Experimental Mechanics

, Volume 57, Issue 4, pp 637–648 | Cite as

Inverse Estimation of Cohesive Fracture Properties of Asphalt Mixtures Using an Optimization Approach

  • B. C. Hill
  • O. Giraldo-Londoño
  • G. H. Paulino
  • W. G. ButtlarEmail author


Tensile cracking in asphalt pavements due to vehicular and thermal loads has become an experimental and numerical research focus in the asphalt materials community. Previous studies have used the discrete element method (DEM) to study asphalt concrete fracture. These studies used trial-and-error to obtain local fracture properties such that the DEM models approximate the experimental load-crack mouth opening displacement response. In the current study, we identify the cohesive fracture properties of asphalt mixtures via a nonlinear optimization method. The method encompasses a comparative investigation of displacement fields obtained using both digital image correlation (DIC) and heterogeneous DEM fracture simulations. The proposed method is applied to two standard fracture test geometries: the single-edge notched beam test, SE(B), under three-point bending, and the disk-shaped compact tension test, DC(T). For each test, the Subset Splitting DIC algorithm is used to determine the displacement field in a predefined region near the notch tip. Then, a given number of DEM simulations are performed on the same specimen. The DEM is used to simulate the fracture of asphalt concrete with a linear softening cohesive contact model, where fracture-related properties (e.g., maximum tensile force and maximum crack opening) are varied within a predefined range. The difference between DIC and DEM displacement fields for each set of fracture parameters is then computed and converted to a continuous function via multivariate Lagrange interpolation. Finally, we use a Newton-like optimization technique to minimize Lagrange multinomials, yielding a set of fracture parameters that minimizes the difference between the DEM and DIC displacement fields. The optimized set of fracture parameters from this nonlinear optimization procedure led to DEM results which are consistent with the experimental results for both SE(B) and DC(T) geometries.


DEM DIC Asphalt Fracture DC(T) Optimization 



This material is based upon work supported by the National Science Foundation under Grant No. 1031218. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.


