Seepage-Induced Spatially-Varied Flow over the Downstream Face of a Rockfill Dam

The combined effects of dynamic pressure and steep bed slope on seepage-induced spatially-varied flow have so far received little research attention. In this study, a depth-averaged equation, which incorporates a higher-order Boussinesq-type correction for these effects, along with its simplified versions, was applied to investigate the two-dimensional problem of steady spatially-varied flow along the seepage face of a rockfill dam. The numerical solutions for these non-linear equations were obtained by means of an implicit finite-difference scheme. The results of the proposed equation were compared with those obtained from the simplified equations and experimental data, resulting in a more accurate agreement with the measurements than the simplified versions. Furthermore, the results of the comparison demonstrated that such a higher-order, depth-averaged equation is sufficiently accurate to capture the complex features of the supercritical spatially-varied flow field. This study concludes that adopting a mild slope approximation greatly affects the accuracy and reliability of the numerical results related to free-surface and bed pressure profiles, especially for such a type of flow problem, where the flow’s dynamic characteristics are significantly influenced by the steepness of the channel bed slope.