Evaluation of Bridge-Scour Research: Abutment and Contraction Scour Processes and Prediction (2011)

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.

34 CHAPTER 5. SCOUR DEPTH ESTIMATION FORMULAS Given the complexity of the various scour processes identified in Chapter 4, and the difficulty of including all of those processes in a single empirical formula, it is not surprising that current abutment scour formulas provide scour depth estimates that vary over a wide range of magnitudes. Furthermore, comparisons of abutment scour depth estimations from existing formulas with field data and with engineering experience can produce mixed results partly because of the misperception that abutment scour formulas apply to all types of abutment scour, even to the most complicated field situations, and partly due to the difficulty of estimating the flow and sediment parameters required in existing scour formulas. It is the purpose of this chapter to present several leading abutment scour formulas, classify them, assess their limitations, and evaluate their usefulness in various types of abutment scour cases. 5.1 PARAMETER FRAMEWORK While dimensional analysis provides a convenient starting point for building a framework of parameters on which abutment scour formulas depend, the specific parameter influences are somewhat less clear than in the case of pier scour. Nevertheless, identification of groups of dimensionless parameters that are used in different scour prediction formulas provides a context for classifying and assessing the applicability of the formulas. Some of the major variables affecting abutment scour in a compound channel are defined in Figure 5-1. A dimensional analysis of these variables leads to the following set of parameters:         = EEm FF m m m f f s FFc Hk k Y Y B B B B B LKK Y W Y L d LLV gY V u u Y Y γ σ µ ρϕ θ ,,,,,,,,,,,., 11 2 1 1 1 2 1 * 1* 1 2 (5.1) in which Y2 = maximum depth of flow after scour in the short contraction presented by the bridge; Y1 = upstream approach flow depth in main channel; YF = upstream approach flow depth in the floodplain; L = length of the abutment/embankment; Bf = width of the floodplain; Bm1 and Bm2 = width of the main channel in the approach flow section and the bridge section, respectively; W = width of the embankment in the flow direction; d = some measure of the sediment size forming the erodible boundary such as the median size by weight, d50; ρ and µ = density and viscosity of the fluid, respectively; V1 = approach flow velocity; u*1 and u*c = shear velocity of the approach flow and the critical value of shear velocity for initiation of sediment motion, respectively; kF and km = roughness height of the floodplain and main channel, respectively; Ks = shape factor of the abutment as it affects scour by the flow field; Kθ = embankment skewness factor as it affects scour; g = acceleration of gravity; σ = bulk shear strength of the embankment fill; γE = bulk density of the embankment material; and, HE = height of the embankment.

35 2 W Bm2Bm1 Bf V1 Floodplain Floodplain Main Channel Main Channel Y1 YF Y2 γ= skew angle Ks = shape factor kf = floodplain roughness Figure 5-1. Definition sketch for abutment terminating in a compound channel. This dimensional analysis does not fully include other scour influences identified in the previous chapter that are less amenable to quantification, such as changes in channel alignment and morphology; erosion of the abutment flank due to flow convergence or drainage; bed degradation due to anthropogenic or natural causes, and heterogeneity of sediments comprising floodplain and main channel. Major groups of dimensionless parameters affecting abutment scour are identified in Table 5-1. These parameter groups tend to overlap. For example, the relative roughness of the floodplain and main channel affect not only the flow distribution as Group G4 parameters, but also influence the magnitude of the flow intensity factors in Group G1 as a consequence. It could be argued that the Group G2 parameter is also a Group G1 parameter in so far as the abutment/embankment length represents some measure of the size of turbulent flow structures. Alternative formulations of the flow intensity factor in Group G1 are also possible such as gd Vor u VIntensityFlow s d c )1/( 1 * 1 − =≈ ρρ F (5.2) in which ρs = density of the sediment; and Fd = sediment number or densimetric grain Froude number. While the numerical values of such parameters are not the same, they measure the ratio of the velocity causing transport to a reference velocity scale associated with initiation of particle movement. The critical shear stress is preferred for characterizing the threshold of sediment motion because it depends only on sediment properties. Critical velocity, on the other hand, depends both on critical shear stress and depth of flow; it can be calculated from Manning’s equation or Keulegan’s equation for fully-rough turbulent flow. For transitional or smooth turbulent flow, an expanded equation is needed (see Sturm 2009). Applying a measured critical velocity from a laboratory flume directly to the field can lead to serious errors.

36 Table 5-1. Classification of abutment scour parameters. Dimensionless Parameter Groups Parameter Names Parameter Group Influences Comments u*1/u*c or V1/Vc, V1/(gY1)0.5, ρV1L/µ Flow intensity, Froude number, Reynolds number G1. Flow/Sediment Stage of sediment transport; effect of gravity on water surface profile; effect of flow separation & bed roughness Flow intensity indicates flow interaction with the sediment and can be used to classify clear-water vs. live- bed scour L/d Relative sediment size G2. Abutment/Sediment scale Unclear, but may be related to model scaling issue Generally not included in abutment scour formulas L/YF, W/YF, Ks, Kθ Floodplain aspect ratio; relative contraction length, abutment shape and skewness factors G3. Abutment/Flow geometry Measures abutment dimensions relative to scale of flow field, and shape and orientation of abutment relative to flow field Abutment scour formulas classified by Melville according to value of L/YF m F f FF m m m f f k k k Y Y Y B B B B B L ,, ,,, 1 1 2 1 Abutment, channel and flow length scales G4. Abutment Flow distribution Taken together, these parameters can be translated into discharges per unit width in the flow approach and contracted sections Discharge contraction ratio or qf2/qf1 determined by these parameters σ /(γE HE) Abutment stability parameter G5. Scour/Geotechnical Failure Scour that leads to slope instability Difficult to model in the laboratory Of the parameter groups listed in Table 5-1, the geotechnical stability parameter is particularly difficult to determine. While strict quality controls may be followed during construction, the mixture of soil materials comprising the embankment may be very site specific and difficult to quantify relative to erosion resistance. Scour gradually causes removal of the toe and subsequent geotechnical instability of the entire fill. In addition, the Group G4 hydraulic parameter that quantifies the change in flow distribution from the approach flow section to the bridge section conveniently encompasses the influence of many geometric length ratios, but it is nonetheless challenging to evaluate, especially with one-dimensional numerical models. In the bridge section itself, the flow contraction is not always fully developed because it is abrupt and relatively short in the flow direction so that significant streamline curvature exists. Under these circumstances, a two-dimensional model for setback abutments on wide floodplains, or even a three-dimensional model for bankline abutments may be necessary to quantify the flow distribution at the bridge section. Finally, it is paramount to have as much information as possible on the sediment itself both in the floodplain and in the main channel, and over soil formation depths commensurate with the abutment foundation depth. Spatial heterogeneity of soils and their erosion resistance is the rule rather than the exception, and a scour resistant layer can be underlain by a very erodible

