Bridges and bridge pier scour gradually varying profile upstream and downstream of bridges as q=Q/b increases, the critical depth increases, thus for F<1 flows there is an increased chance to cross the critical depth. Note that a supercritical flow will remain supercritical bridges represents for open channel flows a lateral (and/or a vertical) contraction.
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Bridges and bridge pier scour - University of Minnesotapersonal.cege.umn.edu/.../bridges_bridgepiers.pdf · Comparison with Bridge Scour A test case using only the turbine support
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Bridges and bridge pier scour
gradually varying profile upstream and downstream of bridges
as q=Q/b increases, the critical depth increases, thus for F<1 flows there is an increased chance to cross the critical depth. Note that a supercritical flow will remain supercritical
bridges represents for open channel flows a lateral (and/or a vertical) contraction.
backwater and overtopping : crucial for flood prevention and alert systems
water above the bridge may be ok
Eagle Creek Bridge, Idaho Panhandle National Forest. Dep. of Agriculture
magdeburg bridge
local passage trough critical condition: no Hydraulic jump downstream as the normal depth decreases rapidly marginal energy losses energy eq. still applicable
Choking of the cross section, going through critical in (2) occurs for r=b2/b4 satisfying equation:
32
4
2
4
3
)21(
)/12(
F
Frr
1 2 3 4 section #
this is a type I-II limiting case: Note that a back water effect is also induced by the drag on the bridge piers (momentum eq. approach, using similar dimensionless variable) BB which one is the undisturbed section?
Bridge contraction modeling (abutment) energy equation
1 2 3 4
41
2
444
2
111410
22 th
g
Vy
g
VyLS
the S0L1-4 term balances the energy losses due to flow resistance in the uniform flow, therefore we can consider : ht1-4 - hbridge 2-3 ~ S0L1-4
g
V
A
A
A
A
g
VKyyh
A
VKhand
hg
V
g
Vyy
nnnt
ntb
b
22*
22
2
2
2
1
2
2
4
21
2
2241
4
2
232
32
2
11
2
4441
mean cross sect. velocity in the contracted section
remember Q=A4V4=A1V1=An2Vn2
where Kt=f(pier geometry, contraction , eccentricity)
distance from 1 4 * slope = Δz14 total head losses 1 4
based on the cross flow geometry we define the bridge opening discharge ratio M0=Qb/Q for the approach section (In the bridge section obviously Qb=Q)
How do we estimate the total bridge head loss coefficient Kt=f(pier geometry, contraction , eccentricity)
Let us consider all the possible factors inducing localized energy losses
Is the condition in which the shear flow stress is near to the critical stress evaluated on that grain size (Shield Theory), or, talking in terms of velocity, U flow is lower than Uc (critical velocity).
𝜏𝑐 = 𝜃𝑐𝑟 𝜌𝑠 − 𝜌𝑤 𝑔𝑑50 𝜃𝑐𝑟 = 𝑎𝐷∗𝑏
𝐷∗ =𝑠 − 1 𝑔
𝜐2
1/3
𝑑50 𝜏0 = 𝜌𝑢∗
2 = 𝜌𝑔𝑆𝑒 (Shear stress in uniform flow)
MOTION
Main channel experiment: comparing the scour of a MHK turbine with the scour of the bridge pier: pier diameter ~5cm, flow depth ~1.2m
Comparison with Bridge Scour A test case using only the turbine support tower was performed at both small-scale (Fig. 4a) and large-scale (Fig. 3a), providing results analogous to a submerged bridge pier. Local scour depths occurring near bridge piers can be described by 𝑑𝑠 = 𝐾𝑦𝑊𝐾𝑙𝐾𝑑𝐾𝑠ℎ𝐾𝜃𝐾𝐺
where K = empirical expressions accounting for the various influences on the scour depth; KyW = depth size; Kl = flow intensity; Kd = sediment size; Ksh = pier or abutment shape; Kθ = pier or abutment alignment; and KG = channel geometry (Melville 1997). Dey et al. (2008) found variations in scour depths between surface-piercing and submerged piers; therefore, they proposed an additional submergence ratio factor, Ksb, to provide an updated estimate of the local scour depth. .