Page 458 - Mechanics of Asphalt Microstructure and Micromechanics

450 C hapter T h ir te en

water flow patterns and the gradients of percent air voids in HMA. Novak et al. (2002)
used the theory of mixture to describe the saturated asphalt pavement and studied the
effects of vehicle speed and permeability on pore pressure with a 2D finite element
program—PlasFEM.
This section presents a brief outline of a recent study on excess pore water pressure
development in asphalt pavement based on the Poroelasticity Theory (Wang, 2000) and
ABAQUS Theory manual. More details can be found in Wang et al. (2010a, 2010b).

13.3.3.2 Constitutive Model
The poroelasticity model treats the pavement (AC) with porous water as a continuum,
assuming that the total stress at each point is the sum of an “effective stress” carried by
the aggregate skeleton and a pore pressure in the fluid permeating the structure. This
fluid pore pressure can change with time, and the gradient of the pressure through the
pavement (or material) that is not balanced by the weight of fluid between the points
will cause the fluid to flow. The flow velocity is proportional to the pressure gradient in
the fluid according to Darcy’s Law. In essence, the fundamental concept is based on
mixture theory.
The model considers the medium as a multi-phase material and adopts an effective
stress principle to describe its behavior. Two fluids are considered. The “wetting liquid”
is assumed to be relatively incompressible. The other is gas, which is compressible. The
total stress at any point, s, is assumed to be made up of an average pressure stress in
the wetting liquid, u w , an average pressure stress in the other fluid, u a , and an “effective
*
stress,” σ , which is defined by:
σ = σ − χ ( u + ( − χ) )I (13-24)
*
u
1
w a
In which χ is a factor that depends on the level of saturation and on the surface ten-
sion of the liquid/solid system.
Equilibrium is expressed by writing the principle of virtual work for the volume
under consideration in its current configuration at any time:
∫ σδεdV = ∫ t ⋅ δvdS + ∫ f ⋅ δvdV (13-25)
ˆ
:
V S V
def
Where dv is a virtual velocity field, δε = sym( δ ∂ v/ ∂x) is the virtual rate of deforma-
ˆ
tion, s is the true stress, t is surface traction per unit area, and f is body forces per unit
volume.
The mechanical behavior of the porous medium consists of the response of the liq-
uid and solid to local pressure and the response of the overall material to the effective
stress.
For the liquid in the system:
ρ u
1
w ≈+ w − ε th (13-26)
ρ 0 K w
w w
0
Where r w is the density of the liquid, r w is its density in the reference configuration,
th
K w is the liquid’s bulk modulus, and e w is the volumetric expansion of the liquid caused
by temperature change.