Temporal Homogenization Modeling of Viscoelastic Asphalt Concretes and Pavement Structures under Large Numbers of Load Cycles
Publication: Journal of Engineering Mechanics
Volume 150, Issue 11
Abstract
This paper aims to introduce a highly efficient computational model compared to the current cycle-by-cycle simulation strategy to compute the viscoelastic responses of asphalt concretes and pavement structures under large numbers of load cycles. An explicit constitutive relation for viscoelastic solids in multiple time scales was developed based on the temporal homogenization. The original initial-boundary value problem was divided into a global part in the slow time scale and a local part in the fast time scale. Two simulation studies were presented to validate the computational accuracy and efficiency of the proposed model: (1) a cylindrical asphalt concrete subject to a uniaxial cyclic compression load, and (2) a pavement structure subject to a locally cyclic loading. The laboratory test results and field measurements were compared with the modeled responses to validate the models before comparing with the reference solutions. Results indicate that the temporal homogenization-based viscoelastic model saves considerable computational cost and maintains a satisfactory accuracy. The absolute values of relative error of the modeled responses between the time homogenization and reference solutions are lower than 1% and 4% for the cylindrical asphalt concrete and pavement structure under locally cyclic loadings, respectively. Based on the proposed computational approach, only 4 min are needed to model the response of a cylindrical asphalt concrete subject to repeated load cycles under a uniaxial compression load. The computational time is reduced from 7 h of the reference solution to 38 min of the temporal homogenization solution to model load cycles of a viscoelastic pavement structure.
Practical Applications
This study introduces a highly efficient computational model to compute the viscoelastic responses of asphalt concretes and pavement structures under large numbers of load cycles. Multiple time scales were applied to an explicit constitutive relation of asphalt concretes to obtain the formula of global and local initial-boundary value problems. Its computational accuracy and efficiency were verified by comparing the temporal homogenization-based solutions with the testing results and reference solutions for a cylindrical sample and a pavement structure. It is the basis for the long-term pavement performance prediction after including the fatigue damage analysis in the present temporal homogenization framework. By successfully implementing a mechanistic framework for the long-term pavement performance prediction, the pavement design can more rely on the material inherent properties instead of using redundant empirical transfer functions. It is promising that the local calibrations of the current empirical performance transfer functions can be minimized as the proposed pavement long-term performance predictions depend on the material inherent properties and constitutive models.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request, including the following: axial strain of the uniaxial cyclic compression test on the cylindrical asphalt concrete, and transverse strain of the creep-recovery test on the field pavement section.
Acknowledgments
The authors would like to acknowledge the financial support of a Ph.D. studentship provided by the University of Nottingham, Nynas, and Colas. This work is also supported by the Asphalt Institute Foundation (AIF). This paper is supported by the Engineering and Physical Sciences Research Council (EPSRC) under Grant No. EP/W000369/1.
References
AASHTO. 2020. Mechanistic-empirical pavement design guide: A manual of practice. Washington, DC: AASHTO.
Abdelfattah, H. F. H., H. Baaj, and H. J. Kadhim. 2021. “Calibration of MEPDG permanent deformation models using Hamburg Wheel Rut Tester and field data.” Int. J. Pavement Eng. 23 (12): 4174–4189. https://doi.org/10.1080/10298436.2021.1937622.
Behnke, R., and M. Kaliske. 2018. “Square block foundation resting on an unbounded soil layer: Long-term prediction of vertical displacement using a time homogenization technique for dynamic loading.” Soil Dyn. Earthquake Eng. 115 (Jun): 448–471. https://doi.org/10.1016/j.soildyn.2018.07.045.
Behnke, R., I. Wollny, F. Hartung, and M. Kaliske. 2019. “Thermo-mechanical finite element prediction of the structural long-term response of asphalt pavements subjected to periodic traffic load: Tire-pavement interaction and rutting.” Comput. Struct. 218 (Jun): 9–31. https://doi.org/10.1016/j.compstruc.2019.04.003.
Bensoussan, A., J.-L. Lions, and G. Papanicolaou. 1978. Asymptotic analysis for periodic structures. Amsterdam, Netherlands: North-Holland Publishing Company.
Bhattacharyya, M., D. Dureisseix, and B. Faverjon. 2020. “A unified approach based on temporal homogenisation and cycle jump for thermo-mechanical combined cycle fatigue.” Int. J. Fatigue 131 (Feb): 105320. https://doi.org/10.1016/j.ijfatigue.2019.105320.
Chen, F., R. Balieu, and N. Kringos. 2017. “Thermodynamics-based finite strain viscoelastic-viscoplastic model coupled with damage for asphalt material.” Int. J. Solids Struct. 129 (Jun): 61–73. https://doi.org/10.1016/j.ijsolstr.2017.09.014.
Cognard, J.-Y., and P. Ladevèze. 1993. “A large time increment approach for cyclic viscoplasticity.” Int. J. Plast. 9 (2): 141–157. https://doi.org/10.1016/0749-6419(93)90026-M.
Cojocaru, D., and A. M. Karlsson. 2006. “A simple numerical method of cycle jumps for cyclically loaded structures.” Int. J. Fatigue 28 (12): 1677–1689. https://doi.org/10.1016/j.ijfatigue.2006.01.010.
