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

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83 APPENDIX A Table A-1. A selection of abutment scour formulas (revised and extended from Melville and Coleman 2000). Reference Formula Notes Garde et al. (1961) δ 1 1 F      − Γ= LB B Y ds Γ and δ are given as functions of the drag coefficient of the sediment Laursen (1960)         −      += 11 5.11 75.2 7.1 111 Y d Y d Y L ss Applies to live-bed scour at an abutment encroaching into the main channel Laursen* (1963)               −             + = 1 1 5.11 75.2 5.0 1 6/7 1 11 c s s Y d Y d Y L τ τ Applies to clear-water scour at an abutment encroaching into the main channel τ1 = grain roughness component of bed shear stress; τc = critical shear stress Liu et al. (1961) 33011.1 4.0 11 . Y L Y d s F      = Applies to live-bed scour at spill- through abutments; F1=V1/(gY1)0.5 Liu et al. (1961) 330115.2 4.0 11 . Y L Y ds F      = Applies to live-bed scour at wing-wall or vertical-wall abutments Liu et al. (1961) β1 1 5.12 F= Y ds Applies to clear-water scour at vertical-wall abutments; β=contraction ratio Gill (1972) 7/3 11 /17/6 25.0 11 2 1375.8 −       +      −      = τ τ τ τββ ccm Y d Y Y Y2 = flow depth at bridge ≈ Y1 +ds Equation given at the threshold condition Sturm and Janjua (1994)       −= 35.07.7 1 cf s MY d F F F1=Froude number of the approach flow upstream of the abutment; Fc=critical Froude number for initiation of motion; M=Qo/Qtot, Qo=portion of approach flow in bridge opening width, Qtot=total flowrate Froehlich (1989) (HEC-18) 61.0 43.0 27.2 F        = f s f s Y LKK Y d θ Applies to live-bed scour; Yf=average depth of flow in the floodplain; F=Ve/(gYf)0.5, Ve=Qe/Ae, Qe=flow obstructed by the embankment, Ae=flow area corresponding to Qe Richardson and Davis (2001) (HIRE) 33.0 1 1 27.7 FθKKY d s s = Applies when L/Y1>25, and for conditions similar to field conditions from which equation was derived Melville (1992, 1997) d K K K K K Ks yL I d s G= θ KYL=2L L/Y1<1 KYL=2(Y1L)0.5 1<L/Y1<25 KYL=10Y1 L/Y1>25 Lim (1997, 1998b) )29.0( 1 −Χ= s s K Y d Applies to clear-water scour 219.09.0 5.0 1 25.0 1 5075.0375.0 −                 +             =Χ − Y L Y d dc Fθ θc = Shields entrainment function Fd = densimetric Froude number

