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Computational and experimental evaluation of hydraulicconductivity anisotropy in hot-mix asphalt
M. EMIN KUTAY†k, AHMET H. AYDILEK‡*, EYAD MASAD{# and THOMAS HARMAN§**
†Turner-Fairbank Highway Research Center-FHWA, 6300 Georgetown Pike Rm. F210, McLean, VA 22101, USA‡Department of Civil and Environmental Engineering, University of Maryland, 1163 Glenn Martin Hall, College Park, MD 20742, USA
{Zachry Department of Civil Engineering, Texas A&M University, 3135 TAMU, College Station, TX 77843, USA§Turner-Fairbank Highway Research Center-FHWA, 6300 Georgetown Pike Rm. F210, McLean, VA 22101, USA
(Received 10 January 2006; in final form 30 April 2006)
Moisture damage in asphalt pavements is one of the primary distresses that is associated with thedisintegration of the pavement surface, excessive cracking and permanent deformation. Moisturedamage is a function of the chemical and physical properties of the mix constituents, and thedistribution of the pore structure (microstructure), which affects fluid flow within the pavement. Thispaper deals with the relationship between the hot-mix asphalt (HMA) microstructure and hydraulicconductivity, which has traditionally been used to characterize the fluid flow in asphalt pavements.
Conventional laboratory or field measurements of hydraulic conductivity only provide informationabout the flow in one direction and do not consider flow in other directions. Numerical modeling of fluidflow within the pores of asphalt pavements is a viable method to characterize the directional distributionof hydraulic conductivity. A three-dimensional lattice Boltzmann (LB) fluid flow model was developedfor the simulation of fluid flow in the HMA pore structure. Three-dimensional real pore structures of thespecimens were generated using X-ray computed tomography (CT) technique and used as an input in theLB models. The model hydraulic conductivity predictions for different HMA mixtures were validatedusing laboratory measurements. Analysis of the hydraulic conductivity tensor showed that the HMAspecimens exhibited transverse anisotropy in which the horizontal hydraulic conductivity was higher thanthe vertical hydraulic conductivity. Analysis of X-ray CT images was used to establish the link betweenfluid flow characteristics and the heterogeneous and anisotropic distributions within the pore structure.
Keywords: Hydraulic conductivity anisotropy; Asphalt concrete; Lattice Boltzmann; X-ray computertomography; Image analysis
1. Introduction
Moisture damage is caused by destruction of the cohesive
bond within the asphalt binder or the adhesive bond
between the aggregate and asphalt binder. Adhesive
debonding, which is manifested by stripping of the binder
from the aggregates, is known to cause cracks, permanent
deformation, and reduction in the load carrying capacity
that might ultimately necessitate replacement of the entire
pavement layer. A mix resistance to moisture damage is
related to a number of factors that include asphalt film
thickness, aggregate shape characteristics, surface energy
of aggregates and binder, and pore structure distribution
(McCann et al. 2005, Masad et al. 2006a,b). Kringos and
Scarpas (2005) have recently introduced a numerical
model to understand the physical and mechanical
processes causing debonding of the binder from the
aggregates due to moisture transport in asphalt pavements.
The model idealized the aggregates as two-dimensional
circular structures coated with a binder film, and analyzed
the diffusion of water into the film and desorption of the
binder film from the aggregate. The work by Kringos and
Scarpas (2005) offered a numerical modeling framework
to incorporate the different mechanisms associated with
moisture damage.
A better understanding of the moisture damage
phenomenon can be achieved through studying the
relationship between the pore structure distribution and
International Journal of Pavement Engineering
ISSN 1029-8436 print/ISSN 1477-268X online q 2007 Taylor & Francis
http://www.tandf.co.uk/journals
DOI: 10.1080/10298430600819147
kFormerly Graduate Research Assistant, Department of Civil and Environmental Engineering, University of Maryland, 1173 Glenn Martin Hall,College Park, MD 20742, USA. Email: muhammed.kutay@fhwa.dot.gov
#Tel: þ1-979-845-8308. Fax: þ1-979-845-0278. Email: emasad@civil.tamu.edu** Email: tom.harman@fhwa.dot.gov
*Corresponding author. Tel: þ1-301-314-2692. Fax: þ1-301-405-2585. Email: aydilek@eng.umd.edu
International Journal of Pavement Engineering, Vol. 8, No. 1, March 2007, 29–43
fluid flow characteristics in hot-mix asphalt (HMA).
Several analytical and empirical equations have been
developed for the estimation of hydraulic conductivity,
which is commonly used to describe fluid flow in porous
media such as HMA (Kozeny 1927, Carman 1956, Walsh
and Brace 1984, Al-Omari et al. 2002). Derivations of
these equations are usually based on the approximation of
pore structure with simple geometries, such as tubes and
cones, and therefore the models may not be applicable to
the complex pore structures of asphalt pavements.
Laboratory or field measured hydraulic conductivity of
asphalt pavements is usually assumed to be the same in all
directions. However, asphalt pavements have an aniso-
tropic and heterogeneous internal pore structure, which
has a direct influence on the spatial and directional
distributions of hydraulic conductivities (Masad et al.
1999). For instance, recent macro-scale numerical studies
concluded that most of the fluid flow in asphalt pavements
occurs in the horizontal direction (Masad et al. 2003,
Hunter and Airey 2005).
Numerical simulations at the micro-structural levels
have been recently used to understand fluid flow
characteristics in HMA. Al-Omari and Masad (2004)
utilized a semi-implicit method for pressure-linked
equations (SIMPLE) finite difference scheme to solve
the Navier-Stokes equations for modeling of flow within
the pore structure of asphalt specimens. They calculated
the hydraulic conductivity tensor of eight different asphalt
specimens, and concluded that longitudinal (kxx) and
transverse (kyy) hydraulic conductivities are close to each
other and are much higher than the vertical ones (kzz).
In spite of the influence of the directional distribution
of hydraulic conductivity on fluid flow in pavements,
information is still lacking about this distribution. The
components of the hydraulic conductivity tensor and their
relation to the pore structure parameters, such as pore
constriction areas in three different directions (i.e. x-, y-
and z-directions), need to be explored to accurately
estimate flow patterns in asphalt pavements. Such flow
patterns can be used in the design of efficient pavement
drainage systems that consider the directional distribution
of hydraulic conductivity. They can also be used as part of
numerical simulations of moisture damage at the
microstructural level similar to the model developed by
Kringos and Scarpas (2005).
