Parametric Model Study of Microstructure Effects on Damage Behavior of Asphalt Samples

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Parametric Model Study of Microstructure Effects onDamage Behavior of Asphalt SamplesQingli Dai & Martin H. Sadda Department of Mechanical Engineering and Applied Mechanics, University of Rhode Island,02881, Kingston, RI, USAVersion of record first published: 31 Jan 2007.

To cite this article: Qingli Dai & Martin H. Sadd (2004): Parametric Model Study of Microstructure Effects on Damage Behaviorof Asphalt Samples, International Journal of Pavement Engineering, 5:1, 19-30

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Parametric Model Study of Microstructure Effects on DamageBehavior of Asphalt Samples

QINGLI DAI and MARTIN H. SADD*

Department of Mechanical Engineering and Applied Mechanics, University of Rhode Island, Kingston, RI 02881, USA

(Received 23 August 2003; Revised 15 April 2004)

This paper presents a computational modeling study of the microstructural influence on damagebehavior of asphalt materials. Computer generated asphalt samples were created for numericalsimulation in indirect tension and compression testing geometries. Our previously developedmicromechanical finite element model was used in the simulations. This model uses a special purposefinite element that incorporates the mechanical load-carrying response between neighboring aggregates.The element was developed from an approximate elasticity solution of the stress and displacement fieldin a cementation layer between particle pairs. The computational model establishes a network of suchelements to simulate an asphalt mass. Continuum damage mechanics was then incorporated within thisscheme leading to the construction of a micro-damage model capable of predicting typical globalinelastic behavior found in asphalt materials. A series of model asphalt samples have been generatedand simulated with controllable microstructure variation in an effort to determine the effects ofparticular microstructural variables on the material response. These simulations explored therelationship between microstructure parameters and damage behavior of particular asphalt samples.

Keywords: Micromechanical modeling; Microstructure; Asphalt concrete; Finite element method;Damage mechanics

INTRODUCTION

Asphalt concrete is a very complex heterogeneous material

generally containing aggregates, mastic and void space,

and thus the macro load carrying behavior depends on

many micro-phenomena that occur at the aggregate/mastic

level. Experimental and modeling studies focusing on such

micromechanical behavior have attracted considerable

recent attention. Some important micro behaviors are

related to mastic properties including volume percentage,

elastic moduli, inelastic/time-dependent response, aging

hardening, microcracking, and debonding from aggregates.

Other microstructural features include aggregate size,

shape, texture and packing geometry. Because of these

issues it appears that a micromechanical model would be

best suited to properly simulate such a material.

Furthermore, micromechanics offers the possibility to

more accurately predict asphalt failure and to relate such

behavior to particular mix parameters such as mastic

properties, aggregate gradation, and sample compaction.

Recently, many studies have been investigating

the micromechanical behavior of particulate, porous

and heterogeneous materials. For example, studies on

cemented particulate materials by Dvorkin et al. (1994)

and Zhu et al. (1996) provided information on the normal

and tangential load transfer between cemented particles.

Applications of such contact-based micromechanical

analysis for asphalt concrete behavior have been reported

by Chang and Gao (1997), Cheung et al. (1999) and Zhu

and Nodes (2000).

Numerical modeling of cemented particulate materials

has generally used both finite (FEM) and discrete (DEM)

element methods. DEM studies on cemented particulate

materials include the work by Rothenburg et al. (1992),

Chang and Meegoda (1993), Trent and Margolin (1994),

Buttlar and You (2001), Ullidtz (2001) and Sadd and Gao

(1998). In regard to finite element modeling, Sepehr et al.

(1994) used an idealized finite element microstructural

model to analyze the behavior of an asphalt pavement

layer. Soares et al. (2003) used cohesive zone elements to

develop micromechanical fracture model of asphalt

materials. A particular finite element approach to simulate

particulate materials has used an equivalent lattice

network system to represent the interparticle load transfer

ISSN 1029-8436 print/ISSN 1477-268X online q 2004 Taylor & Francis Ltd

DOI: 10.1080/10298430410001720783

*Corresponding author. E-mail: [email protected]

The International Journal of Pavement Engineering, Vol. 5 (1) March 2004, pp. 19–30

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behavior. Guddati et al. (2002) recently presented a

random truss lattice model to simulate microdamage in

asphalt concrete and demonstrated some interesting

failure patterns in an indirect tension test geometry.

Bahia et al. (1999) have also used finite elements to model

the aggregate-mastic response of asphalt materials.

