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Pier and Contraction Scour in Cohesive Soils (2004)

Chapter: Chapter 5 - The SRICOS-EFA Method for Maximum Scour Depth at Complex Piers

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Suggested Citation:"Chapter 5 - The SRICOS-EFA Method for Maximum Scour Depth at Complex Piers." National Academies of Sciences, Engineering, and Medicine. 2004. Pier and Contraction Scour in Cohesive Soils. Washington, DC: The National Academies Press. doi: 10.17226/13774.
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Suggested Citation:"Chapter 5 - The SRICOS-EFA Method for Maximum Scour Depth at Complex Piers." National Academies of Sciences, Engineering, and Medicine. 2004. Pier and Contraction Scour in Cohesive Soils. Washington, DC: The National Academies Press. doi: 10.17226/13774.
×
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Suggested Citation:"Chapter 5 - The SRICOS-EFA Method for Maximum Scour Depth at Complex Piers." National Academies of Sciences, Engineering, and Medicine. 2004. Pier and Contraction Scour in Cohesive Soils. Washington, DC: The National Academies Press. doi: 10.17226/13774.
×
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Suggested Citation:"Chapter 5 - The SRICOS-EFA Method for Maximum Scour Depth at Complex Piers." National Academies of Sciences, Engineering, and Medicine. 2004. Pier and Contraction Scour in Cohesive Soils. Washington, DC: The National Academies Press. doi: 10.17226/13774.
×
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Suggested Citation:"Chapter 5 - The SRICOS-EFA Method for Maximum Scour Depth at Complex Piers." National Academies of Sciences, Engineering, and Medicine. 2004. Pier and Contraction Scour in Cohesive Soils. Washington, DC: The National Academies Press. doi: 10.17226/13774.
×
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Suggested Citation:"Chapter 5 - The SRICOS-EFA Method for Maximum Scour Depth at Complex Piers." National Academies of Sciences, Engineering, and Medicine. 2004. Pier and Contraction Scour in Cohesive Soils. Washington, DC: The National Academies Press. doi: 10.17226/13774.
×
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Suggested Citation:"Chapter 5 - The SRICOS-EFA Method for Maximum Scour Depth at Complex Piers." National Academies of Sciences, Engineering, and Medicine. 2004. Pier and Contraction Scour in Cohesive Soils. Washington, DC: The National Academies Press. doi: 10.17226/13774.
×
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Suggested Citation:"Chapter 5 - The SRICOS-EFA Method for Maximum Scour Depth at Complex Piers." National Academies of Sciences, Engineering, and Medicine. 2004. Pier and Contraction Scour in Cohesive Soils. Washington, DC: The National Academies Press. doi: 10.17226/13774.
×
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Suggested Citation:"Chapter 5 - The SRICOS-EFA Method for Maximum Scour Depth at Complex Piers." National Academies of Sciences, Engineering, and Medicine. 2004. Pier and Contraction Scour in Cohesive Soils. Washington, DC: The National Academies Press. doi: 10.17226/13774.
×
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Suggested Citation:"Chapter 5 - The SRICOS-EFA Method for Maximum Scour Depth at Complex Piers." National Academies of Sciences, Engineering, and Medicine. 2004. Pier and Contraction Scour in Cohesive Soils. Washington, DC: The National Academies Press. doi: 10.17226/13774.
×
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Suggested Citation:"Chapter 5 - The SRICOS-EFA Method for Maximum Scour Depth at Complex Piers." National Academies of Sciences, Engineering, and Medicine. 2004. Pier and Contraction Scour in Cohesive Soils. Washington, DC: The National Academies Press. doi: 10.17226/13774.
×
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Suggested Citation:"Chapter 5 - The SRICOS-EFA Method for Maximum Scour Depth at Complex Piers." National Academies of Sciences, Engineering, and Medicine. 2004. Pier and Contraction Scour in Cohesive Soils. Washington, DC: The National Academies Press. doi: 10.17226/13774.
×
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Suggested Citation:"Chapter 5 - The SRICOS-EFA Method for Maximum Scour Depth at Complex Piers." National Academies of Sciences, Engineering, and Medicine. 2004. Pier and Contraction Scour in Cohesive Soils. Washington, DC: The National Academies Press. doi: 10.17226/13774.
×
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Suggested Citation:"Chapter 5 - The SRICOS-EFA Method for Maximum Scour Depth at Complex Piers." National Academies of Sciences, Engineering, and Medicine. 2004. Pier and Contraction Scour in Cohesive Soils. Washington, DC: The National Academies Press. doi: 10.17226/13774.
×
