Calculation of Equivalent Axle Load Factor Based on Artificial Intelligence

Document Type : Regular Paper


1 Ph.D. Candidate, Department of Civil Engineering, Payame Noor University, P.O.Box 19395-4697, Tehran, Iran

2 Associate Professor, Department of Civil Engineering, Payame Noor University, P.O.Box 19395-4697, Tehran, Iran

3 Assistant Professor, Faculty of Engineering, Ferdowsi University, P.O.Box 9177948974, Mashhad, Iran


In most road pavements design methods, a solution is required to transform the traffic spectrum to standard axle load with using equivalent axle load factor (EALF). The EALF depends on various parameters, but in existing design methods, only the axle type (single, tandem, and tridem) and pavement structure number were considered. Also, the EALF only determined for experimental axles and axle details (i.e., axle weight, length, pressure), wheel type (single or dual wheel) plus pavement properties were overlooked which may cause inaccuracy and unusable for the new axle. This paper presented a developed model based on Artificial Neural Network (ANN) for calculation of EALFs considering axle type, axle length, contact area, pavement structure number (SN), tire pressure, speed, and final serviceability. Backpropagation architecture was selected for the model for the EALF prediction based on fatigue criteria. Finally, among all reviewed ANN configuration, a network with 7-13-1 was selected for the optimum network.


