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From page 217... ... 217 acb coefficient, Equation 7-1 b flow parallel wing-wall abutment thickness, Figure 6-9 B upstream width of the flume, Equation 5-19 Bf floodplain width, Figure 7-3 B1 original channel width, Equations 5-4 and 5-6 in Table 5-2 B2 constricted channel width, Equations 5-4 and 5-6 in Table 5-2 C coefficient, Equation 5-18 Cs stability coefficient for incipient failure: 0.3 angular rock, 0.375 rounded rock, Equation 5-14 CT blanket thickness coefficient, given by Figure 1 in Maynord 1993, Equation 5-14 Cv vertical velocity distribution coefficient, Equation 5-14 C* coefficient determined from laboratory and field testing, Equation 5-15 d sediment diameter, Equation 8-7 dabut,avg time-averaged scour depth at abutment, Table 9-2 db distance between the average bed level and the bottom of the apron, Figure 7-13 dc maximum scour at the countermeasure, Table 9-3 dcm,avg time-averaged scour depth at the countermeasure, Table 9-4 dmax,abut maximum scour depth at the abutment foundation, Table 9-11 dmax,abut,inst maximum instantaneous scour depth at abutment, Table 9-4 dmax.col maximum scour near the abutment collar countermeasure, Table 9-11 dmax,sp1,avg maximum scour depth behind the first spur dike, Table 9-9 dmax,sp2,avg maximum scour depth behind the second spur dike, Table 9-9 dmax,sp3,avg maximum scour depth behind the third spur dike, Table 9-9 dmax,sp1,inst maximum instantaneous scour depth in front of the first spur dike dmax,sp2,inst maximum instantaneous scour depth at the second spur dike, Table 9-10 dabut,avg time-averaged scour depth at the abutment, Table 9-2 dmax,ch scour depth in the channel away from the abutment, Table 9-1 dmax,cm,inst maximum instantaneous scour depth at the countermeasure, Table 9-4 dmax,dn,abut scour depth at a short distance downstream of the downstream corner of the abutment, Table 9-1 dmax,sp,avg maximum scour depth at the spur dike, Table 9-8 dmax,up,abut scour depth at the upstream corner of the abutment, Table 9-1 dM tail-water depth immediately downstream of the scour hole, Equation 5-8 dsA scour reduction at the abutment with scour countermeasure, Section 6.4.1 dsAO scour depth at the abutment without scour countermeasure, Section 6.4.1 dsmax maximum scour depth, Section 7.3.4 dsO equilibrium scour depth below the bed surface without countermeasures, Section 8.5.3 ds1 vertical distance from the original top of the apron to the apron settlement near the abutment, Figure 7-13 ds2 vertical distance from the top of the apron to the apron edge settlement, Figure 7-13 dsf depth of the scour hole relative to the floodplain, Figure 8-12 Notation Read the entire page →
From page 218... ... d16 particle size of which 16 percent of the grains are finer, Section 7.2.1 d50 median particle size, Section 6.3.1 d84 particle size of which 84 percent of the grains are finer, Section 7.2.1 D riprap diameter, Table 5-6 DB geobag thickness, Equation 5-23 Dn design diameter of the cable-tied blocks, Equation 5-20 DR equivalent riprap diameter, Equation 7-17 Ds distance between the farthest spur dike tip at the main channel end and the abutment tip, Table 9-8; and spacing between spur dikes or the spur dike and the abutment, Table 9-9 D30 riprap size for which 30 percent by weight are finer, Equation 5-13 D50 median grain or riprap size, Equations 5-6 in Table 5-2 E parameter that has a value of 0.86 for loosely placed stones in flowing water and 1.2 for those that have become embedded, Equation 5-10 Ev kinematic eddy viscosity, Section 8.4.2 f Lacey silt factor, Equation 5-1 in Table 5-2 Fbo Blench's zero bed factor, which is a function of grain size, Equation 5-2 in Table 5-2 Fn Froude number, Equations 5-4 and 5-5 in Table 5-2 Fr flow Froude number, Equation 5-15 Fr2 Froude number in the