Semi-empirical prediction of dam height and stability of dams formed by rock slope failures in Norway
<p>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 (<span class="inline-formula"><i>H</i><sub&g...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2020-11-01
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| Series: | Natural Hazards and Earth System Sciences |
| Online Access: | https://nhess.copernicus.org/articles/20/3179/2020/nhess-20-3179-2020.pdf |
| Summary: | <p>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 (<span class="inline-formula"><i>H</i><sub>D.max</sub></span> in metres) to dam volume (<span class="inline-formula"><i>V</i><sub>D</sub></span> in
10<span class="inline-formula"><sup>6</sup></span> m<span class="inline-formula"><sup>3</sup></span>) and other relevant parameters such as valley width
(<span class="inline-formula"><i>W</i><sub>V</sub></span> in metres) or dam area (<span class="inline-formula"><i>A</i><sub>D</sub></span> in square kilometres). Power laws are
obtained for <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M7" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>H</mi><mrow><mi mathvariant="normal">D</mi><mo>.</mo><mi mathvariant="normal">max</mi></mrow></msub><mo>=</mo><mi>f</mi><mo>(</mo><msub><mi>V</mi><mi mathvariant="normal">D</mi></msub><mo>)</mo></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="69pt" height="13pt" class="svg-formula" dspmath="mathimg" md5hash="4515f2630a1b6c771e13ab38453ac7bc"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="nhess-20-3179-2020-ie00001.svg" width="69pt" height="13pt" src="nhess-20-3179-2020-ie00001.png"/></svg:svg></span></span> and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M8" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>H</mi><mrow><mi mathvariant="normal">D</mi><mo>.</mo><mi mathvariant="normal">max</mi></mrow></msub><mo>=</mo><mi>f</mi><mo>(</mo><msub><mi>V</mi><mi mathvariant="normal">D</mi></msub></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="65pt" height="13pt" class="svg-formula" dspmath="mathimg" md5hash="f63784b1baf5306a548c3ae626ef30ec"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="nhess-20-3179-2020-ie00002.svg" width="65pt" height="13pt" src="nhess-20-3179-2020-ie00002.png"/></svg:svg></span></span>, <span class="inline-formula"><i>W</i><sub>V</sub>)</span>,
while a linear relationship links <span class="inline-formula"><i>H</i><sub>D.max</sub></span> to the ratio
<span class="inline-formula"><i>V</i><sub>D</sub>∕<i>A</i><sub>D</sub></span>. For dams in southwestern Norway, the linear relationship
<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M12" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>H</mi><mrow><mi mathvariant="normal">D</mi><mo>.</mo><mi mathvariant="normal">max</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">1.75</mn><mo>×</mo><msub><mi>V</mi><mi mathvariant="normal">D</mi></msub><mo>/</mo><msub><mi>A</mi><mi mathvariant="normal">D</mi></msub></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="108pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="419603486f79d393d2b973adc87aeb23"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="nhess-20-3179-2020-ie00003.svg" width="108pt" height="14pt" src="nhess-20-3179-2020-ie00003.png"/></svg:svg></span></span> 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.</p> |
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| ISSN: | 1561-8633 1684-9981 |