Local scouring at bed sills under steady and unsteady conditions

Designers are often required to produce safe and economic structures in rivers with erodible beds, which may frequently induce scouring phenomena as they interfere with the natural stream. In CHAPTER 1, an extensive literature is illustrated on scouring by jets at high and low head structures, and predictive formulae are discussed that estimate the equilibrium scour depth of the scour hole, which are most obtained empirically from field and laboratory data. It is also discussed that different stages occur during local scour development. These stages basically include an initial rapid phase of severe scouring, followed by a stabilization phase approaching equilibrium conditions after a long time. CHAPTER 2 describes the theoretical basis to deal with long-term local scouring at bed sills under clear-water and steady-flow conditions. In gravel bed rivers, bed sills are used to limit bed degradation. Local scouring takes place downstream of each sill in addition to the general erosion pattern, and scour hole dimensions increase with the distance between sills. While overall aggradation can be estimated by using 1D morphological models, local scouring requires a more empirical approach. In fact most scouring phenomena are induced by turbulent jets that diffuse within the scour hole, by resulting in extremely complex flow fields. Many approaches are fully empirical, being based on curve fitting of experimental data that link scour depth to hydraulic quantities and sediment properties. In the most recent attempts, a semi-empirical approach has been followed, based on the identification of appropriate dimensionless groups using dimensional analysis before employing best-fitting procedures. The theoretical derivations proposed, which are based on the assumptions of the Buckingham's ­?-theorem, are discussed by showing some further insights on the nature and role of the dimensionless parameters that ensued form dimensional analysis. CHAPTER 3 presents the results of experimental tests carried out by the author in 2003 about the pattern of local scouring generated at the toe of bed sills. The aim of this study is to evaluate the effect of upstream sediment supply on the scour depth and shape. The experiments simulated conditions of a steady upstream sediment supply which had the same grain size composition as the sediment deposit placed on the bed of the flume. The geometric characteristics of three scour holes developed under conditions of steady-flow discharge and steady upstream sediment supply were measured during 48 different tests. It is shown that the imposed sediment transport does not require the introduction of new dimensionless parameters into existing scour depth and length prediction formulae. The effects of sediment feed are shown to be incorporated in the existing dimensionless parameters. The new data set is used to re-calibrate existing scour depth formula. The influence of jet erosion on scour geometry is also discussed. Most research efforts have focused on predicting scour depth, which may affect the structure at the free overfall, as opposed to volumetric scour dimensions and sediment yield contribution due to local scour, which may affect downstream morphology and water quality as well as the structure but are much more difficult to measure in an actively eroding plunge pool. In CHAPTER 4, shape and volume of equilibrium local scour holes at bed sills in high-gradient streams are investigated by analyzing steady-flow scour profiles at the equilibrium stage. Geometric properties of the scour profile are analytically discussed and verified on the basis of new data from experimental tests described in CHAPTER 3 and data from literature. A model is presented to organize data analysis into a conceptual frame, which is based on the formal relationships for scour depth and length ensued from dimensional analysis, and on the assumption that scours exhibit definite geometric properties. Results show evidence of a universal geometric affinity of the scour. Geometric similarity is also found to occur, but only in a limited range of physical conditions. Prediction formulae are proposed which link the eroded volume to the geometric, hydraulic and sediment properties. Evidence on the scaling nature of the scour hole shapes have important implications on the prediction of the eroded volume. In turn, a correct evaluation of the eroded volume is necessary for the optimization of the design of the inter-sill distance. The temporal development of clear-water local scour depth at bed sills in uniform gravel beds is considered in CHAPTER 5. A new experimental program has been carried out by the author, which started at the end of 2006 and was concluded in March 2007 at the Fluid Dynamics Laboratory of The University of Auckland (NZ). Experiments are presented on the development of scour holes under unsteady hydraulic conditions, with the triangular-shaped hydrographs tested being of different durations and different rates of flow variation. Preliminary observations are discussed on the behavior of scour development, which is compared with the scour evolution for the steady-state case. Based on the experimental results and a theoretical framework, a method is given for the definition and prediction of the scouring process under unsteady flows in terms of a dimensionless temporal parameter. A "flash flood" is defined as an event for which the scour doesn't attain its potential magnitude, i.e. the equilibrium value for the peak hydrograph flow rate. It is shown that this flood nature is dependent on both the characteristics of the flood event itself and the characteristics of the stream. A quantitative measure of what constitutes a flash flood is given in terms of the identified temporal parameter, which represents one of the main goal of this study.