Predicting Flow Number of Asphalt Mixtures Based on the Marshall Mix design Parameters Using Multivariate Adaptive Regression Spline (MARS)

Document Type : Research Paper


1 Associate Professor, Department of Civil Engineering, Sirjan University of Technology, Sirjan, Iran

2 M.S Student, Department of Civil Engineering, Sirjan University of Technology, Sirjan, Iran

3 Assistant Professor, Department of Civil Engineering, Sirjan University of Technology, Sirjan, Iran

4 Ph.D. Candidate, National Center for Asphalt Technology at Auburn University, USA


Rutting is one of the major distresses in the flexible pavements, which is heavily influenced by the asphalt mixtures properties at high temperatures. There are several methods for the characterization of the rutting resistance of asphalt mixtures. Flow number is one of the most important parameters that can be used for the evaluation of rutting. The flow number is measured by the dynamic creep test, which requires advanced equipment, notable cost, and time. This paper aims to develop a mathematical model for predicting the flow number of asphalt mixtures based on the Marshall mix design parameters using the Multivariate Adaptive Regression Spline (MARS). The required parameters for developing the model are as follows: percentage of fine and coarse aggregates, bitumen content, air voids content, voids in mineral aggregates, Marshall Stability, and flow. The coefficient of determination (R2) of the model for training and testing set is 0.96 and 0.97, respectively, which confirms the high accuracy of the model.  Moreover, the comparison of the developed model with the existing models shows the superior performance of the developed model. It should be noted that the developed model is valid only in the range of dataset used for the modeling.


