Combining Individual Scour Components to Determine Total Scour (2018)

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

203 CHAPTER 5. Methodology for Scour Depth Prediction 5.1 Introduction Applications of the findings of the research are summarized in this chapter. First, the set of new equations for estimation of scour depths, in situations where interaction among different scour types occurs, is presented along with a listing and definitions of the variables needed to apply the equations. Secondly, a flow chart summarizing the steps involved in applying the equations is given and thirdly, examples of application of the method are given. This chapter features repetition of some material from earlier in the report. This is deliberate, in order that Chapter 5 can stand alone. The experimental and CFD results supporting the proposed scour prediction methodology are contained in Chapter 4. 5.2 Methodology The proposed methodology is described in this section. It is developed to replace Step 3 (“Compute the magnitude of contraction scour”) and Step 5 (“Determine the foundation elevation for abutments”) in HEC-18, Section 2.4: “Detailed procedure and specific design approach”. The equations which are the basis of the methodology are listed in Table 5-1.

204 Table 5-1. Summary of proposed combined scour equations. Category Model Components Included Applicability I Abutment/contraction scour is given by: 8)-(4 ***363.2 2/1 1 1 1 2 2/3 1max2         fc f f f fo f fo f V V q q Y Y Y Y A, L, V Applicable for STA and WWA, LSA II Abutment/contraction scour is given by: 10)-(4 **725.1 2/1 1 1 1 2max2     mc m m m mo m V V q q Y Y A, L, V Applicable for STA and WWA, BLA/SSA IIIa Pier scour as affected by abutment/contraction scour is given by Eq. (4-12) (see Note 2 below): 5.73***906.1 1 2/1 1 1 1 2 2/3 1max2            f p fc f f f fo f excessfo f Y L For V V q q Y Y Y Y P, A, L, V Applicable for STA and WWA, LSA with rectangular and wall piers IIIb Pier scour as affected by abutment/contraction scour is given by Eq. (4-13) (see Note 2 below): 117.5or 3 ***283.1 1 1 2/1 1 1 1 2 2/3 1max2             f p f p fc f f f fo f excessfo f Y L Y L For V V q q Y Y Y Y P, A, L, V Applicable for STA and WWA, LSA with rectangular and wall piers IVa Pier scour is given by the equations in HEC-18, i.e. Eqs. (2-35) and (2-36) for Lp/Yf1>11 (see Note 3 below) P Applicable for piers in free surface flow, in the absence of abutment and lateral contraction scour IVb Pier scour is given by the equations in HEC-18, i.e. Eqs. (2-35) and 2-36 for Lp/Yf1>11 (see Note 3 below) Vertical contraction scour is given by Eq. (2-27) (see Note 4) P,V Applicable for piers in submerged orifice or overtopping flow, in the absence of abutment and lateral contraction scour

205 Table 5-1, continued Notes: 1. A= abutment scour, L= lateral contraction scour, V= vertical contraction scour, P= pier scour, WWA = wingwall abutment, STA = spill-through abutment, LSA = long setback abutment, I = interactive abutment and contraction scour in floodplain, II = interactive abutment and contraction scour in main channel, III = interactive abutment, contraction, and pier scour in floodplain, IV = interactive pier and vertical contraction scour. 2. Excess pier scour from Eq. (4-12) is 0.80 times maximum abutment/contraction scour for Category I given by Eq. (4-8), and the factor for excess pier scour from Eq. (4-13) is 0.54 times maximum abutment/contraction scour given by Eq. (4-8). Because no experiments were conducted with piers in the main channel, it is assumed, pending further experiments, that the same factors of 0.80 and 0.54 can be applied to the Category II abutment/contraction scour given by Eq. (4-10) to obtain excess pier scour. 3. For multi-span bridges featuring piers, pier scour is given by either of the methods recommended in HEC-18, i.e. the CSU equation or the Sheppard-Melville equation (FDOT equation), unless the pier is within the zone of influence of the abutment/ contraction scour hole. 4. For cases where the bridge deck is partially or fully submerged (submerged orifice flow or overtopping flow), vertical contraction scour is given by Eq. (2-27) with A1 = 0.21 and A2 = 0.6. 5. Eq. (4-10) for Category II scour applies to both CWS and LBS with Vm1/Vmc1 set to 1.0 for LBS. The variables in the equations are defined below and shown in Figure 5-1. Bf = approach flow floodplain width; La = length of the approach road embankment to the abutment toe perpendicular to the stream; Lp = distance from the toe of the abutment to the centerline of the pier; Yfo = tail water depth on the floodplain; Yf1 = initial approach flow depth in the floodplain; Ym1 = initial approach flow depth in the main channel; qf1 = average flow rate per unit width in floodplain at approach flow section; qf2 = average flow rate per unit width in floodplain at bridge section; qm1 = average flow rate per unit width in main channel at approach flow section; qm2 = average flow rate per unit width in main channel at bridge section; Vb = average flow velocity at bridge section prior to scour for submerged orifice or overtopping flow; Vf1 and Vm1 = approach flow floodplain and main channel flow velocities, respectively; Vfc1 and Vmc1 = approach flow floodplain and main channel critical velocities, respectively. W.S. Elev. = reference tailwater water surface elevation; Gr. Elev. = ground elevation at pier or abutment toe before scour;

206 Min. Elev. = minimum elevation at bottom of scour hole; ds = scour depth below original ground elevation; Yf2max = depth below water surface (W.S. Elev.) to bottom of scour hole. Figure 5-1. Definition sketch for abutment scour in a compound channel 5.3 Flow Chart For the purposes of scour prediction, the various components of scour are combined in four main categories of interaction and identified as Categories I, II, III, and IV: Category I. Abutment/Lateral Contraction Scour with or without Vertical Contraction Scour for long setback abutments (LSA): combination of local scour around the abutment induced by the turbulent structure of the flow and acceleration of the flow resulting from the width constriction offered by the bridge opening for free flow around LSA with or without vertical contraction scour in submerged orifice and overtopping flows; Lb W LpVf2, qf2 V f1, q f1 La V m1, q m1 Vm2, qm2 Bf BmMain-channel Flood -plain h b Y f1 Y m1 YfoYf2max V p Approach Bridge Main - channel Flood -plain Flood -plain Section A-A Plan Gr. Elev. Min. Elev. ds W.S. Elev.

