Skip to main content
SpringerLink
Log in

Variable-order fractional derivative rutting depth prediction of asphalt pavement based on the RIOHTrack full-scale track

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

Rutting deformation is typical damage to asphalt pavement and can be quantitatively described as the time-varying mechanical deformation feature of the asphalt mixture during the creep process. First, a nonlinear viscoelastic creep model is established based on the Caputo variable-order fractional derivative. The fractional order in this model is not fixed and is defined as a time-varying function. The time-dependent mechanical properties of asphalt mixtures are effectively reflected. Based on the modified Burgers model, the variable-order function is revised to a linear form. Second, the variable-order fractional Burgers rutting model is obtained by fitting the test data of the RIOHTrack full-scale track. The Levenberg-Marquardt optimization algorithm is used to analyze the test data and the corresponding parameters to obtain more accurate and applicable variable-order fractional rutting mechanics and empirical models for different asphalt pavement structures. Finally, according to the classification of the pavement structure, structures III and VI are taken as examples. The rutting prediction and comparison results of several representative pavement structures are obtained to verify that the proposed rutting prediction model can also accurately predict all road sections of RIOHTrack. The new model is also compared with the rutting model of the mechanistic-empirical pavement design guide, the fractional-order Burgers rutting model, and the modified Burgers rutting model. The fitting results are evaluated using the determination coefficient R2. The results show that the variable-order fractional Burgers rutting model proposed in this study exhibits a better fit and is more applicable to describe the rutting deformation of asphalt pavement.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Golalipour A, Jamshidi E, Niazi Y, et al. Effect of aggregate gradation on rutting of asphalt pavements. Procedia-Soc Behaval Sci, 2012, 53: 440–449

    Article  Google Scholar 

  2. Alae M, Zhao Y, Zarei S, et al. Effects of layer interface conditions on top-down fatigue cracking of asphalt pavements. Int J Pavement Eng, 2020, 21: 280–288

    Article  Google Scholar 

  3. Huang W, Liang S M, Wei Y. Surface deflection-based reliability analysis of asphalt pavement design. Sci China Tech Sci, 2020, 63: 1824–1836

    Article  Google Scholar 

  4. Ghuzlan K A, Al-Mistarehi B W, Al-Momani A S. Rutting performance of asphalt mixtures with gradations designed using Bailey and conventional Superpave methods. Construction Building Mater, 2020, 261: 119941

    Article  Google Scholar 

  5. Luo W, Li B, Zhang Y, et al. A creep model of asphalt mixture based on variable order fractional derivative. Appl Sci, 2020, 10: 3862

    Article  Google Scholar 

  6. Barksdale R. Laboratory evaluation of rutting in base course materials. In: Proceedings of the 3rd International Conference on the Structural Design of Asphalt Pavements, London, 1972. 161–174

  7. Archilla A R, Madanat S. Development of a pavement rutting model from experimental data. J Transp Eng, 2000, 126: 291–299

    Article  Google Scholar 

  8. Darabi M K, Al-Rub R K A, Masad E A, et al. A thermo-viscoelastic-viscoplastic-viscodamage constitutive model for asphaltic materials. Int J Solids Struct, 2011, 48: 191–207

    Article  MATH  Google Scholar 

  9. Nahi M, Kamaruddin I, Napiah M. Rutting prediction in asphalt pavement based on viscoelastic theory. In: Proceedings of MATEC Web of Conferences, 2016. 78: 01035

  10. Al-Rub R K A, Darabi M K, Huang C W, et al. Comparing finite element and constitutive modelling techniques for predicting rutting of asphalt pavements. Int J Pavement Eng, 2012, 13: 322–338

    Article  Google Scholar 

  11. Tong J, Ma T, Shen K, et al. A criterion of asphalt pavement rutting based on the thermal-visco-elastic-plastic model. Int J Pavement Eng, 2022, 23: 1134–1144

    Article  Google Scholar 

  12. Gong H, Sun Y, Mei Z, et al. Improving accuracy of rutting prediction for mechanistic-empirical pavement design guide with deep neural networks. Construction Building Mater, 2018, 190: 710–718

    Article  Google Scholar 

  13. Liu H J, Cao J D, Huang W, et al. Complex network approach for the evaluation of asphalt pavement design and construction: a longitudinal study. Sci China Inf Sci, 2022, 65: 172204

    Article  MathSciNet  Google Scholar 

  14. Kamboozia N, Ziari H, Behbahani H. Artificial neural networks approach to predicting rut depth of asphalt concrete by using of visco-elastic parameters. Construction Building Mater, 2018, 158: 873–882

    Article  Google Scholar 

  15. Mirabdolazimi S M, Shafabakhsh G. Rutting depth prediction of hot mix asphalts modified with forta fiber using artificial neural networks and genetic programming technique. Construction Building Mater, 2017, 148: 666–674

    Article  Google Scholar 

  16. Li Z X, Shi X L, Cao J D, et al. CPSO-XGBoost segmented regression model for asphalt pavement deflection basin area prediction. Sci China Tech Sci, 2022, 65: 1470–1481

    Article  Google Scholar 

  17. Huang C W, Al-Rub R K A, Masad E A, et al. Three-dimensional simulations of asphalt pavement permanent deformation using a nonlinear viscoelastic and viscoplastic model. J Mater Civ Eng, 2011, 23: 56–68

    Article  Google Scholar 

  18. Zhang Y, Luo X, Deng Y, et al. Evaluation of rutting potential of flexible pavement structures using energy-based pseudo variables. Construction Building Mater, 2020, 247: 118391

