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Applications of Discrete Element Method   313


                      Problem                               Contact    Micro Parameter
         Author/Year  Studied        Platform  2D/3D  Shape Model      Calibration
         Abas et al./   Prediction  PFC2D     2D     Yes    Burger’s   Assumed values
         2007         mixture dynamic                       model
                      modulus with
                      neat binder and
                      modified binder
         Collop et    Simulation of   PFC3D   3D     No     Burger’s   Literature data/
         al./2006     triaxial and                          model, thin   no experimentally
                      uniaxial testing                      film effects  calibrated
                                                            considered  data for micro
                                                                       parameters, film
                                                                       thickness model
         Per Uliditlize   Failure, the   DEM  2D     Yes    Non-linear   NA
         /2001        strength and                          contact,
                      fatigue                               strength
         Chang,       Stress-strain  True Ball  3D   No     Viscoelastic  NA
         Meegod/1994 relationship
                      including
                      softening
         You and      Mixture modulus  PFC2D  2D     Yes    Linear     Measured mastic
         Buttlar/2004  prediction                                      modulus
         Dai and      Prediction of   PFC2D   2D     Yes    Linear     Measured
         You/2008     creep stiffness                                  mastics
         Liu et al./   Prediction of   PFC2D  2D     Yes    Viscoelastic NA
         2009         creep stiffness
        TABLE 9.11  Major research efforts on DEM applications to AC.



              (Carmona et al., 2007), and fracture modeling (Kim and Buttlar, 2005; Kim et al., 2008),
              and failure (Ullidtz, 2001).
                 Abbas et al. (2007) built a viscoelastic model for mastic and asphalt mixture using
              the Burger model in PFC2D to simulate the dynamic modulus test and low temp frac-
              ture of indirect tensile test. The interaction among the discrete particles was defined
              using two contact stiffness models: the linear contact model and the viscoelastic Burg-
              er’s contact model.
                 Similarly, using the PFC2D code, Liu et al. (2009) built a viscoelastic model of as-
              phalt mixtures in which the viscoelastic behavior of asphalt mastics was represented by
              a Burger’s model, while the aggregate particles were simulated with particles of irregu-
              lar shapes consisting of balls bonded together. The asphalt mastic between aggregates
              was filled with balls bonded with the Burger’s model. The entire micromechanical
              model was developed with four constitutive laws to represent the interactions at con-
              tacts of discrete elements within an aggregate, within mastic, between an aggregate and
              mastic, and between two adjacent aggregates. Three components, i.e., a stiffness model,
              a slip model, and a bonding model, were included in each constitutive law to capture
              the relationship between the contact force and relative displacement as well as to de-
              scribe slipping and tensile strength at a particular contact (Liu et al., 2009). However,
              model parameter characterization presents a challenge.
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