207 Category II. Abutment/Lateral Contraction Scour with or without Vertical Contraction Scour for short setback (SSA) and bankline BLA) abutments: same combination as Category I, but for SSA and BLA; Category III. Abutment/Lateral Contraction Scour with or without Vertical Contraction Scour for LSA with pier scour in free surface, submerged orifice or overtopping flow; Category IV. Vertical Contraction Scour and Pier Scour in the floodplain outside the zone of influence of the abutment scour hole. As described in more detail below, Category III is sub-divided into Categories IIIa and IIIb, depending on the position of a pier with respect to the abutment/contraction scour hole. Similarly, Category IV is sub-divided into Categories IVa and IVb, depending on whether the flow is free flow (IVa) or submerged orifice or overtopping flow (IVb). The steps to execute the method are shown in the flow chart in Figure 5-2. Step 1 is to classify the bridge crossing into Category I or Category II scour: long setback abutments (LSA); or short setback abutments (SSA) and bankline abutments (BLA). Long setback abutments are defined as those for which the abutment scour hole is located wholly in the floodplain rather than the main channel. Conversely, short setback abutments feature the deepest point of the abutment scour hole intruding into the main channel from the floodplain. Bankline abutments also have the scour hole in the main channel but with possible migration into the bank of the main channel immediately downstream of the abutment. The parameter given in Step 1 is used to distinguish LSA cases from SSA/BLA cases. Step 2 involves calculating the combined abutment/contraction scour. Eq. (4-8) is applied for Category I and Eq. (4-10) is applied for Category II scour. These two equations include vertical contraction scour for submerged orifice and overtopping flows. In Step 3, it is necessary to distinguish between single-span bridges (that is, bridges with no piers in the bridge flow section) and multi-span bridges having piers in the bridge flow section. For single-span bridges, the total abutment/lateral contraction scour is the scour calculated in Step 2 and the calculation procedure terminates. For multi-span bridges, the parameter evaluated in Step 4 is used to determine the lateral position of the pier(s) relative to the toe of the abutment. The pier position is necessary to determine the extent of the influence of the abutment/lateral contraction scour hole on maximum pier scour at the upstream face of the pier. The component scour depths are determined in Step 5. There are four possible cases (IIIa, IIIb, IVa and IVb:

208 1. Scour Category IIIa, where the pier is situated in the zone of influence of the abutment/lateral contraction scour hole. The total pier scour is the sum of the normal pier scour plus the pier scour excess calculated by Eq. (4-12) in Scour Category IIIa. 2. Scour Category IIIb, where the pier is also in the zone of influence of the lateral/abutment scour but with less impact than for Category IIIa. The total pier scour is the sum of the normal pier scour plus the pier scour excess calculated by Eq. (4-13) in Scour Category IIIb. 3. Scour category IVa, which is scour at an isolated pier in free surface flow. 4. Scour category IVb, which is scour at an isolated pier in submerged orifice or overtopping flow with vertical contraction scour. Finally, the total scour at piers and abutments (including lateral contraction scour) is calculated in Step 6. The maximum abutment/contraction scour calculated in Step 2 remains unchanged by the piers. Illustrations of the four scour categories are given in Figures 5-3, 5-4, and 5-5 in the form of measured scour contours in specific GT experiments. These are plan views with flow from left to right. In Figure 5-3, the Category I scour hole for a LSA can be observed across from the face of the left abutment while Category II scour is evident for the right abutment which is a BLA. The maximum scour hole depth in the Category II scour hole is in the bed of the main channel downstream of the bridge, but the scour hole extends laterally across the right bank of the main channel into the downstream floodplain. Category III scour is illustrated in Figure 5-4. Excess pier scour due to the influence of the abutment/contraction scour hole is Category IIIb with Lp/Yf1 < 3 as shown in Figure 5-4(a), while it is Category IIIa with 3< Lp/Yf1 < 7.5 as shown in Figure 5-4 (b). Category IVa scour is shown in Figure 5-5 (a) for the set of piers furthest from the left abutment in free flow. In this case, the pier scour is isolated with no other components. In Figure 5-5 (b), Category IVb scour is shown for the piers in submerged orifice flow with only the bridge deck in place without the embankments. In this case, both pier scour and vertical contraction scour are present.

209 Scour Category I: Calculate  abutment/contraction scour using  Eq. (4‐8)  Scour Category II: Calculate  abutment/contraction scour using  Eq. (4‐10)  Does the bridge include  piers?  Yes  Scour Category IIIa:   (1) Calculate pier scour alone &  pier scour excess using Eq. (4‐12)  if Step 2 is Category I  (2) Calculate pier scour alone &  pier scour excess as 0.8×Eq. (4‐ 10) if Step 2 is Category II Scour Category IVa  (Free flow)  Calculate pier scour  Scour Category IVb  (Submerged Orifice or  Overtopping flow)  Calculate pier scour and  vertical contraction scour Total pier scour = pier scour +  pier scour excess  Total abutment/contraction  scour given by Eq. (4‐8) for  Category I and Eq. (4‐10) for  Category II  Total scour =  pier scour  Total pier scour =  pier scour +  vertical  contraction scour  No  Total scour =  abutment/contraction scour  given in Step 2  Scour Category IIIb:   (1) Calculate pier scour alone &  pier scour excess using Eq. (4‐13)  if Step 2 is Category I  (2) Calculate pier scour alone &  pier scour excess as 0.54×Eq. (4‐ 10) if Step 2 is Category II Step 1  Step 2  Step 3  Step 6  Step 4  Step 5  Figure 5-2. Flow chart demonstrating the methodology.

