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1 /6/4 5 Stuctue-Induced Sediment Scou ef: Eosion and Sedimentation, P.Y. Julien, 998 The Mechanics of Scou in the Maine Envionment, B.M. Sume and J. Fedsoe, Evaluating Scou at Bidges (HEC-8), E.. ichadson and S.. Davis, ive Hydaulics, EM --46, USACE, 993 Topics: Defining Scou Contaction Scou Local Scou Live Bed vs. Clea Wate Paametes Affecting Scou Estimating Scou at Bidge Pies Examination of /D 5 Effect Scou The enlagement of a coss section y the emoval of ounday mateial though the action of the fluid in motion. (ive Hydaulics) Eosion of steamed o ank mateial due to flowing wate; often consideed as eing localized. (HEC-8) Types of Scou Geneal Scou - scou due to vaiale ackwate conditions and ed mateial load (flood event, seasonal vaiations, tide) Contaction Scou - scou due to "contaction" of channel flow aea (stuctue addition, vegetation, deis) Local Scou - scou due to flow ostuctions and associated flow acceleations and votices Oiginal Bed Local Scou Contaction Scou

2 /6/4 Stuctue-Induced Scou occus due to the changes in flow due to the intoduction of a stuctue into the channel, inlet, etc. degadation - a geneal and pogessive (long-tem) loweing of the channel ed due to eosion, ove a elatively long channel length. aggadation - geneal and pogessive uildup of the longitudinal pofile of a channel ed due to sediment deposition (i.e. fom an upsteam souce). clea wate - Tanspot of ed mateial some distance away fom the stuctue (i.e., upsteam) is negligile, / c < live ed - Tanspot of ed mateial some distance away fom the stuctue ( i.e., upsteam) is not negligile, / c > Local Scou stuctue causes a change in the flow: down-flow, hoseshoe votex, wake votices esults in scou aound the stuctue Flow ove flat ed Flow ove flat ed with stuctue

3 /6/4 Local Scou Mechanisms downflow wake votices hoseshoe votex ed Definition Sketch Flo y y s

4 /6/4 Clea Wate Scou Equation 5 3 c se D f f y Live Bed Scou Equation = 5 c lp c se D,, f y f y suface olle hoseshoe votex f (y /) = y f y / / c /D 5 = const. = const.

5 /6/4 f (/ c ) Depends on /D y o / = const. 5 / c lp / c f 3 (/D 5 ) / c = y / = const. log(/d 5 )

6 /6/4 Why /D 5? Examine the flow field nea a cicula pile Estimate the velocity and pessue fields using potential flow theoy y Flow a θ x The steam function in pola coodinates fo the flow descied in the figue is a sin ψ= θ ψ steam function, depth mean velocity of the appoach flow, adial coodinate, θ angula coodinate, a adius of the cicula pile = /. The adial and angula components of velocity in tems of the steam function ae: ψ a = = cos θ θ and ψ a θ = = sinθ +. adial component of velocity and θ angula component of velocity.

7 /6/4 The magnitude of the velocity is then 4 a a v = + θ = ( cos θ ) + Benoulli s equation estalishes the elationship etween pessue and velocity, p + p v = +. ρ ρ The pessue on the leading edge of the pile, (the stagnation pessue) is thus p s ρ ρ = p + o ( ps p) =, p pessue at mid elevation in the appoach flow, p s stagnation pessue on the leading edge of the pile and ρ mass density of the wate.. The pessue at any point in the flow field is ( ) ρ p p v p p v = ρ =, o. Nomalizing the equations using the following vaiales v, and a p p p p P = p ps ρ esults in 4 = θ ( cos ) +, and P = cos θ. The gadient of the pessue is a vecto whose magnitude is the maximum spatial change in pessue and whose diection is that of the maximum change. P ) P) P = e + e θ. θ

8 /6/4 3 3 ) ) P = 4 cos e 8 sinθcos θ eθ θ + P nomalized pessue gadient, ê unit vecto in the adial diection and ê unit vecto in the angula diection. θ The magnitude of the pessue gadient at any point in the flow field (in the main ody of flow, outside the wake egion) is then 3 4 P = dp 4 dn = cos θ+ N n a = nomalized coodinate in the diection of maximum change in pessue and n dimensional coodinate in the diection of maximum change in pessue., 3 Nomalized Pessue Gadient Contous FLOW y/ Pile Wake x/

9 /6/4 Next conside the foces acting on a sediment paticle on the ed Sediment Gain p z c p df p = p + c cosβda n β = p + c c d dfp(n) da p n cosβπ sinβ β = df cosβ p n Fd = Cd ρ A u F d dag foce, C d dag coefficient, ρ mass density of the wate, A pojected aea of the paticle = π c fo a sphee c is D 5 / and u appoach velocity at the level of the paticle. The foce on the paticle due to the pessue gadient can e estimated y consideing the paticle to e a sphee and integating the component of the stuctue-induced pessue foce in the diection of maximum pessue gadient ove the suface of the sphee. efe to the definition sketch in Figue 3. p dfp p c da n sin = + β p pessue at the cente of the paticle, da = π c sinβ c dβ= πc sinβ dβ and ( ) ( ) β angula coodinate measued fom the positive n diection, positive counte clock wise. The component of this diffeential foce in the n diection is then df =df cosβ. p(n) p

10 /6/4 Integating the component of the pessue foce in the n diection ove the suface of the paticle esults in π π 4πc ρ d, o Fp(n) = πc psinβcosβd β cos sin cos a θ+ β β β πc ρ Fp(n) = θ+ 3a cos. In ode to see the elative magnitudes of the pe ssue and dag foces the asolute value of the atio F p /F d is computed πc ρ Fp(n) 3a cos θ+ = F d Cd ρπc u d d D5, o 3 4 Fp(n) 6 = cos F 3 C u θ+. Foce atio θ = π/ θ = π /D 5 = 44 /u = 3 C d = Summay Stuctue-induced pessue gadient foce significant nea stuctue Possile explanation fo equiliium scou depth dependence on /D 5 3