37 layer or vice-versa. Fine-grained materials are often found in the river banks and floodplains while sand and gravel may form the erodible boundary of the main channel. The interparticle forces associated with fine-grained soils make evaluation of their erosion resistance particularly challenging. In some states, abutment scour countermeasures may be required as a matter of course for all abutments. Riprap aprons, concrete aprons, and guide banks are especially useful, and guidelines have been developed for their design. In the case of riprap aprons, for example, the rock size and blanket thickness, and the lateral extent of the riprap apron as it wraps around the spill-through abutment can all be specified, as can the extent of a concrete apron (Barkdoll et al. 2007, Melville et al. 2006a, b). Scour is moved to the edge of the riprap apron, and even if a portion of the apron erodes, it serves to protect against further abutment scour in the immediate vicinity of the abutment. There is a danger, however, in assuming that an apron protects an abutment from failure for all discharges. The scour hole may be moved into regions that are more easily scoured and may interact with adjacent pier scour holes depending on their proximity. For this reason, abutment scour formulas must be further developed for cases of riprap aprons in place as well as for those without such countermeasures. Channel morphologic changes are a major concern with respect to abutment scour, but they cannot be conveniently quantified in Table 5-1 nor have abutment scour formulas been developed for this case because of its complexity. River meanders gradually migrate downstream by transporting sediment from the outside of the bend to a point bar at the beginning of the next meander loop. As the outer meander loop boundaries translate laterally they can intersect the abutment and cause failure. The meander loop can also be cut off during a flood leading to a completely new channel path that endangers the bridge abutments. Braided streams are even more unpredictable as multiple channels form and interconnect thereby leaving island deposits and new flow pathways that unexpectedly form and expand in the lateral direction with each new flood. Prevention of abutment failures due to these morphologic changes requires close consultation between the hydraulic engineer and a fluvial geomorphologist such that bridge abutments are located well outside any meander belts or braided stream paths. 5.2 SUMMARY OF ABUTMENT SCOUR FORMULAS Table A-1 of Appendix A presents several abutment scour formulas in an approximately chronological order of publication. In some cases, later refinements of formulas by the same researchers are grouped together. Some of the earliest contributions to the problem of abutment scour estimation were related to research on scour around spur dikes by Garde et al. (1961) and Gill (1972), while Liu et al. (1961) reported the results of extensive flume studies on vertical wall, wing-wall and spill-through abutments in large flumes. These formulas prominently feature the scour depth nondimensionalized by the flow depth as a function of Froude number and the geometric width contraction ratio or the ratio of abutment length to flow depth. Laursen applied the early Straub (1934) solution for equilibrium sediment transport in a long contraction to abutments using his own sediment transport formula for the live-bed case. He assumed that abutment scour was some multiple of the theoretical long contraction scour. Laursen’s (1960, 1963) formulas and Gill’s (1972) formula are similar and are all based on the

38 solution to the idealized long rectangular contraction. The principal difference lies in the contraction ratios used; Gill used the full channel contraction ratio (approach channel width divided by bridge opening width), whereas Laursen used an assumed contraction width equal to the estimated scour hole width, resulting in the contraction ratio = (2.75ds+L)/2.75ds, where ds is scour depth below the undisturbed bed level. Sturm and Janjua (1994) introduced the idea of replacing the geometric contraction ratio with the discharge contraction ratio M for characterizing the change in flow rate per unit width caused by an abutment ending on the floodplain of a compound channel. This formula was further refined in Sturm (2004, 2006) by applying the relationship for the Laursen long contraction such that the independent variable became qf2/qfc in which qf2≈ qf1/M and qfc = critical floodplain velocity times the depth in the contracted bridge section of a compound channel. Extensive experiments were conducted for various abutment lengths on a wide erodible floodplain including both setback and bankline abutments. Three sediment sizes were used, and wingwall, spill-through and vertical abutments were included in the experiments. The abutments were constructed as solid-wall structures and so the results are applicable to sheet-pile foundations and other conditions for which the abutment stub and embankment are not subject to undermining. Chang and Davis (1998, 1999) presented an abutment scour methodology called ABSCOUR which has been further developed by the Maryland State Highway Administration (MSHA 2010). ABSCOUR treats abutment scour as an amplification of contraction scour. For clear- water scour, the reference contraction scour is estimated by a form of the Laursen contraction scour formula as qf2/Vc and adjusted by an abutment shape factor Ks, an embankment skewness factor, Kθ, a velocity correction factor Kv, and a spiral flow correction factor Kf.. In addition, the methodology includes an adjustment/safety factor that is based on the user’s assessment of risk and whether the floodplain is narrower or wider than 800 ft (244 m) (Benedict 2010, MSHA 2010). The velocity correction factor varies with qf1/qf2 based on potential flow theory while the spiral flow factor is intended to account for turbulence effects and is related to the approach flow Froude number based on laboratory data (Palaviccini 1993, MSHA 2010). The method is also applied to live-bed scour. The full ABSCOUR 9 computer program/methodology includes procedures to refine discharge and velocity distributions and channel setback distances under the bridge; evaluate scour in layered soils; consider the effect of pressure scour; evaluate the slope stability problem for the embankment; consider degradation and lateral channel movement and other specific concerns. The program is used to integrate contraction, abutment and pier scour and to draw a scour cross-section under the bridge (MSHA 2010). Extensive experimental work at The University of Auckland by Melville (1992, 1997) resulted in a comprehensive approach to estimating abutment scour that was integrated with earlier pier scour formulas. The Melville approach accounts not only for abutment length in ratio to flow depth but also for effects of flow intensity, bed armouring, abutment shape and orientation, relative sediment size, and channel geometry as separate multiplicative factors obtained from experiments that were conducted primarily in rectangular channels. Melville (1992) showed that his formula for maximum clear-water scour at an intermediate-length, vertical-wall abutment in a rectangular channel agrees with Laursen’s abutment scour formula. The data obtained by Cardoso and Bettess (1999) and Fael et al. (2006) have verified that the Melville formula provides an envelope relationship for the depth of clear-water scour at a vertical-wall abutment

