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9 Table 2. Equilibrium local scour data sources A significant data gap exists in the available laboratory data and quantity. for a/D50 > 1,800. At present the largest laboratory value for a/D50 is 4,159. The histogram in the lower right corner of Number of Data Points Data Source Clear Water Live Bed Figure 4 shows the distribution of a/D50 in the field data. This Field Data illustrates the range of this parameter for prototype piers. Zhuravlyov (1978) 40 147 Because the horizontal axis in this plot is logarithmic, the "4" Froehlich (1988) 17 60 corresponds to a/D50 = 104. A gap in available laboratory data Gao et al. (1993) 119 133 also exists for a/y1 > 10. Mueller and Wagner (2005) 171 241 Figure 5 shows the distribution of normalized scour depth, Total field 347 581 Laboratory Data ys /a, and V1/Vc for the field data set. The largest value of ys /a is Chabert and Engeldinger (1956) 87 6 approximately 1.8. Ettema (1976) 19 0 Shen et al. (1969) 2 21 Jain and Fischer (1979) 2 32 Assessment of Data Quality Ettema (1980) 90 7 Chiew (1984) 11 90 The quality of the data cannot be assessed by using the Chee (1982) 1 36 descriptions of the experimental conditions mainly because Yanmaz and Altinbilek (1991) 14 19 the information in the publications is insufficiently detailed. Graf (1995) 3 0 All of the Yanmaz and Altinbilek (1991) laboratory data were Dey et al. (1995) 18 0 Melville (1997) 17 0 discarded due to the short durations of the tests (from 4 to 6 h), Melville and Chiew (1999) 27 0 which were significantly less than that required for the develop- Ettema et al. (2006) 6 0 ment of equilibrium scour depths. Coleman (unpublished, personal 6 0 The method developed and used to identify and eliminate communication) Jones (unpublished, personal outliers in the data sets included the following steps: 15 2 communication) Sheppard et al. (2004) 12 2 1. Place the data in a three-dimensional Euclidean space with Sheppard and Miller (2006) 4 20 coordinates log(a/D50), V1/Vc, and y1/a. Total laboratory 334 235 2. Compute the variance of the data in each direction. Note: Many of the photographs, figures, and tables in this report have been converted from color to grayscale for printing. The electronic version of the report (posted on the TRB website at http://www.trb.org/Main/Blurbs/164161.aspx) retains the color versions. Figure 1. Dimensional plots of laboratory local equilibrium scour data.
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10 Note: The dashed lines indicate the wide-pier boundary. Figure 2. Plots of normalized laboratory local scour data. Note: The dashed lines indicate the wide-pier boundary. Figure 3. Dimensional plots of field local scour data.
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11 Note: The dashed lines indicate the wide-pier boundary. Figure 4. Plots of normalized field local scour data. 3. Normalize the data values by the variances [i.e., the value 7. Determine the variance in the distances from the point in of log(a/D50) for a data point was divided by the variance question to its neighboring four points (distance variance). of the data in the log(a/D50) direction, etc.]. 8. Compute the ratio of scour variance to distance variance. 4. Compute the three-dimensional distance between data This ratio is referred to here as the "proximity parameter." points. 9. Plot the proximity parameter versus experiment number. 5. For each data point, determine its four closest neighbors 10. Establish a cutoff criterion. that are not from the same experimental data set. 11. Identify the data that exceed the cutoff criteria. These 6. Determine the variance in measured scour depths for the data are considered outliers and eliminated from the five data points (scour variance). data sets. 2 1.5 * ys/a 1 0.5 0 0 1 2 3 4 5 6 7 8 V1/Vc Figure 5. Normalized scour versus normalized velocity for field data.
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12 4 3.5 3 Proximity Parameter 2.5 2 1.5 1 0.5 0 0 100 200 300 400 500 600 Experiment Number Figure 6. Proximity parameter for all laboratory data. The laboratory data were analyzed following the above depths were equilibrium values for the specified flow, sediment, procedure and the results presented in Figure 6. Many of the and structure conditions. In some cases, where scour depths data points with a proximity parameter value greater than 2.0 were measured at the same pier for different flow events, were from one source: Chabert and Engeldinger (1956). These it appeared that the scour hole had not recovered from a pre- data were removed from the data set, the process repeated, vious, more severe, event at the time of the measurement. For and the proximity parameter for the other points recalculated. this reason, field scour depth measurements can be less or The results shown in Figure 7 indicate that removing these greater than the equilibrium depth for the conditions at the data changed the values of the proximity parameter to below time of the measurement. 2.0 for most of the remaining data. A cutoff value of 2.0 was The Zhuravlyov (1978) report included both laboratory selected, which resulted in the removal of two additional and field data from several sources. Data from one field site data points as shown in Figure 7. Most of the outliers had (denoted as the Amu Darya River data) appeared to have V1/Vc values less than 0.8 and very large equilibrium scour unusually large scour values for the reported structure, sedi- depths. ment, and flow conditions. A comparison of these data with This methodology could not be used to determine outliers data from Froehlich (1988) and Mueller and Wagner (2005) in the field data because it was not known if the measured scour with similar values of a/D50 clearly showed an inconsistency 2.5 All Discarded 2 Proximity Parameter 1.5 1 0.5 0 0 100 200 300 400 500 600 Experiment Number Figure 7. Proximity parameter for laboratory experiments [excluding data reported by Chabert and Engeldinger (1956)].
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13 2 Mueller Zhuravlyov Froehlich 1.5 ys/a 1 0.5 0 4.14 4.15 4.16 4.17 4.18 4.19 10 10 10 10 10 10 a/D50 Figure 8. Normalized scour depth versus a/D50. in the measured scour depth values. Data points from the of scour (i.e., degradation and contraction) by making meas- three sources are shown in Figures 8 and 9. Figure 8 shows the urements away from as well as at the piers. There is only one similarity in their a/D50 values. Figure 8 shows that the Mueller Froehlich data point in the range of variables of the Amu and Wagner data and Froehlich data have larger values of y1/a Darya River data and it is in agreement with the Mueller and than that from the Amu Darya River site and therefore should Wagner data. have greater scour depths. The values of V1/Vc were very large The dates and methods used to obtain the data in the for all of these data so flow duration should not have been a Zhuravlyov report (including the Amu Darya River data) are problem. That is, all of the scour depths should have been near not given. However, all of the data in the report were obtained equilibrium values. However, as can be seen in Figure 10, the prior to 1978 (most likely in the late 1960s and early 1970s). scour depth measurements from the Amu Darya River site are There is also no information available about the review process much larger. It is very difficult to make accurate measurements for the Zhuravlyov report. of flow speed and direction and scour depths during a high- Of the conflicting data sets, the Mueller and Wagner (2005) velocity flow event, even with today's sophisticated instrumen- and Froehlich (1988) data were considered to be the more tation. The Mueller and Wagner data were obtained during accurate and credible due to the information provided in their 1965 and 1997 (with 69% being obtained after 1988) using reports regarding instrumentation and methods used. For this state-of-the-art instrumentation and methodology. They also reason the Amu Darya River data were eliminated from the made attempts to distinguish between local and other types field data set. 2 Mueller Zhuravlyov Froehlich 1.5 ys/a 1 0.5 0 0 0.5 1 1.5 2 2.5 3 3.5 4 y1/a Figure 9. Normalized scour depth versus y1 /a.