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Pedestrian Biodynamic Model for Vibration Serviceability of Footbridges in Lateral Direction

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Abstract

Purpose

In the assessment of footbridge lateral vibrations, the modeling of human-structure interaction requires representation of the dynamics of the human body and the forces induced by people walking, and additionally, consideration of the effects of the crowd. This way, this paper presents a single degree of freedom biodynamic model to represent the action of a walking pedestrian in the lateral direction.

Methods

The biodynamic parameters of mass, stiffness and damping, as well as the dynamic load factor were determined from the measured acceleration of people's center of mass. Before the identification of the parameters in the lateral direction, an initial experimental campaign was carried out to identify and characterize the corporal movements of the pedestrians, define a procedure to process the acquired signals and observe the effect of the crowd on such corporal movements, specifically on acceleration and rotation of the pedestrian's pelvis. A second campaign was carried with people walking alone and later in crowd. In the first stage, each participant walked alone with their normal (free) pacing frequency and metronome-controlled pacing frequencies. Subsequently, each individual walked in group with two crowd density conditions.

Results

Comparison between biodynamic parameters of people walking individually and in a crowd allowed the identification of the influence caused by the crowd. Also, regression expressions were obtained by relating the biodynamic parameters to the walking lateral frequency and body mass of the pedestrian, for both free walking and walking in crowd conditions.

Conclusion

The values of the parameters obtained and the regressions expressions of the biodynamic model in the lateral direction can be used in the study of the human-structure interaction in footbridges.

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Data Availability

All data are fully available on request.

References

  1. Fujino Y, Pacheco B, Nakamura SI, Warnitchai P (1993) Synchronization of human walking observed during lateral vibration of a congested pedestrian bridge. Earthq Eng Struct Dyn 22(9):741–758. https://doi.org/10.1002/eqe.4290220902

    Article  Google Scholar 

  2. Dallard P, Flint A, Le Bourva S, Low A, Smith RMR, Willford M (2001) The London Millennium Footbridge. Struct Eng 79(22):17–35

    Google Scholar 

  3. Dallard BP, Fitzpatrick T, Flint A, Low A, Smith RR, Willford M, Roche M (2001) London Millennium Bridge: pedestrian-induced lateral vibration. J Bridg Eng 6(6):412–417. https://doi.org/10.1061/(ASCE)1084-0702(2001)6:6(412)

    Article  Google Scholar 

  4. Strogatz SH, Abrams DM, Mcrobie A, Eckhardt B, Ott E (2005) Crowd synchrony on the Millennium Bridge. Nature 438(7064):43–44. https://doi.org/10.1038/438043a

    Article  Google Scholar 

  5. Macdonald JHG (2009) Lateral excitation of bridges by balancing pedestrians. Proc R Soc A 465(2104):1055–1073. https://doi.org/10.1098/rspa.2008.0367

    Article  MathSciNet  MATH  Google Scholar 

  6. Ingólfsson ET, Georgakis CT, Jönsson J (2012) Pedestrian-induced lateral vibrations of footbridges: a literature review. Eng Struct 45:21–52. https://doi.org/10.1016/j.engstruct.2012.05.038

    Article  Google Scholar 

  7. Casciati S (2016) Human induced vibration vs cable-stay footbridge deterioration. Smart Struct Syst 18(1):17–29. https://doi.org/10.12989/sss.2016.18.1.017

    Article  Google Scholar 

  8. Bocian M, Brownjohn JMW, Racic V, Hester D, Quattrone A, Gilbert L, Beasley R (2018) Time-dependent spectral analysis of interactions within groups of walking pedestrians and vertical structural motion using wavelets. Mech Syst Signal Process 105:502–523. https://doi.org/10.1016/j.ymssp.2017.12.020

    Article  Google Scholar 

  9. Ingólfsson ET, Georgakis CT, Ricciardelli F, Jönsson J (2011) Experimental identification of pedestrian-induced lateral forces on footbridges. J Sound Vib 330(6):1265–1284. https://doi.org/10.1016/j.jsv.2010.09.034

    Article  Google Scholar 

  10. Da Silva FT, Pimentel RL (2011) Biodynamic walking model for vibration serviceability of footbridges in vertical direction. Proceeding of the 8th International Conference on Structural Dynamics (Eurodyn 2011). Belgium, Leuven, pp 1090–1096

    Google Scholar 

  11. Toso MA, Gomes HM, Da Silva FT, Pimentel RL (2016) Experimentally fitted biodynamic models for pedestrian-structure interaction in walking situations. Mech Syst Signal Process 72–73:590–606. https://doi.org/10.1016/j.ymssp.2015.10.029

