteriormente fueron validados y reproducidos en diferentes escalas y dimensiones. Finalmente, con ayuda de un código python, se han reproducido más de 4 mil modelos (infinity slope stability models & finite element models), como una muestra estadísticamente representativa.

Mechanistic modelling 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 twoand 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 15-noded triangular finite element mesh in PLAXIS 2D to examine the length effects in the slope stability of ~3000 2D models across the range of geometric and geotechnical conditions typically found on natural slopes. Furthermore, to examine the width effects in the slope stability a 10-noded tetrahedral finite element mesh in PLAXIS 3D was used, in this case ~1000 3D models across the range of geometric and geotechnical conditions were simulated. We find that: L/H ratios of >14 lead to <10% error in FoS and of >50 lead to <5% error in FoS 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.