Scour at Wide Piers and Long Skewed Piers (2011)

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48 Summary The objective of this research was to develop methods and procedures for predicting time-dependent local scour at wide piers and at long skewed piers, suitable for consideration and adoption by AASHTO. Most predictive methods/equations for equilibrium local scour in the literature do not place limits on the size of the structure and thus they may or may not apply to piers of all practical widths. There is, however, one published equation that provides a multiplier (Johnson and Torrico 1994) for the predictive equation in HEC-18 to account for large pier widths. Equilibrium Scour This research identified 23 methods/equations for predicting equilibrium local scour. The information and data search also resulted in 569 laboratory and 928 field equilibrium local scour data points. A method for assessing the quality of the data was developed and applied to the equilibrium scour data set. This procedure reduced the laboratory and field data to 441 and 791 values, respectively. Laboratory data provide accurate input quantities (water depth, flow velocity, sediment properties, etc.), scour depths, and maturity of the scour hole at the time of measurement, but there are potential problems with scale effects. There are no scale effects with most field data; however, field data are, in general, less accurate. Perhaps the greatest problem with field data is the lack of knowledge regarding the maturity of the scour hole at the time of measurement. In some cases the measured scour hole depth could have resulted from an earlier, more severe flow event. For these reasons laboratory data were used for evaluating the predictive methods/equations. 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 of scour. An initial quality control screening of the equilibrium scour methods/equations reduced the number of equations from 23 to 17. For this screening procedure, the equations were used to compute scour depths for a wide, but practical, range of structure, flow, and sediment parameters. Those methods/ equations yielding unreasonable (negative or extremely large) scour depths were eliminated from further consideration. The remaining 17 methods/equations were then analyzed using both laboratory and field data. Plots of underprediction error versus total error for the laboratory data and underprediction error for field data versus total error for laboratory data along with the error statistics calculations assisted in the ranking of the equations. The equations of Sheppard and Miller (2006) and Melville (1997) were melded and slightly modified to provide the best-performing equation in that it yields the least total error and the nearly least underprediction error of those tested. The recommended equilibrium scour equation for design, referred to as the S/M equation, is a melding and slight modifi- cation of equations that have been in use for a number of years, as follows: f y a 1 1 0 4 = ⎛ ⎝⎜ ⎞ ⎠⎟ ⎡ ⎣ ⎢⎢ ⎤ ⎦ ⎥⎥tanh * . y a f for V V V V s c p c* .= 2 2 1 1 1> y a f V V V V f V Vs c 1p c 1p * . .= − − ⎛ ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟⎟ +1 1 32 2 1 1 2 5 c c p c 1 V V V V for V − − ⎛ ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟⎟ ⎡ ⎣ ⎢⎢⎢⎢ ⎤ ⎦ ⎥⎥⎥⎥ ≤ 1 1 1 1 V V Vc p c ≤ 1 y a f f f for V V s c* . . .= ≤2 5 0 4 1 01 2 3 1 < C H A P T E R 7 Summary and Recommendations for Future Research

49 where a* = Effective Diameter a* = Projected Width * Shape Factor Shape Factor = 1, circular α = skew angle in radians Flow Skew Angle Only limited data exist for the effects of flow skew angle on equilibrium local scour depths. Most predictive methods for the effects of flow skew angle on local scour use some form of projected width of the pier (i.e., the horizontal dimension of the projection of the pier onto a plane normal to the flow) in their analysis. The equation in the current HEC-18 and many other equilibrium scour equations multiply the scour depth computed for zero skew angle by the ratio of projected to actual pier width to some power. The pier width is replaced by the projected width in the S/M equation, thus accounting for the observed effect of water depth on the scour depth’s dependence on flow skew angle. Both methods give conservative predictions over the practical skew angle range from 0° to 45°. The recom- mended method for accounting for flow skew angle on equilib- rium scour depths is from Sheppard and Renna (2005). Scour Evolution Rates Historically, scour evolution rates have received less attention than equilibrium scour. In spite of this, a significant number of laboratory time history local scour records were obtained from several different researchers as part of this study. Only one scour evolution field data set was obtained and it was for a small pile on a bridge over a tidal inlet on the Western Gulf = + − ⎛⎝⎜ ⎞⎠⎟0 86 0 97 4 4 . . ,α π rectangular V V for V V V for V V p p p p p p p 1 1 1 1 1 1 2 1 2 1 2 1 1 = ≥⎧ ⎨⎪ ⎩⎪ > V gyp21 10 6= . V Vp c1 1 5= f a D a D a D 3 50 50 1 2 50 0 4 10 6 = ⎛⎝⎜ ⎞⎠⎟ ⎛⎝⎜ ⎞⎠⎟ + ⎛⎝ * . * . * . ⎜ ⎞⎠⎟ ⎡ ⎣ ⎢⎢⎢⎢ ⎤ ⎦ ⎥⎥⎥⎥ −0 13. f V Vc 2 1 2 1 1 2= − ⎛ ⎝⎜ ⎞ ⎠⎟ ⎡ ⎣⎢ ⎤ ⎦⎥ ⎧⎨⎪⎩⎪ ⎫⎬⎪⎭⎪ . ln Coast of Florida. Eight scour evolution predictive methods/ equations were obtained in the information and data search. Most, but not all, of the scour evolution methods require knowledge of the equilibrium scour depth for their execution. The methods range in complexity from simple algebraic equa- tions to more complex semi-empirical mathematical models that can be applied to unsteady flow conditions. The more complex methods do, however, need more work, especially for live-bed scour conditions. The level of work required for these 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 the methods according to their accuracy. The results were plotted as underprediction versus total error. For design purposes it is desirable to have minimal underprediction while maintaining total error as small as practical. The best- performing (least error) method was a modified form of Melville’s equation in conjunction with the S/M equilibrium equation. The original Melville equation was developed for clear-water scour conditions. The modified equation, referred to as the M/S equation in this report, appears to work equally well for the live-bed data in the database. However, all of the live-bed scour evolution data are for small, laboratory-scale structures. Local scour at small structures, subjected to high- 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 than the data on which they are based. The M/S equation predicts, what appear to be, very conservative scour rates for large structures subjected to high-velocity flows. That is, the predicted scour rate is larger than expected based on experience. This overprediction is most likely due to scale effects that are not properly accounted for in the scour evolution equations for live-bed scour conditions. There is, however, no data (laboratory or field) in the database for these conditions with which to test or modify the equations. The M/S scour evaluation equation is given by: t days V V t90 c e( ) = −⎛⎝⎜ ⎞ ⎠⎟exp 1 83 1. t days C a V V V y a foe c ( ) = −⎛⎝⎜ ⎞ ⎠⎟ ⎛⎝⎜ ⎞⎠⎟3 1 1 1 0 25 0 4. . r y a V Vc 1 16 0 4≤ , .> t days C a V V V for y a V V e c c ( ) = −⎛⎝⎜ ⎞ ⎠⎟2 1 1 1 10 4 6 0. ,> > .4 K C V V t t t c c = ⎛ ⎝⎜ ⎞ ⎠⎟ ⎧⎨⎪⎩⎪ ⎫⎬⎪⎭⎪ exp ln1 1 1 6. y t K yst t s( ) =