In response to this need, a study was conducted to
model fluid flow in asphalt pavements. X-ray CT was used
to acquire real three-dimensional pore structures of
asphalt specimens by eliminating the potential errors
that might stem from idealized pore structure assumptions
(Wang et al. 2003, Masad et al. 2006c). A three
dimensional pore scale-based fluid flow model was
developed by utilizing the lattice Boltzmann (LB)
approach, one of the most reliable methods that is
increasingly being used in various engineering appli-
cations in simulating single-phase, Newtonian and
incompressible fluid flows (Chopard and Droz 1998,
Rothman and Zaleski 1998, Kandhai et al. 1999, Chen and
Doolen 2001, Succi 2001, Hazi 2003, Pilotti 2003). The
hydraulic conductivities estimated by the model were
compared with laboratory experimental measurements.
The characteristics of the hydraulic conductivity of
asphalt pavements in three different directions, longitu-
dinal (kxx), transverse (kyy) and vertical (kzz), and the effect
of constrictions on these hydraulic conductivities were
studied. The relationships between the normal and shear
components of hydraulic conductivity were also
investigated.
2. Modeling of fluid flow using lattice Boltzmann
method
The LB method is a numerical technique for simulating
viscous fluid flow (McNamara and Zanetti 1988). The
method approximates the continuous Boltzmann equation
(a)
(b)
e15=[0,1,1]
e11=[1,0,1]
e7=[1,1,0]e3=[0,1,0]
e14=[–1,0,1]e5=[0,0,1]
e1=[1,0,0]
e12=[1,0,–1]
e10=[1,–1,0]e4=[0,–1,0]
e9=[–1,–1,0]
e2=[–1,0,0]
e8=[–1,1,0]
e18=[0,–1,1]
e13=[–1,0,–1]
e17=[0,–1,–1]
e6=[0,0,–1]
e16=[0,1,–1]
e19=[0,0,0]
x
z
y
Figure 1. (a) Binary image of aggregates (black areas represent theaggregates and white areas represent the pores) and generation of latticenodes at the center of each white pixel, and (b) D3Q19 latticemicroscopic velocity directions.
M. E. Kutay et al.30
by discretizing a physical space with lattice nodes and a
velocity space by a set of microscopic velocity vectors
(Maier et al. 1997). In the LB method, the physical space
is discretized into a set of uniformly spaced nodes (lattice)
that represent the voids and the solids (figure 1(a)), and a
discrete set of microscopic velocities is defined for
propagation of fluid molecules (figure 1(b)). The time- and
space-averaged microscopic movements of particles are
modeled using molecular populations called the distri-
bution function, which defines the density and velocity at
each lattice node. Specific particle interaction rules are set
so that the Navier-Stokes equations are satisfied. The time
dependent movement of fluid particles at each lattice node
satisfies the following particle propagation equation:
Fiðxþ ei; t þ 1Þ ¼ Fiðx; tÞ þVi 2 BF ð1Þ
where Fi, ei and Vi are the particle distribution function,
microscopic velocity and collision function at lattice node
x, at time t, respectively. The subscript i represents the
lattice directions around the node as shown in figure 1(b),
and BF is the body force and is given as BF ¼ 23wi
(ei·fp) where fp is the applied pressure gradient and wi
is the weight factor for the ith direction (Martys et al.
2001). The collision function Vi represents the collision of
fluid molecules at each node and has the following form
(Bhatnagar et al. 1954):
Vi ¼ 2Fi 2 F
eqi
tð2Þ
where Feqi is the equilibrium distribution function, and t is
the relaxation time which is related to the kinematic
viscosity of the fluid n through the relationship
n ¼ (2t 2 1)/6. The pressure gradient that is set to trigger
the flow is often termed as a density gradient in LB
algorithms, since the following relationship (also called
the equation of state) exists between density and pressure
in the lattice space (Maier et al. 1997):
P ¼ c2sr ð3Þ
where P and r are pressure and density, respectively, and
cs is a constant termed the lattice speed of sound.
Equilibrium distribution functions for different models
were derived by He and Luo (1997). The function is given
in the following form for the 3D 19-velocity lattice
(D3Q19) model that was used in the current study:
Feqi ¼ wir 1 þ
ei·u
c2s
þðei·uÞ
2
2c4s
2ðu·uÞ
2c2s
� �ð4Þ
where u is the macroscopic velocity of the node. The
lattice speed of sound, cs, is equal to 1/3 for the D3Q19
lattice. The D3Q19 model has been commonly used by
previous researchers and the weight factors for the model
are w0 ¼ 1/3 for a rest particle, wi ¼ 1/18 for particles
streaming to the face-connected neighbors and wi ¼ 1/36
for particles streaming to the edge-connected neighbors.
The macroscopic properties, density (r) and velocity (u),
of the nodes are defined by the following relations:
r ¼X19
i¼1
Fi u ¼
P19i¼1 Fiei
rð5Þ
Kutay and Aydilek (2005) presented results verifying
the accuracy of the D3Q19 LB model with well-known
analytical and theoretical solutions of simple geometries.
An excellent agreement was observed between these
solutions and the LB simulations for Stokes flow around
a cylinder and flow in circular tubes. The percent error
ranged from 0.1 to 2%. It was also shown that the LB
model was able to simulate fluid flow accurately, even at
relatively low resolutions (low number of lattice sites).
Kutay and Aydilek (2005) further evaluated the perfor-
mance of the D3Q19 LB model through laboratory
hydraulic conductivity tests conducted on unbound
aggregate specimens. X-ray CT and mathematical
morphology-based techniques were used to analyze the
pore structure of the aggregates and these pore structures
were input into the LB model. A relatively good
agreement was observed between the model predictions
and the laboratory data, and the difference in hydraulic
conductivities was less than an order of magnitude.
3. Components of the hydraulic conductivity tensor
Darcy’s law for one dimensional flow is written in the
following form:
kzz ¼ðQz=AÞ
izð6Þ
where Qz is the measured flow rate, iz is the applied
hydraulic gradient, and A is the specimen cross sectional
area perpendicular to the direction of pressure gradient.
