Combining Individual Scour Components to Determine Total Scour (2018)

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

15 CHAPTER 2. Background Research 2.1 Introduction Numerous idealized experimental studies of scour around bridges, conducted since the late 1950s, have generated largely empirical formulas for scour depth estimation at bridge foundations. The resulting separate formulas for maximum abutment, contraction, pressure, and pier scour depths with current guidance for application are provided in HEC-18 (Arneson et al. 2012). Until recently, little attention has been given to the interaction among the different types of scour. Sturm et al. (2011) pointed out that scour processes cannot be assumed to be independent and suggested that scour formula refinements from more realistic experiments and continuous scour monitoring of bridges are needed. As a useful starting point for investigating combinations and interactions of different scour types, the recent literature related to each type is briefly reviewed in this chapter of the report. In addition, field studies of bridge scour and their challenges are reviewed. 2.2 Abutment Scour Sturm et al. (2011) have provided a comprehensive summary of previous studies of abutment scour and scour prediction formulas generated from mostly idealized laboratory flume experiments. Unfortunately, these formulas are unreliable in certain situations and, in particular, can lead to overprediction of scour depths, especially in comparison to field measurements. None of the current scour formulas satisfy all the criteria of an ideal formula because the process of abutment scour is difficult to model due to the complexity of the flow field, complications of fluvial geomorphology at bridge crossings, and inadequate knowledge of the erodibility of natural sediments (Sturm et al. 2011). Another shortcoming of many of the experiments is failure to model the natural compound channel geometry consisting of a floodplain and main channel instead of a simple rectangular channel. In the case of live-bed scour experiments, the erodible main channel bank is unstable, particularly for bankline or short setback abutments. For overtopping experiments, the issue of riprap protection of the embankment becomes important in order to prevent complete embankment failure. In clear-water scour experiments, the required duration of the experiments is of the order of 5 to 10 days to reach equilibrium. Many early experiments failed to satisfy this criterion. Despite these limitations, revisiting existing scour depth prediction formulas can be the first step in formulating a methodology for estimating total scour depths in the presence of interactive scour processes. Early experiments on abutment scour utilized solid embankments and abutments with solid foundations extending to the floor of the flume to model sheet-pile protection, especially for wingwall abutments. More recently, erodible embankments and abutments have been modeled in the laboratory with and without riprap protection because many prototype spill-through abutments are of this type. In what follows, studies of both types of abutments are discussed.

16 Variables are defined in Figure 2-1. Lb W LpVf2, qf2 Vf1, qf1 La Vm1, qm1 Vm2, qm2 Bf BmMain-channel Flood-plain hbYf1 Ym1 YfoYf2max Vp Approach Bridge Main-channel Flood-plain Flood-plain Section A-A Plan Figure 2-1. Definition sketch for abutment scour in a compound channel 2.2.1 Abutment Scour Around Solid Abutment Froehlich’s equations (Froehlich 1989) for clear-water scour (CWS) and live-bed scour (LBS) around abutments were derived from dimensional and regression analysis of the available laboratory data. In total, 164 CWS laboratory experimental results were used in the regression to produce: 178.0 87.1 43.0 50 116.1 63.0 11         gass d Y Y LKK Y d  F (2-1) in which sd is the scour depth, 1Y is the approach flow depth, sK is an abutment shape factor,

17 K is a factor accounting for the abutment alignment to the flow, aL is the length of the embankment and abutment, F is the approach flow Froude number, 50d is median sediment grain size, g is geometric standard deviation of the sediment size distribution, and “+1” is added for the factor of safety (FS). However, Froehlich’s clear-water scour equation seems to greatly overestimate abutment scour depth compared to field measurements (TRB 1989). Thus, HEC-18 (Arneson et al. 2012) recommends the use of Froehlich’s (1989) live-bed abutment scour regression equation because it predicts smaller abutment scour depths. Like the CWS equation, it depends on LBS experimental results obtained in rectangular flumes with solid abutments. It is given by: 127.2 61.0 43.0 11     F Y LKK Y d a s s  (2-2) The HIRE equation is based on field data obtained by the U.S. Army Corps of Engineers for spur dikes in the Mississippi River. This field situation closely resembles the laboratory experiments for abutment scour in that the discharge intercepted by the spur dikes is a function of the spur length. The modified equation, referred to as the HIRE equation, is applicable when the ratio of the projected length ( L a) to the flow depth ( 1Y ) is greater than 25 (long abutment). The HIRE equation is given by: K K Y d ss 55.0 4 33.0 1 F (2-3) in which sd is the scour depth, 1Y is the depth of flow at the abutment on the overbank or in the main channel, F is the Froude number based on the velocity and the depth adjacent to and upstream of the abutment, sK is an abutment shape factor, and K is a factor accounting for the abutment alignment to the flow as for Froehlich’s equation. As recommended by Sturm et al. (2011), the Melville formula is the most applicable formula to short, solid-wall abutments. Including results from Gill (1972), Wong (1982), Kwan (1984, 1988), Kandasamy (1985,1989), Melville (1992, 1997) and Dongol (1994), the formula is based on extensive experimental work at the University of Auckland and is presented by Melville and Coleman (2000). The proposed formula for the maximum abutment scour is: GsdIyls KKKKKKd **  (2-4) in which ylK = abutment length factor, IK = approach flow intensity factor, dK = sediment size factor, *sK = abutment shape factor, *K = abutment alignment factor and GK = channel geometry factor. All the K factors are empirical expressions as follows: ylK is given by

18           2510 251)(2 12 5.0 YLY YLYL YLL K a aa aa yl (2-5) in which La = abutment length, and Y = water depth (Figure 2-1). IK is given by         10.1 1))( c c c ca I VV VV V VVV K (2-6) in which aV = mean flow velocity at the “armour peak” ( aV = cV for uniform sediments). For live-bed conditions ( cVV >1), the value of IK is typically less than unity, but it has been set to unity to be conservative. dK is given by             250.1 2524.2log57.0 50 50 50 dL dL d L K a a a d (2-7) Normally the sediment can be regarded as relatively fine in which dK =1.0, so this parameter appears only when the sediment is relatively coarse in size and when 25/ 50 dLa . * sK is given by              250.1 251011.0)1(67.0 10 * YL YL Y LKK YLK K a a a ss as s (2-8) in which sK is given in the table below (Table 2-1). A vertical-wall abutment has been used as a reference with a sK value equal to unity. The abutment alignment factor ( K ) varies from 0.9 to 1.1 depending on the angle between the abutment and flow direction.

19 Table 2-1. Abutment shape factors for Melville scour formula Abutment Shape Ks Vertical-wall Square End 1.00 Semi-circular End 0.75 45° Wingwall 0.75 Spill -through 0.5:1.0 (H:V) 0.60 1.0:1.0 (H:V) 0.50 1.5:1.0 (H:V) 0.45 GK is given by                                Dcase n n Y Y Ccase Bcase n n Y Y L B Acase K f m m f f m m ff G 2165 35 0.1 11 0.1 (2-9) in which fB is the floodplain width, mY and fY are the flow depths in the main channel and on the floodplain, respectively, mn and fn are the Manning’s roughness values in the main channel and on the floodplain. Cases A to D are shown in Figure 2-2.

20 Figure 2-2. Typical cases of abutment positions in compound channels (reproduced from Melville and Coleman (2000)). Chang and Davis (1998, 1999) applied Laursen’s long contraction scour method and suggested the following two formulas for abutment scour: Live-bed scour: FSY q qkkkYKKd k vfpss         0 1 2 1 2  (2-10) Clear-water scour: FSY V qkkkKKd c vfpss        02857.0 (2-11) in which sd = scour depth, sK = abutment shape factor, K = abutment/embankment alignment factor, 1Y = approach flow water depth, pk = pressure flow coefficient, vk = velocity adjustment factor, fk = spiral flow adjustment factor, 2q = flow rate per unit width in the contracted section, 1q = flow rate per unit width in the approach flow section, 0Y = flow depth at bridge before scour, and FS = factor of safety. Sturm and Janjua (1993, 1994) suggested that the geometric contraction ratio, m, which was proposed by earlier investigators such as Garde et al. (1961) in an idealized rectangular flume, did not apply for the compound channel situation. This is because the flow distribution across the bridge opening is non-uniform and dependent on the compound-channel geometry and roughness difference between the main channel and floodplain. Thus, the authors suggested that the local abutment scour should depend on flow redistribution in the contracted section rather than simply on abutment length or geometric contraction ratio m. It was proposed that the geometric contraction ratio, m, be replaced by the discharge contraction ratio QQM 0 in which 0Q is that portion of the flow in the approach flow section with a width equal to the opening width; and Q is the total approach flow discharge.