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Suggested Citation:"Chapter 5 - The SRICOS-EFA Method for Maximum Scour Depth at Complex Piers." National Academies of Sciences, Engineering, and Medicine. 2004. Pier and Contraction Scour in Cohesive Soils. Washington, DC: The National Academies Press. doi: 10.17226/13774.
×
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30 CHAPTER 5 THE SRICOS-EFA METHOD FOR MAXIMUM SCOUR DEPTH AT COMPLEX PIERS 5.1 EXISTING KNOWLEDGE An extensive review of the literature on the topic of pier scour in cohesive soils led to very few publications. Studies related to the maximum scour depth included those of Hosny (1995), Ivarson (1998), and Molinas et al. (1999). Hosny ran a large number of flume tests on prepared samples of clay and sand mixtures. He recommended multiplying factors to include in the HEC-18 equation for the maximum scour depth in cohesionless soils. These factors are based on sim- ple soil properties and lead to maximum scour depths smaller than the cohesionless soil values by 10% to 40%. Ivarson (1998) developed a modification factor K4 for the HEC-18 equation for maximum scour depth in cohesionless soils. The K4 factor is a multiplier in the HEC-18 equation and makes use of the undrained shear strength of the cohesive soil. Molinas et al. (1999) presented a modification of the Hosny (1995) factors. Studies related to numerical simula- tions were more numerous. 5.2 GENERAL Chapter 4 described the SRICOS method for cylindrical piers in deep water. This chapter deals with piers that can be rectangular, square, or cylindrical; are attacked by the flow at a non-zero angle between the flow direction and the main axis of the pier; and are in shallow water. The influence of pier spacing also is discussed. Figure 5.1 shows the definition of the parameters involved with these influencing factors. The approach consisted of using the solution for the case of the cylindrical pier in deep water: and developing correction factors to include the effect of the various situations deviating from that case. Since the case of the cylindrical pier in deep water was developed on the basis of two fundamental equations (i.e., maximum scour depth and initial maximum shear stress), two sets of correction fac- tors had to be developed. The correction factors for the max- imum scour depth were developed on the basis of flume tests; the correction factors for the initial maximum shear stress were developed on the basis of numerical simulations. Z Rmax .. ( . )mm e( ) = 0 18 5 10 635 5.3 FLUMES AND SCOUR MODELS The in-floor concrete flume, which is 1.5 m wide, 30.48 m long, and 3.48 m deep, was used to conduct the complex pier scour tests. The wooden flume, which is 0.45 m wide, 36 m long, and 1.22 m deep, was used for the contraction scour tests. These two flumes form a closed system (Figure 5.2) in which the water is recirculated without any fresh water being added. False bottoms were designed to make sure that the start and end transitions would not affect the velocity distribution in the test area. For the 1.5-m-wide flume, the slopes of the ramps at the two ends of the false bottom are 1:3 (vertical to horizontal) to guarantee a smooth transition. The distance between the two soil tanks is 7.6 m to make sure there is no interaction between them. Trial tests were conducted before starting the scour tests, and the velocity distributions were measured along the center- line of the channel to confirm the validity of the design. In the 1.5-m-wide flume, the soil tank is 0.6 m deep and 1.5 m long for the front tank and 0.6 m deep and 1.2 m long for the rear tank. The false bottom is built with plastic plates and supported by aluminum frames. The false bottom in the 0.45-m-wide flume was designed for the contraction scour tests. A smooth transition between the uncontracted and contracted channels was constructed. The soil tank is 2.0 m long and 0.3 m deep to provide enough space for both the long contraction flow and the contraction scour hole. This false bottom is made of plywood. Two types of pier models were used in the complex pier scour tests as shown in Figure 5.3. The cylindrical piers were cut from PVC pipes with three different diameters: 273 mm, 160 mm, and 61 mm. The rectangular piers were made of plywood with the same width (61 mm) and different lengths: 61 mm, 122 mm, 244 mm, and so on. For piers with projec- tion Width B′ larger than 160 mm, strutted frames were needed to fix the piers so they would neither sway nor be flushed away during scouring. The abutment models were all made of plywood and are shown in Figure 5.4, which also shows the transition inlets for the contraction scour tests. 5.4 MEASURING EQUIPMENT The Acoustic Doppler Velocimeter (ADV), as shown in Figure 5.5, uses acoustic techniques to measure the velocity in a remotely sensed volume so that the measured flow is