L
Pz-in
Pz-out
=L
Pz–in– Pz–out g neff
kyzuy
=L
Pz–in– Pz–out kzzuz g neff
=L
Pz–in– Pz–out kxzux g neff
Figure 2. Illustration of physical meaning of the hydraulic conductivitytensor.
Hydraulic conductivity anisotropy of HMA 31
Equation (6) can also be written as:
uz ¼ kzz7Pz
gð7Þ
where 7Pz ¼ (Pz2in 2 Pz2out)/L is the pressure gradient
in z-direction, L is the specimen length, and g is the unit
weight of the fluid ( ¼ 9.81 kN/m3 for water). The
velocity vectors in each direction (figure 2) can be defined
using the generalized Darcy’s formula, which is given in a
tensor form as follows (Kutay 2005):
ux
uy
uz
2664
3775 ¼ 2
1
gneff
kxx kxy kxz
kyx kyy kyz
kzx kzy kzz
2664
3775
7Px
7Py
7Pz
2664
3775 ð8Þ
where ux, uy and uz are the average velocities in x-, y-, and
z-directions, respectively. Solving equation (8) for the
directional hydraulic conductivities was performed by
applying a pressure gradient only in the z-direction to
compute the three components of the hydraulic conduc-
tivity tensor (i.e. kxz, kyz and kzz). Applying a pressure
gradient in x-, y-, or z-direction and setting the pressure
gradients in the other two remaining directions equal to
zero in equation (8) (e.g. fPz – 0, fPx ¼ 0 and
fPy ¼ 0 for flow in z-direction) reveals the
following set of equations for directional hydraulic
conductivities:
kxz ¼ 2gneffðux=7PzÞ ð9Þ
kyz ¼ 2gneffðuy=7PzÞ ð10Þ
kzz ¼ 2gneffðuz=7PzÞ ð11Þ
kxx ¼ 2gneffðux=7PxÞ ð12Þ
kyx ¼ 2gneffðuy=7PxÞ ð13Þ
kzx ¼ 2gneffðuz=7PxÞ ð14Þ
0.075 0.3 0.6 1.18 2.36 4.75 9.5 12.5 0
10
20
30
40
50
60
70
80
90
100
Sieve Size (mm)
Per
cent
Pas
sing
(%
)
0
10
20
30
40
50
60
70
80
90
100
Per
cent
Pas
sing
(%
)
0
10
20
30
40
50
60
70
80
90
100
Per
cent
Pas
sing
(%
)
FHWA 0.45 Power Chart9.5 mm Nominal Maximum Size
FHWA 0.45 Power Chart19 mm Nominal Maximum Size
SMA9.5F9.5CMDL
Restricted zoneControl points
0.075 0.6 1.18 2.36 4.75 9.5 12.5 190
10
20
30
40
50
60
70
80
90
100
Sieve Size (mm)
Per
cent
Pas
sing
(%
)
FHWA 0.45 Power Chart12.5 mm Nominal Maximum Size
0.075 0.6 1.18 2.36 4.75 9.5 12.5 19 25 Sieve Size (mm)
0.075 0.6 1.18 2.36 4.75 9.5 12.5 19 25 37.5 Sieve Size (mm)
FHWA 0.45 Power Chart25 mm Nominal Maximum Size
25F
25C
MDL
Control Points
SMA12.5F12.5CMDL
Restricted zoneControl points
SMA19F19CMDL
Restricted zoneControl points
Figure 3. Gradations of laboratory specimens. SMA, stone matrix asphalt; MDL, maximum density line.
M. E. Kutay et al.32
kxy ¼ 2gneffðux=7PyÞ ð15Þ
kyy ¼ 2gneffðuy=7PyÞ ð16Þ
kzy ¼ 2gneffðuz=7PyÞ ð17Þ
4. Materials and methodology
4.1 Material properties
The analysis of fluid flow in HMA included field cores and
laboratory prepared specimens. The laboratory specimens
were fabricated per AASHTO PP28 procedure in order to
study a number of mixture variables that are likely to
affect the pore structure distribution and hydraulic
conductivity. The selected variables included the nominal
maximum aggregate size (NMAS), compaction energy
(number of gyrations in the gyratory compactor), and
aggregate size distribution or gradation. Of the 36
laboratory specimens prepared for this study, 24 were
Superpave dense graded mixtures and 12 were relatively
permeable stone matrix asphalt (SMA) mixtures. For the
Superpave mixtures, NMASs of 9.5, 12.5, 19 and 25 mm
were selected. SMA gradations were selected from three
different NMASs: 9.5, 12.5 and 19 mm. Number of
gyrations was varied from 25 to 75 to cover a range of
compaction energies. Seven 150-mm diameter field
cores were obtained from the test sections of the
accelerated loading facility (ALF) located at the Turner-
Fairbank Highway Research Center (TFHRC) of the
Federal Highway Administration (FHWA). Figures 3 and
4 provide the aggregate gradations of laboratory speci-
mens and field cores, respectively. Table 1 presents the
mix design properties of all the specimens used in this
study.
4.2 Image acquisition and processing
The three-dimensional images of the specimens were
generated using the X-ray CT technique. Two-dimen-
sional image slices of the specimens were captured and
the slices were stacked to reconstruct the 3D structure.
An example of a reconstructed structure of an HMA
specimen is shown in figure 5. The vertical resolution
(Dz) of the two-dimensional grayscale images was
registered by the aperture of the linear detector of the X-
ray CT device, which was 0.8 mm. The horizontal
resolutions, on the other hand, were directly related to
the specimen diameter. A uniform resolution of 0.4–
0.8 mm/pixel was achieved in all directions (x, y and z)
by resizing the image slices using a bilinear interp-
olation. The captured grayscale images were converted
into a binary form (black and white) using a
morphological thresholding technique, where black
areas (pixel values of 0) represent solid particles
and white areas (pixel values of 1) represent air voids
(Kutay 2005).
Following the generation of binary images, an
additional task was performed to increase the speed of
the simulations. An algorithm was developed to eliminate
the isolated pores that had no connection to any of the
outside boundaries (i.e. surface) of the specimen, and
lattice nodes were generated only at the centers of each
white voxel (three-dimensional pixel) that represented the
interconnected pore spaces. It is important to mention that
this step was not required for the LB simulations; however,
the isolated pores were eliminated solely to speed up the
simulation at each time step. Furthermore, decreasing the
number of nodes reduced the total number of time steps
to reach the steady state flow condition. More detailed
discussion on X-ray CT technique, specifications of the
device utilized in this study, and the methods followed for
processing the captured images are provided by Kutay and
Aydilek (2005).