84 Reference Formula Notes Lim ( ) L s L s d L YL Y d Χ      +++Χ + =      + 3/2 1 3/4 1 1tan1 /2.11 2 1 φ Applies to live-bed scour       −=Χ 2 1* 2 *1 u u c L = live-bed parameter Cardoso and Bettess (1999) )( ff s Y Lf Y d = Melville and Dongol curves form envelope for 3<L/Yf < 20 Clear-water scour; wide main channel relative to floodplain Sturm (2004, 2006)         −= 4.014.8 00 1 0 fcx f f s YMV q Y d Clear-water scour; qf1=Vf1Yf1; M=Qo/Qtot, Qo=portion of approach flow in bridge opening width, Qtot=total flowrate;Vx0c = critical velocity in floodplain for setback abutment and in main channel for bankline abutment; Yf0 = undisturbed floodplain flow depth; Yf1 = approach floodplain flow depth Chang and Davis (1998, 1999), MSHA (2010) FSY q qKKKYKKd adj K vpfss         −      = 0 1 2 1 2 θ Live-bed FSY V qKKKKKd adj c vpfss         −      = 0 2857.0 θ Clear-water ds =scour depth; Y0adj = flow depth at bridge before scour; Y1= approach flow depth; Ks= shape factor; Kθ = skew factor; Kp = pressure flow factor; Kf = spiral flow adjustment factor; Kv = velocity adjustment factor; K2= sediment transport factor (0.637-0.857); q2 = unit discharge in bridge section; q1 = unit discharge in flow approach section; FS = calibration/safety factor Oliveto and Hager (2002,2005 ); Kothyari et al. (2007) TK L d dgs R s log068.0 5.15.0 F−= σ T L d dcdg R s log)(272.0 3/25.0 FF −= −σ Clear-water scour; LR = (Y1La2)1/3; Ks = 1.25 for rect. abutment; σg = geometric st. dev. of sediment; Fd = densimetric grain Froude no. = V1/(g′d50)0.5; T = t/tR ; tR = LR/[σg1/3(g′d50)0.5]; g′=g(ρs−ρ)/ρ Fael et al. (2006)       −= 11 1 Y L Y d ss ϕ ρ ρ Function given graphically and combined with Dongol’s data to give ϕ = 2−6 for 1<L/Y1<100 and V/Vc≈ 1 Ettema et al. (2010)       = 1 2 q qf Y Y c MAX (erodible embankment)         = 1 2 f f fc MAX q q f Y Y (erodible embankment) Scour condition A in main channel; Yc = flow depth of live-bed contraction scour in main channel; q2, q1 = discharge per unit width in contracted and approach sections of main channel Scour condition B in floodplain; Yfc = flow depth of clear-water contraction scour in floodplain; qf2, qf1 = discharge per unit width in contracted and approach sections of floodplain Briaud et al. (2009) 7.0 2 1 )57.1(5.6 cplss KKKKY d FF −= θ Y1 = flow depth upstream from the toe of the abutment; F2 = Froude no. at the toe of the abutment =V2/(gY1)0.5; Fc = critical Froude number at the toe of the abutment =Vc/(gY1)0.5 Equations are given for V2 and Vc

85 APPENDIX B Table B-1. A selection of contraction scour formulas (B1 = approach flow channel width; B2 = contracted channel width; Y1 = approach flow channel depth; Y2 = contracted channel depth after scour) Reference Formula Notes Straub (1934) 7/3 2 1 1 2 11 7/6 2 1 1 2 1 22 −                 −+      +      = B B B B Y Y ccc τ τ τ τ τ τ Live-Bed Scour; τc = critical shear stress; τ1 = approach flow shear stress. Based on DuBoys bedload transport formula Laursen (1960) 21 1 2 2 1 7/6 1 2 pp c t n n B B Q Q Y Y                   = Live-Bed Scour; Qc = approach flowrate in main channel ; Qt = total flowrate through bridge opening main channel; n = Manning’s resistance coefficient; p1, p2 = exponents from Laursen’s total sediment transport formula depending on whether sediment load is mostly bedload, mixed load, or mostly suspended load; B1 = approach main channel width; B2 = bridge main channel width. Laursen (1963) 7/3 1 7/6 2 1 1 2             = cB B Y Y τ τ Clear-Water Scour. Shear stress in contracted section equal to the critical shear stress τc at equilibrium Komura (1966) 5/1 1 3/2 2 151 1 1 2 45.1 −      = g / B B Y Y σF Live-bed 2/1 1 3/2 2 151 1 1 2 60.1 −      = g / B B Y Y σF Clear-water Live-Bed and Clear-Water Scour. F1 = approach flow Froude number; σg1 = geometric standard deviation of sediment size distribution in approach channel. Includes effect of armoring in contracted section. Gill (1981) 7/3/1 2 1 11 7/6 2 1 1 2 1 −                     −+      = β τ τ τ τ B B B B Y Y cc Live-Bed Scour. Sediment transport rate assumed proportional to (τ − τc)β Lim and Cheng (1998a) 75.0 2 1 1 2       = B B Y Y Live-Bed Scour. Sediment transport rate assumed proportional to (V – Vc)4 Compared with lab data for both live-bed and clear-water scour. Briaud et al. (2005)        −=      c unif s B B Y d FF1 2 1 1 31.141.1       −=      c s B B Y d FF1 2 1 max1 38.190.1 3/ 1 >BLc Clear-Water Scour of Porcelain Clay. unif = uniform scour depth; max = maximum scour depth; F1 = approach flow Froude number; Fc = Froude number with critical velocity

