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34 12 5.7 SHALLOW WATER EFFECT: FLUME TEST RESULTS 10 It appears that when the water depth exceeds about two Erosion Rate (mm/hr) times the pier width, the maximum scour depth is practically 8 independent of the water depth. When the water depth becomes shallower than that, there is a reduction in the max- 6 imum scour depth. This is attributed to the fact that as the depth of the scour hole increases, the water loses its eroding 4 energy faster in shallow waters than in deep waters. While extensive studies have been carried out on shallow water effects in sands, corresponding studies in clays are nonexis- 2 tent. Gudavalli's flume tests indicate that in cohesive soils the flow depth has no clear influence on the scour depth when 0 H/B1.6 where H is the water depth and B the pier diameter. 0 2 4 6 8 10 In this study, a series of pier scour tests with water depths Shear Stress (Pa) ranging from H/B = 0.2 to H/B = 2.5 were conducted. The Figure 5.7. Erosion function for Gudavalli's Porcelain cylindrical piers had diameters equal to 273 mm and 160 mm clay. and were installed in one of the 1.2 m 1.5 m 0.3 m soil tanks filled with Porcelain clay. The test parameters are presented in Table 5.3 and the 7. Take measurements of the scour depth at regular time measured curves of scour depth z(t) versus time t are plotted intervals; and in Figure 5.9 for the two different pier sizes. The flume tests 8. Empty water, record shape of scour hole, and finish were stopped after a time averaging about 5 days, and then a the test. hyperbola was fitted to the scour depth versus time curve (Briaud et al., 1999, 2001). This technique gave an initial For each test, the primary measurements were flow veloc- i, (initial slope of the hyperbola) and a maximum scour rate, z ity, water depth, scour depth, and time. Water depth and flow scour depth, Zmax, (asymptotic value). The values of the max- velocity were determined in the middle of the channel, 1.5 m imum scour depth, Zmax, and initial scour rate, z i, are shown upstream of the piers. The depth average velocity was calcu- in Table 5.3. lated from the measured vertical velocity profile and was In the case of very shallow water tests, it was observed that used as one of the major parameters in the data analysis. The noticeable surface rolling, formed due to the roughness of the flow velocity was kept constant throughout the experiment. streambed, would probably affect the scour depth, as men- For the measurements of scour depth increment, the point tioned by Ettema (1980). In addition, the velocity in this case gage was moved around the pier to find the location of max- becomes more difficult to measure and control due to the imum scour. limitation of the response distance of the ADV. 5.8 SHALLOW WATER EFFECT ON MAXIMUM PIER SCOUR DEPTH One way to present the data is to plot the relative scour depth Zmax/B versus relative flow depth H/B (Figure 5.10). Figure 5.10 indicates that in clay, much like in sand, the rela- tive scour depth, Zmax/B, increases with the relative water depth, H/B, until a limiting H/B value is reached. The shallow water correction factor, Kw, is defined as the ratio of the max- imum scour depth under shallow water flow to the maximum scour depth under a reference condition where the water depth has no noticeable influence on the maximum scour depth. In this study, the scour depth under the deepest relative water depth, H/B = 2.5, was selected as the reference. Therefore, the average value of Zmax for Tests Sh-1 and Sh-8 in Table 5.3 was called Zmax(deep) and was used to normalize the values of Zmax. Figure 5.11 shows the values of Kw = Zmax/Zmax(deep) as Figure 5.8. Placement of the clay in the soil tank. a function of H/B.

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35 TABLE 5.3 Parameters and results for shallow water cases of pier scour Test H B V Exp. Duration i z Zmax H/B No. (mm) (mm) (m/s) (h) (mm/hr) (mm) Sh-1* 683.00 273.00 0.30 2.502 ----- ---- 112.94 Sh-2 546.00 273.00 0.30 2.000 515.75 1.06 129.62 Sh-3 258.00 273.00 0.30 0.945 262.33 1.57 79.37 Sh-4 137.00 273.00 0.30 0.502 237.42 1.39 57.80 Sh-5 60.00 273.00 0.30 0.220 164.08 1.71 81.30 Sh-6 60.00 273.00 0.30 0.220 111.03 4.49 61.35 Sh-7 25.80 273.00 0.30 0.095 30.50 38.91 35.59 Sh-8 400.00 160.00 0.40 2.500 191.33 1.50 76.92 Sh-9 320.00 160.00 0.40 2.000 129.67 1.82 109.67 Sh-10 170.00 160.00 0.40 1.063 117.17 1.98 77.73 Sh-11 85.00 160.00 0.40 0.531 64.50 2.62 53.48 *: The measured data for test Sh-1 is lost due to the malfunction of computer and Zmax is saved in previous summaries. In Figure 5.11, the correction factor Kw obtained in the cur- rent study on clay is compared to the correction factors rec- 80 ommended for cohesionless soils by Melville and Coleman 70 (1999) and Johnson (1999). Johnson's correction factor depends on both pier size and velocity, so the label "Johnson 60 Scour Depth (mm) 0.273/0.3, Equ(3.6A)" in the figure represents the correction 50 factor for the condition of B = 0.273 m and V = 0.3 m/s fol- 40 Sh-2, H/B=2.000 lowing Johnson's equation. Because Johnson did not provide Sh-3, H/B=0.945 an equation for very shallow flow, a straight line is used to 30 Sh-4, H/B=0.502 connect the origin to the shallowest end of the Johnson 20 Sh-5, H/B=0.220 curves in Figure 5.11. Note also that Johnson's Kw factor is a Sh-6, H/B=0.220 correction factor for the HEC-18 equation while that equa- 10 Sh-7, H/B=0.095 tion already includes a water depth influence so a combined 0 0 100 200 300 400 500 600 Time(hr) 0.7 (Pier: B=0.273m and V=0.3m/s) 0.6 80 70 0.5 60 Scour Depth (mm) 0.4 Zmax/B 50 Sh-8, H/B=2.500 0.3 40 30 Sh-9, H/B=2.000 0.2 Zmax/B = 0.3743(H/B) 0.3661 20 Sh-10, H/B=1.063 R 2 = 0.7517 0.1 10 Sh-11, H/B=0.531 0 0.0 0 50 100 150 200 250 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Time(hr) H/B (Pier: B=0.160m and V=0.4m/s) Figure 5.10. Influence of shallow water depth on Figure 5.9. Flume test results for the shallow water cases. maximum pier scour depth.