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

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160 APPENDIX SCOUR-DEPTH ESTIMATION METHODS A.1 INTRODUCTION This appendix briefly evaluates existing methods for estimating scour depth. It includes methods proposed prior to 1990 though focussing especially on methods developed since 1990. The evaluation considers each method’s capacity to express the scour influences of the primary parameters indentified in Chapter 4, and includes a comparison of scour depths predicted for a range of hypothetical pier conditions. The outcome of the evaluation is to identify the two methods considered further in Chapter 6: the Richardson and Davis (2001) method as presently used in HEC-18, and the Sheppard-Melville method as developed recently in NCHRP Project 24-32. A.2 EVALUATION CRITERIA The evaluation of the scour-estimation methods considers several criteria: 1. Adequacy in addressing scour processes as represented by the primary dimensionless parameters identified in Chapter 4; 2. Limitations of design relationships (ranges of results in hypothetical applications); 3. Categorization and acceptability of laboratory experiments and research techniques (experimental duration, variety of particle sizes and types of sediments, realistic geometries and scales, characterization of flow field, degree of idealization); 4. Verification of design relationships with field and other lab data; and, 5. Applicability and ease of use for design practice (e.g., in AASHTO manual). A.3 EXPRESSION OF PARAMETER INFLUENCES Numerous equations have been proposed for estimation of the depth of local scour at bridge piers. A selection of some of the better known equations is given in Table A-1. The equations are listed chronologically. Table A-2 indicates the parameter influences represented in each of the methods. Table A-1 A chronological listing of pier scour equations Reference Equation Standard format (for comparison) Notes Inglis (1949) 78.03/2 32.2         = + a q a yys a y a q a ys −         = 78.03/2 32.2 q = average discharge intensity upstream from the bridge (m2 Ahmad (1951) /s) 3/2 2qKyy ss =+ a y a q K a y s s −= 3/2 2 q2 = local discharge intensity in contracted channel (m2 Laursen (1958) /s)         −      += 11 5.11 5.5 7.1 y y y y y a ss 5.0 11.1      ≈ a y a ys applies to live-bed scour

161 Chitale (1962) 249.551.065.6 FrFr y ys −−= [ ]      −−= a yFrFr a ys 249.551.065.6 applies to live-bed scour Laursen (1963)                 −             + = 1 1 5.11 5.5 5.0 1 6/7 c s s y y y y y a τ τ At the threshold condition, 5.0 34.1       ≈ a y a ys applies to clear-water scour τ1 τ = grain roughness component of bed shear c Larras (1963) = critical shear stress at threshold of motion 75.005.1 aKKy ss θ= 25.005.1 −= aKK a y s s θ Neill (1964) 3.07.05.1 yays = 3.0 5.1       = a y a ys the factor 1.5 applies for circular piers Breusers (1965) ays 4.1= 4.1= a ys derived from data for tidal flows Blench (1969) 25.0 8.1       = + rr s y a y yy a y a y a y rs −     = 75.0 8.1 yr =1.48(q =regime depth 2/FB) where F 1/3 B=1.9(D)0.5 and q in m , d in mm 2 Shen et al. /s (1969) 619.0 000223.0      = ν Vays 06.0619.0 381.0 34.2 −     = yFr a y a ys standard format equation is given for kinematic viscosity of water, ν = 1x106 m2 Coleman (1971) /s 9.0 6.0 2      = a V gy V s 41.019.1 19.0 54.0 yFr a y a ys      = Hancu (1971) 3/12 1242.2               −= ga V V V a y c c s 3/2 3/1 42.2 Fr a y a ys      = (2V/Vc Standard format equation is given for threshold condition -1) =1 for live-bed scour Neill (1973) aKy ss = s s K a y = Ks=1.5 for round-nosed and circular piers; Ks Breusers =2.0 for rectangular piers et al. (1977) θKKa y V Vf a y s c s                   = tanh0.2 θKKa y a y s s      = tanh0.2 f(V/Vc)=0 V/Vc =(2V/V ≤0.5 c-1) 0.5<V/Vc =1 V/V <1 c Equation (*) given at the threshold condition >1 Jain and Fischer (1980) ( ) 25.0 5.0 86.1 cs FrFra y a y −     = 5.0 86.1      = a y a ys Fr=V/(gy) Fr 0.5 c=Vc/(gy) Standard format equation is given at the threshold condition 0.5 Jain (1981) 25.03.084.1 cs Fra y a y      = 3.0 84.1      = a y a ys Standard format equation is given at the threshold condition Chitale (1988) ays 5.2= Melville and Sutherland (1988) θKKKKKa y sdyI s = θKKKKa y sdy s 4.2= For an aligned pier, ys)max=2.4KsKd Standard format equation is given at threshold condition a Froehlich (1988) 1 32.0 08.0 50 46.0 62.0 2.0 +                    = D a a y a a FrK a y p s s 1 32.0 08.0 50 46.0 62.0 2.0 +                    = D a a y a a FrK a y p s s ap gyVFr /= = projected width of pier 5.2= a ys

