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76 CHAPTER 9 THE SRICOS-EFA METHOD FOR COMPLEX PIER SCOUR AND CONTRACTION SCOUR IN COHESIVE SOILS 9.1 BACKGROUND the piers is necessary because the velocity used for pier scour calculations is the mean depth velocity at the loca- The SRICOS-EFA method for complex pier and contraction tion of the pier if the pier were not there. scour can be used to handle the complex pier problem alone or 2. If the calculations indicate that contraction scour occurs contraction scour alone. It also can handle the combined case at the bridge site, then the pier scour calculations are of complex pier scour and contraction scour (integrated made using the critical velocity, not the actual velocity, SRICOS-EFA Method). Abutment scour is not included in because when contraction scour has stopped (Zmax(Cont) this project but will be added later. A method exists in HEC-18 is reached), the velocity in the contracted section is the to predict bridge scour under the combined influence of con- critical velocity Vc. The value of Vc can be obtained traction scour, pier scour, and abutment scour. This method from the EFA tests for cohesive soils or from the consists of calculating the individual scour depths indepen- equations presented in HEC-18 for cohesionless soils. dently and simply adding them up. Engineers have often stated The water depth for the pier scour calculations is the that the results obtained in such a way are too conservative. The water depth in the contracted section after the contrac- integrated SRICOS-EFA Method is not just adding the com- tion scour has occurred. The bottom profile of the river plex pier scour and the contraction scour. The method consid- after scour has occurred is obtained by adding the con- ers the time factor, soil properties and--most importantly--the traction scour and the pier scour. interaction between the contraction scour and the pier scour. In the following sections, the principle, accumulation algorithm, This approach is valid for the maximum scour depth cal- and step-by-step procedure for the integrated SRICOS-EFA culations. For the time stepping process, the maximum scour Method are presented. depth is not reached at each step but the maximum scour depth is calculated as part of each step and used to calculate 9.2 THE INTEGRATED SRICOS-EFA METHOD: the partial scour depth. Therefore, the above technique is GENERAL PRINCIPLE included in each time step. The other parameter calculated at each time step is the initial maximum shear stress; this shear In the integrated SRICOS-EFA Method for calculating stress is used to read the initial scour rate on the erosion func- bridge scour, the scour process is separated into two steps: tion obtained from the EFA tests. Both parameters, Zmax and (1) calculation of the total contraction scour and (2) calcula- Z i, are used to generate the scour depth versus time curve and tion of pier scour. The contraction scour is assumed to happen the actual scour depth is read on that curve at the value equal first and without considering pier scour. This does not mean to the time step. The details of that procedure are presented that the piers are not influencing the contraction scour; indeed in the next section. the piers are considered in the contraction scour calculations because their total projection width is added to the abutment 9.3 THE INTEGRATED SRICOS-EFA METHOD: projection width to calculate the total contraction ratio. The STEP-BY-STEP PROCEDURE contraction scour is calculated in this fashion for a given hydrograph. Then, the pier scour is calculated. There are two Step I: Input Data Collection (Figure 9.1) options for the pier scour calculations as follows: Water: Flow (mean velocity V1, and 1. If the contraction scour calculations indicate that there water depth H1) upstream of the is no contraction scour at the bridge site, then the pier bridge where the flow is no notice- scour is calculated by following the SRICOS-EFA com- ably influenced by the existence plex pier scour calculation procedure. In this case, HEC- of bridge contraction and piers. RAS, for example, can be used to calculate the water Geometry: Bridge contraction parameters and depth and the velocity in the contracted section after pier geometry. removing the piers obstructing the flow. The removal of Total Contraction Ratio: B2/B1 = (w1+w2+w3+w4)/B1 (9.1)