contracted section, Equations 5-F through 5-H in Table 5-5 h1 main channel bank height, Table 9-1 Ha flow parallel thickness of abutment, Figure 6-3 Hb minimum required block height, Equation 7-2 Ht total drop in head, measured from the upstream to downstream energy grade line m, Equation 5-8 Hcb height of concrete blocks, Equation 5-22 k function of approach conditions, Equations 51 through 5-5 in Table 5-2 ks roughness height, Equation 8-2 K function of drag coefficient (CD) that varies between 2.5 and 5.0, Equation 5-4 in Table 5-2 K1 side slope correction factor, Equation 5-14 Kd slope factor, Equation 5-17 Kh depth parameter, Equation 5-17 Ks shape factor, Equations 5-G and 5-H in Table 5-5 KS shape factor associated with the abutment shape, Equation 7-17 Ksl embankment slope factor, Equations 5-B and 5-C in Table 5-5 KT turbulence adjustment factor, Equation 5-17 La abutment length perpendicular to flow, Equation 5-19 Lb bottom length of cable-tied block, Figure 7-8 Lp pier length, Section 5.7; and projected width of the parallel-wall countermeasure, Figure 9-14 Ls apron spread length, Figure 7-28 Lsd effective length of the spur dike, Equations 55 and 5-7 in Table 5-2 Lsdp spur dike protrusion length, Table 9-8 Lspw wall length, Table 9-4 Lt top length of cable-tied block, Figure 7-8 n Manning coefficient, Equation 7-5 Nsc dimensionless stability factor for riprap stone, Equation 5-10 Nsd number of spur dikes, Table 9-9 pm volume fraction pore space within the mattress, Equation 7-2 Pb protrusion of the blocks above bed level, Equation 7-4 Pe Peclet number, Section 8.4.2 q discharge per unit width, Equations 5-2 and 5-3 in Table 5-2 Q total discharge, Equation 5-1 in Table 5-2 Qf lateral or floodplain flow discharge, Section 9.3.1 QO flow directly upstream of the bridge opening, Figure 8-26 QT total flow in the compound channel upstream of the bridge crossing, Figure 8-26 Q100 discharge in the 100 feet of stream adjacent to the abutment, Section 9.3.1 ra apron width, Figure 6-9 rs assumed multiple of scour at a dike taken as 11.5 by Laursen, Equation 5-7 in Table 5-2 rt radius of the spill-through abutment toe, Equation 5-19 Rb centerline radius of curvature of bend, Equation 5-14 Rdmax distance to the deepest point of the scour hole from the abutment end, Equation 8-9 R50 median grain size of stone that makes up the grade control, weir, or check-dam, Equation 5-9 Sb parallel-wall countermeasure side slope, Table 9-5 Scb specific gravity of the blocks, Equation 7-5 Sfa stability factor varying from 1.6 to 2.0 for abutment protection, Equation 5-C in Table 5-5 218 Read the entire page →
From page 219... ... Sf safety factor >1, Equation 5-14 Sn parallel-wall countermeasure end slope, Table 9-5 Sr the specific gravity of the riprap stones, Equation 5-11 SS specific gravity of riprap stone, Equation 5-20 SSB specific gravity of the geobag, Equation 5-23 t run time, Table 9-2 te experiment run time, Table 9-1 tp thickness of the protection unit, Equation 5-17 TI turbulent intensity at 10 percent of the water depth above the bed, Equation 5-20 U mean flow velocity, Figure 5-34 u* shear velocity, Section 6.3.1 u* Read the entire page →
From page 220... ... fluid kinematic viscosity, Equation 8-3 cb density of the concrete blocks, Equation 5-21 g standard deviation of sediment size, Section 6.3.1 bed shear stress, Equation 8-6 c critical bed shear stress for incipient movement of bed sediment, Equation 8-7 wc critical bed shear tress on local bed slope, Equation 8-8 stability parameter, Equation 7-18 ai downstream apron initiation angle, Equation 5-19 sl slope angle, Equation 5-B in Table 5-5 st stability parameter, Equation 5-23 cr critical shear stress parameter, Equation 5-17 repose angle of the bed material, Equation 8-8 vorticity, Equation 8-1 220 Read the entire page →