162 May and Willoughby (1990)              = sm sc sc s ss y y y yfy 4.2 For circular cylinder: fs 0.10.1 0.152.0166.31 76.1 >= ≤≤      −−= c ccsc s V V V V V V y y = 1.0 0.10.1 7.255.0 6.0 >= ≤     = a y a y a y y y sm sc Breusers and Raudkivi (1991) θσ KKKKKa y dsy s 3.2= θσ KKKKKa y dsy s 3.2= For an aligned pier, ysmax=2.3KsKdKσ Richardson and Davis (1995) a 43.0 35.0 432 Fra yKKKK a y s s      = θ 43.035.0 432 Fra yKKKK a y s s      = θ K3 K = factor for mode of sediment transport 4 y = factor for armouring by bed material smax y =2.4b Fr≤0.8 smax Gao et al.(1993) =3b Fr>0.8 η ς         − − = − 07.0 50 15.060.046.0 cc c s VV VV DyaKy 72.0 50 7 50 14.0 10 1005.66.17               + +      −       = − D y xD a y V sc ρ ρρ cc Va DV 053.0 50645.0       = where ys, a, y, D50, V, Vc, Vc 32.0 07.0 50 4.0 46.0 −           = y D y a yK a ys ζ ’ are in S.I. units. Vc K ′=incipient velocity for local scour at a pier ζ η=1 for clear-water scour =shape and alignment factor <1 for live-bed scour i.e., 50 log23.235.9 D c V V +       =η where D50 Standard format equation is given for threshold condition is in S.I. units Ansari and Qadar (1994) m a ay m a ay pps pps 2.260.3 2.286.0 4.0 0.3 >= <= m a a a y m a a a y pp p s pp p s 2.260.3 2.286.0 6.0 2 >= <= − ap Wilson (1995) = projected width of pier 4.0 ** 9.0       = a y a ys 4.0 ** 9.0       = a y a ys a * = effective width of pier

163 Melville (1997) θKKKKKy sdIybs = θKKKKy sdybs = Kyb K = 2.4a y/a > 1.4 yb = 2(ya)0.5 K 0.2 ≤ y/a ≤ 1.4 yb = 4.5y y/a < 0.2 Standard format of equation is given at the threshold condition 25 1 25 24.2log57.0 0.1 ( 1 0.1 ( ( 50 50 50 10 ) ) ) > = ≤       = ≥ −− = < −− −− = D a if K D a if D aK V VVV if K V VVV if V VVV K D D c clp I c clp c clp I Richardson and Davis (2001) 43.0 35.0 432 Fr a y KKKKK a y ws s       ⋅= θ 43.0 35.0 432 Fr a y KKKKK a y ws s       ⋅= θ K3 K = factor for mode of sediment transport 4 K = factor for armouring by bed material w y = factor for very wide piers after Johnson and Torrico (1994) smax y =2.4a Fr≤0.8 smax Briaud et al. (2004) =3a Fr>0.8 6.0 max 18.0      = νθ aVKKKy spws 1.62 y/a if,1 1.62 y/a if 85.0 34.0 >= <     = w w K a yK Developed for scour of clay boundaries, but claimed suitable for alluvium also Kw K = a flow depth factor sp K = a pier shape factor (limited to cylindrical piers) θ = an approach-flow factor