    Article  Google Scholar 

  12. Dang HV, Živanović S (2015) Experimental characterisation of walking locomotion on rigid level surfaces using motion capture system. Eng Struct 91:141–154. https://doi.org/10.1016/j.engstruct.2015.03.003

    Article  Google Scholar 

  13. Živanović S (2015) Modelling human actions on lightweight structures: experimental and numerical developments. MATEC Web of Conferences 24 (2015) 01005. EDP Sciences. https://doi.org/10.1051/matecconf/20152401005

  14. Wang J, Chen J (2017) A comparative study on different walking load models. Struct Eng Mech. https://doi.org/10.12989/sem.2017.63.6.847

    Article  Google Scholar 

  15. Ingólfsson E (2011). Pedestrian-induced lateral vibrations of footbridges. Experimental studies and probabilistic modelling. PhD thesis, Technical University of Denmark.

  16. Hof AL, van Bockel RM, Schoppen T, Postema K (2007) Control of lateral balance in walking. Experimental findings in normal subjects and above-knee amputees. Gait Posture 25(2):250–258. https://doi.org/10.1016/j.gaitpost.2006.04.013

    Article  Google Scholar 

  17. Bocian M, MacDonald JHG, Burn JF (2012) Biomechanically inspired modelling of pedestrian-induced forces on laterally oscillating structures. J Sound Vib 331(16):3914–3929. https://doi.org/10.1016/j.jsv.2012.03.023

    Article  Google Scholar 

  18. Carroll SP, Owen JS, Hussein MFM (2013) A coupled biomechanical/discrete element crowd model of crowd–bridge dynamic interaction and application to the Clifton Suspension. Bridge Eng Struct 49:58–75. https://doi.org/10.1016/j.engstruct.2012.10.020

    Article  Google Scholar 

  19. McRobie FA (2013) Long-term solutions of Macdonald’s model for pedestrian-induced lateral forces. J Sound Vib 332(11):2846–2855. https://doi.org/10.1016/j.jsv.2012.12.027

    Article  Google Scholar 

  20. Carroll SP, Owen JS, Hussein MFM (2014) Experimental identification of the lateral human-structure interaction mechanism and assessment of the inverted-pendulum biomechanical model. J Sound Vib 333(22):5865–5884. https://doi.org/10.1016/j.jsv.2014.06.022

    Article  Google Scholar 

  21. Varela WD, Pfeil MS, da Costa NPA (2020) Experimental investigation on human walking loading parameters and biodynamic model. J Vib Eng Technol 8(6):883–892. https://doi.org/10.1007/s42417-020-00197-3 (Springer Singapore)

    Article  Google Scholar 

  22. Mohammed AS, Pavic A (2017) Evaluation of mass-spring-damper models for dynamic interaction between walking humans and civil structures. Dynamics of civil structures, vol 2. Springer, Cham, pp 169–177

    Chapter  Google Scholar 

  23. Jiménez-Alonso JF, Sáez A (2014) A direct pedestrian-structure interaction model to characterize the human induced vibrations on slender footbridges. Inf la Constr 66(1):1–9. https://doi.org/10.3989/ic.13.110

    Article  Google Scholar 

  24. Lou J, Zhang M, Chen J (2015) Identification of stiffness, damping and biological force of SMD model for human walking. Dynamics of civil structures, vol 2. Springer, Cham, pp 331–337. https://doi.org/10.1007/978-3-319-15248-6_35

    Chapter  Google Scholar 

  25. Shahabpoor E, Pavic A, Racic V (2015) Identification of mass-spring-damper model of walking humans. Structures 5:233–246. https://doi.org/10.1016/j.istruc.2015.12.001

    Article  Google Scholar 

  26. Van Nimmen K, Maes K, Živanović S, Lombaert G, De Roeck G, Van Den Broeck P (2015) Identification and modelling of vertical human-structure interaction. Dynamics of civil structures, vol 2. Springer, Cham, pp 319–330. https://doi.org/10.1007/978-3-319-15248-6_34

    Chapter  Google Scholar 

  27. Zhang M, Georgakis CT, Qu W, Chen J (2015) SMD model parameters of pedestrians for vertical human-structure interaction. Dynamics of Civil Structures, vol 2. Springer, Cham, pp 311–317. https://doi.org/10.1007/978-3-319-15248-6_33

    Chapter  Google Scholar 

  28. Danbon F, Grillaud G (2005) Dynamic Behaviour of a Long-Span Steel Footbridge. Characterisation and Modelling of the Dynamic Loading Induced by a Moving Crowd on the Solférino Footbridge in Paris. In Footbridge 2005 (Second International Congress), Venezia, 06–08 December 2005 (p. 1).

