Predicting the Bounds of Vehicle-Induced Bridge Responses Using the Interval Analysis Method
Publication: Journal of Bridge Engineering
Volume 21, Issue 9
Abstract
A method for predicting the bounds of vehicle-induced bridge responses with uncertain bridge and vehicle parameters is presented. The uncertainties in the parameters of the bridge and vehicle are represented with interval variables instead of conventional random variables with known probability distributions. First, a three-dimensional vehicle–bridge interaction (VBI) system, which has no closed-form solution and can account for road roughness, is established. Then, by introducing the interval analysis method (IAM) based on the first-order Taylor series expansion, the expressions of the bridge responses, including displacement and bending moment at the midspan, can be explicitly given as functions of the interval parameters, and the lower and upper bounds of the bridge responses are determined by the particle swarm algorithm instead of direct interval arithmetic to avoid excessive overestimation of the responses. The subinterval technique can also be adopted to improve the accuracy of the IAM. A numerical example is provided, and the results show that, compared with the conventional Monte Carlo method, the proposed IAM is capable of obtaining the bounds of the bridge deflection and bending moment without much sacrifice of accuracy while requiring much less computational effort. This indicates that the proposed method can be effectively and efficiently applied to predicting the bounds of the dynamic responses of complicated VBI systems with interval uncertainties. An example is also used to demonstrate the applicability of the IAM to field bridges when only limited information about the bridge and vehicle is available.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors acknowledge the financial support provided by the National Natural Science Foundation of China (Grant Nos. 51208189 and 51478176) and the Excellent Youth Foundation of Hunan Scientific Committee (Grant No. 14JJ1014).
References
AASHTO. (2002). Standard specifications for highway bridges, Washington, DC.
Au, F. T. K., Cheng, Y. S., and Cheung, Y. K. (2001). “Effects of random road surface roughness and long-term deflection of prestressed concrete girder and cable-stayed bridges on impact due to moving vehicles.” Comput. Struct., 79(8), 853–872.
Deng, L., and Cai, C. S. (2009). “Identification of parameters of vehicles moving on bridges.” Eng. Struct., 31(10), 2474–2485.
Deng, L., and Cai, C. S. (2010). “Development of dynamic impact factor for performance evaluation of existing multi-girder concrete bridges.” Eng. Struct., 32(1), 21–31.
Deng, L., Yu, Y., Zou, Q., and Cai, C. S. (2015). “State-of-the-art review of dynamic impact factors of highway bridges.” J. Bridge Eng., 04014080.
Ding, L., Hao, H., and Zhu, X. Q. (2009). “Evaluation of dynamic vehicle axle loads on bridges with different surface conditions.” J. Sound Vib., 323(3–5), 826–848.
Dodds, C. J., and Robson, J. D. (1973). “The description of road surface roughness.” J. Sound Vib., 31(2), 175–183.
Fancher, P. S., Ervin, R. D., Winkler, C. B., and Gillespie, T. D. (1986). “A factbook of the mechanical properties of the components for single-unit and articulated heavy trucks. Phase I. Final report.” UMTRI-86-12, Univ. of Michigan Transportation Research Institute, Ann Arbor, MI.
González, A., Rattigan, P., OBrien, E. J., and Caprani, C. (2008). “Determination of bridge lifetime dynamic amplification factor using finite element analysis of critical loading scenarios.” Eng. Struct., 30(9), 2330–2337.
Han, W., Wu, J., Cai, C. S., and Chen, S. (2015). “Characteristics and dynamic impact of overloaded extra heavy trucks on typical highway bridges.” J. Bridge Eng., 05014011.
Harris, N. K., OBrien, E. J., and González, A. (2007). “Reduction of bridge dynamic amplification through adjustment of vehicle suspension damping.” J. Sound Vib., 302(3), 471–485.
Harwood, D. W., Torbic, D. J., Richard, K. R., Glauz, W. D., and Elefteriadou, L. (2003). “Review of truck characteristics as factors in roadway design.” NCHRP Rep. No. 505, Transportation Research Board, Washington, DC.
Huang, D. Z., Wang, T. L., and Shahawy, M. (1993). “Impact studies of multigirder concrete bridges.” J. Struct. Eng., 2387–2402.
Liu, N., Gao, W., Song, C., Zhang, N., and Pi, Y.-L. (2013). “Interval dynamic response analysis of vehicle-bridge interaction system with uncertainty.” J. Sound Vib., 332(13), 3218–3231.
Ma, Y., Liang, Z., Chen, M., and Hong, J. (2013). “Interval analysis of rotor dynamic response with uncertain parameters.” J. Sound Vib., 332(16), 3869–3880.
Ma, Y., Wang, L., Zhang, J., Xiang, Y., Peng, T., and Liu, Y. (2014). “Hybrid uncertainty quantification for probabilistic corrosion damage prediction for aging RC bridges.” J. Mater. Civ. Eng., 04014152.
Muhanna, R. L., and Mullen, R. L. (2001). “Uncertainty in mechanics problems—Interval-based approach.” J. Eng. Mech., 557–566.
OBrien, E. J., Cantero, D., Enright, B., and González, A. (2010). “Characteristic dynamic increment for extreme traffic loading events on short and medium span highway bridges.” Eng. Struct., 32(12), 3827–3835.
Oliva, J., Goicolea, J. M., Antolín, P., and Astiz, M. Á. (2013). “Relevance of a complete road surface description in vehicle–bridge interaction dynamics.” Eng. Struct., 56, 466–476.
Roy, C. J., and Oberkampf, W. L. (2011). “A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing.” Comput. Methods Appl. Mech. Eng., 200(25–28), 2131–2144.
Sankararaman, S., and Mahadevan, S. (2011). “Likelihood-based representation of epistemic uncertainty due to sparse point data and/or interval data.” Reliab. Eng. Syst. Saf., 96(7), 814–824.
Tabsh, S., and Nowak, A. (1991). “Reliability of highway girder bridges.” J. Struct. Eng., 2372–2388.
Wu, J., Luo, Z., Zhang, N., and Zhang, Y. (2015). “A new uncertain analysis method and its application in vehicle dynamics.” Mech. Syst. Sig. Process., 50–51, 659–675.
Xia, B., and Yu, D. (2012). “Modified sub-interval perturbation finite element method for 2D acoustic field prediction with large uncertain-but-bounded parameters.” J. Sound Vib., 331(16), 3774–3790.
Xia, B., and Yu, D. (2014). “Modified interval and subinterval perturbation methods for the static response analysis of structures with interval parameters.” J. Struct. Eng., 04013113.
Zhang, H., Mullen, R. L., and Muhanna, R. L. (2010). “Interval Monte Carlo methods for structural reliability.” Struct. Saf., 32(3), 183–190.
Information & Authors
Information
Published In
Journal of Bridge Engineering
Volume 21 • Issue 9 • September 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Aug 26, 2015
Accepted: Jan 8, 2016
Published online: Feb 29, 2016
Discussion open until: Jul 29, 2016
Published in print: Sep 1, 2016
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.