OPEN ACCESS
In this paper a simplified biomechanical crowd-structure interaction model is proposed and validated in order to analyse the lateral lock-in phenomenon on real footbridges. The proposed crowd-structure interaction model is organized in three levels: (i) pedestrian-structure interaction; (ii) interaction among pedestrians in the crowd; and (iii) interaction between the crowd and the structure. To this end, first, the human-structure interaction of each pedestrian is modelled via a simplified two degrees of freedom system. Second, the interaction among pedestrians inside the crowd is simulated using a multi-agent model. The considered model simulates the movement of each pedestrian from the dynamic equilibrium of the different social forces that act on him/her. Finally, the crowd-structure interaction is achieved modifying the behaviour of the pedestrians depending on the comfort level experienced. For this purpose, the recommendations established by the French standards have been considered. The integration of the three levels in an overall model is achieved by the implementation of a predictive– corrective method. The performance of the proposed model is validated correlating the numerical and experimental dynamic response of the Pedro e Inês footbridge during the development of a lateral lock-in pedestrian test. As the first lateral natural frequency of the footbridge is inside the range that characterizes the walking pedestrian step frequency in lateral direction, numerical and experimental studies were performed to analyse its behaviour under pedestrian action. The agreement between the numerical and experimental results is adequate. However, further studies are recommended in order to generalize the proposed approach and facilitate its use during the design project of future footbridges.
crowd dynamics, footbridge, human-structure interaction, lateral lock-in, simplified biomechanical model
[1] Ingólfsson, E.T., Georgakis, C.T., Ricciardelli, F. & Jönsson, J., Experimental identifi cation of pedestrian-induced lateral forces on footbridges. Journal of Sound and Vibra tion, 330, pp. 1265–1284, 2011.https://doi.org/10.1016/j.jsv.2010.09.034
[2] Carrol, S.P., Owen, J.S. & Hussein, M.F.M., Modelling crowd-bridge dynamic in teraction with a discretely defined crowd. Journal of Sound and Vibration, 331, pp. 2685–2709, 2012.https://doi.org/10.1016/j.jsv.2012.01.025
[3] Bocian, M., Macdonald, J.H.G. & Burn J.F., Biomechanically inspired modelling of pedestrian-induced forces on laterally oscillating structures. Journal of Sound and Vi bration Sound, 331, pp. 3914–3929, 2012.https://doi.org/10.1016/j.jsv.2012.03.023
[4] Caetano, E., Cunha, A., Magalhães, F. & Moutinho, C., Studies for controlling human induced vibration of the Pedro e Inês footbridge, Portugal. Part 1: Assessment of dynamic behaviour. Engineering Structures, 32, pp. 1069–1081, 2010. https://doi.org/10.1016/j.engstruct.2009.12.034
[5] Caetano, E., Cunha, A., Moutinho, C. & Magalhães, F., Studies for controlling human induced vibration of the Pedro e Inês footbridge, Portugal. Part 2: Implementation of tuned mass dampers. Engineering Structures, 32, pp. 1082–1091, 2010. https://doi.org/10.1016/j.engstruct.2009.12.033
[6] Jiménez-Alonso, J.F., Proposal and calibration of a biodynamic model of human-struc ture interaction by the resolution of the inverse dynamic problem: application to pedes trian bridges, PhD Thesis, University of Seville, 2015.
[7] Jiménez-Alonso, J.F., Sáez, A., Caetano, E. & Cunha, A., Lateral crowd-structure inter action model to analyse the change of the modal properties of footbridges. Submitted for publication.
[8] Jiménez-Alonso, J.F., Sáez, A., Caetano, E. & Magalhães, F., Vertical crowd-structure interaction model to analyse the change of the modal properties of a footbridge. Journal of Bridge Engineering ASCE, 21(8), pp. C4015004/1-19, 2016. https://doi.org/10.1061/(asce)be.1943-5592.0000828
[9] Butz, C.H., Heinemeyer, C.H., Goldack, A., Keil, A., Lukic, M., Caetano, E. & Cunha, A., Advanced load models for Synchronous Pedestrian Excitation and Optimised Design Guidelines for Steel Footbridges (SYNPEX). RFCS-Research Project RFS-CR-03019. 2007.
[10] Helbing, D. & Molnár, P., Social force model for pedestrian dynamics. Physical Review, 51(5), pp. 4282–4286, 1995.https://doi.org/10.1103/physreve.51.4282
[11] Zivanovic, S., Pavic, A. & Ingolfsson, E., Modelling spatially unrestricted pedestrian traffic on footbridges. Journal of Structural Engineering, 136(10), pp. 1296–1308, 2010.https://doi.org/10.1061/(asce)st.1943-541x.0000226
[12] Bertram, J.E.A. & Ruina, A., Multiple walking speed-frequency relations are predict ed by constrained optimization. Journal of Theoretical Biology, 209(4), pp. 445–453, 2001.https://doi.org/10.1006/jtbi.2001.2279
[13] SETRA/AFGC. Guide méthodologique passerelles piétonnes (Technical Guide Foot bridges: Assessment of vibration behaviour of footbridge under pedestrian loading). SETRA, 2006.
[14] Mottershead J.E., Link M. & Friswell M.I., The sensitivity method in finite element model updating: a tutorial. Mechanical System and Signal Processing, 25, pp. 2275– 2296, 2011.https://doi.org/10.1016/j.ymssp.2010.10.012