Theoretical investigation of the use of a moving vehicle to identify bridge dynamic parameters Patrick McGetrick Dr. Arturo González Prof. Eugene OBrien

Introduction A Rational Transport Policy must aim to: Maintain traffic safety Ensure adequate maintenance is provided Maintain levels of transport capacity Budget accordingly Therefore bridge structures need to be monitored as they are subject to continuous degradation due to traffic, ageing and environmental factors General intro 1

Introduction Increasingly, larger bridges are being instrumented and monitored on an ongoing basis Measuring bridge modes and frequencies of vibration Expensive intro Direct Installations – Expensive, time consuming 3 3

Research Outline “Theoretical investigation of the use of a moving vehicle to identify bridge dynamic parameters” Developing a low cost indirect method Use of instrumented vehicle: measure vertical vibration using accelerometers Monitor dynamic response → Bridge damping Vehicle → Accelerometer fitted to axle (Source: Enrique Covián, University of Oviedo)

Bridge structural damping Bridge structural damping has been chosen to be the focus of the research as it is damage sensitive; in a simple model damage to the bridge can be simulated by changing the level of damping

Advantages No on-site installation of measurement equipment Enables more effective and efficient widespread monitoring of existing bridge structures’ condition i.e. numerous structures could be monitored in one day Required maintenance can be instigated at an earlier stage in degradation, which (usually) results in less costly repairs

Background Information Yang et al indicated the feasibility of extracting bridge frequencies from the dynamic response of a vehicle passing over a bridge using a simple model The technique was later verified experimentally by Lin & Yang, observing that it was easier to extract the bridge frequency for vehicle speeds less than 40km/h (11.1m/s) Limitations: only 30m span tested. Just frequency. Simple sprung mass and beam model with closed form solution.

Background Information González et al investigated the method both experimentally and using a 3D FEM model Accurate determination of the bridge frequency is feasible for low speeds & when the degree of dynamic excitation of the bridge is high enough Influence of road profile on vehicle vibration prevented the identification of the bridge natural frequency (Source: Enrique Covián, University of Oviedo)

Theoretical Testing Methodology Simulate vehicle-bridge dynamic interaction using computer model in MATLAB varying: Road Profile (Smooth & ISO Class A) Vehicle Velocities (5m/s - 25m/s) Vehicle Mass (10t & 20t) Bridge Spans (15m, 25m & 35m) “to simulate damage” 18km/h – 90km/h

Methodology cont. Also, vary dynamic properties of each bridge span i.e. Damping varied between 0% - 5% Obtain bridge frequency & measure dynamic response of vehicle to changes in damping in the frequency spectra of vertical vehicle accelerations “to simulate damage”

Matlab Simulation Model Quarter Car & Euler-Bernoulli beam

Quarter Car Properties Property Model 1 (10 tonnes) Model 2 (20 tonnes) Body mass, ms 9000 kg 19000 kg Tyre mass, mu 1000 kg Suspension Stiffness, Ks 8x104 N/m Suspension Damping, Cs 10x103 Ns/m Tyre Stiffness, Kt 2x106 N/m Body mass frequency of vibration, fbody 0.47 Hz 0.32 Hz Tyre mass frequency of vibration, ftyre 7.26 Hz

Bridge Properties Span Length, L (m) Modulus of elasticity, E (N/m2) Second moment of area, J (m4) Mass per unit length, µ (kg/m) Structural damping, ξ 1st natural frequency of vibration, fbridge (Hz) 15 3.5x1010 0.5273 28125 1% to 5% 5.66 25 1.3901 18358 4.09 35 3.4162 21752 3.01

Processing Acceleration Data Vehicle Acceleration Data processed using MATLAB FFT functions Peaks obtained 1 acc signal. 6 psd v f spectra, 1 for each damping level. Different magnitudes due to increasing damping reducing the energy of vibrations. Example of acceleration data & processed acceleration data for Quarter Car-bridge interaction system

Smooth Profile Results

15m Span, Spectra for 20m/s Acceleration spectra for tyre mass @20m/s on 15-m bridge showing higher energy for lower bridge damping values, quarter car mass is 10t

