Analytical and Experimental Investigations of Dam-Break Flows in Triangular Channels with Wet-Bed Conditions

Abstract

Based on the method of characteristics, in this study an analytical solution for one-dimensional shallow-water equations is developed to simulate the instantaneous dam-break flows propagating down a triangular wet-bed channel. The internal relationships between the hydraulic properties associated with dam-break flow are investigated through comparisons with well-known analytical solutions for rectangular channels. Meanwhile, laboratory experiments are conducted in a prismatic, horizontal, and smooth flume with a triangular cross section. Nonintrusive digital image processing is applied to obtain water surface profiles and stage hydrographs. Results show that the dam-break flow propagation depends on the dimensionless parameter hd*, defined as the ratio of initial tailwater depth over the reservoir head. hd* has a significant effect on the dam-break wave in the downstream flooded area. For hd*≤0.4, the water surface profiles in the reservoir for different hd* at a given time remain similar. For hd*≥0.5, extra negative waves occur in the reservoir, leading to water surface undulations. Undular bores are generated at the dam site and propagate downstream. The time evolution of dam-break flows under three different reservoir heads is similar for the same hd*. The inception of water surface profile change is earlier when the reservoir head is larger. The analytical model shows satisfactory agreement with the experimental results, though some errors exist between the analytical solution and measurements due to the formation of extra negative waves, a jet, and undular bores. The similarities and discrepancies between the hydraulics in the triangular and rectangular channels are identified analytically in terms of the profiles of water depth, velocity, discharge, bore height, and wave-front celerity with hd*. The presented solution could be applied to predict the effect of wet-bed conditions on the dam-break wave in triangular channels, while laboratory measurement data could be used for validating analytical and numerical models.