21 In a 3.3-m wide by 5.2-m long flume, Sturm and Janjua (1994) conducted a series of experiments with a compound channel in which the ratio of abutment length to floodplain width varied from 0.24 to 0.62, and M varied from 0.64 to 0.91. Assuming that the floodplain discharge per unit width was uniformly distributed and flow depth change in the contracted section was very small, M was found to be a reasonable estimate of the discharge per unit width ratio in the floodplain 21 ff qq . A modified formula for M was suggested by Hong (2013) for short setback abutments and for the case of embankment overtopping. The best-fit linear equation of Sturm and Janjua was given by         35.070.735.070.7 1 121 1 cf f c s Vq Vq MY d F F (2-12) with a coefficient of determination of 0.91 and a standard error in 1Yds of 0.37. Here sd = maximum scour depth at the abutment, 1Y = approach flow water depth in the floodplain, 1F = approach flow Froude number, and cF = critical Froude number. The ratio of Froude numbers is equivalent to V1/Vc and 21 ff qq has been substituted for M on the right-hand side of Eq. (2-12). The extensive clear water abutment scour experiments for both setback and bankline abutments carried out by Sturm and Sadiq (1996) and Sturm (2006) demonstrated that a common relationship for scour depth can be developed for both setback and bankline abutments, and it is given by      0 0 1 0 C Mq q C Y d cf f r f s (2-13) in which sd = equilibrium abutment scour depth; 0fY = normal depth in the floodplain, corresponding to the downstream unconstricted water surface elevation because backwater can occur upstream of the bridge, rC and 0C are experimental coefficients with rC representing the scour amplification factor and 0C referring to an equation intercept which must be exceeded for scour to occur, 1fq = flow rate per unit width in the approach floodplain, cfq 0 = critical flow rate per unit width in floodplain = 00 fcYV , cV0 = critical velocity corresponding to the unconstricted flow depth 0fY , and M = discharge contraction ratio in bridge approach section. The best-fit relationship for the experimental data yielded coefficient values of rC = 8.14 and 0C = 0.40. To integrate the vertical-wall and spill-through abutment results, a shape correction factor SK for the spill-through abutment was given by 2.167.0 40.0 67.052.1     forKS (2-14) in which )( 001 fcf YMVq , and SK = 1.0 for  ≥ 1.2 while SK = 0 for  ≤ 0.67. This

22 result is consistent with that of Melville and Coleman (2000) in that the abutment shape effect becomes immaterial for long embankments due to dominance of contraction effects in comparison to turbulence. 2.2.2 Abutment Scour Around Erodible Abutment Ettema et al. (2010) adopted a similar approach to that of Chang and Davis (1999) and Sturm (2006) for estimating the maximum abutment scour in a compound channel based on laboratory experiments; however, the abutment was modeled as a pile-supported structure set inside an erodible embankment/abutment, thereby simulating many bridge sites in the field. They presented envelope curves for the ratio of the maximum scour depth to the theoretical contraction scour depth as a function of the unit discharge ratio between the approach and the contracted flow sections for the purpose of design estimation of scour depth. Three distinct scour conditions caused by different erodibility of the bed and floodplain were defined as shown in Figure 2-3 and examined extensively in flume experiments (Ettema at al. 2010, Yorozuya and Ettema 2015):  Scour Condition A: Scour of the main channel portion of a compound channel occurs, either because the channel bed is far more erodible than the floodplain or the abutment encroaches on more than 3/4 of the floodplain.  Scour Condition B: Scour of the floodplain occurs for abutments set well back from the main channel such that the scour hole does not impinge on the bank of the main channel.  Scour Condition C: Scour form that develops when breaching of an abutment’s embankment fully exposes its abutment-column structure such that scour develops at the abutment column as if it were a pier. Ettema et al. (2010) included three heretofore-neglected aspects of abutment scour, i.e., (a) realistic abutment construction and layout, (b) geotechnical nature of abutment scour, and (c) useful analytical framework that related maximum scour depth to amplified theoretical contraction scour depth (Laursen 1960, 1963) with a variable amplification factor. Instead of utilizing a simplified rectangular channel model and rigid abutments, the model spill- through abutments were constructed around a standard-stub abutment structure, which was pile- supported and buried in an erodible earthfill embankment. The model wingwall abutments had similar foundation layouts to the standard-stub abutments, except that they included wing-walls extending from the central stub. All the abutments were modeled according to the design and dimensions of commonly used abutments by the Illinois, Iowa, and New York Departments of Transportation.

23 Scour Condition A Scour Condition B Scour Condition C Figure 2-3. Abutment scour conditions: Scour Condition A - bank failure and failure of the abutment face, Scour Condition B - failure of the abutment face, and Scour Condition C - breaching of the approach embankment (Ettema et al. 2010).

24 An important finding was definition of a geotechnical limit to the maximum scour depth. Due to sliding or even outflanking of the earthfill embankment, the contracted flow through the bridge opening is relieved and maximum scour depth is reduced. The maximum scour depth and width attainable are limited by the geotechnical stability of the embankment upon the channel bank, and by the earthfill, roadway approach embankment behind the abutment. A conceptual model of combined geotechnical and hydraulic processes leading to abutment failure was proposed accordingly. However, Ettema and Fuller (2013) pointed out that this earlier proposed scouring process requires that scour of the floodplain or channel bed deepen very rapidly near the abutment toe, so as to continually destabilize the abutment, and it may not be the main process whereby abutments erode and fail. A more detailed study of embankment failure, where the embankments consisted of compacted sand and sand-clay mixtures, revealed a mechanism of undercutting of the toe of the embankment followed by tension cracks at the waterline on the abutment and toppling of blocks of sand into the channel (Ettema et al. 2015). Ettema et al. (2016) further studied the breaching process associated with Scour Condition C and found that the breaching process was different for spill-through abutment stubs and wingwall abutments owing to differences in geometry, but that the depth of scour depended on the soil strength in both cases. If geotechnical stability is not a consideration, then abutment scour can be related to the theoretical long contraction scour as formulated by Laursen (1960) for live-bed contraction scour and Laursen (1963) for clear-water contraction scour through an amplification factor: CT YrY max (2-15) in which maxY is the flow depth corresponding to the maximum scour depth, CY is the mean flow depth of the theoretical contraction scour, and Tr is the amplification factor. As interpreted by Ettema et al. (2010), the amplification factor is influenced by the local turbulent processes induced by flow blockage and separation at the abutment itself, and by acceleration of the flow caused by the width contraction of the bridge opening. In the case of a short abutment without much flow contraction, Tr is larger due to the local turbulent structures dominating the scour process, while it is smaller for a more constricted bridge opening in which the flow contraction is dominant. Based on Eq (2-15) and for Scour Condition A, the maximum scour depth is given by (Ettema et al. 2010):         1 76 1 276 11maxmax m m ATAmms q qmCYYYd (2-16) and for Scour Condition B, it becomes:

