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

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1   Findings 2.1 Review of Current Practice 2.1.1 Overview This review of current practice describes the flow and scour processes associated with con- traction scour at bridge waterways, summarizes what is known about these processes, identifies existing data sources, and determines what needs to be known for accurate estimation of contraction scour at bridge waterways. This review is structured as follows: 1. Identify flow and sediment transport characteristics through a contraction. 2. Evaluate existing data, and for comparative purposes, summarize existing equations for estimating contraction scour. 3. Identify the significant knowledge and data gaps regarding contraction scour. Prior equations for contraction scour use relatively simplified models of flow contraction and do not take into account several factors that can affect scour depth that should be considered (see discussion in Section 1.1). Lacking in the literature, in particular, are observations and analyses of initial flow choking. Several texts and papers (e.g., Wu and Molinas 2005) describe choking in contracted channels. Most existing laboratory tests on contraction scour were subject to a choking condition. A choked flow condition results from contracting the channel width beyond a limit that forces the flow to pass through critical depth in the contracted reach. A transitional flow state results in which the upstream flow is subcritical and the downstream flow becomes supercritical followed by a hydraulic jump (Wu and Molinas 2005). This condition was not considered in the analysis of many of the datasets available. 2.1.2 Hydraulic Considerations The increase in flow velocity and turbulence due to narrowing or obstruction (notably by bridge abutments and piers) of a channel cross section may cause contraction scour and a lowering of the bed in the contracted channel. The narrowing may occur due to a natural reduction in the width of the main channel for a bank-line abutment, or by redistribution of floodplain flow in the contracted section as a result of flow blockage by the bridge approach embankment for a setback abutment. Although contraction scour may vary across a bridge cross section due to nonrectangular geometry and a non-uniform velocity distribution, contraction scour is often visualized and applied as a uniform decrease in bed elevation across the bridge opening. In compound channels, floodplain contraction scour is usually treated separately from main channel contraction scour. For compound channels, one of the difficulties in applying a contrac- tion scour equation is the determination of the discharge distribution between the floodplain and the main channel in the bridge section. C H A P T E R   2 2-

2-2 Revised Clear-Water and Live-Bed Contraction Scour Analysis Both live-bed and clear-water contraction scour can occur. The former scour condition com- monly occurs in the main channel of an alluvial river, while the latter is more likely to be found on a floodplain or at a relief bridge located on the floodplain. In general, contraction scour equations have been developed analytically for an idealized long contraction. For clear-water scour, the governing principle is that the depth of scour in the contracted section corresponds to the decrease in both velocity and shear stress until the critical value for bed sediment motion is reached and the scour approaches an equilibrium state. For live-bed contraction scour, the limiting condition is continuity of sediment transport between the approach flow section and the contracted section. In the latter condition, the role of differing bedform morphology in the approach and contracted sections may be important but has generally been overlooked in prior studies. As noted in Section 1.1, numerous unresolved questions exist for both clear-water and live-bed scour. The following sections describe the hydraulics of flow through open-channel contractions. The hydraulics of contracted reaches involves unsteady open-channel flow, which can be illustrated using the specific energy diagram and a flow-resistance equation, such as Manning’s n equation. Descriptions of both pre-scour and post-scour conditions are presented. Pre-Scour Conditions Given the initial conditions of a level bed (before scour commences), the approach flow passes through a contraction and enters a narrower channel. The resulting flow profile depends on the extent to which the contraction chokes the approach flow and forces the water level to rise at the contraction entrance, creating a backwater water surface profile extending upstream of the entrance. The magnitude of choking or water-level rise varies from negligible to substan- tial, depending on the geometry of the contraction and the length of the contracted channel. Figure 2-1(a) and (b) provide a plan view of channel contraction and the water surface profile changes in flow approaching and through the contraction. Also shown in Figure 2-1 are the reaches of short-contraction versus long-contraction processes. Note that the water surface elevation at Section 1 is above that at Section 1′, even though the flow depth at Section 1 is less than that at Section 1′. This condition likely does not occur at actual bridge waterways with movable boundaries. In reality, the bed begins eroding as the profiles develop. (a) plan view Bridge Flow ShortLong Approach Channel (b) water surface and bed profiles 1 1'23 2' Figure 2-1. Water surface profiles associated with flow through an open-channel contraction before scour occurs.

Findings 2-3   The variation of flow depth and velocity through the different reaches of Figure 2-1 are accompanied by changes in specific energy. Specific energy, E, is defined as E y V 2g (2.1) 2 = + Values of E are measured vertically from the local invert or bed elevation of a channel. For subcritical flow, the usual flow condition at bridge waterways, the flow profiles are calculated from a known flow depth (e.g., normal flow depth) at the downstream end of the reach. However, contraction hydraulics are illustrated more clearly by describing flow approaching, entering, passing through, and exiting the contracted reach. Figure 2-1 shows the locations of Sections 1, 1′, 2, 2′, and 3 to be considered in Figure 2-2(a) and (b), which present specific energy diagrams to illustrate flow conditions through a contraction. When the flow enters the narrower channel with slight choking (owing to the local energy loss associated with the contraction) [Figure 2-2(a)], the normal flow depth of the approach flow, Y1, increases to Y′1, and the approach flow specific energy, E1, increases to E ′1. This increase is consumed as head loss as flow passes through the contraction. The rate of head loss due to boundary resistance increases, because flow velocity increases along the contracted section where the flow is non-uniform and the energy gradient, Sf , exceeds the bed slope So. The flow depth moves along the path 1 → 1′ → 2 → 2′, attaining specific energy E2′ as shown in Figure 2-2(a). The flow depth Y2′ cannot be sustained as flow at normal depth, as Manning’s n flow-resistance equation indicates: V 1 n Y S (2.2)22 3 f 1 2= If the contraction is long enough, flow depth eventually may attain the critical depth for q2, whereupon the flow passes through a weak hydraulic jump and then reverts to normal flow depth (Y2 as shown in Figure 2-2(b). If the contraction is not long enough, flow along the contraction is non-uniform and a hydraulic jump does not occur before the channel widens out again. Eventually, the flow transitions back into the widened channel. As it passes through the channel expansion, specific energy decreases due to the local loss of energy and then approaches normal flow depth and the associated specific energy at Section 3. If the contraction chokes the approach flow substantially, the flow backs up to attain suffi- cient specific energy to pass through the contraction [Figure 2-2(b)]. The specific energy at the entrance of the contraction, E1′, equals E1 plus the head loss for flow to pass through the contraction. The flow passes through the contraction, with flow depth following path 1 → 1′ in Figure 2-2(b), and a weak hydraulic jump forms early in the contracted channel. Consequently, specific energy decreases from E2 to E2′, as shown in Figure 2-2(b). Post-Scour Conditions Contraction scour is initiated in the contracted reach when flow velocity, shear stress, and turbulence exceed the threshold condition for erosion of the bed material (and possibly the banks). As scour occurs, the specific energy at Section 2 changes and flow hydraulics adjust. The value of specific energy at Section 2 increases as does the flow depth at Section 2 [Figure 2-3(a)]. Figure 2-3(b) indicates the path followed by flow at Section 2.

2-4 Revised Clear-Water and Live-Bed Contraction Scour Analysis (a) Negligible choking, involving a small increase in flow depth immediately upstream of the contraction. (b) Choking, involving a more substantial increase in flow depth immediately upstream of the contraction, and the formation of a weak hydraulic jump at location 2'. Figure 2-2. Specific energy diagrams showing change in flow depth as flow passes from a channel with unit discharge q1 to a narrower channel with unit discharge q2.

