Combining Individual Scour Components to Determine Total Scour (2018)

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81 CHAPTER 4. Research Findings 4.1 Introduction Organization of combined scour into interaction categories as described in the previous chapter provided the framework for explaining how complex scour interactions could be captured and predicted using a practical but effective methodology. The previous chapter also established several CFD approaches employed to characterize the flow fields and the experimental parameter influence to better understand the physics of the combined scour process and give insights needed in developing the combined scour prediction methodology. In this chapter, experimental and CFD results are given in tabular and graphical form. First, basic results of water surface profiles, cross-section distributions of hydraulic and turbulence quantities, time development of scour, and scour contours are presented and discussed. Then a methodology is proposed for predicting scour depths for each of the scour interaction categories described previously in Table 3-2. Finally, the proposed methodology is tested against the current approach of simply adding each type of scour without regard to interactions. Some field data are also included in these comparisons. 4.2 Clear-Water Experimental Results 4.2.1 Summary of Results Experimental results for clear-water scour (CWS) are summarized in Table 4-1. The relative depth to the point of maximum scour below the water surface at the bridge, Yf2max/Yfo, is shown for long setback abutments (LSA) subject to CWS in the table, in which Yfo is the undisturbed floodplain flow depth at the bridge. Long setback abutments are defined as those for which the abutment scour hole is located fully in the floodplain rather than the main channel. Criteria for the identification of LSAs are developed in this chapter. Relative abutment lengths of La/Bf equal to 0.41, 0.50, and 0.77 in Table 4-1 satisfy the criteria for LSA. The data set encompasses free flow, submerged orifice flow and overtopping flow cases, and includes data from Georgia Tech (GT) for a bridge model scale of 1:45 and from the University of Auckland (UoA) for a model scale of 1:30. Furthermore, both wingwall (WW) and spill-through abutments are represented. The independent dimensionless variables of the ratio of discharge per unit width in the bridge section to that in the floodplain approach flow section, q2/q1; the relative backwater ratio Yf1/Yfo, and the relative flow intensity, Vf1/Vf1c, are shown in Table 4-1 and they will be used to develop a relationship to predict maximum CWS depth for Category I interactive scour subsequently. Note that q2 represents only that portion of flow per unit width in the floodplain going under the bridge for overtopping flow. Flow intensity relative to critical conditions as represented by Vf1/Vf1c ranges from approximately 0.5 to 0.8 in the CWS regime. The maximum relative depth of abutment scour in the last column varies between approximately 1.4 and 3.5.

82 Table 4-1. Experimental maximum abutment scour depth results for CWS and LSA. (GT = Georgia Tech, UoA = University of Auckland, F = free flow, SO = submerged orifice flow, OT = overtopping flow, LSA = long setback abutment, WW = wingwall abutment; otherwise, abutments are spill-through) Run Flow Type La/Bf Floodplain Yf2max/Yfo qf2/qf1 Yf1/Yfo Vf1/Vfc1 Yfo (ft) 1 GT F 0.41 1.549 1.081 0.542 0.223 2.408 2 GT SO 0.41 1.520 1.107 0.589 0.290 2.638 3 GT OT 0.41 1.044 1.046 0.561 0.457 1.373 4 GT F 0.41 1.501 1.132 0.655 0.220 2.950 5 GT OT 0.41 1.014 1.067 0.684 0.460 1.943 8 GT F 0.41 1.479 1.136 0.648 0.220 2.800 10 GT F 0.77 1.821 1.244 0.659 0.213 3.469 12 GT OT 0.77 1.154 1.098 0.622 0.457 2.554 18 GT F 0.41 1.670 1.097 0.586 0.29 2.438 19 GT F 0.77 2.103 1.215 0.589 0.265 3.287 22 GT F 0.41 WW 1.578 1.076 0.541 0.223 2.204 23 GT SO 0.41 WW 1.556 1.107 0.589 0.290 2.024 24 GT OT 0.41 WW 1.042 1.044 0.561 0.457 1.612 25 GT F 0.77 WW 1.867 1.239 0.659 0.213 3.277 26 GT SO 0.77 WW 2.001 1.362 0.579 0.265 3.584 27 GT OT 0.77 WW 1.214 1.098 0.622 0.457 2.342 41 GT F 0.41 1.486 1.141 0.648 0.220 2.915 11 UoA F 0.50 1.78 1.0 0.48 0.27 2.536 13 UoA OT 0.50 0.98 1.003 0.49 0.54 1.613 14 UoA F 0.50 1.52 1.018 0.66 0.32 2.625 16 UoA OT 0.50 0.94 1.033 0.79 0.60 2.446 17 UoA SO 0.50 1.07 1.117 0.57 0.34 2.189 18 UoA SO 0.5 WW 1.15 1.117 0.55 0.34 2.145 19 UoA OT 0.5 WW 0.98 1.003 0.49 0.54 1.538 20 UoA OT 0.5 WW 0.94 1.108 0.81 0.46 2.847 21 UoA OT 0.5 WW 0.94 1.033 0.79 0.60 2.341

83 For each scour experiment at Georgia Tech, the right floodplain flow was blocked by a bankline abutment (BLA) for varying abutment lengths on the left floodplain which resulted in scour depth data for the BLA in the main channel as well as for the LSA in the left floodplain. A separate scour prediction relationship was developed for the BLA in terms of the main channel independent variables instead of those on the floodplain. In Table 4-2, the results for scour depth below the water surface at the bridge are given relative to the undisturbed flow depth, Ymo, in the main channel as shown in the last column of the table. The range of CWS conditions for the BLA relative to main channel approach flow velocity is represented by values of Vm1/Vm1c from 0.65 to 0.88. Values of Ym2max/Ymo for the BLA vary from 1.3 to 2.2 which is a smaller range than for the LSA. As the abutment toe approached the bank of the main channel, the scour hole moved into the main channel and the scour depths were comparable to those for the BLA as shown in Table 4-3. These abutments were classified as short setback abutments (SSA) and most of the experiments were done at UoA for this case with La/Bf = 0.8. Threshold live-bed scour conditions were approached with values of Vm1/Vm1c as high as 0.98 in Table 4-3. Values of Ym2max/Ymo for the SSA varied from 1.3 to 2.4 which was very similar to the range observed for the BLA.

84 Table 4-2. Experimental maximum abutment scour depth results for CWS around BLA. (GT = Georgia Tech, BLA = bankline abutment, WW = wingwall abutmentotherwise, spill-through). Run Flow Type La/Bf Main Channel Ym2max/Ymo qm2/qm1 Ym1/Ymo Vm1/Vmc1 Ymo (ft) 1 GT F 0.41 1.487 1.033 0.723 0.479 1.745 2 GT SO 0.41 1.501 1.057 0.725 0.546 1.874 3 GT OT 0.41 1.241 1.029 0.653 0.713 1.265 4 GT F 0.41 1.452 1.061 0.841 0.476 1.708 5 GT OT 0.41 1.140 1.043 0.823 0.716 1.585 6 GT F 0.41 1.456 1.065 0.820 0.476 1.790 7 GT OT 0.41 1.135 1.046 0.822 0.716 1.560 8 GT F 0.41 1.456 1.063 0.820 0.476 1.668 9 GT OT 0.41 1.137 1.045 0.822 0.716 1.501 10 GT F 0.77 1.805 1.111 0.879 0.469 2.256 11 GT SO 0.77 2.178 1.184 0.711 0.521 2.250 12 GT OT 0.77 1.433 1.063 0.784 0.713 1.746 14 GT F 0.77 1.945 1.111 0.878 0.469 2.102 15 GT OT 0.77 1.372 1.066 0.784 0.713 1.736 16 GT F 0.77 1.933 1.113 0.878 0.469 2.058 17 GT OT 0.77 1.351 1.067 0.784 0.713 1.537 18 GT F 0.41 1.419 1.051 0.712 0.546 1.749 19 GT F 0.77 1.980 1.109 0.791 0.521 2.142 22 GT F 0.41WW 1.451 1.031 0.723 0.479 1.952 23 GT SO 0.41WW 1.501 1.057 0.725 0.546 1.660 24 GT OT 0.41WW 1.175 1.028 0.653 0.713 1.305 25 GT F 0.77WW 1.906 1.109 0.879 0.469 1.912 26 GT SO 0.77WW 2.199 1.184 0.711 0.521 2.080 27 GT OT 0.77WW 1.401 1.063 0.784 0.713 1.663 28 GT SO 0.41 1.505 1.059 0.725 0.546 1.936 29 GT SO 0.41 1.503 1.058 0.725 0.546 2.044 30 GT SO 0.77 2.213 1.184 0.711 0.521 2.063 31 GT SO 0.77 2.170 1.184 0.711 0.521 2.163 39 GT F 0.41 1.454 1.069 0.820 0.476 1.948 40 GT SO 0.41 1.503 1.058 0.725 0.546 1.962 41 GT F 0.41 1.455 1.067 0.820 0.476 1.921 42 GT SO 0.41 1.502 1.057 0.725 0.546 1.951 43 GT F 0.53 1.542 1.053 0.831 0.474 1.889 44 GT SO 0.53 1.482 1.056 0.726 0.571 1.923 45 GT SO 0.53 1.417 1.052 0.682 0.581 1.878

85 Table 4-3. Experimental maximum scour depth results for CWS around SSA. (GT = Georgia Tech, UoA = University of Auckland, F = free flow, SO = submerged orifice flow, OT = overtopping flow, SSA = short setback abutment, WW = wingwall abutment otherwise, spill-through). Run Flow Type La/Bf Main Channel Ym2max/ Ymo q2/q1 Y1/Yo V1/Vc Yo (ft) 1 UoA F 0.8 1.389 1.044 0.750 0.523 1.492 2 UoA SO 0.8 1.507 1.058 0.796 0.625 2.073 3 UoA OT 0.8 1.382 1.006 0.712 0.856 1.887 4 UoA F 0.8 1.358 1.052 0.980 0.538 2.027 5 UoA SO 0.8 1.653 1.065 0.912 0.686 2.304 6 UoA OT 0.8 1.481 1.053 0.858 0.812 2.352 7 UoA OT 0.8 1.460 1.051 0.893 0.894 2.206 8 UoA OT 0.8 1.412 1.028 0.605 0.887 1.667 9 UoA F 0.8 1.450 1.003 0.747 0.578 1.951 22 UoA OT 0.8WW 1.492 1.000 0.717 0.737 2.080 23 UoA F 0.8WW 1.406 1.023 0.789 0.554 2.081 24 UoA OT 0.8WW 1.490 1.005 0.495 0.841 1.336 25 UoA OT 0.8WW 1.421 1.026 0.759 0.891 1.915 11 GT SO 0.77 2.178 1.184 0.711 0.521 2.096 In order to study pier scour interaction with lateral contraction/abutment scour and vertical contraction scour, piers were placed in some experiments at variable distances, Lp, from the toe of the abutment. As shown in Table 4-4, the values of relative distance Lp/Yf1 varied from approximately 1.8 to 9.6. Two separate maximum dimensionless scour depths are shown in Table 4-4. One of the depths is the maximum value associated with the abutment while the other is the maximum value just upstream of the pier. If the pier was located in the bottom of the abutment scour hole, these maximum scour depths were essentially the same, and the abutment had its maximum influence on pier scour relative to pier scour acting alone. To either side of the maximum depth in the abutment scour hole, pier scour formed a separate scour hole with a depth that was greater than pier scour alone but decreasing with relative distance from the abutment scour hole. In addition to dual-column piers, wall piers were also incorporated into the model and are indicated by the symbol W in the table.

86 Table 4-4. Experimental maximum scour depth results for CWS with piers in place. (GT = Georgia Tech, F = free flow, SO = submerged orifice flow, OT = overtopping flow, Lp = distance from abutment toe to pier, W = wall pier.) Run Flow Type La/Bf Lp/Yf1 Floodplain (M/C for Run 30 & 31) Y2max/ Yo (Ab.) Y2max/Yo (Pier) q2/q1 Y1/Yo V1/Vc Yo (ft) 6 GT F 0.41 3.59 1.481 1.141 0.648 0.220 2.981 2.867 7 GT OT 0.41 1.83 1.020 1.072 0.684 0.460 1.937 1.887 8 GT F 0.41 7.20 1.479 1.136 0.648 0.220 2.800 2.000 9 GT OT 0.41 3.65 1.009 1.071 0.683 0.460 1.848 2.026 14 GT F 0.77 3.02 1.951 1.244 0.660 0.213 4.065 3.267 15 GT OT 0.77 1.59 1.268 1.103 0.622 0.457 2.466 1.966 17 GT OT 0.77 3.96 1.319 1.105 0.622 0.457 2.280 2.676 28 GT SO 0.41 2.80 1.547 1.110 0.589 0.290 2.476 2.445 29 GT SO 0.41 5.60 1.549 1.109 0.589 0.290 2.778 2.564 30 GT SO 0.77 2.22 2.210 1.184 0.711 0.521 1.842 2.857 31 GT SO 0.77 5.54 2.170 1.184 0.711 0.521 2.456 4.393 39 GT F 0.41 3.57W 1.483 1.145 0.648 0.220 3.122 3.110 40 GT SO 0.41 2.80W 1.571 1.109 0.589 0.290 2.807 2.782 41 GT F 0.41 7.17W 1.486 1.141 0.648 0.220 2.915 2.454 42 GT SO 0.41 5.07W 1.567 1.107 0.589 0.290 2.504 2.824 43 GT F 0.53 3.72 1.914 1.115 0.613 0.218 3.120 3.129 44 GT SO 0.53 5.48 1.975 1.102 0.590 0.315 3.218 3.108 45 GT SO 0.53 4.8 &9.6 1.875 1.092 0.569 0.325 2.571 2.557 4.2.2 Water Surface Profiles Water surface profiles for free flow, submerged orifice flow, and overtopping flow are compared in Figure 4-1 for two different abutment lengths of La/Bf =0.41 and 0.77. Water surface elevations shown are relative to the floodplain elevation of 1.257 ft (0.383 m) while the elevation of the bottom of the main channel is 0.870 ft (0.265 m). The subcritical flow profiles are controlled by the tailwater elevations set by the downstream tailgate. Water surface elevations were measured at eight positions across the cross-section at each longitudinal station, but the water surface elevations at the centerline of the main channel are shown in Figure 4-1. As presented previously in Table 3-1, tailwater elevation and discharge were increased together to generate flow types from F to SO to OT for a particular abutment length as would occur in a prototype river. In all three types of flow, an increase in approach flow water surface elevation relative to the unconstricted flow defined a backwater created by contraction, friction, and expansion head losses. In the case of orifice flow through the bridge opening without overtopping, the tailwater was sufficiently high enough to submerge the outlet of the orifice. As the tailwater and discharge were raised further, the bridge overtopped with simultaneous occurrence of submerged orifice flow through the bridge opening and weir flow over the bridge deck. The increase in abutment length from Figure 4-1(a) to Figure 4-1(b) reduced the area of the

87 orifice such that at the same tailwater elevation, the ratio of overtopping discharge to total discharge, Qot/Q, increased from 0.30 to 0.41 with larger values of headwater elevation and Q. 1.2 1.4 1.6 1.8 30 40 50 60 El ev at io n (ft ) Longitudnal Direction (ft) La/Bf = 0.41 Run 1 Free Flow Run 2 SO Flow Run 3 OT Flow Bridge Flood-Plain Level (a) 1.2 1.4 1.6 1.8 30 40 50 60 E le va tio n (f t) Longitudnal Direction (ft) La/Bf = 0.77 Run 10 Free Flow Run 11 SO Flow Run 12 OT Flow Bridge Flood-Plain Level (b) Figure 4-1. Water surface profiles for CWS in Georgia Tech flume for free, submerged orifice, and overtopping flows: (a) La/Bf = 0.41; (b) La/Bf = 0.77. 4.2.3 Flow Fields and Clear-Water Scour Depth-averaged velocity profiles across the approach flow cross section and the downstream face of the bridge are shown in Figure 4-2 for the same flow conditions and abutment lengths as for the water surface profiles in Figure 4-1. The approach flow velocity distributions in Figure 4-2(a) and (b) depict higher velocities in the main channel relative to floodplain velocities as expected

88 in compound channel flow. The relative magnitude of velocities for different flow types is determined by the tailwater-discharge setting and the resultant upstream flow depth caused by the bridge backwater. For the case of approach flow with La/Bf =0.41, free flow had smaller floodplain velocities than SO and OT flow while maximum main channel velocities occurred for SO flow. Approach flow conditions for La/Bf = 0.77 resulted in higher velocities in the right floodplain (RFP) and in the main channel (MC) at the correspondingly higher discharges and accompanying exchange of flow between the RFP and MC for F and OT flows. Acceleration of both floodplain and main channel flows can be seen in Figure 4-2(c) and (d) but it is decidedly more pronounced for the longer abutment and smaller bridge opening. Maximum velocity at the downstream face of the bridge depends on the percentage of total flow overtopping the bridge as well as total discharge and abutment length. 0.0 0.5 1.0 1.5 2.0 2.5 0.8 1.2 1.6 2.0 2.4 2.8 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Ve lo ci ty (f t/s ec ) Be d El ev at io n (ft ) Cross Section Station (ft) Model Bed Level Depth Average Approach Velocity Run 1 F Flow Depth Average Approach Velocity Run 2 SO Flow Depth Average Approach Velocity Run 3 OT Flow La/Bf =0.41 0.0 0.5 1.0 1.5 2.0 2.5 0.8 1.2 1.6 2.0 2.4 2.8 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Ve lo ci ty (f t/s ec ) Be d El ev at io n (ft ) Cross Section Station (ft) Model Bed Level Depth Average Approach Velocity Run 10 F Flow Depth Average Approach Velocity Run 11 SO Flow Depth Average Approach Velocity Run 12 OT Flow La/Bf =0.77 (a) Approach flow section for La/Bf =0.41 (b) Approach flow section for La/Bf =0.77 0.0 0.5 1.0 1.5 2.0 2.5 0.8 1.2 1.6 2.0 2.4 2.8 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Ve lo ci ty (f t/s ec ) Be d E le va tio n (ft ) Cross Section Station (ft) Model Bed Level Depth Average Br Section Velocity Run 1 F Flow Depth Average Br Section Velocity Run 2 SO Flow Depth Average Br Section Velocity Run 3 OT Flow La/Bf =0.41 0.0 0.5 1.0 1.5 2.0 2.5 0.8 1.2 1.6 2.0 2.4 2.8 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Ve lo ci ty (f t/s ec ) Be d El ev at io n (ft ) Cross Section Station (ft) Model Bed Level Depth Average Br Section Velocity Run 10 F Flow Depth Average Br Section Velocity Run 11 SO Flow Depth Average Br Section Velocity Run 12 OT Flow La/Bf =0.77 (c) Downstream face of bridge for La/Bf =0.41 (d) Downstream face of bridge for La/Bf =0.77 Figure 4-2. Flow acceleration from approach flow section to downstream face of bridge with La/Bf =0.41 and 0.77.

89 As discussed in Chapter 2 (see Eqs. 2-18 and 2-19), lateral contraction scour depth due to an abutment as well as idealized long contraction scour depth can be related to the ratio of discharge per unit width in the contracted bridge section to that in the approach flow section, q2/q1. This variable represents the spatial concentration of flow in the bridge section due to the physical reduction in channel width as well as to the flow-induced contraction and accompanying turbulence caused by flow separation around the face of the abutment. Because the degree of flow acceleration is different in the floodplain and main channel, while the separate lateral distributions of q within the floodplain and main channel are likely to be relatively uniform based on Figure 4-2, it is a reasonable step to treat the value of q2/q1 separately in floodplain and main channel. As a consequence, the distribution of q between floodplain and main channel becomes important in both the approach flow section and the bridge section. The former is influenced by the compound channel geometry, roughness, and relative flow depth while the latter is also determined by interchange of fluid between floodplain and main channel as the constricted section is approached. The degree of interaction is influenced by the length of the abutment and the turbulent processes occurring at the FP/MC interface (Sturm 2004, Kara et al. 2012). The approach flow distribution of q between floodplain and main channel is shown for cross sections of different compound channel geometries in Figure 4-3. The ratio qf1/qm1 increases as the relative depth Yf1/Ym1 increases and approaches the line of equal values. In other words, compound channel effects on the flow distribution diminish with relative depth for a given geometry and roughness distribution and as a result, Vf1/Vm1 approaches unity as for a rectangular channel. 0.00 0.20 0.40 0.60 0.80 1.00 0.00 0.20 0.40 0.60 0.80 1.00 q f 1/q m 1 Yf1/Ym1 CWS GT Experiments Sturm 2004 CWS Hong 2013 LBS UoA CWS UoA Figure 4-3. Distribution of discharge per unit width between floodplain and main channel as affected by relative approach flow depth for five different compound channel geometries.

90 Given the distribution of q established between floodplain and main channel in the approach flow section, the spatial alteration of that distribution at the bridge is illustrated in Figure 4-4. The redistribution is the result of lateral width contraction of the bridge opening in addition to vertical contraction for SO and OT flow, and the flow separation around the abutment. In the approach flow section, the maximum values of q occurred for overtopping flow in both the floodplain and main channel due to the higher values of discharge for this case for both abutment lengths in Figure 4-4(a) and (b). The relative differences between floodplain and main channel values of q1 were much larger in comparison to the velocities in Figure 4-2 because of the larger depths in the main channel. At the downstream face of the bridge, considerable increases in q2 occurred compared to the approach flow section, more so for the longer abutment and corresponding smaller bridge opening area. Maximum values of q2 in the bridge section in Figure 4-4(c) and (d) were measured for submerged orifice flow in which all of the flow was passing under the bridge. Further increases in Q and tailwater for overtopping flow resulted in lower values of q2 because the net flow through the bridge was less than for submerged orifice flow as overtopping provided flow relief for the given set of experimental parameters. For all three flow types and both abutment lengths, the value of q2/q1 in the main channel was greater than unity, but more so for La/Bf = 0.77 which indicates that the main channel flow entrained a significant portion of the floodplain flow between the approach flow and bridge sections. Figure 4-5 illustrates the velocity vectors near the bed through the bridge for La/Bf = 0.41 and for F, SO, and OT flows. Flow separation occurred near the upstream corner of the abutment. The separation zone was significant in size for all three flow types but somewhat less pronounced for OT flow as the overtopping drew a portion of the flow over the bridge deck with nearly parallel streamlines. The separation zone was smaller for the right embankment because less flow came off the right floodplain around the abutment. At the downstream edge of the embankment, the curvilinear flow became nearly parallel upon completion of the acceleration.