25             1 76 1 2 7/3 76 11maxmax f f c f BTBffs q q mCYYYd   (2-17) in which, maxsd = potential scour depth, maxY = maximum flow depth where maximum scour depth is located, 1mY = initial flow depth in the approach main channel, 1fY = initial approach flow depth on the floodplain, TAC = coefficient of turbulent influence for abutment scour in Scour Condition A, TBC = coefficient of turbulent influence for abutment scour in Scour Condition B, Am and Bm are the values 2max qq for the Scour Condition A and B, respectively, maxq = unit discharge coinciding with the location of deepest scour in the main channel, 111 mmm BQq  , 2mq = estimate of the mean value of the unit discharge through the bridge opening in the main channel, f = shear stress in approach flow section on the floodplain, c = critical shear stress for sediment movement, 1fq = average flow rate per unit width on the approach flow floodplain, and 2fq is the average flow rate per unit width at the bridge opening floodplain. Ettema et al. (2010) presented envelope curves for the amplification factors ( TT mCr  in Eqs. (2-15) and (2-16) for Scour Conditions A and B, respectively) based on their laboratory experiments. The envelope curves were plotted in the form of CMAX YY / as a function of 12 / qq for the main channel and floodplain for Scour Conditions A and B, respectively. To simulate extreme hydrologic events that could result in bridge overtopping flow, and to predict the corresponding abutment scour depth, Hong (2013) conducted a series of experiments in a compound channel to investigate the characteristics of abutment scour in free surface flow, submerged orifice flow, and overtopping flow. The bridge deck model used in these experiments was based on a common design for two-lane bridges used by Georgia DOT in a rural region. In these experiments, the bridge deck was supported on varying lengths of erodible embankment/abutment on the floodplain. In accordance with the location of the maximum depth in the scour hole, three clear-water scour cases were considered: Case A – long setback abutment scour ( 53.0,61  faf BLYW and 0.77), Case B – bankline abutment scour ( 0.1,01  faf BLYW ), Case C – short setback abutment scour ( 88.0,61  faf BLYW ), in which W is setback distance and 1fY is the approach flow depth on the floodplain. Based on the assumption that maximum abutment scour can be considered a multiple of theoretical contraction scour depth, which is the modified long contraction assumption, and the hypothesis that the amplification factor depends on the relative magnitude of turbulent kinetic energy (TKE) which may itself vary with ( 12 qq ), the experimental results produced a new scour prediction formula for erodible embankments that includes submerged orifice flow (SO), overtopping flow (OT) and free flow (F) as below: For long setback abutments (LSA):

26 7/6 1 1 1 2 0 1 16.0 1 2max2 75.2                        fc f f f f f f f fo f V V q q Y Y q q Y Y (2-18) For bankline abutments (BLA): 7/6 1 1 1 2 0 1 12.0 1 2max2 75.1                        mc m m m m m m m mo m V V q q Y Y q q Y Y (2-19) in which max2fY = maximum flow depth after scour, 0fY = floodplain flow depth measured downstream of the bridge, assumed to be the same as the unconstricted floodplain flow depth, 1fY = flow depth in the floodplain, 1fq and 2fq are the floodplain discharge per unit width in the approach and bridge sections, respectively, 1mq and 2mq are the main channel discharges per unit width in the approach and bridge sections, respectively, 1fV and 1mV are the approach floodplain and main channel mean flow velocities, respectively, and 1fcV and 1mcV are the critical velocities for initiation of sediment motion in the approach floodplain and main channel, respectively. For short setback abutments (SSA), main channel approach flow variables were selected for the calculation of the normalized independent scour parameters as in Eq. (2-19) because maximum scour occurred in the main channel, and scour depths followed most closely the equation developed for BLA. For OT flow, the values of 2fq and 2mq were evaluated based on that portion of the total flow going under the bridge which can be determined from HEC-RAS or a 2D numerical model. The quantity in curly brackets in Eq. (2-18) and Eq. (2-19) represents Tr which Hong and Sturm (2015) related to the width-averaged TKE near the bed in the scour area prior to scour. Although the study by Hong and Sturm (2015) reproduced river bathymetry, embankment/abutment erodibility and flow conditions on the floodplain that are very similar to those encountered in the field, flow intensity in the main channel may not be consistent with all prototype situations, i.e., during an extreme flood, live-bed flow conditions are likely to prevail in the main channel rather than clear-water flow conditions. Otherwise, this study provided results consistent with those of Ettema et al. (2010) for a different compound channel geometry but for SO flow and OT flow as well as F flow, and it introduced the notion of a relationship between the amplification factor and elevated TKE in the scour region. The weakness of the Laursen approach with an amplification factor is that the assumptions of an idealized long contraction are not satisfied by a bridge contraction so it has to be understood that the computed contraction scour component is a reference scour depth only. 2.3 Lateral Contraction Scour Contraction scour is caused by flow acceleration due to channel narrowing, because of either natural channel width reduction or hydraulic structures blocking the channel. The latter case has

27 been of concern for decades and analytical solutions have been developed for an idealized long contraction both in clear-water and live-bed scour conditions. As observed by Melville and Coleman (2000), most of the published studies on contraction scour have considered the special case of scour in the contracted section of a rectangular channel in which the contraction is long enough that it can be assumed that uniform flow exists in both the approach and contracted reaches. This case is the theoretical long rectangular contraction, as shown in Figure 2-4. Figure 2-4. Definition sketch for idealized long contraction scour ( 1Q = cQ = main channel flow rate at approach flow section; 2Q = tQ = total flowrate in channel at contracted section; B1 = Bm1 = approach-flow main channel width; B2 = Bm2 = contraction main channel width; scd = contraction scour depth). Reproduced from Sturm et al. (2011). As pioneers of long contraction theory, Straub (1934), Laursen (1960, 1963), and Gill (1981) made important contributions to the development of contraction scour formulas based on this theory. Straub (1934) used a simplified one-dimensional approach for the live-bed condition in which it was assumed that the scour was in equilibrium such that the sediment transport rate into the contraction balanced the outflow sediment transport rate, i.e. sediment continuity. Laursen (1960) utilized a similar approach in the case of the live-bed condition with his own sediment transport formula, in which both bed-load and suspended-load were considered: 21 1 2 2 1 76 1 2 PP m m c t n n B B Q Q Y Y             (2-20) in which cQ = approach flowrate in main channel, tQ = total flow rate through bridge opening main channel, n = Manning’s resistance coefficient, 1P and 2P = exponents from Laursen’s total

28 sediment transport formula depending on whether sediment load is mostly bed-load, mixed load, or mostly suspended load, 1mB = approach-flow main channel width, and 2mB = contraction main channel width. Eq. (2-20) implicitly assumes that sediment transport occurs only in the approach-flow main channel. In HEC-18 (Arneson et al. 2012), it is recommended that the Manning’s n ratio be dropped from Eq. (2-20). If the change in velocity heads and the head loss between sections 1 and 2 are neglected, then 12 YYdsc  , which is often assumed. For the clear-water scour case, Laursen (1963) also applied the long contraction theory by assuming that the shear stress in the contracted reach attains its critical value at the equilibrium state with the result given by: 73 1 76 2 1 1 2         cm m B B Y Y   (2-21) As shown by Ettema et al. (2010), Eq. (2-21) can be rewritten as 7/3 1 7/6 1 2 1 2         cq q Y Y   (2-22) in which q2 is the unit discharge, or flow rate per unit width, in the contracted section, and q1 is the unit discharge in the approach flow. An alternative approach applied in HEC-18 is to write the clear-water contraction scour equation relative to the contracted section only such that τ2 = τc. With substitution of Manning’s equation and the uniform flow relationship for shear stress to evaluate τ2, and Shields’ relationship to estimate τc, the flow depth in the scour hole can be expressed directly by 7/3 * 2 2 2 2 )1(     dSG qnY c (2-23) in which n is Manning’s roughness coefficient in the contracted section, c* is Shields’ parameter, SG is the specific gravity of the sediment, and d is a representative grain size. Gill (1981) verified experimentally that Straub’s simple one-dimensional model could be used for predicting scour depth in a long contraction with reasonable accuracy. He suggested that for design purposes, the predicted depths should be scaled up by about 58% to get a maximum local value. His suggested relationship, which covers a range of values of c /1 that includes both clear-water and live-bed scour, is given by 73 11 31 2 1 76 2 1 1 2 158.1                      cc B B B B Y Y (2-24) Based on the continuity of flow and sediment transport, Lim and Cheng (1998a) obtained a simplified formula which is applicable to both live-bed and clear-water scour conditions. The authors analytically formulated the following equation:

29 41 2 1 31 2 1 1* * 1* * 2 1 34 2 1 1                 B B Y Y u u u u B B Y Y cc (2-25) and found that this equation has only one possible solution: 75.0 2 1 1 2     B B Y Y (2-26) in which cu* = critical shear velocity, 1*u = shear velocity in the approach flow section, 1B = approach channel width, 2B = channel width in the contracted section, 1Y = depth of flow in the uncontracted approach section, and 2Y = depth of flow in the contracted section after scour. The limiting assumption for this simplification process is that the sediment transport rate is proportional to  4cVV  along with Laursen’s long contraction idealization. 2.4 Vertical Contraction Scour (Pressure Scour) One aspect of bridge scour estimation technology that has received comparatively limited attention from researchers is the so called “pressure-flow scour”, which can occur when the water surface elevation upstream from the bridge rises above the bridge low chord. As a consequence, the bridge is subject to a vertical contraction of the flow that increases the bridge opening velocity and potentially the sediment transport capacity. Orifice flow can occur through the bridge section if the flow does not overtop the bridge superstructure, or the bridge can be overtopped. Abed (1991) and Jones et al. (1993) conducted some of the early research studies on pressure flow scour. Later, Arneson and Abt (1998), Umbrell et al (1998), Lyn (2008a), Guo et al. (2009), and Shan et al. (2012) completed systematic studies on this topic. Lyn (2008a) pointed out unsatisfactory features of the HEC-18 equation, notably that the basic model of the original (Arneson, 1997) regression analysis suffers from a spurious correlation. Lyn proposed a new equation as follows         2 95.2 1 1 1 ,min A V VA Y d c bs (2-27) in which ds = pressure scour depth below undisturbed bed level, Y1 = approach flow depth, Vb = average flow velocity at bridge section prior to scour, V1c = critical flow velocity for sediment entrainment in the approach flow section and a definition diagram is given in Figure 2-5. The values for A1 and A2 were determined to be 0.105 and 0.5, respectively, for the Arneson data, but Lyn recommended A1 = 0.21 and A2 = 0.6 as an envelope curve.

