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48 CHAPTER 7 Summary and Recommendations for Future Research Summary An initial quality control screening of the equilibrium scour methods/equations reduced the number of equations from The objective of this research was to develop methods and 23 to 17. For this screening procedure, the equations were procedures for predicting time-dependent local scour at wide used to compute scour depths for a wide, but practical, range piers and at long skewed piers, suitable for consideration and of structure, flow, and sediment parameters. Those methods/ adoption by AASHTO. Most predictive methods/equations equations yielding unreasonable (negative or extremely large) for equilibrium local scour in the literature do not place limits scour depths were eliminated from further consideration. on the size of the structure and thus they may or may not apply The remaining 17 methods/equations were then analyzed using to piers of all practical widths. There is, however, one published both laboratory and field data. Plots of underprediction error equation that provides a multiplier (Johnson and Torrico 1994) versus total error for the laboratory data and underprediction for the predictive equation in HEC-18 to account for large error for field data versus total error for laboratory data along pier widths. with the error statistics calculations assisted in the ranking of the equations. The equations of Sheppard and Miller (2006) Equilibrium Scour and Melville (1997) were melded and slightly modified to provide the best-performing equation in that it yields the This research identified 23 methods/equations for predicting equilibrium local scour. The information and data search also least total error and the nearly least underprediction error of resulted in 569 laboratory and 928 field equilibrium local scour those tested. data points. A method for assessing the quality of the data The recommended equilibrium scour equation for design, was developed and applied to the equilibrium scour data set. referred to as the S/M equation, is a melding and slight modifi- This procedure reduced the laboratory and field data to 441 cation of equations that have been in use for a number of years, and 791 values, respectively. as follows: Laboratory data provide accurate input quantities (water ys V1 depth, flow velocity, sediment properties, etc.), scour depths, = 2.5f1f 2 f3 for 0.4 < 1.0 and maturity of the scour hole at the time of measurement, a* Vc but there are potential problems with scale effects. There are no scale effects with most field data; however, field data are, V1 V1p V1 -1 - in general, less accurate. Perhaps the greatest problem with ys Vc Vc Vc V1 V1p = f1 2.2 + 2.5f3 for 1 field data is the lack of knowledge regarding the maturity of a* V1p V1p - 1 -1 Vc Vc the scour hole at the time of measurement. In some cases the Vc Vc measured scour hole depth could have resulted from an earlier, more severe flow event. For these reasons laboratory data ys V1 V1p were used for evaluating the predictive methods/equations. = 2.2f1 for > a* Vc Vc With only a few exceptions the predictive equations should, however, not underpredict the measured values provided care is taken to isolate the local scour from the other types y 0.4 f1 = tanh 1 of scour. a*

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49 V 2 Coast of Florida. Eight scour evolution predictive methods/ f 2 = 1 - 1.2 ln 1 equations were obtained in the information and data search. Vc Most, but not all, of the scour evolution methods require knowledge of the equilibrium scour depth for their execution. a* The methods range in complexity from simple algebraic equa- D50 tions to more complex semi-empirical mathematical models f3 = -0.13 a * 1.2 a* that can be applied to unsteady flow conditions. The more 0.4 + 10.6 complex methods do, however, need more work, especially for D50 D50 live-bed scour conditions. The level of work required for these V1p1 = 5 Vc cases exceeds the time and resources for this project. A procedure for evaluating the predictive methods/equations using the time series data sets was developed and used to rank V1p2 = 0.6 gy 1 the methods according to their accuracy. The results were plotted as underprediction versus total error. For design V1p1 for V1p1 V1p 2 V1p = purposes it is desirable to have minimal underprediction V1p 2 for V1p 2 > V1p1 while maintaining total error as small as practical. The best- performing (least error) method was a modified form of where Melville's equation in conjunction with the S/M equilibrium a* = Effective Diameter equation. The original Melville equation was developed for a* = Projected Width * Shape Factor clear-water scour conditions. The modified equation, referred Shape Factor = 1, circular to as the M/S equation in this report, appears to work equally 4 well for the live-bed data in the database. However, all of the = 0.86 + 0.97 - , rectangular live-bed scour evolution data are for small, laboratory-scale 4 structures. Local scour at small structures, subjected to high- = skew angle in radians velocity flow, occurs very fast and is difficult to measure accurately. The predictive equations, while based on the physics of the processes, are still empirical and, thus, can be no better Flow Skew Angle than the data on which they are based. The M/S equation Only limited data exist for the effects of flow skew angle on predicts, what appear to be, very conservative scour rates for equilibrium local scour depths. Most predictive methods for large structures subjected to high-velocity flows. That is, the the effects of flow skew angle on local scour use some form of predicted scour rate is larger than expected based on experience. projected width of the pier (i.e., the horizontal dimension of This overprediction is most likely due to scale effects that are the projection of the pier onto a plane normal to the flow) in not properly accounted for in the scour evolution equations their analysis. The equation in the current HEC-18 and many for live-bed scour conditions. There is, however, no data other equilibrium scour equations multiply the scour depth (laboratory or field) in the database for these conditions with computed for zero skew angle by the ratio of projected to which to test or modify the equations. The M/S scour evaluation actual pier width to some power. The pier width is replaced by equation is given by: the projected width in the S/M equation, thus accounting for the observed effect of water depth on the scour depth's dependence y st ( t ) = K t y s on flow skew angle. Both methods give conservative predictions over the practical skew angle range from 0 to 45. The recom- Vc t 1.6 mended method for accounting for flow skew angle on equilib- K t = exp C1 ln V1 tc rium scour depths is from Sheppard and Renna (2005). a V1 y1 V t e ( days ) = C 2 - 0.4 for > 6, 1 > 0.4 Scour Evolution Rates V1 Vc a Vc Historically, scour evolution rates have received less attention 0.25 a V1 y y1 V than equilibrium scour. In spite of this, a significant number t e ( days ) = C 3 - 0.4 1 for 6, 1 > 0.4 of laboratory time history local scour records were obtained V1 Vc a a Vc from several different researchers as part of this study. Only one scour evolution field data set was obtained and it was for V t 90 ( days ) = exp -1.83 1 t e a small pile on a bridge over a tidal inlet on the Western Gulf Vc