91 0.0 0.3 0.5 0.8 1.0 1.3 1.5 1.8 0.8 1.2 1.6 2.0 2.4 2.8 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 U ni t D isc ha rg e (ft 2 /s ec ) Be d El ev at io n (ft ) Cross Section Station (ft) Model Bed Level Depth Average Approach Unit Discharge Run 1 F Flow Depth Average Approach Unit Discharge Run 2 SO Flow Depth Average Approach Unit Discharge Run 3 OT Flow La/Bf =0.41 0.0 0.3 0.5 0.8 1.0 1.3 1.5 1.8 0.8 1.2 1.6 2.0 2.4 2.8 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 U ni t D isc ha rg e (ft 2 /s ec ) Be d El ev at io n (ft ) Cross Section Station (ft) Model Bed Level Depth Average Approach Unit Discharge Run 1 F Flow Depth Average Approach Unit Discharge Run 2 SO Flow Depth Average Approach Unit Discharge Run 3 OT Flow La/Bf =0.77 (a) Approach flow q for La/Bf = 0.41 (b) Approach flow q for La/Bf = 0.77 0.0 0.3 0.5 0.8 1.0 1.3 1.5 1.8 0.8 1.2 1.6 2.0 2.4 2.8 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 U ni t D isc ha rg e (ft 2 /s ec ) Be d El ev at io n (ft ) Cross Section Station (ft) Model Bed Level Depth Average Br Section Unit Discharge Run 1 F Flow Depth Average Br Section Unit Discharge Run 2 SO Flow Depth Average Br Section Unit Discharge Run 3 OT Flow La/Bf =0.41 0.0 0.3 0.5 0.8 1.0 1.3 1.5 1.8 0.8 1.2 1.6 2.0 2.4 2.8 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 U ni t D isc ha rg e (ft 2 /s ec ) Be d El ev at io n (ft ) Cross Section Station (ft) Model Bed Level Depth Average Br Section Unit Discharge Run 10 F Flow Depth Average Br Section Unit Discharge Run 11 SO Flow Depth Average Br Section Unit Discharge Run 12 OT Flow La/Bf =0.77 (c) Bridge section q for La/Bf = 0.41 (d) Bridge section q for La/Bf = 0.77 Figure 4-4. Distribution of flow rate per unit width in approach flow and bridge sections.

92 1 ft/sec (a) Free flow 1 ft/sec (b) Submerged orifice flow 1 ft/sec (c) Overtopping flow Figure 4-5. Velocity vectors located 0.20 in. (5 mm) above the bed for La/Bf = 0.41.

93 The connection between spatial scour distribution and the properties of the flow field is illustrated in Figure 4-6 for La/Bf = 0.41 and 0.77 for free, submerged orifice and overtopping flows. In each figure plate, cross-section distributions at the downstream face of the bridge (subscript “2”) and at the downstream toe of the embankment in some cases are illustrated for the depth-averaged resultant velocity (V2(R)), the ratio of discharge per unit width in the bridge section to the average value in the approach-flow section (q2/q1avg), and the turbulent kinetic energy near the bed (Kb). The critical value of shear velocity for initiation of sediment motion (u*c) was used to nondimensionalize V2(R) and Kb. The value of q1avg was calculated separately for the floodplain and main channel approach flows and was used to nondimensionalize the cross- section distribution of q2 in the floodplain and in the main channel. Superimposed on the flow property distributions in Figure 4-6 are the original channel bed and the final bed after reaching equilibrium scour at the downstream toe of the embankment. This cross section was not necessarily the cross section of maximum scour depth, which was found somewhat further downstream of the bridge for La/Bf = 0.77. The resultant velocity in the left floodplain was larger near the abutment in the region of strongly curvilinear flow which coincided with the region of largest floodplain scour depth for the cross section. The resultant velocity remained smaller in the floodplain than the main channel for F and SO flow but was more uniformly distributed in the case of OT flow. Significantly higher values of V2(R) resulted from the increase in abutment length for all three flow types. Turbulent kinetic energy (Kb ) was elevated in the region of the floodplain and main channel scour holes for both abutment lengths, but it was significantly higher for the longer abutment. Separate scour holes formed in the floodplain and main channel for F and OT flows slightly downstream of the cross-section shown in Figure 4-6, but they joined for SO flow. A local rise in Kb was also observed at the interface between the main channel and floodplain, but it was smaller than the increases associated with the scour holes. Finally, distributions of q2/q1avg were relatively uniform in the floodplain and main channel and similar in magnitude; however, the ratios were larger for the longer abutment because of greater flow contraction, and they multiplied larger values of q1avg for the longer abutment to achieve the distributions of q2 shown in Figure 4-4. Bed elevation contours at equilibrium scour for the same abutment lengths and flow types as in Figure 4-6 are shown in Figure 4-7. A complete set of bed elevation contours with photographs of the bed are given in the Appendix. Increasing the abutment length for free flow caused a significant increase in the size and depth of the scour hole as shown in Figures 4-7(a) and (b). The scour hole was directly across from the face of the abutment in Run 1 but moved downstream and further away from the abutment in Run 10 with a more elongated shape. Deposition occurred immediately downstream of the scour hole in both cases, but further distinct deposition occurred for Run 10 in a large recirculation zone downstream of the embankment. Separate scour holes existed in the floodplain and main channel but they adjoined one another at the top of the bank of the main channel in Run 10. For SO flow shown in Figures 4-7 (c) and (d), the floodplain and main channel scour holes were deeper and combined with each other in the main channel. Overtopping flow seen in Figures 4-7(e) and (f) provided enough flow relief in this case that the scour holes were not as deep as for SO flow. For the longer abutment in SO and OT flow, lateral contraction scour extended from the floodplain into the main channel.

94 0 5 10 15 20 25 30 0 0.3 0.6 0.9 1.2 1.5 1.8 0 2 4 6 8 10 12 14 Di m en sio nl es s Va ria bl e El ev at io n , z (f t) Lateral distance, Y (ft) 0 5 10 15 20 25 30 0 0.3 0.6 0.9 1.2 1.5 1.8 0 2 4 6 8 10 12 14 Di m en sio nl es s Va ria bl e El ev at io n , z (f t) Lateral distance, Y (ft) (a) Run 1, Free flow, La/Bf = 0.41 (b) Run 10, Free flow, La/Bf = 0.77 0 5 10 15 20 25 30 0 0.3 0.6 0.9 1.2 1.5 1.8 0 2 4 6 8 10 12 14 Di m en sio nl es s Va ria bl e El ev at io n , z (f t) Lateral distance, Y (ft) 0 5 10 15 20 25 30 0 0.3 0.6 0.9 1.2 1.5 1.8 0 2 4 6 8 10 12 14 Di m en sio nl es s Va ria bl e El ev at io n , z (f t) Lateral distance, Y (ft) (c) Run 2, SO flow, La/Bf = 0.41 (d) Run 11, SO flow, La/Bf = 0.77 0 5 10 15 20 25 30 0 0.3 0.6 0.9 1.2 1.5 1.8 0 2 4 6 8 10 12 14 D im en sio nl es s Va ria bl e El ev at io n , z (f t) Lateral distance, Y (ft) 0 5 10 15 20 25 30 0 0.3 0.6 0.9 1.2 1.5 1.8 0 2 4 6 8 10 12 14 D im en sio nl es s Va ria bl e El ev at io n , z (f t) Lateral distance, Y (ft) (e) Run 3, OT flow, La/Bf = 0.41 (f) Run 12, OT flow, La/Bf = 0.77 Figure 4-6. Cross-section distributions of flow properties and scour for La/Bf = 0.41 and 0.77.

95 -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 ) Figue 4-7(a) Run 1, Free flow, La/Bf = 0.41 Figure 4-7(b) Run 10, Free flow, La/Bf = 0.77 -6 -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 ) Figure 4-7(c) Run 2, SO flow, La/Bf = 0.41 Figure 4-7(d) Run 11, SO flow, La/Bf = 0.77

96 -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 ) Figure 4-7(e) Run 3, OT flow, La/Bf = 0.41 Figure 4-7(f) Run 12, OT flow, La/Bf = 0.77 Figure 4-7. Bed elevation contours after equilibrium scour for La/Bf = 0.41 and 0.77. 4.2.4 Time Development of Scour The location and depth of maximum scour were measured as a function of time in order to ensure the development of equilibrium scour and to observe the path and final location of the point of deepest scour as it moved downstream. Even though it required very long experiments, the time-development measurements were deemed essential to producing a high-quality data set of equilibrium scour depths that could be used by other investigators in the future without time development artifacts. Temporal location of the point of deepest scour was considered useful information for bridge designers in determining the most vulnerable elements of the bridge foundation subject to the homogeneity of the sediment and the critical design flood duration. As shown in Figure 4-8, the floodplain scour hole deepened very rapidly in the first two to three hours of the scour experiments after which the depth (ds) increased slowly and asymptotically towards the equilibrium value in four to five days for La/Bf = 0.41 and 0.77. Equilibrium was considered to be established when the change in scour depth was less than 5% in the final 24 hrs of the experiment. With this definition, the required duration was less than or equal to five days in all experiments. Time development plots are also given in Figure 4-8 in terms of the water depth relative to the undisturbed flow depth (Yftmax/Yfo) as a function of the logarithm of dimensionless time. In these plots, the time development curves display a linear trend with the log of time during the mid-range of the experimental duration followed by an asymptotic approach to equilibrium as reported by many other investigators (Melville and Coleman 2000).

97 An exception to this behavior is Run 11 for SO flow with La/Bf = 0.77 in which the transition from the linear range to the asymptotic range is rather abrupt. In this case, two scour holes developed initially (see Figure 4-7). One of these scour holes was immediately downstream of the bridge on the floodplain with involvement of the main channel bank, and the other was further downstream of the bridge in the main channel bed. At first, the bank scour hole was deepest but then a shift occurred so that the main channel scour hole finished as the deepest. The paths of the points of maximum scour depth with respect to time are shown in Figure 4-9 for the same two abutment lengths and for all three flow types as in Figure 4-8. For the shorter abutment, the pathlines appear to overlay one another as influenced primarily by the flow separation angle of the blocked floodplain flow coming around the corner of the abutment. The F flow path ends across from the downstream face of the bridge, while the SO flow path extends the largest distance downstream of the bridge due to the higher velocities under the bridge. Although the effect is relatively small, the OT flow path straightens in the longitudinal flow direction downstream of the bridge in contrast to the other two flow types. The path straightening is likely due to a more uniform distribution of the approach flow to accommodate outflow across the entire bridge. For the longer abutment in Figure 4-9, the flow paths experience a larger angle of deflection from the longitudinal flow direction in correspondence with the change in flow separation angle resulting from larger transverse velocity components and larger magnitudes of blocked floodplain flow. In this case, the OT flow path also shows straightening downstream of the bridge with an accompanying large extension in length as the scour hole lengthens with time at its downstream end. The abrupt change in path for SO flow can be attributed to the initial development of a scour hole under the bridge which is co-opted by the eventual larger scour hole in the main channel.

98 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 0 50 100 150 d s (f t) t (hrs) La/Bf =0.41 Run 1 F Flow Run 2 SO Flow Run 3 OT Flow 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 0 50 100 150 d s (f t) t (hrs) La/Bf =0.77 Run 10 F Flow Run 11 SO Flow Run 12 OT Flow 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 Y f tm ax /Y fo Vf1*t/Yfo La/Bf =0.41 Run 1 F Flow Run 2 SO Flow Run 3 OT Flow 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 Y f tm ax /Y fo Vf1*t/Yfo La/Bf =0.77 Run 10 F Flow Run 11 SO Flow Run 12 OT Flow Figure 4-8. Time development of maximum depth of scour in linear and log coordinates for La/Bf = 0.41 and 0.77 in F, SO, and OT flows. 0 2 4 6 8 10 12 14 -1 0 1 2 3 4 5 6 Y (ft ) X (ft) La/Bf =0.41 Run 1 F Flow Run 2 SO Flow Run 3 OT Flow Floodplain Flow Direction Floodplain Main Channel 0 2 4 6 8 10 12 14 -1 0 1 2 3 4 5 6 Y (ft ) X (ft) La/Bf =0.77 Run 10 F Flow Run 11 SO Flow Run 12 OT Flow Floodplain Flow Direction Main Channel Floodplain Figure 4-9. Path of maximum scour depth with time for La/Bf = 0.41 and 0.77 in F, SO, and OT flows.

99 4.2.5 Organization of Scour Prediction Methodology Scour components of abutment/lateral contraction scour, vertical contraction scour, and pier scour were found to interact in specific combinations and were organized into categories such that a scour prediction formula could be developed from experimental data obtained for each category. Abutment and lateral contraction scour were treated in the same category because they are a function of the same independent variables, albeit in different proportions, as justified previously in Chapter 2. The scour interaction categories and the experimental approach were described previously in Chapter 3 and summarized in Table 3-2. In addition to the scour components just listed, the types of flow, designated as free (F), submerged orifice (SO), or overtopping (OT), were incorporated into the scour interaction categories. Separate categories were required for different abutment/embankment lengths defined previously as long setback abutments (LSA), short setback abutments (SSA), and bankline abutments (BLA). Both clear- water scour (CWS) and live-bed scour (LBS) were investigated and categorized for separate scour prediction formulas. Finally, some experiments were conducted in which pier scour and vertical contraction scour occurred alone without any interactions for comparison with accepted or recommended formulas. In Table 3-2, it can be seen that LSA and SSA/BLA categories are treated separately for purposes of scour depth prediction. As a result, a criterion is needed to distinguish between the two. By definition, an LSA terminates on the floodplain such that the deepest point of the scour hole is also contained on the floodplain. The combination of complex turbulent flow processes around the face of the abutment, including local turbulent structures generated by flow separation and interaction of main channel and floodplain flows, suggests that a CFD model could best define the ultimate location of the scour hole and the distinction between the LSA vs. SSA/BLA categories. As a practical matter, however, several ad hoc approaches were tried. The HEC-18 criterion of 5/ 1 fyW does not guarantee that 1/ fs BL as required for a LSA as shown in Figure 4-10, where W is the setback of the toe of the abutment from the main channel, and Ls is the distance from the outer edge of the floodplain to the measured point of maximum scour depth. The circled data points in Figure 4-10(b) were classified as SSA based on the location of the deepest part of the scour hole in the main channel. Some of those SSA data points satisfy the SSA criterion of 5/ 1 fyW while others do not. Conversely some LSA data points based on actual scour hole location would be classified as SSA based on the value of 1/ fyW . The reason for this discrepancy is that the abutment setback on the floodplain (W) does not account for the geometric or flow contraction because a given value of W may exist for different abutment lengths which have different geometric and flow contraction ratios. Figure 4-10(b) includes pier scour experiments in which the pier location varied between 1.5≤ Lp/Yf1 ≤7.5 and includes both setback and bankline piers. The presence of the pier caused no apparent change in the classification of SSA vs. LSA.

100 -6 -4 -2 0 2 4 X (ft) 14 12 10 8 6 4 2 0 Y (ft ) Ls Lm Lb Lx Deepest Scour Point W Bf La Lp (a) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 5.0 10.0 15.0 20.0 25.0 L s /B f W/Yf1 Dimensionless Scour Location GT Experiments Dimensionless Scour Location GT Experiments Hong 2013 Dimensionless Scour Location UoA Experiments Dimensionless Scour Location GT Pier Experiments LSA SSA Flood Plain Main Channel H E C -18 C riterion (b) Figure 4-10. Distinguishing LSA from SSA for scour prediction. (a) Definition sketch; (b) Comparison of data for maximum scour location with HEC-18 criterion for LSA. (Scour depths for circled data points were classified as SSA based on the experimental scour hole location.)

101 An alternative approach for categorizing abutment lengths as LSA or SSA is suggested in Figure 4-11 using the same experimental data as in Figure 4-10. The criterion is given as the product of La/Bf and Yf1/Yfo in which the former is representative of the degree of geometric contraction and the latter indicates the degree of flow contraction indirectly through the backwater ratio. The numerical criteria for LSA vs. SSA are given by LSAfor Y Y B L fo f f a 94.01      (4-1a) SSAfor Y Y B L fo f f a 94.01      (4-1b) The circled data points in Figure 4-11 are SSA based on the measured position of the scour hole and they satisfy the criterion given by Eq. (4-1b) based on their plotting position in the figure. 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 0.00 0.20 0.40 0.60 0.80 1.00 1.20 L s /B f La/Bf*Yf1/Yfo Dimensionless Deepest Scour Location GT Experiments Dimensionless Deepest Scour Location GT Experiments Hong 2013 Dimensionless Deepest Scour Location UoA Experiments Dimensionless Deepest Scour Location GT Pier Experiments Main Channel Flood Plain LSA SSA Figure 4-11. Proposed criterion for classifying abutment lengths as SSA or LSA for purposes of scour depth prediction (CWS). 4.2.6 Prediction of Pier Scour Alone Much research has been completed on the physical mechanisms of pier scour and the prediction of pier scour depth as outlined in Chapter 2. A comprehensive review of current pier-scour prediction methods recommends the Sheppard-Melville method because it better reflects the

102 physical mechanisms and parameters that influence those mechanisms, and because of its very large database, particularly covering piers of various width classes (Ettema et al. 2011). The FHWA publication, HEC-18 (Arneson et al. 2012) recommends both the Sheppard and Melville method and the Colorado State University formula. These two formulas were applied to experimental results from the Georgia Tech flume obtained in this study for the cases in which the piers were isolated from scour interactions. The piers were square, two-column piers as described in Chapter 3. The maximum pier scour depth was measured at the upstream pier. Approach-flow velocity was measured at a distance of four flow depths upstream of the pier where it was determined to be constant in the flow direction. Downstream of this point, deceleration of the flow began in response to the obstruction of the pier. Comparison of the experimental results and the predictions from the two aforementioned formulas for CWS are shown in Figure 4-12. The predictions are within 10% of the measurements which is within the interval of experimental uncertainty. These measurements provide confidence in the experimental methodology to reproduce results of many previous investigators. Based on these results, the Sheppard-Melville formula or the CSU formula can be used interchangeably to estimate contributions of pier scour to combined scour situations. 0 1 2 3 0 1 2 3 d s e/a (C al cu la te d) dse/a (Measured) CSU Eq S & M Eq +10% -10% Figure 4-12. Comparison of measured and calculated dimensionless pier scour depth for CWS results at Georgia Tech. (ds = pier scour depth; a = pier width).

103 4.2.7 Prediction of Vertical Contraction Scour Alone In contrast to pier scour, relatively few studies have been completed for vertical contraction scour which occurs for SO and OT flows. This study added to the database of vertical contraction scour results which are shown in Figure 4-13 along with those of a few other investigators. The independent dimensionless variable chosen here is the same as that proposed by Lyn (2008a), the ratio of velocity under the bridge to its critical value, Vb/Vc. The data sets for CWS include those of Arneson (Arneson 1997, Arneson and Abt 1999) and Georgia Tech from this study. In addition, unpublished data sets for both CWS and LBS from Auckland (personal communication, Melville 2016) are given. Reasonable agreement between the Georgia Tech and Auckland data in comparison with the Arneson data can be seen, and this group of data is consistent with Lyn’s Eq. (2-27), which was developed as a best-fit equation for the Arneson data. Eq. 2-27 with A1 = 0.105 and A2 = 0.5 is shown as the lower curve in Figure 4-13. Also shown are the more recent CWS scour data of Shan et al. (2012). The Umbrell et al. (1998) are not shown in the figure because the experimental duration was only three hrs with extrapolation to equilibrium. Given the scatter in the data from all sources shown, it seems prudent for the purposes of this report to adopt the dashed envelope curve of Lyn (2008a) which is given by Eq. 2-27 with A1 = 0.21 and A2 = 0.6.   5.0,/105.0min 95.2 1 cb se VV Y d    6.0,/21.0min 95.2 1 cb se VV Y d  0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0 1 2 3 d s e/Y 1 Vb/Vc Lyn Eq with 0.105 Lyn Eq With 0.21 GT Data Shan et al 2012 Arneson CWS Data Arneson LBS Data Melville CWS Data Melville LBS Data Figure 4-13. Comparison of vertical contraction scour data from this study with data from other sources.