0.075 0.6 1.18 2.36 4.75 9.5 12.5 19 25 0
10
20
30
40
50
60
70
80
90
100
Sieve Size (mm)
Per
cent
Pas
sing
(%
)
FHWA 0.45 Power Chart19 mm Nominal Maximum Size
Gradation A
Gradation AMDLRestricted ZoneControl Points
0.075 0.6 1.18 2.36 4.75 9.5 12.5 190
10
20
30
40
50
60
70
80
90
100
Sieve Size (mm)
Per
cent
Pas
sing
(%
)
FHWA 0.45 Power Chart12.5 mm Nominal Maximum Size
Gradation B
Gradation BMDLRestricted ZoneControl Points
Figure 4. Gradations of field cores. MDL, maximum density.
Hydraulic conductivity anisotropy of HMA 33
4.3 Laboratory test methodology
The vertical hydraulic conductivities (kzz) of the HMA
specimens were determined using a flexible wall
permeameter that was specifically developed for measur-
ing hydraulic conductivity of 150-mm diameter and 70-
mm long HMA specimens. Figure 6 shows the schematic
drawing of the so-called “Bubble Tube Constant Head
Permeameter”. The system allows the application of very
low hydraulic gradients, accommodates high flow rates
that are associated with testing of permeable asphalt
specimens, and significantly minimizes sidewall leakage
due to the existence of a membrane. The unique design
also eliminates the use of valves, fittings and smaller
diameter tubings, all which contribute to head losses that
interfere with the test measurements.
The permeameter was placed in a bath to maintain
constant tail water elevation (figure 6). The tub rim was
located a few millimeters above the specimen top. As
water flowed out of the reservoir tube through the
specimen, air bubbles emerged from the bottom of
the bubble tube. The total head difference through the
specimen (H), which was constant during the test, was
the height difference between the bottom of the bubble
tube and the top of the tub. The total flow rate through
the specimen (i.e. Qz) was determined by noting the
water elevation drop in the reservoir tube and
multiplying it with the inner area of the reservoir tube
minus the outer area of the bubble tube. Finally, the
vertical hydraulic conductivities were calculated using
Darcy’s law.
4.4 Modeling of fluid flow through the asphaltspecimens using the D3Q19 LB model
The developed D3Q19 LB model was used to simulate
fluid flow through reconstructed 3D images of HMA
Table 1. Properties of the asphalt specimens tested.
Specimen ID NMAS (mm) N.Gyr. Gradation Pb (%) Gmm (g/cm3) Gmb (g/cm3) n (%)
9.5F25 9.5 25 Fine 4.85 2.72 2.47 9.29.5C25 Coarse 4.76 2.72 2.42 10.99.5F50 50 Fine 4.85 2.72 2.50 8.39.5C50 Coarse 4.76 2.72 2.53 7.19.5F75 75 Fine 4.85 2.72 2.57 5.79.5C75 Coarse 4.76 2.72 2.58 5.312.5F25 12.5 25 Fine 4.75 2.73 2.58 5.412.5C25 Coarse 5.32 2.71 2.55 5.812.5F50 50 Fine 4.75 2.73 2.61 4.212.5C50 Coarse 5.32 2.71 2.57 5.112.5F75 75 Fine 4.75 2.73 2.64 2.812.5C75 Coarse 5.32 2.71 2.61 3.619F25 19 25 Fine 4.51 2.74 2.52 8.119C25 Coarse 4.85 2.74 2.43 11.419F50 50 Fine 4.51 2.74 2.55 6.819C50 Coarse 4.85 2.74 2.51 8.319F75 75 Fine 4.51 2.74 2.69 1.719C75 Coarse 4.85 2.74 2.60 5.025F25 25 25 Fine 4.00 2.76 2.50 9.525C25 Coarse 4.63 2.75 2.43 11.925F50 50 Fine 4.00 2.76 2.57 6.825C50 Coarse 4.63 2.75 2.50 9.425F75 75 Fine 4.00 2.76 2.60 5.725C75 Coarse 4.63 2.75 2.48 9.99.5SMA-A1 9.5 50 SMA 5.50 2.72 2.32 14.79.5SMA-A2 SMA 5.50 2.72 2.28 16.39.5SMA-B1 25 SMA 5.50 2.72 2.13 21.69.5SMA-B2 SMA 5.50 2.72 2.26 16.812.5SMA-A1 12.5 75 SMA 5.50 2.71 2.27 16.212.5SMA-A2 SMA 5.50 2.71 2.10 22.412.5SMA-B1 50 SMA 5.50 2.71 2.37 12.512.5SMA-B2 SMA 5.50 2.71 2.21 18.519SMA-A1 19 25 SMA 5.50 2.74 2.34 14.719SMA-A2 SMA 5.50 2.74 2.29 16.619SMA-B1 75 SMA 5.50 2.74 2.36 14.019SMA-B2 SMA 5.50 2.74 2.24 18.1L1 12.5 NA Field-B 7.10 2.71 2.24 8.2L2 Field-A 5.30 2.71 2.49 9.6L3 Field-A 5.30 2.71 2.45 5.6L4 Field-A 5.30 2.71 2.56 6.1L5 Field-A 5.30 2.71 2.54 7.3L6 Field-A 5.30 2.71 2.51 7.9L7 Field-A 5.30 2.71 2.50 5.5
Note: Pb, Opt. binder content; Gmm, maximum specific gravity of the mix; Gmb, bulk specific gravity of the mix; N.Gyr., number of gyrations; NMAS, nominal maximumaggregate size; n, porosity.
M. E. Kutay et al.34
specimens. Pressure gradients in the range of
9.97 £ 1027–1 £ 1023 g/mm2 s2 were set between the
inlet and outlet of each asphalt specimen during the LB
simulations, in order to simulate the pressure boundary
conditions occurring in the laboratory test permeameter.
Although the gradients varied based on the resolutions
of the captured images, they were all in the linear
(laminar) region, where Darcy’s law is applicable.