  29. Nakamura S-I (2004) Model for lateral excitation of footbridges by synchronous walking. J Struct Eng 130(1):32–37

    Article  Google Scholar 

  30. Van Nimmen K, Van Hauwermeiren, J, Van den Broeck P (2020) Identification of Human-Structure Interaction Based on Full-Scale Observaions, Eurodyn 2020— XI International Conference on Structural Dynamics, Athens, 23–26 November 2020, Vol. 1, pp 1874–1882.

  31. Rose J, Gamble JG (2006) Human Walking, 3rd edn. Lippnicott Williams & Wilkins, Philadelphia, USA

    Google Scholar 

  32. Saunders VT, Inman VT, Eberhart HD (1953) The major determinants in normal and pathological gait. Jt Bone Jt Surg 35(3):543–558

    Article  Google Scholar 

  33. Ethier CR, Simmons CA (2007) introductory biomechanics: from cells to organisms. Cambridge University Press

    Book  Google Scholar 

  34. Živanović S, Pavic A, Reynolds P (2005) Vibration serviceability of footbridges under human-induced excitation: a literature review. J Sound Vib 279(1):1–74. https://doi.org/10.1016/j.jsv.2004.01.019

    Article  Google Scholar 

  35. Bachmann H, Ammann W (1987) Vibrations in structures: induced by man and machines Vol. 3:Iabse

  36. Bachmann H, Pretlove AJ, Rainer, H (1995) Dynamic forces from rhythmical human body motions. Vibration problems in structures: Practical guidelines. Appendix G.

  37. SÉTRA (2006) Assessment of vibrational behaviour of footbridges under pedestrian loading. Technical guide. SETRA, Paris, France

    Google Scholar 

  38. Ricciardelli F, Pizzimenti AD (2007) Lateral walking-induced forces on footbridges. J Bridg Eng 12:677–688. https://doi.org/10.1061/(ASCE)1084-0702(2007)12:6(677)

    Article  Google Scholar 

  39. Archbold P, Mullarney B (2011) Lateral loads applied by pedestrians at normal walking velocities. Bridg Struct 7(2–3):75–86. https://doi.org/10.3233/BRS-2011-021

    Article  Google Scholar 

  40. Clough RW, Penzien J (2003) Dynamics of structures. Computers & Structures Inc, USA

    MATH  Google Scholar 

  41. Da Silva FT, Brito HMBF, Pimentel RL (2013) Modeling of crowd load in vertical direction using biodynamic model for pedestrians crossing footbridges. Can J Civ Eng 40:1196–1204. https://doi.org/10.1139/cjce-2011-0587

    Article  Google Scholar 

  42. Coermann RR (1962) The mechanical impedance of the human body in sitting and standing position at low frequencies. Hum Factors 4:227–253. https://doi.org/10.1177/001872086200400502

    Article  Google Scholar 

  43. Foschi RO, Neumann G, Yao F, Folz B (1996) Floor vibration due to occupants and reliability-based design guidelines. Can J Civ Eng 23(2):572–572. https://doi.org/10.1139/l95-055

    Article  Google Scholar 

  44. Al-Foqaha'a AA (1997) Design criterion for wood floor vibrations via finite element and reliability analyses. Ph.D. Dissertation, Washington State University, Pullman, USA.

  45. Brownjohn JMW (1999) Energy dissipation in one-way slabs with human participation. In: Proceedings of the Asia-Pacific vibration conference. Nanyang Technological University, p. 155–60.

  46. Falati S (1999) The Contribution of Non-Structural Components to the Overall Dynamic Behaviour of Concrete Floor Slabs Ph.D. Thesis, Oxford University, Oxford, UK.

  47. Zheng X, Brownjohn JM (2001) Modeling and simulation of human-floor system under vertical vibration. Proc. SPIE 4327, Smart Structures and Materials 2001: Smart Structures and Integrated Systems. https://doi.org/10.1117/12.436586

  48. Matsumoto Y, Griffin MJ (2003) Mathematical models for the apparent masses of standing subjects exposed to vertical whole-body vibration. J Sound Vib 260(3):431–451. https://doi.org/10.1016/S0022-460X(02)00941-0

    Article  MATH  Google Scholar 

  49. Setareh M, Gan S (2016) Study of Human-Structure Dynamic Interactions. In: Allen M, Mayes R, Rixen D (eds) Dynamics of Coupled Structures, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-29763-7_39

    Chapter  Google Scholar 

  50. Archbold P (2004) Interactive Load Models for Pedestrian Footbridges. PhD thesis, University College Dublin, Ireland.