31 B Flow V L H B Flow V B S (b) Pier Spacing Effect (c) Pier Shape Effect (a) Water Depth Effect L B B ’ Flow V g (d) Attack Angle Effect Figure 5.1. Parameter definition for complex pier scour. (1) Tail Gate (4) Soil Tank (7) Computer (2) False Bottom (5) Carriage (8) Water Fall (13) Piers (14) Mini Pump (3) Contraction Abutments (6) ADV and Point Gage (9) Switch (10) Pumps (11) Measuring Cage (12) Screen Wire (6) ((3)) (3) (2) (4) (7) (14) (8) (10) (11) (12) (13) (13) (4) 0.45m Flume 1.50m Flume (3) (2) (5) (4) (9) Figure 5.2. Diagram of the flume system (not to scale).

32 the water surface elevation, the water depth, and the change in scour depth. The point gage is designed based on the fact that air, water, and soil have different electrical conductivity. The point gage system forms a closed circuit with one node in the soil or water and the other one in the air. Once the point gage, which contains a needle attached to a vertical ruler, touches the interface between water and air or water and soil, there is a sudden conductivity change that can be read easily on a voltmeter. When the water is dirty, the maximum scour location can be searched point by point using the point gage. As shown in Figure 5.2, the point gage and ADV are installed in a hanging measurement cage riding on a carriage that moves along the longitudinal direction of the flume. In the flume tests, it was found that the presence of piers or contrac- tion abutments had almost no influence on the flow at a dis- tance of one channel width upstream of the obstacle. There- fore, the velocity and water depth were determined at this location for each test. In addition, a digital camera was used to record important phenomena during the tests. 5.5 SOILS AND SOIL BED PREPARATION A Porcelain clay was used as the primary soil; for compar- ison purposes, sands also were used in several tests. The pre- dominant mineral of this commercially available Porcelain clay is Kaolinite. Geotechnical tests were conducted accord- ing to ASTM standards. The geotechnical properties of the Porcelain clay determined at two different times are summa- rized in Table 5.1. Vane shear tests were conducted at three different locations around the future scour hole after the soil Diameter =273mm 61x61 61x122 61x244 61x366 61x488 61x732 Diameter =160mm Diameter =61mm (a, b, c-Contraction Width; a, d, e, f-transition angle, a, g, h, i-contraction length) (a) (f) (g) (h) (i) (b) (c) (d) (e) U V Flow Particle Response Distance 50mm undisturbed by the presence of the probe. An ADV with a velocity range of ±2.5 m/s and a resolution of 0.1 mm/s was used to measure the velocity during the tests. The primary use of the ADV was to measure the vertical velocity profile along the water depth around piers and contractions. The upstream mean depth velocity was the basic velocity recorded for the pier tests. For the contraction tests, the ADV was used to mea- sure the velocity distribution along the centerline of the con- tracted channel at certain water depths before the scour started and after the scour stopped. In some tests, more exten- sive velocity measurements were conducted at specific loca- tions. These included the corners of contraction abutments and rectangular piers. A point gage with a new design was used in this study. Without interrupting the experiments, it was used to measure Figure 5.3. Pier models used in the complex pier scour tests. Figure 5.4. Abutment models for contraction scour tests. Figure 5.5. Diagram of the ADV.

bed was prepared, but before the experiment started; the aver- age value is shown in the Table. The erosion properties of the Porcelain were tested by Cao (2001) in the EFA. Two sam- ples were tested separately using tap water. The erosion rate versus shear stress curve is shown in Figure 5.6. Gudavalli (1997) used three types of clays for his experi- ments: Porcelain, Armstone, and Bentonite. The properties of these clays are presented here because Gudavalli’s tests were the basis of the original SRICOS Method and because these tests are used in this study as well. The geotechnical properties of these soils were measured according to ASTM standards and are given in Table 5.2. The erosion properties of the Porcelain clay were measured in the 0.45-m-wide flume. The bed shear stress was varied from 0.118 Pa to 7.92 Pa by changing the flow velocity. The water depth was maintained constant during the experiments. Each test was conducted for a few hours. The bed shear stress was computed by Prandtl’s equation for the velocity versus depth profile obtained by ADV measurements very close to the soil bed. These exper- iments amounted to running a large-scale EFA test. The rela- tionship between erosion rate and shear stress is shown in Figure 5.7. The Porcelain clay was delivered in blocks of 250 mm × 180 mm × 180 mm. Each block was in a sealed bag. The clay was installed block by block in the soil tank, as shown in Fig- ure 5.8. After the completion of one layer, kneading with a 20-lb concrete block was used to minimize the voids and holes between blocks. The next layer was placed on top of the first one, and so on. Once the soil tank was full, the soil surface was leveled by using a straight-edged spatula. After each test, the excess water was pumped out, a zone of clay was removed around the scour hole until undisturbed clay was reached, and fresh Porcelain clay was placed in the exca- 33 vated portion. It was critical to remove all the soft film and any excess water on the old soil surface; otherwise, the old soil and new soil would not stick tightly together and the new soil could be flushed away in lumps. This requirement was particularly important for the contraction scour tests. 5.6 FLUME TESTS: PROCEDURE AND MEASUREMENT Complex pier scour tests were conducted in the 1.5-m-wide flume and all of the tests were done according to the following procedure: 1. Prepare soil bed and pier installation; 2. Perform vane shear measurements; 3. Take initial readings of the soil surface elevation around the piers; 4. Install the ADV; 5. Perform calculations of water volume in the flume and pump rate to get the expected water depth and velocity; 6. Take measurements of the velocity profile and water surface elevation; Property Test 1 Test 2 1 Liquid Limit, % 40.23 37.7 2 Plastic Limit, % 19.17 14.4 3 Plastic Index (PI), % 21.06 23.3 4 Bulk Unit Weight ( )/ 3mKN 19.65 24.99 5 Water Content, % 27.35 30.5 6 Shear Strength, KPa 10.7 18.1 TABLE 5.1 Geotechnical properties of the Porcelain clay 0 5 10 15 20 25 30 35 0 10 20 30 40 50 Shear Stress (Pa) Er o si o n R a te (m m /h r) Sample A Sample B Figure 5.6. Erosion function for the Porcelain clay. S. No. Property Porcelain Armstone Bentonite 1 Liquid Limit, % 34.40 44.20 67.00 2 Plastic Limit, % 20.25 18.39 27.22 3 Plastic Index (PI), % 14.15 25.81 39.78 4 Specific Gravity 2.61 2.59 2.55 5 Water Content, % 28.51 26.18 39.28 6 Sand Content, % ------ 25(grog) ------ 7 Clay Content, % 100 75 100 8 Shear Strength, KPa 12.51 16.57 39.56 9 CEC, (meg/100g) 8.3 10.0 16.1 10 SAR 5.0 2.0 21.0 11 PH 6.0 5.2 8.5 12 Electrical Conductivity (mmhos/cm) 1.2 1.1 1.1 13 Bulk Unit Weight ( )/ 3mKN 18.0 17.89 17.45 TABLE 5.2 Properties of the soils used in Gudavalli’s research (Gudavalli, 1997)