Devulder, A., D. Aubry, and G. Puel. 2010. “Two-time scale fatigue modelling: Application to damage.” Comput. Mech. 45 (6): 637–646. https://doi.org/10.1007/s00466-010-0476-2.
Eslaminia, M., and M. N. Guddati. 2016. “Fourier-finite element analysis of pavements under moving vehicular loading.” Int. J. Pavement Eng. 17 (7): 602–614. https://doi.org/10.1080/10298436.2015.1007237.
Eslaminia, M., S. Thirunavukkarasu, M. N. Guddati, and Y. R. Kim. 2012. Accelerated pavement performance modeling using layered viscoelastic analysis, 497–506. Dordrecht, Netherlands: Springer. https://doi.org/10.1007/978-94-007-4566-7_48.
Guennouni, T. 1988. “Sur une méthode de calcul de structuressoumises à des chargements cycliques: L’homogénéisation en temps.” ESAIM Math. Model. Numer. Anal. 22 (3): 417–455. https://doi.org/10.1051/m2an/1988220304171.
Haouala, S., and I. Doghri. 2015. “Modeling and algorithms for two-scale time homogenization of viscoelastic-viscoplastic solids under large numbers of cycles.” Int. J. Plast. 70 (Mar): 98–125. https://doi.org/10.1016/j.ijplas.2015.03.005.
Kim, R. 2009. Modeling of asphalt concrete. Edited by Y. Richard Kim. New York: McGraw-Hill.
Kim, S., H. Ceylan, and K. Gopalakrishnan. 2007. “Effect of M-E design guide inputs on flexible pavement performance predictions.” Road Mater. Pavement Des. 8 (3): 375–397. https://doi.org/10.1080/14680629.2007.9690080.
Lee, W., and H. Shin. 2023. “Temporal homogenization formula for viscoelastic–viscoplastic model subjected to local cyclic loading.” Int. J. Numer. Methods Eng. 124 (4): 808–833. https://doi.org/10.1002/nme.7143.
Lemaitre, J., and R. Desmorat. 2005. Engineering damage mechanics: Ductile, creep, fatigue and brittle failures. New York: Springer.
Li, H., and X. Huang. 2004. “Axle load conversion formula based on deflection equivalent for semi-rigid base asphalt pavement under heavy-load.” J. Highway Transp. Res. Dev. 21 (7): 5–8.
Luo, X., H. Wang, S. Cao, J. Ling, S. Yang, and Y. Zhang. 2023. “A hybrid approach for fatigue life prediction of in-service asphalt pavement.” Philos. Trans. R. Soc. A 381 (2254): 20220174. https://doi.org/10.1098/rsta.2022.0174.
Lytton, R. L., J. Uzan, E. G. Fernando, R. Roque, D. Hiltunen, and S. M. Stoffels. 1993. Development and validation of performance prediction models and specifications for asphalt binders and paving mixes. Washington, DC: Strategic Highway Research Program.
Shen, K., H. Wang, H. Zhang, J. Tong, and X. Chen. 2022. “SAPAVE: An improved semi-analytical FE program for dynamic viscoelastic analysis of asphalt pavement.” Int. J. Pavement Eng. 23 (9): 3024–3035. https://doi.org/10.1080/10298436.2021.1878516.
Shin, H. 2020. “Temporal homogenization formulation on general linear viscoelastic materials subjected to locally periodic loading.” Int. J. Solids Struct. 196 (Jul): 1–9. https://doi.org/10.1016/j.ijsolstr.2020.03.026.
Tarefder, R., and J. I. Rodriguez-Ruiz. 2013. “Local calibration of MEPDG for flexible pavements in New Mexico.” J. Transp. Eng. 139 (10): 981–991. https://doi.org/10.1061/(ASCE)TE.1943-5436.0000576.
Yu, Q., and J. Fish. 2002a. “Multiscale asymptotic homogenization for multiphysics problems with multiple spatial and temporal scales: A coupled thermo-viscoelastic example problem.” Int. J. Solids Struct. 39 (26): 6429–6452. https://doi.org/10.1016/S0020-7683(02)00255-X.
Yu, Q., and J. Fish. 2002b. “Temporal homogenization of viscoelastic and viscoplastic solids subjected to locally periodic loading.” Comput. Mech. 29 (3): 199–211. https://doi.org/10.1007/s00466-002-0334-y.
Zhang, H., and Y. Zhang. 2023. “A time-temperature-ageing shift model for bitumen and asphalt mixtures based on free volume theory.” Int. J. Pavement Eng. 24 (1): 2138882. https://doi.org/10.1080/10298436.2022.2138882.
Zhang, Y., B. Birgisson, and R. L. Lytton. 2015. “Weak form equation-based finite-element modeling of viscoelastic asphalt mixtures.” J. Mater. Civ. Eng. 28 (2): 04015115. https://doi.org/10.1061/(ASCE)MT.1943-5533.0001395.
Information & Authors
Information
Published In
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Nov 14, 2023
Accepted: Jun 20, 2024
Published online: Aug 29, 2024
Published in print: Nov 1, 2024
Discussion open until: Jan 29, 2025
ASCE Technical Topics:
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.