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43 TABLE 5.8 Transition of the location of maximum scour depth Attack Angle () Location of the maximum scour depth 2.5cm 0 (1), (4) 5.5cm 0<<45 (1) (4) (4) 45 (1), (3) 6cm 7cm(1) 45<<90 (3) 90 (1), (2), (3), (4) (1) 14cm 8cm 10cm the location of the maximum scour depth will either happen at Corner 1 or Corner 3. When the attack angle increases, the (3) 6cm location of the maximum scour depth gradually moves from (3) 3cm (2) Corner 1 to Corner 3, and this transition is documented in (2) Table 5.8. It also was noted that the scour hole in the tested cohesive soil (Figure 5.27) was much smaller than the scour Figure 5.27. Shape of scour around a skewed pier in a hole in sands sketched by Raudkivi (1991). cohesive soil (left: attack angle = 15 degrees, right: attack angle = 30 degrees). 5.21 MAXIMUM SCOUR DEPTH EQUATION FOR COMPLEX PIER SCOUR In the previous sections, individual effects on the maximum pier scour depth were studied by flume testing. A series of (1) (1) 15 15 (1) 45 (1) 45 figures and equations are given to quantify the corresponding correction factors. However, bridge piers are likely to exhibit (3) (3) (3) (3) a combination of these effects and recommendations are needed to combine these effects in the calculations. It is rec- ommended that the correction factors be multiplied in order to 0.5m 0.5m 0.5m 0.5m 0.5m 0.5m represent the combined effect: Figure 5.28. Configuration of the flume tests to verify the ( BvV ) 0.635 superposition rule. Zmax ( mm ) = 0.18 K w K sp K sh (5.7) where Zmax is the maximum depth of scour (mm); V is depth vidual effects described in previous sections were expected average velocity at the location of the pier if the pier or to happen simultaneously. The main parameters and results bridge was not there (m/s); B is the projection width of are summarized in Table 5.9, and the time history of the the pier (m); v is the kinematic viscosity of water (10E-6 scour development is plotted in Figure 5.29. The final (m2/s) at 20C); Kw is the correction factor for shallow water maximum scour depth was obtained by using the hyper- effect (Equation 5.2), Ksp for pier spacing effect (Equation bola model. 5.3), and Ksh for pier shape effect (1.1 for rectangular piers); The maximum scour depths for the two tests were calcu- and B is the pier projection width (Equation 5.4 for rectan- lated according to Equation 5.7. The calculations are detailed gular pier). This is a common approach that implies that the in Table 5.10, and the measured results also are listed at the effects are independent and has been used in many instances bottom of that table which shows that the difference between before (HEC-18, Melville [1997]). the predictions and measurements is remarkably small (less Two complex pier flume tests were conducted with the than 5%). This tends to indicate that the chosen superposition configuration shown in Figure 5.28 where all of the indi- law works well for complex pier scour predictions. TABLE 5.9 Parameters and results for the complex pier flume tests Test H V L B C g Time Zmax No. (mm) (mm/s) (mm) (mm) (mm) () (h) (mm) Cp-1 375 330 244 61 500 15 115.32 175.4 Cp-2 375 330 244 61 500 45 150.67 285.7

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44 200 160 Scour Depth (mm) 120 80 CP-1 CP-2 40 0 0 50 100 150 200 Time (Hr) Figure 5.29. Scour development curves for the complex pier flume tests. TABLE 5.10 Comparison of calculated and measured maximum pier scour depths PARAMETERS Cp - 1 Cp - 2 CALCULATION NOTE Primary Inputs B (mm) 61 61 Pier width L (mm) 244 244 Pier length H (mm) 375 375 Water depth () 15 45 Attack angle V (mm/s) 330 330 Mean approaching velocity C (mm) 500 500 Center to center pier spacing Attack Angle Effect B' (mm) 122.07 215.67 Projection width following Eq. (5.4) Basic Scour Depth Z1 (mm) 151.19 217.01 SRICOS: simple pier Eq. (5.6) Water Depth H/B' 3.07 1.74 Kw 1.00 1.00 Shallow water effect, Eq. (5.1) Contraction Effect C/B' 4.10 2.32 Ksp 1.0 1.233 Interpolated from Fig. 5.7 Pier Shape Effect Ksh 1.1 1.1 Calculated from Fig. 5.11 Composite Effect K 1.16 1.36 K= KwKspKsh Final Scour Depth Zcal(mm) 174.63 294.33 Zcal=KZ1 Comparison Ztest (mm) 175.44 285.71 (Zcal-Ztest)/Ztest - 0.46 3.02 (%)