Mustoe and Griffiths (1998) developed a finite element

model, which was equivalent to a particular discrete

element approach.

Damage mechanics provides a viable framework for the

description of asphalt stiffness degradation, microcrack

initiation, growth and coalescence, and damage-induced

anisotropy. Continuum damage mechanics is based on the

thermodynamics of irreversible processes to characterize

elastic-coupled damage behaviors. Chaboche (1988),

Simon and Ju (1987) developed strain- and stress-based

anisotropic continuum damage models, and Kachanov

(1987) proposed a microcrack-related continuum damage

model for brittle materials. These models focus on the

relation between damage and effective elastic properties.

With respect to asphalt materials, Ju et al. (1989) proposed

an elastic continuum damage model for cement mastic,

and Lee et al. (1998) developed a viscoelastic constitutive

model to study the rate-dependent damage growth and

damage healing behaviors. Recently, Wu and Harvey

(2003) used a 3D damage coupled viscoelastic model to

simulate cracking initiation and propagation in asphalt

concrete. In related work, Sangpetngam et al. (2003)

presented a displacement discontinuity boundary element

approach for the cracking behavior study of asphalt

mixtures. Gibson et al. (2003a,b) presented a compre-

hensive viscoplastic, viscoelastic and damage modeling of

asphalt concrete in uniaxial unconfined compression and

triaxial confined compression.

For many years, asphalt aggregate properties and mix

parameters have been characterized in order to determine

their effects on the mixture performance. Recent studies in

this area have focused on many details concerning

aggregate geometry. For example, Buchanan (2000)

investigated the effect of flat and elongated particles on

the performance of hot mix asphalt mixtures. Masad et al.

(2001) pointed out that aggregate texture of fine particles

had the strongest correlation with mixture performance

among different aggregate shape properties, while

Fletcher (2002) showed a similar strong relationship

between the texture of coarse aggregates and material

performance. Wang et al. (2003) recently used Fourier

morphology analysis from aggregate profiles to evaluate

the aggregate characteristics. New concepts of aggregate

blending for asphalt mix design were presented by Vavrik

et al. (2002), and this method utilizes aggregate interlock

and aggregate packing to meet volumetric criteria and

provide adequate compaction characteristics. To under-

stand asphalt mastic behavior, Buttlar et al. (1999)

provided several micromechanical models of particulate

composite to conduct numerical analyses.

This paper extends applications of our previous micro-

mechanical finite element asphalt model to investigate

the behavior of several idealized samples with

systematic variation in microstructural properties.

Our model incorporates an equivalent lattice network

approach whereby the local interaction between neighboring

particles is modeled with a special frame-type finite element.

The element stiffness matrix is first constructed by using an

approximate elasticity solution within the interparticle

cementation between particle pairs. Inelastic mastic damage

behaviors are then simulated by incorporating a continuum

damage mechanics theory within the FEM model. Details of

the model development and preliminary applications can be

found in earlier papers (Sadd and Dai, (2001) and Sadd et al.,

2004a,b). The present work is to investigate the micro-

structural influence on the damage behavior of numerically

generated idealized asphalt samples. Typical asphalt

microstructural parameters include aggregate orientation,

shape and gradation, packing fabric and mix percentage.

A series of model asphalt samples have been generated and

simulated with controllable microstructure variation in an

effort to determine the effects of particular microstructural

variables on the material response. Numerical simulations

were conducted on both indirect tension and compression

samples. This study provides a better understanding of how

microstructure affects the behavior of such asphalt samples.

MICROMECHANICAL FINITE ELEMENT

MODEL

Asphalt concrete is a heterogeneous cemented particulate

material composed of aggregates, mastic cement and air

voids. The load carrying behavior of such a material is

strongly related to the local load transfer through the

effective asphalt mastic zone between aggregate particles,

and this is taken as the microstructural response. For

modeling purposes, aggregates are identified by particles

with size approximately greater than 2 mm, while finer

material is taken to be mixed with the asphalt, and

modeled as the composite mastic. In general, asphalt

concrete contains aggregate of very irregular geometry as

shown in Fig. 1(a). Our approach is to allow variable size

and shape using an idealized elliptical aggregate model as

represented in Fig. 1(b). The finite element model then

uses an equivalent lattice network approach, whereby the

interparticle load transfer is simulated by a network of

specially created frame-type finite elements connected at

particle centers as shown in Fig. 1(c). From granular

materials research, the material microstructure or fabric

can be characterized to some extent by the distribution of

branch vectors which are the line segments drawn from

adjacent particle mass centers. The effective mastic area is

defined as a strip of cementation material parallel to the

branch vector and the proposed finite element network

coincides with the branch vector distribution. For each

particle pair, the mastic element is placed based on the

branch vector length and the two particle sizes.

