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110 CHAPTER 7 PROPOSED DESIGN METHODOLOGY 7.1 Introduction This chapter proposes a structured methodology for design estimation of pier-scour depth. The methodology, introduced in Chapter 2, is structured in terms of pier size and shape complexity, as well as site complications. It takes into account the primary parameters determining the scale of scour depth (Chapter 4), recognizes the difficulties introduced by site complications (Chapter 5), and works within the limitations of the leading predictive methods to estimate scour depth (Chapter 6). The design methodology seeks to determine the potential maximum scour depth at a pier site. It does not aim at accurate prediction of scour depth for prescribed combinations of parameters, as would a scientifically oriented relationship aimed at close expression of parameter trends. The potential maximum scour depth is the deepest possible scour associated with the flow field generated at a pier. Two length scales (effective pier width, and approach flow depth) determine the structure of the pier flow field in turbulent open- channel flow and, thereby, the potential maximum depth of scour. The actual scour depth attained depends on the erosion characteristics of the foundation material at a pier. The methodology does not rely on a single, basic equation for scour-depth estimation, but instead comprises several approaches graduated in accordance with pier shape and size, as well as site complications. It does, though, include such an equation for design estimation of scour depth for simpler pier shapes; Eq. (6.8). As pier size increases for a given flow depth and boundary material, pier flow field and scour capacity alter. Larger piers more commonly are less cylindrical in pier-column form and have more complicated foundations (e.g. more supporting piles). Moreover, such piers typically are in the transition- or wide-pier categories for scour (Chapter 4). It soon becomes infeasible to use a single basic equation for accurate estimation of scour depth for all pier sites. Figures 1-2 and 1-3, illustrations of example long- and short- bridge sites, respectively, give a sense of the variability of pier sites. The potentially large number of variables involved, and the multiple influences that some parameters exert on pier flow field, can reduce estimation accuracy quickly. 7.2 Structured Design Methodology The proposed design methodology assigns four levels of complexity, as outlined in Table 7-1. The levels relate to effective pier form, and thereby the complexity of the scouring flow field: 1. Simple, single-column pier forms in the narrow- and transition-pier categories usually cylindrical, for which the influences of the primary parameters identified in Chapter 5 are well defined and can be addressed reasonably well by means of an empirical equation framing the influences. The term âreasonably
111 well,â here, implies that a clear quantitative relationship for scour-depth exists. Chapter 6 identifies and discusses the two leading equations for this purpose. 2. Common pier forms as commonly prescribed for ranges of bridge span and load. It is normal (e.g., most state departments of transportation in the U.S.), for pier forms and dimensions to be reasonably common. Such pier forms typically consist of a column on a pile cap supported by piles, or on a footing; in some designs, the bridge deck may be supported directly on a pile cap. More shape parameters need to be considered (e.g., spacing of piles), and the parameter influences become less independent as the pier flow field becomes more complex. To a certain extent, scour at these pier forms can be addressed using an empirical equation, when reliable pier-shape factors exist. If reliable shape factors do not exist, empirical equations may yield approximate scour-depth estimates that then should be verified with results from a hydraulic model (i.e. system simulation). In the future, scour depth estimates may be feasible by means of proven numerical models. 3. Common pier forms in complicated situations notably caused by the presence of debris or ice accumulation, the close proximity of an abutment, or possibly by channel morphology or geology issues. These pier situations can be addressed using the results from system simulation (hydraulic models, later numerical models), with some rationalization of parameter influences for the pier form under consideration. An approximate estimate of scour depth could be obtained by applying an adjustment factor to a basic, empirical equation. Considerable uncertainty attends such an estimate, however. 4. Complex or uncommon pier forms and situations where the influences of major parameters are insufficiently clear. These situations require a system simulation (holistic) approach to scour-depth estimation (analyzing the whole flow and erosion system at a pier, rather than analyzing individual parameter influences successively). Simulation is needed, by means of hydraulic-models and/or numerical models. The prospects for substantial developments in hydraulic modeling and numerical modeling must be considered for this component of the graduated approach. The proposed methodology reflects the pier situations shown in Figures 1-2 and 1-3, which respectively illustrate the pier supports for a long multi-span bridge and a shorter, three-span bridge. The central pier in Figure 1-2 could be considered a fairly simple pier in isolation, but the local flow fields at other piers are to varying extents affected by flow around the abutments and over the channelâs floodplain. The two piers in the shorter bridge (Figure 1-3) cannot be considered in isolation, and are markedly affected by flow around the abutment and over the floodplain. Similar illustrations can be prepared illustrating piers of more complex construction. No single existing method of scour estimation applies accurately to all pier situations.
