Revised Clear-Water and Live-Bed Contraction Scour Analysis (2021)

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8-1   8.1 Overview Considering the fundamentals of a flow contraction as delineated in Chapter 2, this chapter provides a bridge between the laboratory and computational analyses presented in Chapters 4 through 7 and the suggested revisions to the contraction scour equations. Section 8.2 provides an appraisal of the results of the preceding chapters. Then, Section 8.3 presents suggested revisions to the existing HEC-18 and the NCHRP Project 24-20 (Ettema et al. 2010) clear-water and live-bed contraction scour equations. Section 8.4 applies the revised equations to a bridge- specific field example and compares the results with scour estimates obtained from the existing equations. Section 8.5 evaluates the reliability of the revised equations compared with the established reliability of the existing equations (Lagasse et al. 2013). Finally, Section 8.6 presents a plan for implementing the findings of this research, and Section 8.7 describes the standalone Training Manual (NCHRP Web-Only Document 294) prepared as a separate deliverable to facilitate the implementation of the research results. NCHRP Web-Only Document 294 can be found on the TRB website (www.trb.org) by searching for “NCHRP Project 24-47”. 8.2 Appraisal of Results 8.2.1 Introduction This section analyzes the data and observations presented in the previous chapters to provide insights regarding contraction scour at bridge waterways. The insights are supported by the hydraulic information developed in Chapter 2, which considers how flow passes through fixed bed, contracted open channels under pre-scour conditions. In particular, the analysis addresses the following aspects of contraction scour: (a) The overall trends relating the depth of contraction scour in the vena-contracta region at the throat of the contraction to the parameters B2/B1 and τ1/τc (the main parameters varied in the flume experiment) (b) Bed profiles along the contracted channel (c) Scour depth variation in the vena-contracta formed by flow entering the contracted channel (d) The relationship between the scour depths at the corners of the contraction entrance and in the vena-contracta region An important consideration was defining the key location where the depth of contraction scour should be measured. The analysis indicated that this location is in the vena-contracta region (i.e., the narrowest part of flow through the contraction). Scour also occurs at the corners of the contraction where scour is strongly influenced by the form of the contraction entrance C H A P T E R   8 Revised Contraction Scour Analysis: Appraisal, Results, and Applications

8-2 Revised Clear-Water and Live-Bed Contraction Scour Analysis (abrupt, angled, or conforming to the shape of entrance streamlines). Additionally, the depth of scour along the contracted channel downstream of the vena-contracta varies with the variation of flow depth (a flow-drawdown profile) along the contraction. An additional complicating factor was the deformable roughness of a contracted channel with a mobile (loose) bed or boundary. For the laboratory conditions examined, the bed roughness varied along the contracted channel when the bed developed ripple and dune bedforms. 8.2.2 Overall Trends An important finding from the flume experiments involving the hydraulics of contracted open channels and the similitude considerations associated with contraction scour is that the conditions termed clear-water and live-bed contraction scour form branches of overall trends whereby scour depth and scour profile of a contracted, mobile-bed open channel vary with the shear-stress parameter, τ1/τc, for a given contraction ratio (B2/B1) and contraction-entrance shape. The trends of the clear-water and live-bed relationships bracket the data obtained from the flume in the vena-contracta region and apply generally to contraction scour processes. This finding leads directly to the recommended adjustments to the HEC-18 design relationships widely used for estimating the depth of contraction scour (see Section 8.3). Figure 8-1 depicts conceptually the overall trends bracketing the data from hydraulic con- siderations and the findings from the flume experiments. The data and observations obtained from the flume experiments (involving a mobile-bed approach flow into a contracted section) conform with the overall trend labeled “data” in this figure. The upper branch in Figure 8-1 corresponds to equilibrium scour depths for the condition whereby bed shear stress in the approach flow is less than or equals the shear stress related to the entrainment of the bed material (i.e., a clear-water condition). It should be noted that the laboratory experiments completed under this project did not investigate conditions where the shear-stress ratio (τ1/τc) for the approach flow exceeded a value of one, but no bed sediment enters the contracted channel. This condition could occur under certain situations in the field (e.g., when flow passes through a bridge opening on a heavily vegetated floodplain). The lower branch of Figure 8-1 evolves as the approach flow mobilizes bed sediment and transports that sediment into the contraction. This live-bed condition partially compensates for the loss of bed sediment in the contraction, and consequently, reduces the magnitude of scour depth compared with the values of scour depth associated with the upper branch (the extended curve for clear-water scour). Ds/Yn1 τ1/τc Live-bed Clear-water Data from flume experiments 1.0 Figure 8-1. Conceptual illustration of the variation of the contraction scour depth parameter, Ds / Yn1, with shear-stress parameter, t1 /tc , along the vena-contracta region of a contraction.

Revised Contraction Scour Analysis: Appraisal, Results, and Applications 8-3 For mobile-bed channels that are typical of rivers, the trends indicated by the two branches shown in Figure 8-1 may become complicated by several factors, including the spatially non-uniform formation of bedforms along the contraction and the resulting non-uniform deformation of the bed of the contraction. Bedforms may also exist in the approach section to the contraction. Under field conditions, a further complication is that the bed of an alluvial river generally consists of sediment that is non-uniform in size distribution. As noted in Chapter 3, a relatively uniform fine sand was used in the laboratory experiments for this study, primarily to avoid complications associated with a potential for bed armoring as scour developed. Bedforms also make it difficult to assign accurate values of scour depth in the field and the laboratory, notably when the height of bedforms is comparable with the nominal depth of scour. The interpretation of the results in the laboratory was complicated by the presence of important turbulence structures (flow separation vortices) formed when flow separated from the corners of the entrance walls leading into the contraction. These turbulence structures developed at the corners of the 45o contraction entrance used in the flume experiments and have a major influence on scour depth in relation to entrance shape. The regions of corner scour observed in the flume at the contraction entrance were a consequence of the formation of these turbulence structures. Additionally, two more influences of the large-scale turbulence structures created by flow separation at the corners need to be considered: 1. The turbulence structures were advected downstream, thereby influencing bed-sediment entrainment and bed scour downstream of the entrance. 2. The size of the separation vortices affected the width of the vena-contracta, making the width unsteady, and at times, difficult to determine accurately. These influences were also complicated by the development of bedforms (ripples and dunes). 8.2.3 Bed Profiles and Bedforms Along the Contracted Channel In accordance with the non-uniform profiles of the water surface along a contracted open channel (see Chapter 2), the scour depth varied along the contracted channel in each experiment. The variation of water surface profile along a contraction indicates that the shear stress exerted on the contraction bed should result in an upward curving profile for the bed surface along the contracted section. The flume data show that the bed profile along the contracted channel curved upward, though the bed profiles were complicated by the spatial (streamwise) variation of bedform characteristics along the contracted channel (see Section 8.2.5). The formation of the vena-contracta and the two flow separation zones (at the contraction corners) influenced scour of the bed along the contraction, augmenting the effect of the spatial variations of bedforms developed along the bed of the contracted channel. The combined effect of the non-uniform hydrodynamic loading of the bed was evident in the scour depth variations observed along the contracted channel. These scour depth results were anticipated, and the LiDAR scans from the flume experiments confirmed that scour depths (and scour patterns) differed along the contracted channel for the three contraction ratios used in the flume experiments. The variations in bed bathymetry (quantified and characterized using LiDAR scans of the bed along the contracted channel) were divided into five length-segments of the contracted channel: 1. The first segment (the focal segment of the contraction) included the contraction entrance and a downstream length approximately equal to approach flow width, B1. This region contained the regions of flow separation and vena-contracta formation. After passing through the

8-4 Revised Clear-Water and Live-Bed Contraction Scour Analysis vena-contracta and at a flow length of about B1, the flow reattached to the full width of the contracted channel. 2. The remaining (downstream) length-segments were divided into four parts (termed quartiles 1, 2, 3, and 4) to illuminate the variation of bed elevation changes and bedforms along the contracted channel. In relation to the focal segment of the contraction (Item 1), Figure 8-2 provides a sketch of the key features of the entrance length-segment. Scour development in this region of the contraction segments was affected by the three aspects of the flow field: (a) Formation of a vena-contracta (b) Flow separation at the corners of the contraction entrance (c) Flow reattachment at the full width of the contraction For an assessment of contraction scour processes in the four quartiles referenced in Item 2, see Figure 8-6 and the associated text. For the flume experiments conducted for the present study, flow reattachment was observed to occur within the downstream distance x = B1 along the entrance segment of the contraction, as shown in Figure 8-2. The deepest scour always occurred at the contraction corners within the entrance segment. Scour at this location was caused by the generation of flow separation vortices at the entrance corners of the contracted channel. The scour in this region is herein called corner scour. Scour at this location may be influenced more by the abutment effect than by the width of the contraction (Ettema et al. 2010). The scour associated with the vena-contracta is herein termed vena-contracta scour and occurred along a region delineated in a streamwise direction in Figure 8-2 within the entrance segment. Scour in this region of the entrance segment relates directly to the contraction effect. The location of the maximum contraction of the vena- contracta shifted downstream as the water discharge increased, and thereby, the shear-stress ratio, τ1/τc, increased. Because of the narrowness of the Severe contraction (B2/B1 = 0.25) configuration, the scour along the vena-contracta merged with the corner scour for this contraction ratio. The separa- tion vortices generated at the two corners dispersed downstream across the major portion of the vena-contracta, causing the two corner scour regions to interact, such that the corner scour and vena-contracta scour together produced an essentially level transverse bed at the contraction entrance. This merging of scour regions did not occur for the two larger values of B2/B1 used in the experiments (i.e., the Moderate and Mild contraction configurations). The position of the B1 B2 x B1 B’2Vena-contracta Flow reattachment Corner Figure 8-2. The main regions of the flow field and consequent scour observed within entrance to the contracted channel (Nowroozpour 2020).

Revised Contraction Scour Analysis: Appraisal, Results, and Applications 8-5 local maximum depth (the maximum scour depth in the vena-contracta) shifted as the location of the vena-contracta shifted downstream when parameters B2/B1 and τ1/τc increased. 8.2.4 Scour Depth Variation in the Vena-Contracta Region The varying length of the vena-contracta formed for each contraction ratio, B2/B1, and shear-stress ratio, τ1/τc, used for the experiments introduced uncertainty into the selected values of scour depth along each vena-contracta. The length of the vena-contracta increased as τ1/τc increased for each value of B2/B1. In addition, the presence of bedforms complicated the measurement of scour depth in the vena-contracta because the dune heights were on the same order of magnitude when compared with the scour depths. As noted, the occurrence of bedforms added substantial uncertainty to measurements of contraction scour depth at practically all locations along the contracted channel. To address this uncertainty, a sensitivity analysis was completed to ascertain how the estimated depth of scour varied with the length of the vena-contracta area used to calculate the average scour depth in the vena-contracta area. As shown in Figure 8-3, various measurement lengths, lvc, were selected to represent the length of the region corresponding to the vena-contracta. For this analysis, the start of the vena-contracta was taken to be the start of the contracted channel (channel width B2), as indicated in Figure 8-2. The analysis sought to determine which range would best represent scour depth for the vena-contracta area. The analysis regarding the selection of lvc indicated that the range 0.1 to 0.6B1 covered too much of the upstream end of the vena-contracta, whereas the range 0.2 to 0.9B1 covered too much of the downstream end of the vena-contracta. The latter range had added complications arising from the presence of bedforms. Therefore, the measurements made in these areas were omitted from the selection. The focal sample area extending from 0.2 to 0.6B1 as shown in Figure 8.3 was selected as the most representative of the scour depth for the vena-contracta. The values of vena-contracta scour depth reported in Section 8.2.5 were taken from this range. 8.2.5 Trends in Measured Depths of Contraction Scour This section summarizes the scour depths measured for the three scour regions (vena- contracta, entrance corner, and location of reattachment) for the two conditions conventionally Figure 8-3. Scour regions, including the vena-contracta region and the corners of the contraction under live-bed conditions (Nowroozpour 2020).

