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Pier and Contraction Scour in Cohesive Soils (2004)

Chapter: Chapter 7 - The SRICOS-EFA Method for Maximum Contraction Scour Depth

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Suggested Citation:"Chapter 7 - The SRICOS-EFA Method for Maximum Contraction Scour Depth." 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 7 - The SRICOS-EFA Method for Maximum Contraction Scour Depth." 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 7 - The SRICOS-EFA Method for Maximum Contraction Scour Depth." 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 7 - The SRICOS-EFA Method for Maximum Contraction Scour Depth." 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 7 - The SRICOS-EFA Method for Maximum Contraction Scour Depth." 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 7 - The SRICOS-EFA Method for Maximum Contraction Scour Depth." 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 7 - The SRICOS-EFA Method for Maximum Contraction Scour Depth." 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 7 - The SRICOS-EFA Method for Maximum Contraction Scour Depth." 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 7 - The SRICOS-EFA Method for Maximum Contraction Scour Depth." 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.
×
Page 64
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Suggested Citation:"Chapter 7 - The SRICOS-EFA Method for Maximum Contraction Scour Depth." 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.
×
Page 65
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Suggested Citation:"Chapter 7 - The SRICOS-EFA Method for Maximum Contraction Scour Depth." 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 7 - The SRICOS-EFA Method for Maximum Contraction Scour Depth." 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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56 CHAPTER 7 THE SRICOS-EFA METHOD FOR MAXIMUM CONTRACTION SCOUR DEPTH 7.1 EXISTING KNOWLEDGE Contraction scour refers to the lowering of the river bot- tom due to the narrowing of the flow opening between two abutments or between two bridge piers. In cohesionless soils equations are recommended by HEC-18 (1995) for live bed and clear water contraction scour depths. These equations involve one soil parameter: the mean grain size. The studies on cohesionless soils include those of Straub (1934), Laursen (1960, 1963), Komura (1966), Gill (1981), Lim (1998), Chang (1998), and Smith (1967). For cohesive soils, two methods were found in the literature: Chang and Davis, and Ivarson. Both methods are empirically based and have neither a time nor stratigraphy component. The studies on contraction scour in cohesive soils are even fewer in number than the studies on pier scour in cohesive soils. Chang and Davis (1998) proposed a method to predict clear water contraction scour at bridges. They assumed that the maximum scour depth is reached when the critical flow veloc- ity for the bed material is equal to the average velocity of the flow. The critical velocity is defined as the velocity that causes the incipient motion of the bed particles. The method makes use of Neill’s (1973) competent velocity concept, which is tied to the mean grain size D50. A series of equations to predict the total depth of flow, including the maximum contraction scour depths, is proposed. The equations involve two parameters: the unit discharge at the contraction and the mean grain size. Ivarson et al. (1996) (cited from Ivarson, 1998) developed an equation to predict contraction scour for cohesive soils based on Laursen’s non-cohesive soils contraction scour equation. Ivarson et al. set the shear stress in the contracted section equal to the critical shear stress at incipient motion. For cohesive soils, they use the relationship between critical shear stress and unconfined compressive strength (Flaxman, 1963). Ivarson et al. propose an equation that includes the fol- lowing parameters: the undrained shear strength of the soil, the water depth in the approach uncontracted channel, the dis- charge per unit width in the contracted channel, and Man- ning’s Coefficient in the contracted channel. 