Numerical Analysis of Energy Dissipation in Stepped Spillways with Channel Slope between 8.9o and 26.6o

Dam-integrated stepped spillways function as hydraulic energy dissipators, engineered to attenuate the destructive potential of high-velocity flows that would otherwise induce severe scour at the downstream riverbed. The staircase-like geometry of these structures promotes turbulence and momentum transfer, progressively reducing the hydraulic energy carried by floodwaters before they reach the channel below. Prior research has extensively documented the erosive consequences of residual kinetic energy acting on the riverbed, with findings particularly emphasizing structures built on steep gradients surpassing 26.6°. Yet, the intermediate slope range of 8.9° to 26.6° has received comparatively little scholarly attention with respect to energy dissipation performance, representing a notable knowledge gap that constrains the reliable engineering of stepped spillways within this gradient category. Furthermore, the prevailing model for quantifying energy dissipation across varying slope angles incorporates a friction factor, f, that is inherently difficult to evaluate objectively and is frequently subject to designer interpretation. This study aims to furnish design guidance for stepped spillways within the 8.9° to 26.6° slope range, while simultaneously introducing an approach that eliminates dependence on the friction factor, f. Air-water flow experiments using phase-detection intrusive probes were conducted at a large-scale facility on stepped spillways spanning this slope range, with emphasis on transitional and skimming flow regimes. The resulting models for energy loss estimation yielded Pearson correlation coefficients between 0.79 and 0.99, demonstrating strong agreement with measured data. All outcomes were internally consistent. The proposed models are straightforward in application and offer improved predictive performance relative to existing approaches.