Use of Extreme Value Distributions in Describing the Overloaded Axle Load Data from Pavements
Publication: Journal of Transportation Engineering, Part B: Pavements
Volume 149, Issue 4
Abstract
Analysis of overloaded axles has received scant attention during the pavement design process. Such overloaded axles are well known to cause extensive damage to the pavement, though the number of repetitions of such axles is considerably small. This investigation proposes using extreme value distributions to describe the overloaded axles from the axle load data collected from the two National Highways in India. A detailed statistical analysis is carried out under different cases. In the first case, a mixed-normal distribution function is used to describe the entire axle load spectra without explicitly considering the overloading. Different threshold values are chosen for the second and the third cases to consider an appropriate extreme value distribution for analyzing the overloaded data. The right tail region of the axle load data related to overloading is described using Pareto, Burr, and Gamma distributions, while the rest of the data is analyzed using a mixed-normal distribution. The design traffic is estimated for all three cases by calculating the load spectra factor, which uses the moment statistics of the axle load distribution. A significant increase (20%–50%) in the design traffic is observed for the second and third cases.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, and code generated or used during the study appear in the published manuscript.
Acknowledgments
The authors thank M/s Cube Highways and Transport Assets Advisors Private Limited, Noida, for the help provided during axle load data collection.
References
AASHTO. 1993. AASHTO guide for design of pavement structures. Washington, DC: AASHTO.
AASHTO. 2008. Mechanistic-empirical pavement design guide: A manual of practice. Washington, DC: AASHTO.
Alfredo, H.-S. A., and H. Wilson. 1975. Probability concepts in engineering planning and design. New York: Wiley.
Asphalt Institute. 2001. Thickness design: Asphalt pavements for highways and streets (manual series no.1). Lexington, KY: Asphalt Institute.
Bailey, S. F., and R. Bez. 1999. “Site specific probability distribution of extreme traffic action effects.” Probab. Eng. Mech. 14 (1–2): 19–26. https://doi.org/10.1016/S0266-8920(98)00013-7.
Beguera, S., M. Angulo-Martnez, S. M. Vicente-Serrano, J. I. López-Moreno, and A. El-Kenawy. 2011. “Assessing trends in extreme precipitation events intensity and magnitude using non-stationary peaks-over-threshold analysis: A case study in northeast Spain from 1930 to 2006.” Int. J. Climatol. 31 (14): 2102–2114. https://doi.org/10.1002/joc.2218.
Brazauskas, V. 2003. “Information matrix for pareto (IV), Burr, and related distributions.” Commun. Stat.- Theory Methods 32 (2): 315–325. https://doi.org/10.1081/STA-120018188.
Burnos, P., and D. Rys. 2017. “The effect of flexible pavement mechanics on the accuracy of axle load sensors in vehicle weigh-in-motion systems.” Sensors 17 (9): 2053. https://doi.org/10.3390/s17092053.
Chen, B., Z. Zhong, X. Xie, and P. Lu. 2014. “Measurement-based vehicle load model for urban expressway bridges.” Math. Probl. Eng. 2014 (May). https://doi.org/10.1155/2014/340896.
Coles, S. 2001. An introduction to statistical modeling of extreme values. Bristol, UK: Univ. of Bristol.
Fwa, T. F., B. W. Ang, H. S. Toh, and T. N. Goh. 1993. “Estimation of axle loads of heavy vehicles for pavement studies.” Transp. Res. Rec. 1388 (Apr): 70–79.
Haider, S. W., and R. S. Harichandran. 2007. “Relating axle load spectra to truck gross vehicle weights and volumes.” J. Transp. Eng. 133 (12): 696–705. https://doi.org/10.1061/(ASCE)0733-947X(2007)133:12(696).
Haider, S. W., R. S. Harichandran, and M. B. Dwaikat. 2008. “Estimating bimodal distribution parameters and traffic levels from axle load spectra.” In Proc., Transportation Research Board 87th Annual Meeting. Washington, DC: Transportation Research Board.
Haider, S. W., R. S. Harichandran, and M. B. Dwaikat. 2009. “Closed-form solutions for bimodal axle load spectra and relative pavement damage estimation.” J. Transp. Eng. 135 (12): 974–983. https://doi.org/10.1061/(ASCE)TE.1943-5436.0000077.
Haider, S. W., R. S. Harichandran, and M. B. Dwaikat. 2010. “Effect of axle load measurement errors on pavement performance and design reliability.” Transp. Res. Rec. 2160 (1): 107–117. https://doi.org/10.3141/2160-12.
Hakim, A., I. Fithriani, and M. Novita. 2021. “Properties of burr distribution and its application to heavy-tailed survival time data.” J. Phys.: Conf. Ser. 1725 (1): 012016. https://doi.org/10.1088/1742-6596/1725/1/012016.
Hang, W., X.-H. Li, P. Ju, and J. He. 2005. “Site survey and analysis of highway trucks overloading status quo in Anhui.” J. East. Asia Soc. Transp. Stud. 6 (Jan): 1790–1803. https://doi.org/10.11175/easts.6.1790.