The curved faces of the cylindrical specimens were
confined by solid nodes (i.e. black pixels) to simulate a
typical membrane that confines the specimen in a
laboratory test. The components of the velocity vector
perpendicular to the density gradient at the inlet and outlet
nodes were initially set to zero (i.e. no slip boundary
condition).
The LB fluid flow simulations were run until a steady-
state flow condition was achieved. The steady-state flow
criterion was set such that the difference in the overall
mean velocity in z-direction (uz) between two consecutive
steps was less than a threshold value. This threshold was
selected to be 0.001% of the mean velocity of the current
time step. It was also observed that the number of time
steps required for flow stabilization varied from 1200 to
164,000, depending on the irregularity of the internal pore
structure. In general, less number of time steps was
required for specimens with less irregular pore-solid
interfaces. Similar observations were also made by Duarte
et al. (1992) in their 2D cellular automata-based model of
flow through cylindrical obstacles placed between parallel
plates.
5. Results and discussion
5.1 Simulated hydraulic conductivities andcomparisons with the laboratory measurements
The total and effective porosities of the 43 specimens
employed in the testing program are summarized in
table 2. The effective porosity refers to the percentage of
pores that are connected in the direction of the fluid flow
simulation. The effective porosities were calculated using
an image analysis algorithm that was developed as part of
this study. The algorithm first labeled the interconnected
white pixels by using a build-in-connected-component
function that grouped the connected pixels based on a
neighborhood criterion. The neighborhood criteria can
be 6, 18 or 26 in a 3D model, and the 18-connected
neighborhood criterion was selected for labeling in the
current study. After the labeling was complete, the labeled
groups that were not connected to both ends of specimen
(top and bottom) were eliminated. This produced a pore
channel that was connected to both ends of the specimen.
A more detailed explanation of the image algorithm is
provided by Kutay and Aydilek (2005).
The analyses revealed that 18 specimens had no
interconnected pores between two opposite faces of a
specimen. Some of these specimens could actually have
some interconnectivity, but at a resolution smaller than
that of the X-ray CT images (0.4 mm/voxel dimension).
Of course, even if such interconnectivity existed, the
hydraulic conductivity would be very small due to the
Figure 5. 3D reconstructed image of an asphalt specimen using the X-ray CT.
Hydraulic conductivity anisotropy of HMA 35
small sizes of the connected pores. This was evident in the
laboratory measurements as the laboratory-based hydrau-
lic conductivities of these eighteen specimens were 1–3
orders of magnitude lower than the hydraulic conduc-
tivities of those with effective porosities.
A summary of the vertical hydraulic conductivities (kzz)
based on LB simulations and laboratory measurements is
given in table 2. Computed hydraulic conductivities based
on equation (7) plotted against the laboratory measured
hydraulic conductivities in figure 7 indicate that the
two sets of hydraulic conductivities are in a very good
agreement. It is interesting to note that specimens with
comparable total porosities exhibited different hydraulic
conductivities. For example, specimens 8 and 9 as well as
specimens 4 and 5 had approximately the same porosities,
but their hydraulic conductivities were different by more
than an order of magnitude. An attempt was made to relate
the total porosities to measured hydraulic conductivities,
but the correlation was poor (Kutay 2005). Higher values
of coefficients of determination (R 2) were found when the
laboratory measured and LB-based hydraulic conduc-
tivities were plotted against the effective porosity in
figure 8. However, the R 2 values are still low with 0.4 and
0.51 for laboratory measured and LB-based hydraulic
conductivities, respectively. This finding suggests that the
constrictions of flow channels (the location of minimum
effective porosities) influence the values of hydraulic
conductivities more than the average effective porosity of
the entire channel. These constrictions caused a variation
in flow throughout the depth of the specimens. Figure 9 is
H
150 mm
"O" ring
base stand
bottom port
bottom collar
specimenclamping rod
chamber wall membrane
sliding collar
vent fitting
reservoir tube
bubble tube
top plate
Figure 6. Bubble tube constant-head permeameter.
M. E. Kutay et al.36
given as an example to present the streamlines computed
at the end of LB simulation for specimen 25C75. Herein, a
streamline is defined as a line that is tangent to the velocity
vectors everywhere in space. Flow streamlines in figure 9
clearly indicate that only a portion of the pores were
utilized in the flow beyond a certain depth, i.e. existence of
preferential flow pathways.
In order to study the influence of constrictions on fluid
flow, the change of velocity and pore water pressure along
the depth was investigated. Analysis of X-ray CT images
indicated that the pore pressures and velocities did not vary
linearly along the depth due to heterogeneous nature of the
asphalt specimens. Figure 10 presents an example set
of results for specimen 25C75. The pressure-depth
relationship deviates from the linear behavior (i.e.
nonuniform pressure gradient exists along the depth of
the specimen) due to nonuniform distribution of pores in
the specimens. Such behavior was also observed by Masad
et al. (2006c) in modeling of fluid flow through asphalt
specimens. Figure 10 also indicates that the maximum
velocity and pressure gradient occurred at a depth of
58 mm, which was the depth where the pore cross sectional
area had its lowest value (i.e. the constriction). The
pressure gradient (the slope of the curve in figure 10(b)) at
the constriction zone was significantly higher than the
average pressure gradient possibly due to inertial flow
occurring at this zone. Such high pressure gradients can
lead to high shear stresses at the constriction zone, which in
turn can contribute to the stripping of the binder from the
aggregate and induce damage in the asphalt matrix.
Table 2. Hydraulic conductivities based on laboratory measurements and LB simulations.