This micro-frame element stiffness matrix is

constructed by considering the normal, tangential

Q. DAI AND M.H. SADD20

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and rotation behaviors between cemented particles (shown

in Fig. 2), and this is accomplished by using an

approximate elasticity solution from Dvorkin et al.

(1994) for the stress distribution within the cementation

domain. Details of the calculation of various stiffness

terms have been reported previously by Sadd and Dai

(2001), and the final result is given by

where Knn ¼ ðlþ 2mÞw=�h; K tt ¼ mw=�h; l and m are the

usual elastic moduli, and mastic element geometry sizes

include the average cementation thickness �h and

cementation width w as shown in Fig. 2. For a given

particle pair, the mastic width w ¼ w1 þ w2; is normally

taken to be a percentage of the smaller particle’s radial

dimension. Our model allows arbitrary nonsymmetric

cementation, thus in general w1 – w2 – w=2; and an

eccentricity variable can be defined by e ¼ ðw2 2 w1Þ=2:And r1 and r2 are the radial dimensions from each

aggregate center to the cementation boundary (see Fig. 2).

In general, since the mastic geometry varies for each

neighboring particle pair, each mastic element stiffness

matrix will be different. This procedure establishes the

elastic stiffness matrix, and it is clearly a function of the

micro mechanical material variables including particle

measures, cementation geometry and mastic moduli. This

theoretical formulation has been implemented into the

commercial ABAQUS FEA code using user-defined

elements. The commercial code will perform all necessary

calculations for FEM analysis and will provide particular

post-processing.

DAMAGE MECHANICS MODEL

To simulate the inelastic damage behaviors observed in

asphalt materials, continuum damage mechanics was

incorporated within the inter-particle cementation model.

The approach by Ishikawa et al. (1986) was used for our

finite element model. Damage was connected with the

internal micro-cracks within the matrix cement and

around the aggregates, and these defects will reduce the

effective area of the load transfer. Inelastic and softening

behavior is thus developed by the growth of damage

within the material with increasing loading. The damage

stiffness matrix [Ds] can be expressed in terms of the

initial elastic stiffness matrix [D0] using continuum

damage principles

Ds½ � ¼ ½I�2 ½V�ð Þ D0½ � ð2Þ

and a damage tensor [V] is defined by considering the

reduction of the effective area of load transfer within the

continuum. For the uniaxial inelastic response, the specific

FIGURE 1 Asphalt modeling concept

FIGURE 2 Cementation between two adjacent particles

½K� ¼

Knn 0 Knne 2Knn 0 2Knne

· K tt K ttr1 0 2K tt K ttr2

· · K ttr21 þ

Knn

3w2

2 2 w1w2 þ w21

� �2Knne 2K ttr1 K ttr1r2 2

Knn

3w2

2 2 w1w2 þ w21

� �

· · · Knn 0 Knne

· · · · K tt 2K ttr2

· · · · · K ttr22 þ

Knn

3w2

2 2 w1w2 þ w21

� �

2666666666664

3777777777775

; ð1Þ

PARAMETRIC MODEL STUDY OF ASPHALT SAMPLES 21

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constitutive relation is taken as

s ¼ s0 1 2 e2bð1=10Þ

)›s

›1¼ D0e2bð1=10Þ; ð3Þ

where the material parameters 10 and b are related to the

softening strain and damage evolution rate respectively,

s0 is the material strength, and D0 ¼ s0b=10 is the initial

elastic stiffness. Using the damage stiffness definition (2)

with the exponential damage evolution law (3), the

incremental inelastic stiffness Ds and the damage scalar V

become

Ds ¼ ð1 2VÞD0 ¼ D0e2bð1=10Þ; where

V ¼ 1 2 e2bð1=10Þ:ð4Þ

After critical strength, the softening behavior is taken as

s ¼ s0 1 2 e2b� �

emð121=10Þ )›s

›1

¼ 2D0m

b1 2 e2b� �

emð121=10Þ; ð5Þ

where m is a material parameter related to the softening

rate. The corresponding incremental softening stiffness Ds

and the damage scalar V then becomes

Ds ¼ ð1 2VÞD0 ¼ 2D0m

b1 2 e2b� �

emð121=10Þ;