8-6 Revised Clear-Water and Live-Bed Contraction Scour Analysis analyzed for contraction scour: clear-water scour and live-bed scour. As noted, the focus of this study is on scour in the vena-contracta region, though generally the scour depths were greatest at the corners of the entrance to the contracted channel as a result of the substantial turbulence structures generated there (i.e., an abutment effect). Data on the maximum depth of scour in the vena-contracta region (measured as described in Section 8.2.4) are presented in Figure 8-4. When flow enters the contracted section, the flow streamlines separated from the walls and reattached (for all the experiments) approximately a distance of B1 from the start of the contracted channel (see Figure 8-2). The exact distance to reattachment varied as τ1/τc increased (Nowroozpour 2020). Figure 8-5 shows the average scour depth estimated for the vena-contracta region for the Moderate and Mild contraction scour experiments. As noted, for the Severe contraction, the separation vortices that form at the entrance corners influence scour in the vena-contracta region significantly, thereby complicating estimation of an average depth of scour for this region. Figure 8-6 illustrates the resulting contraction scour pattern when the separation vortices substantially interacted with the contraction flow passing through the vena-contracta region Figure 8-4. Maximum depth of scour in vena-contracta region. The open symbols indicate clear-water tests, and the solid symbols indicate live-bed tests (Nowroozpour 2020). Figure 8-5. Average depth of scour in the vena-contracta region. The open symbols indicate clear-water tests, and the solid symbols indicate live-bed tests (Nowroozpour 2020).

Revised Contraction Scour Analysis: Appraisal, Results, and Applications 8-7 (B2/B1 = 0.25). The interaction distributed turbulence into the vena-contracta and made the vena-contracta region harder to delineate because of oscillations of its boundaries. As a result, a single scour hole developed between corners of the contraction entrance. The scour hole merged with the downstream bed by way of a continuous upwards slope. Other than the scour hole at the start of the contracted channel, no other locally minimum bed-surface area developed in the contraction (Nowroozpour 2020). As shown in Figure 8-6, the bed profile of the contracted channel curved upward in response to the gradually varied water surface (M2 profile) along the channel. Further, the shape of the curve changed as the length of the vena-contracta increased or decreased along the contracted section (see Chapter 2). Figure 8-7 plots the average depth of scour of the bed (bed lowering) at a transect located a distance, B1, downstream of the start of the narrowed width of contracted channel in the reattachment zone (see Figure 8-2). The scour depth at this transect usually had the lowest elevation along the contracted section downstream of this cross section location. A transect strip, of width about 0.2B1, was used for sampling and determining the average bed elevation at this location for each experiment. Figure 8-7 shows that for the Moderate and Mild contraction configurations, the depth of clear-water scour was negligible along the vena-contracta. The flow through the contraction was such that shear stress exerted on the bed was insufficient to move the bed sediment. Additionally, (a) (b) Figure 8-6. Comparison of the LiDAR-scanned bed before and after scour along the contracted channel, Test CW_0.25-0.55: (a) isometric view of the contracted channel; and (b) profile view of the contracted channel (Nowroozpour 2020). Figure 8-7. Average scour depth at a distance B1 downstream of the contraction entrance. The open symbols indicate clear-water experiments and the solid symbols indicate live-bed experiments (Nowroozpour 2020).

8-8 Revised Clear-Water and Live-Bed Contraction Scour Analysis the scour depth in this area was affected by the length of the contraction such that the bed shear stress gradually increased along the contraction (Nowroozpour 2020). The values of corner scour depth typically exceeded the scour depth in the vena-contracta because of the hydrodynamic forces exerted by the separation vortices. Generally, there was a slight difference between the maximum scour depth at the right and left sides of the contraction entrance, with the left corner sometimes developing deeper scour. This difference resulted from small variations in the flow field and slight asymmetrical variations in the roughness gravel placed in the flume at the start of the approach channel. Prior studies, for example, Gill (1981), indicate that asymmetry of scour depth at the corners is not unusual. Figure 8-8 plots values of the maximum depth of corner scour. This figure shows that increas- ing values of the shear-stress ratio caused deeper scour at the contraction corners. However, the rate of scour decreases as the shear-stress ratio or contraction ratio increases. It is noteworthy that, for clear-water Severe contraction tests, the interaction of the separation vortices caused the maximum scour depth to develop at the centerline of flume entrance (Nowroozpour 2020). 8.2.6 Hydraulic Force Decay For contraction scour, a theoretical force decay function can be developed from the existing HEC-18 scour prediction equations (after Kerenyi 2016). The function relates to the reduction in shear stress (or velocity) as the depth of the scour hole increases. For clear-water scour, the force decay function is y y nq K (8.1)s contraction 0 7 3 2 u 2 ( )τ = γ +     − where τ = Shear stress at bottom of scour hole, lb/ft2 γ = Weight of water, 62.4 lb/ft3 ys contraction = Depth of contraction scour, ft y0 = Flow depth before scour occurs, ft n = Manning’s n in the contracted reach q2 = Unit discharge in the contracted reach, ft3/s/ft Ku = Coefficient for U.S. customary units = 1.486 0.00 Figure 8-8. Maximum depths of scour at the entrance corners of the contracted channel. The open symbols indicate clear-water tests, and the solid symbols indicate live-bed tests (Nowroozpour 2020).

Revised Contraction Scour Analysis: Appraisal, Results, and Applications 8-9 Given a unit discharge, Manning’s n, and flow depth prior to scour, the theoretical force decay function can be developed by varying the scour depth in Eq. (8.1) and calculating the asso- ciated shear stress. This was done for all four calibrated clear-water tests. An example is shown in Figure 8-9 for Test CW_0.25-0.75. In Figure 8-9, the theoretical decay function is shown as the blue line. The red dots are the observed scour depths in the short-contraction and long-contraction regions. The shear stress at these locations is determined from the calibrated HEC-RAS model and demonstrates that with a properly calibrated hydraulic model, the red dots do indeed fall on the theo- retical curve. The force decay concept can be applied to situations where the soil stratigraphy varies with depth. In Figure 8-10, the force decay function, shown as the yellow line, is plotted against the erosion resistance of the various soil layers found at depth beneath an existing or proposed bridge -2.5 -2 -1.5 -1 -0.5 0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 Sc ou r d ep th , ft Shear stress, lb/ft2 Long-contraction observed scour Short-contraction observed scour Figure 8-9. Theoretical force decay function versus observed scour, Test CW_0.25-0.75. Figure 8-10. Scour depth function (force decay) versus stratigraphic layering (after Kerenyi 2018).

8-10 Revised Clear-Water and Live-Bed Contraction Scour Analysis site (from Kerenyi 2018). In this figure, if the erosion force (which decreases with scour depth) exceeds the scour resistance of the stratigraphic layer, erosion will proceed. After scour pro- gresses to a certain depth, the erosion forces will equal the scour resistance of the soil layer that has been encountered. When this occurs, scour can no longer proceed, and the true scour depth could be less than the estimated scour depth for a homogeneous soil. 8.2.7 LSPIV Analyses This section describes the LSPIV method used to view the vena-contracta for each experiment and estimate the narrowest width of the vena-contracta. LSPIV is a technique commonly used for observing and measuring velocities at the free surface of open-channel flows (e.g., Muste et al. 2017). The LSPIV software, Fudaa (https://forge.irstea.fr/projects/fudaa-lspiv), was used for con- verting video images of flow at the water surface of each contraction entrance, calculating the pertinent velocity vectors, and estimating the narrowest width of each vena-contracta. The soft- ware version used was Version 1.7.1, which enabled calculation of streamlines, flow discharge, and transforming images to PNG format. The LSPIV techniques required the use of benchmarks to locate the flow and enable ortho- rectification of the video image, which was taken at an oblique angle. The Fudaa LSPIV software used 10 benchmark locations for orthorectification. Figure 8-11 shows the positions of bench- mark locations for the contraction ratio B2/B1 = 0.5 (Fakhri 2020). A requirement for suitably accurate LSPIV is the acquisition of a detailed video image. An Olympus EM-10 video camera was used for this task. The camera had a 4k format, such that the resulting images had a maximum size of 3840 × 2160 pixels recorded at a rate of 30 images per second. The area of interest covered all benchmarks, and it was essential to avoid any vibration or reflection. Paper pieces were used as tracers creating flow pathlines on the water surface. A set of preliminary experiments involved testing different sizes of paper tracers. Video camera images were recorded to capture the displacements of the particles on the water surface by positioning the camera obliquely and vertically to the interest area. The LSPIV software was then used on those images of the flow field and provided free surface velocity by producing 2D vector fields of flow (Fakhri 2020). Figure 8-11. The benchmark locations used for a preliminary experiment with the contraction ratio B2/B1 = 0.5. This experiment involved the larger size of paper tracers (Fakhri 2020).

Revised Contraction Scour Analysis: Appraisal, Results, and Applications 8-11 The LSPIV technique calculated the movement of paper tracers on the water surface and within the contraction entrance. The Fudaa software involves the following steps to calculate flow velocities: 1. Set up the software and select the video record images. 2. Orthorectify the images and define each benchmark location. 3. Define an interrogation area and a search area. 4. Form the estimation grid. 5. Calculate values of the local velocity at each position, and determine average values of velocity at each position. Several of the critical steps and results are illustrated as follows. Figure 8-12 shows the use of the LSPIV software to calculate the average values of the surface velocity vectors. As noted, the Fudaa Version 1.7.1 software had the capacity to display stream- lines in the flow field. This was of considerable use for delineating the vena-contracta. In this step, a straight line was established across the flow to indicate the flow field from which streamlines were to be drawn. Figure 8-13 shows the defined line for B2/B1 = 0.5 and discharge = 8.12 ft3/s (0.23 m3/s), and the streamlines (Fakhri 2020). Figure 8-14 shows an example of the minimum vena-contracta width estimated for B2/B1 = 0.5 and = 8.12 ft3/s (0.23 m3/s). This figure shows the dimensions of the flow entering the contracted channel, and the dimensions measured using the LSPIV technique. Table 8-1 gives measured vena-contracta ratios estimated for all of the experiments (involving different contraction ratios and discharges) (Fakhri 2020). Figure 8-12. The average velocity vectors for B2 /B1 = 0.5 and discharge = 8.12 ft3/s (0.23 m3/s) (Fakhri 2020).

Figure 8-13. The calculated streamlines obtained for B2/B1 = 0.5 and discharge = 8.12 ft3/s (0.23 m3/s) (Fakhri 2020). Figure 8-14. The measured value of vena-contracta width B2’ obtained from a live-bed experiment (Fakhri 2020). Test Test Number B2'(ft) Ratio Q(CMS) B2'/B2 B1/B2-1 V Fr (B1/B2-1)Fr LB28 LB-0.75-2.72 4.98 0.75 0.19 0.8300 0.33 0.438 0.3318 0.1095 LB27 LB-0.75-4.0 4.64 0.75 0.231 0.7733 0.33 0.533 0.4034 0.1331 CW26 CW-0.75-0.9 4.93 0.75 0.111 0.8217 0.33 0.256 0.1939 0.0640 LB29 LB-0.75-1.96 4.80 0.75 0.161 0.8000 0.33 0.371 0.2812 0.0928 LB30 LB-0.75-1.44 4.73 0.75 0.138 0.7883 0.33 0.318 0.2410 0.0795 LB31 LB-0.75-6.25 4.56 0.75 0.288 0.7600 0.33 0.664 0.5030 0.1660 CW25 CW-0.75-0.72 5.28 0.75 0.099 0.8800 0.33 0.228 0.1729 0.0571 CW12 CW-0.25-0.30 1.38 0.25 0.064 0.6900 3.00 0.148 0.1118 0.3353 CW11 CW-0.25-0.56 1.21 0.25 0.087 0.6050 3.00 0.201 0.1519 0.4558 LB20 LB-0.5-4.0 2.56 0.50 0.231 0.6400 1.00 0.533 0.4034 0.4034 LB21 LB-0.5-1.96 2.65 0.50 0.161 0.6625 1.00 0.371 0.2812 0.2812 LB22 LB-0.5-2.72 2.53 0.50 0.19 0.6325 1.00 0.438 0.3318 0.3318 LB23 LB-0.5-1.44 2.73 0.50 0.138 0.6825 1.00 0.318 0.2410 0.2410 CW17 CW-0.5-0.30 3.13 0.50 0.064 0.7825 1.00 0.148 0.1118 0.1118 CW18 CW-0.5-0.42 2.90 0.50 0.076 0.7250 1.00 0.175 0.1327 0.1327 CW19 CW-0.5-0.56 2.81 0.50 0.087 0.7025 1.00 0.201 0.1519 0.1519 CW12_Fixed 0.88 0.25 0.064 0.4400 3.00 0.148 0.1118 0.3353 CW13_Fixed 0.70 0.25 0.092 0.3500 3.00 0.212 0.1607 0.4820 CW14_Fixed 0.75 0.25 0.076 0.3750 3.00 0.175 0.1327 0.3982 Table 8-1. Calculated vena-contracta ratios and details for all experiments (Fakhri 2020).