Sample No ID Specimen ID n (%) neff (%)kzz (mm/s)
Lab. test LB model
1 Coarse graded gyratory specimens 9.5C25 12.3 8.18 0.2290 0.35602 9.5C50 8.5 NA 0.0200 NC3 9.5C75 6.9 NA 0.0137 NC4 12.5C25 7.2 1.13 0.0195 0.03005 12.5C50 6.5 NA 0.0014 NC6 12.5C75 5.0 NA 0.0014 NC7 19C25 14.7 6.56 0.2200 0.27858 19C50 11.5 5.00 0.2210 0.40009 19C75 10.0 5.78 3.5000 7.130010 25C25 15.4 10.82 0.3100 0.280011 25C50 11.7 8.51 0.1700 0.175012 25C75 12.5 8.85 0.5450 0.360013 Fine graded gyratory specimens 9.5F25 9.8 NA 0.0022 NC14 9.5F50 8.8 NA 0.0006 NC15 9.5F75 5.6 NA 0.0011 NC16 12.5F25 5.5 NA 0.0075 NC17 12.5F50 4.1 NA 0.0082 NC18 12.5F75 2.8 NA 0.0089 NC19 19F25 9.4 3.67 0.0250 0.10020 19F50 8.0 NA 0.0057 NC21 19F75 1.7 NA 0.0400 NC22 25F25 11.3 6.35 0.0258 0.022523 25F50 8.7 NA 0.0011 NC24 25F75 7.8 NA 0.0006 NC25 SMA mixtures 9.5SMA-A1 20.1 18.90 2.4233 3.40826 9.5SMA-A2 17.1 11.16 2.3600 4.8627 9.5SMA-B1 21.6 17.70 4.8300 11.528 9.5SMA-B2 16.8 11.44 5.1650 3.110029 12.5SMA-A1 16.2 12.17 2.9000 3.2530 12.5SMA-A2 23.1 17.97 12.6700 20.360031 12.5SMA-B1 12.5 7.63 4.0300 4.26032 12.5SMA-B2 18.5 13.17 4.6400 5.4833 19SMA-A1 14.7 11.02 3.2600 7.560034 19SMA-A2 16.6 12.48 10.5100 7.200035 19SMA-B1 14.0 8.22 2.8600 336 19SMA-B2 18.1 10.60 3.84 3.250037 Field cores L1 8.3 NA 0.0065 NC38 L2 9.6 6.70 0.1290 0.210039 L3 5.6 NA 0.0028 NC40 L4 6.2 1.33 0.0567 0.038041 L5 7.4 1.653 0.0223 0.021042 L6 7.9 NA 0.0029 NC43 L7 5.5 NA 0.0158 NC
Note: NC refers to the specimens with no interconnected macro pores (i.e. minimum size greater than 0.3 mm) between two opposite faces of a specimen; n, porosity; neff,effective porosity; NA, effective porosity was not available due to lack of interconnected pore structure. The hydraulic conductivities observed in these specimens arepossibly due to the flow in micro pores whose size is less than 0.3 mm, and this size could not be determined by the X-ray CT technique.
Hydraulic conductivity anisotropy of HMA 37
5.2 Evaluation of hydraulic conductivity anisotropy
The developed LB model simulates the flow in 3D pore
structures of HMA. In order to investigate the components
of the hydraulic conductivity tensor, a cubical sample was
extracted from the X-ray CT images of the cylindrical
specimens (figure 2). It can clearly be seen in table 3 and
figure 11(a) that the horizontal hydraulic conductivities
(i.e. kxx and kyy) were consistently higher than the vertical
hydraulic conductivity (i.e. kzz), and in some cases the
difference was close to two orders of magnitude (e.g.
19C50 and 19SMA-A2). The kxx/kzz ratio ranged from
1.38 to 58.3 and from 1.53 to 52.7 for coarse-graded
gyratory and SMA specimens, respectively. For the same
specimens, the kyy/kzz ratio ranged from 1.78 to 76.1 and
from 1.47 to 54.9, respectively.
On the other hand, the hydraulic conductivities in the
two horizontal directions (i.e. kxx and kyy) were close to
each other in magnitude. The kyy/kxx ratio ranged from
0.52 to 2.42 for all specimens, a relatively narrower range
as compared to the ranges of the kxx/kzz and kyy/kzz ratios.
A plot of kxx vs. kyy in figure 11(b) confirms that the
hydraulic conductivities in two horizontal directions were
comparable within a 50% confidence interval. These
results indicate that the asphalt specimens exhibited
transverse anisotropy in which there was no anisotropy
within the horizontal plane, while there were significant
differences between the horizontal and vertical directions.
It should be noted that the Superpave mixtures were
prepared under axisymmetric compaction forces that are
not expected to induce directional differences in the pore
structure or hydraulic conductivity within the horizontal
direction. However, it is still possible that specimen
segregation during mix preparation could cause relatively
small differences between the kyy and kxx as obtained in
this study. In general, these findings are in agreement with
the results of another study conducted by Masad et al.
(2006a,b,c).
5.3 Effect of directional distribution of effective porosityon anisotropy of hydraulic conductivity
In order to further investigate the cause of the relatively
lower hydraulic conductivity values in z-direction, the
variation of effective porosity in three different directions
was plotted for all specimens. Example plots for specimen
25C75 in the x-, y- and z- directions are given in figure
12(a)–(c), respectively. The effective porosity at each
distance along a given direction was determined by first
computing the pore area on a plane perpendicular to the
direction of interest. For example, the pore area is
computed in the xy-plane when the effective porosity in
the z-direction is considered. Then, the projected pore area
was divided by the total area of the specimen on the
xy-plane. As seen in figure 12, the minimum porosity in
the z-direction is about an order of magnitude lower than
that of the other two directions, which leads to a lower
hydraulic conductivity in the z-direction.
It is well known that the constriction of the flow
channels control the flow rate and hydraulic conductivity
in porous media (Kenney et al. 1985, Fischer et al. 1996,
Aydilek et al. 2005). These constriction zones are
0.001
0.01
0.1
1
10
100
0.001 0.01 0.1 1 10 100
Laboratory dataCal
cula
ted
afte
r si
mul
atio
n, k
zz (m
m/s
)
Laboratory Measurement, kzz (mm/s)
Line of equality
Field cores
Figure 7. Comparison of laboratory-based hydraulic conductivity withLB simulation results.
10–3
10–2
10–1
100
101
102
0 5 10 15 20
CoarseFineSMAField cores
Labo
rato
ry-b
ased
hyd
raul
ic c
ondu
ctiv
ity (
mm
/s)
neff (%)
R2Laboratory = 0.40
10–3
10–2
10–1
100
101
102
0 5 10 15 20
CoarseFineSMAField cores
LB-b
ased
hyd
raul
ic c
ondu
ctiv
ity (
mm
/s)
neff (%)
R2LB-Model = 0.51
Figure 8. Relation of effective porosity to the measured and calculatedhydraulic conductivities.