112 A structured design methodology is not new. It is fairly normal for difficult or complex pier circumstances to receive additional design attention by means of hydraulic modeling, and possibly numerical modeling. However, the structured design approach proposed here formally outlines a more graduated set of considerations to be followed than is given in existing design guides for pier-scour estimation, such as the guides given by HEC-18 or AASHTO. At bridge sites where large uncertainties attend pier scour, considerable reliance must be placed upon effective monitoring of pier site conditions. Design uncertainties may arise with uncertain changes in channel morphology, the possible construction of other engineered works (e.g., another bridge nearby), the erosion characteristics of bed or floodplain material, unclear combination of scour processes, and the development of scour over time. In addition, as described in Section 7.3, measured conservatism should be used in the design estimation of scour depth. .
113 Table 7-1 Structured design approach Pier Form and Situation Estimation Method 1. Simple pier forms in flow- field categoriesâ ⢠Narrow pier ⢠Transition pier Empirical equation: Transition from Richardson and Davis (2001) to Sheppard et al. (2011, NCHRP Project 24-32) 2. Common pier forms in flow- field categoriesâ ⢠Narrow pier ⢠Transition pier Empirical equation; and, possible resort to a hydraulic model to reduce design uncertainty 3. Common pier forms at complicating sites subject to in flow-field categoriesâ ⢠Narrow pier ⢠Transition pier Empirical equation; and, increased resort to a hydraulic model to reduce design uncertainty
114 4. Complex or unusual pier forms, including ⢠wide piers Resort to a hydraulic model, with possible use of a numerical model (system simulation) For wide piers, use empirical equation developed for wide- pier flow field 7.3 Uncertainty and Conservatism in Design Estimation Design estimation of scour depth at a pier site often entails significant uncertainty regarding the accurate accounting of parameter influences possibly determining scour depth. It reduces when design estimation focuses on the primary parameters determining the potential maximum scour depth at a pier site, and parameters leading to lesser scour depths need not be addressed. This focus introduces a measured, reasonable level of conservatism into design estimation of scour depth, because it indicates the scour depth magnitude that could be attained at a particular pier site. However, while reasonable conservative estimates presently can be made for piers in the narrow- and transition-pier category (y/a exceeding about 1.0 and 0.5, respectively), such estimates become increasingly conservative and unreliable for piers in the wide-pier category. Uncertainty in scour-depth estimation arises from several sources: 1. Changes in flow pier flow field, as characterized in terms of the primary parameters involving pier diameter y/a* and a*/D; 2. Pier site complications, such as inadequate definition and quantification of foundation material erodibility, and as a consequence of debris or ice accumulation; and, 3. The time development of scour introduces significant uncertainties associated with duration of flow conditions and variations in rate of foundation material erosion. For live-bed conditions, an additional source of uncertainty relates to estimation of bedform (dune) amplitude at a pier site, and how to account for bedform amplitude when estimating scour depth. Bedform amplitude depends on approach flow depth and velocity, and varies as they vary. This source of uncertainty is addressable in terms of
115 reliable bedform estimation, and linearly combining bedform amplitude with estimated pier scour depth. For piers in the narrow-pier category, pier flow field scales with pier width, irrespective of waterway boundary material. Therefore, an approximate upper-bound estimate of scour depth can be obtained by relating maximum scour depth to pier width. The extensive body of laboratory data from model cylindrical piers points to a maximum scour depth of approximately 2.5 times the effective diameter of a cylindrical pier. Therefore, a reasonable, conservative estimate of maximum scour depth is ysMAX /a* = 2.5 (7.1) in which the effective pier width, a*, includes factors accounting for pier shape and orientation. Eq. (7.1) is useful as setting an upper-bound magnitude for envisioning scour at simple cylindrical piers. At some pier sites, changeable flow orientation introduces uncertainty into this estimate. It should be noted that