39 in a rectangular channel for L/B < 0.4, where B is channel width. Lim (1997) and Lim and Cheng (1998b) have derived abutment scour formulas for clear-water and live-bed scour, respectively, in a rectangular channel. They assume that the flow rate through the scour hole area is the same before and after scour. Their clear-water scour formula agrees with the Melville formula and the Laursen abutment scour formula for the special case of an intermediate-length, vertical-wall abutment in a rectangular channel. The live-bed abutment scour formula developed by Froehlich (1989) and the HIRE equation are suggested in HEC-18 (Richardson and Davis 2001). Froehlich’s equation is derived from regression analysis applied to a list of dimensionless variables using laboratory data from Liu (1961), Gill (1972), and the Auckland data among other sources. The HIRE equation is based on field scour data for spur dikes in the Mississippi River obtained by the U.S. Army Corps of Engineers. Oliveto and Hager (2002, 2005) conducted extensive experiments on vertical-wall abutments in rectangular channels referred to as the VAW data set from ETH Zurich. They proposed a reference length scale for abutment scour depth to be (Y1L2)1/3 and used the sediment number (or densimetric grain Froude number), Fd, which was described in section 5.1, as the primary independent dimensionless ratio; however, their proposed formula also includes a dimensionless time so that scour depth can be estimated at different times of scour hole development. Kothyari et al. (2007) further refined this relationship by expressing it in terms of the densimetric grain Froude number written in the form (Fd − Fdc), in which Fdc = the critical value of Fd at the beginning of scour. Furthermore, an estimate of the time to “end-scour” conditions is given in terms of Fd. The essential notion underlying the scour prediction methodology proposed by Ettema et al. (2010, Project NCHRP 24-20) is that the potential maximum flow depth near an abutment due to scour can be expressed in terms of an amplified contraction scour estimated as a function of unit- discharge values for flow around an abutment. The maximum scour depth, YMAX, is given as YMAX = α YC, in which YC is the mean flow depth of the contraction scour, and α is an amplification factor whose value varies in accordance with the distribution of flow contracted through the bridge waterway, and on the characteristics of macro-turbulence structures generated by flow through the waterway. Two estimates of αYC should be considered: 1. Amplification of long-contraction scour; and, 2. Amplification of local scour estimated on the basis of the flow contracted locally around an abutment in a channel so wide that flow does not contract through the bridge waterway. The value of α should be assessed for flow contraction in the main channel (Scour Condition A) and/or near the abutment (Scour Condition B). Abutment shape, along with the aspects of channel morphology and roughness that affect flow through the bridge waterway, influence the amplification coefficient, α. The ensuing limits apply to α: 1. When the bridge waterway is contracted only locally around an abutment, and contraction scour is negligibly small in the waterway, α is large. Its value depends on the

40 local contraction of flow passing immediately around the abutment, and the turbulence structures generated by the abutment; and, 2. For a severely contracted bridge waterway, α diminishes to a value slightly above 1. At this limit, the bridge creates a substantial backwater effect that impounds water. The bed shear exerted by highly contracted flow is much larger than the erosive forces exerted by turbulence structures generated by the abutment. In some ways, such extreme contraction is similar to scour at a bottomless culvert. In developing relationships for estimating the scour depths incurred with Scour Conditions A and B, it is convenient to adapt and extend Laursen’s well-known methods for estimating live-bed contraction scour (Laursen 1960), and for clear-water contraction scour (Laursen 1963). His methods are useful for directly identifying the main parameters associated with abutment scour, though they neglect the influence of macro-turbulence. Other contraction-scour methods could certainly be used. The proposed formulation assumes live-bed scour conditions for flow in the main channel, and clear-water scour conditions for flow over the floodplain. The relationships apply to scour of cohesive as well as non-cohesive bed and floodplain boundaries. It is noted that slightly different relationships are given for Scour Conditions A and B. An important consideration in the method proposed by Ettema et al. is the need to take into account the actual manner in which most abutments are constructed; i.e., as an abutment column set amidst an earthfill embankment whose length varies widely in accordance with site conditions. Consequently, geotechnical failure of the embankment is an important aspect of abutment scour, and may limit its development. Geotechnical failure is not a desirable condition, but it occurs frequently for abutments, sometimes leading to flow breaching of the earthfill embankment at abutments as shown previously in Figures 3-1 and 3-2. Ettema et al. also propose a geotechnically based approach for estimating scour depth. This approach is not reliant upon the need to estimate a critical value of erosion resistance for the boundary around an abutment. The approach requires instead an estimate of the geotechnical strength of the earthfill embankment at the bridge waterway. Also, Ettema et al. give a relationship for estimating Scour Condition C, scour depth at an exposed abutment column. A further consideration in choosing abutment scour formulas is the case of predicting scour depth and possible embankment failure when armor protection and an apron have been applied to an embankment. Van Ballegooy (2005) conducted an extensive set of experiments concerning riprap and cable-tied-block (CTB) protection at spill-through and wing-wall abutments. The findings are presented in Melville et al. (2006a, 2006b), as well as in Van Ballegooy (2005). For spill-through abutments, it is shown that armor protection (including apron protection) acts to deflect the scour development a sufficient distance away from the abutment toe that damage is prevented. With increasing toe protection (i.e. increasing apron extent), the scour hole at spill- through abutments sited in the flood channel typically is deflected further away from the abutment and reduces in size. However, for abutment and compound channel configurations where the scour hole forms close to the main channel bank, the scour hole can increase in size as the apron extent is increased. CTB mats allow scour holes to form closer to the abutment, compared to scour holes at abutments protected by equivalent riprap aprons, and result in deeper scour holes. It is axiomatic that wider apron protection is needed to give a certain level of

41 protection, when using CTB compared to riprap aprons. Equations are given to predict the scour depth for spill-through abutments, situated on the flood plain of a compound channel, and the minimum apron width to prevent undermining of the toe at spill-through abutments. A design methodology is proposed for evaluation of the stability of spill-slope fill material at spill-through abutments in terms of the extent of apron protection, and is presented in Melville et al. (2006a, 2006b) and Van Ballegooy (2005). For wing-wall abutments, it is shown that the scour under mobile-bed conditions is directly related to the level of the deepest bed-form trough that propagates past the abutment, which is predictable using existing expressions, together with any localized scour that may occur (Melville et al 2006a, 2006b, and Van Ballegooy 2005). Stones on the outer edge of riprap aprons tend to settle and move away from the abutment pushing the erosion zone further away from the abutment. Conversely, CTB mats remain intact during settlement. The outer edge of the apron settles vertically, allowing the scour to occur closer to the abutment face than for an equivalent riprap apron. Equations are given for prediction of the minimum apron width remaining horizontal after erosion. These predictions, together with prediction of apron settlement, facilitate assessment of the stability of an abutment structure. Briaud et al. (2009) have developed a formula for abutment scour in a compound channel with pure porcelain clay as the sediment and with solid abutments. Experiments were done in a compound channel and a rectangular channel. The ratios of flow depth in the floodplain to that in the main channel, however, were greater than 0.5 so that compound channel effects on the velocity distribution were minimal. The main channel velocity never exceeded the floodplain velocity by more than about 10%. Each experiment was run for more than 10 days, and the abutment scour holes developed usually at the toe of the abutment on the downstream side. The scour formula developed from the data indicates that the maximum abutment scour depth depends on the difference between 1.57 times a flow Froude number near the toe of the abutment and a critical value of the flow Froude number, where “critical” refers to initiation of scour. The reference velocity in the Froude number is determined as the mean velocity in the bridge opening for bankline abutments, and as the mean velocity of the upstream floodplain flow if it were to pass entirely through the floodplain in the contracted section for set-back abutments. The physical significance of Froude number alone when formulating a relationship for scour depth seems somewhat problematic when scour is dominated by flow separation and macroturbulence. Froude number effects are often neglected for small values (considerably less than one); the approach flow Froude numbers in the experiments were of the order of 0.25. It is interesting that the resulting scour formula for cohesive sediments underpredicted the scour data of Sturm (2006) while overpredicting the scour in the database used by Froehlich (1989) in noncohesive sediments; that is, the cohesive sediment scour depths stayed within the bounds of those measured for noncohesive sediments for solid abutments. The maximum scour depth formula by Briaud et al. is part of a larger procedure that involves testing a sediment sample in a pressurized duct flow to determine erosion rate as a function of shear stress (erodibility curve). The critical shear stress is taken as the hydrodynamic stress corresponding to a very low erosion rate of 0.1 mm/hr. The maximum shear stress before scour at an abutment is estimated based on a Reynolds number that uses the mean approach velocity as the velocity scale and the width of the abutment as the length scale. For this maximum shear