Revised Contraction Scour Analysis: Appraisal, Results, and Applications 8-13 The LSPIV technique was useful for measuring values of B2′ for most of the experiments. However, judgment was required for the higher discharges at the smallest value of B2/B1 used (the Severe contraction). Under these conditions, the turbulence from the separation zones at the entrance corners caused the vena-contracta boundaries to oscillate. The following figures provide an example of measurements at a Severe contraction (Figure 8-15), a Moderate contraction (Figure 8-16), and a Mild contraction (Figure 8-17). 8.3 Revised Contraction Scour Analysis 8.3.1 General This section presents potential revisions to the existing HEC-18 contraction scour prediction methods. The emphasis of this section is on modifications applicable to field conditions and the analytical tools reasonably available to the practitioner. These modifications include the following: • Consideration of bedform height in estimates of the maximum scour depth if not otherwise accounted for in the scour evaluation (i.e., an equilibrium depth of scour) Figure 8-15. LSPIV measurement of the vena-contracta at a Severe contraction (B2/B1 = 0.25) (Fakhri 2020). Figure 8-16. LSPIV measurement of the vena-contracta at a Moderate contraction (B2/B1 = 0.50) (Fakhri 2020).

8-14 Revised Clear-Water and Live-Bed Contraction Scour Analysis • Consideration of simplified contraction scour equations developed as part of NCHRP Project 24-20 and applied to abutment scour calculations in HEC-18 • Addition of a vena-contracta width factor, Kv, to the Laursen contraction scour equations to account for observed additional flow contraction immediately downstream of the entrance to a contraction (i.e., in the bridge reach) The vena-contracta factor, Kv, was measured for the flume testing scenarios described in Section 8.2.7 using LSPIV analysis (Fakhri 2020). Kv values can be applied to hydraulic conditions and bridge configurations similar to the 45° entrance configuration and low width-to-depth conditions [i.e., a “hydraulically narrow” cross section as defined by FHWA (2020)] evaluated for this study. Application of the Kv concept is also limited to streams with relatively uniform, non-cohesive bed material. Additional study is recommended (see Section 9.3) to better quantify Kv and to generalize its application. The HEC-18 contraction scour prediction methods are simplified prediction tools that have had a large and unquantified uncertainty and variability relative to the expected value of contraction scour (see Section 2.2). Increased prediction variability necessitates more con- servative scour estimates to achieve a given statistical reliability for design and evaluation. Unfortunately, prior study was not able to fully validate the statistical reliability of existing contraction scour prediction technology (Lagasse et al. 2013). The present study provides both a well-documented physical model dataset for contraction scour and an evaluation of the statistical reliability of the existing contraction scour prediction technology. This study proposes refinements to the HEC-18 methods that may decrease variability and increase prediction bias, resulting in improved statistical reliability (see Section 8.5). Well-quantified and improved statistical reliability would allow the practitioner to account for inherent uncertainties in scour, thereby reducing (unquantified) overconservatism in design. 8.3.2 Procedures for Evaluating Upstream Sediment Supply This study compared simplified hydraulic sediment transport characteristics of a non-contracted reach versus a contracted reach. For the flume experiments, non-contracted (theoretical normal- depth) hydraulic conditions were used to evaluate upstream sediment transport characteristics (live-bed versus clear-water). For live-bed conditions, existing HEC-18 procedures (τ1/τc > 1 or V1 > Vc) were used. These procedures were also used to establish live-bed sediment feed rates for the flume experiments as described in Chapter 3. This approach is plausible for the flume Figure 8-17. LSPIV measurement of the vena-contracta at a Mild contraction (B2/B1) = 0.75) (Fakhri 2020).

Revised Contraction Scour Analysis: Appraisal, Results, and Applications 8-15 environment when evaluating equilibrium scour conditions, as the sediment supply and the bed will interact with the underlying hydraulic controls to produce equilibrium post-scour bed conditions. Table 8-2 presents a partial summary of the experimental results and the reported theoretical normal-depth hydraulics (V1n, y1n) for each experiment. This normal-depth compu- tation to evaluate upstream hydraulics for contraction scour analysis is potentially suitable for application to constant-slope river systems with prismatic channels. In field practice, channel and floodplain configurations ordinarily vary, channel slopes often vary significantly, and normal-depth evaluation using the Manning’s n equation and a practitioner-estimated energy grade line friction slope likely introduces subjectivity and sub- stantial uncertainty into the upstream hydraulic and sediment supply evaluation. Section 8.5 provides a reliability analysis of post-scour depth estimates that used the normal-depth estimates for the well-controlled flume environment available for this study. One alternative to this theoretical normal-depth hydraulic approach to evaluating upstream sediment supply and hydraulic conditions in the field is to use a “pre-bridge” or “natural condi- tions” model (Figures 8-18 and 8-19). Here, the practitioner develops an existing-conditions (pre-scour) model by removing the encroachments associated with a given crossing from the topography and using the resulting unencroached hydraulic model to evaluate the sediment Simulation Discharge Top Width of Channel Upstream Hydraulics Yo (HEC- RAS) Observed Vena-contracta Scour (LiDAR) ft Q B1 B2 B2' Hydraulic Depthft/s Average Velocity ft/s Ft Maximum Equilibrium cfs ft ft ft y1n y1a V1n V1a CW_0.25-0.55 2.24 8 2 1.38 0.57 0.811 0.495 0.35 0.775 0.74 0.64 CW_0.25-0.65 3.26 8 2 n/a 0.70 0.838 0.585 0.49 0.791 0.95 0.85 CW_0.25-0.75 3.05 8 2 1.21 0.56 0.934 0.675 0.41 0.884 1.06 0.98 CW_0.25-0.80 3.26 8 2 n/a 0.57 0.929 0.72 0.44 0.869 1.04 0.95 CW_0.50-0.55 2.26 8 4 3.13 0.57 0.672 0.495 0.42 0.66 0.23 0.19 CW_0.50-0.65 2.67 8 4 2.9 0.57 0.738 0.585 0.45 0.723 0.27 0.20 CW_0.50-0.75 3.09 8 4 2.81 0.57 0.745 0.675 0.52 0.726 0.31 0.23 CW_0.75-0.75 3.09 8 6 n/a 0.57 0.6723 0.675 0.57 0.653 0.12 0.09 CW_0.75-0.85 3.5 8 6 5.28 0.57 0.7079 0.765 0.62 0.6974 0.21 0.15 CW_0.75-0.95 3.91 8 6 4.93 0.57 0.745 0.86 0.66 0.702 0.21 0.15 LB_0.50-1.2 4.89 8 4 2.73 0.57 0.822 1.08 0.74 0.784 0.49 0.39 LB_0.50-1.4 5.7 8 4 2.65 0.57 0.808 1.26 0.88 0.757 0.62 0.53 LB_0.50-1.65 6.72 8 4 2.53 0.57 0.944 1.49 0.89 0.891 0.79 0.65 LB_0.50-2.0 8.14 8 4 2.56 0.57 0.972 1.80 1.05 0.898 0.85 0.72 LB_0.75-1.2 4.89 8 6 4.73 0.57 0.688 1.08 0.89 0.707 0.29 0.20 LB_0.75-1.4 5.7 8 6 4.8 0.57 0.706 1.26 1.01 0.757 0.27 0.17 LB_0.75-1.65 6.72 8 6 4.98 0.57 0.758 1.485 1.11 0.891 0.29 0.18 LB_0.75-2.0 8.14 8 6 4.64 0.57 0.789 1.80 1.29 0.781 0.46 0.27 LB_0.75-2.5 10.18 8 6 4.56 0.57 0.9 2.25 1.41 0.889 0.42 0.29 Table 8-2. Summary of hydraulic inputs to scour evaluation from flume experiments (U.S. customary units).

8-16 Revised Clear-Water and Live-Bed Contraction Scour Analysis Figure 8-18. Example topographic surface for an existing-conditions hydraulic analysis. Note the presence of the roadway embankment and guide banks. Figure courtesy of Colorado Department of Transportation (CDOT). Figure 8-19. Example topographic surface for a pre-bridge hydraulic analysis. Note that the existing embankment and guide banks have been removed from the topography. Figure courtesy of CDOT.

Revised Contraction Scour Analysis: Appraisal, Results, and Applications 8-17 supply and pre-scour contracted-section hydraulic conditions. This approach using a 2D model has the advantage of being analogous to the uncontracted hydraulic assumptions associated with the original Laursen equations and with the experimental conditions of the present study. However, it decouples modeled pre-scour conditions from predicted post-scour hydraulics. In many hydraulic systems, the presence of a roadway embankment and the constriction affect the governing hydrologic conditions (e.g., overtopping, flow spills into other crossings) under which a constriction operates. This hydrologic effect alters both upstream sediment supply characteristics and hydraulic conditions. It also introduces significant uncertainty. Consequently, this approach to evaluating representative sediment supply and upstream hydraulic conditions was not evaluated as part of this study. For additional information, see the References list for Robinson et al. 2019. Table 8-2 also presents calibrated HEC-RAS 1D hydraulic model results (V1a, y1a) for a cross section at the upstream limit of geometric contraction and the upstream end of the fully contracted section (y0). Based on the data collected as part of this study, Section 8.5 quantifies the potential effects on reliability of using a pre-scour approach section upstream of a contraction. It should be noted that when using pre-scour rigid-bed hydraulics, the Laursen scour equations predict a post-scour flow depth relative to the post-scour water surface elevation [i.e., the scour depth is calculated using a pre-scour contracted-section water surface elevation and a predicted post-scour flow depth (ys = y2 − y0), resulting in a decoupled calculation]. Section 8.5 presents a statistical comparison between scour depth (ys) and post-scour flow depth (y2). The current state of analysis and design practice is to use rigid-bed numerical modeling (1D or 2D depth-average), to model pre-scour existing condition topography (which commonly includes existing contractions), and to insert/add a numerical representation of the proposed encroachment for evaluation (Zevenbergen et al. 2012). The practitioner then determines an upstream location (the Approach Section) that is representative of both upstream sediment supply and upstream hydraulic conditions. The resulting rigid-bed model incorporates pre-scour hydraulic and sediment transport effects, which is not consistent with the original Laursen long-contraction scour relationship assumptions. The contraction scour procedures in HEC-18, an adaptation of (Laursen 1960), have been modified and simplified in successive editions of HEC-18 to provide an approximation of Laursen’s original assumptions. Selection and evaluation of approach-section hydraulics is a common source of unquantified uncertainty and potential error in contraction scour evaluation. However, best-practice guidance is available for both 1D and 2D hydraulic modeling for locating an approach section that is representative of both the sediment supply and hydraulic characteristics upstream of a con- traction (Brunner 2016, Robinson et al. 2019). 8.3.3 Analysis of the HEC-18 Equations The following equations are derived from HEC-18. Critical Velocity (for Non-Cohesive Materials) V K y d (8.2)c u 1 6 50 1 3= where Vc = Critical velocity above which bed material size d50 and smaller will be transported, ft/s y = Average depth of flow upstream of the bridge, ft d50 = Particle size in a mixture of which 50% are smaller by weight, ft Ku = 11.17 U.S. customary units