Eq. (7.1) is based on data obtained for small, laboratory-scale piers subject to a scale effect attributable to inadequate scaling of turbulence structures in the pier flow field (Section 4.4.5). It also envelops all known reliable field data. For Eq. (7.1), the condition y/a* > 0.2 should prevail; i.e., design scour conditions place piers in the narrow- and transition-pier categories. As y/a* decreases below the narrow-pier limit (in practical terms, as pier size increases), Eq. (7.1), becomes increasingly conservative. The estimate given by Eq. (7.1) may still be acceptable for piers with the transition pier category (0.2⤠y/a* ⤠1.4), though it increasingly becomes unrelated to the flow field associated with Eq. (7.1) and, thereby, conservative. It completely loses physical meaning for piers in the wide-pier category, because the pier flow field is substantially different than the narrow-pier flow field. For a wide pier, scour predominantly occurs by virtue of flow contraction around the pier flanks, and the erosive influence of turbulence structures at the pier flanks and wake. Scour depth varies with the extent to which flow must contract as it passes around the pier; with scour at each flank becoming practically equivalent to scour at an abutment (or caisson) with a solid deep foundation, such as sheet-piling. At present, there is no upper- bound limit for wide piers comparable to Eq. (7.1). Melville (1997) proposes a design relationship based on curve fitting of laboratory data, but it is insufficiently corroborated for use in estimating an upper-bound scour depth; the relationship, elaborated in Table A- 1, is ys = 4.5y. The structured design methodology in this chapter aims to provide reasonable conservatism in scour-depth estimation for piers in the narrow- to transition-pier categories (or common pier forms in straightforward situations), but also places increased reliance on holistic simulation, and on bridge monitoring for more complex situations. Formal risk-assessment analysis of pier scour is described by Johnson (1994, 1995), and is the subject on NCHRP Project 24-34, Risk-Based Approach for Bridge Scour Prediction, currently underway.
116 7.4 Single-Column Piers in the Narrow- and Transition-Pier Categories Cylindrical pier forms are piers of a single cylindrical body whose flow field comprises the fully developed features illustrated in Figure 3-4 for a single circular cylinder, or a pair of such cylinders as depicted in Table 7-1. This category includes slender elongated piers reasonably well aligned with the flow. The main features of the flow field are well understood, though exactly how the flow field changes with changes in the parameters y/a* and a*/D remains inadequately understood, and quantified, for the purpose of quantifying the erosive forces that the flow exerts on foundation material. The designer estimating scour depth at a pier site should determine the potential maximum depth of scour associated with a given flow field as scaled in terms of effective pier width (a*), flow depth (y), and flow intensity at the site (V/Vc ). A lesser depth can be selected for design use at the designerâs discretion. Doing so entails considering additional parameter influences, and increases design uncertainty. The ensuing thoughts attend this approach: 1. Design estimation must account for the influences of the primary parameters, especially the geometric scale parameter y/a*, and parameters defining an effective pier width, a*; 2. Design estimation recognizes that substantial uncertainty and variability exists for parameters at pier sites. The length-scale parameter y/a* typically is relatively fixed, and has minimal uncertainty for most bridge waterways; 3. Substantial uncertainty occurs in determining, and in actual variations of, V/Vc ; 4. Design estimation of a potential maximum scour depth averts the uncertainties associated with the temporal development of scour; and, 5. There is a mild difference between the potential maximum scour depth for clear- water and live-bed scour conditions, though the latter requires accounting for the additional foundation exposure caused by bedforms on the approach bed. In accordance with these design considerations, design estimation of scour for narrow- and transition-pier categories would proceed as indicated in Figure 7-1. An envelope resides around the clear-water and live-bed scour conditions. The envelope position varies with y/a* and a*/D. If the influence of a*/D is not considered, the envelope lowers with decreasing y/a* for the transition- and wide-pier categories.
