Vibration monitoring of the Iroise cable-stayed bridge

The exemple that follows illustrates the opportunities provided by vibration monitoring to study the complex dynamic behaviour of cable stays of the Iroise bridge in the vicinity of Brest, Finistère, France.

The Iroise bridge is a cable stayed bridge with the following caracteristics 

• length of 800 m
• 5 spans among which a 400 m central span
• 2 piles, 114m high with 83 m below the girder
• 4 tablecloth of 26 inclined cable stays

After maintenance operations, anchor tripods manufactured by Freyssinet compagny that were aimed to damp vibrations tramsmitted to the girder, had been dismantled. Several cable stays started to oscillate after some gust of wind to reach a twenty centimeter peak to peak amplitude of oscillation in their mid span. Such repeated episodes soon triggered important damages like   

• Cracking of formwork tubes surrounding the stays at anchoring
• Removal of anchor heads on top of the bridge pile 

Several scenarios were investigated as an attempt to explain the initiation of such high vibration levels including  

• aerodynamic phenomenon: vortex detachment, wake gallop, wind-rain interaction
• parametric resonance due to stay-girder or stay-pile couplings
• vibration resonance in combination featuring nonlinear components of cable stays
• other origin

A research study has been launched to understand the root of such vibration phenomenon, to design and forecast the dynamic behaviour of the pile-girder-stays mechanical system and in the end to find a mean to reduce and possibly to eliminate unwanted vibrations. A campaign of vibration measurements was launched combining the instrumentation of the civil engineering buiding (pile, girder) and some cable stays with sismic accelerometers as well as the recording of wind speed conditions and finally a monitoring of the cable stays with cameras triggered after some acceleration threshold was reached. A finite element modelling was built in parallel and tuned with data fed by the modal analysis of the bridge. One of the figure above shows the mode shapes of the first two dominant vibration bridge modes associated respectively with an out-of-plane bending of the pile and an in-plane bending of the girder.

Dynamic monitoring of the pile-girder-stays system has been performed under ambiant noise (wind-rain) as well as with traffic excitation to caracterize modal informations (frequency, damping, mode shape) by analyzing for instance the frequency response functions FrF.  The one of interest was obtained by extracting the spectral amplification of vertical component of an accelerometer attached on the H3Q22 cable stay 10 meters in height by reference with the vertical acceleration of the girder at anchoring. Some time-responses shown hereafter illustrate how abnormal the dynamic behaviour of H3Q22 cable stay is compared to the one of its neighbour.

The amplitude of oscillation of both H3Q22 and H3Q26 cable stays is recorded here at the beginning of gust of wind that triggered an episode of vibration. Following features are clearly noticeable:

• first peals are due to heavy trucks passing at the vicinity of accelerometers at the beginning of event
• the amplitude of neighbouring cable stay H3Q26 mounted with a hydraulic damper is soon vanishing
• the amplitude of cable stay H3Q22 reaches a maximum peak to peak value of 25cm at mid-span during an episode of vibration lasting more than 10 minutes

A reduced order model was built as an attempt to understand the behaviour of cable stay H3Q22 coupled with the pile and the girder. The model was restricted to only  embed the first two linear modes of the bridge and a nonlinear cable sub-system borrowed to Irvine theory. Several scenarios were studied by using analytical methods like the normal form theory or the Gendelman-Manevitch technique which enables to uncouple fast vibration from slow varying vibrations within nonlinear responses:

1. Linear parametric resonance between the cable stay mode and the girder mode
2. parametric resonances in combination
3. nonlinear resonance between the cable stay mode and the pile and girder bending modes

None of these models permitted to validate such complex resonance scenarios.

A flattening of the problem finally made it possible to lift the veil on the inexplicable. Recorded accelerograms of the cable stay, the pile and the girder were explored by using the wavelet transform to folloy up the evolution of instantaneous frequencies of modal components. Wavelet scalogram of the horizontal and vertical components of the cable stay and of the pile enabled to track the transient interaction between  vibration modes c:1 (hstay), b:1 (pile, out-of-plane), b:2 (girder, vertical in-plane) and the excitation due to a lateral gust of wind (w). The analysis highlighted the following scenario:

1. Blowing wind w is exciting the pile mode b:1 in the transverse plane
2. Pile H3 transmits the excitation at the head of H3Q22 stay by means of a modal coupling
3. After wind is reinforced, cable stay H3Q22 oscillates more and more fed by energy stored in pile mode. Its amplitude gradually increases in a steady regime.
4. At the end of the gust of wind, cable stays keeps n vibrating under a transient regime with an amplitude that stay high and stable for roughly 10 minutes. H3Q22 indeed is caracterized by a very low specific damping near 0.1% which can only mitigate the vibrations over a large period of time.
5. Girder mode seems to be uncoupled from the other modes during the wind episode.

This scenario was validated numerically by injecting transient excitation due to wind into the reduced order model pile-girder-cable stay. Simulations point out high amplitudes of oscillation of cable stay H3Q22 first mode that match very well with experimentally recorded oscillations. Vibrations of cable stay are indeed weakly damped transient oscillations initiated during an energy transfer with the pile mode. A preventing action also consists in increasing damping by using for instance hydraulic dampers mounted at the anchoring with the girder. Yet, it is interesting to stress that the original cause is related to the slim design of the pile imagined by the bridge architect.