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# "Finding the influence line for a bridge based on random traffic and field measurements on site" presented at CERI2018 by Barbara Heitner

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The influence line of a structure reflects its structural behaviour as well as any possible damage present on the bridge. An iterative algorithm is presented in this paper in order to obtain the shape of the influence line of a bridge together with the load distribution of trucks passing overhead. One great advantage of this approach is that sensor calibration with pre-weighed trucks can be avoided. The only initial information needed are the measurement data and a preliminary estimate of influence line based on engineering judgement. An illustrative example is shown, where strain data have been collected on a reinforced concrete culvert. Apart from the efficiency of the proposed algorithm, the influence of the temperature on the results is also shown.

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### "Finding the influence line for a bridge based on random traffic and field measurements on site" presented at CERI2018 by Barbara Heitner

1. 1. Workshop CERI, UCD, Dublin Wednesday 29th August 2018
2. 2. Eugene J. OBrien, Franck Schoefs, Barbara Heitner, Guillaume Causse, Thierry Yalamas Finding the influence line for a bridge based on random traffic and field measurements on site
3. 3. Introduction • Influence line • Response at a given a point under moving unit load • E.g. can be bending moment, strain, deflection, shear force, etc. • The influence line(s) of a structure reflects its behaviour
4. 4. Introduction • Influence line • Response at a given a point under moving unit load • E.g. can be bending moment, strain, deflection, shear force, etc. • The influence line(s) of a structure reflects its behaviour M 1 M
5. 5. Introduction • Influence line • Response at a given a point under moving unit load • E.g. can be bending moment, strain, deflection, shear force, etc. • The influence line(s) of a structure reflects its behaviour M 1 M
6. 6. Introduction • Influence line • Response at a given a point under moving unit load • E.g. can be bending moment, strain, deflection, shear force, etc. • The influence line(s) of a structure reflects its behaviour M 1 M
7. 7. Introduction • Influence line • Response at a given a point under moving unit load • E.g. can be bending moment, strain, deflection, shear force, etc. • The influence line(s) of a structure reflects its behaviour M 1 M
8. 8. Introduction • Influence line • Response at a given a point under moving unit load • E.g. can be bending moment, strain, deflection, shear force, etc. • The influence line(s) of a structure reflects its behaviour M 1 M
9. 9. Introduction • Influence line • Response at a given a point under moving unit load • E.g. can be bending moment, strain, deflection, shear force, etc. • The influence line(s) of a structure reflects its behaviour M 1 M
10. 10. Introduction • Influence line • Response at a given a point under moving unit load • E.g. can be bending moment, strain, deflection, shear force, etc. • The influence line(s) of a structure reflects its behaviour M 1 M
11. 11. Introduction • Influence line • Response at a given a point under moving unit load • E.g. can be bending moment, strain, deflection, shear force, etc. • The influence line(s) of a structure reflects its behaviour • Change in the influence line suggests change in its • Support conditions; • Connections; • Material or • Geometrical properties. M 1 M
12. 12. Introduction • Bridge Weigh-in-Motion (WIM) • Known influence line (IL) of the structure + measurement under a truck passing →calculating the weight of the truck (forward problem) • A calibration truck and an IL estimate (based on FE model e.g.) is needed
13. 13. Introduction • Bridge Weigh-in-Motion (WIM) • Known influence line (IL) of the structure + measurement under a truck passing →calculating the weight of the truck (forward problem) • A calibration truck and an IL estimate (based on FE model e.g.) is needed • In this work: • Without an estimated IL and a calibration truck: • How to obtain information on truck weights in statistical terms? • Can we use this for damage detection?
14. 14. Scope • Introduction
15. 15. Scope • Introduction • Forward problem (Moses’s algorithm)
16. 16. Scope • Introduction • Forward problem (Moses’s algorithm) • Inverse problem (Quilligan’s algorithm)
17. 17. Scope • Introduction • Forward problem (Moses’s algorithm) • Inverse problem (Quilligan’s algorithm) • Proposed approach
18. 18. Scope • Introduction • Forward problem (Moses’s algorithm) • Inverse problem (Quilligan’s algorithm) • Proposed approach • Case study
19. 19. Scope • Introduction • Forward problem (Moses’s algorithm) • Inverse problem (Quilligan’s algorithm) • Proposed approach • Case study • Results
20. 20. Forwardproblem(Moses’salgorithm) • Basis of Bridge WIM • To calculate the axle weights and so the gross vehicle weight (GVW) of a truck based on the IL and the measured signal where {Q} is the vector of the axle weights [IL] is a matrix based on the influence line and the axle spacings {εm} is the vector of the measured signal 𝑄 = 𝐼𝐿 𝑇 𝜀 𝐼𝐿 𝑇 𝐼𝐿
21. 21. Inverseproblem(Quilligan’salgorithm) • To calculate the influence line ordinates of a structure based on the measurement response and the axle weights and spacings of a truck where {IL} is a vector containing the IL ordinates [A] is a symmetric matrix containing the information of the axle weights {M} is a vector based on the axle weights and the measured signal 𝐼𝐿 = 𝐴 −1 𝑀
22. 22. Proposedapproach • An iterative approach combining Moses’ and Quilligan’s algorithm • To obtain both the relative IL and axle weights of the passing trucks Forward Problem Inverse Problem
23. 23. Proposedapproach • An iterative approach combining Moses’ and Quilligan’s algorithm • To obtain both the relative IL and axle weights of the passing trucks • What information/data is needed? • Response signal • (Speed of the truck) • Number of axles and the axle spacings of the truck • Length of IL • An approximate initial IL shape Forward Problem Inverse Problem
24. 24. Proposedapproach • Steps of the analysis 1. Using an approximate IL shape and Moses’ algorithm to calculate the relative axle weights 2. Using these axle weights and Quilligan’s algorithm to calculate the IL 3. Repeating step 1 and step 2 until convergence is reached
25. 25. Proposedapproach • Steps of the analysis 1. Using an approximate IL shape and Moses’ algorithm to calculate the relative axle weights 2. Using these axle weights and Quilligan’s algorithm to calculate the IL 3. Repeating step 1 and step 2 until convergence is reached • How to use it for damage detection • Assuming that the statistical weight of trucks do not change (in a given time period) or assuming that it changes within some limits • If we find a greater change we can assume that it is caused by some changes in the structure (i.e. in the IL) and not in the weight of the trucks
26. 26. Case study • Culvert bridge in Slovenia • Strain measured in midspan at the bottom of the slab • Temperature data (recorded simultaneously) is collected as well • Temperature change introduces change in the moduli of elasticity of concrete, and so it effects the bridge’s structural response, i.e. the IL
27. 27. Results • Convergence of the IL (from green to blue) • Starting from a triangle IL (dashed line)
28. 28. Results • 5-axle trucks’ measured response compared to the ‘calculated’ response using the results of the proposed approach
29. 29. Results and conclusions • Results • Average GVW calculated by the proposed approach plotted against temperature • For a general truck population (blue line) and for 5-axle trucks only (green line)
30. 30. Results and conclusions • Results • Average GVW calculated by the proposed approach plotted against temperature • For a general truck population (blue line) and for 5-axle trucks only (green line) • Conclusions • Calculated GVW correlates with temperature • Temperature can be used as ‘proxy’ for damage → Being able to track temperature change, suggests that we can track damage as well
31. 31. The TRUSS ITN project (http://trussitn.eu) has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 642453 Thank you for your attention