Findings 2-5   Because the flow is non-uniform and loses energy along the q2 path, the flow depth at 2 moves from 2 to 2′, as shown in Figure 2-3b. Consequently, specific energy decreases from E2 to E2′. The depth eventually returns to location 3, as flow returns to the widened channel downstream of the contracted reach. Flow depth through the scoured contraction may exceed the normal flow depth in the approach channel and the exit channel. It is important to note the temporal variation implied by Figures 2-2 and 2-3. As scour occurs, the flow depth in the contracted section increases, resulting in an increase in specific energy over time as the flow adjusts to a new equilibrium condition. Important Observations Two observations are especially important when considering contraction-flow hydraulics: 1. The contraction scour equations recommended in HEC-18 are essentially semi-empirical. In other words, they do not directly treat the non-uniform flow conditions associated with contraction scour. 2. The condition of non-uniform flow through a contraction typical of a bridge waterway (i.e., a short contraction at the bridge possibly followed by an extended reach of long contraction) can be a major source of error and uncertainty when comparing laboratory and field data with existing predictive relationships for contraction scour. (b) Specific energy diagram (a) Water surface and bed profiles ShortLong E3 E2 E2' E1' 11'23 2' Figure 2-3. Flow hydraulics once contraction scour has occurred (scour indicated). Locations 1 through 3 coincide with those in Figure 2-1.

2-6 Revised Clear-Water and Live-Bed Contraction Scour Analysis Variable Symbol Upstream width Contracted width Streamwise width of bridge deck Angle of the contraction transition Upstream normal flow depth Bed slope of the approach channel Median diameter of bed sediment Geometric standard deviation of bed-sediment diameter Sediment density Critical bed shear stress for entrainment Density of water Kinematic viscosity of water Gravity acceleration Time W1 W2 Lb α Y1 S1 d σg ρs τc ρ ν g t Table 2-1. Essential independent variables considered when analyzing flow and sediment transport through a contraction. (Note: More variables could be considered.) The foregoing description of contracted flow hydraulics is supported by several examples. In terms of the extant literature, Lai and Griemann (2010) use a 2D numerical model to investigate flow profiles through a contracted channel. 2.1.3 Dimensional Analysis Dimensional analysis is a convenient approach for establishing a framework for identifying the main processes associated with contraction scour, and for assessing prior investigations as documented in the literature. The extent of contraction scour depends on kinematic, dynamic, and geometric variables best considered in terms of non-dimensional parameters that characterize the general influences the variables exert. Table 2-1 provides a list of independent variables involved in contraction scour. The ensuing dimensional analysis aims at identifying the main parameters associated with two conditions of contraction scour: (1) a long contraction of uni- form width, and (2) a short contraction associated with a contracting channel. Uniform or (hydraulically) normal flow depth in a long contraction (Condition 1) is inde- pendent of the geometry of the contraction. However, flow depth along a short contraction (Condition 2) is influenced significantly by the geometry of the contraction and involves turbu- lence structures that may lead to non-uniform flow depth through the short contraction. The following assumptions support a dimensional analysis of the contraction process: • The sides of the channel subject to contraction are relatively smooth, rectangular, and resistant to erosion. • Flow through the approach and long-contraction reaches of the channel is steady and uniform (flow may not be uniform if the contraction causes flow choking). • The initial condition of the channel bed consists of uniformly sized sediment leveled to form a smooth and uniform bed slope. • There is an abrupt transition from the approach channel to the contracted channel segment. For the following analysis, the transition is set at an angle of 45o. • The channel configuration acts as a short contraction preceding a long contraction as shown in the schematic of Figure 2-4.

Findings 2-7   Long-Contraction Scour Although several “dependent” variables depend on the effects of the “independent” variables listed in Table 2-1, the variable of primary interest is scour depth in the long contraction. Scour depth, Ds, associated with normal (uniform) flow in a long contraction can be written in terms of the functional relationship: D f W , W , Y , S , L , d, , , , , g, t (2.3)s 1 1 2 1 1 b g s c( )= σ ρ τ ρ Eq. (2.3) can be restated in terms of non-dimensional parameters: D Y f W Y , W W , S , L Y , d Y , , gY S , gt Y (2.4)s 1 2 1 1 2 1 1 b 1 1 g s 1 1 c 2 1 = σ ρ ρ ρ τ     Here, Ds/Y1 is a dependent parameter whose value is influenced by the independent param- eters within the brackets. Note that Y1 is the calculated depth of normal flow in the approach channel. The terms combined as ρgY1S1 can be replaced with the shear stress, τ, exerted on the bed of the approach channel. Figure 2-4. Layout and basic variables associated with flow and sediment transport through an abrupt contraction linking an open channel of two widths.

2-8 Revised Clear-Water and Live-Bed Contraction Scour Analysis Several assumptions lead to a simplification of Eq. (2.4): • The densities of water and sediment particles are taken to be constant. • The streamwise width of bridge deck does not affect normal flow depth. • Contraction transition does not affect normal flow depth in the long contraction. • Channel slope can be held constant. • Of interest is the equilibrium value of Ds. Hereafter, Ds is taken to denote equilibrium scour depth. Eq. (2.4) then becomes D Y f W Y W W , d Y , (2.5)s 1 3 1 1 2 1 1 g c = σ τ τ     Here, the parameters are scour depth normalized with the normal depth of approach flow, relative width, contraction ratio, sediment size, shear-stress ratio (state of bed-sediment mobilization), and normalized time, respectively. Note that the normal depth of flow depth, Y2, in the long contraction is a dependent variable. It depends on the independent parameters in Eq. (2.5). Additionally, the variables regarding bedform dimensions, H and λ in Figure 2-4, depend on these independent parameters. The parameter set in Eq. (2.5) applies to both clear- water and live-bed contraction scour. The relationships recommended for clear-water and live-bed scour in HEC-18 are D Y Y Y Y f W W , d Y , (2.6)s 1 2 0 1 4 2 1 1 c = − = τ τ     − For clear-water contraction scour, HEC-18 adjusts Eq. (2.4) to Eq. (2.6) for the following conditions: W1 = Q/Y1; d1/Y1 embodied in Manning’s n; and W (in HEC-18) being W2. In Eq. (2.6), Y2-0 is the initial (pre-scour) depth of flow just entering the contracted channel (HEC-18 uses the variable y0). For live-bed contraction scour, Eq. (2.4) can be formulated as Eq. (2.7): D Y Y f W W , d Y (2.7)s 2 0 1 4 2 1 1 + =    − HEC-18 also includes the discharge ratio Q2/Q1 as an independent parameter in Eq. (2.7) where Q2 = discharge through the contracted channel and Q1 = discharge in the main channel of the approach flow. The experiments of this project (layout shown in Figure 2-4 and described in Chapter 3) and all other prior experiments on contraction scour consider a single channel that contracts (i.e., Q2/Q1 = 1). A practical difficulty with Eq. (2.6) and Eq. (2.7) occurs when a contraction chokes the approach flow, where the flow depth immediately upstream of the contraction exceeds Y1 owing to a backwater effect created by flow choking. In this situation, a value of Y1 must be calculated from a flow-resistance relationship, such as Manning’s n equation. The hydraulics associated with this difficulty are explained in Section 2.1.2. Short-Contraction Scour The maximum depth of scour in a short contraction (i.e., in the bridge waterway) is influenced by the independent parameters in Eq. (2.3) and parameters defining the geometry