164 Miller and Sheppard (2002)                         +                =                       −=               = >       = <<                                               − − +             − −       = <<                     = − 13.0 50 *2.1 50 * 50 * 3 2 2 4.0 *1 *1* 50 * 3 *1* 50 * 32*1* 6.104.0 ln75.11 tanh 2.2 1 1 5.2 1 1 2.2 47.0 5.2 D a D a D a f V V f a y f V V V V if a yf a y V V V V if D af V V V V V V V V V V a y f a y 1.0 V V if D af V Vf a yf a y c c lp c s c lp c c lp cc lp c lp c s c c s Kothyari et al. (2007) )/log(0068.0 5/1 5.0 16 86 3/1 Rd s ttFr D D a y a y            = where }]))/)([()//{()( 2/150 6/1 1686 3/12 DgDDyat sR ρρρ −= and 2/1 50)(       − = ρ ρρ Dg VFr s d

165 Table A-2 Dimensionless parameters included in the selected pier scour equations (The table is divided to indicate methods proposed since 1990) Reference y/a a/D Pier Shape Pier Alignment V/V Inglis (1949) c Ahmad (1951) Laursen (1958)  Chitale (1962) Laursen (1963)  Larras (1963)   Neill (1964)   Breusers (1965) Blench (1969)  Shen et al. (1969)  Coleman (1971)  Hancu (1971)   Neill (1973)  Breusers et al. (1977)     Jain and Fischer (1980)   Jain (1981)   Froehlich (1988)    Chitale (1988) Melville and Sutherland (1988)      Methods Proposed since 1990 May and Willoughby (1990)    Breusers and Raudkivi (1991)     Gao et al.(1993)      Ansari and Qadar (1994) Richardson and Davis (1995)    Wilson (1995)  Melville (1997)      Richardson and Davis (2001)    Briaud et al. (2004)    Miller and Sheppard (2002)      Kothyari et al. (2007)   Because design estimation focuses on the maximum scour depth at a pier of given structure, it is useful to recall which parameters are important for scour-depth estimation: 1. The parameters of primary importance are those pertaining to pier size (y/a, and a/D), pier shape, and pier alignment. In particular, as explained in Chapter 3. the

166 parameter y/a* defines the scale of the pier flow field (a* is effective pier width), and thereby the potential maximum scour depth; 2. The parameter V/Vc indicates the capacity of flow to erode and convey material on the approach boundary to a pier site, and affects scour depth. In terms of estimating a potential maximum scour depth it can be argued that the flow intensity parameter, V/Vc, is not a parameter of primary importance for pier sites where V/Vc, is likely to exceed unity, and the time development of scour is not an important concern. Scour at piers in most rivers develops sufficiently rapidly, and in high-flow conditions, that V/Vc is at a value producing maximum scour depth. Flow intensity can be important when flow duration is an issue; and, 3. It could be argued that when time development of scour is of concern (e.g., clear- water scour at wide piers), considerable uncertainty attends duration of V/Vc values and scour development. However over sufficient time (e.g., the design life of a bridge), scour may attain its maximum depth; and, 4. Other parameters are of lesser significance, because they do not influence potential maximum scour depth For example, sediment uniformity, σg , is not critical because at design flows the bed material is at, or close to, the point of being fully mobilized. Several of the earlier equations do not include any of the important dimensionless parameters; e.g. Inglis (1949), Ahmad (1951) and Chitale (1962). Further, several of the more recent methods do not either: notably Wilson (1995), Briaud et al. (2004), Richardson and Davis (2001), and Kothyari et al. (2007). The methods by Goa et al. (1993), Melville (1997), and Miller and Sheppard (2002) include all of the dimensionless parameters listed in Table A-2. The flow-scale parameter, y/a, appears in most methods developed since 1990. Several methods do not include the influence of a/D. Some do not include V/Vc . The methods by Breusers et al. (1977), Breusers and Raudkivi (1991), Melville and Sutherland (1988) and Melville (1997) have similar format. Melville (1997), builds upon, and is a refined version, of the earlier methods. Recently, under NCHRP Project 24-32, the Melville (1997) method is merged with the Sheppard and Miller (2006) method to form the Sheppard-Melville method. Similarly, the methods by Richardson and Davis (2001) represent development of the same basic approach (e.g., Richardson and Davis 1995). The elements of the method developed by Sheppard are presented in several publications (e.g., Miller and Sheppard 2002, FDOT 2010). Herein, Sheppard and Miller (2006) is cited as the representative publication. A.4 COMPARISON OF SCOUR-DEPTH PREDICTIONS This section compares the scour depth equations. It does so using the analysis already completed for NCHRP Project 24-32, whose objectives coincide in part with those of the present evaluation. The comparison applies the equations in Table A-1 to a number of hypothetical pier conditions, ranging from laboratory to prototype scales. For