30 Figure 2-5. Definition diagram for pressure-flow scour at bridges (HEC-18). Umbrell et al (1998) assumed that flow velocity over the bridge deck is approximately equal to the approach flow velocity V1, and that the flow velocity under the bridge at scour equilibrium is approximately equal to the incipient motion velocity of the approach flow V1c. They proposed the following dimensionless expression:      11 1 1 1 Y w V V Y dh c sb (2-28) in which hb = vertical distance from bed to low chord of bridge, w = depth of weir flow when flow overtops a bridge deck and w =0 for partially submerged flows. Combining their experimental data and a logarithmic regression analysis, the above equation was modified in order to derive an operational expression 603.0 1 1 11 1102.1         c sb V V Y w Y dh (2-29) Their tests ran for only 3.5 hours, far from equilibrium scour, which makes the results questionable. Guo et al. (2009) divided bridge scour into three cases, i.e. downstream unsubmerged, partially submerged, and totally submerged, according to the tail water surface elevation. For downstream-unsubmerged flows, the maximum bridge scour depth is an open channel flow problem where the conventional methods in terms of critical velocity or bed shear stress can be applied. For partially and totally submerged flows, depending on whether the tailwater elevation is below or above the bridge deck, respectively, the equilibrium maximum scour depth can be described by a scour and an inundation similarity number proposed in their work. The data showed that the horizontal scour extent depends on deck width.

31 In HEC-18, Arneson et al. (2012) combined CFD analysis and experimental data to obtain an estimate of the maximum thickness Yt of the separation zone under the downstream end of the bridge deck in submerged flow. The value of Yt was then proposed as an additional variable to evaluate the depth of scour contributed by the vertical contraction due to submerged orifice flow. The scour depth ds in this formulation is given by bts hYYd  2 (2-30) in which Y2 (Ybs in Figure 2-5) is the flow depth measured below the separation zone due to theoretical lateral contraction scour for a long contraction computed by Eq. (2-20) or (2-23) depending on whether the scour is live-bed or clear-water, respectively, and hb is the vertical height of the low chord of the bridge prior to scour (see Figure 2-5). The value of Yt is estimated from the empirical equation expressed by: 1.0 2 1 15.0          t tb b t h w Y hh h Y (2-31) in which Y1 = approach flow depth, )( 1 bt hYh  , the distance from the upstream water surface to the low chord of the bridge girders, and w = weir-flow head for overtopping = (ht – T) where T is the total height of the bridge obstruction including the girders, deck and parapet. If there is submerged orifice flow without overtopping, then w= 0. In a general dimensional analysis, the pressure-flow scour depth, ds, depends on the applied flow, the bed sediment characteristics and the bridge geometry. For steady, uniform flow conditions, the applied flow can be expressed in terms of the average approach flow velocity (V1) and depth (Y1). The effects of the bed sediment on the sediment erosion process can be represented by the critical flow velocity for sediment entrainment (Vc); while the effect of the bridge geometry on pressure-flow scour can be expressed in terms of bridge elevation (hb) under the assumption that the depth of submergence (w) is excluded from consideration; i.e., it is assumed to exert a relatively minor influence on the scour. This is reasonable in many situations, because the pressure-flow scour is expected to be significantly more dependent on the contracted flow beneath the bridge deck, than on the overtopping flow. Thus, ds can be written in the following simplified form ),,,( 11 bcs hVVYfd  (2-32) or, in dimensionless form ),( 1 1 1 Y h V Vf Y d b c s  (2-33) where V1/Vc is the flow intensity, representing the capacity of the flow to scour the sediment bed, and hb/Y1 represents the degree of vertical flow contraction at the bridge section. To examine this relationship, pressure scour tests have recently been undertaken at the University of Auckland, under live-bed conditions. Nearly all previous data apply to clear-water scour conditions only. The new data, which are as yet unpublished, are given in Figure 2-6. Two

32 sets of data are plotted, the new live-bed data and data from Umbrell et al. (1998) for clear-water scour. The former are plotted with open symbols, while the latter are plotted with solid symbols. In the figure, the same symbol (hollow or solid) signifies the same, or very similar, values of hb/Y1 as shown in the legend. The trends depicted are the same as those for local scour at bridge foundations. Pressure-flow scour is initiated at about V1 = 0.5Vc for lower deck elevations (hb/Y1 = 0.5), this value increasing with increasing hb/Y1. At hb = Y1, it is expected that pressure-flow scour would not occur. For a particular hb/Y, pressure-flow scour, under clear-water conditions, increases rapidly with increasing flow velocity to a peak value at V1 = Vc. Under live-bed conditions, the scour depth decreases from the threshold velocity peak as sediment is transported into the bridge section from upstream. There appears to be a second peak in the scour profile at about V1 = 2Vc, this peak being analogous to the live-bed peak for local scour at bridges. The relationship between pressure scour depth and its independent parameters, flow intensity (V1/Vc) and bridge deck elevation (hb/Y), is a family of curves for different values of hb/Y, with scour depth decreasing with increasing values of hb/Y. Figure 2-6. Effect of flow intensity on pressure-flow scour at bridges The new data are plotted with those of Arneson (1997) and Umbrell et al. (1998) in Figure 2-7. The figure includes 152 scour measurements, representing all of the new data, all of Umbrell et al. (1998) data and all of the Arneson (1997) data except a few data showing negative scour depths and Arneson’s live-bed data which appear to include bed form heights (i.e. dune trough levels were apparently recorded).

33 The equation of the solid (envelope) line is 5.20.145.0 14.04.075.0 1 1 11 1       c s cc s V V Y d V V V V Y d (2-34) Eq. (2-34) shows a maximum possible pressure scour depth equal to about 0.45 times the approach flow depth. Figure 2-7. Available data for pressure-flow scour at bridges 2.5 Pier Scour The objective of the research conducted under NCHRP Project 24-32 was to develop methods and procedures for predicting time-dependent local scour at wide piers and at long skewed piers, suitable for consideration and adoption by AASHTO. The research was limited to non-cohesive soils and steady flow. In the final report for NCHRP Project 24-32, it is stated that the current methods for predicting local scour at bridge piers, including those described in HEC-18, generally over-predict local scour at such piers, leading to the use of unwarranted and costly foundations or countermeasures.

