Pier and Contraction Scour in Cohesive Soils (2004)

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

77 stress of the soil obtained in the EFA; ρ 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 Equation 9.1 and Figure 9.1 by using a program like HEC- RAS. In this case, the engineer needs to use Equation 9.3: where VHec is the maximum velocity in the middle of the con- tracted channel (m/s). If the value of the maximum contraction scour Zmax(Cont) is negative, the flow and contraction are not severe enough to cause any contraction scour and the maxi- mum contraction scour is zero. If there is contraction scour, the shear stress reached on the river bottom at the time of maxi- mum contraction scour Zmax(Cont) is the critical shear stress of the soil τc, and scour at the bridge site is as shown in Figure 9.2. Step III: Pier Scour Calculation 1. If Step II leads to no contraction scour, the pier scour is calculated by using the velocity V and water depth H at the location of the pier in the contracted channel assum- ing that the bridge piers are not there. The velocity Vhec and water depth can be calculated directly by using a program like HEC-RAS. 2. If Step II leads to a maximum contraction scour depth Zmax(Cont), then the maximum pier scour depth is cal- culated by using the critical velocity Vc for the soil and the water depth H2, including the contraction scour depth. These are where H1 is the water depth in the contracted channel before contraction scour starts (m). Then, the maximum pier scour depth Zmax(pier) can be cal- culated by using Equation 9.6: where Kw is the correction factor for pier scour water depth, given by For For H B K H B H B K w w ≤ = ( ) > = 1 6 0 85 1 6 1 9 7 0 34 . . . ( . ) . Z K K K Rw sp sh emax .. ( . )Pier( ) = 0 18 9 60 635 V V H gn Z V Z c c = = ( ) > ( ) =    τ ρ 2 1 3 2 0 0 9 5max max ( . )Cont ContHEC H H Z2 1 9 4= + ( )max ( . )Cont Z K K V gH gnH H L c max . . . ( . ) Cont HEC ( ) = × −         ≥ θ τ ρ 1 90 1 49 0 9 3 1 0 5 1 1 3 1 B1 w1 w2 w3 w4 V1 H1 I I (a) Plan View (b) Cross Section at Bridge (I-I) H1 H1 Zmax(Cont) Figure 9.1. Step I—bridge scour input data and primary calculation. Figure 9.2. Step II—contraction scour calculation and distribution. Soil: Critical shear stress and erosion function. All of the parameters are shown in Figure 9.1. Step II: Maximum Contraction Scour Calculation (Figure 9.2) Based on the upstream flow conditions, soil properties, and total bridge contraction ratio calculated in Step I, the maximum contraction scour can be calculated directly by Equation 9.2 as follows: where Zmax(Cont) (m) is the maximum contraction scour; Kθ is the factor for the influence of the transition angle (Kθ is equal to 1); KL is the factor for the influence of the length of the contracted channel (KL is equal to 1); V1 (m/s) is the velocity in the uncontracted channel; B1 (m) is the width of the uncontracted channel B2 (m) is the width of the contracted 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 the uncontracted channel; τc (kN/m2) is the critical shear Z K K V B B gH gnH H L c max . . . ( . ) Cont( ) = ×   −         ≥ θ τ ρ 1 90 1 38 0 9 2 1 1 2 1 0 5 1 1 3 1

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 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: where V is the mean depth average velocity at the location of 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 projected width (Lsinα + Bcosα); B and L are the pier width and length respectively; α is the attack angle; and v is the kinematic viscosity of water. Step IV: Total Maximum Bridge Scour Calculation The maximum bridge scour is (Figure 9.3): Step V: Maximum Shear Stress around the Bridge Pier (Figure 9.4) In the calculations of the initial development of the scour depth, the maximum shear stress τmax is needed. This maxi- mum shear stress is the one that exists around the bridge pier since the pier is the design concern. This step describes how to obtain τmax. Figure 9.4 shows the parameters. In the case of an uncontracted channel (no abutments), the maximum bed shear stress τmax around the pier is given by τ ραmax . log ( . )= −    k k k k V Rew sh sp
0 094 1 1 10 9 111 2 Z Z Zmax max max ( . )= ( ) + ( )Cont Pier 9 10 R VB ve = ′ ( . )9 9 K B B nBsp = −( ) 1 1 9 8( . ) 78 where ρ is the water mass density (kg/m3); V1 is the mean depth velocity in the approach uncontracted channel (m/sec); Re is the Reynolds Number based (V1B/v) where B (m) is the pier diameter or pier projected width; v is the kinematic vis- cosity of the water (m2/s); and kw, ksh, ksp, kα are the correction factors for water depth, shape, pier spacing, and attack angle, respectively. where H is the water depth, B is the pier diameter or projected width, S is the pier center-to-center spacing, L is the pier length, and α is the angle between the direction of the flow and the main direction of the pier. 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 where V2 (m/s) is the mean depth velocity in the contracted channel at the location of the pier without the presence of the pier. The velocity V2 can be obtained from HEC-RAS or from mass conservation for a rectangular channel τ ραmax . log Re ( . )= −    k k k k Vw sh sp 0 094 1 1 10 9 162 2 kα τ τ α = ( ) = + ( )maxmax .deg . ( . )0 1 1 5 90 9 150 57 k e k L B sh sh circle for circular shape = ( ) = + = −τ τ max max . ( . )1 15 7 9 14 1 4 k e S B sp single= ( ) = + −τ τ max max . ( . )1 5 9 131 1 k e H B w deep= ( ) = + −τ τ max max ( . )1 16 9 12 4 Zmax H1 Zmax (Cont) Zmax (Pier) V1 V2 L B2 B1 Figure 9.3. Steps III and IV—calculations of pier scour and superposition. Figure 9.4. Plan view of complex pier scour and contraction scour.