From page 217...

... 217 acb coefficient, Equation 7-1 b flow parallel wing-wall abutment thickness, Figure 6-9 B upstream width of the flume, Equation 5-19 Bf floodplain width, Figure 7-3 B1 original channel width, Equations 5-4 and 5-6 in Table 5-2 B2 constricted channel width, Equations 5-4 and 5-6 in Table 5-2 C coefficient, Equation 5-18 Cs stability coefficient for incipient failure: 0.3 angular rock, 0.375 rounded rock, Equation 5-14 CT blanket thickness coefficient, given by Figure 1 in Maynord 1993, Equation 5-14 Cv vertical velocity distribution coefficient, Equation 5-14 C* coefficient determined from laboratory and field testing, Equation 5-15 d sediment diameter, Equation 8-7 dabut,avg time-averaged scour depth at abutment, Table 9-2 db distance between the average bed level and the bottom of the apron, Figure 7-13 dc maximum scour at the countermeasure, Table 9-3 dcm,avg time-averaged scour depth at the countermeasure, Table 9-4 dmax,abut maximum scour depth at the abutment foundation, Table 9-11 dmax,abut,inst maximum instantaneous scour depth at abutment, Table 9-4 dmax.col maximum scour near the abutment collar countermeasure, Table 9-11 dmax,sp1,avg maximum scour depth behind the first spur dike, Table 9-9 dmax,sp2,avg maximum scour depth behind the second spur dike, Table 9-9 dmax,sp3,avg maximum scour depth behind the third spur dike, Table 9-9 dmax,sp1,inst maximum instantaneous scour depth in front of the first spur dike dmax,sp2,inst maximum instantaneous scour depth at the second spur dike, Table 9-10 dabut,avg time-averaged scour depth at the abutment, Table 9-2 dmax,ch scour depth in the channel away from the abutment, Table 9-1 dmax,cm,inst maximum instantaneous scour depth at the countermeasure, Table 9-4 dmax,dn,abut scour depth at a short distance downstream of the downstream corner of the abutment, Table 9-1 dmax,sp,avg maximum scour depth at the spur dike, Table 9-8 dmax,up,abut scour depth at the upstream corner of the abutment, Table 9-1 dM tail-water depth immediately downstream of the scour hole, Equation 5-8 dsA scour reduction at the abutment with scour countermeasure, Section 6.4.1 dsAO scour depth at the abutment without scour countermeasure, Section 6.4.1 dsmax maximum scour depth, Section 7.3.4 dsO equilibrium scour depth below the bed surface without countermeasures, Section 8.5.3 ds1 vertical distance from the original top of the apron to the apron settlement near the abutment, Figure 7-13 ds2 vertical distance from the top of the apron to the apron edge settlement, Figure 7-13 dsf depth of the scour hole relative to the floodplain, Figure 8-12 Notation

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From page 218...