  1. 1.
    Islam S, Buttlar WG (2012) Effect of pavement roughness on user costs. Journal of the Transportation Research Record 2285:47–55CrossRefGoogle Scholar
  2. 2.
    Wagoner MP, Buttlar WG, Paulino GP (2005) Development of a single-edge notched beam test for asphalt concrete mixtures. J Testing and Evaluation 33(6):1–9Google Scholar
  3. 3.
    Wagoner MP (2006) Fracture tests for bituminous-aggregate mixtures: laboratory and field investigations. University of Illinois at Urbana-Champaign, PhD DissertationGoogle Scholar
  4. 4.
    Kim H (2007) Investigation of toughening mechanisms in the fracture of asphalt concrete using the clustered discrete element method. Ph.D. Dissertation, University of Illinois at Urbana-ChampaignGoogle Scholar
  5. 5.
    D'Addetta GA (2004) Discrete models for cohesive frictional materials. Rep. No. 42, Institute of Structural Mechanics, Univ. of Stuttgart, Stuttgart, GermanyGoogle Scholar
  6. 6.
    Kim H, Wagoner MP, Buttlar WG (2009) Micromechanical fracture modeling of asphalt concrete using a single-edge notched beam test. Mater Struct 42(5):677–689CrossRefGoogle Scholar
  7. 7.
    Kim H, Wagoner MP, Buttlar WG (2009) Numerical fracture analysis on the specimen size dependency of asphalt concrete using a cohesive softening model. Constr Build Mater 23:2112–2120CrossRefGoogle Scholar
  8. 8.
    Kim H, Wagoner MP, Buttlar WG (2008) Simulation of fracture behavior in asphalt concrete using a heterogeneous cohesive zone discrete element model. J Mater Civ Eng 20:552–563CrossRefGoogle Scholar
  9. 9.
    Kim H, Buttlar WG (2005) Micromechanical fracture modeling of asphalt mixture using the discrete element method. Proc., GeoFrontier 2005, ASCE, Reston, VaGoogle Scholar
  10. 10.
    Aragão FTS, Kim Y (2012) Mode I fracture characterization of bituminous paving mixtures at intermediate service temperatures. Exp Mech 52(9):1423–1434CrossRefGoogle Scholar
  11. 11.
    Kim Y, Aragão FTS (2013) Microstructure modeling of rate-dependent fracture behavior in bituminous paving mixtures. Finite Elem Analysis Des 63:23–32Google Scholar
  12. 12.
    Im S, Ban H, Kim Y (2014) Characterization of mode-I and mode-II fracture properties of fine aggregate matrix using a semicircular specimen geometry. Constr Build Mater 52:413–421CrossRefGoogle Scholar
  13. 13.
    Pop O, Meite M, Dubois F, Absi J (2011) Identification algorithm for fracture parameters by combining DIC and FEM approaches. Int J Fract 170:101–114CrossRefzbMATHGoogle Scholar
  14. 14.
    Shen B, Paulino GH (2011) Direct extraction of cohesive fracture properties from digital image correlation: a hybrid inverse technique. Exp Mech 51:143–163CrossRefGoogle Scholar
  15. 15.
    Shen B, Paulino GH (2011) Identification of cohesive zone model and elastic parameters of fiber-reinforced cementitious composites using digital image correlation and a hybrid inverse technique. Cement Concr Compos 33:572–585CrossRefGoogle Scholar
  16. 16.
    Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Journal of Geotechnique 29:47–65CrossRefGoogle Scholar
  17. 17.
    AASHTO M323 (2004) Standard specification for superpave volumetric mix design. AASHTO Standard Specifications for Transportation Materials and Methods of Sampling and Testing. Washington, D.C.Google Scholar
  18. 18.
    ASTM D7313-13 (2013) Standard test method for determining fracture energy of asphalt-aggregate mixtures using the disk-shaped compact tension geometry. American Society for Testing and Materials International. West Conshohocken, PAGoogle Scholar
  19. 19.
    AASHTO T322 (2007) Standard method of test for determining the creep compliance and strength of hot-nix asphalt (HMA) using the indirect tensile test device. AASHTO Standard Specifications for Transportation Materials and Methods of Sampling and Testing. Washington, D.C.Google Scholar
  20. 20.
    Park S, Kim Y (1999) Interconversion between relaxation modulus and creep compliance for viscoelastic solids. J Mater Civ Eng 11(1):76–82Google Scholar
  21. 21.
    Swaminathan B, Lambros J, Sehitoglu H (2013) Digital image correlation study of mechanical response of nickel superalloy Hastelloy X under thermal and mechanical cycling: Uniaxial and biaxial stress states. J Strain Analysis Special Issue 49(4):233–243Google Scholar
  22. 22.
    Abanto-Bueno J, Lambros J (2002) Investigation of crack growth in functionally graded materials using digital image correlation. J Engineering Fracture Mechanics 69:1695–1711Google Scholar
  23. 23.
    Meite M, Dubois F, Pop O, Absi J (2013) Mixed mode fracture properties characterization for wood by digital images correlation and finite element method coupling. Journal of Engineering Fracture Mechanics 105:86–100Google Scholar
  24. 24.
    Carroll JD, Abuzaid W, Lambros J, Sehitoglu H (2013) High resolution digital image correlation measurements of strain accumulation in fatigue crack growth. Int J Fatigue 57:140–150Google Scholar
  25. 25.
    Poissant J, Barthelat F (2010) A novel subset splitting procedure for digital image correlation on discontinuous displacement fields. Exp Mech 50(3):353–364Google Scholar
  26. 26.
    Hill B, Buttlar WG (2016) Evaluation of polymer modification in asphalt mixtures through digital image correlation and performance space diagrams. J Construction and Building Materials 122:667–673Google Scholar
  27. 27.
    You Z, Buttlar WG (2004) Discrete element modeling to predict the modulus of asphalt concrete mixtures. J Mater Civil Eng ASCE 16(2):140–146Google Scholar
  28. 28.
    Labuz JF, Cattaneo S, Chen L-H (2001) Acoustic emission at failure in quasi-brittle materials. Constr Build Mater 15:225–233Google Scholar
  29. 29.
    Li X, Marasteanu MO (2006) Investigation of low temperature cracking in asphalt mixtures by acoustic emission. Road Materials and Pavement Design 7(4):491–512Google Scholar
  30. 30.
    Li X, Marasteanu M, Iverson N, Labuz JF (2006) Observation of crack propagation in asphalt mixtures with acoustic emission. Transp Res Rec 1970:171–177Google Scholar
  31. 31.
    Hakimzadeh S (2015) Evaluation of bond between pavement layers: fracture mechanics approach. Ph.D. Dissertation, University of Illinois at Urbana-ChampaignGoogle Scholar
  32. 32.
    McDonald DB, Grantham WJ, Tabor WL, Murphy MJ (2007) Global and local optimization using radial basis function response surface models. Appl Math Model 31:2095–2110Google Scholar

Copyright information

© Society for Experimental Mechanics 2017

Authors and Affiliations

  • B. C. Hill
    • 1
  • O. Giraldo-Londoño
    • 2
  • G. H. Paulino
    • 2
  • W. G. Buttlar
    • 3
    Email author
  1. 1.Department of Civil and Environmental EngineeringUniversity of IllinoisUrbanaUSA
  2. 2.School of Civil and Environmental EngineeringGeorgia Institute of TechnologyAtlantaUSA
  3. 3.Department of Civil and Environmental EngineeringUniversity of MissouriColumbiaUSA

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