86 Reference Formula Notes Dey and Raikar (2005) 26.1 2 1 19.0 1 5055.0 1 1 368.0             = − B B Y d Y d e s F Clear-Water Scour (0.9<V1/Vc<1.0) F1e = (V1 – V1c)/[(SG – 1)gY1]1/2 ; SG = specific gravity; V1c = approach flow velocity when V2 = Vc at beginning of scour HEC-18 Richardson and Davis (2001) p B B Q Q Y Y             = 2 1 7/6 1 2 1 2 Live-Bed 7/3 2 2 3/2 2 2 2       = Bd QKY m u Clear-Water Live-Bed formula is the same as Laursen (1960) with the ratio of Manning’s n removed; p = sediment transport factor = 0.637-0.857. Clear-Water formula is derived from Y2 = q2/Vc and it is different in form, but not in principle, from Laursen (1963) because it does not involve the approach flow section. Ku = 0.025 (SI); 0.0077 (EN); dm = 1.25 d50

87 APPENDIX C RESEARCH PROBLEM STATEMENTS C.1 INTRODUCTION This appendix provides brief problem statements for the research needs and associated design- related research tasks listed in Tables 8-1, 8-2, and 8-3 of Chapter 8. The problem statements comprise short outlines indicating the purpose of the research needed. They can be used to develop project scope and objectives. C.2 RESEARCH REGARDING ABUTMENT-SCOUR PROCESSES The ensuing problem statements elaborate the research needs in Table 8-1. Research Need L1: Laboratory experiments to fill knowledge gaps identified in this report. These are divided into subprojects but could easily be incorporated into a single project. a. Additional experiments on realistic abutment foundation structures with and without countermeasures and on methods of modeling embankment material Most investigations of abutment scour have used rigid abutment/embankment models. Ettema et al. (2010) were the first to use erodible embankment models in a comprehensive laboratory study of abutment scour. As shown in Figure 5-8, scour depths at rigid models extending deep into bed material are typically significantly greater than those measured by Ettema et al. (2010) using erodible models. Additional data are needed using an experimental methodology based on that developed by Ettema et al. The experiments of Ettema et al. (2010) featured a sand bed main channel and both rigid and sand floodplains. Similarly, rigid and erodible (sand) spill-through abutment models were tested; these represented the limiting cases of non-erodible and very erodible materials. Methods are available to develop better ways of modeling the channel bank, floodplain and spill-through slope fill materials, to facilitate more realistic laboratory modeling of the erodibility of such materials and thereby, more realistic simulation of field situations. In particular, the experiments would use a suitable range of shear strength values for the bed and bank materials, with shear strength being appropriately scaled according to the length scales for the models. The research would include a representative range of realistic abutment models for both wing-wall and spill-through abutments, and abutment/embankment models with and without armor protection, with a specific focus on toe protection of embankment slope armor.

88 b. Geotechnical stability of embankments exposed to abutment scour Most cases of abutment failure attributable to scour show a geotechnical failure of the earthfill embankment associated with the abutment. The abutment column typically remains standing. Because spill-slope failure increases the flow area through a bridge waterway, and deposits material in the scour area, the maximum scour depth attainable at an abutment, and damage sustained by an abutment, appears to be limited by the geotechnical stability of an abutment’s earthfill embankment. However, the relationship between scour and geotechnical stability of a spill-slope or embankment has never been investigated. There is a need to address the following aspects: 1. Comprehensively define the essential geotechnical aspects associated with scour of spill-through abutments; 2. Show if and how embankment stability limits scour depth; and, 3. Define the conditions requisite for partial failure as opposed to complete failure c. Experiments on intermediate length erodible embankments between bankline and short embankments for which compound channel effects are important Following the successful completion of Research Need L1, or as part thereof, additional data are needed for the case where the abutment is sited on the floodplain with setback distances in the approximate range of 0.4< La/Bf <1.0, such that the scour process is influenced by both main channel and floodplain flows. Current ad-hoc methods and even HEC-RAS are insufficient to properly predict the distribution of flow between the floodplain and main channel in the contracted section on which abutment scour, as related to contraction scour, depends. These experiments should include an erodible embankment and should be accompanied by at least 2D numerical methods, or possibly by 3D methods, to develop a relationship for q2/q1 in terms of the geometric and flow variables on which it depends. The numerical model should include modeling of the free surface as well as a state-of-the art turbulence sub-model. Once verified by the laboratory experiments, the numerical model can be used to generate a much broader array of results than is possible by experiments alone. d. Experiments on the limiting case of a short abutment in a wide channel Following the successful completion of Research Need L1, or as part thereof, additional data are needed for the case where the abutment is sited on the floodplain of a wide channel with relatively large setback distances, such that negligible contraction scour occurs for flow passing through the bridge waterway, and abutment scour is attributable to the flow field generated by the abutment. This abutment situation corresponds to the shaded area in Figure 5.9. For such relatively short abutments scour results from flow contraction locally around the abutment, and turbulence structures generated by flow around the abutment.