34 5.7 SHALLOW WATER EFFECT: FLUME TEST RESULTS It appears that when the water depth exceeds about two times the pier width, the maximum scour depth is practically independent of the water depth. When the water depth becomes shallower than that, there is a reduction in the max- imum scour depth. This is attributed to the fact that as the depth of the scour hole increases, the water loses its eroding 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- tent. Gudavalli’s flume tests indicate that in cohesive soils the flow depth has no clear influence on the scour depth when H/B≥1.6 where H is the water depth and B the pier diameter. In this study, a series of pier scour tests with water depths ranging from H/B = 0.2 to H/B = 2.5 were conducted. The cylindrical piers had diameters equal to 273 mm and 160 mm 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 measured curves of scour depth z(t) versus time t are plotted in Figure 5.9 for the two different pier sizes. The flume tests were stopped after a time averaging about 5 days, and then a hyperbola was fitted to the scour depth versus time curve (Briaud et al., 1999, 2001). This technique gave an initial scour rate, z˙ i, (initial slope of the hyperbola) and a maximum scour depth, Zmax, (asymptotic value). The values of the max- imum scour depth, Zmax, and initial scour rate, z˙ i, are shown in Table 5.3. In the case of very shallow water tests, it was observed that noticeable surface rolling, formed due to the roughness of the streambed, would probably affect the scour depth, as men- tioned by Ettema (1980). In addition, the velocity in this case becomes more difficult to measure and control due to the 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 a function of H/B. 0 2 4 6 8 10 12 0 2 4 6 8 10 Shear Stress (Pa) E ro si on R a te (m m /h r) Figure 5.7. Erosion function for Gudavalli’s Porcelain clay. Figure 5.8. Placement of the clay in the soil tank. 7. Take measurements of the scour depth at regular time intervals; and 8. Empty water, record shape of scour hole, and finish the test. For each test, the primary measurements were flow veloc- ity, water depth, scour depth, and time. Water depth and flow velocity were determined in the middle of the channel, 1.5 m upstream of the piers. The depth average velocity was calcu- lated from the measured vertical velocity profile and was used as one of the major parameters in the data analysis. The flow velocity was kept constant throughout the experiment. For the measurements of scour depth increment, the point gage was moved around the pier to find the location of max- imum scour.

35 In Figure 5.11, the correction factor Kw obtained in the cur- rent study on clay is compared to the correction factors rec- ommended for cohesionless soils by Melville and Coleman (1999) and Johnson (1999). Johnson’s correction factor depends on both pier size and velocity, so the label “Johnson 0.273/0.3, Equ(3.6A)” in the figure represents the correction factor for the condition of B = 0.273 m and V = 0.3 m/s fol- lowing Johnson’s equation. Because Johnson did not provide an equation for very shallow flow, a straight line is used to connect the origin to the shallowest end of the Johnson curves in Figure 5.11. Note also that Johnson’s Kw factor is a correction factor for the HEC-18 equation while that equa- tion already includes a water depth influence so a combined Test No. H (mm) B (mm) V (m/s) H/B Exp. Duration (h) iz˙ (mm/hr) Zmax (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. (Pier: B=0.273m and V=0.3m/s) 0 10 20 30 40 50 60 70 80 0 100 200 300 400 500 600 Time(hr) Sc ou r D ep th (m m) Sc ou r D ep th (m m) Sh-2, H/B=2.000 Sh-3, H/B=0.945 Sh-4, H/B=0.502 Sh-5, H/B=0.220 Sh-6, H/B=0.220 Sh-7, H/B=0.095 (Pier: B=0.160m and V=0.4m/s) 0 10 20 30 40 50 60 70 80 0 50 100 150 200 250 Time(hr) Sh-8, H/B=2.500 Sh-9, H/B=2.000 Sh-10, H/B=1.063 Sh-11, H/B=0.531 Zmax/B = 0.3743(H/B)0.3661 R2 = 0.7517 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.5 1.0 1.5 2.0 2.5 3.0 H/B Zm ax /B TABLE 5.3 Parameters and results for shallow water cases of pier scour Figure 5.9. Flume test results for the shallow water cases. Figure 5.10. Influence of shallow water depth on maximum pier scour depth.