7.2 GENERAL This chapter addresses the problem of contraction scour (Figure 7.1). When contraction of the flow occurs and if the bed shear stress exceeds the critical shear stress of the cohe- sive soils, contraction scour develops and the contraction scour profile looks like that shown in Figure 7.1. This profile identifies two separate scour depths: the maximum contrac- tion scour depth zmax, which occurs xmax after the beginning of the start of the contracted channel, and the uniform scour depth zunif, which occurs after that. As described in this chapter, a series of flume tests were per- formed to develop equations to predict the values of zmax, xmax, and zunif in cohesive soils. One of the inputs was the mean depth velocity of the water. The velocity that controls the con- traction scour was the velocity V2 in the contracted channel; this velocity can be estimated by using the velocity in the uncontracted channel and the contraction ratio B2/B1 or by using a program such as HEC-RAS to obtain V2 directly. These two approaches were developed in the analysis of the flume tests. In Chapter 8, the contraction scour rate issue is addressed through numerical simulation to obtain the initial shear stress before scour starts. 7.3 FLUME TESTS AND MEASUREMENTS The flume used for the contraction tests was the 0.45-m- wide flume because initial tests in the 1.5-m-wide flume led to very large amounts of soil loss. The budget and the sched- ule did not allow the use of such large quantities of soil. The parameters influencing the contraction scour were the mean depth approach velocity V1, the contraction ratio B2/B1, the approach water depth H1, the contraction or abutment transi- tion angle θ, the contraction length L, and the soil properties. In this research, a Porcelain clay, as described in Chapter 4, was used for all flume tests. The erosion function of the clay has been described previously in Section 5.5 and Figure 5.6. The most important parameters were considered to be V1, B2/B1, and H1 and led to the main part of the equation. The influence of the transition angle θ and the contraction length L were incorporated through the correction factors. There- fore, the tentative form of the equation to predict the con- traction depth Z (Zmax or Zunif) is Where, Kθ and KL are the correction factors for transition angle and contraction length, respectively. Z K K f V B B HL=  θ 1 21 1 7 1, , ( . )

Based on the above analysis, the flume tests were divided into two parts: the tests run to obtain the function f (V1, B2/B1, H1), called primary tests, and the tests run for the correction factors Kθ and KL, called secondary tests The contraction geometries were shown in Section 5.3 and in Figure 5.4. The parameters for the tests performed are listed in Table 7.1 (primary tests) and Table 7.2 (secondary tests). There were seven primary tests where the contraction scour was gener- ated in a long, contracted channel with a 90-degree transition angle. Among them, the contraction ratio was varied in Tests 1, 2, and 3; the water depth was varied in Tests 4, 5, and 6; and the velocity was varied in Tests 2, 6, and 7. There were two groups of secondary tests: Tests 2, 9, 10, and 11 were for the transition angle effect on contraction scour, and Tests 2, 12, 13, and 14 were for the contraction length effect on contraction scour. The following measurements were carried out for each flume test: 1. Initial velocity distribution by ADV: vertical velocity profile in the middle of the channel at a location of 1.2 m upstream of the contraction and the longitudinal profile along the centerline of the channel; 57 2. Initial water surface elevation along the centerline of the channel (measured using a point gage); 3. Contraction scour profile along the centerline of the bottom of the channel, as a function of time (measured using a point gage); 4. Two abutment scour measurements, as a function of time (measured using a point gage); 5. Final longitudinal velocity profile along the channel centerline (measured using the ADV); 6. Final water surface elevation along the channel center- line (measured using a point gage); and 7. Photos of the final scour hole shape (taken by a digital camera). 