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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