34 The literature search undertaken for NCHRP Project 24-32 revealed that there is very little information (predictive equations and data) explicitly on scour at wide piers and long skewed piers. However, the predictive equations in the literature are intended to apply equally well to large as well as small piers. For this reason, all local scour equations located in the information search were considered in this study. Twenty-three of the more recent and commonly used equilibrium local scour equations were identified and assembled. As part of the initial screening process, the scour depths predicted by these equations for a wide range of laboratory and field conditions were compared. Six of the equations yielded unrealistic (extremely large or negative) results and were eliminated, leaving 17 for further analysis in this project. The data search resulted in a significant quantity of both laboratory and field equilibrium scour data (approximately 928 field and 569 laboratory). After the initial evaluation of both the equilibrium scour and scour evolution equations, improvements were made to the best performing equations/methods. A melding of Sheppard’s [Sheppard and Miller (2006)] and Melville’s [Melville (1997)] equilibrium equations resulted in the single best performing equation, referred to here as the Sheppard/Melville or S/M equation. Two equations are given in the latest version of HEC-18 (Arneson et al., 2012), namely the Colorado State University (CSU) equation and the Sheppard/Melville equation. Both equations are now well established. The CSU equation is 43.0 35.0 1 3212 F   a YKKK a ds (2-35) in which ds = local scour depth at the pier, a = pier width, Y1 = approach flow depth, V1 = average approach velocity, F = Froude number = V1/(gY1)0.5, K1 = factor for pier shape, K2 = factor for pier alignment, and K3 = factor for bed forms varying from 1.1 for clear-water scour and plane beds in live-bed scour to 1.3 for large dunes. The CSU equation was determined from a plot of laboratory data for circular piers. The data used were selected from Chabert and Engeldinger (1956) and Colorado State University data (Shen et al. 1966). The CSU equation has been progressively modified over the years and is currently recommended by FHWA for estimating equilibrium scour depths at simple piers. The equation includes a multiplying factor, Kw, to be applied to wide piers in shallow flows which was developed by Johnson and Torrico (1994) based on laboratory and field data for large piers. The Sheppard/Melville equation is given below as Eq. (2-36) in which a* = projected width of pier, d50 = sediment median diameter, Vc = sediment critical velocity for d50, and Vlp1 and Vlp2 = velocities used in computing the “live-bed peak velocity”.

35 These two equations are used in the present project when considering combined local scour and contraction scour at bridge piers. According to recommendations in HEC-18, total scour at bridge piers is estimated by simply adding the contraction scour and local scour, inherently assuming that the scour processes for each are independent. This assumption has not been verified. It is postulated that an improved method would be a sequential analysis of first contraction scour and then local scour, with a re-evaluation of the local flow hydraulics after calculation of contraction scour. The enlarged cross-section due to contraction scour (lateral and/or vertical) would lead to a reduced flow velocity and deeper flow, possibly giving reduced local scour depth compared to that estimated independently.                                                                                        112121 211111 1 121 11 13.0 50 *2.1 50 * 50 * 3 2 1 2 4.0 * 1 1 11 1* 11 1 11 3 1 1 1* 1 321* 6.0 5 6.104.0 ln2.11 tanh 2.2 0.1 1 5.2 1 1 2.2 0.14.05.2 ppp ppp p p cp c c p c s c p c c p cc p c p cs c s VVforV VVforV V gYV VV d a d a d a f V Vf a Yf V V V Vforf a d V V V Vfor V V V V V V f V V V V f a d V Vforfff a d (2-36)

36 2.6 Field Studies Sources of field data that might be employed in this research were explored. Criteria for suitable field data to be used were established as:  Continuous, real-time measurements of scour and the velocity field during several storm events;  Documentation of the occurrence of more than one type of scour;  Detailed bathymetry of the flow approach section, the bridge section, and the exit section as required for HEC-RAS modeling;  Detailed geometric data for the bridge;  Continuous measurement of discharge at a USGS rated gauging station during the storm events at the bridge;  Size distribution and other geotechnical properties of collected field samples of the soil materials at the bridge foundation augmented by geotechnical boring data obtained during the bridge design phase. Table 2-2 summarizes selected experimental and field studies of bridge scour that included field measurements. The summary identifies the studies that targeted individual scour types only, and the studies that involved more than one type of scour. The channel shape (compound or rectangular) and flow type (free surface flow, submerged orifice flow or overtopping flow) are indicated for each study. The studies of Hong (2005, 2013), Hong et al. (2006), Hong and Sturm (2009, 2010) and Ettema et al. (2010) have moved abutment research closer to simulation of field scour processes by incorporating realistic compound channel and bridge geometry. Almost all of the studies were done for the case of free flow only. Because of the challenges of real-time measurements of scour and flow fields during flood conditions, many of the studies in Table 2-2 estimated the discharge based on the age of the bridge and computed velocities and depths from HEC-RAS without specifying the method of estimating tailwater elevations which can be very influential in determining the flow field and thus maximum scour depths. In addition, most of the studies do not include measurements of soil erodibility properties, and some rely on post-flood surveys of remnant scour holes long after the flood passage to determine maximum scour depths. After eliminating most of the field studies based on the criteria established, which are necessarily rather strict for the purposes of studying combined scour processes, a limited number of studies are evaluated in more detail below. A large number of factors affect scour processes in the field with the result that the field studies reviewed include some very complex, site-specific cases. One good example is the Houfeng bridge failure in Taiwan (Hong et al. 2012) in 2008. As shown in Figure 2-8, the bridge was located on a large river flowing through a densely populated city. The river has a very wide floodplain on one side and is slightly meandering with a dam and three other bridges located upstream. Failure of the Houfeng Bridge can be attributed to multiple causes. Excessive bed degradation after an earthquake in 1999 along with extensive general scour due to several typhoons resulted in the exposure and partial suspension of the pipeline located just upstream of the bridge. Installation of a downward-tilted casing over the pipeline to protect it caused the formation of a strong impinging jet flow during a subsequent typhoon that

37 affected directly the foundation of the bridge. The failure of the bridge was caused by the combined effect of local scour, bend scour, and contraction scour, together with the impinging jet scour and long-term bed degradation. Figure 2-8. Aerial photograph at Houfeng Bridge in 2007; flow right to left (Hong et al. 2012) Table 2-2. Summary of published field data References Scour Type Channel Shape Flow Type Hydraulic &soil data Measurements P A C V Q Soil Hong and Sturm. (2009) x x Cmpd. OT M After flooding Hong et al. (2006) x x Cmpd. F M After flooding Sturm (2004) x Cmpd. F M x After flooding Zhang et al. (2013) x x x Cmpd. F E x Interpolated Hong et al. (2012) x x Cmpd. F M x After flooding Larsen et al (2011) x x Cmpd. F M M x During flooding Ting et al. (2011) x Main F M x After flooding Lombard and Hodgkins (2008) x Cmpd. U E x Not specified Lu et al. (2008) x x Cmpd. F M M x During flooding

38 References Scour Type Channel Shape Flow Type Hydraulic &soil data Measurements P A C V Q Soil Shatanawi et al. (2008) x Cmpd. U E Not specified Benedict et al. (2007) x Cmpd. U E x After flooding Conaway (2007) x x x Cmpd. F M x During flooding Conaway (2006) x x x Cmpd. F M x During flooding Wagner et al. (2006) x x x Cmpd. F M M x During flooding Guven et al. (2005) x x Cmpd. F M x After flooding Mueller & Wagner (2005) x x x Cmpd. F M M x After flooding Richardson and Trivino. (2002) x x Cmpd. F M x After flooding Coleman and Melville (2001) x x Cmpd. F M x After flooding Holnbeck & Parrett (1997) x x x Cmpd. U E x Not specified Niehus. (1996) x x x Cmpd. F M x After flooding Holnbeck et al. (1993) x x x Cmpd. OT E x After flooding Jarrett and Boyle. (1986) x x x Cmpd. F E During flooding P: Pier scour; A: Abutment scour; C: Contraction scour; Cmpd: Compound channel; Main: Main channel only; F: Free flow; SO: Submerged orifice flow; OT: Overtopping flow; M: Measured; E: Estimated; U: Unknown Another complex field situation is documented in Larsen et al. (2011). They used a two- dimensional numerical model to predict flow distribution at the bend of a compound channel and compared the result with the measured flow distribution at the Big Sioux River Bridge in South Dakota. As shown in Figure 2-9, the river has complex channel and floodplain geometry. The

39 river crossing is located at the sharp bend of a compound channel with an asymmetric floodplain. Because the bridge crossing is located at a sharp bend, the concentrated channel flow is directed towards one particular pier, which would not normally experience the observed high velocity if the channel were straight. Furthermore, because the relative amount of flow in the main channel and floodplain varies with discharge, the behavior of flow at high flows is completely different from that at low flows. This case shows that the scour around a pier and/or an abutment can be affected by bend scour and/or dynamic flow distributions that depend on the discharge. Figure 2-9. Aerial photograph of Big Sioux River Bridge at Flandreau, South Dakota (Larsen et al. 2011). Flow from east to west. Rossel and Ting (2013) used a two-dimensional simulation to predict the hydraulic conditions at a contracted bridge site in a meandering channel and validated their model using flow measurements collected by the USGS during three high flow events. As shown in Figure 2-10, parallel bridges are located in a crossing between the two bends of a meander. Thus, the flow in the bridge section concentrated on the right side of the main channel, and the exchange of flow between the main channel and floodplain occurred during three large hydrologic events.