where V ¼ 1 þm

b1 2 e2b� �

emð121=10Þ

ð6Þ

The uniaxial stress–strain response corresponding to

this particular constitutive model is shown in Fig. 3 for the

case of 10 ¼ 0:2; b ¼ 5 and m ¼ 1:This damage modeling scheme was incorporated into

the finite element network model by modifying the micro-

frame element stiffness matrix given in Eq. (1). Using

the uniaxial relation (4), the incremental normal

and tangential inelastic stiffness terms for the inelastic

behavior can be written as

ðKnnÞs ¼ Knne2bðDun=DUnÞ; ðK ttÞs ¼ K tte2bðDut=DUtÞ ð7Þ

and using Eq. (6) the corresponding incremental normal

and tangential softening stiffnesses are given by

Knnð Þs ¼ 2 Knnm=b� �

1 2 e2b� �

emð12Dun=DUnÞ

K ttð Þs ¼ 2 K ttm=b� �

1 2 e2b� �

emð12Dut=DUtÞ ;

ð8Þ

where Dun and Dut are the normal and tangential

accumulated relative displacements and DUn and DUt

are the normal and tangential displacement softening

criteria. Thus the micro-frame element incremental

damage stiffness matrix [Ks] is constructed from Eq. (1)

by replacing Knn and Ktt with (Knn)s and (Ktt)s.

The initiation of mastic softening behavior for tension,

compression and shear is governed by softening criteria

based on accumulated relative displacements between

particle pairs

DUðtÞn ¼ cnt

�h

DUðcÞn ¼ cnc

�h

DUt ¼ cttw;

ð9Þ

where cnt, cnc, ctt represent tension, compression and shear

softening factors, DUðtÞn ; DUðcÞ

n and DUt are the tension,

compression and shear displacement softening criteria,�h and w are the mastic element average thickness and

width. These criteria correspond to the average mastic

critical strength sc. Further damage behavior could

include evolving microcracking leading to a separation

or debonding between aggregate pairs. In order to

simulate such total failure, elements were given a mastic

failure criterion for tension, compression or shear based on

the average failure strength sf

sf ¼ cfsc; ð10Þ

where cf is a failure factor related to the average failure

strength in each behavior, and sc indicates the average

critical strength in the corresponding behavior. The failure

criteria for the uniaxial behavior is also shown in Fig. 3

with the case of cf ¼ 0:03: The failed elements still

remain in the computation model, but their stiffnesses are

very small and they carry very little load.

MICROSTRUCTURE PARAMETERS

This study is concerned with the relationship between

microstructure parameters and damage behavior of

particular asphalt material. The microstructure parameters

of asphalt concrete can be categorized by: usual mix

percentages; particle/aggregate measures; and packingFIGURE 3 Uniaxial stress–strain response for damage model


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fabric descriptions. Mix parameters commonly include

particle gradation (aggregate weight percent passing

different sieving sizes), and mastic and additive percentage.

After material processing, these lead to sample porosity

(air void percentage) and volume particle percentage.

Particle measures include the particle orientation, shape,

and size. Particle orientation is commonly represented

by an angular measure (with respect to a reference

direction) of the particle’s longest axis. Particle shape ratio

(aspect ratio) is defined as the ratio of the longest axis

dimension to the shortest axis dimension. Particle size is the

longest axis dimension. Packing fabric can be categorized

as the branch vector distribution and particle gradation.

As mentioned previously, branch vectors lie between

adjacent particle mass centers and their orientations

coincide with the micro-frame element directions.

Figure 4 illustrates particle orientation and branch vectors

for a model sample of cemented particulate material. In

order to quantify the distributions of these vectors for an

entire sample, an angular distribution plot (Rose diagram)

is normally constructed. Such a plot indicates the frequency

of the vector lying in a particular direction as a function of

angular measure. These will be used to correlate various

numerically generated asphalt samples for finite element

simulation. It should be noted that changes in particle

measures and particle packing would change the mastic

geometry such as mastic average thickness and width. Thus

many microstructural fabric measures are inter-related and

cannot be changed independently.

MICROSTRUCTURE EFFECTS ON SAMPLEDAMAGE BEHAVIOR

Microstructure effects were investigated through finite

element simulation of a series of model asphalt samples.

Using a specially developed MATLAB code, samples were

generated with controllable microstructure variation in an

effort to determine the effect of a particular microstructural

variable on the material response and damage evolution.