42 stress, the initial erosion rate is determined from the erodibility curve. Then the maximum scour depth and initial erosion rate are substituted into a standardized hyperbolic time development curve to obtain the scour depth for a specific duration of storm, or for a specified time history of flow taken over the life of the bridge. 5.3 CLASSIFICATION OF SCOUR FORMULAS Because existing scour formulas apply to different types of abutment scour situations and rely on different classes of basic parameters on the one hand, and may not apply at all to some cases of abutment scour such as those due to stream morphology changes on the other hand, it is worthwhile to classify the formulas in several different ways. Furthermore, it is imperative that abutment scour formulas not be applied outside the range of variability of the basic dimensionless parameters for which they were derived. In carrying out such a classification exercise, it may be possible to develop a hierarchical approach in which classes of scour formulas are first matched with the type of abutment scour to be expected in a given project, then tested against the range of dimensionless parameters to be experienced in the field, and finally accepted or rejected on the basis of their applicability. In some instances, and especially if more adverse consequences and a resultant higher risk are involved relative to possible bridge failure by scour, it may become clear that no existing formula is acceptable. In this case, combinations of numerical and hydraulic modeling may be needed. In addition, abutment scour formulas that apply when scour countermeasures such as abutment riprap aprons are in place may be required as discussed in the section on further research. 5.3.1. Classification by Parameter Groups Most of the abutment scour formulas presented in Table A-1 utilize dimensionless parameters from one or more of the groups of parameters in Table 5-1. All formulas except those based only on vertical-wall abutments incorporate a shape and orientation factor from Group G3 parameters in Table 5-1. Only the procedure by Ettema et al. (2010) has suggested a geotechnical parameter such as in Group G5 in the table. Ettema et al. argue the importance of considering how abutments are built. A risk in comparing the formulas is that some formulas are developed for quite different abutment structures. Practically all the formulas developed prior to Ettema et al. are based on models that assume abutments to be pier-like structures extending as solid forms deeply into the bed or floodplain of a channel such as would be the case for sheet-pile foundations. The vast majority of abutments are built as earthfill embankments at or surrounding a pier-like abutment column. Formulas are placed into categories in Table 5-2 according to the dominant parameter groups from Table 5-1 that are incorporated into them. A major category of formulas (C1) includes L/y1 from Group G3 and some flow parameter such as F1, and/or Fd or V1/Vc from Group G1. This category includes the formulas by Laursen, Liu, Froehlich, Melville, Lim, Cardoso and Bettess, and Fael et al. which were developed primarily from experiments in rectangular laboratory flumes with relatively short abutments. Note that the live-bed scour formulas in this group tend to include F1, while the clear-water scour formulas incorporate V1/Vc or a similar parameter. As argued by Laursen, the live-bed case is based on equilibrium sediment transport rate, not the relative stage of incipient sediment motion in the approach flow as for clear-water scour. These

43 formulas essentially treat abutments as a “half pier” for small value of L or as a wide pier in shallow flow for larger values of L. Table 5-2. Formulas categorized by parameter groups. Formula Category Parameter Group G1 Flow/Sed G2 Abut/Sed G3 Abut/Flow Geometry G4 Abut/Flow Distribution G5 Scour/Geotech Failure C1 Laursen, Liu, Froehlich, Melville, Lim, Cardoso & Bettess, Fael et al. X X C2 Oliveto & Hager, Kothyari et al., Briaud et al. X C3 Garde et al., Liu, Gill, Sturm, Chang & Davis, Ettema et al. X X C4 Ettema et al. X The formulas by Oliveto and Hager (2002), and by Kothyari et al. (2007) are in a related but second category (C2) because of the inclusion of the sediment number, or densimetric Froude number, from Group G1 parameters, while the abutment length and flow depth are combined into a reference length scale to nondimensionalize scour depth rather than appearing separately as L/y1 from Group G3. The appearance of a dimensionless time in this category of formulas also sets them apart from the first category. The Kothyari et al. (2007) formula introduces (Fd − Fdc) as the primary independent parameter; that is, an excess value of Fd relative to a critical value akin to a sediment transport formula even though it is intended for clear-water scour. However, the critical value is estimated at the contracted section from the geometric contraction ratio so that Fd >Fdc. The formula by Briaud et al. (2009) for maximum scour depth might also be placed in this second category only because it is based on an excess value of the flow Froude number relative to a critical value in the contracted section. The abutment length appears in this formula only as an abutment location correction for abutments very close to the bank of the main channel. A third category of formulas (C3) is one that uses some measure of the flow contraction caused by the bridge (Parameter Class G4). Formulas by Garde et al., Liu, and Gill are for rectangular channels and contain a geometric contraction ratio. The formula by Sturm replaces the geometric contraction ratio with a discharge contraction ratio, which is more appropriate for compound