40 Figure 2-10. Aerial photograph of James River bridge near Mitchell, South Dakota (Rossell and Ting 2013). Flow from west to east. Lombard and Hodgkins (2008) evaluated current scour depth prediction methods by comparing the predicted values with field measurements at selected bridge sites. They measured abutment scour depths at 50 bridge sites in Maine with a median bridge age of 66 years. They surveyed several cross sections including the approach cross section, unconstricted channel approximately one bridge-width upstream from the bridge, an upstream bridge-face cross section, a downstream bridge-face cross section, and an exit cross section during the low-flow seasons. Ground- penetrating radar (GPR) was used to search for in-filled scour holes during flood hydrograph recessions or during subsequent floods. Particle-size distributions were used to characterize bed materials in the main channel upstream from each bridge for the calculation of scour depth. Unfortunately, scour-producing flows were estimated as the peak flow with a 50-percent chance of having occurred during the existing life of the bridge. Hydraulic variables used to predict abutment scour at a site, such as flow depths and velocities, were generated with HEC-RAS software and necessarily depended on the estimated peak discharge during the life of the bridge. Zhang et al. (2013) selected seven bridge sites in Louisiana to compare current scour depth prediction methods with field measurements. They used measured scour data in the LADOT bridge scour database, which contains scour data for bridges at a monitoring frequency of one to several times per year. These scour data were collected at non-flooding times. Six cross sections perpendicular to the river channel were surveyed, and these cross sections were 18, 100, and 200 ft upstream and downstream from the bridge deck centerline. Based on historical flood events, the elevation data from two scour surveys with time spans over each selected flood event were extracted. The soil properties were determined from soil borings at each bridge. The scour- producing flows were estimated by using DEM (Digital Elevation Model) data from satellites and from gaging station data. Similar to the work of Lombard and Hodgkins (2008), HEC-RAS software was used for the calculation of hydraulic variables.

41 Lombard and Hodgkins (2008) and Zhang et al. (2013) concluded that scour depth estimations can be as much as one or two orders of magnitude greater than field measurements of scour. One of the possible reasons for the discrepancy between measured and predicted values is that the scour depths reported in their study may not be same as the maximum scour depths that occurred at the time of flooding. In addition, the scour-producing flow rate was not measured at the time of the flood. Furthermore, as Larsen et al. (2011) and Rossel and Ting (2013) mentioned, one- dimensional modeling cannot estimate hydraulic variables accurately in complex field situations. While these studies may provide some information about field scour processes, they suffer from the inherent shortcomings of scour and flow data collected after flooding rather than in real time. Conaway (2007) collected four years of stage and bed elevation data at 17 bridge sites throughout Alaska to assess streambed-scour in near real-time and identified shortcomings of existing methods used to estimate scour at bridges. The measured bed and water surface elevations at the pier were transmitted via satellite every 6 hours. Conaway (2007) observed that the estimated scour depths were greater than the measured values. However, he found that scour depths measured during flooding at several bridge sites were within acceptable tolerances when compared to estimated scour depths. He argued that the observed disparities between the estimated and observed scour could be attributed to bed armoring and changes in flow distribution. Furthermore, he also mentioned that long-term channel adjustments, lateral channel migration, variations in sediment supply, and complex multidimensional flow are all factors that heavily influenced the observed scour at the monitoring sites, but these factors are not generally considered in traditional scour evaluations. Wagner et al. (2006) collected field data and discussed the hydraulic and geomorphic factors affecting scour at contracted bridge openings. One example is a bridge crossing of the Minnesota River shown in Figure 2-11. They concluded that current laboratory research has failed to capture the complexity of typical field conditions, rendering the resulting equations unreliable for field applications. Thus, they recommended conducting more laboratory research in which the flow and geometry conditions are similar to field conditions. They also recommended additional field observations. However, detailed real-time measurements are difficult under high flow conditions. Nevertheless, because meaningful improvement in flow modeling is a key component of accurate scour predictions, methods for collection of flow-velocity data in such very high (dangerous) flow conditions need to be developed. Lagasse et al. (2013) quantified uncertainty in common hydraulic parameters based on data from experiments and field observations. They pointed out that field data (only pier scour due to the lack of abutment and contraction scour data) show significantly higher bias compared to laboratory data sets because of the difficulty in estimating the hydraulic conditions associated with the event causing the scour, as well as the uncertainty in determining the maturity of the scour hole depths. Simultaneous, real-time measurements of both the flow field and scour hole development during flooding in the field are difficult and sometimes dangerous. As shown in Table 2-2, almost all of the field data were measured after flooding with limited knowledge of the flow conditions that caused the scour. Under these circumstances, the field data have limited value for scour evaluation.

42 Figure 2-11. Minnesota River near Belle Plaine. (Wagner et al. 2006) 2.7 Physical Model Studies Until recently, little attention has been given to the value of physical models in closing the gap between results from idealized laboratory experiments and field data. Physical models are based on principles of dynamic similarity which require that the most important dimensionless parameters in the model and prototype are equal. The first step is ensuring geometric similarity, and the second step is identification of the most important dimensionless parameters as detailed in Sturm et al. (2011) for abutment/contraction scour. One of the most difficult aspects of physical modeling of scour is scaling the sediment size in the laboratory which involves compromises in exact hydraulic similarity. However, physical modeling efforts by Lee et al. (2004), Hong et al. (2006), and Lee and Sturm (2009) have validated effective modeling compromises for scaling of laboratory scour to improve comparisons with field data. Hong (2005) and Hong et al. (2006) conducted physical model studies of the Fifth Street Bridge crossing of the Ocmulgee River in Macon, Georgia using an undistorted geometric scale model with Froude number similarity. In contrast to previous field and laboratory studies of either bridge contraction or pier scour, these studies focused on the interaction between lateral contraction and pier scour. In this case, simultaneous pier and contraction scour occurred with the contraction scour attributed primarily to narrowing of the main channel at the bridge section. As shown in Figures 2-12 and 2-13, the 1:45 model dimensions, as well as the flow conditions including discharge, stage, velocity distributions and river bathymetry, were based on field measurements. The initial sediment size in the laboratory was 1.1 mm. The physical model

43 results shown in Figure 2-14 for the 1998 flood of 1840 m3/s show good agreement with the prototype measurements of total scour at the main bridge pier. However, between the piers, contraction scour is not predicted correctly by the model. To investigate further, the model was run at higher values of V/Vc approaching maximum clear-water scour by increasing the discharge slightly. In addition, two experimental runs were made for a smaller sediment size of 0.53 mm. The local pier scour was separated from the contraction scour using the method of concurrent ambient surfaces and a reference scour surface to eliminate residual contraction scour. The method of concurrent ambient surfaces involves establishing average bed elevations on either side of the local scour hole in the region where scour is absent. A line is drawn between these reference elevations and the local scour depth is the distance below the line to the bottom of the scour hole (Landers and Mueller 1993, Hong et al. 2006). If contraction scour is also occurring, it is separated from the total scour by establishing a river bed profile of average flow depth between upstream and downstream unconstricted river cross sections. The resulting interpolated bed elevation at the bridge location represents the reference elevation that would have been present without the bridge contraction. (Landers and Mueller 1993, Hong et al, 2006). Figure 2-12. Prototype Ocmulgee R. Bridge Figure 2-13. Ocmulgee R. Bridge model (1:45)

44 Bent #4 Bent #2 Bent #3 70 75 80 85 90 95 100 0 20 40 60 80 100 120 140 Cross-section station (m) B ed e le va tio n (m ) 03/10/1998 (1,840 cu m/s) after scouring (Run 1) Figure 2-14. Physical model scour results compared with field data for Ocmulgee R. model. As shown in Figure 2-15, contraction scour for the clear-water case continued to increase until the maximum clear-water scour condition was reached at which point the laboratory contraction scour depth was just slightly larger than the live-bed field scour depth. Although this procedure increased the Froude number slightly, it remained relatively small. Thus, for contraction scour in this case, the modeling compromise of a small relaxation of exact Froude number similarity to reach maximum clear-water scour was successful and consistent with Gill’s claim that the largest contraction scour develops during maximum clear-water scour conditions. In order to investigate the interaction between pier scour and contraction scour, experimental runs were also made with and without the piers in place. The results are shown in Figure 2-15. In this case, there is good agreement between the contraction scour calculated by the method of concurrent ambient surfaces with the piers in place and the directly measured contraction scour without the presence of the piers. These results demonstrate that pier scour and contraction scour can be separated for further analysis to determine the contribution of each to the total scour.

