Evaluation of Bridge Scour Research: Pier Scour Processes and Predictions (2011)

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100 CHAPTER 6 LEADING METHODS FOR SCOUR-DEPTH PREDICTION 6.1 Introduction This chapter is a review of the existing leading methods for design estimation of pier- scour depth. The method best reflecting current understanding of scour processes is identified. An important consideration in reviewing the methods is their possible inclusion of the primary parameters defining the potential maximum depth resulting from scour processes. Based on the evaluation presented in Appendix A, the leading scour-depth prediction methods are Melville (1997, also in Melville and Coleman 2000), Richardson and Davis (2001), Sheppard and Miller (2006), and Sheppard-Melville (NCHRP 24-32). These methods most comprehensively reflect scour processes. The Melville (1997) method differs from the other two insofar that it is directly intended for design estimation of maximum scour depth, doing so by means of envelope curves encompassing data on parameter influences. The other two methods aim to replicate data trends for specific parameters. Each method is based mainly on scour data for cylindrical piers, and to a lesser extent on data from common pier forms consisting of multiple components (as illustrated in Figures 2-1 and 2-2). The Richardson and Davis (2001) method presently is used in FHWA’s HEC-18. It comprises a series of adaptations of what is colloquially known as the CSU equation (e.g., an earlier version of the method is given by Richardson and Davis 1995), which HEC-18 has used for the past several decades. The method provides scour-depth estimates that, considered in terms of the low rate of pier failure attributable to scour, has served bridge designers quite well for common pier sizes. However, concerns exist that it provides unreasonably large values of scour depth for piers in the wide-pier category, and its upper-bound estimate for live-bed scour is too high. Also, research since 1990 shows the method inadequately reflects certain aspects of pier-scour processes. The Melville (1997) method is used quite extensively in several countries, and provides the most comprehensive coverage of parameters influencing scour (as demonstrated by Chapter 4). The following two aspect of the Melville method relate directly to the key considerations stated in Section 1.4: 1. The method is organized in accordance with changes in the pier flow field (as indicated in Sections 3.1 and 4.2 for the parameter y/a). Design relationships differ in accordance as to whether the pier is narrow, transitional, or wide; and, 2. The method provides envelope curves for design use, rather than curves fitted through data. However, the Melville (1997) method is in the process of being merged with the method more recently developed by Sheppard and Miller (2006). NCHRP Project 24-32 has moved forward with developing the Sheppard-Melville method (Sheppard et al. 2011).

101 Therefore, the Melville method per se is not considered further in this section. The method proposed by Sheppard and Miller (2006) was developed in response to short- comings perceived in the Richardson et al. (2001) method recommended in HEC-18. The Sheppard-Melville method builds on the insights contained in Melville (1997) and Sheppard (2006). It uses the two primary parameters y/a and a/D, includes the parameter expressing influences of pier shape relative to flow alignment, and includes the flow intensity parameter, V/Vc . As indicated in the draft final report for NCHRP Project 24-32, and explained subsequently in Section 6.4, further research is needed to complete the method’s development with regard to scour in the wide-pier category (y/a* < 0.2). For the purpose of design estimation of potential maximum scour depths, however, a simplified version of the method can be established, as explained subsequently in Section 6.4. The present evaluation indicates the need to transition from the method currently used in HEC-18 (Richardson and Davis 2001), to the Sheppard-Melville method elaborated in NCHRP 24-32 (Sheppard et al. 2011). The latter (and more recently developed) method better reflects current understanding of pier-scour processes. However, the Sheppard- Melville method requires some additional adjustment to reflect parameter influences. Field verification of the Sheppard-Melville method is a priority for further research. 6. 2 Richardson and Davis (2001) Method The Richardson et al. (2001) for estimating the depth of local scour at piers, colloquially called the CSU equation, extends back about 35 years, and has been updated several times to account for additional parameter influences (Richardson and Davis 1975, 1993, 2001). It is based on the equation 43.0 35.0 43210.2 Fra yKKKKK a y W s      = (6.1) where Fr = V/(gy)0.5; and K1, K2 and K3 = adjustment factors accounting for pier nose shape, angle of attack of flow, and state of bed-sediment motion, respectively. K1 varies between 0.9 and 1.1, K2 varies between 1.0 and 5.0, and K3 (essentially the Laursen and Toch 1960 curves), varies between 1.1 and 1.3. The factor, K4 , is 15.0 4 4.0 RVK = (6.2) where 0 9050 50 > − − = icdcd icd R VV VV V (6.3) xicdV is approach velocity required to initiate scour at the pier for grain size Dx , given by:

102 xx cd x icd Va DV 053.0 645.0      = (6.4) and xcdV is critical velocity for incipient motion for grain size Dx , given by: 3/16/119.6 xcd DyV x = (6.5) K4 decreases scour depths for armouring of the scour hole for bed sediments for which D ≥ 2mm and D90 ≥ 20mm; for D < 2mm or D90 < 20mm, K4 = 1; D90 = the particle diameter for which 90% of particles are finer. The minimum value of K4 is 0.4. The method’s use in HEC-18 includes a factor, Kw, for very wide piers. This correction factor is to be applied when y/a < 0.8, a/D50 > 50 and Fr < 1. Kw is given as 65.0 34.0 58.2 Fr a yKw      = for V/Vc 25.0 13.0 0.1 Fr a yKw      = < 1 (6.6a) for V/Vc ≥ 1 (6.6b) The shape factor K1 applies to simple pier shapes. A procedure is included to account for the shape of complex piers. The local scour at a complex pier is estimated as the sum of the scour due to the proportion of the pier stem in the flow, the scour due to the pile cap or footing in the flow, and the scour due the piles exposed to the flow. A rather complicated set of equations and graphical relationships is given for estimation of each scour component. The rationale for this assumption is questionable, because it does not adequately relate pier structure to pier flow field and erosion processes. For piers comprising multiple columns skewed to the flow, Richardson and Davis (2001) recommend using the composite pier projected width in Eq. (6.1), with K1 = K2 = 1. For multiple columns spaced more than five diameters apart, it is further recommended that the maximum scour depth be limited to 1.2 times that of a single column. In accordance with Froude Number value, the Richardson and Davis (2001) equation has the following upper bounds for round-nose pier aligned with the flow: 8.00.3 8.04.2 >= ≤= Fr a y Fr a y s s (6.7) The higher value of ys /a for live-bed scour is open to question, as it has not been corroborated by data other than the few laboratory data on which it is based.

103 6.3 The Sheppard-Melville Method (NCHRP Project 24-32) The Sheppard-Melville method builds on the method proposed by Sheppard and Miller (2006), following more-or-less the same parameter approach inherent in the Melville (1997) method. The method, described in Sheppard et al. (2011), uses an effective pier diameter, a*, the diameter of a circular pile that will experience the same equilibrium scour depth as the subject structure under the same flow and sediment conditions. In other words, pier shape and alignment factors are used to determine a*, which then is used in the method’s equation set. The Sheppard-Melville method comprises Eqs. (6.8) to (6.12), applied to ranges of bed material mobility. For clear-water scour (0.4 < V/Vc < 1), D af cV Vf a yf a sy                         = 50 * 32*15.2* (6.8) In the live-bed scour range up to the live-bed peak (1 < V/Vc < Vlp/Vc ) D af cV lpV cV V cV lpV cV lpV cV V a y f a sy                                     − − +               − −         = 50 * 3 1 5.2 1 1 2.2*1* (6.9) and in the live-bed scour range above the live-bed peak (V/Vc > Vlp/Vc ) a yf a sy         = *1 2.2 * (6.10) where:                   −         +                =                           −=                   = 13.0* 6.10 2.1* 4.0 * 3 2 ln2.112 4.0 *tanh1 D a D a D a f cV V f a yf (6.11) and Vlp is the live-bed peak velocity, much the same as Va in the Melville (1997) method. The sediment critical velocity, Vc, is calculated using Shield’s curve. The live-bed peak