117 Figure 7-1 Envelope of potential maximum scour depth for clear-water and live-bed scour conditions at piers The evaluation presented in Chapter 6 indicates that two existing rational methods empirically best reflect, at this point in time, the scour-depth variations for the narrow- and transition-pier categories: Richardson and Davis (2001), the method currently used in HEC-18; and, the Sheppard et al. method (2011) as developed in NCHRP Project 24-32. Either of these methods yields credible scour depth estimates for pier sites in the narrow- pier category and subject to clear-water conditions. The methods are well-correlated to the extensive data available for such sites. Of the two methods, however, the Sheppard-Melville method better reflects flow-field changes and thereby scour processes, as expressed in terms of the parameters of primary importance, and therefore is more readily extended to the transition- and wide-pier categories; i.e., it more expressly includes the length scales, y/a* and a*/D, and includes the flow intensity parameter, V/VC . Additionally, it is the method developed (with funding for NCHRP 24-32) in an effort to account for flow-field adaptation to variations of y/a and a/D. A useful aspect of the Sheppard-Melville method is that it can be simplified to reflect potential maximum scour depth associated with the three pier flow- field categories (narrow, transition and wide). A weakness in the Richardson and Davis (2001) method is that it does not. A further weakness is that it uses y/a rather than y/a*. For design estimation of a potential maximum scour depth at a pier site, the Sheppard- Melville method can be simplified so as to avert the uncertainties associated with the parameters V/Vc and a*/D. The simplification relates potential maximum scour depth to the parameter of prime importance, y/a* for clear-water and live-bed scour. In terms of estimating a potential maximum scour depth, related to the scale of the pier flow field, the Sheppard-Melville method, Eq. (6.8), simplifies to *a y tanh2.5 *1 5.2* 4.0             ï£ ï£«=    ï£ ï£«= a yf a sy (7.2)
118 This equation can be used for piers founded in sediment or cohesive soil, and subject to the narrow- and transition-pier flow fields. The designer can use Eq. (6.8) if wishing to account for the influences of a*/D and V/Vc . The designer, however, must recognize the uncertainties introduced with consideration of these parameters. The Richardson and Davis (2001) method (Eq. 6.1) does not lend itself to this simplification in terms of y/a*. Therefore, it is less suited for design estimation of the potential maximum scour depth at piers in the transition-pier through the wide-pier categories; i.e., it does not adequately reflect the influence of parameter y/a*. 7.5 Common Pier Forms Common pier forms typically comprise several structural or form components, as indicated in Table 7-1. Simpler common piers may comprise two cylindrical piles with a pile cap above the design flow elevation. Another basic pier form comprises a pier column supported by a cluster of cylindrical piles. The additional elements add complexity to the flow field, increase the possible number of parameters to consider, and thereby complicate reliance on an empirical equation for scour depth estimation. As pier form complexity increases, estimation uncertainty also increases. The ideal of having a set of scour estimation equations each tailored for common pier form is appealing. However, such a set does not exist, and certainly no one equation applies reliably to all common pier forms. Therefore, it is prudent to use a twofold design approach: 1. Use the Sheppard-Melville method, Eq. (7.1) or Eq. (6.8) adapted with a pier- shape factor so as to estimate scour at complex piers. Because the adaptations for complex piers are approximate and do not relate directly to the pier flow field, it is important to take into account the uncertainty associated with applying the adapted equation; and, 2. Consider the value of conducting hydraulic model tests to address the uncertainty associated with scour depth estimation. If the pier is large, such tests may be a worthwhile design task. If the pier is small, the uncertainty could be addressed by taking a more conservative estimate with a simple-pier equation. There is merit in conducting a series of hydraulic model tests to determine the scour performance of common pier forms. Such a series of tests would seek to obtain the maximum scour depths at each pier for variations of y/a*. The Sheppard-Melville (NCHRP 24-32) and Richardson and Davis (2001) equations offer procedures to account for non-cylindrical pier forms. However, each procedure is approximate and involves substantial uncertainty. 7.6 Common Pier Forms in Complex Situations Two categories of situation complicate, and contribute uncertainty to, design estimation of scour depth at a pier of simple or common form:
