Computational Modelling of Hurricane Wave Forcing on Bridge Decks

Raphael Crowley, Ph.D., P.E. Corbin Robeck, E.I. Assistant Professor Computational Analyst University of North Florida Corvid Technologies Department of Construction Management 45 Overhill Drive Building 50, Room 2400 Mooresville, NC 28117 Jacksonville, FL 32224 r.crowley@unf.edu

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Vulnerable Coastal Bridge Damage Summary (1979 – 2005)

Map of Bridge Failures Due to Hurricanes Since 1979

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Katrina Damage Summary

Mobile Bay Onramp Lake Pontchartrain Causeway Bridge

Biloxi Bay Bridge US-90 Bridge

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Quantification of Vertical Uplift Forcing

UF Physical Wave Model Photographs

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Wave Forcing on Bridge Data

Examples of Wave Forcing on Bridge Physical Data Showing Vertical Forcing (Top Graphs) and Horizontal

Forcing (Bottom Graphs) 5 of 24

Computational Model - Questions

• Can computational model recover Slamming Force?

• “How” to generate waves using computational model?

Schematic of Computational Model

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Computational Model – Summary Parameter Value/Method

Number of Cells ~6.3 Million

Cell Method Polyhedral

Cell Resolution ~1 cm near deck; 5 cm far from deck

Turbulence Model k-ε RANS

Wall Closure All y+ wall treatment

Wave Generation Method Varied

VOF Model Segregated two-phase VOF

Time Step Implicit unsteady

Wave-Generation Methods (Piston/Mesh Morphing)

Inlet for Piston Model

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Wave-Generation Methods (Linear/Fifth Order Wave Theory)

Example of Linear Model

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Wave Optimization

• Linear Wave Theory – 𝜂 = 𝐻

2cos 𝑘𝑘 − 𝜎𝜎

– 𝜎 = 2𝜋𝑇

– 𝑘 = 2𝜋𝐿

– 𝐻 = Wave Height – 𝑘 = Distance Downstream – 𝜎 = Time

• Piston-Driven Wave – 𝜂 = 𝑓 𝑆 – 𝑆 = Piston Stroke – 𝑆 = 𝐴 sin 𝐵𝜎

– 𝐴,𝐵 = Empirically-

determined constants

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Wave Optimization

Wave Signal From Experiment with Representative Linear Signal Overlain

0 5 10 15 201.3

1.4

1.5

1.6

1.7

1.8

1.9

2

Time (s)

Wat

er E

leva

tion(

ft)

ExperimentLinear

1.3 1.4 1.5 1.6 1.7 1.81.3

1.4

1.5

1.6

1.7

1.8

Experiment

Sim

ulat

ion

Datay = xBest-Fit Line

y(x) = a xa = 0.99987R = 0.96579 (lin)

Example of Regression Technique (Optimized Linear Wave Shown)

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Wave Optimization

Contour Plots used to Optimize Linear Signal Contour Plots used to Optimize Piston Signal

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Wave Grid Dependency

Integrated Force on Bridge Deck as a

Function of Number of Cells for Vertical Force (Top) and Horizontal

Force (Bottom)

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0 5 10 15 20

0

50

100

150

Time (s)

Ver

tical

For

ce (l

bf)

3.3M Cells4.1M Cells6.3M Cells

0 5 10 15 20-5

0

5

10

15

20

Time (s)

Hor

izon

tal F

orce

(lbf

)

3.3M Cells4.1M Cells6.3M Cells

Force Time Step Dependency (Piston)

Integrated Force on Bridge Deck as a

Function of Time Step for Vertical Force (Top) and Horizontal Force

(Bottom)

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0 2 4 6 8 10 12 14 16

0

50

100

150

Time (s)

Ver

tical

For

ce (l

bf)

50.0 ms25.0 ms10.0 ms5.0 ms

0 2 4 6 8 10 12 14 16-5

0

5

10

15

20

Time (s)

Hor

izon

tal F

orce

(lbf

)

50.0 ms25.0 ms10.0 ms5.0 ms

Force Time Step Dependency (Linear)

Integrated Force on Bridge Deck as a

Function of Time Step for Vertical Force (Top) and Horizontal Force

(Bottom)

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0 2 4 6 8 10 12 14 16

0

50

100

150

Time (s)

Verti

cal F

orce

(lbf

)

50.0 ms25.0 ms10.0 ms5.0 ms

0 2 4 6 8 10 12 14 16-5

0

5

10

15

20

Time (s)

Hor

izon

tal F

orce

(lbf

)