Findings 2-9   of the contraction transition. Additionally, for a short contraction, bridge-deck (Lb) width becomes a consideration. Initially, it can be assumed the contraction transition reduces the width abruptly in accordance with a wall angle of 90o (i.e., an abrupt change from approach channel width), B1, to contracted channel width, B2. However, other contraction geometries were investigated (see Chapter 3). Also, an objective of numerical modeling was to ascertain the influence of contraction geometry on maximum depth of contraction scour and streamwise distance until normal flow is estab- lished along the contracted channel. For maximum depth of scour in a short contraction whose walls narrow with angle α, the maximum scour depth, Ds-Max, can be expressed by modifying Eq. (2.4) as = σ τ τ α     −D Y f W Y , W W , d Y , L Y , , , gt Y , (2.8)s Max 1 1 1 2 1 1 1 b 1 g c 2 1 Alternatively, Eq. (2.8) can be stated simply as = α      =−D Y f L b Y , D Y K D Y (2.9)s Max 1 1 1 s 1 s s 1 Here, Ds-Max is expressed as an amplification of the depth of long-contraction scour, Ds, associated with normal flow downstream along the contraction, with KS being an amplification factor expressing the influence of contraction geometry on Ds-Max. Eq. (2.9) is similar to the relationship proposed by Ettema et al. (2010) for estimating abutment scour. The parameter Lb/Y1, which is of use in defining the length of a short contraction (associated with a bridge crossing), requires a little more explanation. Essentially, it serves as a length ratio relating bridge-deck width to bedform wavelength and height, where the maximum height of bedforms is about one-third of flow depth. Discussion The sets of parameters in Eqs. (2.4) through (2.9) are useful for evaluating the existing literature on contraction scour and the published data presently available. For example, the parameters W1/Y1 and W2/W1 are non-dimensional parameters that characterize contraction geometry, and thereby, indicate the range of contraction geometries investigated in prior studies. The magnitude of the shear-stress parameter τ/τc indicates whether the conditions studied were clear-water (no bed sediment moving) or live-bed (fully mobilized bed sediment) in the approach channel. Together with considerations of contraction hydraulics, and the physical definition of contraction scour presented in Section 2.1.2, the parameters in Eqs. (2.4), (2.7), and (2.8) provide a framework for the literature review of Section 2.1.4. To be noted, some prior studies (e.g., Sturm et al. 2011 and Lim 1993) use a dimensional analysis to identify pertinent param- eters affecting contraction (and abutment) scour. However, their dimensional analyses do not consider bedforms and related flow-resistance adjustment in the contracted channel. The use of the parameters in Eqs. (2.4), (2.7), and (2.8) to evaluate existing laboratory data facilitates the contraction scour re-analysis that is the objective of this study. 2.1.4 Prior Studies In this section, prior studies are reviewed from several perspectives. It is important to mention that none of the prior studies includes a comprehensive description of contraction

2-10 Revised Clear-Water and Live-Bed Contraction Scour Analysis hydraulics or delineation of the variables influencing contraction scour. Also, none considers the time-varying hydraulics associated with flow in open-channel contractions (as in Section 2.1.2). Indeed, none adequately considers contraction-flow hydraulics and the resulting combined occurrence of both short-contraction and long-contraction scour (as in Figures 2-1 through 2-3). For the following discussion, prior studies are arranged in terms of the parameter τ/τc, in Eq. (2.5) as (1) clear-water scour and (2) live-bed scour. Tables 2-2 and 2-3 indicate prior studies with reference to this arrangement. Table 2-4 summarizes the few numerical-simulation studies of contraction scour (2D and 3D). However, they involve only clear-water scour. Table 2-5 lists known field studies of contraction scour. These include both clear-water and live-bed conditions. The complete citation for each study is given in the References section of this report. Author(s) Publication Year Comment Laursen and Toch 1956 Curves were fitted to laboratory measurements of scour depth at the piers of a multi-span bridge comprising circular piers evenly spaced across the flow. Laursen 1963 Laursen derives a theoretical clear-water scour relationship by using continuity, the energy equation, a critical tractive force approximation, and Strickler's relationship for Manning's n. He simplifies the equation by neglecting the difference in the velocity heads and the loss through the contraction. This simplified equation is often cited as the basis for the HEC-18 design equation. Gill 1981 Gill observes that his results are for non-equilibrium conditions. He used two different transitions but could not prevent abutment scour. The abutment scour depth was greater than the long-contraction scour. Gill used Straub's (1934) equation. Webby 1984 Webby assumed that a contraction is long when the length of the contracted section is at least twice the uncontracted channel width. Lim 1993 This study provides a useful dimensional analysis. Lim developed an equation for a clear-water condition and stated that it can be used for live-bed scour as well. However, the results showed that the equation greatly overpredicts live-bed scour depth. Lim also considered the backwater effect due to choking (which he mentioned was not significant in his experiments). Lim and Cheng 1998 Applicable for both clear-water and live-bed scour. Lim and Cheng compared Lim's equation with four other equations. Their equation is only related to width ratio. All the equations underestimated the scour depth. Laursen 1999 This is a journal discussion article in which Laursen mentions that clear-water scour and scour by flow transporting sediment are two different phenomena. Laursen theorizes that there is no limit for a scour hole to grow under constant clear-water conditions (a research assistant ran a physical model for 3 weeks and gave up at last). Zevenbergen 2004 Zevenbergen presents a method (in a spreadsheet format) to calculate the depth of the scour hole for either clear-water or live-bed conditions. This method can be used for tidal bridges under storm surge, time-dependent conditions. It is noted that this method is also applicable for upland streams with flashy flows. Dey and Raikar 2005 Dey and Raikar conducted 131 laboratory experiments in which they vary a wide variety of parameters. Unfortunately, they do not provide direct measurements of Y2, and 123 of the 131 data points are under choked flow conditions. They also provide a regression analysis and draw comparisons between parameter relationships to the equilibrium scour depth. Table 2-2. Prior studies on clear-water contraction scour.

Findings 2-11   Author(s) Publication Year Comment Straub 1934 This is the earliest study regarding live-bed contraction scour. The water surface was used as the datum. The results on scour depth in coarse sand do not appear to be in good agreement with the equation presented but show good agreement for fine sand. Laursen 1960 Laursen's live-bed equation is used in HEC-18. It is possible to derive another equation with better prediction for high flows, based on Laursen's sediment transport equation. Komura 1966 Komura developed an equation for bed material with non-uniform grain size (σg > 1) for both clear-water and live-bed conditions. Gill 1981 Gill's results are for non-equilibrium conditions. He used two different transitions but could not prevent abutment scour. The abutment scour depth was higher than the long-contraction scour. Gill used Straub's (1934) equation. Lim and Cheng 1998 Applicable for both clear-water and live-bed scour. Lim and Cheng compared Lim's equation with four other equations. Their equation is related only to width ratio. All the equations underestimated the scour depth. Dey and Raikar 2006 As with other studies, bedforms were not taken into account. Dey and Raikar validated their results with experimental data and compared their results with three other equations. Najafzadeh et al. 2016 The authors developed two predictive models by using neural-network models ANFIS and SVM to predict scour depth in a long contraction. They used a 2004 dataset that was gathered from clear-water and live-bed experiments. They showed that an ANFIS model and the Laursen equation had the best results. However, the equation that they describe as Laursen's equation belongs to Lim and Cheng (1998). Table 2-3. Prior studies on live-bed contraction scour. Author(s) Publication Year Comment Weise 2002 This study investigated the utility of a 2D (depth- averaged) numerical model for modeling contraction scour. Results were considered positive. Marek and Dittrich 2004 This study used a 3D numerical model. Minh Duc and Rodi 2008 This study used a 3D numerical model (RANS model). Lai and Greimann 2010 This is a useful summary paper giving the results from prior numerical studies. The study investigated the utility of a 2D (depth-averaged) numerical model for modeling contraction scour. They compared the results from the 2D model with results from 3D models used by prior studies. Additionally, they reviewed the mixed results of prior studies. Zey 2017 This master’s thesis used a 2D numerical model in a comprehensive parametric examination of rigid-bed hydraulic flow fields upstream, at, and downstream of a contraction as a function of contraction ratio, contraction entrance shape, roughness, and bed slope. Table 2-4. Prior numerical studies on contraction scour.