210 -6 -4 -2 0 2 4 x (ft) 14 12 10 8 6 4 2 0 y (ft ) Figure 5-3. The upper abutment is Category I (abutment/lateral contraction scour for long setback abutment); the lower abutment is Category II (abutment/lateral contraction scour for short setback abutment), flow from left to right, Run 1. (a) (b) Figure 5-4. (a) The pier scour is Category IIIb (pier scour is affected by the abutment/ contraction scour with Lp/Yf1 = 1.8, Run 7 (OT flow); (b) the pier is Category IIIa (pier scour is affected by the abutment/contraction scour with Lp/Yf1 = 3.7, Run 9 (OT flow); flow from left to right. -6 -4 -2 0 2 4 x (ft) 14 12 10 8 6 4 2 0 y (ft ) -6 -4 -2 0 2 4 x (ft) 14 12 10 8 6 4 2 0 y (ft )

211 (a) (b) Figure 5-5. (a) Category IVa (pier scour alone, Run 43); (b) Category IVb (pier scour plus vertical contraction scour, Run 37); flow is from left to right. 5.4 Combined Scour Example Problem A comprehensive example of application of the proposed scour prediction equations is given below. The example cross-section has been used by Sturm (2009) to illustrate backwater computations with HEC-RAS (HEC 2016), and it is adapted here to illustrate how to obtain variables needed for bridge scour computations. 5.4.1 Problem Statement A multi-span bridge with a length of 230 ft (70 m) between abutments is planned for a highway crossing of Flat Creek. The abutment is spill-through with an embankment having 2:1 side slopes and a top width of 40 ft (12.2 m). The elevation of the top of the bridge deck is 31.0 ft (9.45 m), and the low chord elevation of the bridge is 28.0 ft (8.53 m). The bed sediment is a relatively uniform medium sand having a median sieve diameter of 2.0 mm. The bridge cross-section is depicted in Figure 5-6. The bridge cross sections are shown at the upstream and downstream toe of the embankment, and the bridge centerline is located at a river station (RS) equal to 1225 ft (373 m). Ineffective flow areas in the left and right floodplains are located to the left and right, respectively, of the two vertical lines connecting the triangular -4 -2 0 2 4 X (ft) 14 12 10 8 6 4 2 0 Y (ft ) -4 -2 0 2 4 X (ft) 14 12 10 8 6 4 2 0 Y (ft )

212 symbols. The ineffective areas are valid for free flow and submerged orifice flow but they become active or effective for overtopping flow. Lateral streambank stations for the main channel are shown at 300 ft (91.4 m) and 430 ft (131 m), and the stream has a constant bed slope of 0.00052 ft/ft. Manning’s n values are 0.042 in the obstructed left and right floodplains (stations 0 to 200 and 430 to 730). The left floodplain from lateral station 200 to 300 has a Manning’s n of 0.07, and the value of n in the main channel is 0.035. The piers are dual square columns each with a width of 3 ft (0.91 m). Piers are numbered from left to right beginning with #1. The pier positions are located at lateral stations of 240 ft (73.2 m), 290 ft (88.4 m), 330 ft (100.6 m), and 380 ft (115.8 m). The toe of the left abutment is at a lateral station of 214 ft (65.2 m), and the toe of the right abutment is at a station of 410 ft (125 m). 0 100 200 300 400 500 600 700 800 0 5 10 15 20 25 30 35 40 RS=1225 Upstream (Bridge) El ev at io n (ft ) Legend Ground Ineff Bank Sta 0 100 200 300 400 500 600 700 800 0 5 10 15 20 25 30 35 40 RS=1225 Dow nstream (Bridge) Station (ft) El ev at io n (ft ) Figure 5-6. Upstream and downstream bridge cross sections from HEC-RAS. HEC-RAS cross sections are shown in Figure 5-7 in which the differences between river stations represent the actual flow lengths, although it is really only necessary to order the stations in ascending numerical value in the upstream direction. Actual flow lengths are entered elsewhere in the input data table. Station 1500 is the approach flow section (APPR) and Station 950 is the bridge exit section (EXIT). These stations are approximately one bridge length upstream and downstream of the bridge using the WSPRO methodology (Shearman et al. 1986, Sturm 2009). Bridge bounding sections are Station 1265 at the upstream toe of the embankment and Station 1185 at the downstream toe. Two cross sections are generated by HEC-RAS inside the bridge. These stations are referred to as BR U and BR D (shown in Figure 5-6).

213 Based on a risk analysis, the pertinent design discharges of interest for scour calculations are Q1 = 16,000 cfs (453 m3/s) in free flow, Q2 = 23,000 cfs (652 m3/s) in submerged orifice flow, and Q3 = 30,000 cfs (850 m3/s) in overtopping flow. Main Stem 2000 1500 1265 1185 950 500 F l a t Cr eek Figure 5-7. Cross-section layout along main stem of Flat Creek for HEC-RAS analysis. Calculate the combined maximum bridge scour depths for the left and right abutments and the four piers using the methods developed in this report for all three discharges given above. Obtain the required variables from HEC-RAS and use the WSPRO method for the free flow case. Choose the “Pressure/Weir Flow” option for submerged orifice and overtopping flow cases. Assume that the embankment is protected by rock riprap and that a riprap apron has been installed around the toe of both left and right embankments according to HEC-23 specifications (Lagasse et al. 2009). Further assume that the bridge and piers are aligned perpendicular to the flow direction.