104 4.2.8 Category I Scour Interactions Category I scour interactions incorporate combined abutment/lateral contraction scour with or without vertical contraction scour for a LSA. Scour contours for Category I can be observed for two different abutment lengths subjected to F, SO, and OT flow as shown in Figure 4-7, except for panel (d) which is a SSA. The analysis proposed herein is a combination of dimensional analysis and theoretical lateral contraction scour analysis. It is further informed by recent research recognizing the relative importance of local abutment scour driven by complex, coherent turbulent structures spawned by flow separation vs. flow acceleration accompanying a constricted channel width caused by the bridge. Several abutment scour and lateral contraction scour formulas have been summarized in Chapter 2, and a comprehensive analysis of abutment and lateral contraction scour research can be found in Sturm et al. (2011). An expansion of the dimensional analysis presented by Sturm (2006) and by Sturm et al. (2011) for LSA, and including the possibility of vertical contraction scour, is given by (see Figure 2-1 and Figure 2- 5):     EEf fff f ba f b sm sf m f m f f a c f fo f s fo f HY tVYV gY V Y L d L Y h k k Y Y B B B L V V Y Y KK Y Y      ,,,,,,,,,,,,,, 1 111 1 1 15011 111 1 max2 (4-2) in which Ks = shape factor of the abutment, Kθ = embankment skewness factor, Yf2max = maximum depth of flow in the equilibrium scour hole,; Yf1 = approach flow depth in floodplain, Yfo = undisturbed flow depth on the floodplain at the bridge, Ym1 = approach flow depth in the floodplain, Vf1 = approach flow velocity in the floodplain, Vc = critical velocity for sediment motion, La = length of the abutment/embankment; Bf = width of the floodplain, Bm = width of the main channel, ksf and ksm = sand-grain roughness height of the floodplain and main channel, respectively, hb = depth below low chord of the bridge, Lb = width of the embankment in the flow direction, d50 = median sediment grain size;  and  = density and viscosity of the fluid, respectively; g = acceleration of gravity,  = bulk shear strength of the embankment fill, E = bulk density of the embankment material, and, HE = height of the embankment. The dimensionless parameters beginning with La/Bf and ending with hb/Yf1 all affect the flow distribution per unit width in the bridge section due to the compound channel flow and its acceleration, and they can be replaced by qf2/qf1, the ratio of discharge per unit width in the bridge section to that in the approach flow section. The effects of La/d50 and Lb/Yf1 are considered negligible based on previous research. Scour depths in this research were not significantly different for spill-through vs. wingwall abutments, and this research did not consider skewed abutments. For riprap-protected embankments with a riprap apron as in this research, the last parameter on the right-hand side is considered to be a constant. With these assumptions, Eq. (4- 2) becomes:     1 1 1 211 2 max2 ,,,,, f f f f c f fo f fo f Y tV q q V V Y Y Y Y 11 ReF (4-3)

105 For equilibrium scour depth, the time parameter can be removed. The Froude number (F1) is considered to be of secondary importance and the approach flow Reynolds number (Re1) was large enough to ensure a fully turbulent flow. Under these circumstances, Eq. (4-2) reduces to     1 211 3 max2 ,, f f c f fo f fo f q q V V Y Y Y Y  (4-4) in which Yf1/Yfo is the backwater ratio, Vf1/Vc is the flow intensity, and qf2/qf1 is the discharge contraction ratio or unit discharge ratio. Laursen’s long contraction theory (1960, 1963) provides the basis for the calculation of abutment scour depth as a fixed amplification factor times the theoretical contraction scour depth. This approach has been applied in a number of investigations such as that by Sturm (2006) for a solid abutment and embankment in compound channel flow and Ettema et al. (2010) for an erodible embankment and abutment in a compound channel. The mathematical expression of such an approach is given by Hong et al. (2015) in terms of the parameters in Eq. (4-4): 7/6 1 211max2      f f c f fo f T fo f q q V V Y Y r Y Y (4-5) in which rT is the amplification factor. Ettema et al. (2010) suggested a variable amplification factor that showed a decreasing function with increasing values of q2/q1. They attributed the trend to a decreasing influence of the local turbulence effects caused by the abutment relative to the increasing acceleration associated with a more severe width constriction. The CWS data from this study for LSAs are plotted in Figure 4-14 in terms of rT on the vertical axis, where Yc is the theoretical contraction scour, as a function of qf2/qf1. While the data of Ettema et al. (2010) for free flow follow their proposed envelope curve, the data in this study show a considerably higher value of rT and a greater degree of scatter, especially for the OT flow case. (For OT flow, the value of qf2/qf1 is taken to be the value under the bridge by first subtracting the overtopping discharge.) Differences in abutment erodibility, additional flow types, and the variation of Vf1/Vc from 0.6 to 0.9 in the present study as opposed to a constant value of 0.9 in the Ettema et al. (2010) data could account for some of the scatter shown in Figure 4-14. While the envelope curve could be moved upward in Figure 4-14, this attempt to extend the concept of rT to SO and OT flow was not entirely satisfactory. Hong et al. (2015) compared a constant value of rT with a variable rT as a function of qf2/qf1 based on the data from the Ph.D. thesis by Hong (2013). These data encompassed all three types of flow and two abutment lengths, but the data were more limited than in the present study. The constant value of rT was 2.54 with a standard error of estimate (SEE) in Yf2max/Yfo of 0.173. Alternatively, a regression analysis in the form of Eq. (4-5), while holding constant the power

106 0.0 1.0 2.0 3.0 4.0 5.0 0.0 1.0 2.0 3.0 4.0 5.0 Y f 2m ax /Y fc (qf2/qf1) Hong F Flow Hong SO Flow Hong OT Flow GT F Flow GT SO Flow GT OT Flow UoA F Flow UoA SO Flow UoA OT Flow Ettema F Flow Ettema Envelope Figure 4-14. Amplification factor for maximum depth of CWS around LSA in the form suggested by Ettema et al. (2010). parameter of 6/7, produced the variation of rT with qf2/qf1 (see Eq. (2-18)) given by: 16.0 1 275.2      f f T q q r (4-6) for which the SEE was 0.132. Eq. (4-6) is consistent with the assumption that scour around a very short abutment is dominated by the turbulent structure of the horseshoe vortex and flow separation which decrease in importance relative to the width contraction with increasing values of the discharge contraction ratio. Figure 2-18 shown previously further confirms a decrease in the initial (fixed bed), width-averaged TKE across the scour hole with increases in qf2/qf1.

107 The two relationships suggested by Hong (2013) for rT were applied to the full complement of available data in Figure 4-14 including the CWS data from Georgia Tech and UoA in the present study, Hong’s data, and the data from Ettema et al. (2010). The statistical performance of Hong’s model (constant rT) and Hong’s modified model (Eq. (4-6)) is shown in the first two rows of Table 4-5 where the models are designated as Model 1 and Model 2. While the full data set filled gaps and extended the range of Hong’s original data, it is evident that the statistical performance declined as evidenced by an increase in SEE when applying Models 1 and 2, which were based only on Hong’s limited data, to the full data set. The attractiveness of the Ettema et al. (2010) approach to LSA scour with a variable amplification factor is its link to a theoretical contraction scour depth that depends on a very long contraction with steady uniform flow occurring upstream and in the contracted section. At the same time, its interpretation is hampered by the mistaken impression that the theoretical contraction scour depth is what should actually be expected and measured in the field when in fact it is only a reference value. The assumptions of the theoretical long contraction are not met by a bridge contraction so that fixing the power in Eq. (4-5) to 6/7 based on Manning’s equation is not necessarily justified in the absence of steady, uniform flow. One important element of the Ettema et al. approach, however, is the observed decrease in the amplification factor with increases in qf2/qf1. This finding is corroborated by Eq. (4-6) based on Hong’s data. An alternative approach is to allow the power parameter of 6/7 to serve as a variable in a regression analysis of the full data set. The combination of Eq. (4-5) and Eq. (4-6) suggests that the power parameter should be something less than 6/7. In Model 3 in Table 4-5, power values on each of the three independent parameters in Eq. 4-5 were allowed to vary independently when regression analysis was applied to the full data set. A least-squares best-fit equaton of the form d f f c cf f b fo f fo f q q V V Y Y a Y Y             1 2 1 11max (4-7) was obtained from the full data set with the results shown as Model 3 in Table 4-5. The SEE was reduced from 0.289 to 0.233 and the coefficient of determination (R2) increased from 0.68 to 0.82. Furthermore, it is of interest that c ≅ d as in the theoretical analysis and that their values are approximately 0.5 in contrast to 6/7. In other words, the lower magnitude of the power incorporates the role of a decreasing amplification factor. In Model 4 in Table 4-5, the variables c and d are forced to be a single parameter, and the statistical performance is essentially unchanged as is the value of b. Finally, in Model 5, the powers b, c, and d are rounded off within the interval of their uncertainty given by their standard errors (SE) in Table 4-5 with virtually no change in SEE or R2. An attempt was also made to drop Yf1/Yfo as a parameter, but the results showed it to be a statistically significant parameter that should be included. The final relationship for Category I combined scour depth is shown in Figure 4-15 and is given by

108 50.0 1 2 1 1 50.1 1max2 363.2                 f f fc f fo f fo f q q V V Y Y Y Y (4-8) with R2 = 0.82 and SEE = 0.230. The data originate from experiments in the Georgia Tech and UoA CWS flumes at two different bridge scales and compound channel geometries as well as from the separate experiments of Ettema et al. (2010). Furthermore, they include F, SO, and OT flows. Shown for comparison in Figure 4-15 is the theoretical long contraction scour relationship for which Yfmax/Yfo is equal to 1.0. The data appear to approach an upper limit of Yfmax/Yfo = 3.6 which is applicable to erodible abutments and embankments subject to riprap protection with some sliding of the riprap apron possible but no catastrophic failure. Table 4-5. Succession of regression models applied to the full CWS, LSA data set (Category I). Model Best Fit Formula R2 SEE Parameter Details 1. Hong (2013) Model 7/6 1 2 1 1 0.1 1max2 **51.2*         f f fc f fo f fo f q q V V Y Y Y Y 0.64 0.312 SEE = 0.173 for Hong (2013) data 2. Hong (2013) Modified Model 7/6 1 2 1 1 16.0 1 2 0.1 1max2 **75.2*              f f fc f f f fo f fo f q q V V q q Y Y Y Y 0.68 0.289 SEE = 0.132 for Hong (2013) data 3. Separate, Variable Powers 51.0 1 2 50.0 1 1 51.1 1max2 *345.2*             f f fc f fo f fo f q q V V Y Y Y Y 0.82 0.233 Parameter Value SE a 2.345 0.105 b 1.514 0.300 c 0.513 0.069 d 0.499 0.096 4. Theo. Contraction Scour as Single Variable 51.0 1 2 1 1 53.1 1max2 *356.2*                 f f fc f fo f fo f q q V V Y Y Y Y 0.82 0.230 Parameter Value SE a 2.356 0.006 b 1.534 0.057 c 0.509 0.037 5. Rounded powers 50.0 1 2 1 1 50.1 1max2 *363.2*                 f f fc f fo f fo f q q V V Y Y Y Y 0.82 0.230 Parameter Value SE a 2.363 0.069 .

109 0.0 1.0 2.0 3.0 4.0 5.0 0.0 1.0 2.0 3.0 4.0 5.0 Y f 2m ax /Y f0 [(Yf1/Yf0)3(Vf1/Vfc1)(qf2/qf1)] Hong F Flow Hong SO Flow Hong OT Flow GT F Flow GT SO Flow GT OT Flow UoA F Flow UoA SO Flow UoA OT Flow Ettema F Flow Model Theoretical CS Yf1/Yfo = 1 Upper Limit for Spill-Through Erodible Abutments Riprap Protected Figure 4-15. Predicted maximum flow depth of scour hole for LSA, Category I scour (Theoretical contraction scour (C.S.) shown for reference). Eq. (4-8) was developed for spill-through abutments, and it is compared to results for wingwall abutments from this study in Figure 4-16. The wingwall data cover the same range as for the spill-through data but there are fewer data points. Experiments were conducted for all three flow types (F, SO, and OT flows) and for three different abutment ratios with La/Bf = 0.41, 0.50, and 0.77 (experiments for La/Bf = 0.50 were conducted at University of Auckland). A separate regression analysis was applied to the wingwall data alone to obtain the best-fit value of the coefficient, a, with the result that a = 2.31 and SEE = 0.329. Similarly, Eq. (4-8) was applied to the wingwall data with the spill-through value of a =2.36, and the resulting SEE was essentially the same with a value of 0.334. While the prediction error is somewhat greater for the wingwall abutment, the difference in a of only two percent indicates that a separate shape factor is not required, and Eq. (4-8) is applicable to either spill-through or wingwall abutments.

110 0.0 1.0 2.0 3.0 4.0 5.0 0.0 1.0 2.0 3.0 4.0 5.0 Y f 2m ax /Y f0 [(Yf1/Yf0)3(Vf1/Vfc1)(qf2/qf1)] Irfan F Flow WW Irfan SO Flow WW Irfan OT Flow WW UoA SO Flow WW UoA OT Flow WW Ettema F WW Model Theoretical CS Yf1/Yfo = 1 Figure 4-16. Predicted maximum CWS flow depth of scour hole for LSA, wingwall abutment, Category I scour (Theoretical contraction scour (C.S.) shown for reference). Comparison of Eq. (4-8) with field data is shown in Figure 4-17. The Towaliga River data point was obtained by the hybrid method discussed in Chapter 2; i.e., the scour depth was measured in the field during and shortly after the flood while the scour prediction parameters were determined from a hydraulic model study (see Figure 2-16 and Figure 2-17). The field data point is in the lower range of the laboratory data and agrees well with Eq. (4-8). A second field data point for scour depth is also shown in Figure 4-17 from the 1993 flood on the Missouri River at I-70 near Rocheport, MO. The nearest USGS gauging station is 17 mi. (27 km) upstream at Boonville, MO. The drainage area at this station is 500,000 mi2 (1.28×106 km2) and a peak discharge of 755,000 cfs (21,400 m3/s) was estimated for the 1993 flood. More uncertainty exists for this data point than for the Towaliga River example, but it is worth considering because it is one of the deepest scour holes known for a LSA with a measured depth of 56 ft (17 m) on the floodplain. The available information for this scour event is documented by Parola et al. (1998). The upstream floodplain flow depth was reported to be 14.1 ft (4.3 m) with a flow depth of 10.8 ft (3.3 m) in the bridge section. The left bank of the main channel was contained by a levee. The bridge spanned approximately 1000 ft (0.3 km) of main channel and 1600 ft (0.5 km) of the right floodplain. The total floodway width was 9500 ft (2.9 km). The

111 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Y f 2m ax /Y f0 [(Yf1/Yf0)3(Vf1/Vfc1)(qf2/qf1)] Hong F Flow Hong SO Flow Hong OT Flow GT F Flow GT SO Flow GT OT Flow UOA F Flow UOA SO Flow UOA OT Flow Ettema F Flow Model Theoretical CS Towaliga River Missouri River Yf1/Yfo = 1 Figure 4-17. Comparison of field data with predicted maximum flow depth of scour hole for LSA, Category I scour. right abutment, where the scour hole occurred, was protected by a guide bank. After the flood, no evidence of upstream erosion was observed, so it was assumed that the scour was CWS. If it is further assumed that the depth was large enough for compound channel effects to be small, then qf2/qf1 can be estimated as 9500/2600 = 3.6. It is also assumed that Vf1/Vfc1 was approximately 0.9. Then substituting into Eq. (4-8), we have   3.66.39.0 8.10 1.14363.2363.2 2/1 2/350.0 1 2 1 1 50.1 1max2                   f f fc f fo f fo f q q V V Y Y Y Y (4-9) which gives an estimated scour depth, ds = (6.3×10.8) – 10.8 = 57 ft compared with the measured value of 56 ft. The extension of Eq. (4-8) in Figure 4-17 shows it to be an envelope curve for this extreme case. While more field data are needed in the intermediate range between maximum scour for a riprap-protected erodible embankment and this field case with guide bank protection, it is encouraging that there is consistency of Eq. (4-8) with the Missouri River data point at the

112 upper limit. For further context, dimensionless scour depth (ds/Yfo) around a solid vertical or spill-through an abutment with significant contraction has been shown to be approximately 10 (Melville and Coleman 2000, Sturm 2006) in contrast to the maximum value of ds/Yfo ≅ 5 (Yf2max/Yfo ≅ 6) in the Missouri River field case. Furthermore, a maximum value of ds/Yfo ≅ 2.6 (Yf2max/Yfo ≅ 3.6) for the riprap-protected abutment was observed in this study. These differences likely reflect the influence of the degree of erodibility or protection of the embankment. The Category I scour classification for CWS around LSAs assumes that lateral contraction and local abutment scour, with vertical contraction scour included for SO and OT flows, can be calculated by the same formula that is based on their interaction. This combination is possible because the scour processes are governed by the same independent dimensionless parameters. In contrast, the HEC-18 procedure, to be on the conservative side, suggests independent calculation of abutment scour and contraction scour followed by simple addition of the components. The degree of conservatism in the HEC-18 procedure for this scour category can be evaluated from the data in this study as shown by Figure 4-18(a). Overprediction by the HEC-18 additive procedure is approximately 20-30% within 95% confidence limits. In contrast, the prediction error of Eq. 4-8 developed in this study is ±4% within the 95% confidence intervals as shown in Figure 4-18(b). Approximately 75% of the predictions of Eq. (4-8) are within ±10% of the measured values. This level of error is consistent with the expected experimental uncertainty. 0.0 1.0 2.0 3.0 4.0 5.0 6.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 (Y f2 m ax /Y fo ) P re di ct ed (Yf2max/Yfo) Measured LSA CWS HEC-18 GT LSA CWS HEC-18 UoA +10% -10% Figure 4-18(a) Clear-water interactive abutment and contraction scour prediction by HEC-18 procedure .

113 0.0 1.0 2.0 3.0 4.0 5.0 6.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 (Y f2 m ax /Y fo ) P re di ct ed (Yf2max/Yfo) Measured LSA CWS Suggested Model GT LSA CWS Suggested Model UoA +10% -10% Figure 4-18(b) Clear-water interactive abutment and contraction scour prediction (suggested model). Figure 4-18. Comparison of measured and predicted clear water, interactive abutment and contraction scour by HEC-18 procedure and suggested Category I Model (dashed lines represent ±10% of perfect agreement). 4.2.9 Category II Scour Interactions Category II scour interactions include combinations of lateral contraction scour and local abutment scour, in addition to vertical contraction scour for SO and OT flows, for CWS around BLAs. Scour contours are shown for a representative experimental run in this category in Figure 4-7(d). A similar regression analysis was applied to the Category II data as described previously for the Category I data, and the results are given in Table 4-6. Models 1 and 2 from the Hong data alone do not perform well on all of the data because the full data set, including all data from this study, extends the range of coverage of the parameters. It is notable that Model 3, however, corroborates the finding for Category I combined scour that the power of 6/7 in the theoretical contraction scour equation reduces to a value close to 0.5 to describe the greater rate of decrease of scour depth with increases in (Vm1/Vmc1)×(qm2/qm1) as an alternative to a variable amplification factor. Furthermore, Model 3 shows that the role of (Ym1/Ymo) is statistically insignificant in the BLA case because the depths are much larger in the main channel than in the floodplain so that the backwater ratio is relatively smaller. In Model 4, the power of 0.55 in Model 3 is rounded to 0.5 within its error limits with almost no change in R2 or SEE. The best-fit equation for Model 4

114 for the BLA (R2=0.70 and SEE = 0.153) is given by 50.0 1 2 1 1max2 **725.1     m m mc m mo m q q V V Y Y (4-10) Table 4-6. Succession of regression models applied to the full CWS, BLA data set (Category II). Model Best Fit Formula R2 SEE Parameter Details 1. Hong (2013) Model 7/6 1 2 1 1 0.1 1max2 **66.1*         m m mc m mo m mo m q q V V Y Y Y Y --- 0.319 2. Hong (2013) Modified Model 7/6 1 2 1 1 12.0 1 2 0.1 1max2 **75.1**              m m mc m m m mo m mo m q q V V q q Y Y Y Y --- 0.292 3. Theo. Contraction Scour as Single Variable 55.0 1 2 1 1 0 1max2 **712.1*         m m mc m mo m mo m q q V V Y Y Y Y 0.71 0.151 Parameter Value SE a 1.712 0.025 b 0.550 0.093 4. Rounded Powers 50.0 1 2 1 1max2 **725.1     m m mc m mo m q q V V Y Y 0.70 0.153 Parameter Value SE a 1.725 0.026 b 0.500 0.056 5. Combined Regression of BLA & SSA 50.0 1 2 1 1max2 **722.1     m m mc m mo m q q V V Y Y 0.59 0.183 Parameter Value SE a 1.722 0.004 b 0.500 0.091 The best-fit curve of Eq. (4-7) is shown in Figure 4-19 in comparison with the available data. The magnitude of dimensionless Category II scour for the BLA is smaller than in the case of Category I scour for the LSA, but it must be emphasized that Category II scour parameters are evaluated relative to the main channel rather than the floodplain as for Category I.

115 0.0 1.0 2.0 3.0 4.0 5.0 0.0 1.0 2.0 3.0 4.0 5.0 Y m 2m ax /Y m o [(Vm1/Vmc1)(qm2/qm1)] Hong F Flow Hong SO Flow Hong OT Flow GT F Flow GT SO Flow GT OT Flow Sturm 2006 Model Theoretical CS Ym1/Ymo = 1 Figure 4-19. Predicted maximum CWS flow depth of scour hole for BLA, Category II scour. (Theoretical long contraction scour shown for reference). Scour data for the SSA, specifically defined such that the deepest point in the scour hole falls in the main channel rather than in the floodplain, are compared with Eq. (4-10) in Figure 4-20. The SSA data in Figure 4-20 were chosen such that they satisfied the criterion given by Eq. (4-1b), and it can be observed that they follow the BLA Category II relationship rather well. The data in Figure 4-20 come from both Georgia Tech and UoA. The regression model shown as Model 5 in Table 4-6 is the result of regression analysis of the SSA and BLA data together. Although there is some deterioration in R2 and SSE, the parameters in Eq. (4-10) are essentially unchanged. Eq. (4-10) is also compared with data from wingwall abutments in Figure 4-21 and the data follow the same trend with no evidence of a shape factor needed within the inherent error of the experimental measurements. As a consequence, Eq. (4-10) is recommended for Category II scour for both BLA and SSA abutment categories including both spill-through and wingwall abutment shapes.

