Yes / Pier scour has been extensively studied in laboratory experiments. However, scour depth relationships based on data at the laboratory scale often yield unacceptable results when extended to field conditions. In this study, non-uniform gravel bed laboratory and field datasets with gravel of median size ranging from 2.7 to 14.25 mm were considered to predict the maximum equilibrium scour depth at cylindrical piers. Specifically, a total of 217 datasets were collected: 132 from literature sources and 85 in this study using new experiments at the laboratory scale, which constitute a novel contribution provided by this paper. From the analysis of data, it was observed that Melville and Coleman's equation performs well in the case of laboratory datasets, while it tends to overestimate field measurements. Guo's and Kim et al.'s relationships showed good agreements only for laboratory datasets with finer non-uniform sediments: deviations in predicting the maximum scour depth with non-uniform gravel beds were found to be significantly greater than those for non-uniform sand and fine gravel beds. Consequently, new K-factors for the Melville and Coleman's equation were proposed in this study for non-uniform gravel-bed streams using a curve-fitting method. The results revealed good agreements between observations and predictions, where this might be an attractive advancement in overcoming scale effects. Moreover, a sensitivity analysis was performed to identify the most sensitive K-factors.

Yes / Pier scour has been extensively studied in laboratory experiments. However, scour depth relationships based on data at the laboratory scale often yield unacceptable results when extended to field conditions. In this study, non-uniform gravel bed laboratory and field datasets with gravel of median size ranging from 2.7 to 14.25 mm were considered to predict the maximum equilibrium scour depth at cylindrical piers. Specifically, a total of 217 datasets were collected: 132 from literature sources and 85 in this study using new experiments at the laboratory scale, which constitute a novel contribution provided by this paper. From the analysis of data, it was observed that Melville and Coleman’s equation performs well in the case of laboratory datasets, while it tends to overestimate field measurements. Guo’s and Kim et al.’s relationships showed good agreements only for laboratory datasets with finer non-uniform sediments: deviations in predicting the maximum scour depth with non-uniform gravel beds were found to be significantly greater than those for non-uniform sand and fine gravel beds. Consequently, new K-factors for the Melville and Coleman’s equation were proposed in this study for non-uniform gravel-bed streams using a curve-fitting method. The results revealed good agreements between observations and predictions, where this might be an attractive advancement in overcoming scale effects. Moreover, a sensitivity analysis was performed to identify the most sensitive K-factors.

This analysis is an expansion of research done by Rollin Hotchkiss during his Ph.D work. The research uses fluid flow, sediment transport, and perturbation theory to predict where scour will occur in a variable-width channel. The resulting equations also determine equilibrium scour depth based upon the stream bed elevation derived from a dimensionless bed slope equation. Hotchkiss perturbed the width of the channel using a second order Taylor Series perturbation but neglected second order terms. The present work follows the same procedures as Hotchkiss but maintains the second order terms. The primary purpose is to examine how the additional terms impact the final equilibrium scour depth and location results. The results of this research show a slight variation from the previous work. With respect to a hypothetical case, there was not a significant amount of change, thereby verifying that scour migrates downstream with an increase in discharge. Interestingly, the comparison shows a slight increase in sediment discharge through the test reach analyzed. Supplementary to previous research, values of scour depth and location in terms of distance from the start of channel-width perturbation are provided; at the lowest discharge maximum scour occurs 4% of a wavelength upstream of the narrowest portion, and at the highest discharge maximum scour occurs at the narrowest point. Additionally, a one-dimensional HEC-RAS sediment transport model and a two- dimensional SRH flow model were compared to the analytical results. Results show that the model output of the HEC-RAS model and the SRH model adequately approximate the analytical model studied. Specifically, the results verify that maximum scour depth transitions downstream as discharge increases.