119 1. Alteration of the pier flow field by several processes, notably abutment proximity, debris or ice accumulation, bridge over-topping, channel morphology issues; and, 2. Unknown foundation erodibility (erosion resistance and manner of erosion) of the bed material at the pier location. Pier sites may have complex boundary materials. These sets of factors require additional design steps to be applied in design estimation of scour depth. The ensuing sections recommend how these complicating situations could be addressed. It is not a straightforward matter to forecast alteration of pier flow field. However, NCHRP Project 24-20 shows that, when a pier is within a certain distance from an abutment, scour at the pier is dominated by the abutment flow field and scour. 7.6.1 Abutment Proximity When a pier is located within the immediate vicinity of an abutment (notably, near the toe of an abutment), abutment scour dominates pier scour. For this situation, the design equations for simple or common pier forms do not apply. Scour depth at the pier is essentially equivalent to scour depth generated by flow around the abutment. A curve developed from NCHRP Project 24-20, âEstimation of Scour at Abutments,â could be used in estimating scour depth at a pier close to an abutment. When the pier is at the abutment toe, or near it, one curve limit indicates scour depth equivalent to abutment scour depth. When the pier is distant from an abutment, the other curve limit indicates scour depth is equivalent to scour at the pier in isolation. In some cases, it may be necessary to superimpose an estimate of pier scour on the estimated abutment scour depth. 7.6.2 Woody Debris or Ice During floods, many rivers carry appreciable quantities of floating debris such as branches and roots of trees. If the debris becomes caught at bridge piers and abutments, it can accumulate into large masses of material. A foundation with accumulated material causes a larger obstruction to the flow than without debris; the additional flow obstruction generally causes local scour depths in excess of depths under conditions without debris accumulation. The designer is recommended to follow the recommendations in NCHRP Project 24-26, Effects of Debris on Bridge Pier Scour, (Lagasse et al., 2010), which in turn is based on earlier studies of debris production and accumulation by Diehl (1997), and scour depth estimation at piers with debris accumulation by Melville and Dongol (1992). Lagasse et al. (2008) present guidelines for predicting the size, location, and geometry of debris accumulations at bridge piers. The guidelines are presented as a series of flowcharts, included as an appendix in their report. Additionally, Lagasse et al. (2010) give equations for estimating an equivalent pier width for use with the Richardson and Davis (2001) pier scour equation; see Section 5.5. The equations are adaptable for use with the method by Sheppard-Melville (NCHRP 24-32). In situations anticipated to be
120 more complicated, or different, than those studied by Lagasse et al. (2010), the designer is encouraged to consider conducting hydraulic modeling to get scour-depth estimates. 7.6.3 Bridge Deck Over-topping The design methods suggested by Guo et al. (2009) provide the most current means of estimating scour at submerged bridge decks. This scour is a form of contraction scour. Their method, however, does not expressly include scour at a pier at a submerged bridge deck. At this time, the designer should linearly combine the scour depths associated with the pier (assuming the deck is not submerged) and the contraction scour attributed to deck submergence. Further research is needed to ascertain how the scour depths actually combine. 7.6.4 Channel Morphology The designer is referred to the findings from NCHRP 24-27(03), Evaluation of Bridge- Scour Research: Geomorphic Processes and Predictions. It is rather usual for the pier to be designed so that its foundation extends lower than the lowest possible elevation of the thalweg passing through the bridge waterway. Considerable designer judgment is required when channel morphology issues come into consideration. 7.6.5 Armoured Boundary Surface, Layered Bed Sediment The designer is referred to Section 5.7 for guidance regarding scour-depth estimation for a pier in layered foundation material. 7.5.6 Weak Rock The designer is referred to the findings from of NCHRP 24-29, Scour at Bridge Foundations on Rock, for insight. To be kept in mind is the fact that scour depths in rock have not been shown to exceed those in non-cohesive sediment or cohesive soils. 7.7 Wide, Complex, or Uncommon Pier Forms For the wide-pier category of pier scour, and generally when pier geometry and site conditions are sufficiently complex as to be beyond the range of parameter values covered by those used in formulating the Sheppard-Melville method (or the Richardson and Davis (2001) method), the designer must take a system simulation approach. System simulation entails the use of hydraulic-model and/or numerical-simulation testing to estimate a design depth of scour. Such testing provides a holistic insight into scour development, serving not only to obtain a design estimate for scour depth, but also revealing how and where scour develops, and adding assurance that the scour depth is within a certain magnitude estimated approximately using the method for a simple pier (such as by the Sheppard-Melville method). For wide piers of cylindrical shape, and extending as a solid cylindrical shape into the foundation material, a scour depth estimate could be obtained using an abutment-scour equation. The deepest scour occurs at the pier flanks, where the pier flow field is similar to flow around this form of abutment (or caisson). Further research is needed to confirm this method for scour-depth estimation at wide piers.
