Analytical solution of dam-break flood wave propagation in a dry sloped channel with an irregular-shaped cross-section

Abstract

Cross-sectional channel shape is a primary factor influencing dam-break floods. However, it is difficult to analytically understand the impact of the cross-sectional shape on flood wave propagation because most of the existing analytical solutions are only applicable to channels with specific cross-sections (e.g., rectangular, parabolic and triangular cross-sections). Here, a polyline cross-section representing a realistic scenario and derivation method were suggested for analyzing dam-break floods down a dry sloping channel. With the proposed model, the flow depth, average velocity and discharge profiles after an instantaneous dam break can be presented as three dimensionless curves. The effect of bed slope on the dam-break wave was evaluated. Both the flood acceleration on a downward-sloping channel and the flood retardation on an upward-sloping channel are illustrated clearly with the analytical solution in an example application. The effect of the bed slope on wave propagation becomes more prominent over time. The flow depth, average velocity and discharge at the dam site remain constant for a horizontal bed and vary with time for a sloping bed. Three-dimensional numerical simulations of the examples were performed using a large eddy simulation (LES) model along with the Volume of Fluid (VOF) approach for surface tracking. A comparison between the analytical and numerical solutions shows that the analytical model can provide the main features of dam-break floods and therefore can be used for the rapid prediction of dam-break flows. The model limitations are also presented.