45 Figure 2-15. Measured contraction scour depths for Ocmulgee R. physical model (ym2a = YMAX = flow depth at location of maximum scour depth in main channel; ym1 = Ym1 = initial flow depth in the approach flow main channel; Vm1 = approach flow main channel velocity; Vmc1 = critical velocity in the approach flow main channel. Hong and Sturm (2009, 2010) conducted a hydraulic model study of the Towaliga River Bridge near Macon, Georgia including the full river bathymetry as shown in Figure 2-16. The Towaliga River is a tributary of the Ocmulgee River, and the drainage area is 816 km2 at the bridge. The field data included measured discharge, bed elevations of cross sections upstream and downstream of the bridge, and selected scour depth measurements. The model was based on Froude number similarity. The abutment/embankment was constructed as an erodible fill with rock riprap protection in order to reproduce the influence of erosion of the end roll of the abutment and pier scour in the region of the toe of the abutment/embankment. Each of the pier bents consisted of two in-line rectangular columns. The comparison between measured bed elevations in the laboratory and observed bed elevations in the field, some of which were measured during Tropical Storm Alberto (1994), while others were reported shortly after the flood, is shown in Figure 2-17 for the case of submerged orifice flow without overtopping. The scour results demonstrate that a physical model study can successfully reproduce observed scour depths in the field for extreme hydrologic events. For this case, Hong and Sturm concluded that abutment scour is a combination of lateral and vertical flow contraction effects in addition to local scour influences and can be computed as a multiple of the contraction component of scour in the case of submerged and overtopping flows in addition to free surface flows. Thus, using scour prediction formulas for separate components of scour in an additive fashion overpredicts the total scour, especially if the additive method is used in the region of multiple scour processes such as the toe of the abutment (interaction of abutment scour due to lateral contraction, submerged orifice flow scour and pier scour).

46 Figure 2-16. Laboratory model of Towaliga River Bridge (Hong and Sturm, 2010) 120 130 140 90 130 170 210 250 y,Lateral Station (m) z, B ed E le va tio n (m ) Initial C.S. Field (Jan-93) Field (Oct-94) Measurement during Alberto Bridge inside C.S.after exp Post-scour report #8 #2#3#4#5#6#7 #1 Figure 2-17. Comparison of measured field and laboratory scour cross sections (C.S.) from submerged orifice flow (Q = 1048 m3/s) for Tropical Storm Alberto in July 1994. Initial C.S. and bridge C.S. after experiment are laboratory measurements (Hong & Sturm 2009).

47 2.8 Scour Component Interaction Direct or indirect research on the interaction between local scour and contraction scour started as early as the work of Laursen and Toch (1956). Their data indicated that scour depth is a function of water shallowness and the width of obstructions such as piers. They investigated the interaction between abutment scour and contraction scour at relief bridges in a floodplain. Their results revealed that contraction scour depth could be reduced significantly by the co-existence of an abutment scour process, and that abutment scour develops faster than contraction scour. The opposing relationship, i.e. the effect of contraction scour on abutment scour, has been explored in a preliminary study by Xiong et al. (2013). They showed that the location and magnitude of abutment scour is insensitive to the streamwise length of the contraction causing contraction scour. Hong (2005) conducted experiments to address the interaction of bridge contraction scour and pier scour under two conditions, i.e. with or without the bridge piers in place. The results confirm that pier scour develops faster than contraction scour and may change the discharge distribution across the bridge cross section, and thereby change the magnitude of contraction scour. Oben-Nyarko and Ettema (2011) presented a study of the influence of pier proximity to the abutment on abutment scour. The experimental results showed that for piers within a distance of three times the flow depth from the abutment toe, pier presence did not significantly affect maximum abutment scour depth because abutment scour processes were dominant. However, when the pier was located at the toe of the spill-through abutment, pier presence decreased scour depth by 10-20% because of riprap protection being held in place by the pier. Abutment scour influence on the maximum pier scour depth decreased with distance from the abutment with pier scour alone occurring for distances greater than ten times the flow depth. In several previous studies (e.g. Sturm 2006, Ettema et al. 2010), the interaction of abutment scour and lateral contraction scour were treated as part of a single process in which the same prediction formula for maximum scour depth could be used for their combined effects. Ettema et al. (2010) presented their results in terms of an amplification factor times the theoretical contraction scour depth in which the factor varied with the relative influence of local turbulent structures and flow acceleration in the narrowed bridge opening. In previous compound channel laboratory studies at Georgia Tech by Hong 2013 and Hong et al. 2015), it was shown that a maximum scour depth formula based on dimensionless variables derived from the theoretical long contraction scour analysis could be used to predict not only scour depths for free flow (F) but also for submerged orifice (SO) and overtopping (OT) flows. The key independent variable in this approach was found to be the discharge per unit width ratio, 12 / qq , calculated or measured from the flow under the bridge only, i.e. overflow discharge was separated from the total discharge in the overtopping case. This approach for SO and OT flows becomes then a method for calculating combined vertical and abutment/lateral contraction scour depths. A significant finding of the Georgia Tech studies was that the amplification factor used to calculate abutment/lateral contraction scour depends on the width-averaged turbulent kinetic

48 energy (TKE = bK ) near the bed in the vicinity of the scour hole for F, SO, and OT flows. As a first order approximation, TKE is shown to depend on 12 / qq in Figure 2-18 in which 1*u .is the approach flow shear velocity. As a practical matter, the amplification factor appears to depend fundamentally on TKE but can be approximated from 12 / qq as shown previously in Eqs. (2-18) and (2-19); however, this observation requires further experiments and investigation using a CFD model. Figure 2-18. Dependence of width-averaged TKE ( bK ) across scour hole on 12 / qq . (Hong et al. 2015). 2.9 Computational Studies The importance of turbulence in the scour process, especially when interactions among different types of scour are of interest, suggests that numerical modeling has an important role to play in this project as discussed in Chapter 1. The concept of numerical modeling of fluid flows, or computational fluid dynamics (CFD), is not new, but its capabilities have advanced rapidly in recent years due to the development of ever faster computer processors placed in parallel. Numerical modeling begins with the basic differential equations of fluid motion (mass conservation or continuity, and momentum conservation or Navier-Stokes equations), and transforms them into algebraic equations that are valid on specified spatial grids overlaid on the

49 flow domain. The size of the grid spacing is very important with respect to accuracy and convergence of the numerical algorithms utilized in the approximation and solution of the governing equations. Specification of appropriate boundary conditions is an essential step in the development of a numerical model. Finally, validation of the model in the form of comparison with analytical solutions and experimental data is necessary to establish its accuracy and applicability to the problem at hand. The effective representation of turbulence is one of the key features of CFD models in hydraulic engineering. While increased energy dissipation caused by turbulence at the boundary of shear flows such as in pipes or open channels is well known (Munson et al. 2013), its contribution to enhanced mixing and transport of sediment is a subject of continuing research (Lyn 2008b). One of the confounding aspects of turbulence with respect to CFD models is that its properties include a wide range in the physical size of eddies, from large-scale eddies that depend on the geometry of the flow domain to the smallest sizes at which energy dissipation occurs. Because the ratio of large-scale to small-scale eddy sizes increases with increasing Reynolds number, modeling high Reynolds number turbulent flows in hydraulic engineering becomes particularly challenging. Mesh sizes small enough to capture the behavior of all eddy sizes through direct numerical simulation (DNS) literally becomes impossible even with today’s computing power (Rodi et al. 2013). An alternative to DNS is the method of large-eddy simulation (LES), in which only the large and most energetic scales (eddies) are resolved and the smaller, less energetic, more universal scales (eddies) are modeled. The chosen grid (size) determines how much of the instantaneous flow field is resolved; in other words, eddies greater than the chosen grid size are simulated directly and eddies smaller than the chosen grid size are modeled via a so called subgrid-scale (sgs) model. These sgs-models are fairly simple, because the processes which they represent are known and fairly straightforward. LES is considered an expensive method in terms of computational effort, and for high-Re flows, such as the ones reported in this report, require the use of high-performance computers. On the other hand, the method of LES offers very good accuracy in comparison with simpler, less-expensive methods such as RANS (see below) and is able to reveal details of the time-averaged and instantaneous flow. Reynolds-Averaged Navier-Stokes (RANS) equation approaches depend on averaging the Navier-Stokes equations in time, and solving for the mean flow quantities only. In the process of time-averaging the non-linear convective terms (flow acceleration terms), interactions between the turbulent fluctuations appear that cannot be solved directly and they are treated as turbulent or Reynolds stresses. The turbulence closure problem then becomes approximating the Reynolds stresses and therefore, a whole range of turbulence models are available (Rodi 1993). RANS- based CFD models, however, do not capture the large-scale unsteadiness and energetics of coherent eddies associated with the horseshoe vortex involved in local scour. Here the term “coherent” refers to a regular, identifiable pattern of eddies superimposed on the random fluctuations engendered by the smaller-scale eddies. For problems such as local scour that include unsteady, large-scale eddies, the LES technique is more suitable as discussed in detail by Rodi et al. (2013). The hydrodynamics of flow through a submerged bridge is extremely complex and several CFD- based studies have examined the flow around abutments (Biglari and Sturm 1998, Chrisohoides