116 0.0 1.0 2.0 3.0 4.0 5.0 0.0 1.0 2.0 3.0 4.0 5.0 Y m 2m ax /Y m 0 [(Vm1/Vmc1)(qm2/qm1)] Hong F Flow Hong SO Flow Hong OT Flow UOA F Flow UOA SO Flow UOA OT Flow Sturm 2006 GT SO Flow BLA Model Theoretical CS Ym1/Ymo = 1 Figure 4-20. Comparison of BLA scour prediction equation with SSA data, Category II scour. (Theoretical long contraction scour shown for reference). 0.0 1.0 2.0 3.0 4.0 5.0 0.0 1.0 2.0 3.0 4.0 5.0 Y m 2m ax /Y m o [(Vm1/Vmc1)(qm2/qm1)] GT F Flow WW BLA GT SO Flow WW BLA GT OT Flow WW BLA UoA OT Flow WW SSA UoA F Flow WW SSA Model Theoretical CS Ym1/Ymo = 1 Figure 4-21. Comparison of BLA scour prediction equation with wingwall (WW) data, Category II scour. (Theoretical long contraction scour shown for reference).

117 As discussed in Chapter 2, adequate field measurements at the peak of the flood event are rarely available for bridge scour; however, three documented flood events were found in the literature for Category II scour. The Towaliga River flood event caused by Tropical Storm Alberto, which occurred in Georgia in 1994, was reproduced in the hydraulics laboratory of the Georgia Institute of Technology. The flow type was submerged orifice flow with an erodible embankment in a compound channel. A long setback abutment was located in the left floodplain and a bankline abutment on the right bank of the main channel. The cross-section is shown in Figure 2-17, and the measured depth of the scour hole in the left floodplain was used previously to verify the Category I scour equation (see Figure 4-17). In the case of Category II scour, the field-measured scour hole depth on the right bank was compared with the scour depth prediction by Eq. (4-10). As in the Category I case, a hybrid method was applied in which the physical model study of the Towaliga River bridge was used to obtain the scour prediction parameters. The comparison is shown in Figure 4-22 and is quite acceptable. The other two field examples are for the April 1997 flood occurring at the Highway 22 bridge over the Pomme de Terre River in Minnesota, and at the Highway 12 bridge located ten kilometers downstream of Highway 22. Data for scour prediction parameters were taken from Sturm (2004) who calibrated a WSPRO model based on cross-section data and water surface elevations supplied by Sterling Jones (personal communication 1998). Mueller and Wagner (2005) also included these two bridges in their analysis of field data using HEC-RAS. Calculated equilibrium scour depths using Eq. (4-10) are compared in Figure 4-22 with field data measurements for all three cases just described. The field data for the Towaliga River bridge and the Minnesota Highway 22 bridge plot at the lower and middle range of the laboratory data, while the Minnesota Highway 12 bridge scour depth prediction agrees with the field measurement at the extrapolated upper end of Eq. (4-10). The calculated scour depths are within 10% of the measured depths. Overall, this is a limited comparison with field data but it does provide some confidence in the validity of Eq. (4-10).

118 0.0 1.0 2.0 3.0 4.0 5.0 0.0 1.0 2.0 3.0 4.0 5.0 Y m 2m ax /Y m o [(Vm1/Vmc1)(qm2/qm1)] Hong F Flow Hong SO Flow Hong OT Flow GT F Flow GT SO Flow GT OT Flow Model Theoretical CS Towaliga River Highway 12 Highway 22 Ym1/Ymo = 1 Figure 4-22. Comparison of Eq. (4-10) with field data for Category II scour. A comparison between predicted and measured combined scour for Category II is shown in Figure 4-23 using the HEC-18 procedure. Scour depths were predicted separately for each scour component according to the HEC-18 equations and then added together. The results in Figure 4- 23 show that this approach overpredicts the combined scour in Category II from approximately 40 to 50% within the 95% confidence limits. All predictions are greater than the ±10% error lines shown in the figure. Predicted scour depths for Category II scour data using the proposed Eq. (4-10) are compared with measured data in Figure 4-24. The data set includes data from both Georgia Tech and the UoA. The prediction error of Eq. (4-10) is approximately ±3% within the 95% confidence limits. Nearly 80% of the predictions are within the ±10% error lines, indicating that as for Category I scour, the approach suggested in this study eliminates the large bias associated with over- predictions by the HEC-18 procedure.

119 0.0 1.0 2.0 3.0 4.0 0.0 1.0 2.0 3.0 4.0 (Y m 2m ax /Y m o) Pr ed ic te d (Ym2max/Ymo) Measured BLA/SSA CWS HEC-18 GT BLA/SSA CWS HEC-18 UoA +10% -10% Figure 4-23. Comparison of measured and predicted maximum CWS depth for Category II scour with predictions from HEC-18 additive methodology. 0.0 1.0 2.0 3.0 4.0 0.0 1.0 2.0 3.0 4.0 (Y m 2m ax /Y m o) Pr ed ic te d (Ym2max/Ymo) Measured BLA/SSA CWS Suggested Model GT BLA/SSA CWS Suggested Model UoA +10% -10% Figure 4-24. Comparison of measured and predicted maximum CWS depths for Category II scour with predictions from proposed Eq. (4-10).

120 4.2.10 Category III Scour Interactions Pier scour interactions between abutment/lateral contraction scour, with or without vertical contraction scour, define Category III scour interactions. Experiments were conducted without the pier and then repeated with different pier locations for all three types of flows (F, SO, and OT flows). The pier was located various lateral distances from the toe of the abutment, Lp, relative to the setback distance, W, while remaining within the zone of influence of the abutment (see Figure 4-10). The pier location was set at Lp/W = 0.18 and 0.35 for La/Bf = 0.41, and in case of La/Bf = 0.77, the pier location was set at Lp/W = 0.40 and 1.0. Interaction of the pier scour and abutment/lateral contraction scour is shown in Figure 4-25 for free flow. Although it appears that the pier altered the shape of the scour hole slightly for both pier positions in comparison to the case of no pier, the maximum depth of the scour hole is not noticeably different based on the bed elevation contours. The scour hole shape was partly affected by diversion of the flow by the pier with a concentration between the pier and the abutment, while the riprap may also have influenced the final shape and location. Similar effects of the pier on the abutment/contraction scour hole can be observed in Figure 4-26 for SO flow but with the additional information of final riprap appearance at equilibrium conditions shown in the photographs. In the absence of a pier, riprap from the apron is distributed along the bottom of the scour hole as shown in Figure 4-26(a). With the pier located in the bottom of the abutment scour hole as shown in Figure 4-26(b), riprap accumulates at the base of the pier columns. Finally, for the pier located at the outside edge of the main abutment scour hole in Figure 4- 26(c), a separate pier scour hole forms in which no riprap is present. From Figure 4-25 and Figure 4-26, it is apparent that pier interaction with abutment/contraction scour is a two-way process. Maximum pier scour occurs at the upstream edge of the upstream pier as in isolated pier scour, but it depends on the distance of the pier from the abutment. For abutment/contraction scour, the deepest point is further downstream, and it varies depending on different scour parameters. Thus, the interaction of pier scour with abutment/contraction scour must consider the effect of the pier on abutment/contraction scour, and the effect of abutment/contraction scour on pier scour.

121 0.3 0.5 0.7 0.9 1.1 1.3 1.5 Elevation Z (ft) -6 -4 -2 0 2 4 x (ft) 14 12 10 8 6 4 2 0 y (ft ) Run 8 Lp/W=0.35 -6 -4 -2 0 2 4 x (ft) 14 12 10 8 6 4 2 0 y (ft ) Run 6 Lp/W=0.18 -6 -4 -2 0 2 4 x (ft) 14 12 10 8 6 4 2 0 y (ft ) Run 4 No pier Abutment Scour Abutment Scour Pier Scour Abutment & Pier Scour F Flow T/W = 1.477 ft Vf1/Vfc1=0.655 Vm1/Vmc1=0.841 Q = 3.7 cfs Figure 4-25. Illustration of pier interaction with abutment/lateral contraction scour for free flow, La/Bf = 0.41. Figure 4-26(a) Run 2 SO flow without pier.

122 Figure 4-26(b) Run 28 SO flow, Lp/W = 0.18. Figure 4-26(c) Run 29 SO flow, Lp/W = 0.35. Figure 4-26. Effect of pier location on abutment/contraction scour and riprap movement for SO flow, La/Bf = 0.41, Vf1/Vfc =0.589, Vm1/Vmc =0.725

123 4.2.10.1 Effect of Pier on Abutment/Contraction Scour (Category III) Table 4-4 was presented previously to show the scour parameters measured for the experiments conducted with the pier placed within the influence of the abutment scour hole along with the pier location, type of flow, abutment length, and the maximum equilibrium scour depth measured at the upstream front of the pier (Yf2max/ Yo (Pier)) and at the deepest point in the abutment scour hole (Yf2max/ Yo (Ab)), where Yo is the undisturbed flow depth at the pier location. The location of the pier relative to the toe of the abutment was varied such that the pier distance normalized by the approach flow depth (Lp/Yf1), ranged between 1.5 and 11 for three abutment lengths (La/Bf = 0.41, 0.53, and 0.77) and for three types of flows (F, SO, and OT flows). The effect of the pier on the maximum abutment/contraction scour depth is shown in Figure 4-26 as a function of pier offset from the abutment. The measured maximum abutment/contraction scour depth with a pier in place is nondimensionalized by the maximum abutment/contraction scour depth calculated from Eq. (4-8) for Category I scour (Yf2maxo) without a pier. Over the full range of pier positions, the ratio of maximum abutment scour depth with a pier to that without a pier is approximately 1.0. All the data points in Figure 4-27(a) fall within ±15% of a value of unity for the ratio which is consistent with the experimental uncertainty in the measured maximum scour depths. A few experiments were conducted with wall piers, and the results are shown in Figure 4-27(b). The wall pier results are essentially the same as for the two-column piers. The conclusion is that despite the seeming disturbance of the flow pattern caused by the pier, the maximum abutment scour depth is not substantively changed by the pier because the basic abutment scour processes do not seem to be fundamentally altered in agreement with Oben and Ettema (2011). This study extends their finding to SO and OT flows as well as F flows. The intensity and location of the abutment scour processes are governed by the position of the abutment and its separate effect on the flow field. As a consequence, adding the calculated pier scour depth to the maximum abutment/contraction scour depth is an unnecessary degree of conservatism. However, the reverse may not be true for the effect of the abutment on the maximum pier scour depth. In summary, the performance of Eq. (4-8) developed for Category I scour in predicting Category III scour depth at the abutment in the presence of a pier is shown in Figure (4-28). The majority of the data points fall inside the ±10% error lines. Further, adding the calculated pier scour depths to the maximum abutment/contraction depth increases the conservatism of scour predictors.

124 0.0 0.5 1.0 1.5 2.0 0.00 3.00 6.00 9.00 12.00 Y f 2m ax /Y f2 m ax o Lp/Yf1 Pier Affected Abutment Scour La/Bf=0.41 Pier Affected Abutment Scour La/Bf=0.77 Pier Affected Abutment Scour La/Bf=0.53 +15% -15% (a) Rectangular column piers 0.0 0.5 1.0 1.5 2.0 0.00 3.00 6.00 9.00 12.00 Y f 2m ax /Y f2 m ax o Lp/Yf1 Pier Affected Abutment Scour La/Bf=0.41 Wall Pier +15% -15% (b) Wall piers Figure 4-27. Category III abutment/contraction scour: Ratio of maximum abutment/contraction scour depth with pier to that without pier for rectangular column piers and wall piers (Yf2maxo from Eq. (4-8) for Category I scour).

125 0.0 1.0 2.0 3.0 4.0 5.0 6.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 (Y f2 m ax /Y fo ) P re di ct ed (Yf2max/Yfo) Measured Interactive Pier Scour Prediction Suggested Model at Abt Scour Hole +10% -10% Figure 4-28. Performance of Eq. (4-8) developed for Category I scour in predicting Category III scour at an abutment in the presence of a pier. 4.2.10.2 Effect of Abutment/Contraction Scour on Pier Scour (Category III) The influence of the abutment on pier scour depth was expected to vary with relative distance of the pier from the abutment as given by Lp/W. Oben and Ettema (2011) showed that a pier placed at the toe of the abutment and short distances away produced negligible scour because it was in the flow separation zone, and the pier was protected by the riprap blanket. As Lp/W increased, the maximum pier scour depth increased as its position passed through the abutment/contraction scour hole, and then it decreased with increasing Lp/W as it began to move out of the influence of the abutment. This behavior is illustrated in Figure 4-28 in terms of a pier scour amplification factor which was determined by dividing the measured total scour at the upstream edge of the pier (dsmax) by the local pier scour depth calculated by the CSU equation (dsmaxo) for isolated pier scour (see Eq. 2-35). The Sheppard-Melville equation (see Eq. 2-36) was also applied for the isolated pier, and the results were practically indistinguishable in Figure 4-28. As the pier was moved away from the abutment, the scour amplification factor increased to the isolated pier scour depth at Lp/Yf1 = 1.5 and then continued increasing to a maximum value at Lp/Yf1 ≈ 6 for all the abutment lengths (La/Bf = 0.41, 0.53, and 0.77). As Lp/Yf1 continued increasing, the amplification factor decreased again to the isolated pier value at Lp/Yf1 = 11. The data from the present study go considerably beyond that from Oben and Ettema (2011) for an erodible floodplain which are shown in the figure. Their data only extended to a value of Lp/Yf1 of about 2.5 with a maximum pier scour amplification ratio of less than 3.

126 The data in Figure 4-29 show considerable variability with respect to La/Bf and the type of flow so that a single relationship for the pier amplification ratio was difficult to develop. However, the figure was used to delineate two zones of influence of abutment/contraction scour on pier scour in terms of magnitude: (1) an upper influence zone within the limits of 3.0< Lp/Yf1<7.5; and (2) a lower influence zone defined by Lp/Yf1 < 3 and 7.5 < Lp/Yf1 < 11. With the width of the riprap apron at Lp/Yf1 = 2, it was assumed from the data distribution that a reasonable lower limit of the upper influence zone at which the riprap began to be less influential was Lp/Yf1 ≅ 3. Similarly, the end of the upper influence zone was taken to be Lp/Yf1 ≅ 7.5 where abutment influence was significantly reduced. The practical effect of the definition of these zones was applied in the analysis that follows next. 0.0 1.0 2.0 3.0 4.0 5.0 0.0 3.0 6.0 9.0 12.0 d s m ax /d sm ax o Lp/Yf1La/Bf=0.41 La/Bf=0.77 La/Bf=0.53 Ettema NCHRP 24/20 Grey Fill SO Open F Dark Fill OT Figure 4-29 Ratio of maximum pier scour depth near an abutment to that for an isolated pier (dsmaxo) as a function of distance of pier from abutment. Rather than defining a pier scour amplification factor as in the foregoing discussion, an excess pier scour ratio was defined to better characterize the influence of the abutment on pier scour. Interactive pier scour was divided into a pier scour component and an abutment/ contraction scour component. The pier scour depth was calculated by the CSU equation (or Sheppard- Melville equation) and was subtracted from total observed scour which left the remaining observed scour as an excess component contributed by abutment/ contraction scour (Yf2max/Yfo)excess. The excess interactive abutment/contraction scour at the upstream face of the pier can be written as

127         fo focalculatedpiersmeasuredpiers excessfo f Y Ydd Y Y )()(max2 ሺ4‐11ሻ Because the abutment scour process dominates the influence on interactive pier scour, it is reasonable to assume that the excess abutment/contraction scour ratio depends on the same variables as Category I abutment/contraction scour as shown in Figure 4-30. The data are segregated into two groups defined by the upper influence and lower influence zones of Figure 4-28 and a best-fit curve is shown for each zone. The best-fit equations are given by: 2/1 1 1 1 2 2/3 1max2 906.1            fc f f f fo f excessfo f V V q q Y Y Y Y Upper ሺ4‐12ሻ 2/1 1 1 1 2 2/3 1max2 283.1            fc f f f fo f excessfo f V V q q Y Y Y Y Lower ሺ4‐13ሻ The coefficient of determination (R2) and standard error of estimate (SEE) are 0.85 and 0.24, respectively, for the upper zone curve, and 0.49 and 0.24 for the lower zone curve. Although there are fewer data points for the lower zone curve and somewhat more scatter in the data, the two-zone delineation from Figure 4-29 seems satisfactory. For comparison, the best-fit coefficient for Category I scour is 2.363 so that the maximum excess scour at the pier due to the abutment is approximately 1.906/2.363, or about 80% of the maximum abutment/contraction scour for the upper curve based on Eq. (4-12). The corresponding percentage of maximum abutment/contraction scour for the lower curve of Eq. (4-13) is 54%. Limited data points were also obtained for wall piers, but they lie almost directly on the best-fit upper and lower curves as shown in Figure 4-31. Application of Eq. (4-12) and Eq. (4-13) for Category III scour (pier) requires that they first be used to calculate the excess pier scour due to the influence of the abutment, and then the isolated pier scour is calculated from the CSU or Sheppard-Melville equations and added to the excess scour depth. (The maximum abutment/contraction scour depth is at a different location than the combined pier scour and is not influenced by the pier regardless of its lateral position, so no pier scour is added to it.) As in the previous discussion of Category II scour, field scour measurements for the Towaliga River flood resulting from Tropical Storm Alberto (1994) were reproduced in the hydraulics laboratory of the Georgia Institute of Technology with scour parameters determined from the physical model study. The flood was submerged orifice flow with an erodible embankment in a compound channel having a long setback abutment on one side of the main channel and a bankline abutment on the other side. Pier numbers 6 and 7 in Figure 2-17 are in the upper scour zone and lower scour zone, respectively, with respect to Category III scour. The excess pier scour depths calculated from the field data are plotted in Figure 4-30 and agree with the two curves from Eq. (4-12) and Eq. (4-13) within 10%.

128 0.0 1.0 2.0 3.0 4.0 5.0 0.0 1.0 2.0 3.0 4.0 5.0 (Y f2 m ax /Y fo ) ex ce ss [(Yf1/Yf0)3(Vf1/Vfc1)(qf2/qf1)] Excess Pier Scour For Lp/Yf1=3.0-7.5 Excess Pier Scour For Lp/Yf1>7.5 Excess Pier Scour For Lp/Yf1<3.0 Pier Excess Scour Model Higher Region Pier Excess Scour Model Lower Region Towaliga River Figure 4-30. Excess Category III pier scour for rectangular column piers in the presence of an abutment. 0.0 1.0 2.0 3.0 4.0 5.0 0.0 1.0 2.0 3.0 4.0 5.0 (Y f2 m ax /Y fo ) ex ce ss [(Yf1/Yf0)3(Vf1/Vfc1)(qf2/qf1)] Excess Pier Scour For Wall Pier Pier Excess Scour Model Higher Region Pier Excess Scour Model Lower Region Figure 4-31. Excess Category III pier scour for wall piers in the presence of an abutment.

129 Measured vs. calculated Category III pier scour depths are shown in Figure 4-32 using the HEC- 18 procedure in which the calculated scour depth is the simple addition of results from the abutment scour and pier scour equations. Considerable overestimation is shown that is approximately 30 to 50% within 95% confidence intervals, which is primarily due to the over- estimation of abutment and contraction scour depths. The CSU equation was used for the calculations in Figure 4-33, but the results are nearly identical for the Sheppard-Melville equation. In Figure 4-33, Eq. 4-12 and Eq. 4-13 were applied to calculate the excess pier scour due to the abutment, which was added to the isolated pier scour prediction, again using the CSU equation. In this approach, approximately 80% of the predicted data points lie within the ±10% error criterion. 0.0 1.0 2.0 3.0 4.0 5.0 6.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 (Y f2 m ax /Y fo ) P re di ct ed (Yf2max/Yfo) Measured Interactive Pier Scour Prediction HEC-18 +10% -10% Figure 4-32. Measured vs. predicted Category III pier scour in the presence of an abutment using HEC-18 procedure (abutment scour depth + contraction scour depth + pier scour depth).

130 0.0 1.0 2.0 3.0 4.0 5.0 6.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 (Y f2 m ax /Y fo ) P re di ct ed (Yf2max/Yfo) Measured Interactive Pier Scour Prediction Suggested Model at Pier Upstream Edge +10% -10% Figure 4-33. Measured vs. predicted Category III pier scour in the presence of an abutment using excess pier scour equations (Eq. 4-12 and 4-13). 4.2.11 Category IV Scour Interactions The interaction of pier and vertical contraction scour was captured in the experiments, which were either conducted without abutments or with the pier location well out of the region of influence of the abutment (Lp/Yf1>11). Vertical contraction scour was measured for both SO and OT flows. Figure 4-34(a) shows the bed elevation contours at equilibrium for the case of vertical contraction scour alone, and the equilibrium contours for the combination of vertical contraction and pier scour can be seen in Figure 4-34(b). The relative uniformity of both the width and depth of the vertical contraction scour depression across the floodplain can be observed in both panels of Figure 4-34. With the addition of the pier, bed elevation depression contours are superimposed onto the vertical contraction contour, and the zone of deposition downstream of the pier is evident. As already discussed, the maximum depth of scour in isolated pier scour experiments satisfied both the CSU equation (Eq. 2-35) and Sheppard-Melville equation (Eq. 2-36) for dual, rectangular column piers in this study (see Figure 4-12). Isolated pier scour depends primarily on pier width and approach flow velocity just upstream of the bridge. In contrast, the Lyn (2008) modified vertical contraction scour model employs the contracted section velocity under the bridge as a parameter (Eq. 2-27). The Lyn (2008) model was shown in Figure 4-13 to serve as an envelope curve for the data in this study as well as data from several other sources for vertical contraction scour alone. Given that the isolated vertical contraction scour is considerably smaller than the isolated pier scour, the effect of the vertical contraction on the pier scour in terms of the

131 approach flow velocity is likely to be small so that their interaction is relatively weak. In this case, the pier scour depth is added to the vertical contraction scour depth to obtain the combined scour. The results are shown in Figure 4-35. The measured data from the experiments in this study are overestimated by about the same amount whether using the CSU or the Sheppard- Melville scour prediction equation. The overestimation is not more than 20% for most of the data which makes it difficult to justify departure from the HEC-18 approach in this specific case of Category IV scour interactions. Further research is needed to better refine the contribution of the vertical scour component to combined scour. Figure 4-35 also includes experiments conducted at the University of Auckland (UoA) for cylindrical piers (for which pier scour was calculated with the Sheppard-Melville equation), and a field example from the Towaliga River flood for Tropical Storm Alberto (1994) for a compound pier, for which the pier scour was calculated from the method presented for compound piers by Melville and Sutherland (1996). The UoA experimental results were provided by Melville (personal communication) and were conducted as CWS experiments in the laboratory with cylindrical piers having a diameter of 0.23 ft (70 mm). The field data point is slightly underestimated while the UoA data are overestimated just beyond the 20% limit. 0.3 0.5 0.7 0.9 1.1 1.3 1.5 Elevation Z (ft) SO Flow Run 33 W/O Pier SO FLOW Run 37 With Pier (a) (b) Figure 4-34. Bed elevation contours for (a) vertical contraction scour alone, and (b) combined vertical contraction and pier scour (Category IV).

