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40 consistently have larger initial scour rates than the cylindri- 80 cal pier. The maximum value occurs for the square pier and 70 the difference in rate decreases with the aspect ratio. Dietz (1972) found that the correction factor Ksh decreased from 1.5 60 Scour Depth (mm) to 1.1 when the L/B ratio increased from 1:1 to 5. 50 40 5.16 PIER SHAPE EFFECT ON PIER HOLE SHAPES 30 Circular Square 20 12 The shape of the scour holes in Tests Sh-2, Sh-4, and Sh-5 4 are roughly reproduced in Figure 5.21. In that figure, the 10 shaded areas indicate the contours of the hole and the darker 0 areas represent the deeper scour zones. The relative size of 0 50 100 150 200 the scour hole produced by the square pier was observed to be Time(hr) much larger than in the other cases. Also, in the case of the square pier, the scour hole surrounds the entire pier. For piers Figure 5.22. Scour curves for piers of different shapes. with aspect ratios L/B greater than 4, the scour hole forms around the front face and the scour hole and scour behind the of tests that need to be performed to find the general correc- pier is negligible. Figure 5.22 summarizes these observations. tion factor. Two perpendicular directions were selected to represent the whole matrix. In the transverse direction, the 5.17 ATTACK ANGLE EFFECT: rectangular pier is kept at L/B = 4 and is changed from FLUME TEST RESULTS 0 degrees to 90 degrees; in the longitudinal direction, is kept constant at 45 degrees and the aspect ratio of the pier changes. The attack angle is the angle between the direction of the During the experiments, the scour depths around the four cor- bridge pier and the direction of the flow. The attack angle ners of the rectangular pier were measured to find the maxi- effect for pier scour is actually a composite effect and several mum scour depth. The scour hole shapes for all of the cases influencing factors are involved. For a given rectangular pier, also were recorded. both the pier shape confronted to the flow and the pier projec- Parameters and major results for the flume tests for the tion width will change with the angle of attack. In addition, due attack angle effect are summarized in Table 5.6. The scour to the change of pier projection width with the attack angle, the depth versus time curves are plotted in Figure 5.23. The max- water depth effect and pier spacing effect will be influenced. imum scour depth and initial scour rate were obtained in the To obtain the "pure" attack angle effect, a filtration process is same way as previously, by using the hyperbola model. necessary to eliminate the additional influences. When the attack angle effect is examined through rectan- 5.18 ATTACK ANGLE EFFECT ON MAXIMUM gular piers, there are two influencing parameters for the pier: SCOUR DEPTH one is the attack angle , the other is the aspect ratio L/B. These two independent parameters form a parameter matrix The correction factor Ka, used to account for the attack angle effect on maximum pier scour depth, is calculated as the ratio of the maximum scour depth for a given pier and a 10cm 16cm given attack angle over the maximum scour depth for the 6cm same pier and an attack angle equal to zero (reference case). r=3cm 5cm For example, the reference case of Test At-2 is Sp-3. If the 3cm reference case were not available, such as for Tests At-7 and 7cm 7cm 8cm 11cm TABLE 5.6 Parameters and results for the attack angle effect 13cm Time Test H B V i z Zmax L/B Lasting No. (mm) (mm) () (m/s) (h) (mm/hr) (mm) At-1 375.00 61.00 15 0.33 4:1 186.00 1.49 103.09 At-2 375.00 61.00 30 0.33 4:1 211.08 2.37 117.65 At-3 375.00 61.00 45 0.33 4:1 115.17 2.07 151.50 10cm At-4 375.00 61.00 60 0.33 4:1 117.25 2.02 196.08 Sh-2: 61mmx 61 mm Sh-4: 61mmx 488mm Sh-5: 61mmx 732mm At-5 375.00 61.00 90 0.33 4:1 117.08 1.88 208.77 At-6 375.00 61.00 45 0.33 1:1 112.67 1.88 147.06 At-7 375.00 61.00 45 0.33 2:1 115.08 2.79 161.29 Figure 5.21. Shape of the scour hole for different At-8 375.00 61.00 45 0.33 6:1 115.08 2.28 185.19 aspect ratios.

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41 120 120 100 Scour Depth (mm) Scour Depth (mm) 100 80 80 a=0 60 60 a=15 L/B=1 a=30 40 L/B=2 40 a=45 L/B=4 20 a=60 20 L/B=6 a=90 0 0 0 50 100 150 200 250 0 50 100 150 Time (hr) Time (hr) (A: Transverse Direction, L/B=4) (B: Vertical Direction, a=45) Figure 5.23. Scour depth versus time curves for attack angle tests. At-8, interpolation between existing reference cases would jection width is equivalent to the pier width, then the correc- be used to calculate the maximum scour depth of the required tion factor Ka can be calculated as reference case. The pier projection width, B, as shown in Figure 5.24, is a widely accepted concept to evaluate the Zmax ( ) L n effect of the attack angle: Ka = = sin + cos (5.5) Zmax (0) B B = L sin + B cos = B L The value of n generally varies from 0.6 to 0.9 and is equal B sin + cos (5.4) to 0.635 in the SRICOS Method for scour depth prediction in cohesive soils. Common scour depth equations for 0-degree attack angle In Figure 5.25, the correction factor obtained in the flume are of the form: Zmax = f Bn, where n is a constant. If the pro- tests is shown together with other solutions using the projec- B' B cos L sin (4) (1) (3) L (2) B A : Pier Projection W idth B : Flow Pattern and C orner N um ber Figure 5.24. Skewed pier definitions. 3.5 7.0 Mostafa, n=0.8 3.0 6.0 Laursen, n=0.68 Richardson, n=0.65 5.0 SRICOS, n=0.635 2.5 Ka' Ka Ka 4.0 Ka Mostafa, n=0.8 2.0 Laursen, n=0.68 3.0 Richardson, n=0.65 1.5 SRICOS, n=0.635 2.0 Ka' Ka 1.0 1.0 0 30 60 90 0 4 8 12 L/B Attack Angle (Degree) (B: Vertical Direction, Attack Angle =45) (A: Transverse Direction, L/B=4) Figure 5.25. Attack angle effect on maximum scour depth.