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Abstract
The vortex equation is often used to estimate the front velocity of debris flows using the lateral slope of the flow surface through a channel bend of a given radius. Here we report on laboratory experiments evaluating the application of the vortex equation to channelized debris flows. Systematic laboratory experiments were conducted in a 8 m long laboratory flume with a roughened bed, semi-circular cross section (top width 17 cm), and two different bend radii (1.0 and 1.5 m) with a common bend angle of 60°, and two channel inclinations (15° and 20°). Four sediment mixtures were used with systematic variations in the amount of fine sediment. In the experiments, 12 kg of water-saturated debris were released in a dam-break fashion, and multiple experiments were conducted to verify the repeatability for a given sediment mixture. Data are available for 69 experimental releases at a channel inclination of 20° and 16 releases at an inclination of 15°. Flow velocity was determined with high-speed video, and flow depth and the lateral inclination of the flow surface (superelevation) were measured using laser sensors. In general, the results from an individual sediment mixture are repeatable. We found that the channel slope as well as centerline radius have a significant influence on the correction factor k used in the vortex equation. Relatively coarse-grained sediment mixtures have larger superelevation angles than finer-grained mixtures. We found a statistically significant relation between the correction factor and Froude number. Correction factors of 1 < k < 5 were found for supercritical flow conditions. However, for subcritical flow conditions the correction factor shows a larger value as a function of the Froude number, which leads to an adaption of the forced vortex formula considering active and passive earth pressures. Finally, based on our experimental results, we present a forced vortex equation for debris-flow velocity estimation without a correction factor.
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