The stage-discharge relationship of a weir is essential for a posteriori calculations of flow discharges. Conventionally, it is determined by regression methods, which is time-consuming and may subject to limited prediction accuracy. With the intention to provide better estimate, the machine learning models, artificial neural network (ANN), support vector machine (SVM) and extreme learning machine (ELM), are assessed for prediction of discharges of rectangular sharp-crested weirs. A large number of experimental data sets are adopted to develop and calibrate these models. Different input scenarios and data management strategies are employed for optimization of the models, for which performance is evaluated in the light of statistical criteria. The results show that all three models are capable of predicting the discharge coefficient with high accuracy, but the SVM exhibits somewhat better performance. Its maximum and mean relative error are respectively 5.44 and 0.99%, and 99% of the predicted data show an error below 5%. The coefficient of determination and root mean square error are 0.95 and 0.01, respectively. The model sensitivity is examined, indicative of the dominant roles of weir Reynolds number and contraction ratio in discharge estimation. The existing empirical formulas are assessed and compared against the machine learning models. It is found that the relationship proposed by Vatankhah exhibits a highest accuracy. However, it is still less accurate than the machine learning approaches. The study is intended to provide reference for discharge determination of overflow structures including spillways.

Owing to effective aeration and energy dissipation, a stepped spillway is commonly used in a roller-compacted concrete (RCC) dam. However, its complex air-water flow features are far from being fully understood. Roughness density, step and cavity shapes are essential parameters. Numerical simulations are carried out to investigate their effects on hydraulic properties. In combination with the realizable k-epsilon turbulence model, the two-phase Mixture Model is used. The results indicate higher air concentrations for the spillway with rounded steps than the ones with trapezoidal steps; the roughness density and cavity shape show no observable effects on the aeration performance with cavity blockages. The characteristic air-water velocity for the trapezoidal steps layout is larger than that for the rounded steps. However, neither layout is sensitive to the roughness density; the velocity results for trapezoidal cavity and rounded cavity cases are almost independent of the roughness density. The velocity for all cases exclusive of trapezoidal steps increase with an increase in roughness density. The min. and max. pressures on the trapezoidal steps are slightly larger than those on the rounded steps; they increase with an increasing roughness density. The cavity shape and roughness density do not evidently influence the extreme pressures. Compared with the conventional step layout, chamfering the step edges slightly enhance the energy dissipation; partially blocking the cavities do not lead to any substantial change. In addition, the energy loss is not clearly related to the roughness density and step edge/cavity shape.

A traditional stepped spillway is prone to cavitation risks. To improve its hydraulic behaviors, distorted step faces and pool weirs are devised. By numerical modelling, comparative studies are conducted to look into the flow features. The pressures on step surfaces of the unconventional layouts exhibit 3D distributions. Pool weirs are essential in increasing both the min. and max. pressure loads. Pressures on the downstream bed show a unique pattern for V- and inverted V-shaped models, with the extreme pressures at the sidewalls for the former and at the central plane for the latter. Symmetrical secondary flows are formed in V- and inverted V-shaped cases with different patterns. Distributions of turbulent kinetic energy suggest differences in flow motions in all cases. Furthermore, the relative energy loss of flat setups is similar to 5.4% lower than that of the pooled ones with the same step face angle; inverting the face angle does not give rise to noticeable change. The results provide reference for relevant projects.

Owing to its effective energy dissipation and aeration, a stepped spillway is commonly used for flood release in hydraulic projects. Its conventional design features horizontal step surfaces. Designed for certain flow rates, it does not function satisfactorily at larger discharges. To improve this, layouts with inclined step surfaces, both downward and upward, are proposed. Computational fluid dynamics (CFD) modelling in 3D is performed to examine and compare their flow properties in the skimming flow. The results suggest that a shift from a downward to an upward layout leads to a gradual decrease in the flow velocity at the chute end; the latter exhibit higher energy dissipation efficiency. Moreover, equations are developed to estimate the velocity and energy loss. The flow velocity in the developing zone, described by a power law, shows a decline with an increase in the angle of inclination. The downward layout is subjected to somewhat higher risk of cavitation if implemented in a prototype. The extreme pressure loads acting upon an upward layout are larger, and a correlation is proposed for its prediction. On an inclined surface, either upward or downward, the pressure demonstrates an S-shaped distribution. On a vertical surface, the flow pressure increases, after an initial decline over a short distance, towards the chute bottom.