36 5.9 SHALLOW WATER EFFECT ON INITIAL SHEAR STRESS For a given scour depth versus time curve, the initial scour rate is the initial slope of that curve. It can be obtained by fitting a hyperbola to the data. These are the rates shown in Table 5.3. The two groups of initial scour rates are plot- ted in Figure 5.12. Test Sh-8 gave a much higher initial scour rate than the other tests (11 mm/hr), so the large pic- ture does not show its value, but the inset one does. The inset indicates that the initial scour rate tends to increase as the water depth decreases and that the increase becomes partic- ularly significant when H/B< 0.5. The figure also shows that the scour rates for the larger pier (B = 0.273 m) are smaller than the rates for the smaller pier (B = 0.160 m). Since the initial scour rate is directly tied to the initial shear stress through the erosion function, it can be stated that the initial shear stress increases when the water depth decreases and decreases when the pier diameter increases. These trends are the opposite of the trends for the maximum scour depth. This means that a pier in shallow water subjected to a con- stant velocity will scour faster at the beginning but will end up scouring to a shallower maximum depth than the same pier in deep water (Figure 5.13). K H B H B H B w =   < <    0 85 1 62 1 1 62 5 2 0 34 . . . ( . ) . Kw = 0.8493(H/B)0.3385 R2 = 0.7753 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 H/B Kw Test Meville Equ(3.7) Johnson 0.273/0.3, Equ(3.6A) 0.273/0.3 , Equ(3.6C) Johnson, 0.16/0.4, Equ(3.6A) 0.16/0.4, Equ(3.6C) Best Fit of Test Figure 5.11. Correction factor for shallow water effect on maximum pier scour depth. 0 1 2 3 4 5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 H/B Er os io n R a te (m m /h r) V=0.3m/s, B=273mm V=0.4m/s, B=160mm 0 2 4 6 8 10 12 0 1 2 3 H/B Er os io n R at e (m m /h r) Figure 5.12. Initial scour rate as a function of water depth. correction factor can be derived. These values correspond to the curves labeled “0.273/0.3, Equ(3.6C)” and “0.160/0.4, Equ(3.6C)” with H/B = 2.5 as the reference cases for B = 0.273 m, V = 0.3 m/s and B = 0.160, V = 0.4 m/s, respectively. Figure 5.11 shows that the shallow water effect factor obtained in this study is close to the correction factors for cohesionless soils. By regression, the expression for the proposed cohesive soil correction factor Kw is

5.10 PIER SPACING EFFECT: FLUME TEST RESULTS The pier spacing effect refers to the interaction between piers when they are closely spaced. In this case, the pier scour depth could be increased due to two reasons: (1) the inter- action and enhancement of horseshoe vortices at the base of the pier, or (2) the acceleration of the flow due to the contrac- tion caused by the piers. The pier spacing effect can be exam- ined for two types of pier installation: (1) in a matrix and (2) in a line. The current study dealt with the effect of pier spacing when cylindrical piers are uniformly spaced and installed in a single row perpendicular to the flow. For these flume tests, the piers were 0.160 m in diameter. The center-to-center distance, C, was called the pier spacing. A distance equal to the space of one pier was kept between the outmost pier and the wall of the flume. Due to the flume width, the maximum number of piers that could be installed was four and the corresponding minimum spacing ratio was C/B = 1.88. The maximum pier spacing ratio was C/B = 4.69 for a single pier. Raudkivi (1991) commented that when the pier spacing is larger than four, the group pier effect is negligible. The parameters and results for the four pier spacing tests are summarized in Table 5.4. The initial scour rate and max- imum scour depth were calculated in the same way as the shallow water cases. The measured scour curves are plotted 37 in Figure 5.14. The maximum scour depth may happen either around the pier or at some intermediate location; its location was determined with the point gage system. 5.11 PIER SPACING EFFECT ON MAXIMUM SCOUR DEPTH The pier spacing effect on the maximum pier scour depth can be incorporated in the general equation by using a correc- tion factor, Ksp, equal to the ratio of the maximum scour depth of the line of piers over the maximum scour depth of the iso- lated pier. In this study, the single-pier case was the case of the single pier in the 1.5-m-wide flume. This case corresponds to a C/B ratio of 4.69 as mentioned previously. Figure 5.15 shows the correction factor. The difference of maximum scour depth between the single pier and a line of two piers was observed to be quite small, which gives some confidence in the use of the C/B ratio of 4.69 as the single-pier case. In Figure 5.15, the pier spacing effect obtained in this study for a Porcelain clay is compared with existing recommenda- tions for cohesionless soils. Elliot and Baker (1985) used oblong piers (46 mm wide and 150 mm long) in their tests on groups of piers. Their pier spacing effect was more severe than the others, possibly due to the aspect ratio of the piers used. Salim and Jones (1998) conducted flume tests on cylindrical and square piers installed in a matrix in the middle of a chan- nel. Each pier in this group configuration was more affected by other piers than in the case of a single line of piers. This may be the reason why Jones’ correction factor is more severe than the one found in this study. The test conditions for Raudkivi’s experiments (1991) are very similar to the current study, with the following exceptions: only two cylindrical piers were installed in the middle of the flume and the soil was sand. In Raudkivi’s tests, the pier spacing effect was examined by varying the distance between the two piers. Several attempts were made to find a prediction equation. First, the single equivalent pier concept proposed by Salim and 0 30 60 90 0 50 100 150 200 250 Time (hr) Sc o u r D e pt h (m m) A B C For H/B, A>B>C Figure 5.13. Comparison between scour in shallow and deep waters. Test No. H (mm) B (mm) V (m/s) C/B Time Lasting (h) iz˙ (mm/hr) Zmax (mm) Gr-1 375.00 160.00 0.33 (1-pier) 4.69 165.00 2.33 165.56 Gr-2 375.00 160.00 0.33 (2-pier) 3.13 122.50 2.83 175.44 Gr-3 375.00 160.00 0.33 (3-pier) 2.34 144.08 5.24 204.08 Gr-4 375.00 160.00 0.33 (4-pier) 1.88 129.83 4.76 250.00 TABLE 5.4 Parameters and results for pier spacing flume tests 0 40 80 120 160 0 50 100 150 200 Time(hr) Sc ou r D ep th (m m ) 1-pier, C/B=4.69 2-pier, C/B=3.13 3-pier, C/B=2.34 4-pier, C/B=1.88 Figure 5.14. Scour depth versus time for the pier spacing cases.