132 0 0.3 0.6 0.9 1.2 1.5 1.8 0 0.3 0.6 0.9 1.2 1.5 1.8 d s e/Y 1(C al cu la te d) dse/Y1 (Measured) CSU Eq GT Experiments S and M Eq GT Experiments UoA Experiments Towaliga River +20% ‐20% Figure 4-35. Comparison of Category IV measured and predicted interactive pier and vertical contraction scour 4.2.10 Summary of Clear-Water Scour Analysis Regression equations developed for total scour depth in Category I, II, and III scour interactions are summarized in Table (4-7). Addition of the scour predictions from the CSU or Sheppard/Melville equations for pier scour and the upper envelope equation proposed by Lyn (2008) for vertical contraction scour are recommended for Category IV scour depth predictions. Prediction uncertainties are shown in the table. The scour interactions produce less scour than predicted by current methods of adding individual scour components in Categories I, II, and III. Overestimation of maximum scour depth ranged from 20% to 45 % at the 95% level of confidence for these three categories. On the other hand, approximately 80% of maximum scour depth estimates using equations developed in this study fell within ±10% of the line of perfect agreement. Using current methods, zero to 15% of the data points fell within ±10% of the line of perfect agreement. For Category IV scour, 100% of the data points fell within ±20% of the line of perfect agreement using the equations suggested herein.

133 Table 4-7. Summary of proposed combined scour equations and prediction errors. Category Model Components Included Applicability % of data falling between ±10% of line of agreement 95% confidence interval of prediction ratio** Current method Proposed model Current method Proposed model I 2/1 1 1 1 2 2/3 1max2 ***363.2         fc f f f fo f fo f V V q q Y Y Y Y (4-8) A, L, V Applicable for spill-through and WWA BLA/LSA 14.5% 75.5% (1.16 to 1.28) (0.97 to 1.04) II 2/1 1 1 1 2max2 **725.1      mc m m m mo m V V q q Y Y (4-10) A, L, V Applicable for spill-through and WWA BLA/SSA 0% 78% (1.38 to 1.47) (0.96 to 1.02) III Abutment and contraction scour not affected by pier scour (Yf2max/Yfo)ab from Eq. (4-8) Same as Type-I P, A, L, V Applicable for spill-through abutment LSA with rectangular and wall piers 0% 74% (1.29 to 1.42) (0.94 to 1.02) Pier scour affected by abutment and contraction scour Eq. (4-12) 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 V V q q Y Y Y Y Eq. (4-13) 117.5 OR 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 V V q q Y Y Y Y piersexcessff dYY )()( max2max2  P, A, L, V Applicable for spill-through abutment LSA with rectangular and wall piers 0% 79% (1.29 to 1.51) (0.94 to 1.06) IV P (CSU or S & M eq) + V (Lyn 2008) : Lp/Yf1>11 Eq. (2-35) or (2-36) + Eq. (2-27) P, V P + V 100%* 100%* - -

134 Table 4-7 continued Note: *These values are for ±20 % from line of agreement, **prediction ratio = mean predicted value/mean observed value Symbols: A= abutment scour, L= lateral contraction scour, V= vertical contraction scour, P= pier scour, WWA = wingwall abutment, LSA = long setback abutment, Category I = interactive abutment and contraction scour in floodplain, Category II = interactive abutment and contraction scour in main channel, Category III = interactive abutment, contraction, and pier scour in floodplain, Category IV = interactive pier and vertical contraction scour.

135 4.3 Live-Bed Scour Experimental Results 4.3.1 Summary of Results The relative depth to the point of maximum scour below the water surface at the bridge, Ym2max/Ymo, is shown for three relative abutment lengths subject to LBS in Table 4-8. (For definition of parameters, see Table 4-2). Unlike the clear-water scour data presented above, scour holes are mostly located in the main channel and on the main channel bank. Therefore, these experiments are categorized as Category II scour, and flow quantities in the main channel are used and presented in Table 4-8. The data set encompasses F, SO and OT flows, and includes data from the University of Auckland for a model scale of 1:45. The independent dimensionless variables of the ratio of discharge per unit width in the bridge section to that in the main channel approach flow section, q2/q1; the relative backwater ratio Ym1/Ym0, and the relative flow intensity, Vm1/Vm1c, are shown in Table 4-8. These parameters are used subsequently to develop a relationship to predict maximum LBS depth for Category II interactive scour. Note that q2 represents only that portion of flow per unit width in the main channel going under the bridge for overtopping flow. For OT flows, the overtopped discharge comprised 38% to 47% of the total flow; therefore, q2/q1 values are relatively small because of significant flow relief. Flow intensity as represented by Vm1/Vm1c ranges from approximately 1.0 to 1.5 in the LBS regime. The maximum relative depth of abutment scour in the last column varies between about 1.4 and 2.3. Table 4-8. Experimental conditions for LBS experiments in UoA 5-ft flume (Bf/Bm = 2.35) Run Flow Type La/Bf M/C Ym2max/ Ymo q2/q1 Y1/Yo V1/Vc Yo (ft) 1 UoA LBS F 0.8 1.23 1.03 1.00 0.50 1.79 2 UoA LBS SO 0.8 1.48 1.09 1.02 0.59 2.15 3 UoA LBS OT 0.8 1.09 1.08 0.99 0.74 2.26 4 UoA LBS F 0.8 1.26 1.08 1.39 0.50 1.93 5 UoA LBS SO 0.8 1.46 1.26 1.35 0.51 2.14 6 UoA LBS OT 0.8 1.10 1.14 1.34 0.72 2.18 7 UoA LBS F 0.5 1.07 0.99 1.08 0.53 1.45 8 UoA LBS SO 0.5 1.15 1.04 1.04 0.61 1.38 9 UoA LBS OT 0.5 0.75 1.02 1.05 0.77 1.72 10 UoA LBS F 0.5 1.01 1.00 1.53 0.53 1.56 11 UoA LBS SO 0.5 1.15 1.15 1.47 0.55 1.69 12 UoA LBS OT 0.5 0.82 1.07 1.42 0.76 1.72 13 UoA LBS F 0.65 1.11 1.01 1.01 0.53 1.40 14 UoA LBS SO 0.65 1.27 1.07 1.03 0.59 1.93 15 UoA LBS OT 0.65 0.89 1.02 1.04 0.77 2.11 16 UoA LBS F 0.65 1.12 1.04 1.45 0.52 1.52 17 UoA LBS SO 0.65 1.27 1.22 1.43 0.51 1.85 18 UoA LBS OT 0.65 0.88 1.09 1.38 0.74 1.99

136 4.3.2 Water Surface Profiles Water surface profiles for F, SO and OT flows are compared in Figure 4-36 for two different abutment lengths of La/Bf =0.80 and 0.50. All water surface elevations shown are relative to the floodplain elevation of 1.30 ft. Water surface elevations were measured at six to eight positions across the cross-section at each longitudinal station, and the averaged water surface elevations for each cross-section are shown in Figure 4-36. In all three types of flow, water surface elevation changes occurred at the bridge section due to contraction, friction, and expansion head losses, and these changes - typically head losses - varied with approach flow velocities and flow types. Figure 4-36 shows that, for similar approach velocities in the main channel, F flows were accompanied by the least head losses at the bridge section, whereas SO flows featured the most head losses. The decrease in abutment length from Figure 4-36(a) to Figure 4-36(b) enlarged the flow area, so that with similar approach flows the head losses reduced for all three types of flow. In addition, SO and OT flows had more pronounced head loss reductions than F flows. At the bridge section, LBS flows featured more pronounced head losses than CWS flows, as supported by a comparison between Figure 4-1 and Figure 4-36. 1.2 1.4 1.6 1.8 2 -30 -20 -10 0 10 20 30 El ev at io n (ft ) Longitudnal Direction (ft) La/Bf=0.80 Run 4 LBS UOA F Flow Run 5 LBS UOA SO Flow Run 6 LBS UOA OT Flow Flood-plain Level Figure 4-36(a)

137 1.2 1.4 1.6 1.8 2 -30 -20 -10 0 10 20 30 El ev at io n (ft ) Longitudnal Direction (ft) La/Bf=0.50 Run 10 LBS UOA F Flow Run 11 LBS UOA SO Flow Run 12 LBS UOA OT Flow Flood-plain Level Figure 4-36(b) Figure 4-36 Water surface profiles for LBS in UoA 5-ft flume for free, submerged orifice, and overtopping flows: (a) La/Bf = 0.80; (b) La/Bf = 0.50. 4.3.3 Flow Fields and Live-Bed Scour Depth-averaged velocity profiles across the approach flow cross section and the downstream face of the bridge are shown in Figure 4-37 for F, SO and OT flows. Two different abutment lengths of La/Bf =0.80 and 0.50 are presented. Similar to Figure 4-2, the approach flow velocity distributions in Figure 4-37(a) and (b) depict higher velocities in the main channel relative to the floodplain. The relative magnitude of velocities for different flow types was mainly controlled by the flow depth and water pump settings (Q) prior to commencing the experiments. For both abutment lengths, the main channel velocities in the approach section were set at similar magnitudes for different flow conditions. For either abutment length, because the roughness elements on the floodplain were unchanged, results show OT flows had the highest floodplain velocities in the approach section, whereas F flows had the lowest. Acceleration of flows in both the floodplain and the main channel can be seen in Figure 4-37(c) and (d), but more significant lateral contractions for La/Bf = 0.80 resulted in higher velocities across the contracted section than for La/Bf = 0.50. The maximum velocity at the downstream face of the bridge varied with relative magnitudes of overtopping discharge (zero for F and SO flows), approach flow condition, abutment length and the relative elevation differences between the floodplain and the bridge deck. For both abutment lengths presented in Figure 4-37, SO flows had the highest flow intensities in the bridge section, whereas F flows had the lowest.

138 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 0.80 1.20 1.60 2.00 2.40 2.80 0.0 1.0 2.0 3.0 4.0 5.0 Ve lo ci ty (f t/s ec ) Be d E le va tio n (f t) Cross Section Station (ft) Model Bed Level Depth Average Approach Velocity Run 4 UOA LBS F Flow Depth Average Approach Velocity Run 5 UOA LBS SO Flow Depth Average Approach Velocity Run 6 UOA LBS OT Flow La/Bf =0.80 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 0.80 1.20 1.60 2.00 2.40 2.80 0.0 1.0 2.0 3.0 4.0 5.0 Ve lo ci ty (f t/s ec ) Be d El ev at io n (ft ) Cross Section Station (ft) Model Bed Level Depth Average Approach Velocity Run 10 UOA LBS F Flow Depth Average Approach Velocity Run 11 UOA LBS SO Flow Depth Average Approach Velocity Run 12 UOA LBS OT Flow La/Bf =0.50 (a) Approach flow section for La/Bf =0.80 (b) Approach flow section for La/Bf =0.50 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 0.80 1.20 1.60 2.00 2.40 2.80 0.0 1.0 2.0 3.0 4.0 5.0 Ve lo ci ty (f t/s ec ) Be d El ev at io n (ft ) Cross Section Station (ft) Model Bed Level Depth Average Br Section Velocity Run 4 UOA LBS F Flow Depth Average Br Section Velocity Run 5 UOA LBS SO Flow Depth Average Br Section Velocity Run 6 UOA LBS OT Flow La/Bf =0.80 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 0.80 1.20 1.60 2.00 2.40 2.80 0.0 1.0 2.0 3.0 4.0 5.0 Ve lo ci ty (f t/s ec ) B ed E le va tio n (ft ) Cross Section Station (ft) Model Bed Level Depth Average Br Section Velocity Run 10 UOA LBS F Flow Depth Average Br Section Velocity Run 11 UOA LBS SO Flow Depth Average Br Section Velocity Run 12 UOA LBS OT Flow La/Bf =0.50 (c) Downstream face of bridge for La/Bf =0.80 (d) Downstream face of bridge for La/Bf =0.50 Figure 4-37. Flow acceleration from approach flow section to downstream face of bridge with La/Bf =0.80 and 0.50. Figure 4-38 depicts the distribution of q measured in the approach flow and the bridge sections. Results show that OT flows had the largest q1 values across the approach section, whereas in the bridge section SO flows had the largest q2 values. In the approach section, different flow types had distinctly different q1 values, whereas at the downstream face of the bridge, differences in q2 values were less obvious for different flow types. For F and SO flows in both abutment lengths, values of q2/q1 were mostly greater than unity across the contracted section, whereas OT flows typically had less than unity values in the floodplain due to flow relief. Therefore, with the increase of overtopped discharges, OT flows are expected to have further reduced q2/q1 values, particularly in the floodplain.

139 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 0.80 1.20 1.60 2.00 2.40 2.80 0.0 1.0 2.0 3.0 4.0 5.0 U ni t D is ch ar ge (f t2 / se c) Be d El ev at io n (ft ) Cross Section Station (ft) Model Bed Level Depth Average Approach Unit Discharge Run 4 UOA LBS F Flow Depth Average Approach Unit Discharge Run 5 UOA LBS SO Flow Depth Average Approach Unit Discharge Run 6 UOA LBS OT Flow La/Bf =0.80 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 0.80 1.20 1.60 2.00 2.40 2.80 0.0 1.0 2.0 3.0 4.0 5.0 U ni t D isc ha rg e (ft 2 /s ec ) Be d El ev at io n (ft ) Cross Section Station (ft) Model Bed Level Depth Average Approach Unit Discharge Run 10 UOA LBS F Flow Depth Average Approach Unit Discharge Run 11 UOA LBS SO Flow Depth Average Approach Unit Discharge Run 12 UOA LBS OT Flow La/Bf =0.50 (a) Approach section q for La/Bf = 0.80 (b) Approach section q for La/Bf = 0.50 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 0.80 1.20 1.60 2.00 2.40 2.80 0.0 1.0 2.0 3.0 4.0 5.0 U ni t D isc ha rg e (ft 2 /s ec ) Be d El ev at io n (ft ) Cross Section Station (ft) Model Bed Level Depth Average Br Section Unit Discharge Run 4 UOA LBS F Flow Depth Average Br Section Unit Discharge Run 5 UOA LBS SO Flow Depth Average Br Section Unit Discharge Run 6 UOA LBS OT Flow La/Bf =0.80 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 0.80 1.20 1.60 2.00 2.40 2.80 0.0 1.0 2.0 3.0 4.0 5.0 U ni t D is ch ar ge (f t2 / se c) B ed E le va tio n (f t) Cross Section Station (ft) Model Bed Level Depth Average Br Section Unit Discharge Run 10 UOA LBS F Flow Depth Average Br Section Unit Discharge Run 11 UOA LBS SO Flow Depth Average Br Section Unit Discharge Run 12 UOA LBS OT Flow La/Bf =0.50 (c) Bridge section q for La/Bf = 0.80 (d) Bridge section q for La/Bf = 0.50 Figure 4-38. Distribution of flow rate per unit width in approach flow and bridge sections. The properties of the flow field are illustrated in Figure 4-39 for La/Bf = 0.80 and 0.50 for F, SO and OT flows. Definitions of parameters in Figure 4-39 follow those in Figure 4-6. Some Kb/u*c2 values are not available for Run 5 LBS due to shallow flows on the floodplain. Values of V2R/u*c were larger in the main channel than those near the abutment, whereas values of Kb/u*c2 generally showed the opposite lateral distributions in which higher Kb/u*c2 values were measured in the region of strongly curvilinear flow near the abutment. The deepest scour holes were mainly observed to be located within or near the main channel bank, rather than in regions featuring relatively high Kb/u*c2 values. This noncompliance between the location of deepest scour holes and relatively high Kb/u*c2 values is probably because the rock riprap protection tended to slide down the slope of the scour hole. Values of V2R/u*c and Kb/u*c2 significantly

140 0 10 20 30 40 50 60 70 0 0.5 1 1.5 2 2.5 3 0 1 2 3 4 5 D im en sio nl es s Va ri ab le El ev at io n , z (f t) Lateral distance, y (ft) 0 10 20 30 40 50 60 70 0 0.5 1 1.5 2 2.5 3 0 1 2 3 4 5 D im en sio nl es s Va ri ab le El ev at io n , z (f t) Lateral distance, y (ft) (a) Run 4 LBS UoA, F flow, La/Bf = 0.80 (b) Run 10 LBS UoA, F flow, La/Bf = 0.50 0 10 20 30 40 50 60 70 0 0.5 1 1.5 2 2.5 3 0 1 2 3 4 5 D im en si on le ss V ar ia bl e E le va tio n , z (f t) Lateral distance, y (ft) 0 10 20 30 40 50 60 70 0 0.5 1 1.5 2 2.5 3 0 1 2 3 4 5 D im en sio nl es s Va ria bl e El ev at io n , z (f t) Lateral distance, y (ft) (c) Run 5 LBS UoA, SO flow, La/Bf = 0.80 (d) Run 11 LBS UoA, SO flow, La/Bf = 0.50 0 10 20 30 40 50 60 70 0 0.5 1 1.5 2 2.5 3 0 1 2 3 4 5 D im en sio nl es s Va ri ab le El ev at io n , z (f t) Lateral distance, y (ft) 0 10 20 30 40 50 60 70 0 0.5 1 1.5 2 2.5 3 0 1 2 3 4 5 D im en sio nl es s Va ria bl e El ev at io n , z (f t) Lateral distance, y (ft) (e) Run 6 LBS UoA, OT flow, La/Bf = 0.80 (f) Run 12 LBS UoA, OT flow, La/Bf = 0.50 Figure 4-39. Cross-section distributions of flow properties and scour for LBS.

141 increased resulting from the increase in abutment length, while the scour depth at the bridge section increased to a lesser degree. In addition, the magnitude of the transverse gradients of V2R/u*c and Kb/u*c2 distributions near the abutment were higher for the longer abutment, indicating more significant kinetic energy and flow exchanges immediately downstream of the longer abutments. For both abutment lengths, the available data in Figure 4-38 presented abrupt Kb/u*c2 value peaks for SO and OT flows for the two investigated cross sections close to the abutment. Results show that the higher Kb/u*c2 values occurred for the cross section downstream of the abutment toe, rather than for the cross section at the downstream face of the bridge deck. Local rises in Kb/u*c2 were observed at the interface between the main channel and floodplain, but these rises were much smaller than the abrupt magnitude changes close to the abutment. For F and SO flows, q2/q1avg values were higher in the floodplain than those in the main channel; however, for OT flows, q2/q1avg values were higher in the main channel than in the floodplain due to non-uniform flow relief across the contracted section. Bed elevation contours at equilibrium scour for the same abutment lengths and flow types as in Figure 4-39 are shown in Figure 4-40. A complete set of bed elevation contours with photographs of the bed are given in the Appendix. For the same abutment length, OT flows caused the deepest scour holes downstream of the abutment, while F flows caused the shallowest scour holes. Here, for similar approach flow velocities, the phenomenon of OT flows causing deeper scour depths than SO flows was opposite to that in Georgia Tech experiments, in which SO flows typically caused deeper scour depths. However, it is understood that flow relief for OT flows would not invariably result in smaller scour depths relative to SO flows. The Auckland experiments had higher overtopping ratios and different degrees of submergence. (See water surface profiles in Figure 4-1 and 4-36). As one of the most distinguishing scour features for LBS experiments, bed forms affected the scour hole geometries and scour depths. For La/Bf = 0.80, Figures 4.39 (a), (c) and (e) showed alternative appearances of dune crests and dune troughs in the main channel for the approach section, whereas within the scour hole downstream of the abutment, bed forms were less obvious. In contrast for La/Bf = 0.50, Figures 4-40 (b), (d) and (f) showed alternative appearances of relatively wide extended dune crests and dune troughs through the whole longitudinal measurement region, resulting in variable locations and depths for the maximum scour holes. To quantify the effect of bed forms on scour depth, the half amplitudes of bed forms were considered in determining the maximum scour depths.