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77 V1 H1 stress of the soil obtained in the EFA; is the mass density of water (kg/m3); and n is Manning's Coefficient (s/m1/3). The engineers may prefer to calculate the velocity Vhec in the contracted channel with a width B2 as calculated according to I w1 w2 w3 w4 I Equation 9.1 and Figure 9.1 by using a program like HEC- B1 RAS. In this case, the engineer needs to use Equation 9.3: (a) Plan View Zmax (Cont ) = K K L 1.90 c 0.5 1.49VHEC H1 - H1 0 (9.3) gH1 gnH11 3 (b) Cross Section at Bridge (I-I) where VHec is the maximum velocity in the middle of the con- Figure 9.1. Step I--bridge scour input data and primary tracted channel (m/s). If the value of the maximum contraction calculation. scour Zmax(Cont) is negative, the flow and contraction are not severe enough to cause any contraction scour and the maxi- Soil: Critical shear stress and erosion mum contraction scour is zero. If there is contraction scour, the function. shear stress reached on the river bottom at the time of maxi- mum contraction scour Zmax(Cont) is the critical shear stress of All of the parameters are shown in Figure 9.1. the soil c, and scour at the bridge site is as shown in Figure 9.2. Step II: Maximum Contraction Scour Calculation (Figure 9.2) Step III: Pier Scour Calculation Based on the upstream flow conditions, soil properties, 1. If Step II leads to no contraction scour, the pier scour is and total bridge contraction ratio calculated in Step I, the calculated by using the velocity V and water depth H at maximum contraction scour can be calculated directly by the location of the pier in the contracted channel assum- Equation 9.2 as follows: ing that the bridge piers are not there. The velocity Vhec and water depth can be calculated directly by using a Zmax (Cont ) = K K L 1.90 program like HEC-RAS. 2. If Step II leads to a maximum contraction scour depth 0.5 Zmax(Cont), then the maximum pier scour depth is cal- 1.38 V1 1 c B B2 culated by using the critical velocity Vc for the soil and - H1 0 (9.2) the water depth H2, including the contraction scour gH1 gnH11 3 depth. These are where Zmax(Cont) (m) is the maximum contraction scour; K H2 = H1 + Zmax (Cont ) (9.4) is the factor for the influence of the transition angle (K is equal to 1); KL is the factor for the influence of the length of 1 V = c H2 3 the contracted channel (KL is equal to 1); V1 (m/s) is the V= c Zmax (Cont ) > 0 (9.5) velocity in the uncontracted channel; B1 (m) is the width of gn 2 the uncontracted channel B2 (m) is the width of the contracted HEC V Zmax (Cont ) = 0 channel as defined in Equation 9.1 and Figure 9.1; g (m/s2) is the acceleration due to gravity; H1 (m) is the water depth in where H1 is the water depth in the contracted channel before the uncontracted channel; c (kN/m2) is the critical shear contraction scour starts (m). Then, the maximum pier scour depth Zmax(pier) can be cal- culated by using Equation 9.6: Zmax ( Pier ) = 0.18 K w K sp K sh Re0.635 (9.6) H1 where Kw is the correction factor for pier scour water depth, Zmax(Cont) given by Figure 9.2. Step II--contraction scour calculation and For H B 1.6 K w = 0.85( H B)0.34 distribution. For H B > 1.6 Kw = 1 (9.7)

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78 Ksp is the correction factor for the pier spacing effect on the pier scour depth, when n piers of diameter B are installed in a row, given by B1 Ksp = (9.8) ( B1 - nB) V1 V2 B1 B2 Ksh is the correction factor for pier shape effect on pier scour. Ksh is equal to 1.1 for rectangular piers with length to width ratios larger than 1. Re is the Reynolds Number: L Re = VB v (9.9) Figure 9.4. Plan view of complex pier scour and where V is the mean depth average velocity at the location of contraction scour. the pier if the pier is not there when there is no contraction scour, or the critical velocity Vc (Equation 9.5) of the bed material if contraction scour occurs; B is the pier diameter or where is the water mass density (kg/m3); V1 is the mean projected width (Lsin + Bcos); B and L are the pier width depth velocity in the approach uncontracted channel (m/sec); and length respectively; is the attack angle; and v is the Re is the Reynolds Number based (V1B/v) where B (m) is the kinematic viscosity of water. pier diameter or pier projected width; v is the kinematic vis- cosity of the water (m2/s); and kw, ksh, ksp, k are the correction factors for water depth, shape, pier spacing, and attack angle, Step IV: Total Maximum respectively. Bridge Scour Calculation max - 4H kw = = 1 + 16e B (9.12) The maximum bridge scour is (Figure 9.3): max (deep) Zmax = Zmax (Cont ) + Zmax ( Pier ) (9.10) max -1.1 S ksp = = 1 + 5e B (9.13) max (single) Step V: Maximum Shear Stress max -4 L ksh = = 1.15 + 7e B (9.14) around the Bridge Pier (Figure 9.4) max (circle) In the calculations of the initial development of the scour ksh = 1 for circular shape depth, the maximum shear stress max is needed. This maxi- max ( ) 0.57 mum shear stress is the one that exists around the bridge pier k = = 1 + 1.5 (9.15) since the pier is the design concern. This step describes how max (0 deg) 90 to obtain max. Figure 9.4 shows the parameters. In the case of an uncontracted channel (no abutments), the where H is the water depth, B is the pier diameter or projected maximum bed shear stress max around the pier is given by width, S is the pier center-to-center spacing, L is the pier length, and is the angle between the direction of the flow and the main direction of the pier. max = kw ksh ksp k 0.094V12 - 1 1 (9.11) log Re 10 In the case of a contracted channel (Figure 9.4), the max- imum bed shear stress around the pier is given by Equation (9.11), except that the velocity in the contracted section V2 is used instead of the approach velocity V1. The equation is max = kw ksh ksp k 0.094 V22 - 1 1 (9.16) H1 log Re 10 Zmax Zmax (Cont) Zmax (Pier) where V2 (m/s) is the mean depth velocity in the contracted channel at the location of the pier without the presence of the Figure 9.3. Steps III and IV--calculations of pier scour pier. The velocity V2 can be obtained from HEC-RAS or from and superposition. mass conservation for a rectangular channel