167 completeness of evaluation, all the equations discussed in the previous section are included in the plots, either individually or in combination for cases where the original equation by a certain author has been replaced or augmented by a newer equation; e.g. the Melville (1997) equation is plotted in preference to that by Melville and Sutherland (1988). To be kept in mind is that some equations were developed expressly to give upper-bound estimates of scour depth (e.g., Melville 1997), while others comprise an equation developed as a close, empirical fit of data trends (e.g., Richardson and Davis 2001). This difference is useful to keep in mind when comparing scour depths obtained from the various methods. The results of these analyses are plotted in Figures A-1 through A-12 for all combinations of the parameter values shown in Table A-3. The equations are plotted chronologically in the figures. Table A-3 Range of parameter values for Figures A-1 through A-12 V/V y/a c D (mm) a(m) 1, 3 0.33, 1, 3 0.2, 3 0.05, 1, 10 In the bar charts, negative scour depths are indicated by missing bars (i.e. they are plotted as zero scour). When viewing the plots it is useful to note that green (a = 0.05m) represents usual laboratory scale, red represents nominally typical pile sizes (a = 1.0m), while blue represents piers considered very wide (a = 10m). In the figures, V1 is equivalent to V, and y1 is equivalent to y. Figures A-1 through A-3 show scour depth predictions for scenarios comprising clear- water to live-bed transition (threshold) flows (V/Vc = 1), fine sand (D = 0.2mm), and three different flow depth-to-pier width ratios (y/a = 3, 1, 0.33). Figures A-4 through A-6 are a parallel set of results for live bed conditions (V/Vc = 3). Similarly, Figures A-7 through A-12 apply to scenarios involving coarser sediment (D = 3mm).

168 Figure A-1 Comparison of normalized local scour depth predictions using 22 different equations/methods for transition from clear-water to live-bed scour conditions. Pier width large compared to the water depth, fine sand. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Ing lis1 94 9 Ah ma d 1 95 3 La urs en 19 58 -63 Ch ita le 19 62 La rra s 1 96 3 Br eu se rs 19 65 Ble nc h 1 96 9 Sh en 19 69 Co lem an 19 71 Ha nc u 1 97 1 Ne ill 19 73 Br eu se rs 19 77 Ja in 19 81 Fr oe hli ch 19 81 Ma y 1 99 0 Br eu se rs 19 91 Ga o 1 99 3 An sa ri 1 99 4 Wi lso n 1 99 4 Me lvi lle 19 97 Ri ch ard so n 2 00 1 Sh ep pa rd 20 06 y s / a V1/Vc=1, y1/a=0.33, D50=0.2 mm a=0.05 m a=1 m a=10 m

169 Figure A-2 Comparison of normalized local scour depth predictions using 22 different equations/methods for a particular live-bed scour condition. Pier width large compared to the water depth, fine sand. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Ing lis1 94 9 Ah ma d 1 95 3 La urs en 19 58 -63 Ch ita le 19 62 La rra s 1 96 3 Br eu se rs 19 65 Ble nc h 1 96 9 Sh en 19 69 Co lem an 19 71 Ha nc u 1 97 1 Ne ill 19 73 Br eu se rs 19 77 Ja in 19 81 Fro eh lich 19 81 Ma y 1 99 0 Br eu se rs 19 91 Ga o 1 99 3 An sa ri 1 99 4 Wi lso n 1 99 4 Me lvil le 19 97 Ric ha rds on 20 01 Sh ep pa rd 20 06 y s / a V1/Vc=3, y1/a=0.33, D50=0.2 mm a=0.05 m a=1 m a=10 m

170 Figure A-3 Comparison of normalized local scour depth predictions using 22 different equations/methods for transition from clear- water to live-bed scour conditions. Pier width equal to water depth, fine sand 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Ing lis1 94 9 Ah ma d 1 95 3 La urs en 19 58 -63 Ch ita le 19 62 La rra s 1 96 3 Br eu se rs 19 65 Ble nc h 1 96 9 Sh en 19 69 Co lem an 19 71 Ha nc u 1 97 1 Ne ill 19 73 Br eu se rs 19 77 Ja in 19 81 Fro eh lich 19 81 Ma y 1 99 0 Br eu se rs 19 91 Ga o 1 99 3 An sa ri 1 99 4 Wi lso n 1 99 4 Me lvil le 19 97 Ric ha rds on 20 01 Sh ep pa rd 20 06 y s / a V1/Vc=1, y1/a=1, D50=0.2 mm a=0.05 m a=1 m a=10 m