142 (a) Run 4 LBS UoA, FS, La/Bf = 0.80 (b) Run 10 LBS UoA, FS, La/Bf = 0.50 (c) Run 5 LBS UoA, SO, La/Bf = 0.80 (d) Run 11 LBS UoA, SO, La/Bf = 0.50 (e) Run 6 LBS UoA, OT, La/Bf = 0.80 (f) Run 12 LBS UoA, OT, La/Bf = 0.50 Figure 4-40. Bed elevation contours after equilibrium scour for La/Bf = 0.80 and 0.50. 4.3.4 Time Development of Scour For LBS experiments, the locations of the maximum scour may vary significantly due to bed forms. To understand the time required to achieve equilibrium scour, scour developments were recorded at appropriate locations for those experiments with relatively stable scour holes in the x- y plane. Figure 4-41 shows the typical scour developments recorded at locations where the maximum scour depths occurred at the end of the experiments. Generally, scour developments depicted steep and approximately linear trends in the early stage of scour followed by asymptotic approaches to equilibrium scour depths. Such scour developments are similar to the CWS results presented in Figure 4-8. Equilibrium scour depth was considered to be established when the centerline of the development trend levelled off. With this definition, the required duration varied greatly with experimental conditions, particularly with the approach flow velocities. For example, Run 2 LBS and Run 3 LBS (Vm1/Vm1c ≈ 1.0) took about 100 hours to achieve equilibrium, while Run 5 LBS and Run 6 LBS (Vm1/Vm1c ≈ 1.4) took about 24 hours.

143 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 0 50 100 150 200 d s (f t) t (hrs) La/Bf =0.80 Run 2 LBS UOA SO Flow Run 3 LBS UOA OT Flow 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 0 5 10 15 20 25 30 d s (f t) t (hrs) La/Bf =0.80 Run 5 LBS UOA SO Flow Run 6 LBS UOA OT Flow 0.0 0.5 1.0 1.5 2.0 2.5 3.0 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 d s /Y f1 Vf1*t/Yf1 La/Bf =0.80 Run 2 LBS UOA SO Flow Run 3 LBS UOA OT Flow 0.0 0.5 1.0 1.5 2.0 2.5 3.0 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 d s /Y f1 Vf1*t/Yf1 La/Bf =0.80 Run5 LBS UOA SO Flow Run 6 LBS UOA OT Flow Figure 4-41. Time development of maximum depth of scour in linear and log coordinates for La/Bf = 0.80 in SO and OT flows under two different approach flow velocities. 4.3.5 LBS Prediction for SSA/BLA (Category II) Live-bed scour experiments at the University of Auckland all produced a scour hole with the maximum scour depth located on the main channel bank or the main channel bed. Consequently, these results were classified as Category II for SSA considering that no BLAs were included in the experimental program. A comparison of the LBS results with the envelope curves for amplification factor suggested by Ettema et al. (2010) is presented in Figure 4-42. Their envelope curves for both an erodible floodplain and a fixed floodplain are shown. For SO and F flow, all but two of the LBS data points from this study lie on or below the envelope curve for an erodible floodplain. The OT results, however, are all above the envelope curve, which is not necessarily unexpected since it was developed for F flow only.

144 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 Y m 2m ax /Y m c (qm2/qm1) UoA LBS F Flow UoA LBS SO Flow UoA LBS OT Flow Ettema et al LBS(BLA/SSA) Ettema et al Curve Erodible F/P Ettema et al Curve Fixed F/P Vm1/Vmc =1 for LBS Figure 4-42. Envelope curves of Ettema et al. (2010) compared with LBS data. The larger values of scour depth for OT flows in Figure 4-42 may be influenced by the relative magnitudes of bridge overtopping discharge and discharge in the approach flow section obstructed by the abutment and embankment, Qot/Qobst. From continuity considerations for a BLA, the value of qm2/qm1 falls below unity if Qot exceeds Qobst. In other words, the overtopping flow relief can balance out the addition of flow to the main channel at the bridge from lateral contraction. An approximate statement of this condition can be obtained for the SSA from the definition of the discharge contraction ratio M as mentioned in Section 2.2.1 (Sturm 2006, Hong 2013). The definition of M for overtopping flow is given by )/(1 )/(1 2 1 QQ QQ Q QQM q q OT obst b obst m m   (4-14) in which Qb is the discharge through the bridge opening and Q is the total discharge. For qm2/qm1 ≥ 1, it follows from Eq. (4-14) that Qot/Q ≤ Qobst/Q. This condition is not satisfied for some of the LBS overtopping data points as shown in Figure 4-43 which is consistent with the corresponding observed values of qm2/qm1 < 1. Under these circumstances, the turbulence introduced by the overtopping flow may be contributing to the total scour depth when the lateral contraction contribution is small, although qm2/qm1 having values less than one may be misleading because it is calculated from width-averaged values, not local values. More work needs to be done to better define the dynamics of excessive overtopping flows in LBS for which Qot/Q > Qobst/Q where Qobst/Q = (1 – M).

145 0.00 0.20 0.40 0.60 0.80 1.00 0.6 0.8 1 1.2 Q ot /Q , Q ob st /Q qm2/qm1 Qobst/Q Qot/Q Figure 4-43. Illustration of Qot/Q > Qobst/Q as a criterion for determining the condition qm2/qm1 < 1. As an alternative to the envelope curve of Figure 4-41, a comparison of the Category II CWS predictive relationship proposed herein for BLA/SSA (Eq. 4-10) with the LBS data is shown in Figure 4-44. The scour depths for SO and F flow are slightly overpredicted while the OT data are slightly underpredicted by Eq. (4-10). The OT flows for CWS data had an overtopping discharge ratio, Qot/Q, ranging from approximately 0.3 to 0.4, while Qot/Q varied between approximately 0.4 and 0.5 for the LBS data shown in Figure 4-42. The LBS data appear to follow the same trend as the CWS relationship. The undisturbed flow depth at the bridge Ym0 is used as the reference depth for Ym2max in Eq. (4-10) rather than the theoretical lateral contraction scour depth, Ymc. For overtopping flow, Ym0 increases as the tailwater elevation and Qot increase with increasing Q, such that Ym2max/Ym0 is an increasing function of qm2/qm1. This trend is followed even for the cases of qm2/qm1 < l for the larger overtopping flows.

146 0.0 1.0 2.0 3.0 4.0 5.0 0.0 1.0 2.0 3.0 4.0 5.0 Y m 2m ax /Y m 0 (Vm1/Vmc*qm2/qm1) BLA CWS Model UoA LBS F Flow UoA LBS SO Flow UoA LBS OT Flow Ettema LBS(BLA/SSA) Theoretical CS Vm1/Vmc =1 for LBS Ym1/Ymo = 1 Figure 4-44. Comparison of LBS scour data for SSA with CWS relationship (Eq. (4-10)) for BLA/SSA (Category II). The CWS scour data for BLA/SSA from all sources are superimposed on the LBS data in Figure 4-45 for a total of 80 experimental data points. Regression of the entire data set for both CWS and LBS produces negligible changes in the coefficient and exponent of Eq. (4-10) and an increase in the standard error from 0.18 to 0.20 due to adding the LBS data to the CWS data set. These statistics indicate that Eq. (4-10) is suitable for predicting Category II scour depths for both CWS and LBS conditions.

147 0.0 1.0 2.0 3.0 4.0 5.0 0.0 1.0 2.0 3.0 4.0 5.0 Y m 2m ax /Y m 0 (Vm1/Vmc*qm2/qm1) BLA CWS Model CWS BLA/SSA UoA LBS F Flow UoA LBS SO Flow UoA LBS OT Flow Ettema LBS(BLA/SSA) Theoretical CS Vm1/Vmc =1 for LBS Ym1/Ymo = 1 Figure 4-45. Comparison of both LBS scour data and CWS data with CWS relationship (Eq. (4-10)) for BLA/SSA (Category II). Predicted maximum LBS depths are compared with observed values in Figure 4-46 in which the HEC-18 additive calculation procedure has been used. Overestimates of as much as a factor of two are shown. Figure 4-47 shows the comparison of observed LBS depths with values predicted by Eq. (4-10), and the data all lie within the ±20% error limits.

148 0.0 1.0 2.0 3.0 4.0 5.0 0.0 1.0 2.0 3.0 4.0 5.0 (Y m 2m ax /Y m o) Pr ed ic te d (Ym2max/Ymo) Measured SSA LBS HEC-18 (UoA) +20% -20% Figure 4-46. Comparison of measured Category II LBS data (SSA) with predictions using HEC-18 additive procedure (Error limits of ±20% relative to line of perfect agreement line are shown). 0.0 1.0 2.0 3.0 4.0 5.0 0.0 1.0 2.0 3.0 4.0 5.0 (Y m 2m ax /Y m o) Pr ed ic te d (Ym2max/Ymo) Measured SSA LBS Suggested Model (UoA) +20% -20% Figure 4-47. Comparison of measured Category II LBS data (SSA) with predictions using Eq. (4-10). (Error limits of ±20% relative to line of perfect agreement are shown).

149 4.4 CFD Model Results This section reports on the analysis of the computational fluid dynamics (CFD) simulations. The six large-eddy simulations are first validated using the experimental data; in particular, detailed water surface elevation and velocity profile comparisons are shown at multiple locations around the bridge, including cross sections just upstream of the abutment, in the bridge opening and downstream of the abutment. After successful validation, the analysis is expanded showing streamlines of the time-averaged flow and streamwise velocities revealing the details of the hydrodynamics of the flow. Further, instantaneous free water surface deformations and isosurfaces of the Q-criterion (a method to educe coherent flow structures) which provide insights into the instantaneous, turbulent flow. Finally, contours of the turbulent kinetic energy overlaid with contours of the bathymetric changes (revealing scour and deposition patterns) are presented which provide evidence of the importance of turbulence for the scour process. 4.4.1 Validation of the Large-Eddy Simulations The goal of CFD code validation is to assess the accuracy of the large-eddy simulations (LES) and to ensure the adequacy of sub- and supergrid models and parameters. In this section, numerically predicted and experimentally measured profiles of normalized time-averaged streamwise velocity, U/Ubulk, and water surface elevation profiles at various locations are plotted to allow direct comparisons between simulated and experimental results. The streamwise time- averaged velocity U is normalized by the bulk velocity Ubulk , which is the cross-sectional average velocity of the approach flow for the respective experimental runs, and plotted in profiles with respect to the vertical distance above the bed of the main channel normalized by the flow depth there, z/h. The comparisons of streamwise velocity profiles between experiment and LES are presented for six runs, i.e. Runs 1, 2, 3, 10, 11 and 12 for the clear-water scour (CWS) experiments conducted at Georgia Tech. Experimental measurements were taken at various cross sections through the bridge. These are located at the approaching foot of the abutment (denoted: up_toe), approaching face of the bridge (up_bridge), downstream face of the bridge (down_bridge), downstream foot of the abutment (down_toe) and lastly a section at 1.066 ft (0.325 m) downstream of the downstream face of the bridge (down_further), and these are plotted in Figure 4-48. The number of cross sections for comparison varies for each run. Runs 1 and 2 have comparisons at all five cross sections while Runs 3, 10 and 12 have three cross sections. For Run 11, only two cross sections are available for comparisons. Experimental measurement profiles were obtained at ten locations within each cross section. The cross-section of the compound channel is presented in Figure 4-49, and it includes outlines of the long setback abutment (dark contour) and the short setback abutment (grey contour). The dashed horizontal line in the profiles represents the estimated water surface height while the thick black line represents the bed height at the respective location. All profiles have the bottom of the main channel as the reference datum. The water surface elevation plots are provided in the same cross sections as the streamwise velocity profiles. The black line represents the water surface while the black circles represent the experimental measurements. Both y-axis and z-axis are normalized by the estimated water depth, h, used as the initial water level at the start of the simulations.

150 Figure 4-48. Schematic top view of the simulation domain, with cross sections highlighted where experimental measurements were taken. Flow from left to right. Figure 4-49. Schematic cross-section view of the domain with y coordinate values across the top, looking downstream.

151 Figure 4-50. Profiles of the normalized streamwise time-averaged velocity for Run 1 (free flow, long setback abutment) at all five cross sections. Each row represents a cross-section with increasing lateral distances shown across the top of each row for each velocity profile. Simulated and measured profiles of the normalized streamwise time-averaged velocity for Run 1 at all five cross sections are presented in Figure 4-50. At each cross section, a horizontal series of panels show the velocity profile comparisons from the left floodplain through the main channel to the right floodplain, and each profile is identified by its y coordinate value and symbols of (a) through (j). Generally, the results from the LES are in reasonably good agreement with the experimental data. In the deeper part of the main channel (profiles (e)-(h)), the LES profile matches the experimental points quite well except the first point off the bed. The biggest discrepancies between simulations and measurements are seen in profiles (i) and (j), particularly

152 for the downstream locations of down_bridge, down_toe and down_further cross sections. Profiles (i) and (j) represent the profiles at the interface between the flood plain and main channel, i.e. downstream of the right (bankline) abutment. As will be shown below, the flow is very complex in this area. It is dominated by the presence of a shear layer between the fast flow in the main channel and a recirculation zone in the right floodplain and influenced by intense coherent vortex shedding between. This is reflected by the non-logarithmic shape of the profile which the LES is able to reproduce. In terms of the magnitude of the velocity at these locations the LES overpredicts by approximately 20%. The profiles on the left floodplain as well as in the main channel are predicted quite well. Figure 4-51. Profiles of the normalized water surface elevation for Run 1 at all five cross sections. Figure 4-51 presents profiles of the normalized water surface elevation as computed via LES (solid line) and as measured (open circles) for Run 1. Overall, good agreement is found; but there is some consistent, very slight overestimation of the water surface by the LES but as the comparison of the velocity profiles has shown, the effect of this on the hydrodynamics is negligibly small. Most noteworthy, is the drop of water surface elevation in the up_bridge and down_bridge profiles, which is a result of the acceleration of flow through the bridge opening. The LES predicts this feature very well.

153 Figure 4-52. Profiles of the normalized streamwise time-averaged velocity for Run 10 (free flow short setback abutment) at three cross sections. Each row represents a cross-section with increasing lateral distances shown across the top of each row for each velocity profile. Simulated and measured profiles of the normalized streamwise time-averaged velocity for Run 10 at three cross sections are presented in Figure 4-52. As before, the LES-predicted profiles are in reasonably good agreement with the experimental data. In the deeper part of the main channel (profiles (e)-(h)), the LES profile matches the experimental points quite well except for some of the first points off the bed, which is where turbulence is greatest and experimental uncertainties as well as the numerical uncertainties in the form of estimated bed roughness are largest. Again, discrepancies between simulations and measurements are seen on the downstream side of the right floodplain, i.e. profiles (j) and at cross-sections down_bridge and down_toe. It appears crucial to match exactly the interface between recirculation zone and fast-flowing main channel flow. The upstream flow on the left floodplain is predicted very well, whereas LES-predicted profiles (a) at cross-section down_bridge and down_toe are somewhat off; however, only very few experimental data points are available for comparison. This is the area where the floodplain flow accelerates into the bridge opening. In the LES, an idealized, smooth abutment is employed, whereas the laboratory abutment was erodible and riprap protected; hence, the LES did not reproduce exactly the near-wall flow. Besides these discrepancies, the match between LES and experiment is quite satisfactory.

154 Figure 4-53. Profiles of the normalized water surface elevation for Run 10 at three cross sections Figure 4-53 presents profiles of the normalized water surface elevation as computed via LES (solid line) and as measured (open circles) for Run 10 at cross sections up_bridge, down_bridge, and down_toe. Overall, very good agreement is found. The acceleration of the flow through the bridge, which produces a significant reduction of the water surface elevation, especially in the up_bridge profile is quite prominent. The LES results predict this feature very well. There is a slight upwelling of the water surface immediately downstream of the bridge opening, i.e. at the down_toe profile, a result of flow deceleration. Again, the LES is able to predict accurately this aspect.

155 Figure 4-54. Profiles of the normalized streamwise time-averaged velocity for Run 2 (submerged orifice flow and long setback abutment) at all five cross sections. Each row represents a cross- section with increasing lateral distances shown across the top of each row for each velocity profile. Figure 4-54 presents simulated and measured profiles of the normalized streamwise time- averaged velocity for Run 2 (SO, LSA) at all five cross sections. Overall, the match between LES and experimental data is satisfactory; most profiles are predicted reasonably accurately. Some discrepancies are obvious, but most noteworthy is the effect of the mismatch of LES- predicted water surface elevations on the downstream side of the bridge. For instance, the LES profiles of the main channel in the down_bridge cross-section near the water surface disagree somewhat with the measurements because the LES predicts the water to be slightly shallower

156 than the experiments (there are some experimental data points above the dashed line which indicates LES-predicted water surface), and hence the LES underestimates the velocity near the water surface. The fact that the highest velocities in the main channel are not near the water surface but in the center of the water column is predicted quite well by the LES. The velocity profiles on the left floodplain as predicted by the LES are in quite good agreement with the experimental data. Again, there are some discrepancies on the right floodplain, i.e. profiles (j) in cross sections down_bridge, down_toe and down_further, but the differences are not as significant as in the free flow runs. Figure 4-55. Profiles of the normalized water surface elevations for Run 2 at all five cross sections. Figure 4-55 presents profiles of the normalized water surface elevation as computed via LES (solid line) and as measured (open circles) for Run 2 at all five cross sections. Overall, the LES results match the measurements satisfactorily, except for the down_bridge profile where the LES slightly overestimates the water surface elevation. The difference in water surface elevation between upstream (up_toe and up_bridge) and downstream (down_toe, down_further) is predicted reasonably well but with a slight underestimation of the water surface for the two most downstream cross sections.

157 Figure 4-56. Profiles of the normalized streamwise time-averaged velocity for Run 11 (submerged orifice flow and short setback abutment) at two cross sections. Each row represents a cross-section with increasing lateral distances shown across the top of each row for each velocity profile. Figure 4-56 presents simulated and measured profiles of the normalized streamwise time- averaged velocity for Run 11 at the two cross sections where experimental data are available. The match between LES and experimental data is quite good. Almost all velocity profiles are predicted quite accurately except for some discrepancies near the water surface, e.g. profiles (e) and (h) in the down_bridge cross-section. Again, the highest velocities in the main channel and on both floodplains are not near the water surface but in the center of the water column and this is predicted quite well by the LES. The LES-predicted velocity profiles on the left floodplain are in good agreement with the experimental data. Figure 4-57. Profiles of the normalized water surface elevation for Run 11 at two cross sections Figure 4-57 presents profiles of the normalized water surface elevation as computed via LES (solid line) and as measured (open circles) for Run 11 at the two cross sections where experimental data are available. The LES slightly overpredicts the measured water surface elevations in both cross sections.

158 Figure 4-58. Profiles of the normalized streamwise time-averaged velocity for Run 3 (overtopping flow and long setback abutment) at three cross sections. Each row represents a cross-section with increasing lateral distances shown across the top of each row for each velocity profile. Figure 4-58 presents simulated and measured profiles of the normalized streamwise time- averaged velocity for Run 3 at the three cross sections where experimental data are available. Almost all LES-predicted velocity profiles match very well the experimental ones. In particular the velocities on both floodplains are predicted accurately, except for some minor discrepancies in profile (a) of cross-section down_bridge, which is probably due to the difference in surface roughness of the abutment apron. The highest velocities in the main channel are not near the water surface, here due to the fact that proportionally more water is being forced through the bridge opening than over the top of the bridge and hence velocities are maximum approximately two-thirds of the distance up the water column.

159 Figure 4-59. Profiles of the normalized water surface elevation for Run 3 at three cross sections. Measured (open circles) and calculated profiles of the normalized water surface elevation for Run 3 at the three cross sections where experimental data are available are presented in Figure 4- 59. The LES slightly overpredicts the measured water surface elevations in all three cross sections; however, the overall match is reasonably good. Figure 4-60. Profiles of the normalized streamwise time-averaged velocity for Run 12 (overtopping flow, short setback abutment) at three cross sections. Each row represents a cross- section with increasing lateral distances shown across the top of each row for each velocity profile.

160 Simulated and measured profiles of the normalized streamwise time-averaged velocity for Run 12 at three cross sections are presented in Figure 4-60. As for the other overtopping run, the results from the LES are in fairly good agreement with the experimental data. In the main channel (profiles (e)-(h)), the LES overestimates slightly but consistently the experimentally measured velocity. The velocity profiles on the floodplains, profiles (a) to (d) and (i) and (j) rare predicted quite well, including the significant reduction of the velocity near the water surface on the downstream side of the bridge, e.g. profiles (a), (b) and (c) in the down_bridge cross-section. Figure 4-61. Profiles of the normalized water surface elevation for Run 12 at three cross sections. Measured (open circles) and calculated profiles of the normalized water surface elevation for Run 12 at the three cross sections where experimental data are available are presented in Figure 4-61. As for the other overtopping run, the LES slightly overpredicts the measured water surface elevations in all three cross sections; however, the overall match is reasonably good. The comparison of LES-predicted velocity profiles at various locations and in various cross sections and water surface elevations with experimentally obtained data for six selected flows show that overall good agreement has been achieved thereby validating the accuracy of the LES and assessing its credibility. Upon the successful validation of the simulations further analysis of the LES follows in subsequent sections. 4.4.2 Time-Averaged Flow In the following figures, a full three-dimensional representation of the flow streamlines is given from the LES results. The color scale shows the relative magnitude of the dimensionless velocity, U/Ubulk. The LES results allow visualisation of the flow structures that is well beyond what can be obtained from the more limited experimental results.

