Stepped spillways have been increasingly used to handle flood releases from large dams associated with hydropower plants, and it is important to evaluate the fluctuating pressure field on the steps. Hydraulic model investigations were conducted on three 53° (1V:0.75H) sloping and relatively large-stepped chutes to characterize the mean, fluctuating, and extreme pressures acting on the most critical regions of the step faces, near their outer edges. The pressure development along the chutes is presented, generally indicating an increase of the modulus of pressure coefficients up to the vicinity of the point of inception of air entrainment, and a decrease further downstream. The extreme pressure coefficients along the spillway are fitted by an empirical formula, and the critical conditions potentially leading to cavitation on prototypes are calculated. The correlation between the cavitation index and the friction factor is also applied for predicting the onset of cavitation on prototypes, and the results are compared with the pressure data-based method. Generally, the results obtained from those methods yield typical values for the cavitation index in the vicinity of the point of inception, varying approximately from 0.8 to 0.6, respectively. In light of these results, maximum unit discharges of about 15–20 m2/s are considered advisable on 53° sloping large-stepped spillways without artificial aeration, for step heights ranging from 0.6 to 1.2 m. For much higher unit discharges, a considerable reach of the spillway may potentially be prone to the risk of cavitation damage.

During floods, stepped spillways have the purpose of dissipating energy over the flow passage through the chute, minimizing stilling basins dimensions. However, stepped spillways have their utilization frequently limited to unit discharges of approximately 15 m³/s/m, due to the risk of cavitation damage. In order to increase the specific yields endured by these structures avoiding cavitation damages, some aeration elements are being studied. These elements allow a jet formation and the air can be introduced through the lower portion, in addition to the surface aeration. The present paper has the purpose of analyze the medium pressures behavior and the jet formation in a flow over stepped spillway through measures conducted on a scale reduced physical model. It was possible to notice that the jet reaches the 7 th step for the higher flows and the 9 th step for the lower. Furthermore, it was observed that, upstream of the jet impact location, the mean pressures were close to zero. These pressures were lower than the same measured at a stepped chute with natural aeration (without aerator elements) for the horizontal faces of the steps and higher for the vertical faces of the steps. Near the jet's impact location, for both faces of the steps, a peak of positive pressures was observed, exceeding the same values on a chute with natural aeration. Downstream of this location, the pressures tend to the values acquired with natural aeration.

Stepped spillways have been widely used for flood runoff due to of their constructive advantages and in regards to energy dissipation during the drop, allowing downstream dissipation structures to be designed in smaller dimensions. Due to the need for further studies on the effect of runoff in the chute of the stepped spillway and the analysis of dimensionless numbers used to characterize the longitudinal distribution of the pressures acting on the faces of the steps of a spillway, this study aims to characterize the acting forces on the steps of said spillways. Analyses were performed on a physical model of spillway with a slope of 1V: 0.75H and steps with a height of 6 centimeters. The pressure fields on the steps were analyzed and compared with results found in literature. As a general finding concerning the pressure in the horizontal faces, it was ascertained that the traction and the compression loads have relatively similar magnitudes, the negative pressures being more intense. Regarding the maximum pressures at the horizontal faces of the steps, it should be emphasized that the maximum values of compression have occurred at the end of the chute and that the lower discharges yielded higher values of pressure coefficients.Keywords: Dams; Stepped spillways; Pressures on spillways. RESUMOVertedouros em degraus vem sendo muito utilizados para escoamento de cheias devido às suas vantagens construtivas e em relação à dissipação de energia durante a queda, possibilitando que as estruturas de dissipação a jusante possam ser projetadas em menores dimensões. Devido a necessidade de estudos mais aprofundados sobre a ação do escoamento na calha de vertedouros em degraus e a análise dos adimensionais utilizados para caracterizar a distribuição longitudinal das pressões atuantes nas faces dos degraus de um vertedouro, o presente estudo objetiva a caracterização dos esforços atuantes nos degraus dos referidos vertedouros. Foram realizadas análises sobre um modelo físicos de vertedouro com declividade de 1V:0,75H e degraus de 6 centímetros de altura. Os campos de pressões nos degraus foram analisados e comparados com os resultados disponíveis na bibliografia. Como constatação geral sobre as pressões nos espelhos verificou-se que os esforços de tração e compressão têm magnitudes relativamente semelhantes, sendo mais intensas as pressões negativas. Sobre as pressões máximas nos patamares, destaca-se que os valores máximos de compressão ocorreram no final da calha, percebendo-se que as menores vazões geraram maiores valores de coeficientes de pressões. Palavras-chave:Barragens; Vertedouros em degraus; Pressões sobre vertedouros.RBRH, Porto Alegre, v. 23, e4, 2018Analysis of the longitudinal distribution of pressures near the ends of the vertical and horizontal faces in stepped spillway of slope 1V: 0.75H

Stepped spillways can dissipate a great amount of energy during the flow passage over the chute, however these structures have limited operation due to the risk of cavitation damage. The induced aeration may protect the concrete chute through the air concentration near the channel bottom. Furthermore, some research studies have indicated that the presence of air in flows may reduce the mean pressures. The present research aims to analyze mean pressures, air entrainment coefficient and flow behavior over a stepped spillway with aeration induced by two different deflectors, comparing the results to natural aeration flow. Despite the jet impact influence, the induced aeration does not change significantly the mean pressures compared to natural aeration flow. The air entrainment coefficient, as well as the jet impact position, is higher for the deflector with the longer extension and, although air bubbles can be seen throughout the extension of the chute due to the air entrainment through the inferior flow surface, the induced aeration did not anticipate the boundary layer inception point position.

ABSTRACT Stepped spillways aim to dissipate part of the upstream energy during the flow passage by the chute. However, the use of these structures is limited to a restrict range of specific discharges due to the risk of cavitation damage. As the air entrainment into the flow assists the concrete protection against the aforementioned damages, a possible solution by aerators installed along the chute, already disseminated to smooth chutes, is being studied to be used also in stepped spillways. The purpose of the present paper is to characterize a flow over a stepped chute with induced aeration by deflector and air supply by an airtight chamber trough tests conducted on a reduced scale physical model. The main regions observed during the tests are presented and were developed four equations that allow to approximately predict the location of the main regions for a given spillway.