8-18 Revised Clear-Water and Live-Bed Contraction Scour Analysis If the average velocity upstream of the contraction (either at the approach section or calcu- lated from a theoretical normal depth) is less than Vc, then the flow is assumed to transport little to no bed material into the flow contraction and is, therefore, evaluated using clear-water contraction scour equations. The bed in the contraction is assumed to degrade until flow can no longer transport significant quantities of bed material. This can be expressed either as a ratio of shear stress to transport-critical shear or in the simplified form presented as follows. HEC-18 Clear-Water Post-Scour Flow Depth Estimation =      y K Q d W (8.3)2 u 2 m 2 3 2 2 3 7 where y2 = Average equilibrium depth in the contracted section after contraction scour, ft Q = Discharge through the bridge or on the setback overbank area at the bridge associated with the width W2, ft3/s dm = Diameter of the smallest non-transportable particle in the bed material (1.25 d50) in the contracted section, ft d50 = Median diameter of bed material, ft W2 = Bottom width of the contracted section less pier widths, ft Ku = 0.0077 U.S. customary units If V1 > Vc, then the approach flow is assumed to transport significant quantities of bed material into the flow contraction, either as contact load or in suspension, and a simplified sediment continuity analysis is performed (presented here for non-cohesive soil conditions): HEC-18 Live-Bed Post-Scour Flow Depth Estimation =            y y Q Q W W (8.4)2 1 2 1 6 7 1 2 K1 where y1 = Average depth in the upstream main channel, ft y2 = Average post-scour flow depth in the contracted section, ft Q1 = Flow in the upstream channel transporting sediment, ft3/s Q2 = Flow in the contracted channel, ft3/s W1 = Bottom width of the upstream main channel that is transporting bed material, ft W2 = Bottom width of main channel in contracted section less pier width(s), ft K1 = Exponent determined below V* / ω K1 Mode of Bed Material Transport < 0.50 0.59 Mostly contact bed material discharge 0.50 to 2.0 0.64 Some suspended bed material discharge > 2.0 0.69 Mostly suspended bed material discharge V* = (g y1 Sf1) 1/2 shear velocity in the upstream section, ft/s ω = Fall velocity of bed material based on the d50, ft/s (see HEC-18, Figure 6.8) g = Acceleration of gravity (32.2 ft/s2) Sf1 = Slope of energy grade line of main channel in the approach section, ft/ft Table 8-3 contains the results of scour calculations using the HEC-18 prediction methods for the experimental conditions of this study. Figure 8-20 presents observed maximum scour depths

Revised Contraction Scour Analysis: Appraisal, Results, and Applications 8-19 Simulation Approach Sediment Supply HEC-18, Using Approach Variables HEC-18 +Kv, Using Approach Variables NCHRP Project 24-20, Using Approach Variables NCHRP Project 24-20 +Kv, Using Approach Variables K1a Y2a Ysa Y2a Ysa q2/q1 Y2a Ysa q2/q1 Y2a Ysa CW_0.25-0.55 CW n/a 0.97 0.19 1.33 0.55 4.00 1.05 0.27 5.80 1.44 0.67 CW_0.25-0.65 CW n/a 1.33 0.54 n/a n/a 4.00 1.45 0.66 n/a n/a n/a CW_0.25-0.75 CW n/a 1.26 0.38 1.94 1.05 4.00 1.37 0.48 6.61 2.10 1.22 CW_0.25-0.80 CW n/a 1.33 0.47 n/a n/a 4.00 1.45 0.58 n/a n/a n/a CW_0.50-0.55 CW n/a 0.54 -0.12 0.66 0.00 2.00 0.58 -0.08 2.56 0.72 0.06 CW_0.50-0.65 CW n/a 0.62 -0.10 0.82 0.09 2.00 0.67 -0.05 2.76 0.89 0.16 CW_0.50-0.75 CW n/a 0.70 -0.02 0.95 0.23 2.00 0.76 0.04 2.85 1.03 0.31 CW_0.75-0.75 CW n/a 0.50 -0.16 n/a n/a 1.33 0.54 -0.11 n/a n/a n/a CW_0.75-0.85 CW n/a 0.55 -0.14 0.62 -0.08 1.33 0.60 -0.10 1.52 0.67 -0.03 CW_0.75-0.95 CW n/a 0.61 -0.09 0.72 0.02 1.33 0.66 -0.04 1.62 0.78 0.08 LB_0.50-1.2 CW n/a 1.04 0.26 1.45 0.66 2.00 1.13 0.35 2.93 1.57 0.78 LB_0.50-1.4 CW n/a 1.19 0.43 1.69 0.94 2.00 1.29 0.53 3.02 1.84 1.08 LB_0.50-1.65 CW n/a 1.37 0.48 2.03 1.14 2.00 1.48 0.59 3.16 2.20 1.31 LB_0.50-2.0 CW n/a 1.61 0.72 2.37 1.47 2.00 1.75 0.85 3.13 2.57 1.67 LB_0.75-1.2 CW n/a 0.74 0.03 0.90 0.20 1.33 0.80 0.09 1.69 0.98 0.27 LB_0.75-1.4 LB 0.64 0.85 0.09 0.98 0.22 1.33 0.90 0.15 1.67 1.09 0.34 LB_0.75-1.65 LB 0.64 0.91 0.02 1.03 0.14 1.33 0.97 0.08 1.61 1.14 0.25 LB_0.75-2.0 LB 0.64 0.95 0.17 1.12 0.34 1.33 1.01 0.23 1.72 1.26 0.48 Note: See Section 8.3.5 for a discussion of the vena-contracta coefficient, Kv. Table 8-3. Summary of scour predictions by different methods. Figure 8-20. Maximum observed vena-contracta scour versus HEC-18 predicted scour using approach-section predicted hydraulics.

8-20 Revised Clear-Water and Live-Bed Contraction Scour Analysis and predicted scour depths using the HEC-18 prediction methods for upstream approach hydraulics. See Section 8.2. for a discussion of the vena-contracta that forms at the entrance to a contracted reach (e.g., single-span bridges with a low width-to-depth ratio). Note that the HEC-18 equations consistently underpredict maximum scour with moderate to high variability. One factor not accounted for in Figure 8-20 is the presence of bedforms in evaluating maximum scour. Consequently, the observed bedform amplitude (half the peak- to-trough height) was subtracted to evaluate equilibrium post-scour predictions. Table 8-4 presents the resulting equilibrium scour depth and post-scour flow depths. Figure 8-21 presents the resulting equilibrium observed vena-contracta scour versus HEC-18 predicted scour using approach-section predicted hydraulics. The HEC-18 pier scour relationships include a factor to account for bedform height (K3). However, if no pier is present, or if designing an abutment or bank revetment scour counter- measure, bedform height should be accounted for in the design along with long-term degradation and contraction scour (Arneson et al. 2012). Van Rijn (1984) presents a bedform height predictor (see Julien 2010). The practitioner should add half of the resulting peak-to-trough bedform height for design scour conditions. In coarse-bed streams, the practitioner should also consider the active layer thickness. Test Observed Bedform amplitude (ft) Max depth (ft) Equilibrium post-scour. flow depth, y2 (ft) Observed equilibrium scour depth, ys (ft) CW_0.25-0.55 0.10 1.48 1.38 0.64 CW_0.25-0.65 0.10 1.70 1.60 0.85 CW_0.25-0.75 0.08 1.84 1.76 0.98 CW_0.25-0.80 0.10 1.84 1.75 0.95 CW_0.50-0.55 0.04 0.87 0.83 0.19 CW_0.50-0.65 0.07 0.97 0.90 0.20 CW_0.50-0.75 0.08 1.00 0.93 0.23 CW_0.75-0.75 0.03 0.77 0.74 0.09 CW_0.75-0.85 0.06 0.90 0.84 0.15 CW_0.75-0.95 0.06 0.90 0.84 0.15 LB_0.50-1.2 0.10 1.18 1.09 0.39 LB_0.50-1.4 0.10 1.37 1.27 0.53 LB_0.50-1.65 0.14 1.60 1.46 0.65 LB_0.50-2.0 0.13 1.70 1.57 0.72 LB_0.75-1.2 0.09 1.00 0.91 0.20 LB_0.75-1.4 0.10 1.00 0.91 0.17 LB_0.75-1.65 0.10 1.10 0.99 0.18 LB_0.75-2.0 0.18 1.20 1.01 0.27 LB_0.75-2.5 0.13 1.20 1.07 0.29 Table 8-4. Observed equilibrium scour depth, ys, and equilibrium post-scour flow depth, y2 (considering bedforms).

Revised Contraction Scour Analysis: Appraisal, Results, and Applications 8-21 In Figure 8-21, note that the HEC-18 scour equation still substantially underpredicts scour. However, a comparison of post-scour equilibrium flow depths presents a more conservative prediction and more conservative results. Figure 8-22 presents equilibrium post-scour flow depths for observed and predicted HEC-18 approach-section hydraulics. In Figure 8-22, note that the degree of apparent underprediction and the apparent prediction variability for y2 is substantially reduced compared with that of ys. This observation indicates that using a decoupled (pre-scour) contracted flow depth (y0) value to calculate a post-scour bed elevation change is non-conservative due to the backwater associated (in this case) with Figure 8-21. Equilibrium vena-contracta scour depth versus HEC-18 predicted scour using approach-section predicted hydraulics. Figure 8-22. Post-scour flow depths (y2) versus HEC-18 predicted scour (y2) using approach-section predicted hydraulics.

8-22 Revised Clear-Water and Live-Bed Contraction Scour Analysis pre-scour conditions. This degree of prediction variability will change depending on the indi- vidual case modeled and is not easily generalized using the findings of this study. The reliability effect of this decoupling is quantified in Section 8.5. The Severe contraction y2 values in Figure 8-22 also noticeably underpredict observed conditions relative to the Mild and Moderate contraction conditions. This is consistent with observations noted in Section 8.2, which indicated that flow separation and turbulent structures associated with the entrance condition (i.e., turbulence associated with corner scour at the contraction entrance), interacted across the entire channel for the Severe contraction condi- tions. Note also that the Moderate and Mild equilibrium post-scour depths qualitatively track the line of equal agreement reasonably well. Figure 8-23 presents observed equilibrium y2 values and predicted post-scour y2 values for reported theoretical normal-depth hydraulics using HEC-18 methods. Live-bed versus clear- water calculations were performed based on the critical velocity criteria presented in HEC-18 using reported theoretical normal-depth hydraulics. Clear-water calculation results are not dependent on upstream hydraulics, and therefore, are identical to the predicted approach- section hydraulics values. 8.3.4 Analysis of the NCHRP Project 24-20 Equations NCHRP Project 24-20 provides simplified forms of the HEC-18 contraction scour equations (Ettema et al. 2010). Critical velocity is calculated [see Eq. (8.2)], and the following relationships are used for clear-water and live-bed post-scour flow depth estimation. NCHRP Project 24-20 Clear-Water Post-Scour Flow Depth Estimation y q K d (8.5)2 2 u 50 1 3 6 7=     where y2 = Flow depth including clear-water contraction scour at maximum contraction, ft q2 = Unit discharge in the constricted opening at the point of maximum contraction, ft2/s Figure 8-23. Observed equilibrium y2 values and predicted post-scour y2 values for the theoretical normal-depth hydraulics using HEC-18 methods.

