Mechanics of Time-Dependent Materials

, Volume 18, Issue 1, pp 197–215 | Cite as

Using the poker-chip test for determining the bulk modulus of asphalt binders

  • Arash Motamed
  • Amit Bhasin
  • Kenneth M. Liechti


The properties of asphalt binders strongly influence the overall mechanical response of asphalt mixture composites. A thorough understanding of the mechanistic behavior of asphalt binders is important in order to fully and accurately characterize the behavior of the asphalt mixture. The mechanical properties of the asphalt binder, the matrix in the asphalt mixture composite, are time and temperature dependent and have a lower stiffness compared to the inclusions (aggregate particles). However, computational methods used to model the micromechanics of asphalt mixtures typically assume a constant bulk modulus or Poisson’s ratio for asphalt binders. This research investigates the time-dependence of the bulk modulus of asphalt binders. Several approaches for measuring the bulk modulus were explored and the poker-chip geometry was found to be the most suitable one. The boundary value problem for the poker-chip geometry was solved to determine the bulk modulus and Poisson’s ratio of asphalt binders as a function of time. The findings from this research improve our understanding of the viscoelastic behavior of asphaltic materials, and also guide important assumptions that are typically made during computational modeling of asphaltic materials.


Asphalt binder Bulk modulus Poisson’s ratio Laboratory measurement Poker-chip geometry Dynamic Shear Rheometer (DSR) Viscoelastic Pavement 



The authors would like to acknowledge the Federal Highway Administration FHWA and Asphalt Research Consortium for supporting this study.