Step VI: Time History of the Bridge Scour This part of the method proceeds like the original SRICOS- EFA Method, which has been described in Step III. The initial shear stress τmax around the pier is calculated from Equation 9.16 and the corresponding initial erosion rate Z˙ i is obtained from the erosion function (measured in the EFA), the maximum scour depth due to contraction scour and pier scour is calculated from Equation 9.10. With these two quan- tities defining the tangent to the origin and the asymptotic value of the scour depth versus time curve, a hyperbola is defined to describe the entire curve: where Z(t) is the scour depth due to a flood; t is the flood duration; Z˙ i is the initial erosion rate; and Zmax is the maxi- mum scour depth due to the flood (Equation 9.10). In the case Z t t Z t Zi ( ) = + 1 9 18 ˙ ( . ) max V V B B2 1 1 2 1 14 9 17=  . ( . ) 79 of a complete hydrograph and of a multilayer soil system, the accumulation algorithms are as follows. Multiflood System The hydrograph of a river indicates how the velocity varies with time. The fundamental basis of the accumulation algorithms is that the velocity histogram is a step function with a constant velocity value for each time step. When this time step is taken as 1 day, the gage station value is constant for that day because only daily records are kept. The case of a sequence of two different constant veloc- ity floods scouring a uniform soil is considered (Figure 9.5). Flood 1 has velocity V1 and lasts time t1 while Flood 2 has a velocity V2 and lasts time t2. After Flood 1, a scour depth Z1 is reached at time t1 (Point A on Figure 9.5b) and can be cal- culated as follows: For Flood 2, the scour depth will be Z t Z t Zi 2 2 2 2 2 1 9 20= + ˙ ( . ) max Z t Z t Zi 1 1 1 1 1 1 9 19= + ˙ ( . ) max Figure 9.5. Scour due to a sequence of two flood events.

The scour depth Z1 also could have been created by Flood 2 in time te (Point B on Figure 9.5c). The time te is called the equivalent time. The time te can be obtained by using Equa- tions 9.19 and 9.20 with Z2 = Z1 and t2 = te. When Flood 2 starts, even though the scour depth Z1 was due to Flood 1 over time t1, the situation is equivalent to hav- ing had Flood 2 for time te. Therefore, when Flood 2 starts, the scour depth versus time curve proceeds from Point B on Figure 9.5c until Point C after time t2. The Z versus t curve for the sequence of Floods 1 and 2 follows the path OA on the curve for Flood 1 then switches to BC on the curve for Flood 2. This is shown as the curve OAC on Figure 9.5d. The procedure described above is for the case of velocity V1 followed by velocity V2 higher than V1. In the opposite case, where V2 is less than V1, Flood 1 creates scour depth Z1 after time t1. This depth is compared with Zmax2 due to Flood 2. If Z1 is larger than Zmax2, it means that, when Flood 2 starts, the scour hole is already deeper than the maximum scour depth that Flood 2 can create. Hence, Flood 2 cannot create any additional scour and the scour depth versus time curve remains flat during Flood 2. If Z1 is less than Zmax2, the pro- cedure of Figure 9.5d should be followed. t t Z Z t Z Z Z e i2 i1 i2 = + −  1 1 1 2 1 1 9 21 ˙ ˙ ˙ ( . ) max max 80 In the general case, the complete velocity hydrograph is divided into a series of partial flood events, each lasting ∆t. The scour depth due to Floods 1 and 2 in the hydrograph will be handled by following the procedure of Figure 9.5d. At this point the situation is reduced to a single Flood 2 that lasts te. Then the process will consider Flood 3 as a “new Flood 2” and will repeat the procedure of Figure 9.5d applied to Flood 2 last- ing te2 and Flood 3. Therefore, the process advances with only two floods to be considered: the previous flood with its equiv- alent time and the “new Flood 2.” The time step ∆t is typically 1 day and the velocity hydrograph can be 70 years long. Multilayer System In the multiflood system analysis, the soil is assumed to be uniform. In reality, the soil involves dif- ferent layers and the layer characteristics can vary signifi- cantly with depth. It is necessary to have an accumulation process that can handle the case of a multilayer system. Con- sider the case of a first layer with a thickness equal to ∆Z1 and a second layer with a thickness equal to ∆Z2. The riverbed is subjected to constant velocity V (Figure 9.6a). The scour depth Z versus time t curves for Layer 1 and Layer 2 are given by Equations 9.19 and 9.20 (Figure 9.6b, Figure 9.6c). If the thickness of Layer 1 ∆Z1 is larger than the maximum scour depth Zmax1, given by Equation 9.10, then the scour process only involves Layer 1. This case is the case of a uni- form soil. On the other hand, if the maximum scour depth Zmax1 exceeds the thickness ∆Z1, then Layer 2 will also be Figure 9.6. Scour of a two-layer soil system.

