Page 95 - MODELING OF ASPHALT CONCRETE

Overview of the Stif fness Characterization of Asphalt Concr ete 73

Tire

Confinement
pressure

Expansion

FIGURE 3-5 Effect of large compressive Poisson’s ratios.

stiffens the asphalt concrete, resists lateral plastic deformation, and presses closed any
microcracks that may be growing in the asphalt. This is illustrated in Fig. 3-5.
More recent work on cross-anisotropic pavement materials has shown that the same
phenomenon of large radial strains can be predicted using the elastic work potential shown
in Eq. (3-4) without requiring either of the Poisson’s ratios to rise above 0.5 (Lytton 2000).

I
α 1 dI + βτ zx dτ zx dJ′
1
W = ∫ 9 + 2 (3-4)
E
ABCDA
xx 2 G xy
where α = 2 + 1 − 4n − 2r
m
β =2 +2r − s
m
E
m = yy
E
x xx
n = n
xy
r = n
xz
E
s = xx
G
xy
E = horizontal modulus
xx
E = vertical modulus
yy
W = cross-anisotropic elastic work potential
It is still useful to use an “effective” Poisson’s ratio to describe the formation of large
radial strains in a cross-anisotropic elastic asphalt concrete. The determination of all
five of the material properties of a cross-anisotropic material cannot be determined
from the measurements of the axial and radial stresses and strains of a triaxial test using
the stress-strain relations of the material alone. Instead, it requires the use of an extra
relation which solves for the shear modulus using the deviatoric strain energy that is
measured during a test in which only the second invariant of the deviatoric stress tensor
is applied (Adu-Osei 2000). Other methods using a constrained optimization approach
to get a realistic estimate of the shear modulus have been suggested (Tutumluer and
Seyhan 2002).