Technical Papers
Aug 20, 2015

Improvement of Axle Load Spectra Characterization by a Mixture of Three Distributions

Publication: Journal of Transportation Engineering
Volume 141, Issue 12

Abstract

Traffic is one of the most important variables used in pavement design methods. There are currently two methods for characterizing wheel load repetitions: equivalent single axle load (ESAL) and load spectra, which is a more precise characterization of traffic but relies on the same input data used to calculate ESALs. Although the load spectra are described using a bimodal mixture distribution, samples taken in Colombia indicate that the load spectra exhibit an intermediate region that can be modelled with an additional distribution. This research proposes the use of a mixture of three distributions: two log-normal distributions for the description of the peaks and a normal distribution for the intermediate region, finding a closed statistical solution for the formal evaluation of its properties, and deduces the expression of the nth moment that facilitates obtaining important features of the proposed distribution. In a case of application in two geographic regions of Colombia, with more than 53,000 tandem and tridem observed axles, it was found that the proposed model effectively improves the characterization of the load spectra.

Get full access to this article

View all available purchase options and get full access to this article.

Acknowledgments

The authors are grateful to the Atlantic Department Government and the Colombian General Royalties System, for having partially financed this work through the Project LOGPORT, BPIN20120001001911050672 (Agreement No. 0103-2013-000016), in relation to the data analysis of the Caribbean Colombian region. The authors also wish to thank the National Roads Institute (INVIAS) of Colombia, for partially financing this research that was derived from the contract 1326 to 2011, signed between the Universidad del Norte and INVIAS.