214 5.4.2 Water Surface Profiles from HEC-RAS Water surface profiles PF1, PF2, and PF3 were computed for Q1, Q2, and Q3 using HEC-RAS v. 5.0.3 (HEC 2016). Profiles are shown in Figure 5-8, and the flow types can be observed to be free flow, submerged orifice flow, and overtopping flow for Q1, Q2, and Q3, respectively. For each water surface profile, the downstream reach boundary condition was chosen to be uniform flow at the given bed slope of 0.00052. Both the water surface elevation (W.S.) and the energy grade line elevation (EG) for each Q are shown in Figure 5-8. 400 600 800 1000 1200 1400 1600 1800 2000 0 5 10 15 20 25 30 35 Flat Creek - Combined Scour Example Plan: Plan 02 8/4/2017 Main Channel Distance (ft) El ev at io n (ft ) Legend EG PF 3 WS PF 3 EG PF 2 WS PF 2 EG PF 1 WS PF 1 Crit PF 3 Crit PF 2 Crit PF 1 Ground Flat Creek Main Stem Figure 5-8. Water surface profiles for design flows of Q1, Q2, and Q3. Additional output data for the three water surface profiles are shown in Table 5-2 (Standard Profile Summary Table with some columns deleted for legibility). The water surface elevations immediately upstream of the bridge are 26.88 ft (8.19 m), 29.11 ft (8.87 m), and 32.76 ft (9.98 m) for Q1, Q2, and Q3, respectively, in comparison with the low chord elevation of 28.0 ft (8.53 m) and the top-of-deck elevation of 31.0 ft (9.45 m). For the overtopping weir flow, the overtopping discharge is QOT = 5460 cfs (154.6 m3/s) from the HEC-RAS Detailed Output Table: Bridge, and the overtopping ratio is then QOT/Q3 = 0.18. If backwater is defined as the difference between the water surface elevations for constricted and unconstricted flow at the approach flow section (RS 1500), then backwater values are h1*= 0.82 ft (0.25 m), 1.28 ft (0.39 m), and 2.20 ft (0.67 m) for Q1, Q2, and Q3. The initial unconstricted water surface elevation is assumed to be that for uniform flow in this example; that is, h1* = 27.65 – (26.31 + 1000×0.00052) = 0.82 ft (0.25 m) for Q1. For a nonprismatic channel in gradually-varied flow, the unconstricted water surface profile can be computed by HEC-RAS for the same cross sections but without the bridge in place.

215 Table 5-2. Water surface profile output data for all three discharges (Profile Summary Table). 5.4.3 Scour Calculations for Free Flow (Q1) Detailed HEC-RAS output results for Q1 (free flow) are given in Tables 5-3, 5-4, and 5-5 for the approach flow section (RS = 1500), the cross-section inside the bridge at the downstream end (BR D), and the cross section immediately downstream of the bridge (RS = 1185), respectively. (See Detailed Output Tables: Cross Sections in HEC-RAS). These tables contain the variables needed in the scour prediction equations given in Table 5-1. In order to determine whether the expected abutment/contraction scour depth is clear-water or live-bed, the critical velocity for the left floodplain is computed from Manning’s equation for fully-rough turbulent flow in which Manning’s n = 0.034 d501/6 with d50 in ft, and Shields’ parameter τc* is taken to be 0.039. The equation for critical velocity as given in HEC-18 with English units is applied to both the floodplain and main channel: m/s) (0.82 ft/s 68.2)305/0.2(39.42.112.11 3/16/13/16/111  dYV fcf (5-1) m/s) (1.0 ft/s29.3)305/0.2(91.142.112.11 3/16/13/16/111  dYV mcm (5-2) in which Yf1 is approach flow depth in the left floodplain, Ym1 is approach flow depth in the main channel, both from Table 5-3, and d is sediment size taken here to be the median sieve size, d50.

216 The mean velocity in the left floodplain in the approach flow section is 1.48 ft/s (0.45 m/s), and in the main channel it is 4.81 ft/s (1.47 m/s) from Table 5-3. As a result, the abutment/contraction scour in the left floodplain is clear-water scour, while it is live-bed scour in the main channel for the bankline abutment (BLA). Table 5-3. Detailed cross-section output at approach flow section (RS 1500) for PF1 (Q1). Table 5-4. Detailed cross-section output at bridge (BR D) for PF1 (Q1).

217 Table 5-5. Detailed cross-section output at RS 1185 just downstreamof bridge for PF1 (Q1). Variables required for the scour calculations and their sources are summarized in Table 5-6. Table 5-6. Variables for scour calculations for Q1, free flow. (LOB = left overbank, MC = main channel). Variable Source Value Bf Cross-section geometry input as plotted in Figure 5-6 Bf = 300 ft La Cross-section geometry input as plotted in Figure 5-6 La = 214 ft Lp1 , Lp2 Lp3 , Lp4 Cross-section pier input as plotted in Figure 5-6 Lp1 = (240 - 214) = 26 ft Lp2 = (290 - 214) = 76 ft Lp3 = (410 - 330) = 80 ft Lp4 = (410 - 380) = 30 ft W.S. Elev. Table 5-5 26.54 ft Yfo Table 5-5 (LOB) Yfo = Area/Top Width = (960/248) = 3.87 ft* Yf1 Table 5-3 (LOB) Yf1 = 4.39 ft Ymo Table 5-5 (MC) Ymo = 13.97 ft Ym1 Table 5-3 (MC) Ym1 = 14.92 ft qf1 Table 5-3 (LOB) qf1 = Flow/Top Width =1786/275 = 6.49 cfs/ft qf2 Table 5-4 (LOB) qf2 = Flow/Top Width = 1373/90 = 15.26 cfs/ft qm1 Table 5-3 (MC) qm1 = Flow/Top Width = 9327/130 = 71.8 cfs/ft qm2 Table 5-4 (MC) qm2 = Flow/Top Width = 14627/120 = 121.9 cfs/ft Vb (LOB) Table 5-4 (LOB) Vb = 2.90 ft/s Vb (MC) Table 5-4 (MC) Vb = 9.10 ft/s Vf1 Table 5-3 (LOB) Vf1 = 1.48 ft/s Vm1 Table 5-3 (MC) Vm1 = 4.81 ft/s * Yfo is calculated from the total area (including ineffective flow areas) in the floodplain to obtain an average depth at the downstream toe of the embankment.

