Modelling cracking damage of asphalt mixtures under compressive monotonic and repeated loads using pseudo J-integral Paris’ law

Yuqing Zhang*, Fan Gu, Bjorn Birgisson, Robert L. Lytton

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Field observations and mechanical analyses have shown that cracks accompany rutting in asphalt mixtures under external compressive loads. This study aims to model crack growth in asphalt mixtures under compressive monotonic and repeated loads. Using energy equilibrium and viscoelastic Griffith fracture criterion, a damage density characterising the cracks in mixtures is derived as a function of stress, nonlinear viscofracture strain, asphalt film thickness and bond energy. Crack evolution is modelled by pseudo J-integral Paris’ law. Six types of asphalt mixture were tested by monotonic compressive strength tests at 40°C. Two were further tested at four more temperatures and four more loading rates, respectively. Repeated load test results for the same mixtures were obtained from previous studies. The different shape of the damage density curve (S-shape for monotonic load and increasing exponential shape for repeated load) demonstrates the dependence of damage growth on loading mode, due to different energy release rates. Pseudo J-integral Paris’ law can model the crack growth in mixtures and capture the post-peak softening behaviour under a monotonic load. The Paris’ law coefficients (A and n) are independent of loading mode (monotonic or repeated), rate or temperature. They are fundamental material properties and can be used to predict crack growth under varying loading and temperature conditions.

Original languageEnglish
Pages (from-to)525-535
Number of pages11
JournalRoad Materials and Pavement Design
Issue number3
Early online date27 Dec 2017
Publication statusPublished - 1 Apr 2018

Bibliographical note

© 2017 Informa UK Limited, publishing as Taylor & Francis. This is an Accepted Manuscript of an article published by Taylor & Francis in Road Materials and Pavement Design on 27th December 2017, available online:


  • asphalt mixture
  • crack growth
  • damage density
  • Paris’ law
  • pseudo J-integral


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