involved in the scour process. In this case, the scour depth ∆Z1 (Point A on Figure 9.6b) in Layer 1 is reached after time t1; at that time, the situation is equivalent to having had Layer 2 scoured over an equivalent time te (Point B on Figure 9.6c). Therefore, when Layer 2 starts to be eroded, the scour depth versus time curve proceeds from Point B to Point C on Fig- ure 9.6c. The combined scour process for the two-layer sys- tem corresponds to the path OAC on Figure 9.6d. In reality, there may be a series of soil layers with differ- ent erosion functions. The computations proceed by stepping forward in time. The time steps are ∆t long, the velocity is the one for the corresponding flood event, and the erosion function (z˙ versus τ) is the one for the soil layer correspond- ing to the current scour depth (bottom of the scour hole). When ∆t is such that the scour depth enters a new soil layer, the computations follow the process described in Figure 9.6d. 9.4 INPUT FOR THE SRICOS-EFA PROGRAM The input includes parameters for the soil, water, and geometry of the problem. Soil Properties In the SRICOS-EFA Method, the soil properties at the bridge site are represented by the soil erosion function, which is a measure of the erodibility of the soil. The soil erosion function is the relationship between the erosion rate z˙ of the soil and the hydraulic shear stress τ applied on the bottom of riverbed. It is obtained by performing an EFA test on the soil sample (Briaud et al., 2002). The erosion function (Figure 9.7) is needed for each layer within the potential scour depth at the bridge site. Hydrologic Data The water flow is represented by the velocity hydrograph. This hydrograph can be obtained from a nearby gage station. The hydrograph should last as long as the required period of prediction. Furthermore, if the hydrograph obtained from the gage station does not contain a 100-year flood, it can be spiked artificially to include such a large event if required by design. The hydrograph is typically in the form of discharge as a func- 81 tion of time. Because the input for scour calculations is the velocity and not the discharge, it is necessary to transform the discharge data at the gage station into velocity data at the bridge site. This can be done by using a program such as HEC- RAS (Hydrologic Engineering Center—River Analysis Sys- tem, HEC-RAS, 1997), which was developed by the U.S. Army Corps of Engineers. In order to run HEC-RAS, several geographic features are necessary, such as the average slope of the channel bed, the channel cross section, and the roughness coefficient of the riverbed. Figure 9.8 shows the discharge hydrograph, the discharge versus velocity curve (HEC-RAS results), and the mean depth velocity at one of the piers ver- sus time (velocity hydrograph) for the Woodrow Wilson Bridge on the Potomac River in Washington D.C. between 1960 and 1998. Geometry The geometry includes channel geometry and bridge geom- etry. The channel and bridge geometry are used for contrac- tion scour evaluation, including the determination of the con- traction ratio. The pier’s size, shape, spacing, and angle of attack are used for pier scour calculations. Table 9.1 elaborates on aspects of geometry. 9.5 THE SRICOS-EFA PROGRAM The SRICOS-EFA program automates the SRICOS-EFA Method. The first version of the program was solving the problem of a cylindrical pier in deep water (Kwak, 1999; Kwak et al., 2001). In this study the program was extended to predict complex pier scour and contraction including the superposition of both scour modes. Using the input described in the previous section, the program automates the calcula- tions of all of the parameters: transformation of discharge into velocities, maximum shear stress, initial slope of the scour rate versus shear stress curve, maximum scour depth, and so on. Then, it proceeds with the techniques described to handle multiflood and multilayer systems. The program was written in FORTRAN by using Visual FORTRAN 5.0. The flow chart of the program in Figure 9.9 gives an overall view of the SRICOS-EFA Method, includ- ing all of the equations. As can be seen, there is one branch to handle complex pier scour alone, one branch to handle contraction scour alone, and one branch to handle the con- current occurrence of complex pier scour and contraction scour. The SRICOS-EFA program is a user-friendly, inter- active code that guides the user through a step-by-step data input procedure except for velocity or discharge data. This program, however, is not in the Windows™ environment and needs to be implemented in such an environment for easier use. For the hydrograph, the number of velocity or discharge data points can be at least several tens of thousands for the time duration corresponding to the design life of bridges and if the velocity data is given on a daily basis. The velocity or discharge data should be prepared in the format of an ASCII file or a text document before running the program. The input Shear Stress (N/m2) 0 10 20 30 40 50 60 70 80 Sc o u r R a te (m m /h r) 0 5 10 15 20 τc = 7 N/m2 Figure 9.7. Typical EFA test result.

