Page 425 - Mechanics of Asphalt Microstructure and Micromechanics

Characterization and Modeling Anisotropic Proper ties of Asphalt Concrete 417

1.801E+10 Time (s) Viscoelastic Elastic
Relaxation Modulus (Pa) 1.201E+10 10 1 5 13.8 4.25
Relaxation Modulus (GPa)
0.91
9.24
0.47
5.6
0.29
2.06
20
30
0.21
0.76
0.18
0.28
40
6.010E+09
Elastic solution
Viscoelastic solution
1.000E+07
0 5 10 15 20 25 30 35 40 45
Time (s)
FIGURE 12.17 Modulus estimated by elastic and viscoelastic solutions.

Where d (t) is the dirac delta function and this item in Equation 12-24 is related to
the initial material response. The relaxation modulus is plotted in Figure 12.17 and the
values at certain time points are calculated and listed in the same figure. These values
of the relaxation modulus are comparable with the values reported in the literature
(Secor and Monismith, 1965; Khanal and Mamlouk, 1995). The modulus evaluated with
the elastic solution in Equation 12-20 is plotted in the same graph. The obvious differ-
ence between these two curves implies the necessity of a viscoelastic solution.

12.7.5 Conclusions
The measurement and analytical procedures developed for the four-point bending
beam test present an effective method to evaluate the bimoduli of AC. The viscoelastic
analysis developed allows the use of the above test for evaluating the relaxation modu-
lus of asphalt materials in tension and compression. While it might be difficult to de-
velop an analysis of pavements that considers the bimoduli, the measured difference
that is consistent with literature data provides a basis for future pavement design and
analysis that may consider the bimoduli effects.

12.8 Anisotropy in Permeability
Harris (2007) conducted a study to experimentally evaluate the anisotropy properties of
AC. A horizontal permeability test device and a field permeability test device were de-
veloped for both laboratory and field permeability tests (Figure 12.18). An FEM simula-
tion of the field permeability test was also performed. Both the vertical permeability
calculated using Equation 12-25 and the horizontal lab permeability calculated using
Equation 12-26 utilized the falling head method.
⋅
k = aL ⋅ln ⎛ ⎜ h ⎞ ⎟ (12-25)
1
v A⋅ Δ t ⎝ h ⎠
2