7.4 FLUME TESTS: FLOW OBSERVATIONS AND RESULTS The water surface profiles along the channel centerline at the beginning and at the end of Test 2 are plotted in Figure 7.2. The approaching flow of Test 2 was in the subcritical flow regime (all tests were subcritical except Test 1, which was supercritical at the beginning of the test); as a result, there was a drop in water surface elevation in the contracted section. This H1 V 1 Z ma Z uni X ma V 2 L q B 2 B 1 Turbulence (a) (b) Figure 7.1. Concepts and definitions in contraction scour. Test No. V1 (before) (cm/s) V1 (after) (cm/s) V (Hec) (cm/s) B2/B1 H1 (before) (mm) H1 (after) (mm) H (Hec) (mm) θ (°) L/B1 Zmax (mm) Zunif (mm) Xmax (mm) 1 13.8 34.1 103 0.25 297 164.77 170 90 2.932 357.143 227.273 80 2 29 31 67 0.5 171.15 162.03 150 90 3.868 116.279 70.423 285 3 45 45.9 79 0.75 121.6 106.4 100 90 3.38 72.993 47.847 620 4 20.5 20.5 53 0.5 108.2 108.22 100 90 3.38 28.653 11.862 210 5 20.5 20.7 41 0.5 251.4 251.4 240 90 3.38 37.736 19.881 210 6 20.5 20.5 46 0.5 171.76 171.76 160 90 3.38 36.101 13.021 210 7 39 39 84 0.5 174.19 174.19 160 90 3.38 142.857 142.857 210 TABLE 7.1 Parameters and results for the primary contraction scour tests

difference decreased as contraction scour developed. When the equilibrium scour depth profile was reached, the water sur- face elevation in the contracted section could be considered as level with the water surface elevation in the approach channel. This observation is also mentioned by other researchers (Laursen 1960, Komura 1966). As a result, the contraction scour depth can be simply calculated by subtracting the upstream water depth H1 from the total water depth in the con- traction section H2. At equilibrium contraction scour, the con- traction scour depth is In the final profile of the water surface elevation, it was also noticed that the upstream water surface gradually lowered to the downstream water surface. In other words, the equilibrium water surface elevation was intermediate between the initial upstream and downstream elevations. The longitudinal velocity profiles along the channel center- line at the beginning and at the end of Test 2 are presented in Figure 7.3. The velocity was measured at a depth of 0.4 H from the water surface with the ADV. As expected, the veloc- ity increased in the contracted channel since the water eleva- tion decreased. As contraction scour deepened, the difference Z H Hmax ( . )= ( ) −2 1 7 2equi 58 decreased but did not become zero. Instead, it was observed that the final value of the velocity in the contracted channel reached the same approximate value for all flume tests on the Porcelain clay. This tends to indicate that contraction scour stops at the critical velocity in the contracted channel no mat- ter what the contraction geometry is. It also was observed that the highest velocity and the low- est water surface elevation in the contracted channel hap- pened at the same approximate location behind the contrac- tion inlet, but this location was different from the maximum contraction scour location as described later. HEC-RAS (Hydraulic Engineering Center—River Analy- sis System, 1997) is a widely used program in open channel analysis. It was used with the flume cross-section profiles before scour started to predict the quantities measured during the tests. The HEC-RAS outputs are listed in Tables 7.1 and 7.2 and compared with the measured water surface elevation and velocity profiles in Figures 7.2 and 7.3. It is found that HEC-RAS leads to relatively constant values of the water sur- face elevation and velocity before and after the contraction, which is a significant simplification of the measured behavior. V Vc2 7 3equi( ) = ( . ) 0 60 120 180 -1000 -500 0 500 1000 1500 X(mm) W at er S ur fa ce El ev at io n (m m ) Before After HEC-RAS 0 30 60 90 -1000 -500 0 500 1000 1500 X(mm) Ve lo ci ty (cm /s) Before After HEC-RAS Test No. V1 (before) (cm/s) V1 (after) (cm/s) V (Hec) (cm/s) B2/B1 H1 (before) (mm) H1 (after) (mm) H (Hec) (mm) θ (°) L/B1 Zmax (mm) Zunif (mm) Xmax (mm) 2 29 31 67 0.5 171.15 162.03 150 90 3.868 116.279 70.423 285 9 30 30.2 68 0.5 161 160.21 150 15 3.868 90.909 ----- 785 10 30 30.2 78 0.5 153.6 152 110 45 3.38 128.205 95.234 385 11 30 29.3 69 0.5 166.59 163.25 150 60 3.38 80 41.322 785 12 29 33 75 0.5 172.37 160.5 130 90 0.844 111.11 ----- 85 13 29.2 33 72 0.5 170.54 162.34 140 90 0.25 128.21 ----- 152 14 29.2 34.1 70 0.5 180 164.77 140 90 0.125 208.33 ----- 385 TABLE 7.2 Parameters and results for the secondary contraction scour tests Figure 7.2. Water surface elevations along the channel centerline in Test 2. Figure 7.3. Velocity distribution along the channel centerline in Test 2.