Hu, Z., and X. Du. 2017. “A mean value reliability method for bimodal distributions.” In Proc., 2017 Int. Design Engineering Technical Conf. and Computers and Information in Engineering Conf. New York: ASME.
Huang, Y. 2009. Pavement analysis and design. 2nd ed. Hoboken, NJ: Pearson Prentice Hall.
IRC (Indian Road Congress). 2009. Dimensions and weights of road design vehicles. IRC:3-1983. New Delhi, India: IRC.
IRC (Indian Road Congress). 2018. Guidelines for the design of flexible pavements. IRC:37. New Delhi, India: IRC.
Ji, S., R. Wang, M. Shu, W. Han, X. Lan, X. Wang, W. Yin, and Y. Cheng. 2021. “Improvement of vehicle axle load test method based on portable WIM.” Measurement 173 (Mar): 108626. https://doi.org/10.1016/j.measurement.2020.108626.
Karian, Z. A., and E. J. Dudewicz. 2016. Handbook of fitting statistical distributions with R. Boca Raton, FL: CRC Press.
Kim, J. R., L. Titus-Glover, M. I. Darter, and R. K. Kumapley. 1998. “Axle load distribution characterization for mechanistic pavement design.” Transp. Res. Rec. 1629 (1): 13–23. https://doi.org/10.3141/1629-03.
Macea, L. F., L. Márquez, and H. LLinás. 2015. “Improvement of axle load spectra characterization by a mixture of three distributions.” J. Transp. Eng. 141 (12): 04015030. https://doi.org/10.1061/(ASCE)TE.1943-5436.0000801.
Mohammadi, J., and N. Shah. 1992. “Statistical evaluation of truck overloads.” J. Transp. Eng. 118 (5): 651–665. https://doi.org/10.1061/(ASCE)0733-947X(1992)118:5(651).
OBrien, E. J., B. Enright, and A. Getachew. 2010. “Importance of the tail in truck weight modeling for bridge assessment.” J. Bridge Eng. 15 (2): 210–213. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000043.
Omey, E., F. Mallor, and E. Nualart. 2009. An introduction to statistical modelling of extreme values: Application to calculate extreme wind speeds. Brussels, Belgium: Hogeschool-Universiteit Brussel.
Packard, R. G. 1984. Thickness design for concrete highway and street pavements. Skokie, IL: Portland Cement Association.
Prozzi, J. A., and F. Hong. 2007a. “Effect of weigh-in-motion system measurement errors on load-pavement impact estimation.” J. Transp. Eng. 133 (1): 1–10. https://doi.org/10.1061/(ASCE)0733-947X(2007)133:1(1).
Prozzi, J. A., and F. Hong. 2007b. “Optimum statistical characterization of axle load spectra based on load-associated pavement damage.” Int. J. Pavement Eng. 8 (4): 323–330. https://doi.org/10.1080/10298430600949902.
R Development Core Team. 2011. “R: A language and environment for statistical computing.” Accessed February 1, 2019. http://www.R-project.org.
Schmidt, F., X. Y. Zhou, and F. Toutlemonde. 2013. “A peaks-over-threshold analysis of extreme traffic load effects on bridges.” In Proc., Young Research Seminar 2013, 13. Champs-sur-Marne, France: French Institute of Sciences and Technologies for Transportation, Development and Networks.
Timm, D. H., S. M. Tisdale, and R. E. Turochy. 2005. “Axle load spectra characterization by mixed distribution modeling.” J. Transp. Eng. 131 (2): 83–88. https://doi.org/10.1061/(ASCE)0733-947X(2005)131:2(83).
Turochy, R. E., D. H. Timm, and S. M. Tisdale. 2005. Truck equivalency factors, load spectra modelling and effects on pavement design. Auburn, AL: Highway Research Center.
Yang, X., J. Zhang, and W.-X. Ren. 2018. “Threshold selection for extreme value estimation of vehicle load effect on bridges.” Int. J. Distrib. Sens. Networks 14 (2): 1550147718757698. https://doi.org/10.1177/1550147718757698.
Zaninetti, L., and M. Ferraro. 2008. “On the truncated pareto distribution with applications.” Cent. Eur. J. Phys. 6 (1): 1–6. https://doi.org/10.2478/s11534-008-0008-2.
Zhao, Y., Y. Tan, and C. Zhou. 2012. “Determination of axle load spectra based on percentage of overloaded trucks for mechanistic-empirical pavement design.” Road Mater. Pavement Des. 13 (4): 850–863. https://doi.org/10.1080/14680629.2012.735796.
Information & Authors
Information
Published In
Journal of Transportation Engineering, Part B: Pavements
Volume 149 • Issue 4 • December 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Aug 21, 2022
Accepted: Jun 18, 2023
Published online: Aug 31, 2023
Published in print: Dec 1, 2023
Discussion open until: Jan 31, 2024
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.