2-12 Revised Clear-Water and Live-Bed Contraction Scour Analysis Prior studies also can be grouped into three categories: Category 1. Formulation of contraction scour in terms of an idealized, long contraction with uniform flow occurring in the approach section and the contracted section Category 2. Semi-empirical equations based on data from laboratory flume experiments Category 3. Observations and measurements obtained from field cases The earliest studies are of Category 1, whereas more recent studies are generally of Category 2. Only a few field studies have been done (Category 3). Studies in Category 2 are assessed in terms of the non-dimensional parameters in Eq. (2.4). Further analysis of the experimental conditions used in prior tests is summarized in Sec- tion 2.2. Also included in Section 2.2 is an assessment of whether choking occurred (as inferred from the data available). Several fundamental equations have been developed considering the long-contraction scour process, generally for rather idealized or simplified conditions (e.g., Straub 1934, Laursen 1960 and 1963). Considerations of flow non-uniformity and temporal variation of flow were not considered. Table 2-6 summarizes the equations reviewed. The earliest equation of idealized contraction scour was by Straub (1934). Straub established the equilibrium condition for live-bed contraction scour as the scour depth that satisfies sediment continuity through a contracted flow section. He used the DuBoys bedload (sediment) transport equation in estimating the bedload transport rate in the approach flow and contracted sections (American Society of Civil Engineers 2008). Straub’s work eventually led to subsequent studies of contraction scour based on the idealized concept of a long contraction. Laursen (1960, 1963) developed several methods for estimating contraction scour under live-bed and clear-water conditions. His interest in contraction scour was prompted by extensive floods that, in June 1947, destroyed bridges from Minnesota to Florida. Laursen began by studying pier and abutment scour (Laursen and Toch 1956), using Straub’s method for live-bed contraction scour and its effect on pier scour. Laursen (1960) utilized a similar approach to that of Straub, but he applied his own sediment transport equation to the live-bed case with the result shown in Table 2-6. This equation is traditionally referenced as the Laursen live-bed contraction scour equation. In compound channels, he assumed that all of the sediment transport occurs in the main channel. Laursen’s sediment transport Author(s) Publication Year Comment Wagner et al. 2006 Collected data at 15 bridge sites where 4 out of 15 bridges have velocity data. Benedict et al. 2007a The collection of the historic scour data is reasonably straightforward for the clear-water condition, but to find the historic depth of scour for the live-bed condition is problematic because of the partial or complete refill of the holes. The U.S. Geological Survey utilized ground- penetrating radar in South Carolina to address this issue. There are, however, uncertainties regarding the results. Benedict and Caldwell 2009 The authors provide an envelope curve for live-bed pier and contraction scour. Data were gathered from 87 bridges, with a total of 89 measurements of live-bed contraction scour depth. Benedict and Caldwell 2005 Benedict and Caldwell provide envelope curves for clear-water pier and contraction scour. Data were gathered from 116 bridges. Table 2-5. Prior field studies on contraction scour.

Straub (1934) Live-Bed Scour; τc = critical shear stress; τ1 = approach flow shear stress. Based on the DuBoys bedload transport equation. Laursen (1960) Live-Bed Scour; Qc = approach flow rate in main channel; Qt = total flow rate through bridge opening main channel; n = Manning's n resistance coefficient; p1, p2 = exponents from Laursen's total sediment transport equation depending on whether sediment load is mostly bedload, mixed load, or mostly suspended load; B1 = approach main channel width; B2 = bridge main channel width. Laursen (1963) Clear-Water Scour. Shear stress in contracted section equal to the critical shear stress τc at equilibrium. Komura (1966) Live-bed: Clear-water: Clear-water: Live-Bed and Clear-Water Scour. F1 = approach flow Froude number; σg1 = geometric standard deviation of sediment size distribution in approach channel. Includes effect of armoring in contracted section. Gill (1981) Live-Bed Scour. Sediment transport rate assumed proportional to (τ − τc)β. Froehlich (1995) Clear-Water Scour. Extended Laursen (1963) equation to take into account bed armoring; Da = median diameter of armor particles; n = Manning's n. Lim and Cheng (1998) Live-Bed Scour. Sediment transport rate assumed proportional to (V – Vc)4. Compared with lab data for both live-bed and clear-water scour. Briaud et al. (2005) Clear-Water Scour of Porcelain Clay. unif = uniform scour depth; max = maximum scour depth; F1 = approach flow Froude number; Fc = Froude number at critical velocity. Dey and Raikar (2005) Clear-Water Scour (0.9 < V1/Vc < 1.0) F1e = (V1 – V1c)/[(SG – 1)gY1]1/2 ; SG = specific gravity; V1c = approach flow velocity when V2 = Vc at beginning of scour. FHWA 2012 Live-Bed: Ds = Y2 – Y0 where Y0 = depth of flow in contracted section before scour occurs The live-bed equation is the same as Laursen (1960) with the ratio of Manning's n removed; p = sediment transport factor (0.59 – 0.69). The clear-water equation is derived from Y2 = q2/Vc and is different in form, but not in principle, from Laursen (1963) because it does not involve the approach flow section. Assuming a dimensionless Shields parameter of 0.039 for sand-gravel bed material and Strickler's relationship between grain size and Manning’s n yields Ku = 0.025 (SI) 0.0077 (English) dm = 1.25 d50 Table 2-6. Contraction scour equations (B1 = approach flow channel width; B2 = contracted channel width; Y1 = approach flow channel depth; Y2 = contracted channel depth after scour). See References for source of equations.