89 Research Need L2: Overtopping of embankments and abutment scour under pressure scour conditions Within the context of climate change and more commonly occurring pressure scour and overtopping events, experimental research is needed on abutment scour for these flow conditions with realistic compound channel geometry and erodible embankments. Even with riprap protection, the abutment is subject to catastrophic failure under this combination of flow types, especially for moderate to small setback distances from the main channel. The experimental program should include a range of values of relative flow depth on the floodplain with a realistic tailwater curve for the proposed compound channel geometry. Free surface flows that occur prior to submergence of the bridge opening should be included in the experimental program for comparison with the pressure flow and overtopping cases. It is essential to pinpoint the flow conditions for which maximum scour depth occurs in order to develop an assessment of the vulnerability of existing bridges to failure and to devise design criteria for new bridges under climate change scenarios. Research Need FS1: Field studies with continuous hydraulic and scour monitoring that assess uncertainties in measurement and that can be compared with laboratory physical models Simultaneous measurement of bed elevations and the flow field are possible with in situ sensing devices that record the data and transmit it for real-time bridge monitoring on the internet . Sites without a large number of complicating factors could be identified, and full reliable data sets of simultaneous hydraulic conditions and bed elevations could be obtained to better understand field scaling issues and the simultaneous interaction of various scour processes driven by the hydrodynamics of the flow. This research would be targeted at specific bridges from which the most useful data sets could be obtained for verification of abutment scour formulas. Research Need N1: Sound use of 2D (depth-averaged models) for determining flow distribution through bridge waterways for the short term combined with 3D CFD models and laboratory turbulence measurements to shed further light on hydraulic model scaling issues for the long term. Immediate need exists for informed use of the best possible 2D numerical models, including appropriate turbulence submodels, to develop flow-field parameters needed in the unified scour estimation technique outlined in this report. The most important parameter needed in the short term is the distribution of the discharge per unit width in the bridge contraction section. Extensive opportunities also exist for hybrid modeling (laboratory hydraulic modeling and numerical modeling) to elucidate the flow structure around the various forms of abutment. The brunt of this effort will need to be completed using numerical models because they best reveal the three-dimensional and unsteady features of flow around abutments, particularly those at abutments with solid-wall foundations. Connection of the turbulent structure with appropriate dimensionless variables would allow improved representation of the complex flow fields of the prototype in a physical laboratory model and point the way toward future handling of the more difficult prototype abutment scour problems involving complex flow fields.