104 velocity, Vlp, is computed using a modification of van Rijn’s (1993) prediction of the conditions under which the bed planes out. Hence Vlp is computed as the larger of: gyVlp 6.0= (6.12a) or clp VV 5= (6.12b) The method reflects well-known data trends (Figures 4-14 and 6-1) indicating that there are two local maximums in the scour depth versus V/Vc plots. The first local maximum occurs at transition from clear-water to live-bed scour conditions, i.e. at V/Vc =1. The second maximum, referred to here as the “live-bed peak” is thought to occur at the conditions where the bed planes out. The velocity that produces the live-bed scour peak is referred to as the live-bed peak velocity and is denoted by, Vlp . Figure 6-1 Normalized equilibrium scour depth, ys/a*, versus flow intensity ratio, V/Vc, for constant values of y/a* and a* /D (Sheppard et al, 2011) 6.4 Discussion For the ranges of laboratory-based, parameter values on which they are based, the Richardson and Davis (2001) and Sheppard-Melville (Sheppard et al. 2011) methods are acceptably accurate, and give reasonably comparable estimates (Appendix A). They were developed for essentially cylindrical piers, and empirically relate measured scour depths to selected parameters. However, each method is not entirely reconciled with

105 aspects of the flow field and erosion processes at piers; the Sheppard-Melville method is better reconciled than the Richardson and Davis method. In accordance with the third objective set for this project (Section 1.4), three criteria must be considered when further evaluating the two methods: 1. Reflection of proven relationships between parameters and scour processes; 2. Capacity to encompass recently identified parameter influences; and, 3. Reasonable expectation that the methods, semi-empirical equations generally, give acceptably accurate estimates of scour depth. The ensuing sub-sections address these questions with respect to the methods developed by Richardson and Davis (2001) and Sheppard et al. (2011). An important consideration is that an effective design method need not reflect all parameter influences, but rather ensure that it has the capacity to the estimate potential maximum scour depth for a pier site. This consideration entails that the method use the primary parameters identified in Chapter 4. 6.4.1 Reflection of Proven Parameter Relationships The parameters of prime importance for estimating potential maximum depth of pier scour are y/a and a/D, because these parameters delineate the maximum potential dimensions and shape of the scour hole for given a pier site. Pier shape and alignment factors qualify pier width a, which then could be expressed as an effective width, a*. The parameter V/Vc is important for ascertaining whether the approach flow has the capacity to attain the potential maximum scour depth. However, as Section, 5.3 states, it is not necessary to know V/Vc in order to estimate that scour depth. Neither the Richardson and Davis (2001) method nor the Sheppard-Melville method is configured in accordance with the three categories of pier width indicated in Table 4-1 in terms of y/a. The narrow- and wide-pier categories entail two substantially different flow fields and dominant scour processes, with the transition-pier category evolving between the two flow fields. Though both methods recognize that a difference exists between narrow- and wide-pier flow fields, the methods do not expressly relate to the different flow fields. This deficiency is a weakness in the scour-estimation approach taken by both methods. The Sheppard-Melville method is configured in terms of two ranges of V/Vc, clear-water and live-bed. It expressly includes the three parameters, though presently is unclear as to how best to include them, for live-bed scour. The Richardson and Davis method expressly includes y/a, but not a/D and V/Vc. It instead empirically links state of bed motion through the combined influences of K4 and Fr. As explained in sub-section 6.4.2, this linkage is not readily extended. Though both methods include y/a, they do not deal satisfactorily with very wide piers, particularly in live-bed scour; there is a paucity of data for this wide-pier condition.

