Semi-empirical prediction of dam height and stability of dams formed by rock slope failures in Norway

Abstract

Based on an inventory of 69 dams formed by rock slope failures in southwestern Norway and published inventories from other parts of the world, we developed semi-empirical relationships linking the maximum dam height (HD.max in metres) to dam volume (VD in 106 m3) and other relevant parameters such as valley width (WV in metres) or dam area (AD in square kilometres). Power laws are obtained for HD.max=f(VD) and HD.max=f(VD, WV), while a linear relationship links HD.max to the ratio VD∕AD. For dams in southwestern Norway, the linear relationship HD.max=1.75×VD/AD has the least uncertainties and provides the best results when comparing predicted dam heights with a validation dataset composed of existing dams in northern Norway and numerically modelled dams for possible rock slope failures. To assess the stability of future dams, we use the predicted dam heights in the dimensionless blockage index (DBI) and relating this index to the probability of dam failure derived from our dataset and other published databases on landslide dams. This study underlines the potential of semi-empirical relationships for assessing dam height and stability that needs to be included in preliminary hazard and risk assessment for unstable rock slopes, because damming of a river is an important secondary effect of landslides due to upstream flooding and possible outburst floods in the case of dam failure.