218 In the following example problem calculations, the values of Yf2max or Ym2max are determined from the proposed combined scour prediction equations, and they represent the vertical distance below the reference tailwater elevation (W.S. Elev.) just downstream of the bridge to the minimum bed elevation (Min. Elev.) at the point of maximum scour depth (see Figure 5-1). This can be written, for example, as max2..... fYElevSWElevMin  (5-3) The Min. Elev. is the primary scour variable of interest so that foundation elevations can be set below that level. For comparison with HEC-18 formulas, which are given for the scour depth (Ys or ds) below the local ground elevation, Min. Elev. is determined from HEC-18 variables as: sdElevGrElevMin  .... (5-4) in which Gr. Elev. is the ground elevation at a pier or the toe of an abutment before scour (see Figure 5-1). 5.4.3.1 Scour Calculations for Left Abutment, Pier #1 and Pier #2 The scour calculations are presented according to the flow chart given in Figure 5-2 beginning with the left abutment. Equations are given in Table 5-1, and required variables can be found in Table 5-6. Step 1 (left abutment) 81.013.171.0 87.3 39.4 300 2141  fo f f a Y Y B L Step 2 ICategory Scour and (LSA)abutment setback Long 94.0  f a B L Calculate abutment/contraction scour from Eq. 4-8: 5.-5 Table See m). (8.09ft 26.54 f Elev. W.S.below m) (3.84ft 6.1287.326.3 26.3 68.2 48.1 49.6 3.15 87.3 39.4363.2*363.2 max2 2/12/32/1 1 1 1 2 2/3 1max2 oY V V q q Y Y Y Y f fc f f f fo f fo f              From these calculations, the minimum elevation in the scour hole is )24.4(9.136.125.26..... max2 mftYElevSWElevMin f 

219 No other scour components should be added to this estimate regardless of whether there are piers or not because the piers have negligible influence on the maximum abutment/contraction scour depth. Step 3 Yes, there are piers, so proceed to calculate maximum scour at the upstream face of the piers. Step 4 (Pier #1) Calculate Lp/Yf1 for Pier #1: 9.5 39.4 26 1 1  f p Y L Step 5 (Pier #1) The flow chart in Figure 5-2 indicates that this is Scour Category IIIa, so calculate excess pier scour from Eq. 4-12: 5.-5 Table Seem). (8.09ft 26.54 of Elev. W.S.below m) (3.11ft 2.1087.363.2)( 63.2 68.2 48.1 49.6 3.15 87.3 39.4906.1*906.1 max2 2/12/32/1 1 1 1 2 2/3 1max2                 excessf fc f f f fo f excessfo f Y V V q q Y Y Y Y The HEC-RAS estimate of pier scour depth at Pier #1 using the local approach flow velocity and depth is (ds)pier = 4.26 ft (1.30 m) from the CSU equation. The combined pier scour depth below the tailwater water surface elevation is then )42.4(5.1426.42.10)()( max2max2 mftdYY piersexcessff  Step 6 (Pier #1) The minimum bed elevation for combined pier scour due to the influence of the abutment is )66.3(0.125.145.26..... max2 mftYElevSWElevMin f  Repeat Steps 4 through 6 for Pier #2:

220 Step 4 (Pier #2) Calculate Lp/Yf1 for Pier #2: 3.17 39.4 76 1 2  f p Y L Step 5 (Pier #2) The flow chart in Figure 5-2 indicates that because Lp/Yf1 > 11 with no vertical contraction scour (free flow), this is Scour Category IVa with pier scour only. The HEC-RAS calculation of pier scour at Pier #2 using the CSU equation and the local depth and velocity gives a value of (ds)pier = 4.4 ft (1.3 m) for maximum pier scour depth. Step 6 (Pier #2) The minimum bed elevation for scour at Pier #2 with an initial ground elevation of 20.2 ft (6.16 m) becomes:   )82.4(8.154.42.20.... mftdElevGrElevMin piers  5.4.3.2 Scour Calculations for Right Abutment, Pier #3 and Pier #4 Piers #3 and #4 are in the main channel and are likely in the zone of influence of the right abutment. In this case, the flow chart is started from the beginning for the right abutment which is a bankline abutment. Step 1 (right abutment) The right abutment toe is at the right channel bank. Step 2 The classification is a bankline abutment subject to live-bed scour in Scour Category II. Calculate abutment/contraction scour from Eq. 4-10: 5.-5 Table See m). (8.09ft 26.54 f Elev. W.S.below m) (9.57ft 4.3197.1325.2 25.20.1 8.71 9.121725.1*725.1 max2 2/12/1 1 1 1 2max2 oY V V q q Y Y m mc m m m mo m         From these calculations, the minimum elevation in the scour hole is )49.1(9.44.315.26..... max2 mftYElevSWElevMin m 