2-14 Revised Clear-Water and Live-Bed Contraction Scour Analysis equation considers both bed load and suspended-load transport; where the exponent p varies according to the relative contribution of bed load and suspended load to the total sediment transport rate. Laursen (1963) also applied the assumption of a long contraction to the case of clear-water scour by assuming that the shear stress in the contracted section has reached its critical value τc at the end of the scouring process. Using Manning’s n equation for the approach and contracted flow, he obtained a ratio of τ1/τc that when combined with the continuity equation yielded the clear-water contraction scour equation given in Table 2-6. Other equations in Table 2-6 entail semi-empirical relationships developed from laboratory data. These equations, while giving some insight into contraction scour, are of limited use. They do not adequately reflect contraction hydraulics and its complexities. Indeed, a common criti- cism concerning these equations is related to the data upon which they are based. In particular, it is apparent that most data relate to the short-contraction reach. Komura (1966) emphasized the influence of armoring on live-bed scour depth by arguing that the ratio of the sediment sizes in the approach flow section and contracted section influ- ence the contraction scour depth for large values of B1/B2 and σg. He applied dimensional analysis to a series of laboratory experiments on live-bed and clear-water contraction scour in a long contraction (Lc/B1 ≥ 1.0) and proposed an equation based on his experimental results. In his equation, dimensionless scour depth depends on F1, B1/B2, and σg1 as shown in Table 2-6. Lim and Cheng (1998) derived a long-contraction scour equation for live-bed scour along the same lines as that of Gill (1981) using a bedload equation in which β = 4, but then showed that the only solution of the equation was one in which the dimensionless live-bed contraction scour depth depends on B1/B2 alone as shown in Table 2-6. Lim and Cheng com- pared their equation with several sets of laboratory data for long contractions and concluded that it gave reasonable agreement, not only with live-bed scour laboratory data but also with several sets of clear-water scour laboratory data. Froehlich (1995) used laboratory data to extend the Laursen (1963) equation to account for bed armoring but his results have not been widely applied. Briaud et al. (2005) conducted flume experiments on clear-water scour of a cohesive sedi- ment (porcelain clay) in a long contraction. From their experimental results, they proposed an equation for maximum dimensionless contraction scour depth (Ds/Y1) that depends on Froude number in the approach channel (F1), B1/B2, and the critical value of approach flow Froude number (Fc) as shown in Table 2-6. They concluded that contraction length has no influence on the scour depth as long as Lc/B2 ≥ 0.25. In addition, their results showed no influence of the transition angle on scour depth. Dey and Raikar (2005) conducted a set of flume experiments on a long contraction using both sand and gravel beds and varied the geometric standard deviation (σg) of the sediments. They maintained flow conditions such that 0.9 < V1/Vc <1.0 (this range translates to 0.81 < τ1/τc <1.0) (i.e., their equation in Table 2-6 applies to maximum clear-water contraction scour). Their results showed a significant effect of sediment gradation for 1.4 < σg < 3 with a minimum value of scour depth due to armoring given as 25% of the value for uniform sediment. The value of the exponent on (B1/B2) in their equation is 1.26, which is somewhat different than the theoretical value and the values derived by others from experimental results. The current HEC-18 live-bed scour equation in Table 2-6 is identical to that of Laursen (1960) with the exception of the Manning’s n ratio. For the HEC-18 equation under live-bed conditions, it was assumed that n2 = n1 (see HEC-18, Appendix C).

Findings 2-15   2.2 Evaluation of Existing Clear-Water and Live-Bed Contraction Scour Laboratory Data 2.2.1 Overview Existing laboratory data on clear-water and live-bed contraction scour (see Tables 2-2 and 2-3, respectively) were evaluated considering the known flow and scour processes (see Sec- tion 2.1.2) and gaps in knowledge about these and related processes. Knowledge and data gaps were weighed to assess their relevance for obtaining design estimates of scour depth. If deemed substantially important, this missing information was addressed in the laboratory tests con- ducted for this project (see Chapter 3). Based on an evaluation of existing laboratory studies, one must conclude that the body of laboratory data on pure contraction scour is not large. Much of the existing data pertain to abutment scour in connection with contraction scour, and thus include the influence of abutment shape and, likely, compound-channel shape. To a certain extent, this condition is inevitable, because flow contractions at bridge waterways are usually not the hydrodynamic, smooth transitions that fluid mechanics texts depict (e.g., for contracting stream-tubes). In actual field settings, the geometry of flow contraction through a bridge waterway is much more complex. The evaluation also includes a discussion of clear-water contraction scour datasets previously examined under NCHRP Project 24-34. The evaluation concludes with a discussion of live-bed contraction scour laboratory studies (Section 2.2.4). A further impression, reinforced by experience with NCHRP Project 24-20 (Ettema et al. 2010), is that live-bed contraction scour in alluvial bed material will likely involve changes in bedform geometry along the region of contraction scour. The bedforms are primarily dunes, which change in height and wavelength in response to changing flow conditions. It appears that only the study done for NCHRP Project 24-20 has recognized the possible influences of dune bedforms on contraction scour depth. 2.2.2 Evaluation of Clear-Water Laboratory Data on Contraction Scour The HEC-18 clear-water contraction scour equation was not developed from laboratory or field data, but instead was derived from sediment transport concepts and theory. In U.S. customary units, the HEC-18 clear-water contraction scour equation is computed as the difference between two flow depths: y y y (2.10)s 2 0= − =      y K Q d W (2.11)2 u 2 m 2 3 2 3 7 where y2 = Normal depth of flow in contracted section after scour has occurred, and well down- stream of the contraction, ft (m) Ku = Conversion factor equal to 0.0077 for U.S. customary units (0.025 for SI units) Q = Discharge in contracted section, ft3/s (m3/s) dm = Representative particle size equal to 1.25 times d50, ft (m) W = Width of contracted section, ft (m) ys = Depth of scour in contracted section, ft (m) y0 = Depth of flow in contracted section before scour occurs, ft (m) A definition sketch showing these variables is provided in Figure 2-5.

2-16 Revised Clear-Water and Live-Bed Contraction Scour Analysis The research conducted under NCHRP Project 24-34 demonstrated quite clearly that, in terms of the reliability index β, the HEC-18 contraction scour procedure exhibits the most uncertainty of all the scour equations. Reliability index β is a useful indicator to compute the failure probability. Lagasse et al. (2013) explain its application for bridge design involving risk and reliability. This necessitates multiplying the design contraction scour depth by a large scour factor to provide an acceptable level of reliability in the context of the Load and Resistance Factor Design (LRFD) bridge design procedures (see Section 8.5). This does not mean, however, that the fault lies with the HEC-18 clear-water and live-bed contraction scour equations, which are based on sediment transport theory. Three major issues were encountered during the analysis of the contraction scour datasets: 1. None of the published datasets from contraction scour studies measured the depth of flow in the contracted section before scour occurs (y0). This value had to be calculated using the methods described in NCHRP Report 761 (Lagasse et al. 2013), and this calculation was complicated by the choking phenomenon. Therefore, in the NCHRP Project 24-34 analysis, this flow depth must be considered an estimate, not a measurement. 2. All but one of the published studies assumed that the depth of flow in the contracted section prior to scour (y0) was the same as the depth of flow in the approach section (y1), thereby ignoring the importance of hydraulic drawdown in the contraction. In some cases, the researchers measured the depth of scour by taking bed elevation measurements, which was considered a reliable measurement. In other cases, the researchers simply assumed that the scour depth was the difference between y2 (the depth of flow in the contracted section after scour has reached equilibrium) and y1. Those datasets had to be eliminated. 3. Most of the previous laboratory studies were done under clear-water conditions. There were insufficient laboratory data with which to assess the reliability of the HEC-18 live-bed contraction scour equation. Consequently, NCHRP Project 24-34 identified a need to develop accurate and reliable data on scour in long contractions, using a range of contraction ratios, flow rates, and grain sizes. NCHRP Project 24-34 noted that the choking phenomenon should be accurately documented and the backwater effects and energy losses associated with choking should be precisely accounted for. A study conducted under these conditions would provide much more reliable data to accurately assess the bias and coefficient of variation (CV) of the HEC-18 contraction Figure 2-5. Definition sketch used for the clear-water contraction scour equation in HEC-18. W1 , q1 W2 , q2 y1, V1 y0 , V0 y2 , V2 Bed after scour Bed before scour A. PLAN B. PROFILE L