44 channels, to obtain the discharge per unit width in the contracted section in ratio to its critical value, q2/qc. The scour methodology of Chang and Davis (1998, 1999) utilizes q2/q1 as an independent variable for live-bed scour and q2/Vc for clear-water scour. Ettema et al. directly employ the ratio q2/q1 and embed the effect of V/Vc in the reference contraction scour depth for the clear-water case. Ettema et al. also use the live-bed contraction scour as a reference length for live-bed abutment scour in the main channel (Scour Condition A) for bankline abutments. A significant difference in the data obtained by Ettema et al. is that it was taken for an erodible abutment/embankment instead of a rigid one which sets this formula apart from the others in this respect. In addition, their unique methodology for evaluating hydraulic scour and geotechnical failure in a combined design process has been identified as Parameter Class G5 in Table 5-2. 5.3.2. Classification by Channel Type and Bridge Crossing When considering scour at bridge abutments, a diverse range of situations is possible based on the geomorphic type of channel that a bridge must cross. The following three classes of bridge crossings encompass most actual cases and provide a useful classification. First, the description of each type of crossing is given, and then abutment scour formulas appropriate for each class are given. 1. Class I: Shorter crossings over incised channels Class I refers to narrower bridge crossings of incised channels, where the channel is reasonably well represented by a rectangular channel. This class also includes narrow crossings for conditions up to bank-full flows. Some examples are shown in Figure 5-2. At Class I bridge crossings, bridge foundations may be single or multiple span. The bridge abutments are typically located at the channel bank. From the perspective of abutment scour analysis, many such sites can be considered to have essentially no flood channels. Vertical wall abutments, with or without wing-walls, are common. The abutment column may be founded on piles, or a slab footing, in which case undermining of the abutment structure by scour is a common type of failure. Alternatively, a protective wall (e.g., sheet- piling) may be constructed below the abutment structure, effectively extending the non- erodible abutment surface deeper into the underlying bed material. Outflanking of the abutment column, due to lateral channel migration and/or flow skewness at the abutment, is also common. 2. Class II: Wider crossings over compound river channels Class II refers to wider bridge crossings, where the channel is typically compound, comprising a main channel and wide flood channels. At such sites, significant flows may be diverted from the flood channels towards the main channel at the bridge section. Some examples are shown in Figure 5-3.

45 (a) (b) Figure 5-2. Bankline abutment in a narrow channel. (a) (b) Figure 5-3. Bridge crossing for a compound channel. At Class II bridge crossings, bridge foundations are typically multi-span. The bridge abutments are usually located on the flood channels, and may be near to the main channel bank or set back from it. From the perspective of abutment scour analysis, such sites exhibit significant flow diverted from the floodplain towards and into the main channel at the bridge section. Spill-through abutments, with or without countermeasure protection to the embankment slopes and toe, are common. Toe protection may be a protective apron or sheet-pile protection, or equivalent. The abutment column may be founded on piles, or a slab footing, in which case undermining of the abutment structure, due to slope failure initiated by scour at the toe of the embankment by scour, is the common type of failure.

46 3. Class III: Wider crossings over braided river channels Class III refers to bridges spanning wide braided river channels, where the river channel can be approximated by a rectangular channel under extreme flood flow conditions. At such sites, the bridge foundations may be significantly skewed to the flow at lesser flood flow conditions. An example is shown in Figure 5-4. At Class III bridge crossings, bridge foundations are usually multi-span. The bridge abutments may be located at the channel bank or extend into the channel. In the latter case, significant flow contraction may occur. Spill-through abutments, with or without countermeasure protection to the embankment slopes and toe, are common. Toe protection may be a protective apron or sheet-pile protection, or equivalent. The abutment column may be founded on piles, or a slab footing, in which case undermining of the abutment structure, due to slope failure initiated by scour at the toe of the embankment by scour, is the common type of failure. Figure 5-4. Bridge crossing of a braided channel. Class I and Class III are the simplest situations to model in the laboratory and many of the existing laboratory data apply to these two classes which can be modeled approximately as rectangular channels. It is important to recognize, however, that nearly all known data in these two classes were collected using rigid abutment models extending below the maximum measured scour depth. Equations derived from such data give the “maximum possible” scour depth that can occur and should then be conservative for design. Such equations are not suitable for prediction of scour depths that develop where undermining of the pile cap or slab footing occur, because slope failure may then limit further scour.

47 The following equations in Table A-1 may be considered applicable for estimation of “maximum possible” scour depths at non-erodible abutments/embankments at Class I and Class III crossings: • Liu et al. (1961) • Garde et al. (1961) • Laursen (1960, 1963) • Gill (1972) • Froehlich (1989) • Melville (1992, 1997) • Lim (1997, 1998b) • Oliveto and Hager (2002, 2005) • Fael et al.(2006) If the abutment/embankment structure is erodible, then the formula by Ettema et al. (2010) is also applicable to this case and would correspond to Scour Conditions A and C. Class II crossings are the most difficult to predict because of the interaction between the main channel and floodplain flows and the resultant redistribution of the flow in the contracted bridge section depending on how much of the floodplain flow is blocked by the embankment. As a result, Class II crossings are further sub-classified according to the three scour types identified by Ettema et al. and discussed in the following section. 5.3.3. Classification by Scour Condition in Class II Compound Channel The following three scour conditions can occur in a Class II compound channel as described in more detail in Section 4.1. They were classified by Ettema et al. (2010) and lead to abutment scour being defined on a continuum of relative importance of local flow constriction due to the abutment versus channel-wide flow contraction as a result of increasing lengths of the embankment. • Scour Condition A. Scour of the main-channel bed, when the floodplain is far less erodible than the bed of the main channel. This condition can lead to instability of the main channel bank and the abutment embankment which collapse into the scour hole. This scour condition is usually live-bed scour in the main channel. • Scour Condition B. Scour of the floodplain around the abutment. This condition can be equivalent to scour at an abutment placed in a rectangular channel, if the abutment is set back far enough from the main channel, but the distance required is not well defined. As the amount of bed-sediment transport on a floodplain usually is quite low, this scour condition usually occurs as clear-water scour. For an erodible embankment, it can be undercut and fail by collapsing into the scour hole. • Scour Condition C. Scour Conditions A and B may eventually cause the approach embankment to breach near the abutment, thereby fully exposing the abutment column. For this condition, scour at the exposed stub column essentially progresses as if the abutment column were a pier. For the same reasons as given for Condition B, this scour condition usually occurs as clear-water scour.

48 To these three scour conditions, a fourth might be added: • Scour Condition AB. This condition is a combination of A and B in which the floodplain as well as the embankment is erodible, and the scour hole on the floodplain can extend into the main channel. The following equations in Table A-1 may be considered to apply to Class II crossings, with boundary material as specified: • Cardoso and Bettess (1999) – rigid, with relatively narrow flood channel • Melville (1992, 1997) - rigid • Van Ballegooy – erodible with protection • Ettema et al. – erodible • Richardson and Davis (2001) – HIRE equation, based on field data • Laursen – rigid • Briaud – rigid (clay) • Sturm - rigid 5.4. EVALUATION OF ABUTMENT SCOUR FORMULAS From the foregoing classifications of existing abutment scour formulas, it appears that no single formula can apply to all possible cases of abutment scour, and in fact, none of the equations apply to the more difficult geomorphic transformations characteristic of meandering and braided streams. Nevertheless, it is useful to evaluate existing formulas in order to identify those that may provide promise and direction or even a framework for future research. For this purpose, the following criteria were established for evaluating abutment scour formulas: 1. Adequacy in addressing parameters that reflect important physical processes governing abutment scour; 2. Limitations of formulas in design applications with respect to ranges of controlling parameters on which they are based; 3. Categorization and acceptability of laboratory experiments and research methods that led to the development of the formula (e.g., experimental duration, variety of particle sizes and types of sediments, realistic geometries and scales, characterization of flow field, degree of idealization, large database) 4. Attempts to verify and compare formulas with other lab data and field data, if any, with which a valid comparison can be made; 5. Applicability and ease of use for design (notably, as recommended in AASHTO Standard Specifications for Highway Bridges) 5.4.1. Parameter Groups With respect to parameters included in an abutment scour formula, it was shown in Section 5.3.1 how different parameters can be used to reflect the same physical process such as the approach flow conditions in clear-water scour. Parameters that utilize critical velocity as opposed to critical shear stress must include the flow depth because velocity alone is insufficient to characterize the propensity to transport sediment and generate scour.