221 No other scour components should be added to this estimate regardless of whether there are piers or not because the piers have negligible influence on the maximum abutment/contraction scour depth. Step 3 Yes, there are piers, so proceed to calculate maximum scour in front of the piers. Step 4 (Pier #3) Calculate Lp/Ym1 for Pier #3: 4.5 91.14 80 1 3  m p Y L Step 5 (Pier #3) The flow chart in Figure 5-2 indicates that this is Scour Category IIIa with Category II abutment/contraction scour, so calculate excess pier scour from the modification factor of 0.8 times Eq. 4-10 (see Note 2 following Table 5-1):   5.-5 Table See m). (8.09ft 26.54 of Elev. W.S.below m) (7.65ft 1.2597.1380.1 80.10.1 8.71 9.12138.1*725.18.0 max2 2/12/1 1 1 1 2max2            excessm mc m m m excessmo m Y V V q q Y Y The HEC-RAS estimate of pier scour depth at Pier #3 using the local approach flow velocity and depth is (ds)pier = 8.4 ft (2.56 m) from the CSU equation. The combined pier scour depth below the tailwater water surface elevation is then )2.10(5.334.81.25)()( max2max2 mftdYY piersexcessmm  Step 6 (Pier #3) The minimum bed elevation for combined pier scour at Pier #3 due to the influence of the abutment is )13.2(0.75.335.26..... max2 mftYElevSWElevMin m  Steps 4, 5, and 6 for Pier #4 Repeating Steps 4, 5, and 6 for Pier #4 produces a value of Lp/Yf1 = 30/14.91 = 2.0 so that Pier #4 is in Category IIIb with abutment/contraction scour in Category II. The excess pier scour is then 0.54 times the abutment/contraction scour from Eq. (4-10):

222   5.-5 Table See m). (8.09ft 26.54 of Elev. W.S.below m) (5.15ft 9.1697.1321.1 21.10.1 8.71 9.12193.0*725.154.0 max2 2/12/1 1 1 1 2max2            excessm mc m m m excessmo m Y V V q q Y Y The HEC-RAS estimate of pier scour depth at Pier #4 using the local approach flow velocity and depth is (ds)pier = 8.3 ft (2.53 m) from the CSU equation. The combined pier scour depth below the tailwater water surface elevation is then )68.7(2.253.89.16)()( max2max2 mftdYY piersexcessmm  The minimum bed elevation for combined pier scour at Pier #4 due to the influence of the abutment is )40.0(3.12.255.26..... max2 mftYElevSWElevMin m  5.4.3.3 Comparison with HEC-RAS Calculations Based on HEC-18 The foregoing scour calculations are summarized in Figure 5-9 in terms of the minimum bed elevation at each abutment and pier due to scour for Q1, which is a free flow. The water surface elevation at the bridge is 26.54 ft (8.09 m) and is shown in the figure. The connected data points do not show the sides of the scour holes but rather represent the locus of minimum bed elevations after scour for both NCHRP 24-37 calculations and for HEC18 calculations as implemented in HECRAS and shown in Table 5-7. The HEC-18 calculations were made for an abutment shape factor corresponding to wingwall abutments since the present experiments and those of Ettema et al. (2010) and Sturm (2006) showed virtually no difference between maximum scour depths for wingwall and spill-through abutments with significant lateral contraction. The most notable difference in scour elevations occurs at the left and right abutments where the HEC-18 values are considerably lower. The HEC-18 abutment plus contraction scour depths are 2.5 times the NCHRP 24-37 values at the left abutment and 1.8 times greater at the right abutment. Because HEC-18 predicts zero contraction scour at the left abutment, an estimate of abutment/lateral contraction scour as an amplification factor times the theoretical long contraction scour would predict no scour at all at the left abutment. At Pier #1, HEC-18 predicts no lateral contraction scour so that only pier scour is plotted at this point. However, the HEC-RAS output in Figure 5-10 shows the pier scour hole engulfed by the abutment scour hole with an assumed top width of 4ds, so the minimum elevation for Pier #1 is plotted at the same minimum elevation as the abutment scour hole in Figure 5-9. The results of the NCHRP 24-37 procedure predict some excess scour due to interaction with the abutment scour hole in addition to pier scour at Pier #1. The pier scour values at Pier #2 are exactly the

223 same because the pier is isolated from the influence of the abutment in the NCHRP 24-37 method, and because there is no lateral contraction scour predicted by HEC-18. As a result, only pier scour is represented at Pier #2 by both methods. The minimum bed elevations are in close agreement at Pier #3, but the NCHRP 24-37 value is the result of excess pier scour due to the influence of the abutment in addition to pier scour, while the HEC-18 value is the simple addition of idealized lateral contraction scour and pier scour. The HEC-RAS output indicates incorporation of the scour hole due to Pier #4 into the right abutment scour hole as for Pier #1, and so the minimum elevation is plotted as being the same for both in agreement with Figure 5- 10. These comparisons provide some insight into the effect of scour component interactions, but sweeping conclusions should not be drawn based only on this example problem. Instead, the reader should rely on the statistical comparisons of the two methods with experimental data given in Chapter 4. -30 -20 -10 0 10 20 30 40 0 100 200 300 400 500 600 700 800 E le va tio n (ft ) Station (ft) Bridge Scour RS = 1225 NCHRP 24-37 HEC-18 Figure 5-9. Comparison of minimum scour elevations for NCHRP 24-37 and HEC-18 methods.

