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

where Kt=f(pier geometry, contraction , eccentricity, skewness) K= sum(Ki , ΔKi)

abutment geometry and related contraction coefficient

M0=Qb/Q for the approach section

USGS

bridge pier scour abutment scour

scour mechanism: localized vorticity and enhanced shear stress

bridge scour: crucial for structural stability

How about bridge scour ?

How to quantify it? Depends on the sediment transport regime. We distinguish between: 1) clear water experiments (no

sediment transport in the uniform flow, undisturbed reach)

2) live bed (with sediment transport and, possibly, migrating bedforms)

Scour mechanisms slightly change: sediment bedform propagation usually amplifies scour/deposition intensity

Critical Mobility

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

Tilting flume small scale experiment: rotor diameter ~0.15m, flow depth ~ 0.2m

zoom

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. .

Small-scale Large-scale

KyW 2.4cm 8.6cm

Kl 0.83 0.72

Kd 1.44 2.17

Ksh 1 1

Kθ 1 1

KG 1 1

Ksb 0.68 0.64

ds 1.9cm 8.6cm

Actual 1.6cm 7.5cm

% error 15.8% 12.8%

Table 2: Factors used for bridge scour comparison

analysis.