106 The Richardson and Davis method, though well-correlated empirically to the available data upon which it is based, has the following limitations: 1. Scour is estimated as proportional to Fr0.43 . Since Froude numbers (Fr) are typically higher in streams with coarser beds, estimated local scour depths tend to be larger in coarser materials; for example, an increase in Fr from 0.3 to 0.8 leads to about a 50% increase in scour depth. This is inconsistent with laboratory data. The Froude number dependence expressed in Eq. (6.1) may be valid when comparing results for the same bed materials, but not when comparing different bed materials. As argued in the parameter framework, and pointed out by others (e.g. Neill 1993), Fr would seem not to have prominent physical significance in scour processes, other than indicating sub- or super-critical flow condition through the bridge waterway. 2. The parameter a/D is missing from Eq. (6.1). Consequently, this equation does not expressly reflect several significant affects of bed particle size (or boundary material erodibility), including the parameter’s influence on flow-field vorticity, an important aspect driving scour. 3. It is unclear why the maximum value of ys/a would increase from 2.4 when Fr ≤ 0.8, to 3.0 when Fr > 0.8. There is no sustained body of laboratory or field data indicating that ys /a reaches 3.0 for circular cylindrical piers, at least not without the influence of a scale effect such as attributable to inaccurate scaling of turbulence structures (as discussed in sub-section 4.4.8). 4. The veracities of factors K4 and KW in Eq. (6.1) are uncertain. They pertain to bed sediment non-uniformity and wide pier effects, respectively. The Sheppard-Melville method (Sheppard et al. 2011) reflects some of the recent understandings of the influences exerted by the parameter a/D. It reflects several aspects of pier scour, as explained in Section 4.4.2: i.e., scaling of vorticity generated by flow around a pier (and around components of a pier (column, pile cap, pile), relative roughness of particle size relative to pier diameter. Lee and Sturm’s (2008) data show that the peak of ys/a occurs at a/D~25 and is followed by a sharp decay of ys/a until a/D~100. The decay rate decreases for a/D > 200, such that ys/a becomes approximately constant for a/D > 500. This trend implies that the sediment coarseness effect should decay with increase in the ratio a/D for fine sediments. Data from Sheppard (2007) for wide piers also show that ys/a reduces with increasing a/D for fine sediments. However, Sheppard proposes a monotonic decay of ys /a with a/D after the maximum scour depth is reached. To be kept in mind is the fact that these trends are indicated for a simple pier form, and include a mix of ripple-forming sands and coarser particle sizes. The trends become more complicated for pier designs involving a pier column, pile cap, and piles. The Richardson and Davis method is based on (what is known as) the CSU equation, progressively refined over the years to incorporate new research findings, but the basis of

107 the method has remained essentially the same. According to Richardson et al (1990), the CSU6 equation was determined from a plot of laboratory data for circular cylindrical piers. The data used were derived from Chabert and Engeldinger (1956) and CSU (Shen et al, 1966), the majority of the data being from the former source. Sediment sizes ranged from 0.24 mm to 0.52 mm, so that ripples would have formed on the bed of the laboratory flume. As is now well known (Chapter 4), ripple formation at flow velocities approaching the threshold condition for bed material entrainment significantly reduces scour depths measured in the laboratory. The outcome of the influence of ripple formation is an apparent dependence on flow velocity for live-bed scour depth, not demonstrated in data for uniform non-ripple-forming sediments. The discussion leads to the conclusion that the Sheppard-Melville method better expresses the physical relationships between more of the principal parameters (y/a, a/D, and V/Vc,) and processes than does the Richardson and Davis method, and therefore is the more robust method for predicting scour depth over a broader range of parameter values. Yet the Sheppard-Melville method is unclear regarding the variation of ys /a for -- 1. Live-bed conditions. It is unclear why the parameter a*/D is not significant for flow conditions producing high bed mobility; i.e., V/Vc > Vlp/Vc , but is significant for clear-water scour. 2. Wide-pier scour. The method does not indicate when the scouring flow field is in the narrow-pier, transitional-pier, or wide-pier category. The original Melville (1997) method better defines these categories. 6.4.2 Capacity to Include Recently Identified Parameter Influences An important point made in Chapter 4 is that some variables exert multiple influences that do not lend themselves to evaluation in isolation of each other. For example, particle diameter is such a variable. Therefore, it is increasingly difficult for a method based on a semi-empirical, or rational, equation to include more parameter influences, especially if the equation does not expressly include the primary parameters forming the parameter framework. By virtue of its use of the primary parameters y/a and a/D, along with V/Vc, expressing stage of bed mobility, the Sheppard-Melville method is better configured to include additional recently identified parameter influences than is the Richardson and Davis method. The Sheppard-Melville method, though, requires more research to resolve the points mentioned above. In particular, the method’s present arrangement in terms of three ranges of value for V/Vc, and use of a single term (f1 (y/a)) may hamper its capacity to be extended for estimating scour depth for narrow-, transitional-, and wide-pier categories. The Richardson and Davis method has been extended several times to reflect additional parameter influences, notably non-uniformity of bed particle diameter, bed particle mobility, and wide-pier scour. Experience with these extensions, though, has been 6 Colorado State University, where extensive research on pier scour has been conducted