Findings 2-17   scour equations, and would either (1) lead to better values of the reliability index β, or (2) result in a better equation for contraction scour design (i.e., not a best-fit prediction). Under NCHRP Project 24-34, contraction scour data obtained from controlled laboratory conditions were assembled from eight sources, yielding 182 independent measurements of contraction scour in non-cohesive soils. Only long contractions were considered because (as noted in Section 2.1.4) short contractions inevitably include an abutment scour effect in addition to the contraction scour. Here, a contraction is considered to be long if the length, L, of the contracted section is greater than the width, W1, of the approach section as shown in Figure 2-6. It should be noted, however, comprehensive studies by Webby (1984) suggest that a long contraction is defined when the length, L, is twice the width of the approach section, W1. All datasets consisted of studies where the following information was documented: (1) scour depth ys, (2) approach flow depth y1, (3) approach flow velocity V1, (4) median sediment size d50, (5) approach width W1, (6) width of contracted section W2, and (7) length of contracted section L. Data from 182 test runs as summarized in Dey and Raikar (2005) were obtained from that reference. In that publication, data from other researchers (Komura 1966, Gill 1981, Webby 1984, and Lim 1993) were included along with the tests performed by Dey and Raikar. All 182 tests involved clear-water conditions in the approach flow (V1/Vc < 1.0), where Vc is the critical velocity for each test estimated using the relationship presented in HEC-18: V y K S 1 d n (2.12)c 1 6 s s 50( )= − Figure 2-6. Water surface and bed elevations at different times during a clear-water contraction scour experiment (from Webby 1984).

2-18 Revised Clear-Water and Live-Bed Contraction Scour Analysis where Vc = Critical velocity for particle motion, ft/s y = Approach flow depth, ft Ks = Dimensionless Shields parameter (0.03 for gravel, 0.047 for sand) Ss = Specific gravity of particle (assumed equal to 2.65 unless otherwise indicated) d50 = Median particle diameter, ft n = Manning’s n resistance coefficient, estimated as n = 0.034(d50)1/6 (d50 in ft) Table 2-7 provides a summary of the laboratory clear-water contraction scour data compiled for NCHRP Project 24-34 (U.S. customary units are shown, with the exception of particle diameter in millimeters). Figure 2-6 presents measured data taken during a contraction scour experiment (Webby 1984) that clearly shows there is a significant difference between y0 and y1 as scour begins to take place during the early stages of a test. The Dey and Raikar (2005) tests that utilized well-graded bed materials were also re-examined. Although Dey and Raikar do not provide the grain size curves for the materials, they do provide the d50 size and the geometric standard deviation σg, defined as σ = d d (2.13)g 84 16 For the Dey and Raikar tests using well-graded bed materials, σg ranged from 1.46 to 3.60. Further investigation revealed that when σg is greater than 1.9, there is a sufficient number of larger particles present in the bed material matrix to create a self-armoring condition that limits the depth of scour. Therefore, the Dey and Raikar tests that used well-graded bed material for which σg was greater than 1.9 were eliminated. After screening the 182 data points, 119 data points remained with which to assess the reliability of the HEC-18 clear-water contraction scour equation. In practice, the depth of flow, y0, in the contracted section before scour occurs is typically determined by use of a water surface profile model, such as HEC-RAS (Hydraulic Engineering Source No. DataPoints d50 (mm) V1 (ft/s) V1/Vc Y1 (ft) W1 (ft) W2 (ft) ys observed (ft) Dey & Raikar 2005 uniform sand 24 0.81 – 2.54 1.02 – 1.86 0.79 – 0.95 0.28 – 0.43 1.97 0.79 – 1.38 0.08 – 0.51 Dey & Raikar 2005 uniform gravel 75 4.1 – 14.25 1.89 – 3.05 0.83 – 0.95 0.22 – 0.45 1.97 0.79 – 1.38 0.07 – 0.47 Dey & Raikar 2005 well-graded sand 12 0.81 – 2.54 1.09 – 1.86 0.81 – 0.95 0.41 – 0.43 1.97 1.18 0.05 – 0.21 Dey & Raikar 2005 well-graded gravel 20 4.1 – 14.25 2.16 – 2.98 0.86 – 0.93 0.40 – 0.45 1.97 1.18 0.05 – 0.24 Komura 1966 12 0.35 – 0.55 0.57 – 0.81 0.66 – 0.88 0.09 – 0.28 1.31 0.33 – 0.66 0.11 – 0.26 Gill 1981 22 0.92 – 1.53 0.67 – 1.26 0.54 – 0.88 0.09 – 0.27 2.49 1.64 0.03 – 0.16 Webby 1984 11 2.15 0.70 – 1.22 0.38 – 0.68 0.29 – 0.43 5.20 1.72 0.15 – 0.38 Lim 1993 6 0.47 0.68 – 0.73 0.81 – 0.84 0.08 – 0.09 1.31 0.39 – 0.85 0.03 – 0.17 Total 182 0.35 – 14.25 0.57 – 3.05 0.38 – 0.95 0.08 – 0.45 1.31 – 1.97 0.33 – 1.72 0.03 – 0.51 Table 2-7. Summary of laboratory clear-water contraction scour datasets.

Findings 2-19   Center-River Analysis System). However, because the laboratory data did not include a direct measurement of this flow depth (presumably because in the laboratory, scour occurs before the target flow conditions are established), y0 must be estimated from available data. As a first approximation, the velocity, V0, and flow depth, y0, in the contracted section before scour occurs can be estimated as From continuity, V Q A Q y W (2.14)0 1 2 = ≈ Assuming no energy losses, the specific energy in the contracted section is equal to that in the approach section, so y y V 2g V 2g (2.15)0 1 1 2 0 2 = + − V0 is then recalculated as V Q A Q y W (2.16)0 0 2 = = For the laboratory data, this approach yielded estimates of y0, which in many cases were unreasonably small, and for a significant number of data points, negative values of y0 were obtained using this first approximation. Further investigation revealed that the contraction ratios W2/W1 in the laboratory tests were severe enough to create a “choked” condition at the entrance to the contraction. The threshold of choking occurs when the actual contraction ratio is less than the critical ratio σ, defined by Wu and Molinas (2005); 3 2 F F (2.17) 1 2 3 2 1( ) σ = +     It was found that 113 of the 119 tests were conducted with some degree of choking. Figure 2-7 presents the dimensionless choking ratio, σW2/W1, plotted versus the unit discharge in the contracted section. To resolve this issue, the estimate of y0 was refined by comparing the initial depth ratio, y0/y1, with the contraction ratio, W2/W1. If the depth ratio from the initial approxi- mation was less than the contraction ratio, the depth, y0, was re-estimated as y1 times the contraction ratio as a limiting condition. This second iteration yielded more reasonable values for assessing the HEC-18 equation clear-water contraction scour prediction. Three additional data points were identified as outliers, leaving a final dataset of 116 points for analysis. Figure 2-8 shows the results of the analysis with the reduced dataset. The bias of the HEC-18 clear-water contraction scour equation was determined to be 0.92 as the mean value of the ratio ys (observed) to ys (predicted). The CV of the data is the standard deviation divided by the mean, determined to be 0.21 for this dataset. The clear-water scour equation underpredicted the observed scour for 23.3% of the data points (27 tests out of 116). The reliability index β for the clear-water contraction scour equation was determined to be 0.44 and 0.52 for normal and lognormal distributions, respectively. These relatively low values of β are not surprising, considering that the HEC-18 clear-water contraction scour equation was

2-20 Revised Clear-Water and Live-Bed Contraction Scour Analysis 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 D im en si on le ss C ho ki ng R ati o Unit Discharge q2 in Contracted Section, ft3/s/ft Choked Not choked Figure 2-7. Dimensionless choking ratio versus unit discharge in the contracted section, 119 laboratory tests. y = 1.1648x 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 y s Pr ed ic te d by H EC -1 8 , ft ys Observed , ft Per fec t ag ree me nt Dey and Raikar 2005 uniform sand Dey and Raikar 2005 uniform gravel Dey and Raikar sand, sigma < 1.9 Dey and Raikar gravel, sigma < 1.9 Webby 1984 Figure 2-8. Predicted versus observed clear-water contraction scour, 116 laboratory tests (data outliers removed).