M. E. Kutay et al.38
typically associated with the location of minimum
effective porosities. In order to investigate the effect of
these constrictions on flow, minimum effective porosities
in each direction were plotted against the hydraulic
conductivity in the same direction in figure 12(d)–(f).
It can be seen that the degree of relationship between the
minimum effective porosity and hydraulic conductivity
varies in different directions. A relatively good relation-
ship was observed (R 2 ¼ 0.89) when the minimum
effective porosity in the z-direction (n zeff-min) was plotted
against the hydraulic conductivity in the same direction.
However, the coefficients of determination between the
horizontal hydraulic conductivities (i.e. kxx and kyy) and
the minimum effective porosities in their corresponding
Figure 9. Streamlines computed at the end of LB simulation forspecimen 25C75.
0 100 2 10–5 4 10–5 6 10–5
0
20
40
60
80
uz (mm/s)
Dep
th (
mm
) max. velocity
(a)
18.4 18.8 19.20
20
40
60
80
Pressure (Pa)
Dep
th (
mm
)
Pz–in (pressure at inlet)
Pz–out (pressure at outlet)
max. pressure gradient(slope)
linear decreasein pressure(the slope = averagepressure gradient)
(b)0
20
40
60
80
0 100 1 103 2 103 3 103 4 103
Dep
th (
mm
)
Pore Cross Sectional Area (mm2)
min. pore area = 60.4 mm2
(pore constriction)
(c)
Figure 10. Change in (a) mean velocity, (b) pressure, and (c) pore cross sectional area with depth for specimen 25C75.
0.1
1
10
100
0.1 1 10 100
kxxkyy
k xx or
kyy
(m
m/s
)
kzz (mm/s)
Line of equality
(a)
0.1
1
10
100
1000
0.1 1 10 100 1000
k yy
(mm
/s)
kxx (mm/s)
Line of equality
(b)
–50% line
+50% line
Figure 11. (a) The relationship between (a) vertical (i.e. kzz) andhorizontal (i.e. kxx and kyy) hydraulic conductivities, and (b) twohorizontal hydraulic conductivities (i.e. kxx vs. kyy).
Hydraulic conductivity anisotropy of HMA 39
Table 3. Hydraulic conductivity anisotropy of the asphalt specimens tested.
Sample No ID Sample kxx/kzz kyy/kzz kyy/kxx
1 Coarse graded gyratory specimens 9.5C25 2.45 3.64 1.487 19C25 24.75 12.81 0.528 19C50 58.30 76.10 1.309 19C75 28.14 15.71 0.5610 25C25 2.21 1.78 0.8111 25C50 1.38 3.33 2.4212 25C75 3.68 2.10 0.5725 SMA mixures 9.5SMA-A1 6.59 5.58 0.8526 9.5SMA-A2 6.50 8.64 1.3327 9.5SMA-B1 1.53 1.47 0.9628 9.5SMA-B2 12.12 11.99 0.9929 12.5SMA-A1 7.14 6.98 0.9830 12.5SMA-A2 28.16 26.92 0.9631 12.5SMA-B1 6.49 6.04 0.9332 12.5SMA-B2 3.81 2.15 0.5633 19SMA-A1 29.33 54.90 1.8734 19SMA-A2 52.70 81.09 1.5435 19SMA-B1 29.60 32.37 1.0936 19SMA-B2 5.29 7.21 1.36
0.1
1
10
100
0 16 32 48 64 80
n eff
Distance along z–direction (mm)
nzeff–min (a)
10–2
10–1
100
101
102
10–3 10–2 10–1 100 101 102
y = 0.89004x R2 = 0.89k z
z (m
m/s
)
n zeff–min (%)
(d)
0.1
1
10
100
0 21 42 60 84 105
n eff
Distance along x–direction (mm)
nxeff–min
(b)10–1
100
101
102
103
10–1 100 101 102
y = 3.8849x R2= 0.34
k xx
(mm
/s)
n xeff–min (%)
(e)
0.1
1
10
100
0 21 42 63 84 105
n eff
Distance along y–direction (mm)
nyeff–min
(c)10–1
100
101
102
103
10–1 100 101 102
y = 4.6066x R2= 0.44
k yy
(mm
/s)
n yef f–min (%)
(f)
Figure 12. The variation in effective porosities in specimen 25C75 along three different directions: (a) z-, (b) x- and (c) y-directions, and therelationship between the minimum porosity and the hydraulic conductivity in (d) z-, (e) x-, and (f) y-direction.
M. E. Kutay et al.40
directions (i.e. n xeff-min and n y
eff-min) were much lower
(R 2 ¼ 0.34 and R 2 ¼ 0.44 in x- and y-directions,
respectively). This phenomenon was attributed to the
differences in the pore structure variation in different
directions. For instance, figure 12(a) indicates that there
was only one location where the effective porosity was
minimal in the z-direction (at a depth of 50 mm for
specimen 25C75). The constriction point of the flow
channel controlling the hydraulic conductivity in that
direction was most likely located in this zone. Conversely,
the lowest values of effective porosities were present at
two separate locations in x- and y- directions (figure 12(b)
and (c), respectively) (e.g. at 42 and 72 mm in x-direction
and at 39 and 80 mm in y-direction). Therefore, it is
difficult to relate the hydraulic conductivity to a single
variable, such as minimum effective porosity, in x- and
y-directions.
5.4 Relationship between the normal and shearcomponents of the hydraulic conductivity tensor
Physical meaning of the hydraulic conductivity of a
porous medium is that it relates the pore water pressure
gradient to the resulting fluid velocity in the voids. For
example, equation (7) simply implies that kzz (herein
called “normal component” in z-direction) is a ratio of the
average velocity to the applied pressure gradient in z-
direction. Similarly, the “shear components” (i.e. kxz and
kyz) of the hydraulic conductivity tensor in z-direction
relate the pressure gradient in z-direction to the velocities
in the other two directions (figure 2). Three commonly
observed field cases where shear components of the
hydraulic conductivity tensor can be used to calculate the
fluid velocities are presented in figure 13. Case-1
illustrates a pavement laying on a flat surface. In this
case, the flow can be triggered by a rain event creating a
pressure gradient in the z-direction. The velocities in
different directions can easily be computed by using the
three components of the hydraulic conductivity tensor.