  51. Ferris DP, Louie M, Farley CT (1998) Running in the real world: adjusting leg stiffness for different surfaces. Proc Biol Sci 265(1400):989–994. https://doi.org/10.1098/rspb.1998.0388

    Article  Google Scholar 

  52. Arampatzis A, Brüggemann GP, Metzler V (1999) The Effect of Speed on Leg Stiffness and Joint Kinetics in Human Running. J Biomech 32:1349–1353. https://doi.org/10.1016/S0021-9290(99)00133-5

    Article  Google Scholar 

  53. Farley CT, González O (1996) Leg stiffness and stride frequency in human running. J Biomech 29(2):181–186. https://doi.org/10.1016/0021-9290(95)00029-1

    Article  Google Scholar 

  54. Cohen J (1988) Statistical Power Analysis for The Behavioral Sciences, 2nd Edition, L. Lawrence Earlbaum Associates, USA

  55. Racic V, Brownjohn JMW (2012) Mathematical modelling of random narrow band lateral excitation of footbridges due to pedestrians walking. Comput Struct 90–91(1):116–130. https://doi.org/10.1016/j.compstruc.2011.10.002

    Article  Google Scholar 

  56. Wang ZY, Zhang S, Wang HY, Song ZG (2016) Spectral characteristics of pedestrian loads under different crowd densities based on the modified bipedal walking model. Int Conf Mater Sci Civil Eng (MSCE 2016). https://doi.org/10.12783/dtmse/msce2016/10444

    Article  Google Scholar 

  57. Peng Y, Chen J, Ding G (2015) Walking load model for single footfall trace in three dimensions based on gait experiment. Struct Eng Mech 54(5):937–953. https://doi.org/10.12989/sem.2015.54.5.937

    Article  Google Scholar 

  58. Yang QS, Qin JW, Law SS (2015) A three-dimensional human walking model. J Sound Vib 357:437–456. https://doi.org/10.1016/j.jsv.2015.07.017

    Article  Google Scholar 

  59. Fang Z, Lo SM, Lu JA (2003) On the relationship between crowd density and movement velocity. Fire Saf J 38(3):271–283. https://doi.org/10.1016/S0379-7112(02)00058-9

    Article  Google Scholar 

  60. Bruno L, Venuti F (2008) The pedestrian speed–density relation: modelling and application. In: Proceedings of Footbridge, Porto, Portugal, July.

  61. Venuti F, Bruno L (2009) Crowd-structure interaction in lively footbridges under synchronous lateral excitation: a literature review. Phys Life Rev 6(3):176–206. https://doi.org/10.1016/j.plrev.2009.07.001

    Article  Google Scholar 

  62. Venuti F, Reggio A (2018) Mitigation of human-induced vertical vibrations of footbridges through crowd flow control. Struct Control Health Monit 25(12):e2266. https://doi.org/10.1002/stc.2266

    Article  Google Scholar 

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Acknowledgements

The authors acknowledge the financial support of CAPES-Brazil and CNPQ-Brazil to carry out this research project.

Funding

The research leading to these results received funding from CAPES-Brazil and CNPQ-Brazil.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Brasilia, Brasília, DF, 70910-900, Brazil

    Andrea Nataly Pena Pena & José Luis Vital de Brito

  2. Federal University of Paraíba, João Pessoa, PB, 58051-900, Brazil

    Felipe Feliciano Gomes da Silva

  3. Department of Civil and Environmental Engineering, Federal University of Paraíba, João Pessoa, PB, 58051-900, Brazil

    Roberto Leal Pimentel

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  1. Andrea Nataly Pena Pena
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  2. José Luis Vital de Brito
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  3. Felipe Feliciano Gomes da Silva
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Correspondence to José Luis Vital de Brito.

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Pena, A.N.P., de Brito, J.L.V., da Silva, F.F.G. et al. Pedestrian Biodynamic Model for Vibration Serviceability of Footbridges in Lateral Direction. J. Vib. Eng. Technol. 9, 1223–1237 (2021). https://doi.org/10.1007/s42417-021-00292-z

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