15m Span PSD-damping trends Minimum 16% decrease in peak PSD for a 1% increase in damping Peak PSD-damping trends at bridge frequency peak for tyre mass on 15-m bridge, showing higher sensitivity for lower velocity

25m Span, Spectra for 20m/s Acceleration spectra for tyre mass @20m/s on 25-m bridge showing higher energy for lower bridge damping values

25m Span PSD-damping trends Minimum 20% decrease in peak PSD for a 1% increase in damping Peak PSD-damping trends at bridge frequency peak for tyre mass on 25-m bridge, showing higher sensitivity for lower velocity

35m Span, Spectra for 20m/s Acceleration spectra for tyre mass @20m/s on 35-m bridge, again showing higher energy for lower bridge damping values

35m Span PSD-damping trends Minimum 20% decrease in peak PSD for a 1% increase in damping Longer span most sensitive, more data obtained, more energy in vibrations Peak PSD-damping trends at bridge frequency peak for tyre mass on 35-m bridge, showing higher sensitivity for lower velocity

Frequency Results Very accurate frequency obtained if I take more measurements free vibration etc. Measurements here were just on bridge. Estimated and true bridge frequency for all bridge spans and velocities (10t & 20t)

ISO Class A Profile Results

15m Span, Spectra for 20m/s Could Use heavier vehicle. Acceleration spectra for tyre mass @20m/s on 15-m bridge showing higher energy for lower bridge damping values @ vehicle peak, quarter car mass is 10 tonnes

15m Span, Spectra for 5m/s Acceleration spectra for tyre mass @5m/s on 15-m bridge showing bridge frequency peak & vehicle peak, quarter car mass is 10 tonnes

15m Span PSD-damping trends Maximum 2.8% decrease in peak PSD for a 1% increase in damping Peak PSD-damping trends at bridge frequency peak for tyre mass on 15-m bridge, vehicle velocity 5m/s

15m Span PSD-damping trends Maximum 0.35% decrease in peak PSD for a 1% increase in damping Peak PSD-damping trends at vehicle frequency peak for tyre mass on 15-m bridge, vehicle velocity 5m/s

Conclusions Smooth Profile: Bridge frequency peak was detected for all velocities Frequency peak diverges from bridge frequency as velocity increases For all vehicle velocities a decrease in Peak PSD with increasing damping level was found: suggests that it is possible to monitor bridge damping through vehicle acceleration measurements Higher Sensitivity of Peak PSD to a 1% change in damping for: lower velocities, longer bridge span, changes between lower damping levels; Maximum 71% for 35m span @5m/s, minimum 16% for 15m span @25m/s

Conclusions ISO Class A Profile: Bridge frequency peak only detected @5m/s, Tyre Mass frequency peak detected The road profile’s influence on the vehicle vibration dominates the spectra, hiding the bridge frequency. This influence also masks changes in the bridge damping properties However, for all vehicle velocities a decrease in Peak PSD with increasing damping level still existed @ obtained peaks Remove/minimise influence of road profile

Acknowledgements The authors wish to express their gratitude for the financial support received from the 7th European Framework ASSET Project towards this investigation.

Thank You

References 1. Y B Yang, C W Ling and J D Yau, ‘Extracting bridge frequencies from the dynamic response of a passing vehicle’, Journal of Sound and Vibration, 272, pp 471-493, 2004. 2. C W Ling and Y B Yang, ‘Use of a passing vehicle to scan the fundamental bridge frequencies. An experimental verification’, Engineering Structures, 27, pp 1865-1878, 2005. 3. A González, E Covián and J Madera, ‘Determination of Bridge Natural Frequencies Using a Moving Vehicle Instrumented with Accelerometers and GPS’, Proceedings of the Ninth International Conference on Computational Structures Technology, Athens, Greece, paper 281, September 2008. 4. R O Curadelli, J D Riera, D Ambrosini and M G Amani, ‘Damage detection by means of structural damping identification’, Engineering Structures, 30, pp 3497-3504, 2008. 5. D Cebon, ‘Handbook of Vehicle-Road Interaction’, Swets & Zeitlinger, the Netherlands, 1999. 6. ISO 8608:1995, ‘Mechanical vibration-road surface profiles-reporting of measured data’, International Standards Organisation, 1995.