224 Figure 5-10. HEC-RAS scour output with depiction of predicted scour holes using HEC-18 methods.

225 Table 5-7. Bridge Scour; River=Flat Creek; Reach= Main Stem; RS = 1225 BR (HEC-RAS) ___________________________________________________ Contraction Scour Left Channel Right Ys (ft): 0.00 9.18 Vc (ft/s): 2.68 3.29 Equation: Clear Live Pier Scour #1 (CL = 240) Ys (ft): 4.26 #2 (CL = 290) Ys (ft): 4.38 #3 (CL = 330) Ys (ft): 8.42 #4 (CL = 380) Ys (ft): 8.31 Abutment Scour Left Right Abutment Ys (ft): 18.49 30.77 Froude #: 0.17 0.31 Equation: HIRE HIRE Combined Scour Depths Pier: #1 (CL = 240) (Contr + Pier) (ft): 4.26 Pier: #2 (CL = 290) (Contr + Pier) (ft): 4.38 Pier: #3 (CL = 330) (Contr + Pier) (ft): 17.60 Pier: #4 (CL = 380) (Contr + Pier) (ft): 17.49 Left abut + contr (ft): 18.49 Right abut + contr (ft): 39.95 _________________________________________________

226 5.4.4 Scour Calculations for Submerged Orifice Flow (Q2) and Overtopping Flow (Q3) To avoid repetition, only abutment/contraction scour at the left and right abutments are considered for submerged orifice and overtopping flows to illustrate an application for these two flow types. The relevant variables are taken from the detailed HEC-RAS output variables as in the previous calculations. These are summarized in Table 5-8. Variables were determined in Table 5-8 as for free flow with the notable exception of qf2 and Vb for overtopping flow which have to be calculated so that they represent only the flow through the bridge opening without the overtopping flow. The overtopping flow is 5,460 cfs (155 m3/s) for a total flow of 30,000 cfs (850 m3/s) from the HEC-RAS output, so the net flow through the full bridge opening is 24,540 cfs (695 m3/s). The distribution of the bridge opening flow alone cannot be obtained from the BR D output table for 30,000 cfs (850 m3/s). Instead, the net flow is assumed to be distributed between floodplain and main channel by the ratio of conveyances in the bridge opening only, which is available from the BR D output table for submerged orifice flow because the geometry is the same. The BR D output table for submerged orifice flow (Q2) gives the ratio of floodplain conveyance to total conveyance for full flow to be 0.109. As a result, the floodplain discharge inside the bridge for overtopping flow is estimated to be 0.109×24,540 = 2675 cfs (75.8 m3/s) , and the discharge per unit width is qf2 = 2675/94 = 28.5 cfs/ft (2.65 m3/s/m) for a floodplain width of 94 ft (28.6 m) under the bridge after subtracting pier widths. The value of Vb also depends on the fully submerged area under the bridge. The overbank area of 641 ft2 (59.5 m2) comes from the BR D section for submerged orifice flow (Q2). The result is Vb (LOB) = 2675/641 = 4.2 ft/s (1.3 m/s). Similar calculations were made for qm2 and Vb (MC), and they appear in the table.

227 Table 5-8. Variables for scour calculations for Q2, submerged orifice flow, and Q3, overtopping flow, in left overbank. (RS 1500 = approach flow section; RS 1265 = upstream toe of embankment; BR D = inside bridge downstream; RS 1185 = downstream toe of embankment, LOB =left overbank, Vp = pier approach velocity, Yp = pier approach depth.) Variable River Station (RS) Q2 Q3 W.S. Elev. 1185 28.20 ft 32.23 ft Yfo* 1185 4.87 ft 7.20 ft Yf1 1500 6.73 ft 9.18 ft Ymo 1185 15.6 ft 18.0 ft Ym1 1500 17.6 ft 20.1 ft qf1 1500 12.4 cfs/ft 19.3 cfs/ft qf2 BR D 26.6 cfs/ft 28.5 cfs/ft qm1 1500 89.5 cfs/ft 106.7 cfs/ft qm2 BR D 165 cfs/ft 176 cfs/ft Vb (LOB) BR D 3.91 ft/s 4.17 ft/s Vb (MC) BR D 11.2 ft/s 12.0 Vf1 1500 1.84 ft/s 2.11 ft/s Vm1 1500 5.10 ft/s 5.31 ft/s Vf1c 1500 2.88 ft/s 3.03 ft/s Vm1c 1500 3.38 ft/s 3.46 ft/s * Yfo is calculated from the total area (including ineffective flow areas) in the floodplain to obtain an average depth at the downstream toe of the embankment. 5.4.4.1 Scour Calculations for Left And Right Abutments (Q2) The scour calculations for submerged orifice flow (Q2) are presented according to the flow chart beginning with the left abutment and using the variables in Table 5-8. Step 1 (left abutment) 98.038.171.0 87.4 73.6 300 2141  fo f f a Y Y B L Step 2 (SSA)abutment setback Short 94.0  f a B L This is Category II scour, and it is live-bed scour because Vm1>Vm1c (see Table 5-8). Calculate abutment/contraction scour from Eq. 4-10:

228 m) (8.60ft 28.20 f Elev. W.S.below m) (11.1ft 5.366.1534.2 34.20.1 5.89 165725.1*725.1 max2 2/12/1 1 1 1 2max2 oY V V q q Y Y m mc m m m mo m         From these calculations, the minimum elevation in the scour hole is )5.2(3.85.362.28..... max2 mftYElevSWElevMin m  Because the right abutment is a bankline abutment, Eq. 4-10 is also applied to it with the identical result of a minimum scour elevation of ˗8.3 ft (˗2.5 m). In this case, the SSA scour hole and the BLA scour hole are likely to join based on the experimental results with the maximum scour depth occurring in the main channel. 5.4.4.2 Scour Calculations for Left and Right Abutments (Q3) The scour calculations for overtopping flow (Q3) are presented according to the flow chart beginning with the left abutment and using the variables in Table 5-8. Step 1 (left abutment) 91.028.171.0 20.7 18.9 300 2141  fo f f a Y Y B L Step 2 ICategory Scour and (LSA)abutment setback Long 94.0  f a B L with clear-water scour Calculate abutment/contraction scour from Eq. 4-8: m) (9.82ft 32.23 f Elev. W.S.below m) (7.56ft 8.2420.745.3 45.3 03.3 11.2 3.19 5.28 20.7 18.9363.2*363.2 max2 2/12/32/1 1 1 1 2 2/3 1max2 oY V V q q Y Y Y Y f fc f f f fo f fo f              From these calculations, the minimum elevation in the left abutment scour hole for OT flow is )3.2(4.78.242.32..... max2 mftYElevSWElevMin f 

