Page 408 - Mechanics of Asphalt Microstructure and Micromechanics

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400 Ch a p t e r w e l v e

z 0
x or r
Layer 1 0 h 1
z 1

z k-1
…
Layer k h k
z k

…
z p-1
Layer p h p

z p
z
FIGURE 12.5 Illustration of the multiple layered system (courtesy Ernie Pan).

u(, , ) = u e + u e + u e
xyz
xx y y z z
+∞ +∞ ⎡ ⎡ ⎧ ⎪ S ∂ S ∂ ⎤ ⎡ ∂ ⎤ ⎫ ⎪ (12-7)
= ⎢ ⎨ ∫ ∫ U M () +Uz ⎥ x + U () ∂S −Uz () S ⎥ e y +Uz()Se ⎬ αβ
e
()
z
d d
⎢
z
S
L
N
M
z
N
−∞ −∞ ⎣ ⎩ ⎪ x ∂ y ∂ ⎦ ⎣ ∂y ∂x ⎦ ⎭ ⎪
t(, , ) = σ e +σ e +σ e
xyz
xz x yz y zz z
+∞ +∞ ⎡ ⎧ ⎪ S ∂ ∂S⎤ ⎡ S ∂ S ∂ ⎤ ⎫ ⎪ (12-8)
= ⎢ ⎨ ∫ ∫ Tz x ∂ + Tz S ⎥ e x + ⎢ Tz () y ∂ − Tz () x ∂ ⎥ e y + T (()zSe ⎬ αβ
()
()
d d
y ∂
z
L
N
M
N
M
−∞ −∞ ⎣ ⎩ ⎪ ⎦ ⎣ ⎦ ⎭ ⎪
Finally, through the propagator matrix method, they solved for the stress, strain, and
displacement fields under various loading and boundary conditions. A program (Mul-
tiSmart3D) has also been developed by this group to allow convenient computation of the
stress, strain, and displacement fields. Through Laplace transform, the analytical solu-
tions have been further derived for the corresponding viscoleastic materials (Chen et al.,
2009). Pan’s work placed a foundation for considering the anisotropic material properties
in the flexible layered pavement design.
12.6 Characterization of the Anisotropic Properties
Using a True Triaxial Testing Device
12.6.1 General State
While significant efforts have been devoted to the study of the fundamental properties
of soils, limited efforts have been devoted to AC. Properties such as stress path depen-
dency, anisotropy, yielding, plastic deformation rates, etc. are barely studied in AC.