W o o d r o w W ils o n B r id g e H y d r o g r a p h y (fr o m 1 9 6 0 to 1 9 9 8 ) 0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 1 2 0 0 0 1 9 6 0 1 9 6 3 1 9 6 6 1 9 6 9 1 9 7 2 1 9 7 5 1 9 7 8 1 9 8 1 1 9 8 4 1 9 8 7 1 9 9 0 1 9 9 3 1 9 9 6 1 9 9 9 Y e a r D isc ha rg e (m 3 /s ec ) R e la tio ns hip o f D is c ha rg e a nd V e lo c ity (W o o do w W ils o n B ridg e a t Pie r 1 E ) 0 .0 0 0 .5 0 1 .0 0 1 .5 0 2 .0 0 2 .5 0 3 .0 0 3 .5 0 4 .0 0 0 5 0 0 0 1 0 0 0 0 1 5 0 0 0 2 0 0 0 0 2 5 0 0 0 D i s c har g e (m 3 /s ) V el o c it y (m /s ec ) W o o d ro w W ils o n B r id g e F lo w V e lo c ity C h a rt (fro m 1 9 6 0 to 1 9 9 8 ) 0 0 .5 1 1 .5 2 2 .5 3 1 9 6 0 1 9 6 3 1 9 6 6 1 9 6 8 1 9 7 1 1 9 7 4 1 9 7 7 1 9 8 0 1 9 8 3 1 9 8 5 1 9 8 8 1 9 9 1 1 9 9 4 1 9 9 7 Y e a r V el oc ity (m /se c) Bridge Geometric Factors Channel Geometric Factors Bridge contraction ratio Channel contraction ratio Bridge opening Bridge contraction length Channel contraction length Type, shape Attack angle Channel water depth Size, length, width (diameter) Manning coefficient Pier spacing Channel hydraulic radius Bridge piers Number of piers Channel characteristics Soil stratigraphy TABLE 9.1 Summary of geometry factors Figure 9.8. Example of hydrograph transformation for Pier 1E of the Woodrow Wilson Bridge on the Potomac River in Washington, D.C.

83 Figure 9.9. Flow chart of the SRICOS-EFA Program.

data can be either in the metric system or U.S. customary sys- tem; the output also can be in either system. The User’s Man- ual for SRICOS-EFA is presented in Appendix D of the research team’s final report, which is available from NCHRP. 9.6 OUTPUT OF THE SRICOS-EFA PROGRAM Once the program finishes all of the computations success- fully, the output file is created automatically. The output file includes the following columns: time, flow velocity, water depth, shear stress, maximum scour depth (pier, contraction, or total), and instantaneous scour depth (pier, contraction, or total). The first few days of a typical output file of the program are shown in Table 9.2. For this example, the critical shear stress was 4 N/m2; as can be seen, no scour occurred until the velocity was high enough to overcome the critical shear stress on day 11. The format of the output file is a text file. This file can be used to plot a number of figures (Figure 9.10). The most commonly plotted curves are water velocity versus time, water depth versus time, shear stress versus time, and scour depth ver- sus time. The scour depth versus time curve indicates whether the final scour depth Zfinal (scour depth at the end of the hydro- graph) is close to the maximum scour depth for the biggest flood in the hydrograph Zmax or not. Typically, in sand the answer is yes, but in low erodibility clays the difference is sig- nificant enough to warrant the analysis in the first place. Kwak et al. (2001) showed the results of a parametric analysis indi- cating the most important parameters in the prediction process. 84 Woodrow Wilson Bridge Flow Velocity Chart (from 1960 to 1998) 0 0.5 1 1.5 2 2.5 3 19601963196619681971197419771980198319851988199119941997 Year V el oc ity (m /se c) Scour Depth Vs Time 0 1000 2000 3000 4000 5000 6000 7000 1960 1965 1970 1975 1980 1985 1990 1995 Time (year) Sc ou r D ep th (m m) TABLE 9.2 Example of SRICOS-EFA Program output file Figure 9.10. Example of plots generated from SRICOS- EFA output.