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

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x LIST OF SYMBOLS a = pier width (without debris) ae a = width of an equivalent uniform pier a * = effective pier width F a = pier foundation width (e.g., caisson width) p = projected width of the pier; ap b = pier length = b sinθ + a cosθ for rectangular piers Bd c = parameter describing soil cohesion effects = width of floating debris raft D = median diameter of bed particle Dx Eu = Euler number; Eu = V = diameter of bed material of which x% are smaller 2 f = Darcy-Weisbach resistance coefficient /ga Fr = Froude number; Fr=V/(gy) Fr 0.5 c = critical Froude number Frc=Vc/(gy) Fr 0.5 a = critical Froude number defined with pier width Fra=V/(ga) Fr 0.5 d 2/1 50)(       − = ρ ρρ dg VFr s d= densimetric Froude number; g = acceleration of gravity H = depth of region within the scour hole covered by coarse sediment Hd L = height of debris d L = length of debris upstream from the pier face p K = pier distance from the abutment toe s K = pier aspect ratio parameter θ K = pier alignment parameter I n=shedding frequency of large scale vortices in the wake of the pier = flow intensity parameter q = average discharge intensity upstream from the bridge (m2 q /s) 2 = local discharge intensity in contracted channel (m2 Re = Reynolds number; Re=ρVa/µ /s) St = Strouhal number; St=na/V t = time; t* = equilibrium time scale; t*=Vte t /a e T = time to develop the equilibrium depth of scour d V = thickness (vertical dimension) of floating debris or ice raft * V = shear velocity *c V = mean approach flow velocity; = critical shear velocity for bed sediment entrainment fVV 8*= Va V = threshold velocity for the transition from clear-water to live-bed conditions for non-uniform sediments in Melville (1997) method c V = critical approach flow velocity for entrainment of bed sediment c′ = incipient velocity for local scour at a pier

xi Vlp = live-bed peak velocity in the Sheppard method, similar to Va xcdV in the Melville (1997) method = critical velocity for incipient motion for grain size D xicdV x = approach velocity required to initiate scour at the pier for grain size D W x d y = undisturbed approach flow depth = width of debris in the direction normal to the flow ycs y = uniform flow depth over a flat bed of particle sizes equivalent to the upstream coarse surface particles fs y = uniform flow depth over a flat bed of particle sizes equivalent to the underlying surface fine particles f y = flow depth at the abutment toe or on the floodplain for abutments on floodplains r y = regime depth in Blench (1967) pier scour formula S y = local maximum total scour depth Sf y = local maximum scour depth in the layer of fine sediment s-p y = scour-depth component for the pier column in the flow s-cap y = scour-depth component for the pile cap or footing in the flow s-pile group y = scour-depth component for the piles exposed to the flow Spier y = scour depth at the pier with the abutment present S0pier y = scour depth at the pier without the abutment Sabutment y = abutment scour depth t Y = level of the top of the footing, cap or caisson measured from general bed level = local scour depth at current time t Greek Symbols γ = specific weight of water µ = molecular viscosity of water ν = kinematic viscosity of water Ω = parameter describing the shape of the pier face (upstream side) ρ = water density ρs σ = sediment density g τ = geometric standard deviation of the boundary particle size distribution 1 τ = grain roughness component of bed shear c θ = angle of approach flow relative to pier alignment = critical shear stress at threshold of motion