161 Figure 4-62. Streamlines of the mean flow of Run 1 (free flow, long setback abutment) color- coded with the normalized time-averaged mean streamwise velocity (U/Ubulk). Streamlines of the mean flow of Run 1 are presented in Figure 4-62. In the free flow runs, the water is below the bridge deck. The approach flow upstream of the abutments is forced around the abutments and through the bridge opening, resulting in flow contraction and significant flow acceleration as shown by the streamlines. The flow in the main channel accelerates to values as high as two times the bulk velocity. At the leading edges of the abutments, the flow separates, which causes the formation of substantial recirculation zones on both floodplains with the one on the left floodplain being considerably larger than the one on the right floodplain. Immediately downstream of the left abutment, a small three-dimensional (3D) eddy is observed, counter- rotating with regards to the large recirculation vortex downstream, which drives this small eddy. The three-dimensionality is the result of the sloping abutments. In terms of length, the large recirculation zone is approximately two times the entire width of the channel, and it is just slightly wider than the length of the abutment. The recirculation vortex behind the right abutment extends only around 0.7 times the channel width. It is slightly wider than the length of the right abutment. The strong recirculation zones and the fact that they are wider than the length of the abutment, as driven by the flow separation, results in a flow contraction that is slightly greater than the geometric constriction of the bridge cross-section. What follows is that the highest streamwise velocities in the main channel are found just downstream of the bridge opening which is where the deepest scour occurred in the experiments. x/b=0.0 x/b=1.0

162 Figure 4-63. Streamlines of the mean flow of Run 10 (free flow, short setback abutment) color- coded with the normalized time-averaged mean streamwise velocity (U/Ubulk). Figure 4-63 shows streamlines of the mean flow of Run 10 (free flow, short setback abutment) color-coded with the normalized time-averaged mean streamwise velocity (U/Ubulk). The effect of abutment length has a dramatic effect on the hydrodynamics around the bridge. The flow is forced through a much smaller bridge opening between the abutments, causing a significant velocity increase, up to more than 2.5 times the bulk velocity. The presence of the longer left abutment results in a significantly larger recirculation zone which extends much further downstream (approximately 5 times the length of the left abutment) than the one observed for the long setback abutment. The recirculation zone is again wider than the length of the left abutment and as a result all of the flow is forced into the main channel and even onto the right floodplain. The counter-rotating secondary recirculation zone downstream of the left abutment is also greater than the one observed behind the long setback abutment. Both LSA and SSA runs have similar recirculation zones behind the right abutment in terms of length and width. Similar to Run 1 the highest streamwise velocities in the main channel are found just downstream of the bridge opening. x/b=0.0 x/b=1.0

163 Figure 4-64. Streamlines of the mean flow of Run 2 (submerged orifice, long setback abutment) color-coded with the normalized time-averaged mean streamwise velocity (U/Ubulk). Figure 4-64 presents three-dimensional streamlines color-coded with the normalized time- averaged streamwise velocity for the long setback (LSA), submerged orifice (SO) run (Run 2). In this run, the upstream water surface is approximately at the level of the bridge deck and the downstream water surface is slightly below the deck resulting in a pressurized flow through the opening. As before, the approach flow contracts into the opening and accelerates to more than two times the bulk velocity. At the trailing edge of the abutments the flow separates but the recirculation zones immediately downstream of the abutments are not as clearly defined as in the free flow runs. This is probably due to the pressure-driven flow and the immediate relief that flow experiences as it exits the bridge opening. In comparison to the free flow the streamlines downstream of the abutment are almost parallel, and the variation of streamwise velocity across the cross-section is not as pronounced as for the free flow run. A large horizontal vortex is found further downstream than for free flow. The negative flow near both side walls of the channel is less strong than in the free flow run. x/b=0.0 x/b=1.0

164 Figure 4-65. Streamlines of the mean flow of Run 11 (submerged orifice, short setback abutment) color-coded with the normalized time-averaged mean streamwise velocity (U/Ubulk). Streamlines of the mean flow color-coded with the normalized time-averaged streamwise velocity of Run 11, (SO flow and SSA) are presented in Figure 4-65. The flow is accelerated to as high as three times the bulk velocity when it is forced through the narrow bridge opening and under pressure due to the water level drop between upstream and downstream sides of the bridge. Small recirculation zones are observed in the corners of the upstream side of the abutments. On the downstream side of the bridge opening the flow expands and the flow separates at the trailing edges of the abutments. Large recirculation vortices form downstream of the bridge and in contrast to the recirculation zones of the free flow, these vortices adopt significant three- dimensionality. In particular, the recirculation zone on the left floodplain appears to rotate about a horizontal axis rather than a vertical axis, whereas the recirculation zone on the right floodplain is predominantly rotating about a vertical axis. The highest velocities are found on the downstream side of the abutment and primarily in the main channel. x/b=0.0 x/b=0.5

165 Figure 4-66. Streamlines of the mean flow of Run 2 (overtopping, long setback abutment) color- coded with the normalized time-averaged mean streamwise velocity (U/Ubulk). Figure 4-66 presents three-dimensional streamlines color-coded with the normalized time- averaged streamwise velocity for the long setback (LSB) overtopping (OT) run (Run 3). Some of the total discharge flows through the bridge opening and some flows over the deck, which provides some relief to the channel bed, in terms of velocity, shear and turbulence. The flow accelerates through the bridge opening, and the maximum streamwise velocities are found in the main channel where they are less than two times the bulk velocity. In the long setback abutment overtopping run, the flow over the bridge deck is fairly weak; the large opening allows a significant portion of the discharge (approximately 70%) to pass through the opening. The overtopping flow accelerates at the trailing edge of the bridge deck due to the flow plunging into the downstream area of the bridge. The overtopping causes a vertical recirculation zone downstream of the abutments on both floodplains. Both recirculation zones are rather weak due to the relatively low flow that is coming over the bridge deck. A small and weak horizontal recirculation zone forms near the trailing edge of the left abutment. x/b=0.0 x/b=0.5

166 Figure 4-67. Streamlines of the mean flow of Run 12 (overtopping, short setback abutment) color-coded with the normalized time-averaged mean streamwise velocity (U/Ubulk). Streamlines of the mean flow color-coded with the normalized time-averaged streamwise velocity of Run 12 (OT flow for SSA) are presented in Figure 4-67. In comparison with the long setback run, flow acceleration through the opening is more significant and maximum velocities are approximately 2.5 times the bulk velocity. The overtopping flow plunges into the downstream area where it accelerates and drives the vertical recirculation zones that form on the downstream side of the abutments. The recirculation vertical recirculation zone on the left floodplain is better defined than the one observed in the long setback run, and a small horizontal recirculation zone is formed near the foot of the abutment. The recirculation zone on the right hand side is fully three-dimensional with horizontal recirculation near the bed as a result of flow separation from the trailing edge of the abutment, and vertical recirculation near the water surface, which is driven by the overtopping flow. Maximum streamwise velocities are found in the main channel. x/b=0.0 x/b=0.5

167 4.4.3 Instantaneous Flow and Turbulence Figure 4-68 presents an instantaneous snapshot of the water surface for the free flow, long setback run (Run 1). The flow accelerates into the bridge opening and flow separation takes place at the leading edges of the abutments. The resulting water surface deformations reflect the instantaneous hydrodynamics: small separation vortices are observed just downstream of the separation point, and these are recognizable in the form of local free surface dips (marked a and c in Figure 4-68). A larger, instantaneous recirculation zones is identified via the large depression (marked b) immediately downstream of the left abutment. Small free surface waves are found upstream and downstream of the bridge opening signifying local accelerations. Figure 4-68. Free surface of the instantaneous flow of Run 1 (free flow, long setback abutment) color-coded with the water surface elevation. Dark blue represents areas of lower water surface.

168 Turbulence structures are educed by means of the Q-criterion (related to rate of rotation of turbulent vortex filaments), and these are plotted for Run 1; that is, free flow and long setback abutment, in Figure 4-69. Three elongated coherent structures are identified and these are highlighted by a black line and are labelled A, B and C. Coherent structures A and C are the signatures of the smaller vortices a and c which are shed from the abutments and then convected downstream along the shear layer that forms between fast flowing and accelerated flow through the opening and the recirculating, low-momentum zones on the floodplains and downstream of the abutments. Another area of significant shear is observed at the interface between main channel and left floodplain, annotated as the vortex labelled B, which is the large vortex observed in the main channel resulting from interaction of higher velocities in the main channel and slower velocities on the floodplain. All three vortices lose their coherence and break up some distance downstream of the bridge. Figure 4-69. Coherent turbulence visualised by isosurfaces of the Q-criterion color-coded with the normalized time-averaged streamwise velocity (U/Ubulk). (free flow, long setback abutment). A B C x/b=0.0 x/b=0.5

169 Figure 4-70 shows contour lines of normalized near-bed turbulent kinetic energy (TKE) overlaid onto contours of the scoured experimentally observed bathymetry (a) and vice versa (b). The TKE contour plane is extracted at the height of 0.016 ft (5 mm) above the floodplain to best represent the turbulence experienced at the bed level. The TKE values are normalized by the squared critical shear velocity, u*c = 0.075 ft/s (0.023 m/s). The coordinates x and y are normalized by the width of the channel, b = 14.0 ft (4.26 m), while z is normalized by the mean depth of the flow, 0.669 ft (0.204 m), in this run. Reference datum (z/h = 0) is set at the floodplain level, i.e. positive values indicate areas of deposition whereas negative values indicates areas of erosion and the main channel. Two peaks of TKE are found near the tip of the abutments, clearly the signatures of the shear layer and turbulence structures A and C, as detected in Figure 4-69 and best seen as the dark red contours in Figure 4-70 (b). There is an obvious correlation between simulated TKE contours and scour/deposition patterns at the left abutment. The scour hole is on the fast-flowing side of the shear layer, i.e. where elevated levels of turbulence coincide with high magnitudes of bed shear stress (due to the high velocity) and the deposition is found where the levels of TKE are relatively low and where the flow recirculates with almost zero velocity. Near the right abutment the deepest scour coincides with the area of highest TKE, and this is also where the path of the separation vortex occurs along the main channel-floodplain interface. Contours of the normalized bed shear stress are plotted in Figure 4-70 (c). Elevated levels of the bed shear stress are fairly consistent with elevated levels of the TKE with the location of the peaks of these two quantities nearly coinciding suggesting that both quantities contribute to local scour. The elevated shear stress spreads out over a wider area, the result of the local flow acceleration due to the recirculating flow behind the abutment (negative bed shear stress) and the subsequent contraction of the flow.

170 (a) (b) (c) Figure 4-70: Contour lines of normalized, near-bed turbulent kinetic (TKE) overlaid onto contours of the scoured experimentally observed bathymetry (a) and vice versa (b) for the free flow, long setback abutment run. Normalized bed shear stress (τ/τmax) in (c).

171 Figure 4-71 presents a snapshot of the instantaneous water surface for the free flow, short setback run (Run 10). The water surface deformation is exaggerated by a factor of two to highlight the significance of the turbulence structures. Flow accelerates into the bridge opening and as a result of water surface build-up on the upstream side of the abutment and local flow separation zones (marked as a and b), the flow is contracted to a greater extent than what the abutments alone would produce (this is highlighted by the two converging lines upstream of the bridge). The flow separation at the leading edges of the abutments results in two water surface dips with generation of significant turbulence as signified by the strongly varying water surface elevation. Two large recirculation zones occur downstream of the abutments and these are marked as c and d. The recirculation zone on the left floodplain is larger as a result of the longer abutment. Figure 4-71. Free surface of the instantaneous flow of Run 10 (free flow, short setback abutment) color-coded with the water surface elevation. Dark blue represents areas of lower water surface.

172 Figure 4-72 presents visualised turbulence structures educed by isosurfaces of the Q-criterion for free flow around the short setback abutment. The turbulence structures are highlighted via black lines and they are labelled A to F. Coherent structures A, C and D are the signatures of the flow separation vortices being shed at the leading edges of the abutments. These are convected with the accelerated flow downstream along the shear layer that forms between fast flowing and accelerated flow through the opening and the recirculating, low-momentum zones on the floodplains and downstream of the abutments. Structure D appears to originate near the top of the abutment whereas structure C is created near the abutment toe. Shear layer turbulence is observed on the interface between main channel and left floodplain and this area of turbulence merges with turbulence structure A, a short distance downstream of the bridge. Turbulence structure F is the result of the interface shear between the large horizontal recirculation zone downstream of the left abutment and the high velocity main channel flow. Figure 4-72. Coherent turbulence visualised by isosurfaces of the Q-criterion color-coded with the normalized time-averaged streamwise velocity (U/Ubulk). (free flow, short setback abutment). A B C D F E x/b=0.0 x/b=0.5

173 Figure 4-73 presents contour lines of normalized near-bed turbulent kinetic (TKE) overlaid onto contours of the scoured experimentally observed bathymetry (a) and vice versa (b). Four areas of elevated TKE are found; two such areas originate near the tip of the abutments stretching towards the downstream side of the bridge and are the result of shear layer turbulence structures A and D. The other two areas of elevated TKE originate in the main channel, one as the signature of turbulence structure C due to the right abutment, and one at the left bank of the main channel at the interface with the left floodplain. As for the LSA, the TKE appears to correlate with the scour patterns. The scour hole in the main channel is in the area of high TKE and the maximum streamwise velocities. The areas of elevated TKE on the left floodplain coincide with the deep scour hole there albeit the area of scour is wider and spans the entire width of the floodplain between the abutment and the main channel. a) b) Figure 4-73: Contour lines of normalized, near-bed turbulent kinetic (TKE) overlaid onto contours of the scoured experimentally observed bathymetry (a) and vice versa (b) for the free flow, short setback abutment run.

174 For submerged orifice flows, the instantaneous water surfaces were similar for the long setback and short setback abutments, so Figure 4-74 presents a snapshot of the instantaneous water surface for the submerged orifice flow, short setback run (Run 11). On the upstream side of the bridge, the water surface is quite smooth while some deformations are observed downstream of the bridge; however, in comparison with the free flow runs, the deformations are fairly marginal. In the areas downstream of the abutment the water surface is relatively calm. Figure 4-74. Free surface of the instantaneous flow of Run 11 (submerged orifice flow, short setback abutment) color-coded with the water surface elevation. Dark blue represents areas of lower water surface.

175 Isosurfaces of the Q-criterion of the instantaneous flow for the submerged orifice flow with a long setback abutment are plotted in Figure 4-75. In this flow not so many prominent turbulence structures are found, except for some small roller-type vortices near the water surface, which are a result of the negative velocity gradient near the surface. Shear layer or interface turbulence is observed in a line downstream of each abutment. The structures are relatively incoherent in comparison with the interface/shear layer turbulence found in the free flow runs. Figure 4-75. Coherent turbulence visualised by isosurfaces of the Q-criterion color-coded with the normalized time-averaged streamwise velocity (U/Ubulk) for the submerged orifice flow with a long setback abutment. A B x/b=0.0 x/b=0.5

176 Figure 4-76 presents contour lines of normalized near-bed turbulent kinetic (TKE) overlaid onto contours of the scoured experimentally observed bathymetry (a) and vice versa (b) for the submerged orifice, long setback abutment (Run 2). The distribution of TKE is generally fairly uniform and the magnitude of the TKE increases immediately downstream of the bridge. The highest levels of TKE are observed near the right bank and this correlates rather well with the deepest scour. There is some interface turbulence near the left bank and in the line downstream of the left abutment; however maximum TKE magnitudes are approximately 40% less than those observed for the free flow run and this reflects the fact that the turbulence is less energetic and less coherent for the submerged orifice flow. There is a scour hole on the left floodplain immediately next to the toe of the abutment and no elevated levels of TKE, suggesting that the increase in near-bed velocity (and hence bed shear stress) alone is responsible for the scouring of the floodplain. a) b) Figure 4-76. Contour lines of normalized, near-bed turbulent kinetic (TKE) overlaid onto contours of the scoured experimentally observed bathymetry (a) and vice versa (b) for the submerged orifice flow, long setback abutment run.

177 Isosurfaces of the Q-criterion of the instantaneous flow for Run 11, i.e. submerged orifice flow and short setback abutment, are plotted in Figure 4-77. The turbulence structures appear to be more coherent and energetic than the ones observed in the long setback run. Rollers marked C and D, the result of negative velocity gradients near the water surface, is observed and they extend over the entire width of the opening. Immediately downstream of the bridge these rollers break up and lose their coherence as they are convected downstream. Interface turbulence is found on both sides of the bridge opening. The structure near the right bank (marked B) is more significant than the one on the left floodplain (structure A). Figure 4-77. Coherent turbulence visualised by isosurfaces of the Q-criterion color-coded with the normalized time-averaged streamwise velocity (U/Ubulk) for the submerged orifice flow with a short setback abutment. A C B D x/b=0.0 x/b=0.5

178 Figure 4-78 presents contour lines of normalized near-bed turbulent kinetic (TKE) overlaid onto contours of the scoured experimentally observed bathymetry (a) and vice versa (b) for the submerged orifice, short setback abutment run. For this flow, elevated areas of TKE are more distinct in comparison with the TKE distribution of the submerged orifice flow for a long setback abutment. Turbulence originates near the abutment toes and at the interface between main channel and left floodplain. Correlation between high TKE and scour is noticeable; however, the very high velocities, and hence high bed shear stresses, appear to be the main driver for erosion. Maximum levels of TKE are approximately 10% less than for the equivalent free flow run. a) b) Figure 4-78. Contour lines of normalized, near-bed turbulent kinetic (TKE) overlaid onto contours of the scoured experimentally observed bathymetry (a) and vice versa (b) for the submerged orifice flow, short setback abutment run.

179 Figure 4-79 presents a snapshot of the instantaneous water surface for the overtopping flow, short setback run (Run 12). The water surface of the overtopping long setback run is almost identical and hence is not shown for brevity. On the upstream side of the bridge, the water surface is fairly smooth and the water surface starts to drop as the flow encounters the bridge deck. The presence of the rails results in a small wave and then the water surface drops rapidly as the flow plunges into the downstream area of the bridge. As a result of the plunging, a persistent standing wave occurs immediately downstream of the bridge which is then followed by successively smaller waves. These waves appear to be more defined downstream of the abutments where the flow underneath is less strong than in the bridge opening. Further downstream, the water surface continues to be fairly rough, but it smooths out with downstream distance from the bridge. Figure 4-79. Free surface of the instantaneous flow of Run 12 (overtopping flow, short setback abutment) color-coded with the water surface elevation. Dark blue represents areas of lower water surface.

180 Figure 4-80 presents visualised turbulence structures which are educed by isosurfaces of the Q- criterion for the overtopping flow and long setback abutment. Similar to all other runs, interface turbulence is found downstream of both abutments. The structure near the right bank (marked B) is more significant than the one on the left floodplain (structure A), which is due to the shear layer at the interface between the main channel and the right floodplain being stronger than the one on the left floodplain because of the absence of a horizontal recirculation zone. The plunging of water into the downstream area of the bridge results in rollers, fairly coherent immediately downstream of the bridge with the structures spanning almost the entire width of the bridge; however, they lose coherence quickly, breaking into smaller structures and dissipating rapidly as they are convected downstream. Figure 4-80. Coherent turbulence visualised by isosurfaces of the Q-criterion color-coded with the normalized time-averaged streamwise velocity (U/Ubulk) for the overtopping flow with a long setback abutment. A B x/b=0.0 x/b=0.5

181 Figure 4-81 presents contour lines of normalized near-bed turbulent kinetic (TKE) overlaid onto contours of the scoured experimentally observed bathymetry (a) and vice versa (b) for the overtopping, long setback abutment run. For this flow, elevated areas of TKE are visible on the floodplain, due to the flow acceleration, and distinct peaks of TKE are found near the abutment toes and subsequently along the interface between main channel and right floodplain. Again there is noticeable correlation between high TKE and scour, but high bed shear stress as a result of local flow acceleration appears to be the main driver for erosion. Maximum levels of TKE are approximately 10% less for than the equivalent free flow run and very similar to the submerged orifice run with the long setback abutment. Contours of the normalized bed shear stress are plotted in Figure 4-81 (c). The entire area under the bridge is characterized by high bed shear stresses in response to the vertical contraction of the flow. Comparing Figures 4-81 (a), (b) and (c) it can be concluded that high local bed shear stresses are mainly the result of vertical and horizontal contraction and flow acceleration around the abutment. For this case the bed shear stress is mainly responsible for the vertical contraction caused erosion on the floodplain, while the high local shear stress together with the high local turbulence in the form of elevated TKE levels from the shear layer appears responsible for the local scour hole. Figure 4-81(a) Figure 4-81(b)

182 Figure 4-81(c) Figure 4-81. Contour lines of normalized, near-bed turbulent kinetic (TKE) overlaid onto contours of the scoured experimentally observed bathymetry (a) and vice versa (b) for the overtopping flow, long setback abutment run. Normalized bed shear stress in (c). Isosurfaces of the Q-criterion which are used to visualise instantaneous turbulence structures of the overtopping flow for short setback abutment are presented in Figure 4-82. Interface turbulence is found downstream of both abutments, and similar to the long setback abutment run, the structure near the right bank (marked B) is more significant than the one on the left floodplain (structure A). There is no horizontal recirculation zone on the left floodplain and hence fluid shear on the floodplain is less than at the interface between the main channel and the right floodplain. As for Run 3, the plunging of water into the downstream area of the bridge results in rollers, fairly coherent immediately downstream of the bridge and these rollers span the entire width of the bridge. As the water plunges into the area downstream of the bridge, they lose coherence quickly, breaking into smaller structures and dissipating rapidly as they are convected downstream.