Jones (1998) was used by adding the widths of all of the piers in the row. This was done by using Equation 5.1 with the equivalent width. The Ksp curve obtained in such a way is shown under the label “Projection Width” in Figure 5.15. That curve does not fit the measured data well (too conservative). Even after accounting for the water depth effect, the Ksp curve is still too high as shown under the label “Projection Width (Kw)” in Figure 5.15. This indicates that the single equivalent pier model would overestimate the pier spacing effect at least for piers installed in a row. It was found that the ratio of the width of the channel without the piers over the unobstructed width of the channel with the piers fit the data quite well. This equation is shown in Figure 5.15 under the label “Velocity Ratio” because the velocity also can be estimated through that ratio. For example, if the flume width is B1, the approaching velocity V1, and there are n piers installed in a row with same diameter B, then the velocity with n piers can be estimated by: Vn = (V1B1)/(B1 − nB), and the velocity ratio is: Vn/V1 = B1/(B1 − nB). The equation proposed for Ksp is: 5.12 PIER SPACING EFFECT ON INITIAL SCOUR RATE The initial scour rate for the pier spacing flume tests is pre- sented in Table 5.4 and plotted in Figure 5.16 where C is the center-to-center distance and B the pier width. It shows that the initial scour rate tends to increase as the piers become more closely spaced. In summary, both the maximum pier scour depth and the initial scour rate will increase as the piers become more closely spaced. This means that curves such as those presented in Figure 5.17 can be expected. K B B nBsp = − ( ) 1 1 5 3( . ) 38 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 3 .5 4 .0 1 3 5 7 C /B K sp A .J .R a ud k ivi S te rling J o ne s K e ith R . E llio t V e lo c ity ra tio P ro je c tio n W id th P ro je c tio n W id th(K w ) M e a s ure m e nt Figure 5.15. Correction factor for pier spacing effect. 2 3 4 5 6 1 2 3 4 5 C/B In iti al S co u r R a te (m m ) Figure 5.16. Initial scour rate for the group pier tests. 0 30 60 90 120 150 180 0 50 100 150 200 Time (hr) Sc ou r D ep th (m m) A B C For C/B, A>B>C Figure 5.17. Scour curves for groups of piers in a line.

5.13 PIER SHAPE EFFECT: FLUME TEST RESULTS The shape of a bridge pier can strongly affect the flow pat- tern around it. In this study, only rectangular piers were con- sidered. Bridge piers are most often installed with the longer side parallel to the major flow direction; therefore, the length over width ratio, L/B, is kept greater than one for all piers in this study. The rectangular pier was installed with a 0-degree attack angle in the middle of the soil tank. Major scour always occurred around the four corners of the rectangular pier but only the time history of the maximum scour depth was used in the analysis. The shapes of the scour holes for different rectangular piers were recorded and compared. In addition, cylindrical piers with a diameter equal to the width of the rectangular pier were used as the reference case. Para- meters and major results for the flume tests for pier shape effect are summarized in Table 5.5. Again, the maximum scour depth and the initial scour rate were calculated in the same way as in the case of the other flume tests. The scour depth development curves are plotted in Figure 5.18. 5.14 PIER SHAPE EFFECT ON MAXIMUM SCOUR DEPTH The cylindrical pier test, SP-1, was chosen as the reference case. The correction factor, Ksp, is the ratio of the maximum scour depth for a given shape over the maximum scour depth for the cylinder (Figure 5.19). The results on Figure 5.19 indi- cate that there is no noticeable effect on scour depth due to the pier shape. Indeed, the correction factor varies from 1:1 to 1:12. This conclusion is consistent with the correction factor for sand listed in HEC-18. Therefore, it is concluded that a pier shape correction factor of 1.1 is a good approximation for the maxi- mum scour depth around rectangular piers in both clay and sand as long as the L/B ratio is larger than 1. The case of the L/B ratio smaller than 1 was not covered in this research project. 5.15 PIER SHAPE EFFECT ON INITIAL SCOUR RATE The initial scour rate for the flume tests on the rectangular piers having the same width but different lengths are com- pared in Figure 5.20. As can be seen, the rectangular piers 39 Test No. H (mm) B (mm) V (m/s) L/B Time Lasting (h) iz˙ (mm/hr) Zmax (mm) Sp-1 375.00 61.00 0.33 Circular 151.92 1.45 68.03 Sp-2 375.00 61.00 0.33 1:1 129.50 5.00 73.53 Sp-3 375.00 61.00 0.33 4:1 124.42 2.05 72.99 Sp-4 375.00 61.00 0.33 8:1 131.58 1.93 74.63 Sp-5 375.00 61.00 0.33 12:1 131.50 1.84 75.19 TABLE 5.5 Parameters and results for pier shape effect flume tests 0 10 20 30 40 50 60 70 0 50 100 150 Time(hr) Sc ou r D ep th (m m ) Circular Square L/B=12 L/B=8 L/B=4 Figure 5.18. Scour depth versus time curves for pier shape effect tests. 0 1 2 3 4 5 6 0 5 10 15 L/B In itia l S co u r R a te (m m /h ) Rectangular Circular Figure 5.20. Initial scour rates for the shape effect flume tests. 0.0 0 .4 0 .8 1 .2 1 .6 2 .0 0 5 10 15 L/B Ks h HE C -18 , K s h= 1.1 fo r S quare Nos e Figure 5.19. Correction factor for pier shape effect.