It is also noted that the maximum velocity predicted by HEC- RAS in the contracted channel is less than the measured value. 7.5 FLUME TESTS: SCOUR OBSERVATIONS AND RESULTS An example of the measurement results is shown in Figure 7.4 for Test 1. Figure 7.5 shows a sketch of the contraction distribution in plan view. The measurement emphasis was placed on obtaining four parameters at the equilibrium con- traction scour: the maximum contraction scour depth Zmax, the uniform contraction scour depth Zunif, the location of the max- imum contraction scour Xmax, and the contraction profile along the channel centerline. The maximum and uniform contrac- tion scour depths at equilibrium are listed in Tables 7.1 and 7.2. These values were obtained by fitting the scour depth ver- sus time curve with a hyperbola and using the ordinate of the asymptote as the equilibrium value. The fit between the mea- sured data and the hyperbola was very good for Zmax and Zunif 59 in Test 1, as is shown on Figures 7.6 and 7.7. The R2 values were consistently higher than 0.99. The results of tests involv- ing the transition angle and the length of the contraction are shown on Figures 7.8 and 7.9; Figure 7.10 regroups all of the measurements taken for the primary tests (Table 7.1). For the uniform contraction scour depth, the average value of the last four points (over a 0.4-m span) in the contraction scour depth profile was used as the uniform scour value. In addition, it should be noted that for short contraction lengths (Tests 13 and 14), a fully developed uniform contraction did not exist. The location of the maximum contraction scour, Xmax, is measured from the beginning of the fully contracted section. It can be seen that Xmax oscillates at the beginning of the test but becomes fixed in the late stages. This value was chosen for Xmax and is the one shown in Tables 7.1 and 7.2. An important observation was noted during the tests: the abutment scour never added itself to the contraction scour. In fact, the abutment scour and the contraction scour were of the same order of magnitude. Figure 7.11 shows the different 0 50 100 150 200 250 300 -300 -100 100 300 500 700 900 1100 1300 X(mm) Z( x, t) ( mm ) 0.50 4.50 14.25 27.00 40.67 50.00 64.08 77.42 99.08 124.08 148.58 FLOW S ed im en t D ep o s itio n B ack C o n trac tio n S co u r M ax im u m C o n trac tio n S co u r A b u tm en t S co u r Figure 7.4. Contraction scour profiles along the channel centerline as a function of time for Test 1 (the numbers in the legend are the elapsed times in hours). Figure 7.5. Plan view sketch of the contraction scour pattern.

configurations that occurred during the tests. If the combina- tion of contraction ratio and transition angle is small, then the contraction scour is downstream from the contraction inlet and the abutment scour exists by itself at the contraction inlet. If the combination of contraction ratio and transition angle is medium, the abutment scour and the contraction scour occur within the same inlet cross section but do not overlap. If the combination of contraction ratio and transition angle is severe, the abutment scour and the contraction scour overlap but do not add to each other. 7.6 MAXIMUM AND UNIFORM CONTRACTION DEPTHS FOR THE REFERENCE CASES The reference case for the development of the basic equa- tion is the case of a 90-degree transition angle and a long con- 60 traction length (L/B2 > 2, Figure 7.5). The maximum depth of contraction scour Zmax is the largest depth that occurs along the contraction scour profile in the center of the contracted channel. The uniform contraction scour depth Zunif is the scour depth that develops in the contracted channel far from the transition zone (Figure 7.1). The Reynolds Number (inertia force/gravity force) and the Froude Number (inertia force/viscous force) were used as basic correlation parameters. Both Zmax and Zunif were normal- ized with respect to H1, the upstream water depth. Figure 7.12 shows the attempt to correlate the contraction scour depths to the Reynolds Number defined as V1B2/υ. As can be seen, the Reynolds Number is not a good predictor of the contraction scour depths. Figures 7.13 and 7.14 show the correlation with the Froude Number. Although there are only seven points for the correlation, the results are very good. 0 40 80 120 160 200 0 50 100 150 200 250 Time(H) Z( t)( mm ) Measurement Hyperbola 0 50 100 150 200 250 300 0 50 100 150 200 250 Time(H) Z( t)(m m ) Measurement Hyperbola 0 0.25 0.5 0.75 1 -400 0 400 800 1200 1600 Distance X (mm) Re la tiv e Sc ou r D ep th (Z /Z m ax ) Angle=15 Angle=45 Angle=60 Angle=90 Figure 7.6. Maximum contraction scour and hyperbola model for Test 1. Figure 7.7. Uniform contraction scour and hyperbola model for Test 1. Figure 7.8. Contraction scour profile along the channel centerline for transition angle effect.

61 0 0.25 0.5 0.75 1 -400 0 400 800 1200 1600 Distance X (mm) Re la tiv e Sc ou r D ep th (Z /Z m ax ) L/B2=0.5 L/B2=1 L/B2=1.69 L/B2=6.76 Figure 7.9. Contraction scour profile along the channel centerline for contraction length effect. Original Bottom (a) Ridge (b) Valley (c) Plain is the location of maximum contraction Figure 7.11. Overlapping of scour for contraction scour and abutment scour. 0 0.2 0.4 0.6 0.8 1 1.2 -500 0 500 1000 1500 Distance X (mm) R el a tiv e Sc o u r D ep th (Z /Z m a x) Figure 7.10. Contraction scour profiles along the channel centerline for standard tests.