90 Research Need N2: Education of engineers concerning limitations of 1D abutment scour estimation formulas and the potential and applicability of 2D and 3D numerical modeling in combination with physical modeling Implementation of advanced numerical models requires commensurate education of modelers. Because turbulence is inherently three-dimensional, engineers require basic instruction in the structure of turbulence and how it is modeled in 3D numerical models followed by an introduction to the simplifications concomitant with 2D and 1D numerical models. There is considerable need for engineers to use 2D (depth-averaged flow) numerical models for assessing flow conditions at bridge waterways. The optimal use of such models (their configuration, capabilities, and limitations) has yet to be adequately determined. Various turbulence submodels should be discussed along with issues of grid generation, boundary conditions, discretization techniques, flow resistance, calibration, and verification. In concert with this effort, physical models and their principles should be taught to encourage the hybrid use of physical and numerical models to resolve the most complex bridge abutment scour problems. Significant potential exists for 3D numerical models to illuminate flow field conditions at abutments. However, further work (and advances in computer technology) is needed to bring such models to a level that they can be used for performing parametric studies on scour processes, and for design purposes. C.3 RESEARCH TASKS RELATED TO ABUTMENT DESIGN The ensuing problem statements elaborate the research tasks given in Table 8-2. The task aim at satisfying the research needs listed in Table 8-1. Task 1. Determine if and how the ABSCOUR method (MSHA 2010) and that proposed by Ettema et al. (2010) can be merged and further developed. From diagnostic field studies determine method veracity. ABSCOUR (MSHA 2010) and the hydraulic method proposed by Ettema et al. (2010) share the concept that abutment scour is fundamentally an amplification of contraction scour. The two methods have similarities in formulation and prompt the question as to whether they could be developed further as a single method better reflecting improved understanding of scour as amplification of abutment scour. This research effort entails additional critical review of the two methods, and transition to an updated method to be validated using laboratory and field data. Task 2. Further develop and check the validity of the geotechnical approach to estimating scour depth. From diagnostic field studies determine method veracity. On the basis of the geotechnical stability of the earthfill embankment at an abutment, Ettema et al. (2010) propose a comparatively simplified formulation for estimating abutment scour depth; if indeed further research shows that a simplified formulation is feasible. Further research is needed to validate or improve upon the formulation, exploring its utility as a practical method relating abutment scour depth to the shear strength of the abutment’s earthfill embankment. The

91 relationship would provide a useful check on scour depth estimated using hydraulics-based methods for scour-depth estimation. Task 3. Ascertain how the methods in Tasks 1 and 2 apply to, or should be adjusted for, embankments under pressure scour conditions and possibly over-topping. From diagnostic field studies determine method veracity. The situation termed pressure scour may occur commonly at bridge abutments. Accordingly there is a need to determine how the leading methods for estimating abutment scour depth apply during pressure scour situations. When feasible, conduct diagnostic field studies to determine method veracity. Task 4. Refine the methods in Tasks 1 and 2 for the limiting case of short abutment as the channel becomes very wide. From diagnostic field studies determine method veracity. The scour estimation formulations described in problem statements E1 and F1 should be examined for the limiting condition indicated by the shaded area in Figure 5-9. Of interest is whether the formulations can be extended for use for short abutments. The necessary research entails the execution of laboratory flume experiments and verification using field data. Task 5. Determine the extent to which the methods proposed by Sturm (2006) and Melville (1997) can be merged and further developed for solid-wall abutments. From diagnostic field studies determine method veracity. The estimation methods proposed by Sturm (2006) and Melville (1997) were developed for estimating scour depth at solid-wall abutments. Both methods contain parameters reflecting scour processes. The question to be investigated is whether they could be developed further as a single method best reflecting improved understanding of scour. This research effort entails additional critical review of the two methods, and transition to an updated method to be validated using laboratory and field data tailored to the types of abutments for which they were developed. This effort could also be unified with the method developed in E1. Task 6. Ascertain how the methods in Task 5 apply, or should be adjusted, for embankments under pressure scour conditions and possibly over-topping. From diagnostic field studies determine method veracity. The situation termed pressure scour may occur commonly at bridge abutments. Accordingly there is a need to determine how the leading methods for estimating abutment scour depth apply during pressure scour situations. When feasible, conduct diagnostic field studies to determine method veracity. Task 7. Determine how the methods in Tasks 1 and 5 should be adjusted, for embankments fitted with scour countermeasures, notably an armored apron around the abutment toe or sheet-pile skirt. From diagnostic field studies determine method veracity.

