## 5 Conclusions  
A stepped spillway is a flood release structure with effective aeration and energy dissipation. Along with the rapid construction of roller-compacted concrete (RCC) dams, many such spillways have been built. Conventionally, the stepped chute features horizontal step surfaces. Due to large dam heights, the cavitation risk associated with local low pressure is often an issue of concern in design. Revised flood criteria might require that a dam spillway should safely discharge extreme floods higher than the original design flood. With an aim to overcome the shortcomings of the conventional layout, a few step arrangements are devised with modifications in the step angling. CFD modelling is performed to evaluate how they affect the flow behaviors. The results are analyzed to look into flow velocity, pressure, cavitation potential and level of energy dissipation. The major conclusions are as follows:  
* In the step cavities, the extent of flow circulations becomes larger with an increase in inclination angle. At a step vertex in the developing flow region, the power law gives a good description of the flow velocity above the pseudo-bottom, exhibiting an inverse correlation with the inclination angle. * Along the horizontal step surface, the flow pressures exhibits an S-shaped change, except for at the 20\({}^{\circ}\) downward inclination. The min. and max. pressures become lower at a larger flow discharge and higher at a smaller inclination angle. A high-pressure zone is observed on the step surface, with a smaller pressure magnitude in the downward layouts than in the upward ones. A correlation is suggested to estimate the extreme pressures. * Along the vertical step surface, the water pressure declines from the bottom, followed by a slight increase. The entire vertical face is subjected to negative pressure if the downward step angle is large (i.e., \(-\)20\({}^{\circ}\)). Both the min. and max. pressure demonstrates a descending trend with an increase in flow discharge. In the small-angle layouts, the extreme pressures are lower than in the large-angle ones. * An increase in the drop number leads to an increase in the velocity ratio at the chute end. With an increase in flow discharge at a given step angle, the energy dissipation becomes less effective (lower energy loss). A gradual change from a downward to an upward step results in more energy loss. In comparison with the conventional layout, the 20\({}^{\circ}\) upward inclination dissipates 6.3% more energy, while a 20\({}^{\circ}\) downward angle dissipates 21.3% less energy. Empirical equations are presented to predict the velocity and energy dissipation. This study shows that it is feasible to improve the hydraulic behaviors of a stepped chute if the horizontal step angling is modified. A layout with a moderately upward step (e.g., 10\({}^{\circ}\)) is recommended if energy dissipation is a major issue of concern. For example, compared with the horizontal steps, the 10\({}^{\circ}\) upward step reduces the end velocity by 10.7% and enhances on average the energy dissipation by 8.0%. Meanwhile, the lowest pressures on both the horizontal and vertical step surfaces are improved, which mitigates the cavitation risk in a prototype. Because of its less effective energy dissipation and low-pressure on the whole vertical surface, the downward steps are not advisable to use. Conceptualization, methodology, formal analysis, investigation and writing--original draft preparation: S.L. Supervision, resources, project administration, funding acquisition and writing--review and editing: J.Y. All authors have read and agreed to the published version of the manuscript. This study is part of the research project \"Two-phase flow modelling: Evaluations and simulations for safer spillway discharge\", funded by Swedish Hydropower Centre (VKU14126).