Case-2 illustrates a pavement on a slope. In this case, the
pressure gradients are present in two directions and, thus,
six components of the hydraulic conductivity tensor are
required to calculate the fluid velocities. Case-3 illustrates
a pavement on a curvature and going downhill, which may
experience pressure gradients in all three directions. In
this case, all nine components of the hydraulic
conductivity tensor are needed to compute the velocities.
These three cases illustrate the significance of the
components of the hydraulic conductivity tensor to
calculate the fluid velocities in the pore structure of
asphalt pavements.
Figure 14 shows the relationship between the normal
and shear components of the hydraulic conductivity tensor
in three different directions. In all three directions, the
shear components of the hydraulic conductivity are 1–3
orders of magnitude lower than the normal components
(e.g. kxz and kyz vs. kzz for z-direction). A careful
observation indicates that the data in z-direction (figure
14(a)) are closer to the line of equality than the data in
x- and y-directions. This is attributed to the fact that the
presence of smaller constrictions in z-direction (figure
12(a)) diverted the flow towards the other two directions
(i.e. x and y) when a pressure gradient was applied in
that direction (e.g. Case-1 in figure 13) This was further
evident in the observations made for the shear components
of hydraulic conductivity in the x- and y-directions.
0>∇ zP , xP∇ =0 , yP∇ =0
u x = – k xz zP∇ / γ neff
u y = – k yz zP∇ / γ neff
u z = – k zz zP∇ / γ neff
Case–1: Gravity
0>∇ zP , xP∇ >0 , yP∇ =0
ux = – ( k xx xP∇ + k xz zP∇ ) / γ neff
uy = – ( k yx xP∇ + k yz zP∇ ) /γ n eff
uz = – ( k zx xP∇ + k zz zP∇ ) / γ neff
Case–2: Gravity and slope
0>∇ zP , xP∇ > 0 , yP∇ > 0
ux = – ( kxx xP∇ + k xy yP∇ + kxz zP∇ ) / γ neff
uy = – ( kyx xP∇ + k yy yP∇ + kyz zP∇ ) /γ neff
uz = – ( kzx xP∇ + k zy yP∇ + kzz zP∇ ) / γ neff
Case–3: Gravity, slope and curve
ux
uz
u y
uz uy
ux
u x
u z
uy
ux
Figure 13. Three different cases in which the components of the hydraulic conductivity tensor are used in engineering design.
Hydraulic conductivity anisotropy of HMA 41
Figure 14(b) and (c) show that the shear components
pointing in the z-direction (i.e. kzx and kzy) are, in general,
lower than the shear components pointing the other two
directions (i.e. kyx and kxy), indicating that the flow is
prevented in the z-direction and is diverted towards the
other two directions. These results, along with the data
presented in table 3, suggest that the asphalt specimens
exhibited anisotropic hydraulic performance.
6. Summary and conclusions
Understanding fluid flow characteristics of asphalt
pavements is critical in the design and performance
prediction of these structures. The fluid penetrating into
the pores of an asphalt pavement can quickly cause
distresses such as cracks and permanent deformation
due to the damage of the adhesive bond between the
aggregates and the binders. An algorithm was developed
for conducting three-dimensional fluid flow simulations
through the pores of the asphalt pavements using the LB
technique. In a previous study, the accuracy of these
simulations was verified with well known analytical and
theoretical solutions of fluid flow and hydraulic conduc-
tivity of simple geometries. It was shown that the LB
model was able to simulate fluid flow accurately, even at
very low resolutions (low number of lattice sites).
X-ray CT and mathematical morphology-based tech-
niques were used to capture the three-dimensional pore
structure of asphalt specimens prepared using different
materials, aggregate size distribution, and compaction
levels. These pore structures were input into the LB
model, and a very good agreement was observed between
the model predictions and the laboratory measurements of
hydraulic conductivity.
Analysis of hydraulic conductivity tensor revealed that
the horizontal hydraulic conductivities (i.e. kxx and kyy) were
up to two orders of magnitude higher than the vertical
hydraulic conductivity (i.e. kzz) for the asphalt pavements
tested. On the other hand, the hydraulic conductivities in two
horizontal directions (i.e. kxx and kyy) were comparable
within a 50% confidence interval. This phenomenon was
observed for both coarse-graded gyratory specimens and
SMA mixtures. In all three directions, the shear components
of the hydraulic conductivity were 1–3 orders of magnitude
lower than the normal components (e.g. kxz and kyz vs. kzz for
z-direction).
Analysis of X-ray CT images indicated that the pore
pressures and velocities varied nonlinearly along the depth
due to the heterogeneous nature of the asphalt specimens.
The maximum values of pore pressures and velocities
consistently occurred at the constriction zones (within the
zones that minimum effective porosities were located).
The results also indicated that constrictions of flow
channels rather than the average effective porosity of the
entire channel are likely to be responsible for hydraulic
conductivities.
The findings of the research study suggest that caution
should be exercised when interpreting the field and
laboratory measurements of asphalt hydraulic conduc-
tivity. The lack of proper confinement in the current field
test procedures causes inaccurate measurements of the
vertical hydraulic conductivity. In addition, both labora-
tory and field methods do not allow for measuring lateral
hydraulic conductivity, which is needed for accurate
predictions of fluid flow in pavements.
Acknowledgements
The funding for this project was provided by the US Depart-
ment of Transportation-Federal Highway Administration
10–3
10–2
10–1
100
101
102
103
kxzkyz
k zz
Line of equality
z–direction
kyxkzx
k xx
Line of equality
x–direction
10–3 10–2 10–1 100 101 102 103
kxy or kzy (mm/s)
kxz or kyz (mm/s)
k yy
Line of equality
y–direction
kyx or kzx (mm/s)
10–3
10–2
10–1
100
101
102
103
10–3
10–2
10–1
100
101
102
103
10–3 10–2 10–1 100 101 102 103
10–3 10–2 10–1 100 101 102 103
kxykzy
Figure 14. Relations between the normal and shear components of thehydraulic conductivity tensor.
M. E. Kutay et al.42
(FHWA) through contract No. 03-X00-501. This support is
gratefully acknowledged. The opinions expressed in this
paper are solely those of the authors and do not necessarily
reflect the opinions of the FHWA.
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Hydraulic conductivity anisotropy of HMA 43