Revised Contraction Scour Analysis: Appraisal, Results, and Applications 8-23 Ku = 11.17 U.S. customary units d50 = Particle size with 50% finer, ft NCHRP Project 24-20 Live-Bed Post-Scour Flow Depth Estimation y y q q (8.6)2 1 2 1 6 7=     where y2 = Flow depth including live-bed contraction scour, ft y1 = Upstream flow depth, ft q1 = Upstream unit discharge, ft2/s q2 = Unit discharge in the constricted opening, ft2/s The present study evaluated the reliability of the NCHRP Project 24-20 equations in relation to the observed data. Figure 8-24 presents observed equilibrium y2 values and predicted post- scour y2 values using NCHRP Project 24-20 contraction scour equations and approach-section hydraulics. Note that these equations are qualitatively identical to the HEC-18 methods and vary only in the application of different constants for Ku (for the clear-water case) and K1 (for the live-bed case). In most applications, the NCHRP Project 24-20 contraction scour equations predict slightly deeper (more conservative) post-scour depths. Figure  8-25 presents predicted NCHRP Project 24-20 post-scour depths compared with HEC-18 predicted post-scour depths. Note the similar trend and slightly increased conservatism of the NCHRP Project 24-20 predictors compared with the HEC-18 prediction equations. 8.3.5 Vena-Contracta Analysis and Revised Equations This study observed and quantified a significant vena-contracta effect for all tests (see Section 8.2.7). The point of maximum vena-contracta narrowing was closely correlated to the region in which the maximum scour elevation was observed. The Laursen equations as Figure 8-24. Observed equilibrium y2 values and predicted post-scour y2 values using NCHRP Project 24-20 contraction scour predictors and approach-section hydraulics.

8-24 Revised Clear-Water and Live-Bed Contraction Scour Analysis presented in HEC-18 only consider physical (geometric) flow contraction. One-dimensional models cannot predict the vena-contracta effect, and typical 2D hydraulic models do not consistently reproduce the effect at practical grid cell resolutions (Zey 2017). Consequently, the present study quantified the ratio of the equilibrium scour vena-contracta versus the physi- cal contraction (B2′ versus B2). Table 8-5 contains the vena-contracta data and the post-scour approach-section hydraulics for which vena-contracta data were available. 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 Pr ed ic te d po st -s co ur fl ow d ep th N CH RP P ro je ct 2 4- 20 u sin g ap pr oa ch v ar ia bl es (ft ) Predicted post-scour flow depth HEC-18 using approach variables (ft) Figure 8-25. Predicted NCHRP Project 24-20 post-scour equilibrium flow depths versus HEC-18 predicted post-scour depths. Test Kv Unit discharge cfs/ft Fr1f Observed Approach Contracted Observed (q2/q1-1)Fr1f CW_0.25-0.55 0.69 0.28 1.12 0.08 0.23 CW_0.25-0.65 NO DATA CW_0.25-0.75 0.61 0.38 1.53 0.10 0.29 CW_0.25-0.80 NO DATA CW_0.50-0.55 0.78 0.28 0.57 0.10 0.10 CW_0.50-0.65 0.73 0.33 0.67 0.10 0.10 CW_0.50-0.75 0.70 0.39 0.77 0.12 0.12 CW_0.75-0.75 NO DATA CW_0.75-0.85 0.88 0.44 0.58 0.14 0.05 CW_0.75-0.95 0.82 0.49 0.65 0.15 0.05 LB_0.50-1.2 0.68 0.61 1.22 0.18 0.18 LB_0.50-1.4 0.66 0.71 1.43 0.20 0.20 LB_0.50-1.65 0.63 0.84 1.68 0.21 0.21 LB_0.50-2.0 0.64 1.02 2.04 0.23 0.23 LB_0.75-1.2 0.79 0.61 0.82 0.18 0.06 LB_0.75-1.4 0.80 0.71 0.95 0.20 0.07 LB_0.75-1.65 0.83 0.84 1.12 0.21 0.07 LB_0.75-2.0 0.77 1.02 1.36 0.28 0.09 LB_0.75-2.5 0.76 1.27 1.70 0.32 0.11 Table 8-5. Vena-contracta width ratios (Kv) (after Fakhri 2020).

Revised Contraction Scour Analysis: Appraisal, Results, and Applications 8-25 Figure 8-26. Vena-contracta and effective width adjustment factor, Kv. Figure 8-26 presents a best-fit regression line for the vena-contracta data. This additional contraction was applied as a linear width adjustment factor to help account for the observed contraction. This application was evaluated to determine whether it explained the moderate underprediction for the HEC-18 scour prediction equations and if it improved contraction scour predictions. The quantitative effect on the scour predictions is presented in Section 8.5. This contraction width adjustment factor, Kv, was applied to the existing scour equations to test whether it improved the moderate post-scour depth underprediction by current HEC-18 and NCHRP Project 24-20 scour prediction equations (Figures 8-23 and 8-24). Based on the available Kv testing and regression analysis performed (see Fakhri 2020), the following Kv estimation is obtained: −      < = ≤ −      < = −           ≤ −      = − For q q 1 Fr 0.02, K 1 For 0.02 q q 1 Fr 0.3, K 0.5 q q 1 Fr For 0.3 q q 1 Fr , K 0.6 2 1 1 v 2 1 1 v 2 1 1 0.18 2 1 1 v where q1 = Upstream unit discharge, ft2/s q2 = Unit discharge in the constructed opening, ft2/s Fr1 = Upstream Froude number, where Fr V gy 1 1 = V1 = Upstream flow velocity (ft/s) y1 = Upstream flow depth, ft g = Acceleration of gravity (32.2 ft/s2)

8-26 Revised Clear-Water and Live-Bed Contraction Scour Analysis This effective width adjustment factor, Kv, can be incorporated into the HEC-18 and NCHRP Project 24-20 post-contraction scour flow depth equations as follows: HEC-18 clear-water post-contraction scour flow depth equation with vena-contracta modification. y K Q D K W (8.7)2 u 2 m 2 3 v 2 3 7 ( ) =     HEC-18 live-bed post-contraction scour flow depth equation with vena-contracta modification. y y Q Q W K W (8.8)2 1 2 1 6 7 1 v 2 k1 =         NCHRP Project 24-20 clear-water post-contraction scour flow depth equation with vena- contracta modification. y q K K d (8.9)2 2 v u 50 1 3 6 7=     NCHRP Project 24-20 live-bed post-contraction scour flow depth equation with vena-contracta modification. y y q K q (8.10)2 1 2 v 1 6 7=     where Kv = Vena-contracta width adjustment factor And all other variables are as defined in Sections 8.3.3 and 8.3.4 Table 8-3 (see Section 8.3.3) contains flow depth estimates using these modified contraction scour equations. Figure 8-27 presents predicted post-scour flow depths for the HEC-18 equations incorporating Kv, and Figure 8-28 presents predicted post-scour flow depths for the NCHRP Project 24-20 equations incorporating Kv. As shown in Figures 8-27 and 8-28, the adjustment increases post-scour flow depths by (Kv)–6/7 for both the HEC-18 and NCHRP Project 24-20 clear-water scour prediction equations and the NCHRP Project 24-20 live-bed prediction. The adjustment increases the HEC-18 live-bed prediction by (Kv)–K1. Application of Kv to a live-bed illustrative example is presented in Section 8.4. The quantitative effects of the adjustment factor on the scour predictions are presented in Section 8.5. The vena-contracta adjustment factor, Kv, is dependent on multiple factors, including end contraction shape, degree of constriction, and approach flow conditions. Consequently, the measured values of Kv and the regression equation based on approach-section hydraulic conditions, presented in Figure 8-26 and discussed in this section, should only be applied for bridges in the width/depth ratio range evaluated in this study, W/y < 8. However, this range corresponds well to single-span bridges characterized in the National Bridge Inventory (NBI) as “hydraulically narrow (W/y < 7.6)” by FHWA (FHWA 2020). Approximately one-third of all bridges tabulated in the NBI are less than 40 ft in length and have single-span configurations. Figure 8-29 presents NBI bridge lengths based on the NBI

Revised Contraction Scour Analysis: Appraisal, Results, and Applications 8-27 database. Consequently, the width adjustment factor, if adopted, would have significant direct application for the practitioner. Conversely, this vena-contracta effect is not observed in field conditions for high width- to-depth ratio flows (i.e., wide and shallow cross sections). Consequently, additional study is needed to generalize this factor and to fully integrate this insight into future revisions of contraction scour technology (see Section 9.3). Figure 8-27. Predicted post-scour equilibrium flow depths for the HEC-18 equations, incorporating observed values of Kv. Observed Post-Scour Flow Depth Y2 (ft) Pr ed ic te d Po st -S co ur F lo w D ep th N CH RP P ro je ct 2 4- 20 + K v u sin g Ap pr oa ch V ar ia bl es Y 2 a ( ft) Figure 8-28. Predicted post-scour equilibrium flow depths for the NCHRP Project 24-20 equations incorporating observed values of Kv.

8-28 Revised Clear-Water and Live-Bed Contraction Scour Analysis In the interim, for bridges that do not meet these criteria, the application of the existing best-practice modeling methods (see, for example, Robinson et al. 2019) and the NCHRP Project 24-20 contraction scour equations are recommended. 8.3.6 Additional Considerations for Scour Depth Prediction This study also suggests that the exit flow depth [or a water surface elevation projected from the downstream (exit) cross section flow depth for the unvegetated region conveying sediment] is a more statistically reliable scour datum for calculating scour depths from the post-scour flow depth predicted by the scour prediction equations presented in HEC-18 (see Section 8.5). Current hydraulic modeling practices provide guidance for locating three standard cross sections at a bridge (Brunner 2016). These include one cross section upstream where flow is fully expanded, one cross section where flow is fully contracted at the bridge location, and one cross section downstream where flow is fully expanded again. The cross sections are a necessary part of 1D hydraulic modeling and a calculated outcome when 2D or 3D modeling is applied. Robinson et al. (2019) present best-practice methods for locating the approach, contracted, and exit sections for 2D models. Figure 8-30 provides an illustrative example for 2D modeling and Section 8.4 presents an example application. Current HEC-18 contraction scour evaluation methods utilize the approach and contracted cross sections as a source of variables. However, the water surface elevations and flow depths within the approach and contracted sections are not independent of scour processes, changing as scour occurs. Current practices use the pre-scour flow depth within the contracted section (y0) as a reference point. The calculated post-scour flow depth is reduced by y0 to find the contraction scour depth (ys ). However, because the pre-scour flow depth in the contraction (y0) is not independent from the scour itself, a source of error is created by using it as a reference datum for calculating scour depth. Under ordinary field conditions, the water surface elevation in the bridge opening is controlled by downstream hydraulics. Regardless of conditions at the approach section or the magnitude Figure 8-29. Bridge length histogram from NBI 2020 data (FHWA 2020).

Revised Contraction Scour Analysis: Appraisal, Results, and Applications 8-29 of scour, the water surface within the bridge opening is controlled by the water surface elevation at the fully expanded downstream section and the head losses associated with the region of flow expansion. As scour progresses, the shear stresses in the contraction and the resulting changes in water surface elevation tend to reduce the water surface elevation toward a “no-embankment” or “natural conditions” condition. Thus, the flow depth at the exit section provides a conservative estimate of the corresponding flow depth datum. This flow depth is largely independent from scour processes and could provide a more reliable reference datum for plotting scour depth within the bridge opening. Instead of using the pre-scour flow depth within the contraction (y0), the practitioner could use the flow depth at the fully expanded downstream cross section (y3) as the reference datum. Such that y y y (8.11)s 2 3= − where ys = Depth of scour from the original bed elevation y2 = Equilibrium flow depth calculated for the post-scour condition at the contracted cross section y3 = Pre-scour flow depth at the downstream fully expanded cross section The laboratory test plan as summarized in Chapter  3 used a normal-depth downstream boundary to establish a downstream control, which was applied as a reasonable proxy for scour estimation purposes. This study did not include an expansion reach. Consequently, additional research incorporating downstream flow expansion is needed to fully evaluate the degree of conservatism and the range of uncertainty associated with this y3 substitution in scour evalua- tion. Section 8.5 presents the reliability effects of modifying existing practice to use downstream hydraulics to establish the scour depth datum. Figure 8-30. Approach, contracted, and exit section example based on 2D hydraulic modeling.