49 Abutment scour formulas that were developed from experiments in rectangular channels must be used very carefully in compound channel flow. The geometric contraction ratio does not properly represent the flow contraction effect in a compound channel. Furthermore, the abutment must be set well back on the floodplain from the main channel in order to apply a rectangular channel formula; or more precisely, the amount of floodplain flow blocked by the embankment must be small in comparison to the total flow. Thus, geometric criteria based on the values of L/Bf and Bf/Bm are useful, but they may not be sufficient. In addition, the floodplain flow depth relative to the main channel depth is an important criterion to consider in terms of the degree of interaction of floodplain and main channel flows. Interactions become less important as Yf/Y1 >0.5. A discharge contraction ratio is a better measure of the flow redistribution from the floodplain to the main channel as the bridge opening is approached. The geotechnical parameter measuring embankment stability does not appear explicitly in any of the formulas, but the procedure recommended by Ettema et al. includes a check of embankment stability in addition to predicting the depth of scour. Finally, the inclusion of d50 as the sole measure of grain stability is conservative in that it does not account for the armoring effect. For pure clays, grain size is not necessarily the correct parameter to determine critical shear stress although it may be important in some coarser soil mixtures. 5.4.2. Limitations and Databases of Abutment Scour Formulas The ranges of dimensionless parameters to which several abutment scour formulas apply are given in Table 5-3. The dependent parameter of ds/Y1 is related to Y2/Y1 as Y2/Y1 = ds/Y1 + 1 only if the change in velocity head and the head loss between the approach flow and contracted sections can be neglected. This is generally true only if the flow is decidedly subcritical; that is, if the Froude number is relatively small. Backwater effects can also become important at higher values of the undisturbed approach flow Froude number as embankment length increases. The classification scheme of Melville (1992) based on L/Y1 is useful in comparing the applicable ranges of different abutment scour formulas: 0 < L/Y1 < 1 Short abutments similar to pier obstructions 1 < L/Y1 < 25 Intermediate length abutments 25 < L/Y1 Long abutments Only a few of the formulas in Table 5-3 include experiments with abutments in the “long” category. This classification scheme should be accompanied by one that measures the flow distribution between floodplain and main channel in compound channels; Bf /Bm and L/Bf are not quite sufficient in this regard as discussed in Section 5.4.1. It is important to distinguish between clear-water scour and live-bed scour because the required parameters are different as discussed previously. Only a few formulas are applicable to both cases. The Melville formula accomplishes this by using a different function for the flow intensity factor in clear-water and live-bed scour, while the formulation by Ettema et al. is referenced to a contraction scour depth that is computed by different principles for the two cases.

50 Table 5-3. Limitations and experimental databases of abutment scour formula. METHOD Dependent Variable Primary Independent Variables. LIMITS CMPD. -C RECT. -R CLEAR WATER; LIVE- BED d50 mm Time hr Garde et al. (1961) ds /Y1 F1, m = (B – 2L )/B 0.1 < F1 < 0.4 0.5<m<0.9 R CW 0.2, 0.45, 1.0, 2.25 3-5 Liu et al. (1961) CSU ds /Y1 F1, L/Y1 0.3 < F1 < 1.2 1 <L/Y1 < 10 R LB 0.56 5-150 Liu et al. (1961) CSU ds /Y1 F1, m 0.1<F1<0.6 0.5<m<0.9 R CW 0.56, 0.65 -- Laursen (1963) ds /Y1 L/Y1, u*/u*c Liu (CSU) data R CW -- -- Gill (1972) ds /Y1 Y1/d, m, τc/τ1 20<Y1/d<90 0.6<m<0.9 R CW, LB 0.9, 1.5 6 Froehlich (1989) ds /Y1 Ks, Kθ, F1, L/Y1, Y1/d, σg Liu,Garde, Gill, Auckland data R CW -- -- Froehlich (1989) ds /Y1 Ks, Kθ, F1, L/Y1 Liu, Garde, Gill data R LB -- -- Melville (1992) (1997), Melville and Coleman (2000) ds /Y1 Ks, Kθ, L /Y1, L /d, σg , V1/Vc , KG 1 <L/Y1 < 69 0.7<V1/Vc<6.4 R, C CW, LB 0.9 50-200 HIRE(2001) Y2/Y1 Ks, Kθ, Fab L/Y1 > 25 C LB Field Lim (1997) (1998) ds /Y1 L/Y1, u* /u*c Gill, Liu, Cunha, Auckland R CW LB Cardoso & Bettess (1999) ds /Y1 L/Bf Yf /Bf 0.2< L/Bf<1 3< L/Yf < 20 Bf /Bm=0.5 0.4<Yf /Y1 <1.0 C CW 0.84 6-120 (Teq) Sturm (2004, 2006) ds /Y1 Ks, qf1/(Mq0c) where M=(Q−Qobst)/Q q0c = Vc Yf0 qf1 = Vf1 Yf1 12 <L/Y1 < 80 0.17<L/Bf<1. 0.2<Yf /Y1<0.5 Bf /0.5Bm= 6.7 0.26<M<0.90 C CW 1.1, 2.7, 3.3 20-60 Maryland Chang & Davis (1998, 1999), MSHA (2010) ds ds Ks, Kθ, q2/q1, F1 Ks, Kθ, q2/Vc , F1 Compared with Sturm (2004) lab data in HEC-18; SC field data in Benedict (2010) R, C R, C LB CW -- -- Oliveto & Hager (2002, 2005) ds/dR dR= (La2Y)1/3 Fd, σ, T 1.5< Fd <3.7 R CW 0.6-5 6-330 Fael et al.(2006) ds /Y1 (ρs/ρ−1), L/Y1 9<L/Y1 < 36 V1/Vc ≈1.0 L/B < 0.4 R CW Quartz – 1.3 Pumice – 1.2 20-120 Ettema et al. (2010) Y2/Yc A: q2/q1, α B: qf2/qf1, α α=amplification 0.2<L/Bf<2 0.23<Bf/0.5Bm<1 R, C LB CW 0.45 4-24 Briaud et al. (2009) ds /Y1 (1.57 F2 − Fc)0.7 0.5<L/Bf<1 (Compound) 0.28<L/B<0.75 (Rectangular) 3<L/Y1 < 8 0.48<Yf /Y1<0.67 Bf /0.5Bm=2 R, C CW Porcelain clay 320