62 So the critical Froude Number can be written as The contraction scour depths are likely to be proportional to the difference (Fr-Frc). However, as mentioned before, the velocity used to calculate Fr may require a factor β. The final form of the equation sought was The factors α and β were obtained by optimizing the R2 value in the regression on Figures 7.13 and 7.14. The pro- posed equations are where Zmax is the maximum depth of contraction scour; H1 is the upstream water depth after scour has occurred; V1 is the mean depth upstream velocity after the contraction scour has occurred; B1 is the upstream channel width; B2 is the con- tracted channel width; g is the acceleration due to gravity; τc is the critical shear stress of the soil (obtained from an EFA test); ρ is the mass density of water; and n is the Mannings Coefficient. Note that V1 and H1 are the upstream velocity Z H V B B gH gnH c unif 1 1 1 2 1 1 2 1 1 31 41 1 31 7 10=   −       . . ( . ) τ ρ Z H V B B gH gnH c max . . ( . ) 1 1 1 2 1 1 2 1 1 31 90 1 38 7 9=   −         τ ρ Z H c1 7 8= −( )α βFr Fr* ( . ) Frc c cV gH gnH= ( ) = ( ) ( )1 1 7 70 5 0 5 0 33. . . ( . )τ ρ τ ρc cgn V H= ( ) ( )2 2 1 0 33 7 6. ( . ) 0.0 0.5 1.0 1.5 2.0 2.5 0 50000 100000 150000 200000 Re=V1B2/n Z / H 1 Max Contraction Unif Contraction y = 1.0039x - 0.0013 R2 = 0.9885 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 − × × 3/1 1 2/1 1 1 2 138.1 9.1 gnHgH B BV cρ τ 1 max H Z y = 0.9995x - 4E-06 R2 = 0.9558 0 0.3 0.6 0.9 1.2 1.5 0 0.5 1 1.5 − × × 3/1 1 2/1 1 1 2 131.1 41.1 gnHgH B BV cρ τ 1H Zunif Figure 7.12. Correlation attempt between contraction scour depth and Reynolds Number. Figure 7.13. Normalized maximum contraction scour depth versus Froude Number. Figure 7.14. Normalized uniform contraction scour depth versus Froude Number. The Froude Number was calculated as follows. From sim- ple conservation, we have V1B1H1 = V2B2H2. Because the water depth H2 may not be known for design purposes and because other factors may influence V2, the velocity used for correla- tion purposes was simply V1B1/B2. As will be seen later, a fac- tor will be needed in front of V1B1/B2 for optimum fit. Then the Froude Number was calculated as The relationship between the critical shear stress and the critical velocity for an open channel was established (Richardson et al., 1995). Fr* ( . ).= ( ) ( )V B B gH1 1 2 1 0 5 7 5 V V B B* ( . )= 1 1 2 7 4

and water depth after contraction scour has occurred. The difference between the V1 and H1 values before and after con- traction scour is small in most cases and, except for in Test 1, the correlations were good when using the values of V1 and H1 before the contraction scour occurred. Test 1 had a very small contraction ratio (B2/B1 = 0.25) and an initial super- critical flow, whereas all other tests had larger contraction ratios and an initial subcritical flow. In the case of Test 1, Equations 7.9 and 7.10 worked only when using the values of V1 and H1 after contraction scour had occurred. This use of values after scour occurs is consistent with the approach taken by other researchers (Laursen, 1960,1963; Komura, 1966; Gill, 1981; and Lim 1998). The value of the β factor is shown as a function of the con- traction ratio for all of the flume contraction tests on Figure 7.15. An average value of 1.38 was chosen for Zmax and 1.31 for Zunif. Since β should be equal to 1 when B2/B1 is equal to 1 (no contraction), the best-fit line on Figure 7.15 should go through that point. It was decided to achieve that result as shown on Figure 5.15. An attempt was made to find a relationship between Zunif and Zmax. The following equation gave a high R2 value: 7.7 LOCATION OF MAXIMUM CONTRACTION DEPTH FOR THE REFERENCE CASES Knowledge of the location of the maximum contraction scour depth is very important for the design of a bridge. Indeed, the bridge is usually a fairly narrow contraction and the maximum contraction scour depth in this case can be downstream from the bridge site. Based