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

41 jection width is equivalent to the pier width, then the correc- tion factor Ka can be calculated as The value of n generally varies from 0.6 to 0.9 and is equal to 0.635 in the SRICOS Method for scour depth prediction in cohesive soils. In Figure 5.25, the correction factor obtained in the flume tests is shown together with other solutions using the projec- K Z Z L Ba n = ( ) ( ) = +  max max sin cos ( . )α α α 0 5 5 (B: Vertical Direction, a=45) 0 20 40 60 80 100 120 0 50 100 150 Time (hr) Sc ou r D ep th (m m ) L/B=1 L/B=2 L/B=4 L/B=6 0 20 40 60 80 100 120 0 50 100 150 200 250 Time (hr) Sc ou r D ep th (m m ) a=0 a=15 a=30 a=45 a=60 a=90 (A: Transverse Direction, L/B=4) Figure 5.23. Scour depth versus time curves for attack angle tests. A: Pier Projection W idth B: Flow Pattern and Corner Number B cosα L sinα B’ L B (4) (1) (3) (2) α Figure 5.24. Skewed pier definitions. At-8, interpolation between existing reference cases would be used to calculate the maximum scour depth of the required reference case. The pier projection width, B′, as shown in Figure 5.24, is a widely accepted concept to evaluate the effect of the attack angle: Common scour depth equations for 0-degree attack angle are of the form: Zmax = f Bn, where n is a constant. If the pro- ′ = + = + B L B B LBsin cos sin cos ( . )α α α α 5 4 (A: Transverse Direction, L/B=4) 1.0 1.5 2.0 2.5 3.0 3.5 0 30 60 90 Attack Angle (Degree) Ka Mostafa, n=0.8 Laursen, n=0.68 Richardson, n=0.65 SRICOS, n=0.635 Ka' Ka (B: Vertical Direction, Attack Angle =45) 1.0 2.0 3.0 4.0 5.0 6.0 7.0 0 4 8 12 L/B Ka Mostafa, n=0.8 Laursen, n=0.68 Richardson, n=0.65 SRICOS, n=0.635 Ka' Ka Figure 5.25. Attack angle effect on maximum scour depth.

tion width and Equation 5.5 in both the transverse and the longitudinal direction. The difference between Ka and Ka′ is linked to the influence of the water depth and pier spacing effect that occur when the angle of attack becomes more severe. In order to examine the pure attack angle effect, the shallow water effect and pier spacing effect need to be elim- inated. The proposed equations for shallow water depth and pier spacing are used to isolate the angle of attack effect. The results of the calculations are shown in Table 5.7. The cor- rection factor, Ka′, for pure attack angle effect on scour depth is obtained based on the following relationship: Figure 5.25 shows that when the attack angle is less than 30 degrees, the correction is not significant and that for angles of attack larger than 30 degrees, the correction factor would be overestimated if the correction was not done. Fig- ure 5.25 also shows that using the projection width with the SRICOS exponent of 0.635 leads to a reasonable and often conservative prediction of the correction factor Ka′. There- fore, this approach is adopted for the proposed method. K K K Ka w sp a= ′  ( . )5 6 42 5.19 ATTACK ANGLE EFFECT ON INITIAL SCOUR RATE The initial scour rates for the attack angle flume tests are plotted in Figure 5.26 for both the transverse and vertical direction. In this case, the scour rates show a large scatter pattern. This is because several opposing factors are involved in the initial shear stress or the initial scour rate under a given attack angle condition. Based on the observations in previous sections, the scour rate will decrease with an increase in pier width and flow depth, but increase with an increase in pier contraction and the sharpness of pier corners. There- fore, the relative magnitude of the scour rate under a given attack angle depends on the balance between these influ- encing factors. 5.20 ATTACK ANGLE EFFECT ON SCOUR HOLE SHAPE The attack angle also strongly affects the shape of the scour hole. If the four corners of the rectangular pier are numbered as in Figure 5.24, test observations indicate that α (˚) L/B B′ (mm) B′/B Zmax (mm) Zmax(0) (mm) H/B′ Kw Ksp Ka Ka′ 15 4:1 61.00 1.00 72.99 72.99 6.15 1.00 1.00 1.00 1.00 30 4:1 122.07 2.00 103.09 72.99 3.07 1.00 1.00 1.41 1.41 45 4:1 174.83 2.87 117.65 72.99 2.14 1.00 1.02 1.61 1.59 60 4:1 215.67 3.54 151.50 72.99 1.74 1.00 1.05 2.08 1.98 90 4:1 241.81 3.96 196.08 72.99 1.55 0.99 1.08 2.69 2.51 45 1:1 86.27 4.00 208.77 72.99 1.54 0.98 1.09 2.86 2.67 45 2:1 129.40 1.41 147.06 73.53 4.35 1.00 1.00 2.00 2.00 45 6:1 301.93 2.12 161.29 73.20 2.90 1.00 1.00 2.20 2.20 (A: Transverse Direction, L/B=4) 1.0 1.5 2.0 2.5 3.0 0 30 60 90 Attack Angle (Degree) In iti al R at e (m m /h r) (B: Vertical Direction, Attack Angle =45) 1.0 1.5 2.0 2.5 3.0 0 2 4 6 L/B In iti al R at e (m m /h r) TABLE 5.7 Calculations for isolating the attack angle effect in pier scour depth Figure 5.26. Initial scour rates for the attack angle flume tests.