171 Figure A-4 Comparison of normalized local scour depth predictions using 22 different equations/methods for a particular live-bed scour condition. Pier width equal to water depth, fine sand 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Ing lis1 94 9 Ah ma d 1 95 3 La urs en 19 58 -63 Ch ita le 19 62 La rra s 1 96 3 Br eu se rs 19 65 Ble nc h 1 96 9 Sh en 19 69 Co lem an 19 71 Ha nc u 1 97 1 Ne ill 19 73 Br eu se rs 19 77 Ja in 19 81 Fro eh lich 19 81 Ma y 1 99 0 Br eu se rs 19 91 Ga o 1 99 3 An sa ri 1 99 4 Wi lso n 1 99 4 Me lvil le 19 97 Ric ha rds on 20 01 Sh ep pa rd 20 06 y s / a V1/Vc=3, y1/a=1, D50=0.2 mm a=0.05 m a=1 m a=10 m

172 Figure A-5 Comparison of normalized local scour depth predictions using 22 different equations/methods for transition from clear- water to live-bed scour conditions. Deep water relative to pier width, fine sand 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Ing lis1 94 9 Ah ma d 1 95 3 La urs en 19 58 -63 Ch ita le 19 62 La rra s 1 96 3 Br eu se rs 19 65 Ble nc h 1 96 9 Sh en 19 69 Co lem an 19 71 Ha nc u 1 97 1 Ne ill 19 73 Br eu se rs 19 77 Ja in 19 81 Fro eh lich 19 81 Ma y 1 99 0 Br eu se rs 19 91 Ga o 1 99 3 An sa ri 1 99 4 Wi lso n 1 99 4 Me lvil le 19 97 Ric ha rds on 20 01 Sh ep pa rd 20 06 y s / a V1/Vc=1, y1/a=3, D50=0.2 mm a=0.05 m a=1 m a=10 m

173 Figure A-6 Comparison of normalized local scour depth predictions using 22 different equations/methods for a particular live-bed scour condition. Deep water relative to pier width, fine sand 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Ing lis1 94 9 Ah ma d 1 95 3 La urs en 19 58 -63 Ch ita le 19 62 La rra s 1 96 3 Br eu se rs 19 65 Ble nc h 1 96 9 Sh en 19 69 Co lem an 19 71 Ha nc u 1 97 1 Ne ill 19 73 Br eu se rs 19 77 Ja in 19 81 Fro eh lich 19 81 Ma y 1 99 0 Br eu se rs 19 91 Ga o 1 99 3 An sa ri 1 99 4 Wi lso n 1 99 4 Me lvil le 19 97 Ric ha rds on 20 01 Sh ep pa rd 20 06 y s / a V1/Vc=3, y1/a=3, D50=0.2 mm a=0.05 m a=1 m a=10 m

174 Figure A-7 Comparison of normalized local scour depth predictions using 22 different equations/methods for transition from clear- water to live-bed scour conditions. Pier width large compared to water depth, very coarse sand 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Ing lis1 94 9 Ah ma d 1 95 3 La urs en 19 58 -63 Ch ita le 19 62 La rra s 1 96 3 Br eu se rs 19 65 Ble nc h 1 96 9 Sh en 19 69 Co lem an 19 71 Ha nc u 1 97 1 Ne ill 19 73 Br eu se rs 19 77 Ja in 19 81 Fro eh lich 19 81 Ma y 1 99 0 Br eu se rs 19 91 Ga o 1 99 3 An sa ri 1 99 4 Wi lso n 1 99 4 Me lvil le 19 97 Ric ha rds on 20 01 Sh ep pa rd 20 06 y s / a V1/Vc=1, y1/a=0.33, D50=3 mm a=0.05 m a=1 m a=10 m

