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

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. 1.

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

  2. 2.

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

  3. 3.

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

  4. 4.

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

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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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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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Keywords

  • DEM
  • DIC
  • Asphalt
  • Fracture
  • DC(T)
  • Optimization