A series of the finite element simulations were conducted on

indirect tension and compression samples. Displacement

controlled boundary conditions were used and two different

sets of model parameters were incorporated in these

simulations. For the indirect tension modeling, model

boundary conditions constrain both horizontal and vertical

displacements of the bottom pair of aggregates, while

the top particle pair accept the applied vertical dis-

placement loading. The model parameters were chosen as

E ¼ 75 MPa; v ¼ 0:3; b ¼ 1:0; m ¼ 1:0; with softening

factors cnc ¼ 0:1; cnt ¼ 0:04; ctt ¼ 0:1 and failure factor

cf ¼ 0:02: For the compression simulations, the x- and

y-displacements of the particles on the bottom layer and the

x-displacements of the particles on the top layer were

constrained. The y-displacement loading was incrementally

imposed on particles of the top layer while particles on each

side had free boundary conditions. The model parameters

were E ¼ 75 MPa; v ¼ 0:3; b ¼ 1:0; m ¼ 1:0; softening

factors cnc ¼ 0:05; cnt ¼ 0:01; ctt ¼ 0:03; and a failure

factor cf ¼ 0:02: Binder characterization tests were

conducted by using a specially prepared specimen composed

of only asphalt binder and fine aggregates, model elastic

constants were calibrated with these compression test data.

Other simulation parameters were chosen to demonstrate

particular microstructure effects on the model damage

behavior.

Aggregate Orientation

In order to investigate the effect of particle orientation on

damage behavior, three indirect tension models were

generated, as shown in Fig. 5. Each model is shown along

FIGURE 4 Vector microstructure measures in particulate materials.


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with its orientation vector diagram and element thickness

frequency distribution plot. It is observed that model A-1

has vertical-dominant particle orientation distribution,

model A-2 has a uniformly distributed orientation

and model A-3 has horizontal-dominant orientation. Each

model had the same number of particles (181) and elements

(574), and had identical particle locations, size, shape, and

mix percentages. Distributions of elements in compression

vs. element average thickness �h are also shown in Fig. 5.

It was calculated that model A-1 has 269 elements with

thickness (2 mm or less), model A-2 had 260 such elements

and model A-3 had 253 elements. Based on the micro-

frame element stiffness formulation (1), lower mastic

thickness will lead to higher element stiffness.

Damage simulations were conducted on these

three samples using identical model parameters, and the

overall force-displacement responses under incremental

displacement loading are shown in Fig. 6. These simulation

results indicate that initial sample stiffness correlates with

the element thickness distributions and thus model A-1

stiffness is greater than model A-2 which is greater than

model A-3. During the incremental loading, all elements

FIGURE 5 Indirect tension models for different particle orientation

FIGURE 6 Indirect tension damage simulations with different particleorientation


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within the model were monitored for softening behavior.

When the imposed sample vertical displacement reaches

4 mm, model A-1 had 238 softening elements, model A-2

had 242 softening elements and model A-3 had 250 such

elements. More softening elements will lead to more

extensive damage behavior, and the softening behaviors in

Fig. 6 correlate with this concept. Additional particle

orientation studies were also conducted on two-dimensional

compression specimens. These investigations also indicate

that samples with vertical-dominant particle orientation had

the highest initial model stiffness and generated the lowest

overall softening or damage. Referring to Fig. 6, it should be

noted that these differences among model samples A-1, A-2

and A-3 are all small.

Aggregate Shape (Aspect Ratio)

The effect of the aggregate aspect ratio on the damage

simulation results were investigated with three

compression samples as shown in Fig. 7. The three

samples (B-1, B-2, B-3) were generated with particle

aspect ratios of 1.0, 1.25 and 1.5. These model

samples had the same number of particles (142)

and elements (447), and had identical particle

location, particle orientation (p/4) and particle area

percentage (63.2%). All samples had zero porosity.

Element distributions vs. element average thickness �h

for these three samples are shown in Fig. 7, and these

figures indicate that the average mastic thickness

deceases with an increase of aggregate aspect ratio.

Again based on the micro-frame element stiffness

formulation (1), lower mastic thickness will lead to

higher element stiffness. Thus the overall simulation

response of load vs. sample deformation gives the

expected prediction that initial model stiffnesses are

ranked as model B-3 . model B-2 . model B-1.

These results would support the statement that with

the same aggregate percentage and packing geometry,

FIGURE 7 Compression damage simulation with different particle aspect ratio


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the model composed of larger aspect ratio aggregates

would have higher stiffness.