8-30 Revised Clear-Water and Live-Bed Contraction Scour Analysis 8.4 Application Example 8.4.1 Introduction In this section, the existing and revised live-bed contraction scour equations are applied to a field case study. The bridge selected for this case study falls into the FHWA-defined “hydraulically narrow” category for which the revised contraction scour equations are considered directly applicable. First, the current HEC-18 live-bed contraction scour equations and the recommended modifications with the vena-contracta width adjustment, Kv, method are applied. Then, the NCHRP Project 24-20 equations [from Ettema et al. (2010) and HEC-18] and the modified NCHRP Project 24-20 equations (with the Kv adjustment factors) are also illustrated. Finally, the quantitative results of this application are compared and discussed. 8.4.2 Background U.S. Highway 287 crosses Spring Creek in Fort Collins, Colorado, with a 30-ft single-span bridge. The opening features vertical concrete abutments with wing walls. The creek also shares the bridge opening with a 10-ft-wide pedestrian trail, leaving just 20 ft for the creek’s main channel and alluvial bottom. Figure 8-31 shows the upstream face of the bridge. A 2D hydraulic model has been provided by CDOT, which performed a detailed analysis on this highway crossing. Note that flow inputs and other hydraulic parameters have been modified for this illustrative example. Example results are not representative of actual hydraulic conditions at this bridge. Figure 8-32 shows the computational mesh as well as the terrain dataset of the 2D model. An approach section was selected upstream of the bridge, where flow was fully expanded and provided a reasonable representation of upstream hydraulic conditions. The main channel portion (the unvegetated width where flow is intense enough to transport sediment) of the approach section was identified. For the contracted section inside the bridge, the main channel alluvial portion was identified. Finally, an exit section was selected. These cross sections are illustrated in Figure 8-33. The necessary hydraulic variables were extracted from the hydraulic model and supplemented with field data, as summarized in Table 8-6. Figure 8-31. Photograph looking downstream at U.S. Highway 287 upstream bridge face.

Revised Contraction Scour Analysis: Appraisal, Results, and Applications 8-31 Figure 8-32. Numerical mesh and terrain dataset for the U.S. Highway 287 bridge crossing. Flow is from left to right. Image courtesy of CDOT. Figure 8-33. Approach, contracted, and exit cross sections for the U.S. Highway 287 bridge over Spring Creek.

8-32 Revised Clear-Water and Live-Bed Contraction Scour Analysis 8.4.3 HEC-18 Method The recommended existing method for calculating contraction scour is described in Chapter 6 of the HEC-18. The first step is to determine if the bridge is being supplied with a sediment from upstream. This is done by evaluating HEC-18 Equation 6.1, the critical velocity equation, and comparing it with the approach-section hydraulics (see Section 8.3.3). V K y d V 11.17 8.7 ft 0.25mm 304.8 mm ft 1.5 ft s c u 1 6 50 1 3 c 1 6 1 3( ) = =       = The average velocity in the approach section of the main channel was found to be 5.81 ft/s, which is in excess of the critical velocity of 1.5 ft/s. Therefore, live-bed equations were selected. The value of the k1 variable is required before beginning the main calculation. This variable is based on the mode of bed material transport, as described in Section 6.3 of HEC-18. This mode of bed material transport is based on a ratio of the shear velocity (V*) to the sediment fall velocity (ω). The fall velocity of 0.25-mm sand can be referenced from Figure 6.8 in HEC-18 as, 0.033 m/s or 0.11 ft/s. The shear velocity can be calculated as V* gy S V* 32.2 ft s 8.7 ft 0.0077 ft ft 1.47 ft s V* 1.47 0.11 13.4 1 1 1 2 2 1 2 ( ) ( )= =     = ω = = Therefore, the ratio of shear velocity to fall velocity is 13.4 and corresponds to a k1 value of 0.69, as given in Section 6.3 of HEC-18. Knowing this value allows the calculation of live-bed contraction scour using Equation 6.2, as given in HEC-18 (see Section 8.3.3). =         y y Q Q W W 2 1 2 1 6 7 1 2 k1 Variable Description Variable Name Variable Value Flow in the upstream channel transporting sediment Q1 602 cfs Width of the upstream main channel that is transporting bed material W1 11.9 ft Average depth in the upstream main channel y1 8.7 ft Slope of energy grade line S1 0.0077 Flow in the contracted channel Q2 1819.3 cfs Width of main channel in contracted section W2 20.0 ft Existing depth in the contracted section before scour y0 9.8 ft Existing depth in the exit section before scour y3 5.3 ft Median diameter of bed material d50 0.25 mm Table 8-6. Hydraulic variables for the U.S. Highway 287 bridge.

Revised Contraction Scour Analysis: Appraisal, Results, and Applications 8-33 y y Q Q W W y 8.7 ft 1819.3 ft s 602.0 ft s 11.9 ft 20.0 ft 15.69 ft 2 1 2 1 6 7 1 2 k 2 3 3 6 7 0.69 1 ( ) =         =               = Equation 6.3 from HEC-18 allows the conversion from the post-scour flow depth (y2) to the scour depth (ys) by using the pre-scour flow depth in the contracted section (y0). y y y y 15.7 ft 9.8 ft 5.9 ft s 2 0 s = − = − = By using the methods described in Chapter 6 of HEC-18, the expected contraction scour is predicted to lower the bed elevation by 5.9 ft. 8.4.4 Modified HEC-18 Method The findings of this research suggest that the prediction of contraction scour may be improved by the following: 1. Accounting for the further reduction of effective flow width produced by the vena-contracta of the bridge opening (see Section 8.3). 2. Using a representative downstream hydraulic datum to calculate the change in bed elevation (see Section 8.3). The first step in this procedure is the application of the vena-contracta coefficient (Kv). This reduction in flow width can be accounted for by using the following equation (see Section 8.3.5). K 0.5 q q 1 Frv 2 1 1 0.18 = −        − Where q1 and q2 represent the unit discharge, or volumetric discharge per unit of width, at the approach and contracted sections, respectively. Fr1 is the Froude number of flow at the approach section. These values can be calculated as follows. q Q W 602 ft s 11.9 ft 50.59 ft s q Q W 1819.3 ft s 20.0 ft 90.97 ft s Fr V gy 5.81 ft s 32.2 ft s 8.7 ft 0.35 1 1 1 3 2 2 2 2 3 2 1 1 1 2 ( ) = = = = = = = =           =

8-34 Revised Clear-Water and Live-Bed Contraction Scour Analysis With this result, the vena-contracta coefficient (Kv) can be calculated as follows (see Section 8.3.5). K 0.5 90.97 ft s 50.59 ft s 1 0.35 0.63v 2 2 0.18 = −                     = − Once Kv has been determined, the practitioner can calculate the contraction scour using a modified HEC-18 live-bed equation. All other variables match those from the prior example of the unmodified HEC-18 contraction scour method. y y Q Q W K W y y Q Q W K W y 8.7 ft 1819.3 ft s 602.0 ft s 11.9 ft 0.63 20.0 ft 21.58 ft 2 1 2 1 6 7 1 v 2 k 2 1 2 1 6 7 1 v 2 k 2 3 3 6 7 0.69 1 1 ( ) ( ) =        =        =               = This method produces a post-scour flow depth of 21.6 ft. Equation 6.3 from HEC-18 allows the conversion from the post-scour flow depth (y2) to the scour depth (ys) by using the pre-scour flow depth in the contracted section (y0). However, as discussed in Section 8.3.6, as an alternative to using the pre-scour flow depth within the contracted section (y0), this application applies the hydraulic depth at the downstream exit section (y3) as the hydraulic datum for scour. An exit section was identified as shown in Figure 8-33 with a hydraulic depth of 5.3 ft. = − = − = y y y y 21.6 ft 5.3 ft 16.3 ft s 2 3 s By using the modified HEC-18 equation to account for the vena-contracta and adjusting the scour datum, the expected contraction scour is predicted to lower the bed elevation by 16.3 ft. 8.4.5 NCHRP Project 24-20 Method The NCHRP Project 24-20 report provides a simplified method for calculating contraction scour (see Chapter 8 of the HEC-18). This simplified live-bed equation is as follows (see Section 8.3.4). y y q q 2 1 2 1 6 7=     Where q1 and q2 represent the unit discharge, or volumetric discharge per unit of width, at the approach and contracted sections, respectively, and y2 is the post-scour equilibrium flow depth in the contraction.

Revised Contraction Scour Analysis: Appraisal, Results, and Applications 8-35 q Q W 602 ft s 11.9 ft 50.59 ft s q Q W 1819.3 ft s 20.0 ft 90.97 ft s y y q q 8.7 ft 90.97 ft s 50.59 ft s 14.38 ft 1 1 1 3 2 2 2 2 3 2 2 1 2 1 6 7 2 2 6 7 = = = = = = =     =           = This method produces a post-scour flow depth of 14.4 ft. Equation 6.3 from HEC-18 allows the conversion from the post-scour flow depth (y2) to the scour depth (ys) by using the pre-scour flow depth in the contracted section (y0). y y y y 14.4 ft 9.8 ft 4.58 ft s 2 0 s = − = − = By using the methods developed for NCHRP Project 24-20, the expected contraction scour is predicted to lower the bed elevation by 4.6 ft. 8.4.6 Modified NCHRP Project 24-20 Method The NCHRP Project 24-20 method can also be modified to account for the vena-contracta and to adjust the scour datum as suggested by the findings of this study. The modified version of the NCHRP Project 24-20 live-bed equation is presented as follows (see Section 8.3.5). y y q K q 2 1 2 v 1 6 7=     Where Kv is defined as K 0.5 q q 1 Frv 2 1 1 0.18 = −        − This can be applied as follows: Fr V gy 5.81 ft s 32.2 ft s 8.7 ft 0.35 K 0.5 q q 1 Fr 0.5 90.97 ft s 50.59 ft s 1 0.35 0.63 1 1 1 2 v 2 1 1 0.18 2 2 0.18 ( ) = =           = = −        = −                     = − −

8-36 Revised Clear-Water and Live-Bed Contraction Scour Analysis ( ) =     =           =y y q K q 8.7 ft 90.97 ft s 0.63 50.59 ft s 21.38 ft2 1 2 v 1 6 7 2 2 6 7 This method produces a post-scour flow depth of 21.4 ft. Equation 6.3 from HEC-18 allows the conversion from the post-scour flow depth (y2) to the scour depth (ys) by using the pre-scour flow depth in the contracted section (y0). However, as discussed in Section 8.3.6, as an alternative to using the pre-scour flow depth within the contracted section (y0), this application applies the hydraulic depth at the downstream exit section (y3). An exit section was identified, as shown in Figure 8-33, with a hydraulic depth of 5.3 ft. y y y y 21.4 ft 5.3 ft 16.1 ft s 2 3 s = − = − = By using the modified NCHRP Project 24-20 equation to account for the vena-contracta, the expected contraction scour is predicted to lower the bed elevation by 16.1 ft. 8.4.7 Discussion Both the NCHRP Project 24-20 equations and the HEC-18 equations, when modified to account for the Kv vena-contracta factor and adjusted to a downstream scour datum, predict substantially more contraction scour. Section 8.5 discusses the improved statistical reliability of these results, indicating that these scour depth results are moderately conservative (statistical reliability factor of approximately 0.8 and 1.3 for the NCHRP Project 24-20 method and the modified HEC-18 method, respectively). However, the HEC-18 modified method also has substantially more vari- ability (i.e., is a more variable predictor) versus the modified NCHRP Project 24-20 method. In addition, note that prior study under NCHRP Project 24-34 indicated that, in the LRFD context, resistance reduction factors, such as those applied to estimated contraction scour depths, should be calculated to produce total scour statistical reliability factors between two and four (Lagasse et al. 2013). In other words, the scour factor should be selected to overpredict total scour between approximately 90% and 99.99% of the time. The limited contraction scour data available to the NCHRP Project 24-34 team indicated that the HEC-18 contraction scour prediction technology required substantial scour factors (multipliers of scour depth) to achieve reliability factors in the desirable range. For example, to achieve a β of 3.0 (a typical target reliability index for the LRFD approach), the HEC-18 contraction scour depth for a bridge similar to the Spring Creek example would need to be doubled. The results of this study similarly indicate that, if a design equation (versus a predictive one) is desired, significantly more contrac- tion scour depth should be predicted for design [i.e., the base (unmodified) HEC-18 equations are non-conservative for design or analysis purposes]. Additional consideration would be required if the existing structure has a substantial residual scour hole because the proposed downstream scour datum will not take the additional depth into account directly. 8.5 Reliability of Contraction Scour Equations 8.5.1 Background Model (equation) uncertainty depends on how well a given scour equation predicts observed scour. For this study, model uncertainty is determined from the statistical properties of the