121 The ensuing sub-sections briefly evaluate the prospects for improved scour-depth estimation using hydraulic modeling and numerical modeling, or hybrid modeling involving both approaches. 7.7.1 Hydraulic-Modeling For some pier situations there is little alternative other than hydraulic modeling to estimate a design pier scour depth. Such situations arise when complex flow patterns or intricate transport processes are involved, and reliable answers cannot be obtained by means of existing methods for estimating scour depth. Indeed, the existing design methods for pier scour were themselves developed by means of hydraulic modeling using laboratory flumes. As with all loose-bed hydraulic modeling, care is needed to address potential scale effects associated with the three length scales involved (pier width, flow depth, bed material). At this point in time, the complexity of the flow and sediment movement around a pier is still beyond the capability of numerical simulation models based on computational fluid dynamic (CFD) codes. However, numerical simulation holds substantial promise for greater design use. Over the past decade, hydraulic modeling is increasingly used in combination with computational models to investigate difficult flow situations that each modeling method alone would be inadequate to address. These combined modeling techniques are discussed in Section 1.6, which outlines modeling strategies. Besides their direct use to produce information that cannot be reliably obtained by some other means for design or operational purposes, hydraulic models have additional benefits. They can be a form of relatively inexpensive insurance, reducing the uncertainty associated with a design or an operational procedure. A comparatively small investment in a hydraulic model study, especially in the case of expensive constructed works, may help allay concerns regarding the viability of a design or a procedure. The cost of a model study typically is insignificant compared to the cost of the actual installation, herein (and traditionally) called the prototype. A hydraulic model also can be useful for public relations purposes, demonstrating to the lay person as well as the sceptical engineer how a design or a procedure will function. It usually is a convenient device for communicating complex hydraulic ideas. The similitude principles that form the basis for hydraulic modeling are fairly straightforward. However, a difficulty incurred with preparation of a manual on hydraulic modeling is determining the extent of background information to be covered in order to adequately present the similitude criteria. A diverse range of flow or dynamic situations are treatable using hydraulic modeling. Though an attractive feature of hydraulic modeling is that similitude principles and criteria are readily understood, their implementation requires a sound understanding of the underlying physical processes and recognition of a modelâs capacity to replicate those processes. Few models exactly replicate all the processes involved with a particular flow situation. Shortcomings in models usually are termed scale effects or laboratory effects. The former term describes the incomplete satisfaction of a full set of similitude criteria
122 associated with a particular situation. Scale effects increase in severity as the ratio of prototype to model size increases or the number of physical processes to be replicated simultaneously increases. Laboratory effects arise because limitations in space, model constructability, or instrumentation impede precise replication or measurement. They also arise from incorrect replication of boundary conditions. Ever since the establishment of hydraulics laboratories, there has been a trend for more accurate quantitative information from hydraulic models. This trend has required refinement of similitude criteria for improved definition of processes, and finding means to overcome practical constraints, such as being limited largely to one model liquid (water). It also has required innovative efforts to overcome some of the restrictions imposed by laboratory facilities, such as limits in space and instrumentation capabilities. ASCE Manual 97 (ASCE 2000) provides useful guidance concerning the effective employment of hydraulic models to address a broad range of hydraulic engineering issues. Significant improvements have been made in instrumentation and laboratory equipment and modeling methodology. Many of the improvements have been facilitated by the computer and ancillary electronic instrumentation. Though much had been accomplished with point gauge and Pitot tube, newer hydraulics problems required more sophisticated instrumentation. Computer-aided data-acquisition systems increased the sophistication of modeling by facilitating measurement and collection of large amounts of data hitherto considered impractical or impossible to acquire. Models could now be run with greater flexibility in terms of location, scheduling, variables measured, as well as processes observed. A major advance has been in the capacity to observe and measure features of large-scale turbulence structures, such as exist in pier flow fields. Hydraulic modeling is reliant on instrument technology, and has evolved in scope as instrumentation developments have enabled aspects of flow to be illuminated and measured. In this sense, hydraulic modeling is as sophisticated as the instrumentation used to conduct the modeling. As instrumentation and computer technologies continue to progress, so too will hydraulic modeling and its utility for pier scour investigations. 7.7.2 Numerical Modeling A growing number of numerical methods can be usefully applied to study flow at bridge piers and pier scour. An important limitation, at present, is that numerical simulations with a loose bed are not yet sufficiently reliable to predict bed evolution or equilibrium scour bathymetry. However, fully three-dimensional numerical simulations can provide critical information on the complex flow fields and bed shear stress distributions at different stages of the pier scour process. This advantage holds for complex pier forms. Used together with hydraulic models, numerical investigations can provide a better understanding of scour processes and mechanisms at bridge piers of complex geometries. Information on the flow patterns and turbulence structure at relevant flow conditions (e.g., from normal to flood conditions) obtained from simulations of flow past bridges containing piers and abutments can be used in the design process before a bridge is built. The potential for improved design and the minimization of over-design is substantial.
