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

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A Correction to this article was published on 01 June 2018

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Abstract

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.

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Change history

  • 01 June 2018

    The following correction should be noted: On page 642, in the seventh line of the third paragraph, the phrase “the Poisson’s Ratio is taken as v = 0.33” should be replaced with “the Poisson’s Ratio is taken as v = 0.25 for the asphalt mastic group and v = 0.16 for the aggregate group”.

  • 01 June 2018

    The following correction should be noted: On page 642, in the seventh line of the third paragraph, the phrase ?the Poisson?s Ratio is taken as v = 0.33? should be replaced with ?the Poisson?s Ratio is taken as v = 0.25 for the asphalt mastic group and v = 0.16 for the aggregate group?.

  • 01 June 2018

    The following correction should be noted: On page 642, in the seventh line of the third paragraph, the phrase ?the Poisson?s Ratio is taken as v = 0.33? should be replaced with ?the Poisson?s Ratio is taken as v = 0.25 for the asphalt mastic group and v = 0.16 for the aggregate group?.

  • 01 June 2018

    The following correction should be noted: On page 642, in the seventh line of the third paragraph, the phrase ?the Poisson?s Ratio is taken as v = 0.33? should be replaced with ?the Poisson?s Ratio is taken as v = 0.25 for the asphalt mastic group and v = 0.16 for the aggregate group?.

  • 01 June 2018

    The following correction should be noted: On page 642, in the seventh line of the third paragraph, the phrase ���the Poisson���s Ratio is taken as v = 0.33��� should be replaced with ���the Poisson���s Ratio is taken as v = 0.25 for the asphalt mastic group and v = 0.16 for the aggregate group���.

Notes

  1. Future research could explore 3D DEM simulations using DIC measurements.

  2. Future research could focus on aggregate fracture property identification using fracture tests in conjunction with DIC measurements.

  3. Additional future research could investigate the optimization of mixed-mode fracture properties.

  4. This is questionable, however, in the absence of experimental information, this assumption was used.

References

  1. Islam S, Buttlar WG (2012) Effect of pavement roughness on user costs. Journal of the Transportation Research Record 2285:47–55

    Article  Google Scholar 

  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):1–9

    Google Scholar 

  3. Wagoner MP (2006) Fracture tests for bituminous-aggregate mixtures: laboratory and field investigations. University of Illinois at Urbana-Champaign, PhD Dissertation

    Google Scholar 

  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-Champaign

  5. D'Addetta GA (2004) Discrete models for cohesive frictional materials. Rep. No. 42, Institute of Structural Mechanics, Univ. of Stuttgart, Stuttgart, Germany

  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):677–689

    Article  Google Scholar 

  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 23:2112–2120

    Article  Google Scholar 

  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 20:552–563

    Article  Google Scholar 

  9. Kim H, Buttlar WG (2005) Micromechanical fracture modeling of asphalt mixture using the discrete element method. Proc., GeoFrontier 2005, ASCE, Reston, Va

  10. Aragão FTS, Kim Y (2012) Mode I fracture characterization of bituminous paving mixtures at intermediate service temperatures. Exp Mech 52(9):1423–1434

    Article  Google Scholar 

  11. Kim Y, Aragão FTS (2013) Microstructure modeling of rate-dependent fracture behavior in bituminous paving mixtures. Finite Elem Analysis Des 63:23–32

  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 52:413–421

    Article  Google Scholar 

  13. Pop O, Meite M, Dubois F, Absi J (2011) Identification algorithm for fracture parameters by combining DIC and FEM approaches. Int J Fract 170:101–114

    Article  MATH  Google Scholar 

  14. Shen B, Paulino GH (2011) Direct extraction of cohesive fracture properties from digital image correlation: a hybrid inverse technique. Exp Mech 51:143–163

    Article  Google Scholar 

  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 33:572–585

    Article  Google Scholar 

  16. Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Journal of Geotechnique 29:47–65

    Article  Google Scholar 

  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.

  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, PA

  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.

  20. Park S, Kim Y (1999) Interconversion between relaxation modulus and creep compliance for viscoelastic solids. J Mater Civ Eng 11(1):76–82

  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):233–243

  22. Abanto-Bueno J, Lambros J (2002) Investigation of crack growth in functionally graded materials using digital image correlation. J Engineering Fracture Mechanics 69:1695–1711

  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 105:86–100

  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 57:140–150

  25. Poissant J, Barthelat F (2010) A novel subset splitting procedure for digital image correlation on discontinuous displacement fields. Exp Mech 50(3):353–364

  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 122:667–673

  27. You Z, Buttlar WG (2004) Discrete element modeling to predict the modulus of asphalt concrete mixtures. J Mater Civil Eng ASCE 16(2):140–146

  28. Labuz JF, Cattaneo S, Chen L-H (2001) Acoustic emission at failure in quasi-brittle materials. Constr Build Mater 15:225–233

  29. Li X, Marasteanu MO (2006) Investigation of low temperature cracking in asphalt mixtures by acoustic emission. Road Materials and Pavement Design 7(4):491–512

  30. Li X, Marasteanu M, Iverson N, Labuz JF (2006) Observation of crack propagation in asphalt mixtures with acoustic emission. Transp Res Rec 1970:171–177

  31. Hakimzadeh S (2015) Evaluation of bond between pavement layers: fracture mechanics approach. Ph.D. Dissertation, University of Illinois at Urbana-Champaign

  32. McDonald DB, Grantham WJ, Tabor WL, Murphy MJ (2007) Global and local optimization using radial basis function response surface models. Appl Math Model 31:2095–2110

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Acknowledgements

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.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Illinois, Urbana, IL, 61801, USA

    B. C. Hill

  2. School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    O. Giraldo-Londoño & G. H. Paulino

  3. Department of Civil and Environmental Engineering, University of Missouri, Columbia, MO, 65211, USA

    W. G. Buttlar

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  1. B. C. Hill
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  2. O. Giraldo-Londoño
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  3. G. H. Paulino
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  4. W. G. Buttlar
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Correspondence to W. G. Buttlar.

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Hill, B.C., Giraldo-Londoño, O., Paulino, G.H. et al. Inverse Estimation of Cohesive Fracture Properties of Asphalt Mixtures Using an Optimization Approach. Exp Mech 57, 637–648 (2017). https://doi.org/10.1007/s11340-017-0257-3

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  • DOI: https://doi.org/10.1007/s11340-017-0257-3

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