... d16 particle size of which 16 percent of the grains are finer, Section 7.2.1 d50 median particle size, Section 6.3.1 d84 particle size of which 84 percent of the grains are finer, Section 7.2.1 D riprap diameter, Table 5-6 DB geobag thickness, Equation 5-23 Dn design diameter of the cable-tied blocks, Equation 5-20 DR equivalent riprap diameter, Equation 7-17 Ds distance between the farthest spur dike tip at the main channel end and the abutment tip, Table 9-8; and spacing between spur dikes or the spur dike and the abutment, Table 9-9 D30 riprap size for which 30 percent by weight are finer, Equation 5-13 D50 median grain or riprap size, Equations 5-6 in Table 5-2 E parameter that has a value of 0.86 for loosely placed stones in flowing water and 1.2 for those that have become embedded, Equation 5-10 Ev kinematic eddy viscosity, Section 8.4.2 f Lacey silt factor, Equation 5-1 in Table 5-2 Fbo Blench's zero bed factor, which is a function of grain size, Equation 5-2 in Table 5-2 Fn Froude number, Equations 5-4 and 5-5 in Table 5-2 Fr flow Froude number, Equation 5-15 Fr2 Froude number in the contracted section, Equations 5-F through 5-H in Table 5-5 h1 main channel bank height, Table 9-1 Ha flow parallel thickness of abutment, Figure 6-3 Hb minimum required block height, Equation 7-2 Ht total drop in head, measured from the upstream to downstream energy grade line m, Equation 5-8 Hcb height of concrete blocks, Equation 5-22 k function of approach conditions, Equations 51 through 5-5 in Table 5-2 ks roughness height, Equation 8-2 K function of drag coefficient (CD) that varies between 2.5 and 5.0, Equation 5-4 in Table 5-2 K1 side slope correction factor, Equation 5-14 Kd slope factor, Equation 5-17 Kh depth parameter, Equation 5-17 Ks shape factor, Equations 5-G and 5-H in Table 5-5 KS shape factor associated with the abutment shape, Equation 7-17 Ksl embankment slope factor, Equations 5-B and 5-C in Table 5-5 KT turbulence adjustment factor, Equation 5-17 La abutment length perpendicular to flow, Equation 5-19 Lb bottom length of cable-tied block, Figure 7-8 Lp pier length, Section 5.7; and projected width of the parallel-wall countermeasure, Figure 9-14 Ls apron spread length, Figure 7-28 Lsd effective length of the spur dike, Equations 55 and 5-7 in Table 5-2 Lsdp spur dike protrusion length, Table 9-8 Lspw wall length, Table 9-4 Lt top length of cable-tied block, Figure 7-8 n Manning coefficient, Equation 7-5 Nsc dimensionless stability factor for riprap stone, Equation 5-10 Nsd number of spur dikes, Table 9-9 pm volume fraction pore space within the mattress, Equation 7-2 Pb protrusion of the blocks above bed level, Equation 7-4 Pe Peclet number, Section 8.4.2 q discharge per unit width, Equations 5-2 and 5-3 in Table 5-2 Q total discharge, Equation 5-1 in Table 5-2 Qf lateral or floodplain flow discharge, Section 9.3.1 QO flow directly upstream of the bridge opening, Figure 8-26 QT total flow in the compound channel upstream of the bridge crossing, Figure 8-26 Q100 discharge in the 100 feet of stream adjacent to the abutment, Section 9.3.1 ra apron width, Figure 6-9 rs assumed multiple of scour at a dike taken as 11.5 by Laursen, Equation 5-7 in Table 5-2 rt radius of the spill-through abutment toe, Equation 5-19 Rb centerline radius of curvature of bend, Equation 5-14 Rdmax distance to the deepest point of the scour hole from the abutment end, Equation 8-9 R50 median grain size of stone that makes up the grade control, weir, or check-dam, Equation 5-9 Sb parallel-wall countermeasure side slope, Table 9-5 Scb specific gravity of the blocks, Equation 7-5 Sfa stability factor varying from 1.6 to 2.0 for abutment protection, Equation 5-C in Table 5-5 218

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From page 219...

... Sf safety factor >1, Equation 5-14 Sn parallel-wall countermeasure end slope, Table 9-5 Sr the specific gravity of the riprap stones, Equation 5-11 SS specific gravity of riprap stone, Equation 5-20 SSB specific gravity of the geobag, Equation 5-23 t run time, Table 9-2 te experiment run time, Table 9-1 tp thickness of the protection unit, Equation 5-17 TI turbulent intensity at 10 percent of the water depth above the bed, Equation 5-20 U mean flow velocity, Figure 5-34 u* shear velocity, Section 6.3.1 u*

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From page 220...

... fluid kinematic viscosity, Equation 8-3 cb density of the concrete blocks, Equation 5-21 g standard deviation of sediment size, Section 6.3.1 bed shear stress, Equation 8-6 c critical bed shear stress for incipient movement of bed sediment, Equation 8-7 wc critical bed shear tress on local bed slope, Equation 8-8 stability parameter, Equation 7-18 ai downstream apron initiation angle, Equation 5-19 sl slope angle, Equation 5-B in Table 5-5 st stability parameter, Equation 5-23 cr critical shear stress parameter, Equation 5-17 repose angle of the bed material, Equation 8-8 vorticity, Equation 8-1 220

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