123 Most current numerical investigations of bridge pier flows used steady RANS models with wall functions (e.g., see Olsen and Melaaen, 1993, Richardson and Panchang, 1998, Olsen and Kjellesvig, 1998, Wang and Jia, 2000, Ali and Karim, 2002, Salaheldin et al., 2004, Roulund et al., 2000). This method can easily be applicable for bridge piers and bridge abutments of complex geometry at field Reynolds numbers. For the case of a highly unsteady flow characterized by large-scale unsteady vortex shedding and severe adverse pressure gradients, the use of the wall-function approach which assumes the validity of the law-of-the-wall near solid boundaries is questionable. The use of a steady model excludes capturing not only of the unsteady vortex shedding behind the pier but also the unsteady dynamics of the horseshoe vortex system. Thus, the use of this approach to understand the flow physics is very limited. More importantly, the accuracy of the mean flow and turbulence predictions obtained using steady RANS simulations is relatively poor due to the flow complexity. Unsteady RANS methods are somewhat more accurate (e.g., Wei et al., 1997, Paik et al., 2004, Ge et al., 2005). For example, Paik et al. (2004) performed RANS simulations of a complex bridge pier configuration at a Reynolds number of 100,000. The geometry corresponded to a rectangular open channel with four bottom-mounted rectangular piers located one behind the other along the flow direction. The simulation successfully captured the unsteady large-scale vortex shedding and wake-boundary layer interactions present in such flows. One should mention several attempts (e.g., Wei et al., 1997, Nurtjahyo et al., 2002, Chen, 2002, Nagata et al., 2005) to use RANS methods coupled with a movable bed module to predict the flow field and the bed evolution and equilibrium bathymetry. For example, Chen (2002) calculated the scour evolution around a complex system of multiple piers (e.g., one of the cases contained four rectangular piers and two abutments) using grids containing approximately 500,000 cells at a Reynolds number of 24,000. The contraction and local scour patterns around the piers were found to be in fair agreement with general experimental observations of the scouring process. Though certainly an important direction for future research, 3D steady RANS simulations with movable bed are not yet sufficiently reliable to predict scour depth for bridge pier design in natural waterways. For simple circular-cross-section, narrow piers (y/a > 1.4), some such simulations (e.g., Rouland et al. 2005) predict reasonable estimates of scour depth, especially at the upstream side. The main disadvantages of the RANS approach is that it cannot accurately predict massively separated flows and flows in which large adverse pressure gradient are present. It cannot give any information on the temporal dynamics of the main eddies which drive the scour process. Past experience shows that both steady and unsteady RANS models fail, to a variable extent, to predict important aspects of massively separated flows dominated by unsteady vortex shedding and large- scale vortex interactions (e.g., see Rodi, 1997, Rodi et al., 1997, Tokyay and Constantinescu, 2006, McCoy et al., 2008). For example, RANS simulations cannot correctly predict the structure of the horseshoe system vortex during the initial stages of the scour process when the scour hole is very small. Additionally, such simulations fail to predict the bimodal nature of the large scale oscillations of the main horseshoe vortex
124 in front of the pier. Thus, RANS simulations have marginal use for understanding pier flow fields and consequent erosion and deposition processes. Research over the last ten years has proven that eddy-resolving three-dimensional numerical simulations of flow past bridge piers can provide a detailed description not only of the mean flow field and turbulence structure at a level that is very hard to obtain from experiments but also of the coherent structures controlling the bed erosion phenomena. Information from fully three-dimensional numerical investigations that can characterize in a qualitative and quantitative way mean flow, turbulence and scour processes and the strength of the scour processes function of the main flow and pier geometry parameters are essential to be able to improve existing methods or propose new methods to estimate scour depths at bridge piers. For example, scour prediction equations neglect the scaling of the large-scale coherent structures present in the region surrounding the pier. This is a major deficiency of present methods to estimate scour. To take this into account in scour design, a detailed qualitative and quantitative knowledge of the dynamics of the coherent structures at different stages of the scour process is needed. Of course, a major direction for future scour research is how the additional information and insight into the fundamental flow and sediment