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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 [email protected]
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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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