Scour at Wide Piers and Long Skewed Piers (2011)

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53 L I S T O F S Y M B O L S Symbol Description Units Dimensions a Pier width ft (m) L a* Projected width of pier ft (m) L B Rectangular channel width ft (m) L D50 Median grain diameter mm L Fdi Densimetric particle Froude number for — — inception of scour Fr Froude Number of the approach flow — — Frc Critical Froude Number of the approach flow — — g Acceleration of gravity ft/s2 (m/s2) L/T2 K3 Factor for mode of sediment transport — — K4 Factor for armoring by bed material — — Ks Pier shape factor — — Kθ Discharge approach angle correction — — Kw Wide pier correction factor — — q Average discharge intensity upstream from ft3/s (m3/s) L3/s the bridge q2 Local discharge intensity in contracted channel ft3/s (m3/s) L3/s R Hydraulic radius ft (m) L Ss Specific gravity of bed sediment — — t Time s, h, day T te Time to “end” scour Kothyari et al. (2007) s, h, day T u* Shear velocity in the upstream section ft/s (m/s) L/T u*c Sediment critical shear velocity ft/s (m/s) L/T V1 Average velocity at upstream main channel ft/s (m/s) L/T Vc Sediment critical velocity for D50 ft/s (m/s) L/T Vc84 Sediment critical velocity for D84 ft/s (m/s) L/T Vlp1 Velocity used in computing “live-bed peak velocity” ft/s (m/s) L/T Vlp2 Velocity used in computing “live-bed peak velocity” ft/s (m/s) L/T y1 Average depth in the upstream main channel ft (m) L yr Regime depth ft (m) L ys Equilibrium scour depth ft (m) L yst Time dependent scour depth ft (m) L α Flow skew angle radians Plane Angle ν Kinematic viscosity ft2/s (m2/s) L2/T

54 ρ Density of water slugs/ft3 (kg/m3) FT2/L4 ρs Density of sediment slugs/ft3 (kg/m3) FT2/L4 σg Geometric standard deviation of particle size – — distribution τ1 Grain roughness component of bed shear stress lbf/ft2 (kPa) F/L2 τc Critical shear stress at threshold of motion lbf/ft2 (kPa) F/L2 ϕ Angle of repose of bed sediment radians Plane Angle Symbol Description Units Dimensions