transport processes available from state- of-the-art experimental and numerical techniques can be used to develop more accurate relationships to predict local scour depth around bridge piers. Among the eddy resolving techniques the most popular is Large Eddy Simulation (LES). In LES, the unsteady dynamics of the energetically important scales in the flow is directly computed, and only the effect of the filtered (small) scales on the resolved scales is modelled. Eddy resolving simulations can provide three-dimensional visualizations of the entire (averaged and instantaneous) flow field, thereby bringing into view the main coherent structures in the flow, their dynamics, and the nature of their interactions with other large-scale eddies or with the bed. Thus, they can be used as an effective tool to better understand the physics of bridge pier flows. In particular, such simulation can elucidate the role of the large-scale coherent structures in the scouring process. Eddy resolving numerical simulations are much less expensive than comprehensive PIV experimental investigations of the flow around bridge piers. Moreover, eddy resolving simulations can provide information on quantities that are very difficult to estimate accurately based on experimental measurements. For example, it is feasible to visualize the distribution of the bed shear stress on the whole bed surface, get information on the distribution of the pressure fluctuations in the near bed region, visualize the whole horseshoe vortex system at a certain moment in time, and capture the interactions between the necklace vortices and the eddies that populate the detached shear layers at the sides of the pier. Earlier LES simulations of flow past circular and rectangular bridge piers with flat and deformed bed were reported by Tseng et al. (2000) and by Choi and Chang (2002) at relatively low Reynolds numbers. Though these LES simulations performed on relatively coarse meshes appear to better capture the mean flow compared to RANS simulations, the simulations were less successful in capturing the structure of the horseshoe vortex system in the mean and instantaneous flow fields.
125 More recent LES simulations using state of the art subgrid-scale models and fine meshes (e.g., Kirkil et al, 2008, Koken and Constantinescu, 2008a-b) have allowed the investigation of the role of coherent structures in the scouring process at bridge piers and abutments of simplified geometry. These simulations were shown to accurately predict the flow patterns and turbulence structure compared to other numerical methods. These studies provided a detailed investigation of the structure of the horseshoe vortex system as it wraps around the upstream base of the pier. For example, the simulation of Kirkil et al. (2008) captured the presence of bimodal aperiodic oscillations inside the HV system region, as well as the associated increase in the turbulence intensity. The simulation results showed the interactions among these large-scale structures (necklace vortices, wake vortices, vortices present in the separated shear layers) are controlling, to a large extent, the scouring mechanisms around the pier. Several mechanisms that can explain the growth of the scour hole laterally and behind the cylinder were identified. LES simulations allowed for the first time a detailed study of the distributions of the pressure root-mean-square fluctuations at the bed and of the distributions of the instantaneous and time-averaged bed shear stress that are very difficult to estimate accurately from experiments. Hybrid RANS-LES methods like Detached Eddy Simulation (DES) are a good alternative to LES (e.g., Paik et al., 2007, Kirkil et al., 2009, Koken and Constantinescu, 2009). Their big advantage is that they facilitate simulation of flow past bridge piers at field Reynolds numbers without using wall functions. One of the disadvantages of DES, which is the most popular non-zonal RANS-LES method, is that the subgrid-scale model employed in regions where DES is in LES mode has much less physics and is significantly more dissipative compared to the dynamic Smagorinsky model or to other state-of-the-art LES models. Both LES and DES allow investigation of flow past bridges in river reaches of complex bathymetry. Based on the proven success of LES and DES for simpler pier geometries, similar simulations can be conducted with bathymetries corresponding to the different stages of the scouring process, between initiation and equilibrium, to understand the flow and scour mechanisms at complex piers. This is important because the role and relative importance of the different coherent structures may change during the scour process. Also, the nature of their interactions may change. Several specific applications addressing important gaps in knowledge of scour processes at bridge piers in which numerical, eddy resolving techniques may help understand the flow structure and scour processes are mentioned in Chapter 8.