-       Alavi, A. H., Ameri, M., Gandomi, A. H. and Mirzahosseini, M. R. (2010)  “Formulation of flow number of asphalt mixes using a hybrid computational method”, Construction and Building Materials, Vol. 25, No. 3, pp. 1338-1355.
-       Ashrafian, A., Amiri, M. J. T., Rezaie-Balf, M., Ozbakkaloglu, T. and Lotfi-Omran, O. (2018) “Prediction of compressive strength and ultrasonic pulse velocity of fiber reinforced concrete incorporating nano silica using heuristic regression methods”, Construction and Building Materials, Vol. 190, pp. 479-494.
-       Bahuguna, S. (2003) “Permanent deformation and rate effects in asphalt concrete: Constitutive modeling and numerical implementation”,  Ph.D. dissertation, Montana State University,.
Bhattacharya, S., Murakonda, P. and Das, S. (2018) “Prediction of uplift capacity of suction caisson in clay using functional network and multivariate adaptive regression spline”, Scientia Iranica, Vol. 25, No 2, pp.517-531.
-       Cooper, K. E., Brown, S. and Pooley, G. (1985) “The design of aggregate gradings for asphalt base courses”,  Paper presented at the Association of Asphalt Paving Technologists Proc, United States, Vol. 54, pp 324-346
-       Fakhri, M. and Ghanizadeh, A. R. (2014) “Modelling of 3D response pulse at the bottom of asphalt layer using a novel function and artificial neural network”, International Journal of Pavement Engineering, Vol. 15, No. 8, pp. 671-688.
-       Friedman, J. H. (1991) “Multivariate adaptive regression splines. The annals of statistics”,  Vol. 19, No. 1, pp. 1-67.
-       FHWA. (1998) “DTFH 61-94-R-00045 : Interim task C report of preliminary recommendations for the simple performance test”, FHWA
-       Gandomi, A. H., Alavi, A. H., Mirzahosseini, M. R. and Nejad, F. M. (2011) “Nonlinear genetic-based models for prediction of flow number of asphalt mixtures”,  Journal of Materials in Civil Engineering, Vol. 23, No. 3, pp. 248-263.
-      Georgiou, P., Plati, C. and Loizos, A. (2018) “Soft computing models to predict pavement roughness: A comparative study”, Advances in Civil Engineering, Vol. 2018, No. 43, pp. 1-8.
-       Ghanizadeh, A. R. (2017)  “Application of support vector machine regression for predicting critical responses of flexible pavements”, International Journal of Transportation Engineering, Vol. 4, No. 4, pp. 305-315.
-       Ghanizadeh, A. R. and Ahadi M. (2015) “Application of artificial neural networks for analysis of flexible pavements under static loading of standard axle”,  International Journal of Transportation Engineering, Vol. 3, No. 1, pp. 31-43.
-       Ghanizadeh, A. R. and Fakhri, M. (2014) “Prediction of frequency for simulation of asphalt mix fatigue tests using MARS and ANN”, The Scientific World Journal, Vol. 2014, No. 20, pp. 1-16.
-       Ghanizadeh, A. R. and Fakhri, M. (2018) “Quasi-static analysis of flexible pavements based on predicted frequencies using Fast Fourier Transform and Artificial Neural Network”, International Journal of Pavement Research Technology, Vol. 11, No. 1, pp. 47-57.
-       Goh, A. T. C., Zhang, W., Zhang, Y., Xiao, Y. and Xiang, Y. (2018) “Determination of earth pressure balance tunnel-related maximum surface settlement: a multivariate adaptive regression splines approach”,  Bulletin of Engineering Geology and the  Environment, Vol. 77, No. 2, pp. 489-500.
-       Gu, F., Luo, X., Zhang, Y., Chen, Y., Luo, R. and Lytton, R. L. (2018) “Prediction of geogrid-reinforced flexible pavement performance using artificial neural network approach”,  Road Materials Pavement Design, Vol. 19, No. 5, pp. 1147-1163.
Hastie, T., Tibshirani, R. and Friedman, J. (2009) “Unsupervised learning. The elements of statistical learning”,  New York.  Vol. 21, pp. 485-585.
-       Hinislioğlu, S. and Agar, E. (2004)  “Use of waste high density polythylene as bitumen modifier in asphalt concrete mix”,  Materials Letters, Vol. 58, No. 3-4, pp. 267-271.
-       Lavin, P. (2003)  “Asphalt pavements: a practical guide to design, production and maintenance for engineers and architects”, London:  CRC Press.
-       Kaloush, K. E. (2001) “Simple performance test for permanent deformation of asphalt mixture”, Ph.D. dissertation, Arizona State University., Tempe, AZ.
-       Kaloush, K. E., Witczak, M. Roque, R., Brown, S., D'Angelo, J., Marasteanu, M. and Masad, E. (2002) “Tertiary flow characteristics of asphalt mixtures”,  Asphalt Paving Technology, Vol. 71, pp. 248-280.
-       Kaya, O., Rezaei-Tarahomi, A., Ceylan, H., Gopalakrishnan, K., Kim, S. and Brill, D. R. (2018. “Neural network–based multiple-slab response models for top-down cracking mode in airfield pavement design”,  Journal of Transportation Engineering, Part B: Pavements, American Society of Civil Engineers, Vol. 144, No. 2, pp. 04018009-1-04018009-9.
-       Khadka, M., Paz, A. and Singh, A. (2018) “Generalised clusterwise regression for simultaneous estimation of optimal pavement clusters and performance models”,  International Journal of Pavement Engineering; Published Online On 19 Sep 2018, pp. 1-13.
-       Kim, Y. R. (2008) “Modeling of asphalt concrete, 1st edition”, McGraw-Hill Education.
-       Milborrow, S. (2014) “Notes on the earth package”, pp. 1-60: CRAN. org.
-       Mirzahosseini, M. R., Aghaeifar, A., Alavi, A. H., Gandomi, A. H. and Seyednour, R. (2011) “Permanent deformation analysis of asphalt mixtures using soft computing techniques”,  Expert Systems with Applications, Vol. 38, No. 5, pp. 6081-6100.
-       Mohanty, R., Suman, S. and Das, S. K. (2018) “Prediction of vertical pile capacity of driven pile in cohesionless soil using artificial intelligence techniques. International”,  Journal of Geotechnical Engineering, Vol. 12, No. 2, pp. 209-216.
-       Najafi, S., Flintsch, G. W. and Khaleghian, S. (2019)  “Pavement friction management–artificial neural network approach”,  International Journal of Pavement Engineering, Vol. 20, No. 2, pp. 125-135.
-       Nivedya, M. and Mallick, R. B. (2018)  “Artificial neural network-based prediction of field permeability of hot mix asphalt pavement layers”, International Journal of Pavement Engineering; Published online: 14 Sep 2018, pp. 1-12.
-       Pardhan, M. (1995) “Permanent deformation characteristics of asphalt-aggregate mixture using varied material and modeling procedure with Marshall method”,  Ph.D. dissertation, Montana State University, Bozeman, MT.
-       Saltan, M. and Terzi, S. (2005) “Comparative analysis of using artificial neural networks (ANN) and gene expression programming (GEP) in backcalculation of pavement layer thickness”, Vol. 12, pp. 42-50.
-       Samui, P. (2013) “Multivariate adaptive regression spline (Mars) for prediction of elastic modulus of jointed rock mass”, Pijush Geotechnical Geological Engineering, Vol. 31, No. 1, pp. 249-253.
-       Sousa, J. B., Craus, J. and Monismith, C. L. (1991) “Summary report on permanent deformation in asphalt concrete (No. SHRP-A-318).
-       Williams, R. C., Robinette, C. J., Bausano, J. and Breakah, T. (2007) “Testing of wisconsin asphalt mixtures for the forthcoming aashto mechanistic-empirical pavement design procedure: Final Report”,  Wisconsin Highway Research Program.
-       Witczak, M. W., Kaloush, K., Pellinen T., El-Basyouny, M. and Von Quintus, H. (2002) “Simple performance test for superpave mix design, Vol. 465”,  Transportation Research Board, National Cooperative Highway Research Program, Washington, D.C,  
-       Yan, K.-z., Ge, D.-D. and Zhang, Z. (2014) “Support vector machine models for prediction of flow number of asphalt mixtures”, International Journal of Pavement Research Technology, Vol. 7, No. 1, pp. 31-39.
-       Zhang, W. and Goh, A. T. (2018) “Modelling of pile drivability using soft computing methods”,  Big Data in Engineering Applications, Vol. 7, pp. 279-301.
-       Zhang, W., Zhang, R., Wang, W., Zhang, F. and Goh, A. T. C. (2019) “A Multivariate Adaptive Regression Splines model for determining horizontal wall deflection envelope for braced excavations in clays”,  Tunnelling Underground Space Technology, Vol. 84, pp. 461-471.
-       Zhou, F., Scullion, T. and Sun, L. (2004) Verification and modeling of three-stage permanent deformation behavior of asphalt mixes”,  Journal of Transportation Engineering, Part B: Pavements, Vol. 130, No. 4, pp. 486-494.
-       Zoorob, S. H. and Suparma, L. B. (2000) “Laboratory design and investigation of the properties of continuously graded Asphaltic concrete containing recycled plastic aggregate replacement”,  Plastiphalt, Vol. 22, No. 4, pp. 233-242.