Findings 2-21   not developed from laboratory or field data, but instead was derived from sediment transport concepts and theory. It is therefore a predictive equation, not a design equation, and as such does not have built-in conservatism. Values of β near zero indicate that on average, observed scour is underpredicted by about the same magnitude and frequency as it is overpredicted. Table 2-8 provides a summary of the prediction statistics for the HEC-18 clear-water contraction scour equation. 2.2.3 Conclusions from Assessment of Clear-Water Laboratory Data The following conclusions can be drawn from the assessment of existing laboratory data and observations: 1. Scour processes: The results support the currently accepted concepts regarding the scour processes in a long contraction (i.e., that scour continues to deepen until V = Vc and τ = τc). 2. Pre-scour versus post-scour hydraulic conditions: All prior studies make the implicit assumption that the flow depth, y1, in the upstream channel remains constant before, during, and after scour occurs in the contracted section. HEC-RAS (Brunner 2016) simulations of laboratory tests conducted by Dey and Raikar (2005) prove that this is not the case. Any amount of flow contraction at a bridge reach creates backwater upstream, which may be relieved after scour has occurred. In the case where the contraction is severe enough to create a choked flow condition, this effect is even more pronounced. 3. Previous investigations: Previous laboratory investigations as reported in the literature do not provide hydraulic conditions before scour occurs; therefore, y1 and y0 are not readily available from existing datasets and must be estimated by an appropriate hydraulic model to reliably assess the predictive accuracy of contraction scour equations. 4. Relationship between short and long contractions: The relationship between short- contraction scour and abutment scour had not been adequately addressed in previous studies but was addressed in this study. 2.2.4 Evaluation of Live-Bed Laboratory Studies of Contraction Scour The data and observations stemming from the live-bed laboratory studies are of the same quality as those produced by the laboratory studies on clear-water contraction scour. Therefore, the same considerations pertain as mentioned in Section 2.2.2 for clear-water contraction scour (i.e., the significance of flow choking in waterway hydraulics and the locations where scour depth was measured are critical issues). In addition, previous studies with live-bed conditions do not report the initial flow depth, Y1, in the approach reach before scour occurs; rather, the simple assumption is made that this flow depth remains constant before, during, and after scour. Dataset No. Data Points Bias CV1 Percent Underpredicted Reliability β Normal Lognormal All data (clear water) 116 0.92 0.21 23.3% 0.44 0.52 1 Coefficient of variation. Table 2-8. Bias and CV of the HEC-18 clear-water contraction scour equation with laboratory data, outliers removed.

2-22 Revised Clear-Water and Live-Bed Contraction Scour Analysis Some additional aspects of the quality of the data are generally not described for live-bed scour: 1. There is little or no description of the variation in bedform morphology through the contrac- tion and narrowed channel in previous studies. 2. The live-bed predictive methods do not include the influence of the parameter, Lb/Y1, relating bridge geometry and bedform morphology. In general, maximum crest-to-trough bedform height is about one-third of the flow depth. For comparatively deep flows, bedform amplitude below the live-bed mean bed level can lower local bed elevation substantially. 3. The live-bed relationships do not indicate how contraction scour, especially short-contraction scour, relates to abutment scour. 4. The live-bed predictive methods rely on a flow depth, Y1, in the approach reach prior to scour, and in practice, this is readily obtained from standard hydraulic models in use. How- ever, all previous laboratory studies do not report this value. It is important to note that the backwater effect at an open-channel constriction relaxes significantly as scour develops in the contracted section. The principal sources of laboratory data on live-bed contraction scour are Straub (1934), Komura (1966), Gill (1981), and Dey and Raikar (2005). Heretofore, these studies have not been reviewed in terms of contraction hydraulics and the pertinent parameters influencing contraction scour. 2.3 Evaluation of Field Data on Clear-Water and Live-Bed Contraction Scour 2.3.1 Overview The following sections evaluate the extent and quality of field data regarding contraction scour at bridge waterways. Prior field studies on contraction scour are identified in Table 2-5. Only a modest amount of field data exists regarding contraction scour, and much of these data include the influence of bridge abutments. The most comprehensive source of field data is the National Bridge Scour Database (NBSD), which contains a fairly extensive section focused on contraction scour observations at bridge sites. In this regard, Benedict (2003), Benedict and Caldwell (2015), and Benedict et al. (2007b, 2006) give the major compilations of field data regarding abutment scour that include the presence of contraction scour. 2.3.2 Field Data on Contraction Scour As with abutment scour, there is a lack of reliable field data for comparison with the contraction scour equations in Table 2-6. Three major problems with such comparisons are as follows: 1. The equations are based on a much simpler set of flow conditions in the laboratory than found in the field. 2. Existing field data are based either on measurements of contraction scour long after the flood event for which the hydraulic parameters may not be known, or on “flood chasing” techniques in which the time of scour measurement may not coincide with the occurrence of maximum temporal scour depth. 3. Distinguishing contraction scour from other types of scour is not a straightforward process. Local pier scour is often separated from contraction scour using a concurrent ambient bed surface for the cross section. Essentially this relies on a graphical estimate of the cross section that would exist without pier scour at the time of the cross section measurement (Landers and

Findings 2-23   Mueller 1996). After elimination of pier scour, field contraction scour is determined as the difference between the average bed elevation of the contracted bridge section and an assumed average bed elevation that would have existed without the bridge (uncontracted section). The uncontracted bed elevation can only be estimated from plots of the concurrent bed profile both upstream and downstream of the bridge (Landers and Mueller 1996). Mueller and Wagner (2005) conducted a comprehensive analysis of the available field data for contraction scour (even though the data are rather limited). They compared field data with contraction scour estimates from the equations proposed by Straub 1934, Laursen 1999, and Komura 1966. In general, the results were mixed with overprediction in most cases, but instances of underprediction also occurred. More detailed real-time measurements of flow velocities and bed elevations were available for a flood in 1997 on the Pomme de Terre River in Minnesota. The velocity data were not reproduced well by HEC-RAS, because the flow through the bridge opening was not 1D. The contraction scour for the bridge was significantly underestimated using the equations recommended in HEC-18. This comparison, however, may have been biased by an attempt to separate abutment scour and contraction scour. Mueller and Wagner (2005) concluded that future efforts for computing contraction scour (and abutment scour) require a better balance between the complexity of field conditions and the simplicity of idealized laboratory conditions. Benedict (2003) measured clear-water contraction scour in the South Carolina Piedmont as the depth of remnant scour holes in the floodplain. Flow data were not available for many of the sites so the 100-year peak discharge was taken as representative for these sites, while the historic peak discharge was used where it had been measured or could be estimated from surrounding gauges. The Laursen equation was shown to greatly overpredict the contraction scour under these assumptions. Instead, an envelope curve for contraction scour was recommended as a function of the geometric contraction ratio defined as (1 – B2/B1). The contraction scour depths were shown to vary from nearly zero to the limit of the envelope for all values of the geometric contraction ratio without any apparent trend. Benedict (2003) concluded that “because the envelope was developed from a limited sample of bridges in the (South Carolina) Piedmont, scour depths could exceed the envelope.” In a follow-up study of live-bed contraction scour in the South Carolina Piedmont and the Coastal Plain, Benedict and Caldwell (2009) estimated the elevation of buried scour surfaces using ground-penetrating radar. They proposed eliminating Q2/Q1 from the Laursen live-bed scour equation by assuming that all flow remains in the main channel to justify an envelope curve for the contraction scour depth that depends only on the geometric contraction ratio. By comparing the maximum depth of scour with soil boring data, they concluded that the Piedmont data for scour depth were limited by a scour-resistant subsurface layer that consisted primarily of bedrock. In a few cases, the subsurface layer was composed of gravel or clay. The coastal plain data exhibited a similar scour-resistant layer, although some cutting into this layer (no more than 1.6 m) was evident. Hong et al. (2006) showed that field contraction scour can be modeled in the laboratory using Froude number similarity and equality of V1/Vc in model and prototype by judicious choice of the model geometric scale and the model sediment size. A 1:45 scale model of a bridge on the Ocmulgee River in Macon, Georgia, was constructed in the hydraulics laboratory at Georgia Institute of Technology, and bathymetry of a 750-m reach of the river was reproduced. Good agreement was obtained between model and prototype velocity distributions for the 1998 historical flood of 1,840 m3/s (50-year flood peak = 2,240 m3/s). The maximum clear-water contraction scour in the laboratory (V1/Vc = 1) agreed with the measured field live-bed contrac- tion scour depth within 5%.