on the flume test observations, the maximum contraction scour generally Z Z V gBunif Fr where Frmax . ( . )= = ( )4 7 111 1 0 5 63 1 1.1 1.2 1.3 1.4 1.5 1.6 1 1.5 2 2.5 3 3.5 4 4.5 B1/B2 B B - max - Measurement B - unif - Measurement B - max - Propose B - unif - Propose 0 50 100 150 200 250 300 -500 0 500 1000 1500 X (mm) Sc ou r D ep th (m m) B2/B1=0.25 B2/B1=0.5 B2/B1=0.75 Figure 7.15. The factor β as a function of the contraction ratio. Figure 7.16. Influence of the contraction ratio on the longitudinal scour profile. Xmax/B2= 2.2519(B2/B1) + 0.1457 R2 = 0.9999 0 0.5 1 1.5 2 2.5 0 0.2 0.4 0.6 0.8 1 B2/B1 Xm ax /B 2 Figure 7.17. Relationship between Xmax and the contraction geometry. occurs close to and behind the opening of the contraction. For the primary tests, the data listed in Tables 7.1 and 7.2 indi- cate that Xmax is mostly controlled by the contracted channel width B2 and the contraction ratio B2/B1. The wider the con- traction opening is, the bigger the Xmax is (Figure 7.16). Fig- ure 7.17 shows the relationship between Xmax/B2 versus B2/B1. By regression, the best-fit equation for Xmax is Equation 7.12 indicates that the location of the maximum depth of contraction scour is independent of the velocity and, therefore, remains constant during the period associated with a hydrograph. This means that an accumulation method such as the SRICOS Method can be used to predict the maximum X B B B max . . ( . ) 2 2 1 2 25 0 15 7 12= +

64 Figure 7.18 indicates that Xmax is at (B2/2)/tanθ if the flow follows the prolongation of the transition sides, but Equation 7.13 shows that the real location of the maximum contraction scour is farther downstream of this estimated point. In summary, if Test 2, the test with the 90-degree transition angle, is selected as the reference case for the transition angle effect, and the correction factors are calculated as the ratios between the value for θ over the value for 90 degrees, the tran- sition angle effect for contraction scour, in three aspects of Zmax, Zunif, and Xmax, is K K K Z Z X θ θ θ θ max max . . . tan . ( . ) = = = +    1 0 1 0 0 48 0 95 7 14 unif X X max max . tan . ( . )θ θ( ) °( ) = + 90 0 4793 0 9475 7 13 θ 0 30 60 90 120 150 0 15 30 45 60 75 90 Zm ax (m m) Transition Angle θ (Degree) 0 0.5 1 -400 0 400 800 1200 1600 Distance X (mm) Re la tiv e Sc ou r D ep th (Z /Zm ax ) Angle=15 Angle=45 Angle=60 Angle=90 Figure 7.18. Flow around contraction inlets. Figure 7.19. Transition angle effect on maximum contraction scour depth. Figure 7.20. Transition angle effect on scour profile and uniform contraction scour. depth of contraction scour after the bridge site has been sub- jected to a long-term hydrograph. 7.8 CORRECTION FACTORS FOR TRANSITION ANGLE AND CONTRACTION LENGTH There are seven secondary tests listed in Table 7.2. Tests 2, 9,10, and 11 are for the transition angle effect, and Tests 2, 12, 13, and 14 are for the contraction length effect. Test 2 is the reference case for both groups and comparisons to Test 2 are used to derive the correction factors for the equations that give Zmax, Zunif, and Xmax. A smooth transition angle is generally built to ease the effect of the approaching flow (Figure 7.18). As can be seen, the approaching flow runs against the abutments and then is guided toward the contracted channel at an angle related to the transition angle θ. The location of the maximum contraction scour depth will be pushed further back from the contraction inlet when the transition angle becomes smoother. Even though the transition angle can change the local flow pattern around the contraction inlet, this influence decreases into the contraction channel where a uniform flow develops. This indicates that the transition angle may affect the maximum contraction scour but not the uniform contraction scour. Figure 7.19 shows the influence of the transition angle θ on the maximum contraction scour depth Zmax. It can be seen that θ does not have a clear impact on Zmax. This observation is con- sistent with Komura’s (1977) observation on sands where he stated that a smooth transition angle was not helpful in reducing the scour depth around the abutment inlets. If Test 10 is ignored due to its odd scour profile, the uniform con- traction scour depth Zunif is practically independent of the tran- sition angle θ (Figure 7.20), as expected. However, the transition angle has a significant impact on the location of the maximum contraction scour Xmax, as shown in Figure 7.21. Regression analysis of the data leads to the following rela- tionship between the Xmax and θ:

Bridge contractions are often short, and the abutments work like a thin wall blocking the flow. The uniform con- traction scour depth cannot develop under these conditions. Instead, two back contraction scour holes behind the con- tracted section can develop (Figure 7.5). Further, as shown in Figure 7.9, when the contraction length is between 6.76B2 and 0.5B2, the maximum depth of contraction scour Zmax and the location of that depth Xmax are unaffected by the length of the contracted channel. If the long contraction channel of Test 2 is chosen as the reference case, the correction factors KL for contraction length are Test 14 has the shortest contraction length with L/B1 = 0.125. The maximum scour depth is 1.79 times the scour depth in Test 2, and Xmax is also multiplied at the same time. This situation is very like the “thin wall” pier scour. There- fore, when L/B2 is smaller than 0.25, it is necessary to increase the predicted Zmax and Xmax values. This case has not been evaluated in this research. 7.9 SRICOS-EFA METHOD USING HEC-RAS GENERATED VELOCITY Equations 7.9 and 7.10, which have been proposed to calcu- late contraction scour depths, have a shortcoming: they are developed from tests in rectangular channels. For channels with irregular cross sections, which is the case in most real situa- tions, some researchers have recommended the use of the flow rate ratio Q1/Q2 instead of the contraction ratio B1/B2 to account for the flow contraction (e.g., Sturm et al., 1997). Here, Q1 is the total flow rate in the approach channel and Q2 is the flow K K void K Z Z X L L L unif max max . . ( . ) = = =    1 0 1 0 7 15 65 rate in the part of the approach channel limited by two lines rep- resenting the extensions of the banks of the contracted channel. The approach recommended here, however, is to replace the nominal velocity V1B1/B2 used in Equations 7.9 and 7.10 by the velocity VHec obtained by using a program like HEC-RAS. With this approach, the complex geometry of the approach channel can be handled by the program, and a more repre- sentative velocity can be used. The problem is to find the proper relationship between the HEC-RAS calculated veloc- ity, VHec, and the nominal velocity V1B1/B2. This was done by conducting a series of HEC-RAS analyses to simulate the flow condition in the flume tests, obtaining the resulting velocity VHec, and correlating it to V1B1/B2. The velocities are listed in Tables 7.1 and 7.2 and the correlation graph is shown in Figure 7.22. Regression analysis gave the following rela- tionship between the two variables: In this figure, the point for Test 1 is still outstanding because of the severe backwater effect during that test, which exhibited an extreme contraction case ((B2/B1) = 0.25). Now, it is possible to rewrite Equations 7.9 and 7.10 using VHec. For maximum contraction scour For uniform contraction scour Z H V gH gnH c unif Hec 1 1 1 2 1 1 31 41 1 57 7 18= −       . . ( . ) τ ρ Z H V gH gnH c max . . ( . ) 1 1 1 2 1 1 31 9 1 49 7 17= −       Hec τ ρ V V B BHec = 1 14 7 161 1 2 . ( . )  y = 0.4621x + 1 R2 = 0.9923 0 0.5 1 1.5 2 2.5 3 0 1 2 3 4 K q Test 10 1/Tan (θ ) y = 1.1352x R2 = 0.8173 30 60 90 120 150 30 60 90 120 150 V1(B1/B2)(cm/s) VH ec (cm /s) Test 1 Figure 7.21. Transition angle effect on the location of the maximum scour depth. Figure 7.22. Relationship between the nominal velocity and the HEC-RAS calculated velocity.