References

AASHTO. (2002). “Guide for design of pavement structures.” Washington, DC.
Ahmed, A. W., and Erlingsson, S. (2015). “Characterisation of heavy traffic axle load spectra for mechanistic-empirical pavement design applications.” Int. J. Pavement Eng., 16(6), 488–501.
Conn, A. R., Gould, N. I. M., and Toint, P. L. (2000). Trust-region methods, Society for Industrial and Applied Mathematics, Philadelphia, PA.
Garnica, P. (2009). Espectros de carga y daño para diseño de pavimentos. Quinta conferencia magistral “Alfonso Rico Rodríguez”, Sociedad Mexicana de Ingeniería Geotécnica, Mexico D.F.
Haider, S. W., and Harichandran, R. S. (2007). “Relating axle load spectra to truck gross vehicle weights and volumes.” J. Transp. Eng., 696–705.
Haider, S. W., and Harichandran, R. S. (2009). “Effect of axle load spectrum characteristics on flexible pavement performance.”, 101–114.
Haider, S. W., Harichandran, R. S., and Dwaikat, M. B. (2009). “Closed-form solutions for bimodal axle load spectra and relative pavement damage estimation.” J. Transp. Eng., 974–983.
Haider, S. W., Harichandran, R. S., and Dwaikat, M. B. (2010). “Effect of axle load measurement errors on pavement performance and design reliability.”, 107–117.
Haider, S. W., Harichandran, R. S., and Dwaikat, M. B. (2011). “Impact of systematic axle load measurement error on pavement design using mechanistic-empirical pavement design guide.” J. Transp. Eng., 381–386.
Huang, Y. H. (1993). Pavement analysis and design, 2nd Ed., Pearson Prentice-Hall, Upper Saddle River, NJ.
Jiang, Y., Li, S., Nantung, T. E., and Chen, H. (2008). “Analysis and determination of axle load spectra and traffic input for the mechanistic-empirical pavement design guide.”, Joint Transportation Research Program, Indiana Dept. of Transportation and Purdue University, West Lafayette, IN.
Kuo, C.-M., and Lin, S.-H. (2001). “An analytical study of axle load equivalency factors of concrete pavements.” J. Chin. Inst. Eng., 24(2), 119–130.
LLinás, H. (2014). Introducción a la teoría de probabilidad, Universidad del Norte, Barranquilla, Colombia.
Macea, L. F. (2012). Espectros de carga y factores camión de la flota vehicular colombiana en vías del territorio nacional, Universidad del Norte, Barranquilla, Colombia.
Marquardt, D. W. (1963). “An algorithm for least-squares estimation of nonlinear parameters.” J. Soc. Ind. Appl. Math., 11(2), 431–441.
MATLAB [Computer software]. Natrick, MA, MathWorks Inc.
McElvaney, J. and Snaith, M. S. (2002). “Chapter 15—Analytical design of flexible pavements.” Highways, 4th Ed., C. A. O’Flaherty, A. Boyle, M. J. Brennan, J. Knapton, H. A. Khalid, J. McElvaney, D. McMullen, C. A. O’Flaherty, J. E. Oliver, M. S. Snaith, A. R. Woodside, W. D. H. Woodward, and S. E. Zoorob, Butterworth-Heinemann, Oxford, 395–423.
Morton, B. S., Luttig, E., Horak, E., and Visser, A. T. (2004). “The effect of axle load spectra and tyre inflation pressures on standard pavement design methods.” 8th Conf. of Asphalt Pavements of Southern Africa (CAPSA).
Prozzi, J. A., and Hong, F. (2007a). “Effect of weigh-in-motion system measurement errors on load-pavement impact estimation.” J. Transp. Eng., 1–10.
Prozzi, J. A., and Hong, F. (2007b). “Optimum statistical characterization of axle load spectra based on load-associated pavement damage.” Int. J. Pavement Eng., 8(4), 323–330.
Salama, H. K., and Chatti, K. (2011). “Evaluation of fatigue and rut damage prediction methods for asphalt concrete pavements subjected to multiple axle loads.” Int. J. Pavement Eng., 12(1), 25–36.
Sridhar, B. K. (2008). “Characterization and development of axle load spectra to enhance pavement design and performance on the basis of new mechanistic-empirical design guide in Louisiana.” Doctoral dissertation, Louisiana State Univ.
Timm, D., Peters, K., and Turochy, R. (2008). “Effects of axle load spectra shifts on highway infrastructure damage and cost.” Proc., Int. Conf. on Heavy Vehicles, Laboratoire Central des Ponts et Chaussées, Paris.
Timm, D. H., Bower, J. M., and Turochy, R. E. (2006). “Effect of load spectra on mechanistic-empirical flexible pavement design.”, 146–154.
Timm, D. H., Tisdale, S. M., and Turochy, R. E. (2005). “Axle load spectra characterization by mixed distribution modeling.” J. Transp. Eng., 83–88.
Tran, N. H., and Hall, K. D. (2007). “Development and influence of statewide axle load spectra on flexible pavement performance.”, 106–114.
Turochy, R. E., Baker, S. M., and Timm, D. H. (2005a). “Spatial and temporal variations in axle load spectra and impacts on pavement design.” J. Transp. Eng., 802–808.
Turochy, R. E., Timm, D. H., and Tisdale, S. M. (2005b). “Truck equivalency factors, load spectra modeling and effects on pavement design.”, Highway Research Center, Auburn Univ.
Wang, Y., Hancher, D. E., and Mahboub, K. (2007). “Axle load distribution for mechanistic-Empirical pavement design.” J. Transp. Eng., 469–479.

Information & Authors

Information

Published In

Go to Journal of Transportation Engineering
Journal of Transportation Engineering
Volume 141Issue 12December 2015

History

Received: Sep 29, 2014
Accepted: Jul 7, 2015
Published online: Aug 20, 2015
Published in print: Dec 1, 2015
Discussion open until: Jan 20, 2016

Permissions

Request permissions for this article.

Authors

Affiliations

Luis F. Macea
Graduate Research Assistant and Ph.D. Candidate, Dept. of Civil and Environmental Engineering, Universidad del Norte, Km. 5 Vía Puerto Colombia, Barranquilla 080001, Colombia.
Luis Márquez [email protected]
Associate Professor, School of Transportation and Highways Engineering, Universidad Pedagógica y Tecnológica de Colombia, Avenida Central del Norte 39-115, Tunja 150001, Colombia (corresponding author). E-mail: [email protected]
Humberto LLinás
Associate Professor, Dept. of Mathematics and Statistics, Universidad del Norte, Km. 5 Vía Puerto Colombia, Barranquilla 080001, Colombia.

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.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share