    Article  Google Scholar 

  19. Deng Y, Zhang Y, Shi X, et al. Stress-strain dependent rutting prediction models for multi-layer structures of asphalt mixtures. Int J Pavement Eng, 2022, 23: 2728–2745

    Article  Google Scholar 

  20. Chen L, Liu G, Yao B, et al. Rutting prediction model for semirigid base asphalt pavement based on Hamburg wheel tracking test. Int J Geomech, 2021, 21: 04021215

    Article  Google Scholar 

  21. Liu G, Chen L, Qian Z, et al. Rutting prediction models for asphalt pavements with different base types based on RIOHTrack full-scale track. Construction Building Mater, 2021, 305: 124793

    Article  Google Scholar 

  22. Schapery R A. On the characterization of nonlinear viscoelastic materials. Polym Eng Sci, 1969, 9: 295–310

    Article  Google Scholar 

  23. Baglieri O, Santagata E, Sapora A, et al. Fractional viscoelastic modeling of antirutting response of bituminous binders. J Eng Mech, 2017, 143: D4016002

    Google Scholar 

  24. Fukunaga M, Shimizu N. Fractional derivative constitutive models for finite deformation of viscoelastic materials. J Comput Nonlinear Dyn, 2015, 10: 061002

    Article  Google Scholar 

  25. Celauro C, Fecarotti C, Pirrotta A, et al. Experimental validation of a fractional model for creep/recovery testing of asphalt mixtures. Construction Building Mater, 2012, 36: 458–466

    Article  Google Scholar 

  26. Samko S. Fractional integration and differentiation of variable order: an overview. Nonlinear Dyn, 2013, 71: 653–662

    Article  MathSciNet  MATH  Google Scholar 

  27. Wu F, Liu J F, Wang J. An improved Maxwell creep model for rock based on variable-order fractional derivatives. Environ Earth Sci, 2015, 73: 6965–6971

    Article  Google Scholar 

  28. Tang H, Wang D, Huang R, et al. A new rock creep model based on variable-order fractional derivatives and continuum damage mechanics. Bull Eng Geol Environ, 2018, 77: 375–383

    Article  Google Scholar 

  29. Gao Y, Yin D. A full-stage creep model for rocks based on the variable-order fractional calculus. Appl Math Model, 2021, 95: 435–446

    Article  MathSciNet  MATH  Google Scholar 

  30. Wang X, Zhou G, Liu H, et al. Key points of RIOHTRACK testing road design and construction. J Highway Transp Res Dev (Engl Ed), 2020, 14: 1–16

    Article  Google Scholar 

  31. Wu J, Wang X, Wang L, et al. Temperature correction and analysis of pavement skid resistance performance based on RIOHTrack full-scale Track. Coatings, 2020, 10: 832

    Article  Google Scholar 

  32. Podlubny I, Chechkin A, Skovranek T, et al. Matrix approach to discrete fractional calculus II: partial fractional differential equations. J Comput Phys, 2009, 228: 3137–3153

    Article  MathSciNet  MATH  Google Scholar 

  33. Caputo M. Linear models of dissipation whose Q is almost frequency independent–II. Geophys J Int, 1967, 13: 529–539

    Article  Google Scholar 

  34. Diethelm K. The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Operators of Caputo Type. Berlin: Springer, 2004. 55–58

    Google Scholar 

  35. Podlubny I. Fractional Differential Equations: An Introduction to Fractional Derivatives. San Diego: Academic Press, 1998. 20–150

    Google Scholar 

  36. Ministry of Transport of China. Field Test Methods of Subgrade and Pavement for Highway Engineering (JTG E60–2008). Beijing: China Communications Press, 2008

    Google Scholar 

  37. Wang X, Zhou X, Xiao Q, et al. Review of researches of RIOHTrack in 2017 (in Chinese). J Highway Trans Res Dev, 2018, 35: 1–13

    Google Scholar 

  38. Li S, Fan M, Xu L, et al. Rutting performance of semi-rigid base pavement in RIOHTrack and laboratory evaluation. Front Mater, 2021, 7: 590604

    Article  Google Scholar 

  39. ARA Inc. ERES Consultants Division. Guide for Mechanistic-Empirical Design of New and Rehabilitated Pavement Structures. NCHRP Project 1–37A Final Report, 2004

Download references

Acknowledgements

This work was supported in part by National Key Research & Development Project of China (Grant No. 2020YFA0714301) and National Natural Science Foundation of China (Grant No. 61833005).

Author information

Authors and Affiliations

  1. School of Mathematics, Southeast University, Nanjing, 210096, China

    Yu Wang, Jiaojiao Yan & Jinde Cao

  2. Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, Southeast University, Nanjing, 210096, China

    Yu Wang, Jiaojiao Yan & Jinde Cao

  3. Intelligent Transportation System Research Center, Southeast University, Nanjing, 210096, China

    Wei Huang

  4. Systems Research Institute of the Polish Academy of Sciences, Warsaw, 01-447, Poland

    Leszek Rutkowski

  5. Institute of Computer Science, AGH University of Science and Technology, Krakow, 30-059, Poland

    Leszek Rutkowski

  6. Information Technology Institute, University of Social Sciences, Lodz, 90-113, Poland

    Leszek Rutkowski

  7. Yonsei Frontier Lab, Yonsei University, Seoul, 03722, Republic of Korea

    Jinde Cao

Authors
  1. Yu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiaojiao Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wei Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Leszek Rutkowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jinde Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jinde Cao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Y., Yan, J., Huang, W. et al. Variable-order fractional derivative rutting depth prediction of asphalt pavement based on the RIOHTrack full-scale track. Sci. China Inf. Sci. 66, 152205 (2023). https://doi.org/10.1007/s11432-022-3647-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11432-022-3647-7

Keywords

Search

Navigation