Users of Equations 7.17 and 7.18 should be aware that the velocity VHec also has its limitations. These limitations are tied to the ability of the program HEC-RAS to simulate the flow at the contraction. As an illustration, the water surfaces and velocity distributions measured and predicted by different means along the centerline of the channel are compared for Test 2 in Figure 7.23. As can be seen, the HEC-RAS gener- ated velocity profile cannot give the peak velocity value in the contracted channel. Instead, HEC-RAS gives a step function that parallels the bank contraction profile. 7.10 CONSTRUCTING THE COMPLETE CONTRACTION SCOUR PROFILE Three characteristic dimensions of the contraction scour profile have been determined by the flume tests Zmax, Zunif, and Xmax. Additional information was obtained from the tests in order to develop a procedure to draw the complete contraction scour profile. It was found that the contraction scour hole, much like the pier scour hole, is determined by both the flow 66 0 60 120 180 -1000 -500 0 500 1000 1500 X(mm) W at er S u rfa ce E le va tio n (m m) Before After HEC-RAS 0 30 60 90 -1000 -500 0 500 1000 1500 X(mm) Ve lo ci ty (cm /s) Before After HEC-RAS Nominal A B C D Xmax Zmax Zmax Zunif 3 1 Contraction Original Soil Bed a =Zmax/2 Flow a a Figure 7.24. Generating the complete contraction scour profile. Figure 7.23. Comparison of water depth and velocity between HEC-RAS simulations and measurements for contraction Test 2. and soil strength. In the front part of the scour hole, the flow vortex can generate a steep slope that stresses the soil beyond its shear strength. Therefore, it is the soil strength that controls the front slope of the scour. At the back of the scour hole, the slope is usually gentle and slope stability is not a problem. Based on these and other observations, the following steps are recommended to draw the full contraction scour profile (Figure 7.24): 1. Plot the position of the bridge contraction, especially the start point of the full contraction; 2. Calculate Xmax by Equations 7.13, 7.14, and 7.15, and mark the position where the maximum contraction scour happens in the figure; 3. Calculate Zmax by Equations 7.10, 7.14, and 7.15, draw a horizontal line at this depth and extend it 0.5 Zmax on both sides of the location of Zmax (B and C on Figure 106); 4. Plot A, the starting point of the contraction scour pro- file at a distance equal to Zmax from the starting point of the full contraction; 5. Connect A and B as the slope of the contraction scour profile before the maximum scour; 6. Calculate Zunif by Equations 7.11, 7.14, and 7.15, and draw a line with an upward slope of 1 to 3 from Point C to a depth equal to Zunif (D on Figure 106); Line CD is the transition from the maximum contraction scour depth to the uniform contraction scour depth. 7. Draw a horizontal line downstream from Point D to represent the uniform contraction scour. 7.11 SCOUR DEPTH EQUATIONS FOR CONTRACTION SCOUR The following equations summarize the results obtained in this chapter. Z K K V B B gH gnH H max . . . ( . ) Cont L c ( ) = ×   −         ≥ θ τ ρ 1 90 1 38 0 7 19 1 1 2 1 0 5 1 1 3 1

where Zmax(Cont) is the maximum depth of scour along the centerline of the contracted channel, Zunif (Cont) is the uniform X B K K B B max . . ( . ) 2 2 1 2 25 0 15 7 23= × + θ L Z K K gH gnH H c unif L Hec Cont( ) = × −         ≥ θ τ ρ 1 41 1 57 0 7 22 1 0 5 1 1 3 1 . . ( . ) . Z K K V B B gH gnH H c unif LCont( ) = ×   −         ≥ θ τ ρ 1 41 1 31 0 7 21 1 1 2 1 0 5 1 1 3 1 . . ( . ) . Z K K V gH gnH H c max . . . ( . ) Cont L Hec ( ) = × −         ≥ θ τ ρ 1 90 1 49 0 7 20 1 0 5 1 1 3 1 67 depth of scour along the centerline of the contracted channel, Xmax is the distance from the beginning of the fully contracted section to the location of Zmax, V1 is the mean velocity in the approach channel, VHec is the velocity in the contracted chan- nel given by HEC-RAS, B1 is the width of the approach chan- nel, B2 is the width of the contracted channel, τc is the critical shear stress as given by the EFA, ρ is the mass density of water, n is Manning’s Coefficient, H1 is the water depth in the approach channel, Kθ is the correction factor for the influence of the transition angle as given by Equation 7.24 below, and KL is the correction factor for the influence of the contraction length as given by Equation 7.25 below. K K void K L Z L Z L X max unif max = = =    1 0 1 0 7 25 . . ( . ) K K K θ θ θ θ Z Z X unif max max . . . tan . ( . ) = = = +    1 0 1 0 0 48 0 95 7 24

Next: Chapter 8 - The SRICOS-EFA Method for Initial Scour Rate at Contracted Channels »
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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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