43 vidual effects described in previous sections were expected to happen simultaneously. The main parameters and results are summarized in Table 5.9, and the time history of the scour development is plotted in Figure 5.29. The final maximum scour depth was obtained by using the hyper- bola model. The maximum scour depths for the two tests were calcu- lated according to Equation 5.7. The calculations are detailed in Table 5.10, and the measured results also are listed at the bottom of that table which shows that the difference between the predictions and measurements is remarkably small (less than 5%). This tends to indicate that the chosen superposition law works well for complex pier scour predictions. Attack Angle (°) Location of the maximum scour depth 0 (1), (4) 0<α<45 (1) 45 (1), (3) 45<α<90 (3) 90 (1), (2), (3), (4) (1) (1) 15° 15° (3) (3) 0.5m 0.5m 0.5m (1) 45° (1) 45° (3) (3) 0.5m 0.5m 0.5m the location of the maximum scour depth will either happen at Corner 1 or Corner 3. When the attack angle increases, the location of the maximum scour depth gradually moves from Corner 1 to Corner 3, and this transition is documented in 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 hole in sands sketched by Raudkivi (1991). 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 figures and equations are given to quantify the corresponding correction factors. However, bridge piers are likely to exhibit 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 represent the combined effect: where Zmax is the maximum depth of scour (mm); V is depth average velocity at the location of the pier if the pier or bridge was not there (m/s); B′ is the projection width of the pier (m); v is the kinematic viscosity of water (10E-6 (m2/s) at 20°C); Kw is the correction factor for shallow water effect (Equation 5.2), Ksp for pier spacing effect (Equation 5.3), and Ksh for pier shape effect (1.1 for rectangular piers); and B′ is the pier projection width (Equation 5.4 for rectan- gular pier). This is a common approach that implies that the effects are independent and has been used in many instances before (HEC-18, Melville [1997]). Two complex pier flume tests were conducted with the configuration shown in Figure 5.28 where all of the indi- Z K K K B V v w sp shmax . . ( . )mm( ) = ′( )0 18 5 70 635    14cm 7cm 2.5cm 3cm 10cm 8cm 6cm 5.5cm 6cm (4) (4) (1) (1) (3) (3) (2) (2) TABLE 5.8 Transition of the location of maximum scour depth Figure 5.27. Shape of scour around a skewed pier in a cohesive soil (left: attack angle = 15 degrees, right: attack angle = 30 degrees). Figure 5.28. Configuration of the flume tests to verify the superposition rule. Test No. H (mm) V (mm/s) L (mm) B (mm) C (mm) g (˚) Time (h) Zmax (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 TABLE 5.9 Parameters and results for the complex pier flume tests

44 0 40 80 120 160 200 0 50 100 150 200 Time (Hr) Sc o u r D e pt h (m m) CP-1 CP-2 PARAMETERS Cp - 1 Cp - 2 CALCULATION NOTE Primary Inputs B (mm) L (mm) H (mm) α (˚) V (mm/s) C (mm) 61 244 375 45 330 500 61 244 375 15 330 500 Attack Angle Effect Pier width Pier length Water depth Attack angle Mean approaching velocity Center to center pier spacing 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= Kw·Ksp·Ksh Final Scour Depth Zcal(mm) 174.63 294.33 Zcal=K·Z1 Comparison Ztest (mm) 175.44 285.71 (Zcal-Ztest)/Ztest (%) - 0.46 3.02 TABLE 5.10 Comparison of calculated and measured maximum pier scour depths Figure 5.29. Scour development curves for the complex pier flume tests.

Next: Chapter 6 - The SRICOS-EFA Method for Initial Scour Rate at Complex Piers »
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TRB’s National Cooperative Highway Research Program (NCHRP) Report 516: Pier and Contraction Scour in Cohesive Soils examines methods for predicting the extent of complex pier and contraction scour in cohesive soils.

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