108 mixed7 . It has not proven straightforward to tune-up the basic equation (based on Froude number) so as to embody additional parameter or process influences. 6.4.3 Limits of Methods For the data ranges of the parameters on which they are based, the Richardson and Davis, and Sheppard-Melville methods yield acceptable scour-depth predictions. As shown in Figure A-1 through A-12 of Appendix A, the two methods give on the whole comparable scour-depth predictions for cylindrical piers in the narrow-pier category. As expected with semi-empirical equations generally, the two methods become limited in their capacity for accurate estimation pier scour depth when extended beyond the parameters and data range upon which they are based. However, the Sheppard-Melville method is less constrained in this regard because it better reflects scour processes framed in terms of the primary parameters y/a and a/D. It is more readily used to identify the potential maximum scour depth at a pier site. The utility of an empirical or “rational-method” approach, whereby scour depth is related to a combination of individual parameter influences, diminishes when the number of parameter influences increases. Additionally, the linked influences of parameters, makes it infeasible for a single equation, such as Eqs (6.1) and (6.8), to embody more than the main parameter influences associated with either the narrow-, transitional-, or wide-pier categories of scour at cylindrical piers and the simpler common pier forms. For design estimation of potential maximum scour depth, though, it is not necessary to account for more than the primary parameters mentioned in chapter 4. Chapter 7 suggests how the Sheppard-Melville method should be simplified for design estimation of potential maximum scour depth. Additionally, a common difficulty for design estimation of a potential maximum scour depth at piers, and limit in the use of the leading predictive equations, is determining the value of effective pier width a* to used in the estimation. For these piers, the flow field usually is not adequately defined, and therefore accurate selection of a* and estimation of scour depth cannot be expected from a predictive equation based on other pier forms. To overcome the limits of the two leading predictive methods (or any single method), it is practicable to identify a structured design approach to be applied in accordance with pier size and form complexity, and site complications. The approach would use the best information and techniques currently available for estimating scour depth: 1. For piers in the narrow-, transition-, and wide-pier categories, develop simplified forms of the leading equations for design estimation of potential maximum scour depth at cylindrical piers; 7 Anecdotal discussion with designers

109 2. Tailor the simplified forms of the equations for application to common pier forms. This effort may require conducting hydraulic model tests with a selection of such pier forms; 3. Use modeling (hydraulic and possibly numerical) to determine design scour depth at uncommon and very wide piers. If scour at a very wide pier were essentially scour at an abutment with a deep foundation, it may be possible to adapt an abutment scour equation so as to estimate wide-pier scour. The methodology can be applied to obtain estimates of potential maximum scour depth, whose uncertainty can be offset by the use of a margin of safety (e.g., from an upper- bound design curve, or a safety factor).