175 Figure A-8 Comparison of normalized local scour depth predictions using 22 different equations/methods for a particular live-bed scour condition. Pier width large relative to water depth, fine sand, very coarse sand 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Ing lis1 94 9 Ah ma d 1 95 3 La urs en 19 58 -63 Ch ita le 19 62 La rra s 1 96 3 Br eu se rs 19 65 Ble nc h 1 96 9 Sh en 19 69 Co lem an 19 71 Ha nc u 1 97 1 Ne ill 19 73 Br eu se rs 19 77 Ja in 19 81 Fro eh lich 19 81 Ma y 1 99 0 Br eu se rs 19 91 Ga o 1 99 3 An sa ri 1 99 4 Wi lso n 1 99 4 Me lvil le 19 97 Ric ha rds on 20 01 Sh ep pa rd 20 06 y s / a V1/Vc=3, y1/a=0.33, D50=3 mm a=0.05 m a=1 m a=10 m

176 Figure A-9 Comparison of normalized local scour depth predictions using 22 different equations/methods for transition from clear-water to live-bed scour conditions. Pier width equal to water depth, very coarse sand 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Ing lis1 94 9 Ah ma d 1 95 3 La urs en 19 58 -63 Ch ita le 19 62 La rra s 1 96 3 Br eu se rs 19 65 Ble nc h 1 96 9 Sh en 19 69 Co lem an 19 71 Ha nc u 1 97 1 Ne ill 19 73 Br eu se rs 19 77 Ja in 19 81 Fro eh lich 19 81 Ma y 1 99 0 Br eu se rs 19 91 Ga o 1 99 3 An sa ri 1 99 4 Wi lso n 1 99 4 Me lvil le 19 97 Ric ha rds on 20 01 Sh ep pa rd 20 06 y s / a V1/Vc=1, y1/a=1, D50=3 mm a=0.05 m a=1 m a=10 m

177 Figure A-10 Comparison of normalized local scour depth predictions using 22 different equations/methods for a particular live-bed scour condition. Pier width equal to water depth, very coarse sand 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Ing lis1 94 9 Ah ma d 1 95 3 La urs en 19 58 -63 Ch ita le 19 62 La rra s 1 96 3 Br eu se rs 19 65 Ble nc h 1 96 9 Sh en 19 69 Co lem an 19 71 Ha nc u 1 97 1 Ne ill 19 73 Br eu se rs 19 77 Ja in 19 81 Fro eh lich 19 81 Ma y 1 99 0 Br eu se rs 19 91 Ga o 1 99 3 An sa ri 1 99 4 Wi lso n 1 99 4 Me lvil le 19 97 Ric ha rds on 20 01 Sh ep pa rd 20 06 y s / a V1/Vc=3, y1/a=1, D50=3 mm a=0.05 m a=1 m a=10 m

178 Figure A-11 Comparison of normalized local scour depth predictions using 22 different equations/methods for transition from clear- water to live-bed scour conditions. Deep water relative to pier width, very coarse sand. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Ing lis1 94 9 Ah ma d 1 95 3 La urs en 19 58 -63 Ch ita le 19 62 La rra s 1 96 3 Br eu se rs 19 65 Ble nc h 1 96 9 Sh en 19 69 Co lem an 19 71 Ha nc u 1 97 1 Ne ill 19 73 Br eu se rs 19 77 Ja in 19 81 Fro eh lich 19 81 Ma y 1 99 0 Br eu se rs 19 91 Ga o 1 99 3 An sa ri 1 99 4 Wi lso n 1 99 4 Me lvil le 19 97 Ric ha rds on 20 01 Sh ep pa rd 20 06 y s / a V1/Vc=1, y1/a=3, D50=3 mm a=0.05 m a=1 m a=10 m

179 Figure A-12 Comparison of normalized local scour depth predictions using 22 different equations/methods for a particular live-bed scour condition. Deep water relative to pier width, very coarse sand 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Ing lis1 94 9 Ah ma d 1 95 3 La urs en 19 58 -63 Ch ita le 19 62 La rra s 1 96 3 Br eu se rs 19 65 Ble nc h 1 96 9 Sh en 19 69 Co lem an 19 71 Ha nc u 1 97 1 Ne ill 19 73 Br eu se rs 19 77 Ja in 19 81 Fro eh lich 19 81 Ma y 1 99 0 Br eu se rs 19 91 Ga o 1 99 3 An sa ri 1 99 4 Wi lso n 1 99 4 Me lvil le 19 97 Ric ha rds on 20 01 Sh ep pa rd 20 06 y s /a V1/Vc=3, y1/a=3, D50=3 mm a=0.05 m a=1 m a=10 m