2-24 Revised Clear-Water and Live-Bed Contraction Scour Analysis 2.3.3 Evaluation of Field Data There is a lack of reliable field data for comparison with the contraction scour equations in Table 2-6. The preponderance of these data include the influence of abutments and possibly the presence of piers. A comprehensive source of field data is the NBSD, which contains a fairly extensive section focused on contraction scour observations at bridge sites. Figure 2-9 illustrates a typical site described by Benedict and Caldwell (2009). As this figure indicates, it is likely that many of the cases included in the database document regions of scour that are rather complicated and 3D. Field data may represent, primarily, short-contraction scour (i.e., flow contracted through a portion of the bridge waterway). The most useful sources of field data and discussion of field data are Wagner et al. (2006) and Benedict and Caldwell (2005, 2009). These three references demonstrate the practical difficulties of determining contraction scour at field sites. None of the sites documented by the studies identified in Table 2-5 involved pure contraction scour, or long-contraction scour. The studies present useful data indicating overall magnitude of scour in several forms, though it is almost impossible to discern pure contraction scour with any degree of accuracy. Additionally, there is substantial evidence that lateral erosion, as well as vertical erosion, occurred at most field sites. A useful approach to evaluating the overall quality and extent of field data on contraction scour is to summarize some of the main observations that Wagner et al. (2006) and Benedict Figure 2-9. A typical example of clear-water contraction scour at a bridge in the coastal plain of South Carolina (Source: Benedict and Caldwell 2009).

Findings 2-25   and Caldwell (2009) make about the field data. The following observations include additional commentary by the Research Team. The main observations are as follows: 1. Neither Wagner et al. (2006) nor Benedict and Caldwell (2009) consider the hydraulics of flow through an open-channel contraction in any detail. They do not discuss flow choking, and take the approach flow depth, y1, to be at the entrance to a bridge waterway. Additionally, there are at best only sketches of the flow field through contracted bridge waterways. 2. Bridge waterways commonly have contraction ratios (W2/W1) ranging from about 0.25 to 1.0. 3. All the bridge sites documented involve geometric and sediment complexities that cause the contraction scour depth estimates to be site-specific and inherently approximate. Generally, it is difficult to separate contraction scour and abutment scour. It is evident that at each site there was a strong influence of local geometry on scour location, shape, and depth. Complicating factors included abutment geometry, bed sediment, approach angle, and floodplains. 4. Simplifying approximations are needed when using the HEC-18 methods for predicting contraction scour at field sites. For example, the channel can be treated as being rectangular in cross-sectional shape, and Y1 can be equated to the average flow depth across the approach channel. For clear-water scour, a median diameter (d50) of bed-particle size needs to be assessed and a critical shear stress selected in accordance with d50. 5. The studies underscore the difficulties in making contraction scour predictions based on field data. 6. Field studies suggest that 1D numerical models are generally inadequate for contraction scour estimation because they do not readily handle the boundary complications usually found in the field at bridge-waterway sites. 7. For clear-water scour, the field applications demonstrate the inherent difficulty of scour depth estimation based on an estimated value of critical shear stress for bed-particle entrainment. If the value is not accurate and if the bed sediment is non-uniform, considerable inaccuracy is introduced. 8. Benedict and Caldwell (2010) indicate that the HEC-18 clear-water equation overestimated scour depths by about 2 to 40 times the contraction scour depth observed in the field. This discrepancy can be attributed to many of the factors herein. Of all the field data presentations, the plot shown in Figure 2-10 seems best to summarize field data as compared with the live-bed scour relationship recommended by HEC-18. This figure uses normalized measured depths of scour that Benedict and Caldwell (2009) obtained for the U.S. Geological Survey’s NBSD and data for live-bed and clear-water contraction scour at bridges in South Carolina. 2.3.4 Lateral Erosion An additional complicating factor with contraction scour field data is that vertical erosion of a contracted channel may be accompanied by lateral erosion of the channel. As scour lowers the channel bed, geotechnical instability may cause the channel banks to collapse. Flow may also entrain material directly from banks. Moreover, when a channel bed contains a stratum of rock or very coarse sediment, the bed may be more resistant to erosion than the channel banks, and lateral erosion may be the dominant process in contraction scour. This factor has been largely overlooked in field studies of contraction scour at bridge waterways. Molinas and Bailey (2004) describe three cases of substantial lateral erosion at bridge sites in Wyoming. A feature of the three sites is an erosion-resistant layer of sedimentary rock a short distance below the bed surface. Once the rock stratum was exposed, flow eroded the weaker soil, forming the channel banks and spill-through slopes of abutments at the bridge sites. Figure 2-11 shows the eroded spill-slope of one abutment at the Murphy Creek site crossed by Interstate 25.

2-26 Revised Clear-Water and Live-Bed Contraction Scour Analysis Figure 2-10. Comparison of normalized, measured depths of contraction scour and the scour depth predicted using HEC-18. Figure 2-11. Lateral scour of a spill-through slope abutment of Interstate 25 crossing Murphy Creek, Wyoming (Molinas and Bailey 2004).

Findings 2-27   In effect, the channel contraction through the bridge site resulted in both vertical and lateral erosion, as shown in Figure 2-12. 2.3.5 Conclusions from Evaluation of Field Data The following conclusions can be drawn from the evaluation of existing field data: 1. The available reports regarding field data are not supported by a description of the hydraulics of the contracted reaches involved. 2. None of the available field studies includes an adequate analysis of similitude on which to base reported data and observations. 3. At bridge sites in the field, contraction scour can involve both vertical and lateral erosion of a channel, which complicates interpretation of the data. 4. As is evident from site bathymetrics such as those in Figure 2-9, many factors make field data sites an unreliable source for developing prediction equations. Temporal considerations also add uncertainty regarding the relationship between the measurements and equilibrium or ultimate scour conditions at a field site. Figure 2-12. Sketch of channel cross section indicating combined vertical and lateral erosion in a channel subject to contraction scour.