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

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 (inline-formulaHD.max in metres) to dam volume (inline-formulaVD in 10inline-formula6 minline-formula3) and other relevant parameters such as valley width (inline-formulaWV in metres) or dam area (inline-formulaAD in square kilometres). Power laws are obtained for inline-formula $M7inlinescrollmathml{H}_{\mathrm{normal D}.\mathrm{normal max}}=f\left({V}_{\mathrm{normal D}}\right)$ 69pt13ptsvg-formulamathimg4515f2630a1b6c771e13ab38453ac7bc nhess-20-3179-2020-ie00001.svg69pt13ptnhess-20-3179-2020-ie00001.png and inline-formula $M8inlinescrollmathml{H}_{\mathrm{normal D}.\mathrm{normal max}}=f\left({V}_{\mathrm{normal D}}$ 65pt13ptsvg-formulamathimgf63784b1baf5306a548c3ae626ef30ec nhess-20-3179-2020-ie00002.svg65pt13ptnhess-20-3179-2020-ie00002.png , inline-formulaWV), while a linear relationship links inline-formulaHD.max to the ratio inline-formulaVDAD. For dams in southwestern Norway, the linear relationship inline-formula $M12inlinescrollmathml{H}_{\mathrm{normal D}.\mathrm{normal max}}=normal 1.75×{V}_{\mathrm{normal D}}/{A}_{\mathrm{normal D}}$ 108pt14ptsvg-formulamathimg419603486f79d393d2b973adc87aeb23 nhess-20-3179-2020-ie00003.svg108pt14ptnhess-20-3179-2020-ie00003.png 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.

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Oppikofer, Thierry / Hermanns, Reginald L. / Jakobsen, Vegard U. / et al: Semi-empirical prediction of dam height and stability of dams formed by rock slope failures in Norway. 2020. Copernicus Publications.

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