51 The duration of scour experiments has been discussed extensively in the literature. In general, live-bed scour experiments approach an equilibrium state, albeit with fluctuating bedforms, in a relatively short period of time compared to clear-water scour which only approaches equilibrium in an asymptotic manner. Formulas have been developed for estimating the time to equilibrium for abutment scour (Coleman et al. 2003). The result differs with flow intensity and the relative shallowness of the flow blocked by the embankment. The time to reach equilibrium in the experiments of Briaud et al. (2009) on pure clay is exceedingly long because of the time required to break the inter-particle bonds of the clay structure. Some of the formulas in Table 5-3 are based on a relatively small number of experiments, while others have a robust database that includes wide ranges in values of the various independent parameters. The experimental databases of Liu et al. (1961), Melville (1992, 1997), Sturm (2004, 2006), Oliveto and Hager (2002, 2005) and of Ettema et al. (2010) include large numbers of scour experiments, for example. 5.4.3. Comparisons of Abutment Scour Formulas To evaluate abutment scour formulas, it is necessary to compare the scour predictions of leading formulas with experimental data of other studies, provided that the comparisons are made for similar ranges of the governing parameters. Comparing a live-bed abutment scour formula with clear-water abutment scour data is not necessarily valid, for example. In addition, it must be recognized that comparisons between scour data for erodible abutments and foundations versus solid abutments and sheet pile foundations will likely produce different results, but in this case, it may be informative to explore how much different the scour depth predictions are with all other factors being equal. Comparisons of various abutment scour formulas must also take into account the inherent uncertainty in the data and the confidence limits of the formulas. The study by Sturm (2004), for example, shows that most of the data fall within limits of ±25% of the best-fit relationship for maximum scour depth. Similarly, Oliveto and Hager (2002, 2005) report limits of ±30% for their extensive data set, although their comparisons for dimensionless scour depth include dimensionless time as an additional independent variable. Abutment scour data at a spill-through abutment in a laboratory compound channel are compared in Figures 5-5 and 5-6 with predictions from the formulas proposed by Sturm (2004, 2006) and Melville and Coleman (2000, also see Melville 1997) in Figures 5-5 and 5-6, respectively. For the abutments considered, riprap protection extended below the level of the floodplain so that the abutment was less likely to erode. Reasonable agreement between the data and the Sturm formula is shown in Figure 5-5. In Figure 5-6, the envelope lines given by Melville and Coleman are in good agreement with the data when the scour hole is located on the floodplain but underestimate the data for a scour hole extending from the floodplain into the main channel. It could be argued that the Melville and Coleman (2000) formula applies to a setback abutment for shallow flow in a wide floodplain, because it does not explicitly include the effect of flow contraction.

52 Figure 5-5. Comparison between scour data at a spill-through abutment (with riprap protection extended below the surface of the floodplain) and the formula by Sturm and Chrisohoides (1998a, see also Sturm 2004, 2006). Reproduced from NCHRP Report 587 by Barkdoll et al. (2007). Figure 5-6. Comparison between scour data at a spill-through abutment (with riprap protection extended below the surface of the floodplain) and the formula by Melville and Coleman (2000, essentially the same formula as proposed by Melville, 1997). Reproduced from NCHRP Report 587 by Barkdoll et al. (2007).

53 Ettema et al. (2010) have compared their data with the ABSCOUR formula for clear-water abutment scour depth (Chang and Davis 1999, MSHA 2010). Although both approaches use contraction scour depth as a reference depth, Ettema et al. concluded that there are significant differences in the adjustment factors in the two formulas. ABSCOUR includes a velocity adjustment Kv, which is given as a function of q1/q2 and is derived for potential flow, and a spiral flow adjustment Kf determined as a function of approach flow Froude number. On the other hand, the Ettema et al. adjustment factors for flow concentration and turbulence are combined into one factor given in a design curve as a function of q2/q1. As a result, the asymptote of YMax/YC in ABSCOUR for large values of q2/q1 tends to be controlled by the value of Kf and thus the Froude number, while the design curve by Ettema et al. approaches a value of unity as abutment scour becomes increasingly dominated by channel flow contraction. Although the ABSCOUR methodology limits the values of Kf to a range of 1.0 to 1.4, the laboratory studies by Kerenyi et al. (2007) on bottomless culverts show that Kf is not a function of Froude number. Likewise, application of the Maryland formula to the field clearwater abutment scour data of Benedict (2003) shows that the spiral flow factor appears to have no statistically significant dependence on Froude number (Benedict 2010). Briaud et al. (2009) have compared their method for prediction of maximum scour depth with the data envelopes developed by Ettema et al. (2010) for erodible embankments in Scour Condition B as shown in Figure 5-7. Briaud et al. assumed a rectangular channel and made calculations from their formula for three velocity ratios (V1/Vc = 1.0, 0.95, 0.75) and for a spill-through as well as wing-wall abutment. Good agreement is obtained at the peak of the Ettema et al. curve for the spill-through abutment, but for both abutment shapes, the Briaud et al. formula shows a more gradual decrease in YMAX/YC with q2/q1. At q2/q1 = 4, the Briaud et al. formula predicts a relative abutment scour depth that is approximately 2.5 times greater than the Ettema et al. value for wing-wall abutments and approximately 1.8 times greater for spill-through abutments. .In large part, the difference can be attributed to the difference in model abutments used. Briaud et al. use a pier-like abutment whose solid body extended at depth into the boundary. As scour developed at such an abutment, flow can entrench around the solid abutment form. Ettema et al. use erodible abutments prone to failure as scour deepens. An important consideration in the development of scour is the strength of the earthfill embankment.

54 Figure 5-7. Comparison of Briaud et al. (2009) formula with experimental results of Ettema et al. (2010) for Scour Condition B. [Reproduced from Briaud et al. (2009). Final design curves are Figs. 12.3 and 12.4 of the NCHRP 24-20 report by Ettema et al. (2010)] The abutment scour formula of Melville (1992, 1997) and the abutment scour data from Sturm (2004, 2006) are shown in Figure 5-8 in comparison with the data from Ettema et al. (2010) for Scour Condition B. The Melville formula is plotted on these axes by using the Laursen assumption that the flow contraction takes place at the end of the abutment in a flow width of 2.75ds. Experiments show that this width is actually variable; a flow width of 3.5ds is shown in the figure for a slightly better correspondence with the data, but the main purpose here is only to place into perspective the Melville formula and the Sturm data, which are both for solid abutments with sheet pile foundations, relative to the Ettema et al. data for a riprap-protected embankment on an erodible floodplain. The reference to “long” and “intermediate” length abutments in the figure is according to the classification by Melville (1992). The data from Sturm (2006) have been adjusted to apply for V1/Vc = 1.0 in agreement with the Melville curves