92 The inclusion of a countermeasure such as an apron or skirt alters abutment form. As such countermeasures often are recommended for use in abutment design, the scour-estimation methods mentioned for research topics E1 and F1 should be adjusted for abutment forms that include them. The necessary research entails a series of laboratory tests to determine the adjustments. Task 8. Estimation of contraction scour and its amplification at an abutment will be enhanced when a 2-D flow model is used to determine peak values of flow velocity, unit discharge or shear stress in the vicinity of an abutment, especially if the abutment is located in a channel of irregular geometry. Two-dimensional, depth-averaged flow models can be used to study the distribution of flow around abutments situated in compound channels and rectangular channels (flow on very wide floodplains may be treated as rectangular channels). Research is needed to acquire useful insights regarding distributions of flow velocity, unit discharge, and boundary shear stress at abutments. Estimation of the peak magnitudes of flow velocity, boundary shear stress, and unit discharge is of substantial importance for design estimation of scour at bridge abutments. Research also is needed to show how abutment flow fields adjust in response to variations of abutment length, floodplain width, and main channel dimensions, and identify trends regarding the magnitude of amplification factors for depth-averaged velocity, unit discharge, bed shear stress, and distance to peak unit discharge. C.4 RESEARCH NEEDS REGARDING ABUTMENT MONITORING AND MAINTENANCE The ensuing problem statements elaborate the research needs in Table 8-3. I1-a. Instrumentation and techniques for remote-sensing of abutment and bridge waterway state, and for accessible data and image storage. Research is needed on innovative instrumentation and techniques to facilitate image-processing software to readily quantify and document waterway features in the vicinity of bridge abutments, possibly including the free-surface velocity distribution near abutments. The research could use images acquired from close range with conventional photographic techniques. The images can be rectified before mapping the characteristic elements of the banks and floodplain. Methods like Particle Image Velocimetry can used to estimate the surface velocities in the stream. The instrumentation and software exist today to enable highly versatile techniques for conducting routine bridge inspections, providing quantitative information for a variety of geomorphic and hydraulic waterway parameters. Periodic inspections at bridges followed by processing of the acquired images can provide convenient and accurate means for tracking temporal changes in abutment state and channel conditions at an abutment.

93 I1-b. Instrumentation for monitoring embankment soil condition. There is a need to have effective instrumentation for monitoring the strength of embankment soil, especially over time. Instrumentation developed for monitoring slope-stability conditions should be considered for application to bridge abutments whose embankments require monitoring or are of uncertain strength. I1-c. Low-cost instrumentation and techniques for small bridges or bridges in regions with limited resources to monitor bridges. The majority of bridges are small bridges, whose number exceeds the capacity of agencies to monitor. Additionally, there are many bridges in regions inadequately resourced to monitor bridge conditions. There is considerable need to develop instrumentation and techniques that facilitate relatively easy and inexpensive monitoring of bridges. Routine monitoring of bridge abutments potentially can avert avoidable failure. I2-a Instrumentation for obtaining waterway bathymetry data during flood flows. A major difficulty in developing and verifying methods for design estimation of abutment scour is obtaining bathymetric and flow data during flood-flow conditions. Considerations such as access, safety, and flow-induced loads contribute to the difficulty. Yet, such data and observations are needed to check scour-depth magnitudes and trends obtained from laboratory flume tests and numerical models. In conjunction with IR1 above, good prospects exist for extending various forms of remote-sensing techniques to assist in this regard. I2-b. Instrumentation for monitoring embankment soil parameters during flood hydrograph passage. In line with problem statement IF1, there is a similar need for instrumentation for monitoring embankment soil condition during flood hydrograph passage. Information from such instrumentation will assist diagnostic analysis of embankment failure during abutment scour. I3. Training of appropriate staff to conduct monitoring activities, and complete effective abutment maintenance. Advanced or new instrumentation and techniques for monitoring require suitably educated staff for successful implantation. M1. Innovative efficient methods for repairing, stabilizing, or replacing weakened components of abutments (e.g., strengthening weakened spill-slope soil at abutment column) There is considerable scope for developing various methods for repairing, stabilizing or replacing components of abutments. It is anticipated that effective methods will be developed from technologies used for bank stabilization under diverse circumstances.