Department of Mechanical and Structural Engineering and Materials Science,University of Stavanger,Norway

Etienne CheynetJasna Bogunović Jakobsen

Science Meets Industry, Stavanger, 29.3.2017

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1.Overview of the Lysefjord Bridge response to wind turbulence

2.Role and modelling of the wind coherence

3.Consequence of an erroneous modelling of the wind coherence

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Main span: 446 mTower height: 102 mAltitude at mid-span: 55 m

The Lysefjord Bridge Rogaland, Norway

Accelerometers

Anemometers

Moving GNSS station Reference GNSS station4

North tower

South tower

Instrumentation of the Lysefjord Bridge

Along-wind turbulence and lateral bridge response

(26/10/2014)

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Vertical wind turbulence and vertical bridge response

(26/10/2014)

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Power spectral density of the lateral bridge response

1 h of acceleration record (26/10/2014)U = 11.2 m/sIu = 13.9 %

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1 h of acceleration record (26/10/2014)U = 11.2 m/sIw = 7.5 %

Power spectral density of the vertical bridge response

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15 m/s > U > 10m/s99 samples (26/10/2014)

Power spectral density of the wind turbulent components

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The wind coherence

Wind coherence ≡ correlation function that takes into accountspatial dimensions and temporal variation of wind gusts

Longitudinal coherence ( = 1 if frozen turbulence)

Vertical coherence

Lateral coherence

u

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Wind direction

Modelling of the wind coherence

Simplest model:

Davenport model [1]:

𝛾𝑢 = 𝑒−𝐶𝑓𝑑/𝑈

where:𝛾𝑢 = co-coherenceC = 7 f = frequency (Hz)d = cross-wind separation (m)U = mean wind speed (m/s)

Davenport model

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Modelling of the wind coherence

Simplest model:

Davenport model [1]:

𝛾𝑢 = 𝑒−𝐶𝑓𝑑/𝑈

where:𝛾𝑢 = co-coherenceC = 7 f = frequency (Hz)d = cross-wind separation (m)U = mean wind speed (m/s)

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Modelling of the wind coherence

Simplest model:

Davenport model [1]:

𝛾𝑢 = 𝑒−𝐶𝑓𝑑/𝑈

where:𝛾𝑢 = co-coherenceC = 7 f = frequency (Hz)d = cross-wind separation (m)U = mean wind speed (m/s)

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Modelling of the wind coherence

More realistic models:

• Coherence calculated with Mann’s turbulence model [2]

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The Davenport model may oversimplify the «real» wind coherence [7]

Modelling of the wind coherence

More realistic models:

• Coherence calculated with Mann’s turbulence model [2]• The Krenk coherence model [3]

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The Davenport model may oversimplify the «real» wind coherence [7]

Modelling of the wind coherence

More realistic models:

• Coherence calculated with Mann’s turbulence model [2]• The Krenk coherence model [3]• The von Karman coherence model [4]

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The Davenport model may oversimplify the «real» wind coherence [7]

Modelling of the wind coherence

More realistic models:

• Coherence calculated with Mann’s turbulence model [2]• The Krenk coherence model [3]• The von Karman coherence model [4]• The 4-parameter exponential decay function [5] 𝛾𝑢 = 𝑒

−𝑑𝑈 𝑐1𝑓 2+ 𝑐2 2

𝑐3

cos 𝑐4𝑑𝑓

𝑈

The Davenport model may oversimplify the «real» wind coherence [7]

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Along-wind component

15 m/s > U > 10m/s

216 deg > Dir > 205 deg

73 samples

Markers: measured

Lines: fitted

𝑐1 = 8.5𝑐2 = 0.04 𝑠−1

𝑐3 = 1.1𝑐4 = 5.4

Coherence measured on the Lysefjord bridge (26/10/2014) for a wind from S-SW

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Along-wind component

15 m/s > U > 10m/s

216 deg > Dir > 205 deg

73 samples

Markers: measured

Lines: fitted

Coherence measured on the Lysefjord bridge (26/10/2014) for a wind from S-SW

𝑐1 = 5.8𝑐2 = 0.2 𝑠−1

𝑐3 = 1.4𝑐4 = 5.2

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How does an inaccurate modelling of the wind coherence affect the structural

response of a suspension bridge ?

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Inaccurate modellingAccurate modelling

Case study with U = 15 m/s; 𝐿𝑢 = 160 𝑚

𝑐1 = 9.0𝑐2 = 0.1 𝑠−1

𝑐3 = 1.00𝑐4 = 4.7

𝐶 = 13.7

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Consequence of an inappropriate coherence modelling on the bridge response ?

• Buffeting response of a long-span suspension bridge using:• U = 15 m/s• Wind spectrum from N400 handbook ( terrain category 2)• Simplified Bridge model (SBM) [6]• 10 min averaging time• Uncoupled motion of the bridge deck (lateral motion)• Quasi steady theory

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Case 1: Lysefjord Bridge simplified Bridge model (SBM). Main span length: L = 446 m

Response at mid-span

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Conclusions

An inaccurate description of the wind coherence may lead to :• An overall small difference for the dynamic response.

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Conclusions

An inaccurate description of the wind coherence may lead to :• An overall small difference for the dynamic response.• A considerable discrepancy for the background response.

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Conclusions

An inaccurate description of the wind coherence may lead to :• An overall small difference for the dynamic response.• A considerable discrepancy for the background response.• A small discrepancy for the resonant response.

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Conclusions

An inaccurate description of the wind coherence may lead to :• An overall small difference for the dynamic response.• A considerable discrepancy for the background response.• A small discrepancy for the resonant response.

A larger span leads to :• An overall response dominated by the resonant part• Resonant peaks that may be affected to a greater extent by the coherence

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References

[1] Davenport, A. G. (1961). The spectrum of horizontal gustiness near the ground in high winds. Quarterly Journal of the Royal Meteorological Society, 87(372), 194-211.[2] Mann, J. (1994). The spatial structure of neutral atmospheric surface-layer turbulence. Journal of fluid mechanics, 273, 141-168.[3] Krenk, S. (1996). Wind field coherence and dynamic wind forces. In IUTAM symposium on advances in nonlinear stochastic mechanics (pp. 269-278). Springer Netherlands.[4] von Karman, T. (1948). Progress in the statistical theory of turbulence. Proceedings of the National Academy of Sciences, 34(11), 530-539.[5] Cheynet, E., Jakobsen, J. B., & Snæbjörnsson, J. (2016). Buffeting response of a suspension bridge in complex terrain. Engineering Structures, 128, 474-487.[6] Cheynet, E. (2016). Wind-induced vibrations of a suspension bridge: A case study in full-scale. PhD thesis. University of Stavanger.[7] Kristensen, L., & Jensen, N. O. (1979). Lateral coherence in isotropic turbulence and in the natural wind. Boundary-Layer Meteorology, 17(3), 353-373.

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