50 where ys = S/M equilibrium scour equation C1 = −0.04 C2 = 200 C3 = 127.8 te = reference time t90 = time to reach 90% of equilibrium scour depth The M/S equation is the best performing of the equations/ methods analyzed. The accuracy and range of structure pier widths for the clear-water scour data far exceeds that for the live-bed scour data. For this reason there is greater confidence in the prediction of scour evolution rates in the clear-water scour range. There are many situations where the pier is large and the design flow velocity is relatively small and/or of short duration. Scour evolution rates are important for these cases because equilibrium scour depths are not likely to be achieved during the design event. Substantial bridge foundation cost savings could be realized if scour evolution rate were considered when predicting design scour depths. However, due to the lack of data for even moderate size structures in the live-bed scour range even the best-performing scour evolution equation (M/S equation) should not be used for design at this time. It can be used for estimating the level of conservativeness of design scour depths based on equilibrium scour values. More research, including controlled, live-bed tests with larger structures, is required before scour evolution rate predictions can be used in the development of design scour depths. Recommendations for Future Research The recommended equations for predicting equilibrium scour depths and scour evolution rate are empirical, although they are based on the physics of the sediment scour processes. As such, they can be no better than the data on which they are based. Because there are gaps in both the laboratory and field data, there are practical combinations of structure, sediment, and flow conditions where the equations have not been tested. Several experiments are proposed to address this problem. Detail regarding the recommended research is given in Appendix B (available on the NCHRP Report 682 summary web page: www.trb.org/Main/Blurbs/164161.aspx). A list of these experiments is presented below, in ranked order: 1. Laboratory live-bed equilibrium scour and scour evolution rate experiments with uniform, fine sediment, and larger- model pile structures. The data for these conditions are extremely limited and yet many, if not most, bridge piers in the United States fall into this category (i.e., relatively large structures and high-velocity design flows). 2. Experiments to obtain equilibrium scour depths, and scour evolution rates, at rectangular piers, aligned with and skewed to the flow, under controlled laboratory con- ditions. Reported scour data for piers skewed to the flow is extremely limited. These tests could be performed with moderate size structures. 3. Similar experiments to those described in the first item above, but with much larger piers. These tests will have to be conducted in a large stream where the flows are sufficiently high and controlled and the sediment cohesionless. 4. Experiments to investigate equilibrium scour depths and scour evolution rates at complex and multiple piers. The vast majority of local scour experiments have been performed with circular or square cylinders while most prototype piers are more complex in shape. While methods exist (Richardson and Davis 2001, Sheppard and Renna 2005) for estimating local scour depths at piers with complex shapes, more laboratory data are needed to test the accuracy of these methods. 5. Experiments to investigate influences of sediment gradation, σg, on equilibrium scour depths. Armoring of the bed in the vicinity of a structure due to large sediment size distributions (large σg) can have a substantial impact on equilibrium scour depths. More data are needed before this effect can be predicted to sufficient accuracy for use in design. 6. Experiments to investigate local clear-water scour at low values of V1/Vc (V1/Vc < 0.7). Some reported laboratory and field scour depth data for low values of V1/Vc are larger than would be expected. This investigation will improve scour depths for typical daily flows (which are sometimes used for ship impact analyses). 7. Experiments associated with testing the theory regarding pressure gradient–induced local scour (Sheppard 2004). There are several explanations for why equilibrium scour depends on a/D50. Understanding the underlying mecha- nisms responsible for this dependence is important for the extrapolation of predictive equations to conditions where laboratory data cannot be easily obtained due to flume size limitations, etc. The experiments described above are self-contained and can be conducted in parallel. Some could be conducted at more than one location while others, such as the one with large structures in an outside open channel, will require special channels and there will be limited location options.