229 Finally, for the right abutment, we have Step 1 (right abutment) 0.1 f a B L Step 2 (BLA)abutment Bankline 0.1  f a B L This is Scour Category II with live-bed scour. Calculate abutment/contraction scour from Eq. 4-10: m) (9.82ft 32.23 f Elev. W.S.below m) (12.1ft 8.390.1821.2 21.20.1 107 176725.1*725.1 max2 2/12/1 1 1 1 2max2 oY V V q q Y Y m mc m m m mo m         From these calculations, the minimum elevation in the right abutment scour hole for OT flow is )3.2(6.78.392.32..... max2 mftYElevSWElevMin f  In summary, minimum bed elevations due to scour for the left abutment are 13.9 ft (4.2 m), ˗8.3 ft (˗2.5 m), and 7.4 ft (2.3 m) for free flow, submerged orifice flow (SO) and overtopping flow (OT), respectively, with the caveat that the left abutment is an SSA with the scour hole in the main channel for submerged orifice flow, while it is an LSA for the other two flow types with the scour hole in the floodplain. The effect of OT flow in contrast to SO flow is that the more uniform lateral distribution of the OT flow shifts the SO scour hole from the main channel back into the floodplain. This effect was observed in the experimental results. It is also of interest that the maximum scour depth (minimum bed elevation) occurs for SO flow in this example in agreement with the GT experimental results. However, it is quite possible that the maximum scour could occur for OT flow with a different combination of tailwater rating curve, abutment length and overtopping ratio. In any case, the scour prediction equations proposed for abutment/contraction scour herein accommodate either result. At the right BLA abutment, minimum scour bed elevations are 4.9 ft (1.5 m), ˗8.3 ft (˗2.5 m), and ˗7.6 ft (˗2.3 m) for free flow, submerged orifice flow, and overtopping flow, respectively. The relative magnitudes of scour for the three flow types are in the same order as for the LSA, but the relative differences for different flow types are considerably smaller at the right abutment than the left abutment. For the right abutment, the maximum scour depth for submerged orifice flow is only slightly greater than for overtopping flow.

230 5.4.5 Application Considerations This study is based on extensive laboratory experiments, and it has been verified with some field data and data from experiments of others. The experiments were conducted with realistic compound channel and bridge geometry based on typical prototype bridge crossings, and they included both clear-water and live-bed scour as well as free, submerged orifice, and overtopping flows. Abutment, lateral contraction, vertical contraction and pier scour were studied both experimentally and with CFD tools to determine their interactions and to propose a more rational approach to scour depth prediction than simply adding interacting components. Despite these extensive efforts to produce practical, true-to-life representations of bridge scour, some practical conditions were imposed. These conditions included:  Installation of rock riprap protection of the embankment and a rock riprap apron following guidelines in HEC-23 to assure similar equilibrium scour end points without catastrophic failure of the bridge embankment and abutment;  Absence of extensive ongoing river bed adjustments such as meandering, braiding; and aggradation/degradation processes;  Presence of predominantly sand and silt river beds rather than cohesive sediments;  Construction of perpendicular bridge crossings, although small degrees of skewness should not drastically affect the results (HEC-18);  Use of spill-through and wingwall abutments with rectangular pier columns and wall piers. In addition to the conditions given above, the numerical ranges of variables covered in the laboratory experiments, including both live-bed and clear-water scour experiments, are shown in Table 5-9. Measured field values of Yf2max/Yfo = 2.0 and 6.0, and field values of Ym2max/Ymo = 1.1, 1.7, and 3.0 all agreed with the combined scour prediction relationships developed in this report. Table 5-9. Ranges of variables in laboratory experiments. Dimensionless Variables Laboratory Values La/ Bf 0.4-1.0 Vf1/Vfc1 0.4-0.9 Vm1/Vmc1 0.5-1.5 Yf1/ Yfo 1.0-1.4 Yf1/ Ym1 0.4-0.7 qf2/qf1 1.0-2.1 qm2/qm1 0.9-2.2 QOT/Q 0.1-0.5 Yf2max/Yfo 1.3-3.0 Ym2max/Ymo 1.3-2.4

231 Although the experiments performed in this research showed essentially no difference between wingwall and spill-through abutments with respect to maximum scour depths, additional confirmation may be useful. Experiments by Sturm (2006) and Ettema et al. (2010) also indicated a minor influence of abutment shape when the primary driving force for scour was flow contraction. In general, the relationships proposed herein should apply to small to medium alluvial river bridge crossings that satisfy the conditions above. For very large rivers with high risk, including extensive loss of life associated with failure, a combination of CFD and physical model studies are recommended to adequately design a bridge foundation that is reasonably safe. The problem is somewhat similar to small vs. large dams in which the 100-year design flood may be sufficient for small dams while large dams may be designed for a higher return period flood such as the 500-year flood or the probable maximum flood. Scour design flood return intervals are recommended to be larger than hydraulic design flood return intervals (HEC-18). In any case, these risk decisions fall to local, state and federal highway agencies, and the level of scour evaluation required should be based on a formal risk analysis.