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Mechanical Proper ties of Constituents   41


              ometer software. The complex shear modulus, G*, is the ratio of total shear stress to
              total shear strain and is given by the following formula:
                                                τ  − τ
                                           G*    max  min                        (2-17)
                                                γ  − γ
                                                 max  min
                 Where τ is the shear stress and γ is the shear strain. Permanent deformation is con-
              trolled by limiting G*/sin δ to values greater than 1 kPa for original binder and 2.2 kPa
              for RTFO aged binder. For fatigue cracking, the G*sin δ parameter is desired to be less
              than 5000 kPa at test temperatures for PAV aged material. In general, multiple single
              frequencies or frequency sweep (ranging from 0.0001 to 1000 Hz) are used within the
              DSR to construct the master curves in order to determine the rheological properties of
              binders and mastics. Testing procedures are covered by ASTM D 7405 or AASTHO T
              315 or TP70.
              2.1.9.7  Low Temperature Cracking Resistance—Thermal Cracking
              To determine binder properties at low pavement temperatures, SHRP researchers pro-
              posed two devices: the Bending Beam Rheometer (BBR) and the Direct Tension Tester
              (DTT).

              Bending Beam Rheometer (BBR)
              The BBR apparatus is used to measure how much deflection or creeping a binder can
              sustain under a constant load at a constant temperature (Anderson et al., 2001; Asphalt
              Institute, 2007). For this purpose, asphalt samples from RTFO and PAV aging tests are
              formed into rectangular beams and tested at low pavement service temperatures for
              thermal cracking. Beam theory is used to calculate the stiffness of an asphalt beam under
              a creep load. During testing a constant creep load of 100 g is applied in bending mode at
              constant temperature for 240 s and creep stiffness S(t) and creep rate (m-value) are pro-
              vided by the rheometer software. The creep load simulates thermal stresses that gradu-
              ally build up in a pavement when temperatures get very low. Creep stiffness (S) is the
              resistance of the asphalt binder to creep loading and m-value is the change in asphalt
              stiffness with time during loading. Creep stiffness is given by the following equation:

                                                   PL 3
                                            St ()                                (2-18)
                                                    δ
                                                    3
                                                      t
                                                 4 bh ()
                  where P = applied constant load (N)
                       L = distance between beam supports (102 mm)
                       b = beam width (12.5 mm)
                       h = beam thickness (6.25 mm)
                     δ(t) = deflection (mm)
                 The Superpave specification requires that the creep stiffness not exceed 300 MPa
              and m-value be greater than or equal to 0.3 at 60 s. Testing procedure for BBR is covered
              by ASTM D 6648 or AASTHO T 313.

              Direct Tension Tester (DTT)
              The amount of binder strain before failure at very low temperatures is measured by the
              Direct Tension Tester (DTT) (Asphalt Institute, 2007). The test is performed at the tem-
              perature range where asphalt generally exhibits brittle behavior (0°C to –36°C). Fur-
              thermore, the test is performed on binders that have been aged in both a RTFO and the
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