Revised Contraction Scour Analysis: Appraisal, Results, and Applications 8-37 ratio of observed post-scour flow depth to predicted post-scour flow depth for a given scour equation. This definition is dependent on a common zero value. Consequently, ys, scour depth, which depends on a variable zero determined by y0, cannot be accurately evaluated using this ratio if y0 is decoupled from the predictor (as in this case); instead, post-scour flow depth, y2, is evaluated. The mean of these ratios X– is known as the equation bias (λ). The standard deviation of the ratios divided by the bias is the CV. The CV value is one measure of the predicted variability of the sample about X–. A lower CV indicates a more accurate prediction. From the values of λ and CV, the reliability index β can be calculated for the scour prediction equation being investigated. β represents the number of standard deviations from the mean that the predicted value will be greater than the observed value. A positive value of β indicates that the equation is conservative (i.e., it overpredicts by β times the standard deviation). A perfect predictor, one which exactly predicts the expected value of scour for any given set of input variables, has β = 0. Assuming that the ratio of observed to predicted values follows a normal distribution, the equation for the reliability index β is as follows: 1 CV (8.12)( ) ( ) β= − λ λ ∗ If the ratio of observed to predicted values follows a lognormal distribution, then ln 1 CV 1 ln CV 1 (8.13) 2 2( ) β= λ +    + Contraction scour is widely accepted as a sediment transport problem. However, finding reliable laboratory and field contraction scour data has been an ongoing problem for many previous research teams, as described in Chapter 2 of this report. For example, none of the previously published datasets included a measurement or estimate of yo, the depth of flow in the contracted section before scour begins. Considering that the current edition of HEC-18 recommends that ys be estimated as y2 – yo, this is a serious shortcoming of many previous datasets. The datasets examined in this section considered only the 19 laboratory tests performed as part of this research because each test has a unique, calibrated HEC-RAS model associated with it. No data points from previous laboratory or field studies were added. Ultimate live-bed contraction scour is reached when the rate of sediment transport in the bridge opening matches the supply of sediment from the upstream channel. Ultimate clear-water contraction scour is reached when the flow can no longer erode the bed. Most bridge-waterway openings are short contractions. However, the HEC-18 contraction scour equations were derived using a long-contraction assumption, thus introducing additional uncertainty. The incorpora- tion of the vena-contracta effect, described in Sections 8.2 and 8.3, is an important first step in addressing this issue. 8.5.2 Reliability Analysis In this section, there are four predictive equations used for reliability analyses. The observed values and the predicted values correspond to the vicinity of the vena-contracta. The bias and CV for each of the four scour equations were evaluated based on the laboratory data from

8-38 Revised Clear-Water and Live-Bed Contraction Scour Analysis the 19 flume experiments conducted by CSU as part of this study. The reliability indices (β) for assumed normal and lognormal distributions were then determined for the following conditions: 1. Two contraction scour prediction methods presented in HEC-18, using input variables predicted at the upstream limit of contraction from a calibrated HEC-RAS model with pre-scour bed geometry a. Contraction scour methods based on the Laursen long-contraction scour prediction methods (see Section 8.3.3) b. Contraction scour methods developed as part of NCHRP Project 24-20 and applied as a base for abutment scour evaluation (see Section 8.3.4) 2. Contraction scour methods as mentioned and modified to account for the additional contrac- tion associated with the observed vena-contracta as presented in Section 8.3.5 3. HEC-18 contraction scour methods using input variables calculated using theoretical normal-depth variables a. Contraction scour methods based on the Laursen long-contraction scour prediction methods b. Contraction scour methods modified to account for the vena-contracta adjustment, Kv For each flume test, the velocity in the approach section V1 was compared with the critical velocity, Vc, to determine if the test was a clear-water or live-bed test. For the approach-section predictions, V1, corresponding to pre-scour conditions, was taken from the calibrated HEC-RAS values in the approach section upstream of the contraction. For the theoretical normal-depth predictions, V1 was calculated using the theoretical normal-depth values developed for testing. Vc for the 0.26-mm sand was estimated using the HEC-18 equation =V K y dc u 11 6 501 3 where Ku = 11.17 when y1 and d50 are in ft, and Vc is in ft/s. Using these criteria, the predicted approach-section hydraulics indicated that 15 of the 19 tests conducted by CSU would be classified as clear-water tests; the remaining 4 tests corresponded to live-bed conditions in the approach section. The appropriate equation for estimating y2 in the contracted reach was then applied to each test, using both the standard HEC-18 equations and equations with the vena-contracta correction factor, Kv. Table 8-7 contains, for each of the 19 CSU tests, the summary information used to perform the reliability analyses for approach-section hydraulics. Tables 8-8 and 8-9 contain the results of the reliability analyses for the approach-section cases described previously. Note that the Severe contraction data (CW_0.25-XX) were not included when evaluating the statistical reliability of the existing and proposed revised equations. As presented in Section 8.2 and discussed in Section 8.3, the Severe contraction scour flow conditions included substantial interaction between the entrance condition (corner) flow separation turbulent structures and the vena-contracta across the entire channel. This intense turbulence tends to increase total scour due to local scour (abutment scour) effects and is distinct from the contraction scour effects considered for this study. As a result, tests with observed merged flow separation turbulent structures were not included in the statistical evaluation of the long-contraction equations. 8.5.3 Discussion of Results Calculated bias values greater than one and negative reliability factors for the published methods indicate that the current HEC-18 equations consistently underpredict the observed post-scour flow depths. This is consistent with the qualitative discussion in Section 8.3.

Revised Contraction Scour Analysis: Appraisal, Results, and Applications 8-39 CSU Test No. Approach-Section Hydraulics (Calibrated HEC-RAS) Post-Scour Equilibrium Flow Depth V1, ft/s Vc, ft/s V1/Vc Clear-Water or Live-Bed Published Methods Kv Applied Y2 obs Y2 H-18* Y2 obs Y2 24-20** Y2 obs Y2 H-18 Y2 obs Y2 24-20 CW_0.25-0.55 0.35 1.02 0.342 CW 0.97 1.05 1.33 1.44 CW_0.25-0.65 0.49 1.03 0.476 CW 1.33 1.45 2.04 2.21 CW_0.25-0.75 0.41 1.05 0.391 CW 1.26 1.37 1.94 2.1 CW_0.25-0.80 0.44 1.05 0.42 CW 1.33 1.45 2.01 2.18 CW_0.50-0.55 0.42 0.99 0.424 CW 0.54 0.58 0.66 0.72 CW_0.50-0.65 0.45 1.01 0.447 CW 0.62 0.67 0.82 0.89 CW_0.50-0.75 0.52 1.01 0.516 CW 0.7 0.76 0.95 1.03 CW_0.75-0.75 0.57 0.99 0.575 CW 0.5 0.54 0.56 0.6 CW_0.75-0.85 0.62 1.00 0.62 CW 0.55 0.6 0.62 0.67 CW_0.75-0.95 0.66 1.01 0.654 CW 0.61 0.66 0.72 0.78 LB_0.50-1.2 0.74 1.03 0.722 CW 1.04 1.13 1.45 1.57 LB_0.50-1.4 0.88 1.02 0.861 CW 1.19 1.29 1.69 1.84 LB_0.50-1.65 0.89 1.05 0.848 CW 1.37 1.48 2.03 2.2 LB_0.50-2.0 1.05 1.05 0.996 CW 1.61 1.75 2.37 2.57 LB_0.75-1.2 0.89 1.00 0.894 CW 0.74 0.8 0.9 0.98 LB_0.75-1.4 1.01 1.00 1.01 LB 0.85 0.9 0.98 1.09 LB_0.75-1.65 1.11 1.01 1.097 LB 0.91 0.97 1.03 1.14 LB_0.75-2.0 1.29 1.02 1.267 LB 0.95 1.01 1.12 1.26 LB_0.75-2.5 1.41 1.04 1.355 LB 1.08 1.15 1.29 1.46 *H-18: HEC-18. **24-20: NCHRP Project 24-20. Table 8-7. Summary of test parameters used for reliability analyses. Statistic Method Published methods NCHRP Project 24-47 Kv applied HEC-18 NCHRP Project 24-20 HEC-18 NCHRP Project 24-20 N observations 15 15 15 15 n underpredicted 13 10 6 5 Underpredicted fraction 0.87 0.67 0.40 0.33 mean (bias) 1.22 1.13 0.980 0.896 standard deviation 0.209 0.190 0.223 0.209 CV 0.172 0.168 0.228 0.233 Beta (normal) -1.05 -0.69 0.09 0.50 Beta (Lognormal) -1.08 -0.66 0.20 0.59 Table 8-8. Reliability: post-scour flow depth (y2) predicted versus observed Moderate and Mild contraction data. Calculated using predicted approach-section hydraulics.

8-40 Revised Clear-Water and Live-Bed Contraction Scour Analysis HEC-18 calculations using a theoretical normal depth were found to have a lower CV and substantially underpredicted post-scour depth, even when Kv was applied. This result combined with the difficulty and subjectivity of selecting a representative theoretical normal depth (or calculating it from an assumed friction slope using the Manning’s n equation) supports the conclusion that this approach is not recommended for use by the practitioner. Using approach-section hydraulics and applying the vena-contracta correction coefficient, Kv, developed during this research project substantially reduces the number of underpredictions compared with the standard HEC-18 and the NCHRP Project 24-20 equations. When the vena- contracta correction factor, Kv, is applied, bias is less than one, and the reliability factor is significantly increased. The base CV calculated for the published contraction scour methods indicates that the NCHRP Project 24-20 predictions have a reduced variability compared with the HEC-18 equations. When Kv is applied, the NCHRP Project 24-20 methods have an improved statistical reliability factor relative to the HEC-18 method. Overall, the results of this study indicate that the NCHRP Project 24-20 approach predicts post-scour flow depth more reliably than the HEC-18 methods. The NCHRP Project 24-20 methods are also simpler for the practitioner to apply. Note that application of Kv increases CV relative to the published equations. This may indicate that a direct linear application of Kv, as evaluated here, does not fully capture the sediment transport effects of the additional contraction associated with the vena-contracta. Qualitative review of a sample CFD hydraulic analysis indicates that there is significant vari- ation in contraction effects between the surface (LSPIV) observations and those closer to the bed predicted by the CFD model (see, for example, Figure 7-15). Further study incorporating calibrated CFD modeling is recommended to refine the relationship of Kv to contraction scour processes and to generalize its application. 8.5.4 Post-Scour Flow Depth and Scour Depth As discussed in Section 8.3, the scour estimation equations presented in HEC-18 decouple the prediction of the post-scour depth (y2) from the change in bed elevation (ys = y2 − y0). HEC-18 methods recommend using a pre-scour estimate of flow depth, y0. As noted in Section 8.3, the results of this study indicate that using the pre-scour flow depth results in a substantial increase in scour variability and uncertainty relative to the scour flow depth prediction equations themselves. The results of this study indicate that to accurately convert the post-scour depth to Statistic Method HEC-18 HEC-18 Kv applied N observations 15 15 n underpredicted 15 14 Underpredicted fraction 100% 93% mean (bias) 1.49 1.23 standard deviation 0.151 0.130 CV 0.102 0.105 Beta (normal) -3.23 -1.76 Beta (Lognormal) -3.87 -1.91 Table 8-9. Reliability: post-scour flow depth (y2) predicted versus observed Moderate and Mild contraction data. Calculated using theoretical normal-depth hydraulics.