183 Figure 4-82. Coherent turbulence visualised by isosurfaces of the Q-criterion color-coded with the normalized time-averaged streamwise velocity (U/Ubulk) for the overtopping flow with a short setback abutment. Figure 4-83 presents contour lines of normalized near-bed turbulent kinetic (TKE) overlaid onto contours of the scoured experimentally observed bathymetry (a) and vice versa (b) for the overtopping short setback abutment run. For this flow, elevated areas of TKE are visible on the floodplain due to the flow acceleration, and distinct peaks of TKE are found near the abutment toes and subsequently along the interface between main channel and right floodplain as well as at the interface between main channel and left floodplain. Another significant area of elevated levels of TKE is found immediately downstream of the left abutment, which is where the vertical recirculation zone is located. It spans the entire length of the abutment. There is correlation between high TKE and scour downstream of the abutments, but high bed shear stress as a result of local flow acceleration in the bridge opening appears to be equally important for erosion, especially on the left floodplain and the main channel directly underneath the bridge deck. Maximum levels of TKE are comparable with those found for the equivalent submerged orifice run and are approximately 10-15% less than the equivalent free flow run. A B x/b=0.5 x/b=0.0

184 (a) (b) Figure 4-83. Contour lines of normalized, near-bed turbulent kinetic (TKE) overlaid onto contours of the scoured experimentally observed bathymetry (a) and vice versa (b) for the overtopping flow, short setback abutment run. 4.4.4 Effect of Scoured Bathymetry on Flow and Turbulence Analysis and visualisation of contours of the near-bed turbulent kinetic energy (TKE) as predicted by the large-eddy simulations of Runs 1, 2, 3, 10, 11 and 12 have demonstrated that for most runs a direct link exists between turbulence and scouring of the bed, but that for some other runs this links appears absent. The large-eddy simulations, however, have been carried out for the un-eroded bed, and hence it might be argued that near-bed turbulence is modified with the progression of scour and accompanying change in bathymetry. Thus, a large-eddy simulation of experimental Run 18 is carried out to assess the effect of scoured bathymetry on the flow and turbulence in the near-field of the scour hole. Figure 4-84 presents contour lines of near-bed turbulent kinetic (TKE) at various elevations overlaid onto the experimentally observed bathymetry for Run 18, i.e. free flow with a long setback abutment. The contour distributions of the turbulent kinetic energy appear to describe the topology of the scour hole quite well. Areas of maximum TKE, originating from the toe of the abutment (top left), coincide with the deeper parts of the scour hole, and high levels of TKE are found almost all the way to the bottom of the hole (bottom left). Near the bed in the scour hole the levels of TKE have decreased significantly, suggesting the absence of shear and turbulence and potentially the cause for the scour hole to have reached equilibrium.

185 Figure 4-84. Contour lines of near-bed turbulent kinetic (TKE) at various elevations overlaid onto the experimentally observed bathymetry. Figure 4-85 presents streamlines of the near-bed flow through the equilibrium scour hole colored by the normalized time-averaged streamwise velocity. The flow accelerates around the abutment and streamlines of high velocity converge into the scour hole. The area of converging streamlines and highest velocities coincide with the deepest part of the scour hole and contours of maximum TKE (seen in Figure 4-84). There is a local recirculation region just downstream of the abutment toe and some recirculating fluid is entering this recirculation zone which borders the high-momentum flow through the scour hole. The near-bed, low-momentum flow through the scour hole is deflected towards the main channel as a result of the steepness of the scour hole.

186 Figure 4-85. Streamlines of the near-bed flow through the scour hole. Figure 4-86 presents contours of the resultant velocity magnitude (Umag = (U2 + V2)1/2) together with streamlines (top row) without (left column) and with (right column) scour hole on the floodplain for the free flow, long setback run. Similarly, contours of the normalized TKE in a near-bed plane are shown in the second row without (left) and with (right) the scour hole. There are marked differences in the hydrodynamics between these two runs. Most noteworthy are the differences in the low velocity recirculation region near the trailing edge of the abutment. With the existence of the scour hole, this region is slightly wider, and local recirculation occurs on the sloped bank of the scour hole. As a result, higher velocities are observed just upstream of this low- momentum zone and the highest velocities are found just above the scour hole. This larger region of low-momentum flow appears to push the area of high TKE towards the main channel, and it coincides with the interface between high and low velocity areas. In the non-scoured run, the area of high TKE is a bit further downstream, past the trailing edge of the abutment. Whereas the magnitudes of the TKE between scoured and non-scoured runs are almost identical, the exact location and extent of high-TKE zones is slightly different and is affected by the local bathymetry.

187 Figure 4-86. Contours of the streamwise velocity together with streamlines (top row) and contours of the normalized TKE in a near bed plane without (left column) and with (right column) scour hole on the floodplain (Runs 1 and 18). 4.4.5 Three-Dimensional RANS Simulations In addition to the large-eddy simulations, Reynolds-Averaged Navier-Stokes (RANS) simulations were carried out with the goal to determine the effect of abutment length on the dimensionless scour predictor variables and hence to determine the potential impact on the resulting scour. The RANS simulations were chosen for this task in order to include more abutment lengths than possible using LES because of its prohibitive demand on computing resources. 4.4.5.1 Validation of the Three-Dimensional RANS Simulations RANS-simulated and measured profiles of the normalized streamwise time-averaged velocity for Run 1 (free flow, long setback abutment) at three cross sections are presented in Figure 4-87.

188 The RANS-predicted profiles are in reasonably good agreement with the experimental data on the left floodplain, i.e. profiles (a)-(d). In the deeper part of the main channel (profiles (e)-(h)), the RANS predictions are not as good as the LES; there is clear underestimation of flow on the left-hand side of the main channel (profiles (e) and (f)). It is hypothesized that the RANS cannot cope with the non-isotropic interface turbulence, especially if it is enhanced by the presence of the abutment. Arguably, there is somewhat better agreement on the right side of the main channel, except for the first few points above the bed, which is where uncertainties regarding main channel bed roughness are largest. As for the left floodplain, discrepancies between simulations and measurements are seen on the downstream side of the right floodplain, i.e. profiles (j) and at cross sections down_bridge and down_toe. Not surprisingly, the RANS cannot match exactly the interface between the recirculation zone and fast-flowing main channel flow, similar to the LES. The upstream flow on the right floodplain is predicted reasonably well, except for the near-bed velocity. Besides some obvious and expected discrepancies, the match between RANS results and experimental data is satisfactory for exploring the effect of abutment length on the flow field, at least for the free flow run. Figure 4-87. RANS-simulated and measured profiles of the normalized streamwise time- averaged velocity for Run 1 at three cross sections. 4.4.5.2 Effect of Abutment Length on Hydrodynamics and Potential Scour Figure 4-88 presents depth-averaged 3D RANS simulation results for four selected scenarios. To gain further insight on the effect of different opening lengths between abutments on the overall velocity field and the scour predictors, two additional scenarios to the long and short setback setups (LSA and SSA, respectively) are presented. For the medium setback (MSA) the left abutment’s length is in-between the long and short runs, while for the bankline abutment (BLA) run, the left abutment is extended all the way to the left bank, leaving the gap between abutments reduced to the main channel exclusively with both floodplains blocked. The main difference

189 induced by the increasing the length of the left abutment in terms of the velocity field is the increasing predominance of the recirculation area behind the abutment. For the MSA, SSA, and BLA runs, the high-velocity, high-momentum flow through the bridge opening is forced towards the right bank of the main channel and onto the right floodplain. For the LSA and MSA configurations, a significant counter-rotating recirculation zone behind the left abutment is formed, which gradually decreases as the main eddy becomes larger for the SSA and BLA Runs, due to the increasing negative velocities near the left bank. Comparison of the 3D RANS predicted streamlines with the ones predicted by the LES (see Figures 4-62 and 4-63) suggest that the RANS model overpredicts the extent and strength of this recirculation zone, and this is a known issue of RANS simulations of massively separated flows. The relative discharge (q2/q1) and horizontal resultant velocity magnitude (V2(R)/u*c) scour predictors clearly illustrate how the flow is forced through an increasingly narrow gap, exhibiting a larger concentration of momentum in the main channel. The turbulent kinetic energy predictor (Kb/u*c2) consistently shows two peaks around the edges of the abutments. Turbulence generation is higher around the left abutment because the blockage is more relevant on the left side, i.e. more water from the left floodplain is forced around the left abutment than the right. The presence of the counter-rotating vortex in the MSA run seems to dissipate some of the TKE behind the left abutment at the down_toe line when compared to the SSA Run.

190 Figure 4-88. (left) Depth-averaged streamwise velocity field and streamlines predicted by the 3D RANS simulations for the long (LSA), medium (MSA), short (SSA) and bank setbacks (BLA); (right) normalized scour predictors (q2/q1, V2(R)/u*c, and Kb/u*c2) at the down_toe.

191 Figure 4-89. Profiles of measured and 3D RANS -predicted scour predictors (q2/q1, V2(R)/u*c, and Kb/u*c2) at the down_toe location (free flow, long setback abutment). Figure 4-89 plots profiles of measured (symbols) and 3D-RANS predicted (solid lines) scour predictor variables at the down_toe location together with the original bed (solid black line). First of all, the 3D-RANS predicted profiles are in reasonably good agreement with the measurements, in particular for the q2/q1 variable, but also for V2(R)/u*c. For the latter, a maximum underestimation of approximately 10% is found in the main channel and a maximum overestimation of approximately 10% near the left abutment. The TKE profile of the 3D RANS exhibits some significant differences between measurement and simulation; most noteworthy, the TKE as predicted by RANS is much higher near the left abutment than the experimental values and also much lower RANS-predicted TKE occurs near the right abutment. Between the two abutments, low values of TKE are experimentally observed and numerically predicted. In summary, the 3D RANS simulation results for free flow suffer from significant overprediction of the size of the recirculation zone, which is important in the scour process based on the LES results. Overprediction of recirculation areas is a known problem of RANS simulations due to the large-eddy viscosities which make the flow much more viscous than it actually is. On the other hand, the LES captured the highly three-dimensional zone downstream of the left abutment for submerged orifice and overtopping flows very well. Vertical circulations with a horizontal axis were set up for these flows which moved the horizontal recirculation zone significantly downstream. For this reason, the 3D RANS results were not considered as useful as the LES results in visualising the physics of the flow field and its connection to the scour process. Furthermore, the 2D model results described next were just as effective in predicting integral scour parameters associated with the mean flow velocity field such as q2/q1. Additional LES is suggested for further exploration of the turbulence structures responsible for bridge scour, while 2D RANS can be used for estimating parameters for scour prediction with the caveat that it cannot reproduce secondary currents that might be generated in a bend upstream of a bridge.

192 4.4.6 Two-Dimensional or Depth-Averaged RANS 4.4.6.1 Validation of the RANS Simulations Figure 4-90 plots profiles of the depth-averaged normalized streamwise velocity as measured (open circles) and predicted by LES (solid line) and 2D RANS (dashed line) for the free flow, short setback abutment at all five cross sections. Overall, the agreement of predicted velocities with experimental data is very good. Generally, the LES predictions are slightly better, in particular in areas with steep velocity gradients, i.e. near the abutments. Also the 2D RANS cannot fully reproduce the sloping abutments and hence quite naturally the 2D RANS predictions are slightly off there. Figure 4-90. Profiles of the depth-averaged normalized streamwise velocity as measured (open circles) and predicted by LES (solid line) and 2D RANS (dashed line) for the free flow, long setback abutment at all five cross sections.

193 Figure 4-91 plots profiles of the depth-averaged normalized lateral velocity as measured (open circles) and predicted by LES (solid line) and 2D RANS (dashed line) for the free flow, long setback abutment at all five cross sections. As for streamwise velocities, the agreement of predicted lateral velocities with experimental data is very good. Figure 4-91. Profiles of the depth-averaged normalized lateral velocity as measured (open circles) and predicted by LES (solid line) and 2D RANS (dashed line) for the free flow, long setback abutment at all five cross sections.

194 4.4.6.2 Effect of Bridge Opening on Hydrodynamics and Scour Predictions Similar to the 3D RANS simulations, Figure 4-92 presents the depth-averaged velocities together with profiles of the scour predictor variables for four different scenarios as predicted by the 2D RANS simulations. A comparable trend to the 3D RANS results is observed in the 2D RANS simulations where the extension of the left abutment’s length produced an increasing size of the recirculation area. For the MSA and SSA Runs, the most energetic flux is diverted slightly towards the right boundary of the computational domain by the recirculation zone. Unlike the 3D RANS simulations, the existence of a counter-rotating vortex behind the left abutment is absent. The relative discharge (q2/q1) and velocity (V2(R)/u*c) scour predictors show the highest peak in the main channel (y = 8.2-12 ft or 2.5-3.7 m), clearly demonstrating how the flow is forced through the increasingly narrow bridge opening. The turbulent kinetic energy predictor (Kb/u*c2) consistently shows two peaks around the edges of the abutments, with the higher peak near the left abutment as the flow constriction appear to be more pronounced on the left shallow floodplain. Figure 4-93 plots profiles of measured (symbols) and 2D-RANS predicted (lines) scour predictor variables at the down_toe location together with a cross section of the original bed and scoured bed (at the left abutment) at equilibrium (solid black line) for free flow around the LSA. Very similar to the 3D-RANS-predicted profiles, the 2D model is able to calculate with reasonable accuracy the measured q2/q1 and V2(R)/u*c profiles. There are some discrepancies near the abutments, due to the use of a “depth-averaged” geometry of the abutments, but for the rest of the profile the 2D predictions are only about 5% off. The match between simulated and measured TKE profiles is not good at all, as expected, for a 2D model when applied to a highly 3D turbulent flow region. The 2D RANS simulation for TKE is generally significantly different than the measured values. Overestimation of around 100% is found for almost the entire profile, except near the abutments, which is where the match seems better but this is more or less coincidental. Clearly, the depth-averaged RANS turbulence model is unable to reproduce realistically the turbulence. However, the scour prediction formulas derived above do not rely on the TKE so scour depth predictions that are based on RANS are expected to be reliable.

195 Figure 4-92. (left) Depth-averaged streamwise velocity field and streamlines predicted by the 2D RANS simulations for the long (LSA), medium (MSA), short (SSA) and bankline (BLA); (right) normalized scour predictors (q2/q1, V2(R)/u*c, and Kb/u*c2) at the down_toe.

196 Figure 4-93. Profiles of measured and 2D RANS -predicted scour predictors (q2/q1, V2(R)/u*c, and Kb/u*c2) at the down_toe location (free flow, long setback abutment). Table 4-9. Predicted scour depths for Category I and Category II scour and 2D RANS model calculated predictor variables for various abutment lengths. Category I Category II Yf1/Yf0 Vf1/Vfc1 qf2/qf1 Yf2max/ Y f0 Vm1/Vmc1 qm2/qm1 Ym2max/ Y m0 LSA 1.15 0.48 1.62 2.56 - - - MSA 1.20 0.47 1.70 2.80 0.75 1.60 1.88 SSA - - - - 0.68 1.89 1.95 BLA - - - - 0.63 2.50 2.16 Table 4-9 provides the predicted normalized scour depths, Yf2max/ Y f0, for Category I and Ym2max/ Ym0, for Category II scour which have been calculated from the predictor variables as obtained from the 2D RANS model for various abutment lengths with free flow. The flow through the medium setback abutment (MSA) opening indicates possible side-by-side scour holes in the floodplain and the main channel because the hydrodynamics show strong acceleration through both the floodplain and the main channel openings. As seen in Table 4-9, for the MSA run, larger dimensionless scour occurs for the LSA on the floodplain than for the BLA in the main channel. The absolute scour depths for the MSA abutment are computed as Yf2max = 0.70 ft (0.21 m) on the floodplain for Category I and Ym2max=1.03 ft (0.31 m) in the main channel for Category II scour. Normalized scour depths were calculated from Eqs. (4-8) and (4-10) using 2D RANS computed predictor variables for Category I and Category II scour, respectively, in free flow. The results are shown together with experimental data in Figures 4-94 and 4-95. As expected, the numerical predictions fall exactly on the black curve; however, they also are consistent with scour depths observed in the experiment for similar abutment lengths and flow type.

197 Figure 4-94. Predicted maximum normalized depth of scour hole for Category I scour as measured in the laboratory (squares) and as predicted by the 2D RANS obtained predictor variables (grey symbols) together with proposed Category I Model curve. Figure 4-95. Predicted maximum normalized depth of scour hole for Category II scour as measured in the laboratory (squares) and as predicted by the 2D RANS obtained predictor variables (grey symbols) together with proposed Category II model curve. 4.4.6.3 Application of the Two-Dimensional RANS Model to Prototype Geometry Given the success of the 2D model in calculating the required scour predictor variables for the experimental results as shown in the last section, a full-scale computation was made on a prototype bridge which had been modeled previously in the Georgia Tech Laboratory in a

198 physical model study. A reach of the Ocmulgee River in Macon, Georgia, which included the Fifth Street Bridge where the drainage area is 2240 mi2 (865 km2), was simulated using the 2D shallow water model SRH-2D. The mesh consists of approximately 500,000 triangular elements with the largest of the order of 200 ft2 (19 m2) and the smallest of less than 1 ft2 (0.1 m2) near the bridge piers. The bridge piers, which are cylindrical with a diameter of 6 ft (1.83 m), were resolved explicitly, i.e. the mesh is fine enough so that the no-slip condition can be applied on the piers. The numerical domain is presented in Figure 4-96 using contour plots of the bathymetry. The CFD model is run until the flow reaches a steady state using the k-epsilon turbulence model with the same flow conditions as in the prototype and the physical model study. The Manning coefficient is set to 0.025. The inflow discharge is set to 65,000 cfs (1,840 m3/s), which was measured by the USGS for the 25-year flood of 1998. A water depth of 29.95ft (9.13 m) is set at the outlet according to the USGS rating curve. Figure 4-96. Bathymetry of the Ocmulgee River Bridge at Macon, GA

199 Three different cross sections are selected to provide a quantitative comparison of the computed 2D results with the prototype data and the physical model data. The cross sections are highlighted in Figure 4-97, where C.S.-3b is a cross section upstream of the bridge, C.S.-4 is at the beginning of the upstream piers and C.S.-5 is immediately after the downstream piers. Figure 4-97 also shows the fine unstructured mesh built with triangular elements which is refined near the bridge piers so as to provide an adequate resolution to capture the local effects. Figure 4-97. Mesh and Location of the cross sections of interest and the unstructured mesh used during the 2D RANS simulations. The velocity contours and vectors obtained near the bridge opening are shown in Fig. 4-98 together with the location of the cross sections 4 and 5. The bridge is located in a bend and hence high velocities are observed near the left bank. The presence of the piers leads to some low- momentum wakes behind the piers. Overall, the velocity contours look qualitatively realistic and reasonable.

200 Figure 4-98 Velocity vectors around the bridge piers. A more quantitative assessment of the predictive capabilities of the 2D RANS model is possible with Fig. 4-99, which presents profiles of the velocity magnitude obtained from the 2D RANS simulations using two different mesh resolutions (Coarse and Fine) together with physical model study data (denoted Model, dots) and field data (Prototype, crosses). The two different meshes provide quite similar results and are in good agreement with the experimental results obtained from the Georgia Tech physical model study and the prototype data. The high velocity areas computed by the CFD model coincide fairly well with the experiments. Minor discrepancies are found near the right bank which is where the 2D RANS model overestimates the velocity. This could be due to inlet boundary conditions (discharge distributed uniformly over the inlet) or due to some local change/variation in bed roughness. Nevertheless, the 2D model appears to reproduce reasonably accurately the hydrodynamics through the Fifth Street Bridge opening.

201 ’ Figure 4-99. Comparison of SRH-2D velocity distribution at C.S.-4 with physical model and prototype data. Figure 4-100. Comparison of HEC_RAS velocity distribution at C.S.-4 with physical model and prototype data.

202 The 1D HEC-RAS water surface profile program was also applied to the Ocmulgee River reach for comparison with the physical model study and prototype data. The same Manning’s n of 0.025 and flow conditions as set in the SRH-2D CFD model were applied. The HEC-RAS velocity distribution, which is estimated by the ratio of conveyances of streamtubes, is shown in Figure 4-100. The resulting velocity results are as much as 12% less than the measured values in the center of the main channel, and the decrease in velocity as the piers are approached is not captured. The velocity near the left abutment is significantly overestimated. This prototype example is one without a severe bridge contraction or significant floodplains, so no conclusions can be reached about the suitability of 1D models in more challenging situations. 4.4.7 CFD Summary Large-eddy, 3D RANS and 2D RANS simulations were carried out to complement the experimental work detailed in previous sections of Chapter 4. The six LES covering the three principal flows, i.e. free, submerged orifice and overtopping flows with short and long setback abutments were validated first by comparing simulated streamwise velocities and water surface elevations with measured data. Overall good agreement between measurement and simulations were found which allowed analyses of mean and instantaneous flows. The time-averaged flow has been visualised with streamlines colored by the streamwise velocity, and the three different flows exhibit markedly different features. The free flow runs are characterized by distinct horizontal recirculation zones downstream of the abutments while the recirculation is vertical for overtopping flow. The submerged orifice flow does not feature distinct recirculation zones, and the flow is dominated by the strongly accelerated flow through the opening as a result of the pressure difference between upstream and downstream faces of the bridge. The instantaneous flow is characterized by distinct water surface deformations that are most pronounced in the overtopping flow in which the bridge acts similar to a short, broad-crested weir; however, a significant portion of the flow passes through the bridge opening underneath the deck. Significant separation vortices in the free flow run are shown by local depressions in the water surface, and the water surface elevation plots reveal the distinct unsteadiness of this flow. Isosurfaces of the Q-criterion were employed to educe coherent flow structures, and the most prominent flow structures occur at locations with the highest shear, or with the greatest velocity gradient. Turbulence has been quantified by contour plots of the turbulent kinetic energy and these contours plotted together with experimentally observed bathymetric changes (in the form of scour) reveal the tight interconnection between near-bed turbulence and local erosion of the bed. 3D RANS was employed to investigate the sensitivity of the flow and its integral scour- relevant quantities to the length of the abutment. While the 3D RANS is able to reproduce fairly reliably scour-relevant quantities, it is unable to reproduce accurately the hydrodynamics, which is due to the highly-unsteady nature of the flow. Hence, further engineering-practice-type simulations have been carried out with a 2D RANS model. Indeed the 2D RANS model is able to reproduce as well the main scour-relevant quantities, and it has been demonstrated that a 2D RANS model is able to predict scour depths that are in line with the experimental observations. Finally, the 2D RANS model demonstrated applicability to a real field site, the Ocmulgee River in Georgia, by being able to reproduce reasonably accurately the flow through the bridge opening. The HEC-RAS results were not as good even for a relatively simple channel geometry