Main Subjects

[1]     Zaghloul, S., White, T. D. (1994). “Guidelines for Permitting Overloads; Part 1: Effect of Overloaded Vehicles on the Indiana Highway Network,” West Lafayette, IN. DOI: 10.5703/1288284313233.
[2]     Chatti, K., Lee, D., Kim, T. (2000). “Truck Damage Factors Using Dissipated Energy versus Peak Strains,” in 6th international Symposium on Heavy Vehicle Weights and Dlmensiolns, pp. 175–183.
[3]     Abdel Motaleb, M. E. (2007). “Impact of high-pressure truck tires on pavement design in Egypt,” Emirates Journal for Engineering Research, vol. 12, no. 2, pp. 65–73.
[4]     Judycki, J. (2010). “Determination of Equivalent Axle Load Factors on the Basis of Fatigue Criteria for Flexible and Semi-Rigid Pavements,” Road Materials and Pavement Design, vol. 11, no. 1, pp. 187–202. DOI: 10.1080/14680629.2010.9690266.
[5]     Chaudry, R., Memon, A. B. (2013). “Effects of Variation in Truck Factor on Pavement Performance in Pakistan,” Journal of Engineering and Technology, vol. 32, no. 1, pp. 19–30.
[6]     Amorim, S. I. R., Pais, J. C., Vale, A. C., Minhoto, M. J. C. (2014). “A model for equivalent axle load factors,” International Journal of Pavement Engineering, vol. 16, no. 10, pp. 881–893. DOI: 10.1080/10298436.2014.968570.
[7]     Rys, D., Judycki, J., Jaskula, P. (2016).  “Determination of vehicles load equivalency factors for polish catalogue of typical flexible and semi-rigid pavement structures,” Transportation Research Procedia, vol. 14, pp. 2382–2391. DOI: 10.1016/j.trpro.2016.05.272.
[8]     Zhang, H., Gong, M., Yu, T. (2018). “Modification and application of axle load conversion formula to determine traffic volume in pavement design,” International Journal of Pavement Research and Technology, vol. 11, no. 6, pp. 582–593. DOI: 10.1016/j.ijprt.2017.12.007.
[9]     Singh, A. K., Sahoo, J. P. (2020). “Analysis and design of two layered flexible pavement systems: A new mechanistic approach,” Computers and Geotechnics, vol. 117, no. April 2019, pp. 103238, Jan. DOI: 10.1016/j.compgeo.2019.103238.
[10]    Deng, Y., Luo, X., Zhang, Y., Lytton, R. L. (2021). “Evaluation of flexible pavement deterioration conditions using deflection profiles under moving loads,” Transportation Geotechnics, vol. 26, pp. 100434. DOI: 10.1016/j.trgeo.2020.100434.
[11]    Al-qadi, I. L., Wang, H., Tutumluer, E. (2010). “Dynamic Analysis of Thin Asphalt Pavements by Using Cross-Anisotropic Stress-Dependent Properties for Granular Layer,” Transportation Research Board, vol. 2154.1, pp. 156–163. DOI: 10.3141/2154-16.
[12]    Chen, Y. (2009). “Viscoelastic modeling of flexible pavement,” Akron.
[13]    Alkaissi, Z. A. (2020). “Effect of High Temperature and Traffic Loading on Rutting Performance of Flexible Pavement,” Journal of King Saud University - Engineering Sciences, vol. 32, no. 1, pp. 1–4. DOI: 10.1016/j.jksues.2018.04.005.
[14]    Zaghloul, S. M., White, T. (1993). “Use of a three-dimensional, dynamic finite element program for analysis of flexible pavement,” Transportation research record, no. 1388.
[15]    Zarei, B., Shafabakhsh, G. A. (2018). “Dynamic Analysis of Composite Pavement using Finite Element Method and Prediction of Fatigue Life,” vol. 04, no. June, pp. 33–37.
[16]    Huang, Y. H. (2004). Pavement Analysis and Design, Second Edi. Pearson Education.
[17]    Kim, M. (2007). “Three-Dimensional Finite Element Analysis Of Flexible Pavements Considering Nonlinear Pavement Foundation Behavior,” University of Illinois.
[18]    Cebon, D. (1999). Handbook of vehicle-road interaction.
[19]    Papagiannakis, A., Oancea, T., N. A., Chan, J., Bergman, A. T. (1991). “Application of ASTM E1049-85 in Calculating Load Equivalence Factors from In Situ Strains,” Transportation Research Record, vol. 1307, pp. 82–89.
[20]    Filho, P. B., Raymundo, H., Machado, S. T., Leite, A. R. C. A. P., Sacomano, J. B. (2016). “Configurations of tire pressure on the pavement for commercial vehicles: calculation of the n number and the consequences on pavement performance,” Independent Journal of Management & Production, vol. 7, pp. 584–605. DOI: 10.14807/ijmp.v7i5.419.
[21]    Uddin, W., Garza, S. (2004). “3D-FE modeling and simulation of airfield pavements subjected to FWD impact load pulse and wheel loads,” in Airfield Pavements: Challenges and New Technologies, pp. 304–315. DOI: 10.1061/40711(141)19.
[22]    Sebaaly, P., Tabatabaee, N., Kulakowski, B., Scullion, T. (1992). “Instrumentation for Flexible Pavements-Field Performance of Selected Sensors Volume I: Final Report”. DOI: 10.1520/JTE10409J.
[23]    Solatifar, N., Lavasani, S. (2020). "Development of An Artificial Neural Network Model for Asphalt Pavement Deterioration Using LTPP Data," Journal of Rehabilitation in Civil Engineering, vol. 8, no. 1, pp. 121-132. DOI: 10.22075/jrce.2019.17120.1328.
[24]    Abbaszadeh, M., Sharbatdar, M. (2020). "Modeling of Confined Circular Concrete Columns Wrapped by Fiber Reinforced Polymer Using Artificial Neural Network," Journal of Soft Computing in Civil Engineering, vol. 4, no. 14, pp. 61-78. DOI: 10.22115/scce.2020.213196.1153.
[25]    Van Gerven, M., Bohte, S. (2017). “Editorial : Artificial Neural Networks as Models of Neural Information Processing,” vol. 11, no. December, pp. 10–11. DOI: 10.1038/nature14539.
[26]    Moradi, E., Naderpour, H., Kheyroddin, A. (2018). “An artificial neural network model for estimating the shear contribution of RC beams strengthened by externally bonded FRP,” Journal of Rehabilitation in Civil Engineering, vol. 6, no. 1, pp. 88–103. DOI: 10.22075/jrce.2018.376.1072.
[27]    Darvishan, E. (2021). "The Punching Shear Capacity Estimation of FRP- Strengthened RC Slabs Using Artificial Neural Network and Group Method of Data Handling," Journal of Rehabilitation in Civil Engineering, vol. 9, no. 1, pp. 102-113. DOI: 10.22075/jrce.2020.20335.1407.
[28]    Naderpour, H., Nagai, K., Fakharian, P. and Haji, M. (2019). "Innovative models for prediction of compressive strength of FRP-confined circular reinforced concrete columns using soft computing methods,” Composite Structures, vol. 215, pp. 69–84. DOI: 10.1016/j.compstruct.2019.02.048
[29]    Adeli, H. (2001). “Neural Networks in Civil Engineering” Computer‐Aided Civil and Infrastructure Engineering, vol. 16, no. 2, pp. 126–142. DOI: 10.1111/0885-9507.00219.
[30]    Nunes, I., Hernane, D., Flauzino, R. A., Bartocci Liboni, L. H., Reis Alves, S. F. D. (2017). Artificial Neural Networks (A Practical Course). Switzerland: Springer International Publishing. DOI: 10.1007/978-3-319-43162-8_2.
[31]    Abdulla, N. (2020). "Using the Artificial Neural Network to Predict the Axial Strength and Strain of Concrete-Filled Plastic Tube," Journal of Soft Computing in Civil Engineering, vol. 4, no. 2, pp. 63-84. DOI: 10.22115/scce.2020.225161.1198.
[32]    Gajewski, J., Sadowski, T. (2014). “Sensitivity analysis of crack propagation in pavement bituminous layered structures using a hybrid system integrating Artificial Neural Networks and Finite Element Method,” Computational Materials Science, vol. 82, pp. 114–117. DOI: 10.1016/j.commatsci.2013.09.025.
[33]    Profillidis, V. A., Botzoris, G. N. (2018). “Modeling of Transport Demand,” Elsevier.
[34]    Naderpour, H., Rezazadeh Eidgahee, D., Fakharian, P., Rafiean, A. H., and Kalantari, S. M. (2020) “A new proposed approach for moment capacity estimation of ferrocement members using Group Method of Data Handling,” Engineering Science and Technology, an International Journal, vol. 23, no. 2, pp. 382–391. DOI: 10.1016/j.jestch.2019.05.013
[35]    Hagan, M. T.,  Demuth, H. B., Beale, M. H., Jess, O. De. (2014). Neural network design, 2nd ed. USA, Martin Hagan.
[36]    Angus, J. E. (1991). “Criteria for choosing the best neural network,” Sandiego.