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79 of a complete hydrograph and of a multilayer soil system, the V2 = 1.14V1 1 B (9.17) accumulation algorithms are as follows. B2 Multiflood System The hydrograph of a river indicates how the velocity varies with time. The fundamental basis of Step VI: Time History of the Bridge Scour the accumulation algorithms is that the velocity histogram is This part of the method proceeds like the original SRICOS- a step function with a constant velocity value for each time EFA Method, which has been described in Step III. The step. When this time step is taken as 1 day, the gage station initial shear stress max around the pier is calculated from value is constant for that day because only daily records are Equation 9.16 and the corresponding initial erosion rate Z i is kept. The case of a sequence of two different constant veloc- obtained from the erosion function (measured in the EFA), ity floods scouring a uniform soil is considered (Figure 9.5). the maximum scour depth due to contraction scour and pier Flood 1 has velocity V1 and lasts time t1 while Flood 2 has a scour is calculated from Equation 9.10. With these two quan- velocity V2 and lasts time t2. After Flood 1, a scour depth Z1 tities defining the tangent to the origin and the asymptotic is reached at time t1 (Point A on Figure 9.5b) and can be cal- value of the scour depth versus time curve, a hyperbola is culated as follows: defined to describe the entire curve: t1 Z1 = (9.19) 1 t t + 1 Z (t ) = (9.18) Z i1 Zmax 1 1 t + Zi Zmax For Flood 2, the scour depth will be where Z(t) is the scour depth due to a flood; t is the flood t2 i is the initial erosion rate; and Zmax is the maxi- Z2 = (9.20) duration; Z 1 t2 mum scour depth due to the flood (Equation 9.10). In the case i 2 + Zmax 2 Z Figure 9.5. Scour due to a sequence of two flood events.

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80 The scour depth Z1 also could have been created by Flood In the general case, the complete velocity hydrograph is 2 in time te (Point B on Figure 9.5c). The time te is called the divided into a series of partial flood events, each lasting t. The equivalent time. The time te can be obtained by using Equa- scour depth due to Floods 1 and 2 in the hydrograph will be tions 9.19 and 9.20 with Z2 = Z1 and t2 = te. handled by following the procedure of Figure 9.5d. At this point the situation is reduced to a single Flood 2 that lasts te. t1 Then the process will consider Flood 3 as a "new Flood 2" and te = (9.21) Zi2 1 1 will repeat the procedure of Figure 9.5d applied to Flood 2 last- i1 + t1 Zi2 Zmax 1 - Zmax 2 Z ing te2 and Flood 3. Therefore, the process advances with only two floods to be considered: the previous flood with its equiv- When Flood 2 starts, even though the scour depth Z1 was alent time and the "new Flood 2." The time step t is typically due to Flood 1 over time t1, the situation is equivalent to hav- 1 day and the velocity hydrograph can be 70 years long. ing had Flood 2 for time te. Therefore, when Flood 2 starts, the scour depth versus time curve proceeds from Point B on Multilayer System In the multiflood system analysis, the Figure 9.5c until Point C after time t2. The Z versus t curve soil is assumed to be uniform. In reality, the soil involves dif- for the sequence of Floods 1 and 2 follows the path OA on ferent layers and the layer characteristics can vary signifi- the curve for Flood 1 then switches to BC on the curve for cantly with depth. It is necessary to have an accumulation Flood 2. This is shown as the curve OAC on Figure 9.5d. process that can handle the case of a multilayer system. Con- The procedure described above is for the case of velocity sider the case of a first layer with a thickness equal to Z1 and V1 followed by velocity V2 higher than V1. In the opposite a second layer with a thickness equal to Z2. The riverbed is case, where V2 is less than V1, Flood 1 creates scour depth Z1 subjected to constant velocity V (Figure 9.6a). The scour after time t1. This depth is compared with Zmax2 due to Flood depth Z versus time t curves for Layer 1 and Layer 2 are 2. If Z1 is larger than Zmax2, it means that, when Flood 2 starts, given by Equations 9.19 and 9.20 (Figure 9.6b, Figure 9.6c). the scour hole is already deeper than the maximum scour If the thickness of Layer 1 Z1 is larger than the maximum depth that Flood 2 can create. Hence, Flood 2 cannot create scour depth Zmax1, given by Equation 9.10, then the scour any additional scour and the scour depth versus time curve process only involves Layer 1. This case is the case of a uni- remains flat during Flood 2. If Z1 is less than Zmax2, the pro- form soil. On the other hand, if the maximum scour depth cedure of Figure 9.5d should be followed. Zmax1 exceeds the thickness Z1, then Layer 2 will also be Figure 9.6. Scour of a two-layer soil system.