  1. Al-Khateeb, G., Shenoy, A., Gibson, N., Harman, T.: A new simplistic model for dynamic modulus predictions of asphalt paving mixtures. Proc. Assoc. Asph. Paving Technol., Tech. Sess. 75, 1254–1293 (2006) Google Scholar
  2. Anderson, D.A., Christensen, D.W., Bahia, H.U., Dongre, R., Sharma, M.G., Antle, C.E., Button, J.: Binder Characterization and Evaluation. Physical Characterization, vol. 3. Reported to Strategic Highway Research Program. Report No.: SHRP-A-369 (1994) Google Scholar
  3. Arzoumanidis, G.A., Liechti, K.M.: Linear viscoelastic property measurement and its significance to some nonlinear viscoelasticity models. Mech. Time-Depend. Mater. 7, 209–250 (2003) CrossRefGoogle Scholar
  4. Bahia, H.U.: Low-temperature isothermal physical hardening of asphalt cement. Ph.D. Dissertation, The Pennsylvania State University (1991) Google Scholar
  5. Carreau, P.J., De Kee, D.C.R., Chhabra, R.P.: Rheology of Polymeric Systems—Principles and Applications. Hanser/Gardner, Cincinnati (1997) Google Scholar
  6. Delgadillo, R.: Nonlinearity of Asphalt Binder and the Relationship with Asphalt Mixture Permanent Deformation. Ph.D. Thesis, University of Wisconsin at Madison (2008) Google Scholar
  7. Di Benedetto, H., Olard, F., Sauzeat, C., Delaporte, B.: Linearly viscoelastic behavior of bituminous materials: from binders to mixes. Road Mater, Pavement Des. 5, 163–202 (2004) CrossRefGoogle Scholar
  8. Di Benedetto, H., Delaporte, B., Sauzéat, C.: Three-dimensional linear behavior of bituminous materials: experiments and modeling. Int. J. Geomech. 7(2), 149–157 (2007) CrossRefGoogle Scholar
  9. Ferry, J.D.: Viscoelastic Properties of Polymers. Wiley, New York (1980) Google Scholar
  10. Gent, A.N., Lindley, P.B.: The compression of bonded rubber blocks. Proc. Inst. Mech. Eng. 173(1), 111–122 (1959) CrossRefGoogle Scholar
  11. Hiel, C.C., Cardon, A.H., Brinson, H.F.: Viscoelastic modeling of epoxy-resins for adhesive and composite applications. In: Proceeding of the 5th International Conference on Experimental Mechanics, Montreal, pp. 263–267 (1984) Google Scholar
  12. Huang, C.: Development and Numerical Implementation of Nonlinear Viscoelastic–Viscoplastic Model for Asphalt Materials. Ph.D. Thesis, Texas A&M University (2008) Google Scholar
  13. Johnson, C.M.: Estimating asphalt binder fatigue resistance using an accelerated test method. Ph.D. Thesis, University of Wisconsin at Madison (2010) Google Scholar
  14. Karki, P.: Computational and experimental characterization of bituminous composites based on experimentally determined properties of constituents. Ph.D. Thesis, University of Nebraska at Lincoln (2010) Google Scholar
  15. Kim, Y., Lutif, J.S.: Computational micromechanics modeling for damage-induced behavior of asphalt mixtures considering viscoelasticity and cohesive zone fracture. In: Special Publication of ASCE Geo-Institute, Symposium on Pavement Mechanics and Materials at the Inaugural International Conference of the Engineering Mechanics Institute, Minneapolis, Minnesota, May 18–21, pp. 17–25 (2008) Google Scholar
  16. Kim, M.: Development of differential scheme micromechanics modeling framework for predictions of Hot-Mix Asphalt (HMA) complex modulus and experimental validations. Ph.D. Thesis, University of Illinois at Urbana-Champaign (2009) Google Scholar
  17. Kim, J., Lee, H., Kim, N.: Determination of shear and bulk moduli of viscoelastic solids from the indirect tension creep test. J. Eng. Mech. 136(9), 1067–1075 (2010) CrossRefGoogle Scholar
  18. Lakes, R.S.: Viscoelastic Materials. Cambridge University Press, Cambridge (2009) CrossRefGoogle Scholar
  19. Lee, M.A.: Resilient modulus and dynamic Poisson’s ratio of asphaltic concrete mixes. Master Degree Thesis, McMaster University (1976) Google Scholar
  20. Lindley, P.B.: Compression moduli for blocks of soft elastic material bonded to rigid end plates. J. Strain Anal. Eng. Des. 14(1), 11–16 (1979) CrossRefGoogle Scholar
  21. Long, F.M.: Permanent deformation of asphalt concrete pavements: a nonlinear viscoelastic approach to mix analyses and design. Ph.D. Thesis, University of California at Berkeley (2001) Google Scholar
  22. Luo, R., Lytton, R.L.: Self-consistent micromechanics models of an asphalt mixture. J. Mater. Civ. Eng. 23(1), 49–55 (2011) CrossRefGoogle Scholar
  23. Ma, Z., Ravi-Chandar, K.: Confined compression: a stable homogeneous deformation for constitutive characterization. Exp. Mech. 40, 38–45 (2000) CrossRefGoogle Scholar
  24. Macosko, C.W.: Rheology Principle, Measurements, and Applications. Wiley, New York (1995) Google Scholar
  25. Maher, A., Bennert, T.: Evaluation of Poisson’s ratio for use in the mechanistic empirical pavement design guide (MEPDG). Reported to FHWA, Report No.: FHWA-NJ-2008-004, (2008) Google Scholar
  26. Maillard, S., de La Roche, C., Hammoum, F., Such, C., Piau, J.M.: Bitumen healing investigation using a specific fracture test. Road Mater, Pavement Des. 5(1), 45–63 (2004) CrossRefGoogle Scholar
  27. Masuoka, M., Nakao, K.: Effect of aspect ratio on tensile bond strength for butt joint of internal fracture: theoretical and experimental analysis. In: Adhesion Measurement of Thin Films, Thick Films and Bulk Coatings, ASTM, pp. 342–359 (1978) CrossRefGoogle Scholar
  28. Motamed, A., Bahia, H.U.: Influence of test geometry, temperature, stress level, and loading duration on binder properties measured using DSR. J. Mater. Civ. Eng. 23(10), 1422–1432 (2011) CrossRefGoogle Scholar
  29. Motamed, A., Bhasin, A., Liechti, K.M.: Interaction nonlinearity in asphalt binders. Mech. Time-Depend. Mater. 16(2), 145–167 (2012) CrossRefGoogle Scholar
  30. Motamed, A., Bhasin, A., Liechti, K.M.: Constitutive modeling of the nonlinear viscoelastic response in asphalt binders; incorporating three-dimensional effects. Mech. Time-Depend. Mater. 17(1), 83–109 (2013) CrossRefGoogle Scholar
  31. Park, S.: Durability of adhesive joints between concrete and FRP reinforcement in aggressive environments. Ph.D. Thesis, The University of Texas at Austin (2004) Google Scholar
  32. Park, S.J., Liechti, K.M., Roy, S.: Simplified bulk experiments and hygrothermal nonlinearly viscoelasticity. Mech. Time-Depend. Mater. 8, 303–344 (2004) CrossRefGoogle Scholar
  33. Qvale, D., Ravi-Chandar, K.: Viscoelastic characterization of polymers under multiaxial compression. Mech. Time-Depend. Mater. 8, 193–214 (2004) CrossRefGoogle Scholar
  34. Read, J.M.: An assessment of Poisson’s ratio for bituminous materials. In: Institute of Asphalt Technology Yearbook, pp. 37–41 (2000) Google Scholar
  35. Read, J., Whiteoak, D.: The Shell Bitumen Handbook. Shell U.K. Limited, London (2003) Google Scholar
  36. Shariff, M.H.B.M.: An approximate analysis of infinitesimal deformations of bonded elastic mounts. J. Strain Anal. Eng. Des. 23(3), 115–120 (1988) CrossRefGoogle Scholar
  37. Stroup-Gardiner, M., Newcomb, D.E., Drescher, A., Zhang, W.: Influence of test method variables on Mn/Road hot mix asphalt mixture test results. Reported to U.S. Army Corps of Engineer. Report No.: MN/RC—P2000-03, (1997) Google Scholar
  38. You, Z., Adhikari, S., Dai, Q.: In: Two Dimensional and Three Dimensional Discrete Element Models for HMA. The Special Publication of ASCE Geo-Institute, Blacksburg, Virginia, June 3–6, pp. 117–126 (2007) Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Arash Motamed
    • 1
  • Amit Bhasin
    • 1
  • Kenneth M. Liechti
    • 2
  1. 1.Dept. of Civil, Architectural and Environmental EngineeringUniversity of Texas at AustinAustinUSA
  2. 2.Dept. of Aerospace Engineering and Engineering MechanicsUniversity of Texas at AustinAustinUSA

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