50.0 ms25.0 ms10.0 ms5.0 ms

Wave Time Step Dependency

Water Elevation Just Before Bridge as a Function of Time Step for Piston (Left) and Linear (Right)

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0 5 10 151.4

1.5

1.6

1.7

1.8

1.9

2

Time (s)

Wat

er E

leva

tion

(ft)

50.0 ms25.0 ms10.0 ms5.0 ms

0 5 10 151.4

1.5

1.6

1.7

1.8

1.9

2

Time (s)

Wat

er E

leva

tion

(ft)

50.0 ms25.0 ms10.0 ms5.0 ms

Slamming Force

Integrated Force on Bridge Deck as a Function of Time Step for Vertical Force (Top) and Horizontal Force

(Bottom)

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0 2 4 6 8 10 12 14 16-100

0

100

200

300

Time (s)

Ver

tical

For

ce (l

bf)

Linear (2.5 ms)Piston (2.5 ms)Linear (1.0 ms)Piston (1.0 ms)

0 2 4 6 8 10 12 14 16-10

0

10

20

30

Time (s)

Hor

izon

tal F

orce

For

ce (l

bf)

Linear (2.5 ms)Piston (2.5 ms)Linear (1.0 ms)Piston (1.0 ms)

Slamming Force

Integrated Force on Bridge Deck as a

Function of Time Step for Vertical Force (Top) and

Horizontal Force (Bottom)

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8.4 8.6 8.8 9 9.2 9.4 9.6 9.8-100

0

100

200

300

Time (s)

Ver

tical

For

ce (l

bf)

Linear (2.5 ms)Piston (2.5 ms)Linear (1.0 ms)Piston (1.0 ms)

8.4 8.6 8.8 9 9.2 9.4 9.6 9.8-10

0

10

20

30

Time (s)

Hor

izon

tal F

orce

For

ce (l

bf)

Linear (2.5 ms)Piston (2.5 ms)Linear (1.0 ms)Piston (1.0 ms)

Spectral Analysis

2 4 6 8 10 12 14 160

20

40

60

80

100

120

Frequency (Hz)

Spe

ctra

l Den

sity

5 10 15 200

2

4

6

8

10

12

14

16

18

Frequency (Hz)

Spe

ctra

l Den

sity

Spectral Density vs. Frequency for Piston Method at 1.0 ms

Spectral Density vs. Frequency for Linear Method at 1.0 ms

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Filtered Signal

Slamming/Quasi-Static Forces for Piston Method

Slamming/Quasi-Static Forces for Linear Method

4 5 6 7 8 9

0

50

100

150

200

250

Time (s)

Ver

tical

For

ce (l

bf)

Full SignalQuasi-Static Force

4 5 6 7 8 9

0

50

100

Time (s)

Sla

mm

ing

Forc

e (lb

f)

4 5 6 7 8 9

0

50

100

150

200

250

Time (s)

Ver

tical

For

ce (l

bf)

Full SignalQuasi-Static Force

4 5 6 7 8 9-60

-40

-20

0

20

40

60

Time (s)

Sla

mm

ing

Forc

e (lb

f)

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Comparison With Data (Summary) Test Case

Vertical Max

Vertical Min

Quasi Max

Quasi Min

Horiz Max

Horiz Min

Slam

Data

194.99 -35.16 112.81 -26.28 7.96 -2.35 82.17

Piston 2.5 ms

218.40 -17.76 83.41 -22.64 21.70 -3.31 137.02

Piston 1.0 ms

237.88 -20.98 139.55 -19.35 23.38 -3.53 106.04

Linear 2.5 ms

152.12 -10.11 96.38 -20.17 17.30 -2.91 59.55

Linear 1.0 ms

169.74 -9.95 125.54 -9.48 19.01 -3.19 52.13

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Comparison With Data (% Error) Test Case

Vertical Max

Vertical Min

Quasi Max

Quasi Min

Horiz Max

Horiz Min

Slam

Piston 2.5 ms

12.00 49.48 26.06 13.84 172.65 40.66 66.76

Piston 1.0 ms

22.00 40.33 23.70 26.36 193.77 50.03 29.05

Linear 2.5 ms

21.98 71.25 14.57 23.24 117.32 23.82 -27.53

Linear 1.0 ms

12.95 71.70 11.28 69.93 138.76 35.79 36.56

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Summary and Conclusions • Both piston and linear methods can reproduce a vertical

slamming component if a small time step is used • Unclear which method is “better”

– Piston • Quasi-static – high • Slamming – low, closer than linear, but wrong number of

oscillations – Linear

• Quasi-static – high, but closer than piston • Slamming – low, but correct number of oscillations

• Horizontal Force – poorly reproduced for both methods

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