Revised Contraction Scour Analysis: Appraisal, Results, and Applications 8-41 post-scour change in ground elevation (needed for design or stability analysis), an improved estimate of the post-scour water surface elevation is needed. One approach that is available to the practitioner using rigid-bed model technology would be as follows: 1. Evaluate the scour depth using appropriate modeling and scour prediction technology as recommended previously. 2. Then, adjust the bed elevations and the modeling based on pre-scour water surface eleva- tions to reflect a reasonable configuration of the contraction scour hole based on that scour prediction. 3. Then, run a post-scour model evaluation to determine a revised water surface elevation at the point of maximum contraction. 4. Iterate as necessary until the water surface elevation does not change significantly between post-scour model simulations. An example of such a model is presented in Figure 8-34. This approach would likely require rigid-bed model iteration and the development of best-practice guidance for adjusting the bed for scour. Sediment transport analysis with well- calibrated mobile-bed CFD hydraulic models would render this iteration unnecessary, but this is not reasonably available to the practitioner as of this writing. A more practical approach to improve scour depth estimation is to use the downstream (exit) cross section flow depth for the unvegetated region conveying sediment downstream, as described in Section 8.3. Table 8-10 presents reliability analysis of current scour depth prediction methods (using ys = y2 – y0) compared with the reliability of scour depth prediction using the downstream control (ys = y2 − y3) flow depth as the scour datum. Note that application of downstream hydraulic depth, y3, as the scour depth datum signifi- cantly reduces the standard deviation and CV for the prediction as compared with using the pre-scour contracted flow depth (y0). In combination with the application of Kv, this results WSEL: water surface elevation. Figure 8-34. Example pre- and post-scour bed and water surface from a HEC-RAS model.

8-42 Revised Clear-Water and Live-Bed Contraction Scour Analysis in a positive statistical reliability factor for a lognormally distributed parameter for both the HEC-18 and NCHRP Project 24-20 methods. The NCHRP Project 24-20 method with Kv applied and using downstream (y3) hydraulic depth as the scour datum produces an improved CV and positive reliability factor. Section 8.4 includes an illustrative example incorporating Kv and evaluating scour depth using y3 for both HEC-18 and NCHRP Project 24-20 scour predic- tion methods. The data indicate that the NCHRP Project 24-20 predictors produce the least variable and most reliable scour depth estimators of those evaluated here. 8.6 Implementation of Research Results 8.6.1 Background The product of this research is revised and enhanced live-bed and clear-water contraction scour equations suitable for use in risk-based bridge design for a range of hydraulic and geometric conditions. As noted in the request for proposals (RFP) (special Note B), NCHRP projects are intended to produce results that will be applied in practice, and proposals and the project final report must contain implementation plans for moving the results of the research into practice. “The Final Report must include an Implementation Plan that describes activities to promote application of the product of this research. It is expected that the implementation plan will evolve during the project; however, proposals must describe, as a minimum, the following: (a) the “product” expected from the research, (b) the audience or “market” for this product, (c) a realistic assessment of impediments to successful implementation, (d) the institutions and individuals who might take leadership in applying the research product, (e) the activities necessary for successful implementation, and (f) the criteria for judging the progress and consequences of implementation.” 8.6.2 The Product This research provides suggestions for revising and enhancing live-bed and clear-water contraction scour equations suitable for use in risk-based bridge design for evaluating existing bridges and designing new bridges. Statistic Method HEC-18 Kv applied NCHRP Project 24-20 Kv applied ys = y2 − y0 ys = y2− y3 ys = y2− y0 ys = y2− y3 N observations 15 15 15 15 n underpredicted 8 4 5 3 Underpredicted fraction 0.53 0.27 0.33 0.20 mean (bias) 4.26 0.44 0.31 0.72 standard deviation 12.34 1.81 1.93 0.65 CV 2.90 4.11 6.20 0.91 Beta (normal) -0.062 0.705 1.147 0.597 Beta (Lognormal) -0.220 1.333 1.567 0.813 Table 8-10. Reliability: scour depth (ys) predicted versus observed, Moderate and Mild Contraction data, calculated using predicted approach-section hydraulics and downstream scour datum.

Revised Contraction Scour Analysis: Appraisal, Results, and Applications 8-43 8.6.3 The Market The market or audience for the results of this research includes bridge engineers, hydraulic engineers, and bridge maintenance and inspection personnel in state, federal, and local agen- cies with a bridge-related responsibility for design, installation, evaluation, and maintenance of bridge foundations considering the impacts of scour, including contraction scour and stream instability at bridges and other highway facilities. These would include the following: State Highway Agencies FHWA City/County Bridge Engineers Railroad Bridge Engineers U.S. Army Corps of Engineers U.S. Bureau of Land Management National Park Service U.S. Forest Service Bureau of Indian Affairs Any other governmental agency with highway facilities under their jurisdiction Consultants to these agencies 8.6.4 Impediments to Implementation A serious impediment to successful implementation of results of this research will be difficulties involved in reaching a diverse audience scattered among numerous agencies and institutions; however, this can be countered by a well-planned technology transfer program. Because of the complexity and geographic scope of channel instability and scour problems, a major challenge will be to present the results in a format that can be applied by agencies with varying levels of engineering design capabilities and maintenance resources. Presenting the guidelines and methods in a format familiar to bridge owners, who are the target audience, will facilitate their use of the results of this research. Using the HEC-18 format (FHWA format), which has successfully reached a diverse audience, will help ensure successful implementation. As with the results of any research, there may be segments of the target audience that may be reluctant to adopt or rely on new approaches. Highway engineers may consider the conditions in their state or region unique. This concern can be countered by an enhanced contraction scour design procedure applicable to a range of hydraulic and geometric conditions at geomorphically diverse sites. 8.6.5 Leadership in Application FHWA. Because of its broad-based mission to provide guidance to the state highway agencies, the FHWA will likely take a leading role in disseminating the results of this research. Through the National Highway Institute (NHI) and its training courses, FHWA has the pro- gram in place to reach a diverse and decentralized target audience. TRB. TRB can also play a leading role in disseminating the results of this research to the target audience through its annual meetings and committee activities, and publications, such as the Transportation Research Record, as well as periodic international bridge conferences. AASHTO. AASHTO is the developer and sanctioning agency for standards, methods, and specifications. Thus, it will be important that the research results be formally adopted through

8-44 Revised Clear-Water and Live-Bed Contraction Scour Analysis the AASHTO process. As a collective representation of individual state DOTs, AASHTO can also suggest any needed training to be developed by FHWA or others. The AASHTO Technical Committee on Hydrology and Hydraulics could provide centralized leadership through the involvement of state DOT bridge engineers. ASCE. Professional societies such as ASCE host conferences and publish peer-reviewed journals through which the latest advances in engineering research and applications reach a wide audience, including many state, federal, and local hydraulic engineers. Regional Bridge Conferences. Regional bridge conferences, such as the Western Bridge Engineer Conference or the International Bridge Engineering Conferences, reach a wide audience of bridge engineers, manufacturers, consultants, and contractors. The groups would have an obvious interest in enhanced computational procedures for estimating contraction scour at bridge crossings and their acceptance of the results of this research will be key to implementation by bridge owners. 8.6.6 Activities for Implementation The activities necessary for successful implementation of the results of this research relate to technology transfer activities, as discussed previously, and the activities of appropriate AASHTO committees. The guidelines and suggestions that result from this research will be presented to AASHTO for consideration. “Ownership” by AASHTO will be key to successful implementation. Task 9 of this project was intended to facilitate dissemination of the results of this research. A specific deliverable for NCHRP Project 24-47 was a companion workshop in the form of a manual to provide training on the empirical basis for the enhanced live-bed and clear-water contraction scour equations and guidance examples of their application (see Section 8.7). 8.6.7 Criteria for Success The best criteria for judging the success of this implementation plan will be acceptance and use of the guidelines and suggestions that result from this research by state highway agency engineers and others with responsibility for design, maintenance, rehabilitation, or inspection of highway facilities. Progress can be gauged by peer reviews of technical presentations and publications and by the reaction of state DOT personnel during presentation of results at workshops based on the companion Training Manual and at NHI courses. The desirable consequences of this project, when implemented, will be more efficient plan- ning, design, maintenance, and inspection of highway facilities using enhanced procedures for calculating bridge contraction scour under live-bed and clear-water conditions at highway facilities. The ultimate result will be a reduction in damage to highway facilities attributable to contraction scour and reduced long-term life-cycle costs of bridge foundations. 8.6.8 Applicability of Results to Highway Practice Approximately 82% of the 600,000 bridges in the NBI are built over waterways. Many, especially those on more active streams, will experience problems with scour, bank erosion, and channel instability during their useful life. The magnitude of these problems is demonstrated by the estimated average annual flood damage repair costs of approximately $50 million for bridges on the federal aid system.

Revised Contraction Scour Analysis: Appraisal, Results, and Applications 8-45 Highway bridge failures caused by scour and stream instability account for most of the bridge failures in this country, resulting in substantial direct cost for repair and replacement. This cost does not include the additional indirect costs to highway users for fuel and operating costs resulting from temporary closure and detours and to the public for costs associated with higher tariffs, freight rates, additional labor costs, and time. The indirect costs associated with a bridge failure have been estimated to exceed the direct cost of bridge repair by a factor of five (Rhodes and Trent 1993). Rhodes and Trent document that $1.2 billion was expended for the restoration of flood-damaged highway facilities during the 1980s. Although it is difficult to be precise regarding the actual cost to repair damage to the nation’s highway system from problems related to bridge scour, and specifically contraction scour, the number is large. The revised and enhanced contraction scour equations suggested by this research will provide improved quantitative guidance to bridge owners for risk-based and data-driven bridge foundation design and maintenance, and evaluation of scour critical status for existing bridges on the national highway system. The result will be a more efficient use of highway resources and a reduction in costs associated with the impacts of bridge scour on highway facilities. 8.7 Training Manual for Implementation of Research Results The Training Manual for implementation of research results from this project was developed as a standalone document to support the project implementation plan. The Training Manual includes a companion workshop that incorporates lesson plans, photographs, and videos to provide training on the revised contraction scour methodologies. The Training Manual is avail- able as NCHRP Web-Only Document 294: Revised Clear-Water and Live-Bed Contraction Scour Analysis Training Manual. A PowerPoint presentation supporting the Training Manual is also available on the TRB website (www.trb.org) by searching for “NCHRP Research Report 971”. This deliverable meets all current Instructional Systems Design (ISD) standards established by FHWA’s NHI and after review and approval by NHI, could be incorporated into NHI course offerings as additional or optional workshops. Moreover, the contraction scour workshop pro- vides the basic instructional components for the development of a distance learning (web-based) presentation in the future. For the 390-min workshop on “Revised Contraction Scour Analysis,” lesson development adheres to the guidance promulgated by NHI and the International Association of Continuing Education and Training (IACET) for adult learning. The workshop is organized in modular fashion to support presentations in various venues, including a mini-workshop at conferences, such as the TRB Annual Meeting, ASCE, FHWA’s National Hydraulic Engineering Conferences, and others, such as the International Association for Hydro-Environment Engineering and Research (IAHR). TRB (via NCHRP) may also choose to make this material available on an expedited basis to state highway agencies and bridge owners who could use it for in-house training of DOT hydraulic engineers and their consultants. The modular organization of the workshop would support presentations of 1, 2, or 3 hours, as well as the full 6.5-hour format. The seven sessions of the workshop (presented in two parts) include the following topics and are designed to achieve the following user-oriented, performance-based learning outcomes. Part I Topics • Contraction hydraulics and scour: current practice • Evaluation of existing laboratory and field data

8-46 Revised Clear-Water and Live-Bed Contraction Scour Analysis Learning Outcomes At the end of Part I, Participants will be able to • Describe contraction hydraulics and scour, and current evaluation techniques. • Identify the quality and shortcomings of existing laboratory and field data. Part II Topics • NCHRP Project 24-47 laboratory and computational analyses • Revised contraction scour methodologies (clear-water and live-bed) • Group workshop on the application and appraisal of the revised methodologies Learning Outcomes At the end of Part II, Participants will be able to • Describe the laboratory and computational techniques used in NCHRP Project 24-47. • Discuss and evaluate the revised contraction scour methodologies developed under NCHRP Project 24-47. • In a group workshop setting, apply the NCHRP Project 24-47 methodologies for a single-span bridge under live-bed contraction scour conditions. • Compare the reliability of the revised contraction scour methodologies with current techniques.