55 shown in the figure. It is interesting to note that both the Melville formula and the Sturm data for YMAX/YC follow the same trend of an increase to a maximum relative scour depth followed by a gradual decrease as q2/q1 increases. The peak occurs at q2/q1 = 1.5−2 in comparison to a value of 1.25 from the Ettema et al. data. The most useful insight is perhaps that the maximum value of YMAX/YC for the solid abutment with sheet pile foundation is approximately 6.5 in comparison with the Ettema et al. value of 2.5 for a riprap-protected but erodible embankment. Evidently, the manner of abutment construction plays an important role in the development of scour and the depth attained. It would appear that the solid abutment holds the vortex system in place relative to the abutment with scour progressing downward unimpeded by riprap rolling into the scour hole and limited in horizontal extent by deposition downstream. The scour depths indicated by the Sturm (2004, 2006) data and Melville (1997) curves provide an upper limit because they apply to a solid abutment while conceivably embankments of greater strength or more conservative riprap design than in the Ettema et al. experiments could be represented by intermediate curves in Figure 5-8. This is a matter for further research. 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 q f 2/q f 1 Y m ax /Y fc Sturm - ST; Long; 0.32<=La/Bf<=0.65 Sturm - ST; Long; 0.88<=La/Bf<=1 Sturm - WW; Long; 0.44<= La/Bf<=0.61 Ettema et al. B - ST Ettema et al. B - WW Melville - Long; V1/Vc = 1.0 Melville Intermediate, V1/Vc=1.0 ` Figure 5-8. Comparison of Melville (1997, also Melville and Coleman 2000) formula and Sturm (2004, 2006) data for rigid abutments with Ettema et al. (2010) data for erodible embankments and Scour Condition B. Ettema et al. (2010) have further considered the limiting cases of an abutment approaching zero length in a floodplain of fixed width versus an abutment of fixed length in a floodplain of increasing width as shown in Figure 5-9. In the latter case, the limiting condition is a scour depth that is greater than the contraction scour depth because it is governed by the local turbulence and flow separation associated with the abutment obstruction and flow concentration alone. Further research is needed to define this limiting case.

56 Figure 5-9. Scour depth trends for Scour Condition B. (Ettema et al. 2010). Comparisons between leading scour formulas and field data are more challenging than for the laboratory case. Mueller and Wagner (2005) compared measured contraction and abutment scour depths in the field with predictions from formulas recommended by HEC-18 and concluded that the formulas do not account for the complexity of flow conditions in the field. Comparisons by Wagner et al. (2006) between abutment scour formulas and field data generally showed large overpredictions by several abutment scour formulas including those by Froehlich, Sturm, and the HIRE equation. In some cases, the formula by Sturm predicted abutment scour depths that agreed with the field data within the ±25% uncertainty of the formula, most notably on the Pomme de Terre River in Minnesota, while predictions were excessive on the Minnesota River near Belle Plaine, Minnesota. In the latter case, a skewed crossing with two small radius meanders immediately upstream of the bridge resulted in a very complex flow field (see Figure 5-10). In other cases, the field data included silt or silty sand with some clay content at the bridge crossing which makes the estimation of critical velocity a challenge. Unfortunately, such complex field situations are not uncommon.

57 Figure 5-10. Minnesota River near Belle Plaine, MN for 2001 flood. (Wagner et al. 2006). Other important issues to be considered when comparing abutment scour formulas with field data are the different mechanisms associated with scour at abutments. Besides considerations of embankment strength, time of measurement of scour, and location of maximum scour depth, abutment scour often is associated with lateral shifting of the approach channel. Comparisons between measured post-flood scour depths at bridges in South Carolina with several abutment scour formulas have been reported by Benedict et al. (2007). In most cases, the hydraulic variables used in the scour formulas were assumed to be those calculated for the 100 year flood without knowledge of the actual flow conditions that caused the scour. In a smaller number of cases, measured flood discharges were available. Excessive abutment scour depth estimates were given by the Sturm formula due in part to the fact that critical velocities were estimated by the equation given in HEC-18, which is valid only for coarse sediments. Approximately two-thirds of the sediment samples at the South Carolina sites, especially in the Piedmont, were fine-grained sediments exhibiting cohesive characteristics according to the classification by Benedict et al. (2007). In further examination of the sensitivity of estimated scour depths to critical velocity, Benedict (2010) concluded that significant errors in existing scour prediction formulas, when compared to field data, may occur because of poor definition of this parameter. In addition, the long time duration required to reach equilibrium scour in cohesive soils calls into question the advisability of direct comparisons of predictions of equilibrium scour formulas developed for coarse-grained soils with scour data for cohesive soils.

58 5.4.4. Ease of Use of Abutment Scour Formulas Ease of use of abutment scour formulas is a function of how easily and how accurately the important parameters can be estimated. The critical velocity or shear stress is of paramount concern in clear-water scour formulas, while the estimate of flow-field parameters such as velocity and discharge per unit width in the approach flow and in the contracted bridge section are important in both clear-water and live-bed scour. In the former case, relationships for critical velocity may be misapplied, and so further education is needed in this regard; however, the inescapable inference is that better methods are needed with respect to making initial estimates of critical velocity or critical shear stress in the case of fine-grained sediments. Adequately characterizing the required flow-field parameters for any of the abutment scour formulas that have been discussed is also a challenging problem. One-dimensional methods such as HEC-RAS leave much to be desired, but they are preferred with respect to rules of thumb in estimating flow distribution at a bridge, for example. Two-dimensional methods require experienced users for calibration and can be an improvement to 1D methods in the hands of experienced users. For the case of a bankline abutment, even 3D methods with standard turbulence models are available now. The difficulty of estimating critical shear stress/velocity and flow-field parameters responsible for scour makes it unlikely that any one scour formula holds any advantage over others in terms of ease of use and accuracy of application. In fact, the estimation of representative values for these two classes of parameters is a limitation of all the methods discussed. 5.5 GEOTECHNICAL APPROACH Given the difficulty of applying abutment scour formulas and the rather common geotechnical failure of the embankment, an additional consideration might be to use the geotechnical approach to scour estimation along with the leading abutment scour formulas. One point of view is that methods based solely on hydraulic considerations give “potential scour depths” in the absence of embankment failure. Often, as evident in the field, the abutment embankment fails before the potential depth is attained. A direct geotechnical estimate entails the following considerations (Figure 5-11): 1. Embankment failure back to the abutment column defines maximum scour depth; failure opens the flow area, relieves flow; and, 2. Determination of values of internal resistance angle, θS, of the embankment and floodplain materials. Further details are given by Ettema et al. (2010).

59 (a) (b) Figure 5-11. Scour depth estimation based on geotechnical stability of embankment; (a) variables, (b) failure of embankment past abutment column relieves flow so that maximum scour depth is attained (Ettema et al. 2010).