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Modeling of Asphalt Binder Rheology and Its Application to Modified Binders      33


                                    10                                     100
                                                 0%   c%   2c%             80
                                   G* at 10 r/s, log Pa  6                 60  Delta at 10 r/s, °
                                    8


                                                                           40
                                    4


                                                                           0
                                    2                                      20
                                       −30        0       30       60
                                                  Temperature, °C
                                             (a) Modified with an SB-polymer
                                    100

                                     80                          G* CRM     9
                                   Phase angle, °  60            Delta CRM  7 5 G* at 25°C, log Pa


                                                                 G* AC
                                     40
                                     20                          Delta AC   3

                                      0                                     1
                                      −5        0        5        10       15
                                                Reduced frequency, log(s)
                                              (b) Modified with crumb rubber
                    FIGURE 2-7  Isochronal rheological curves for an asphalt before and after modifi cation with two
                    types of additives. (a) Modifi ed with an SB polymer; (b) modifi ed with crumb rubber.


                    rheological mastercurves measured using a dynamic shear rheometer for an asphalt
                    before and after modification with an styrene-butadiene (SB) polymer at two different
                                                                         ∗
                    concentrations (c = 3 and 2c = 6 percent). Changes in both G  and d as a function of
                    temperature are shown. The effects of this modifier show favorable trends of change: at
                                      ∗
                    high temperatures, G  is higher while d is lower. This indicates an increase in rigidity and
                    in elasticity, which results in better resistance to permanent deformation. At intermediate
                                                          ∗
                    temperatures (0 to 30°C) lower values of G  can be observed while  d values remain
                                              ∗
                    indifferent. The reduction in G  values is favorable for fatigue cracking under strain-
                    controlled conditions, typical of conditions for thin pavements. At low temperatures
                                                                                 ∗
                    (−20 to 0°C), a similar, or more pronounced, reduction is observed for G  and a minor
                    increase in d is seen. Both these effects are favorable since they make the binder less rigid
                    and less elastic or more prone to stress relaxation under load. The changes shown appear
                    to improve the properties with respect to pavement performance at all temperatures.
                                                          ∗
                       Considering the relative changes in the G  and d, it is evident that the main effect is
                                                                   ∗
                    the change in the rigidity of the binder as measured by G . The data shown in Fig. 2-7(a)
                                         ∗
                    indicate that while the G  value is increased at 60°C by 100 to 200 percent, the d value is
                    reduced by approximately 16 to 30 percent. At low temperatures the same trend can be
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