50 et al. 2003, Paik et al. 2004, Paik and Sotiropoulos 2005, Koken and Constantinescu 2008, 2009, 2011, Kara et al., 2015b). These have been very helpful in revealing complex turbulence structures such as the horseshoe vortex near the abutment bed and its periodic and energetic nature and its capability of eroding the bed and entraining sediments into the flow. There are only a few studies reported in the literature on flow over inundated bridges and the accompanying water surface profiles. Malavasi and Guadagnini (2003) carried out experiments to examine the hydrodynamic loading on a bridge deck and extended their experimental studies with CFD to analyze mean force coefficients and vortex shedding frequencies for various flow conditions due to different elevations of the deck above the channel bottom (Malavasi and Guadagnini 2007). Guo et al. (2009) investigated experimentally and numerically hydrodynamic loading on an inundated bridge and the flow field around it. An experiment was conducted for a six-girder bridge deck model and the experimental data was used to validate complementary numerical simulations. The numerical data were analyzed for different scaling factors to determine the effects of scaling on hydrodynamic loading. Lee et al. (2010) focused on water surface profiles formed as a result of different bridge structures. They investigated experimentally and numerically three cases: a cylindrical pier, a deck, and a bridge (i.e. cylindrical pier and deck). Overtopping flow was considered only for the deck and bridge cases, and a 3D RANS model with k-ε turbulence closure was used to simulate all the cases. The volume of fluid method was utilized for modeling the free surface. Finally, comparisons of velocity distributions and water surface levels obtained from experiments and simulations showed that the model estimates velocity distributions very well. However, it underestimates the water level rise around the structure due to inability of the k-ε turbulence model to represent such a complex flow having significant streamline curvature and body force effects. Kara et al. (2015a) simulated overtopping of a model bridge using a large-eddy simulation approach. In their model the free water surface was computed using the level set method (LSM) developed by Osher and Sethian (1988), which is an interface-capturing method for a two-phase (water and air) flow performed on a fixed grid. The method is more accurate than typical volume of fluid (VOF) methods for tracking the free surface which is essential for the complex flow over the bridge. The LSM was validated with complementary laboratory experiments. Figure 2-19 (top) presents an overall three-dimensional view of the time-averaged water surface of this flow as predicted by the numerical simulation. Also plotted (bottom right) is a close-up photograph of the corresponding flow over the bridge in the experiment. The flow accelerates over the bridge, which results in a marked drop of the water surface. The flow plunges downstream of the bridge, which produces a standing wave or an undular hydraulic jump. Downstream of the standing wave the flow recovers gradually, exhibiting wavy motion, to the uniform flow condition. In general, Figure 2-19 shows very good qualitative agreement between the numerical results and the conditions observed in the laboratory experiment.

51 Figure 2-19. Simulated water surface (top), measurement locations (bottom left) and close-up photograph of the laboratory experiment (bottom right). A more quantitative assessment of the predictive capabilities of the simulation results is provided in Figure 2-20 depicting measured (dots) and simulated (lines) for longitudinal water surface profiles. The simulated profiles (Figure 2-20 along A and B (see sketch in the lower left of Figure 2-19) are in very good agreement with the observed data. Figure 2-20. Longitudinal water surface profiles along two locations, which are at the channel centerline (Profile A) and at one-third of the channel width (Profile B) at the abutment face.

52 The advantage of using LES for the simulation of such complex flows is that the method is able to capture the instantaneous turbulent flow and thus, when time-averaged, provides accurate flow statistics. After successful validation of their simulation Kara et al. (2015a) provided more details of the bridge overtopping flow. For instance, Figure 2-21 provides a three-dimensional view of the time-averaged flow over the model bridge, depicting streamlines color coded by the turbulent kinetic energy (TKE). Kara et al. visualised the plunging flow over the deck and the vortex structures of this flow and quantified its effects on the near-bed turbulent kinetic energy. The separation vortex SV1 formed by the overtopping flow interacts with the lateral separation vortex SV2c to enhance the TKE near the bed. Figure 2-21. Streamlines of the time-averaged flow over a submerged bridge. a) oblique view from behind and b) in a horizontal plane near the bed 2.10 Summary The literature review in this chapter has concentrated on existing scour formulas for abutment scour, contraction scour, and pier scour treated as separate processes without interaction. In addition, available field data for various types of scour have been summarized and discussed as well as physical model studies of combined scour. Finally, a background of advanced numerical modeling techniques and their capabilities have been presented. Some observations can be made from this review for the purposes of the present project. With respect to abutment scour, it seems reasonable to conclude that abutment and contraction scour processes occur simultaneously such that calculating them separately and adding them together is potentially responsible for overestimation of scour near an abutment. Determination of the distribution of simultaneous abutment and contraction scour across the bridge section as a function of the flow distribution would be a further improvement of present scour prediction procedures. The scour prediction method of applying an amplification factor to theoretical contraction scour is one potential method to advance the state of practice, but more knowledge

53 about its evaluation is needed when pressure scour and overtopping are components of the total scour. At a more fundamental level, the contribution of turbulence to the amplification factor is not well known, and the question of whether its evaluation can be done using surrogate variables needs to be explored. The existence of two well established and validated pier scour formulas is encouraging because the combination of pier scour with other scour processes may require only an appropriate adjustment of pier-scour prediction parameters due to scour interactions. The interference of the pier bent closest to the bridge abutment with all of the other scour processes occurring there poses another challenge that can be addressed in the project. The first step in evaluating scour interactions is to separate scour components by measuring scour experimentally with and without a particular obstruction in place, such as a pier or the bridge deck. Of all the field studies evaluated, those by Wagner et al. (2006) and Conaway (2006, 2007) come closest to satisfying the criteria established for this study; however, as pointed out by the authors of those reports, many of the field cases included complex flow situations that were beyond the scope of currently established scour formulas. In addition, these studies did not cover the cases of submerged orifice flow or overtopping flow for obvious reasons due to the difficulty and danger involved. Finally, the studies attempted to isolate one type of scour alone in order to test independent scour formulas instead of exploring scour interactions which are of primary interest in this project. In order to achieve the project objectives, it is clear that the experimental work should incorporate as many of the complicating factors in prototype bridges as possible in the laboratory studies. These factors include compound channel geometry, realistic bridge geometry, erodible embankments, both clear-water and live-bed scour regimes, and pressure scour in both overtopping and non-overtopping cases. On the other hand, the field bridge studies show that additional complicating factors such as channel migration and highly variable channel roughness and sediment transport properties cannot be completely realized in physical or numerical models; rather, a framework can be built for incorporating the essential aspects of prototype bridge scour components and their interactions. Finally, field studies that include real-time measurements of both the flow field and the scour development during a flood are rare because of their difficulty. However, such studies are not only possible given recent advances in instrumentation but essential to further refinements of the framework proposed in this project. As a compromise between oversimplified laboratory studies and the full complexity of field cases without all of the data needed, physical model studies validated by field measurements offer an alternative to the difficulties of conducting traditional field studies. If results of the physical model can be validated by a limited set of field data, then the laboratory model can be used to explore issues of scour interaction in more detail. Finally, a review of the use of computational fluid dynamics models to study the flow through bridge openings has been provided. Advances in computational methodologies have only very recently allowed researchers to study in great detail the underlying flow physics of bridge abutment scour. The method of large-eddy simulation, combined with an appropriate model that can capture accurately the free surface of such flows appears well suited for this project.