180 The methods used in Figures A-1 through A-12 were developed during the period 1949 to 2006. Improvements in the understanding of pier scour processes inevitably have resulted in improvements to scour-depth predictive methods. For example, several of the earlier equations give negative scour depths. Also, the variability amongst the equations tends to reduce with time. Considering the variation in the predictions of local scour for different sized piers (“laboratory” to “typical field” to “very large field”), it is evident that some methods have scour depth ratios decreasing with increasing pier size, while other equations show constant values of scour depth ratio from laboratory to field. Conversely, the Coleman (1971) equation shows larger scour depth ratios in the field than in the laboratory, which is unlikely to be correct. The main objective of these plots is to identify the methods producing unrealistic results for prototype scale piers and thus should be eliminated from further consideration. The regime equations proposed by Inglis (1949), Ahmad (1951) and Chitale (1962) yield negative scour depths in some cases. As noted above the, Coleman (1971) equation has an unrealistic trend with increasing pier size and therefore is eliminated. Several other equations predict unacceptably high scour depth ratios; i.e., Inglis (1949), Ahmad (1951), Chitale(1962), Hancu (1971) and Shen et al. (1969), and thus are eliminated as well. This leaves 23 methods/equations for further consideration. Referring to Table A-2, several of the remaining equations include few or none of the important dimensionless parameters. In this category are the methods by Laursen (1958, 1963), Larras (1963), Neill (1964, 1973), Breusers (1965), Blench (1969), Jain and Fischer (1980), Jain (1981), Chitale (1988), Ansari and Qadar (1994), Briaud et al. (2004), and Kothyari(2007). These methods are eliminated from further consideration on this basis. It is noted also, that the method by Ansari and Qadar (1994) can lead to very low scour depths compared to predictions by most of the other more recent equations. The remaining 11 methods include those by Breusers et al. (1977), Breusers and Raudkivi (1991), Melville and Sutherland (1988) and Richardson and Davis (1995). As discussed earlier, these equations have been superseded by more recent equations, notably Melville (1997) and Richardson and Davis (2001). The method by Gao et al. (1993) can lead to excessively high scour depths in fine sediments, as shown in the comparison plots for D = 0.2mm. In addition, it is noted that the equation by May and Willoughby (1990) was developed from data pertinent to large offshore structures. Eliminating these 6 methods leaves the following 5 methods for further consideration: Froehlich (1988), Wilson (1995), Melville (1997), Richardson and Davis (2001), and Sheppard and Miller (2006, or Sheppard-Melville). A.5 DISCUSSION By virtue of its extensive use in the U.S., and its current use in HEC-18, the Richardson and Davis (2001) method requires further consideration. Moreover, the Sheppard and Miller (2006, now Sheppard-Melville) method, recommended based on the extensive

181 appraisal in NCHRP Project 24-32, also requires further consideration. The two methods yield overall comparable estimates of scour depth in the assessment shown in Section A.4. However, this finding does not mean that each method automatically yields an estimate of the potential maximum scour depth at a pier. These two methods can be identified as the two leading methods, and accordingly are examined further in Chapter 6. Of the five remaining methods mentioned above, two can be dropped because they include fewer parameters, as indicated in Table A-4, which shows the number of parameters each method includes, and because they are unlikely to be adopted for use in HEC-18; i.e., Froehlich (1988) and Wilson (1995). The Melville (1997) method has been merged with the Miller and Sheppard (2002) method, under NCHRP Project 24-32, and therefore Melville (1997) is not considered further herein. However, it is worth noting the method’s strengths as a design method, and in delineating differences in scour-depth trends with varying values of y/a. As a design method, Melville (1997) provides an upper-bound estimate of scour depth estimated in accordance with a wide set of parameter influences. The method’s characterization of parameter influences is more physically based than prior methods. Table A-4 Some characteristics of the remaining 5 equations Method Main data sources No. of important dimensionless parameters Froehlich (1988) field and laboratory 3 Wilson (1995) field 1 Melville (1997) laboratory 6 Richardson and Davis (2001) laboratory 4 Sheppard and Miller (2006, Sheppard- Melville) laboratory 6