Aggregate Percentage

The previous case had three compression samples of

different particle aspect ratio, but with the same particle

area percentage. We now wish to study the case where

the aggregate percentage will also be allowed to vary.

Three compression samples (C-1, C-2, C-3) shown in

Fig. 8, were generated with particle aspect ratios of 1.0,

1.25 and 1.5, and particle percentages of 63.2%, 70% and

73.8%, respectively. The other microstructural model

parameters were the same as in the previous aggregate

aspect ratio study.

As before, simulations were conducted with incre-

mental compression displacement loading, and each

element was monitored for softening and failure behavior.

Results of softening elements are indicated with black

lines and failure elements are artificially removed as

shown in Fig. 8 for the case of an imposed displacement of

3 mm. At this stage in the loading history, model C-1 had a

total of 335 softening elements including 106 failed

elements, model C-2 had a total of 325 softening elements

including 85 failed elements and model C-3 had 310

softening elements with 66 failed elements. Again, more

softening elements will lead to more extensive damage

behavior and will result in lower load carrying ability of

the sample as seen in Fig. 8. The three overall load-

deformation results in Fig. 8 also show a slightly larger

FIGURE 8 Compression damage simulation with different particle aspect ratio and particle percentage


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difference when compared to the corresponding results

from Fig. 7. This occurs because both the aggregate aspect

ratio and aggregate percentage are being increased in

Fig. 8, while only the aspect ratio was changed in Fig. 7.

Model Porosity

Porosity is another important factor that affects the

behavior of asphalt material. Figure 9 illustrates three

indirect tension simulations on models with porosities of

1.1%, 4.6%, 6.7%. These numerical models had identical

aggregate location, size, shape, orientation and percen-

tage, and all samples had the same branch vector

distribution as shown in the figure. The model porosity

was ideally modified by only changing the mastic width w.

Simulation results indicated that lower porosity models

had higher initial stiffness and larger load carrying

capacity. Similar porosity studies were also conducted

on compression samples shown in Fig. 10. Three com-

pression models were generated with porosities of 0%,

3.1%, 6.3% by changing the mastic width. Again the other

micro-parameters are identical including the branch vector

distribution as shown. The overall load-deformation

behaviors of these samples also indicated that lower

porosity resulted in stiffer model behavior with higher

load carrying capacity.

Aggregate Gradation

In order to investigate the effect of aggregate gradation,

pairs of numerical models were generated with variation in

the smaller-sized particles. Figure 11 illustrates two such

compression models that contain different percentages of

FIGURE 9 Indirect tension simulations with different model porosity

FIGURE 10 Compression simulations with different model porosity

FIGURE 11 Compression simulations with added fine aggregates


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the finer material. Model F-1 has been generated using a

mix of four different particle size groupings (2, 4, 7 and

9 mm), while model F-2 was created from F-1 by adding

additional fine aggregates of 1 mm size. The gradation

curves for each model are shown in Fig. 11 and are

compared with typical gradations of some actual asphalt

concrete. Adding aggregates to create model F-2 led to an

increase in the number of model elements from 628 to 855

and the particle percentage increased slightly from 60.2%

to 61.8%. The other micro-parameters are identical in

these two models. The overall load-deformation behavior

of these two models indicates that model F-2 had higher

initial stiffness and greater load carrying capacity.

Two indirect tension models were also generated

for studying the effect of gradation modification

through the addition of fine aggregates. The two models

G-1 and G-2 shown in Fig. 12, were created from

five different particle size groupings: 2, 4, 7, 11 and

14 mm. Model G-1 was composed of a mix of 96 particles

from these sizes groupings, and this resulted in a model

with 292 finite elements and a particle percentage of

57.6%. Model G-2 included additional small aggregates of

2 and 4 mm size leading to 181 total particles, 448

finite elements and a particle percentage of 64.1%.

The gradation curves for each of the models are shown

in Fig. 12 and are again compared with actual material.

As before, all other micro-parameters are identical in the

two models. The overall load-deformation behavior of

these numerical samples again illustrates that the added

small aggregates increase the model stiffness and load

carrying capacity.

Evolving Aggregate Orientation

During typical loading processes many of the previously

defined microstructural parameters will change with

developing deformation. In order to investigate this

behavior, aggregate orientation was monitored at various

loading steps in a finite element simulation of a

compression model shown in Fig. 13. The model was

generated from an actual asphalt sample using an image

analysis procedure discussed in a previous study Dai et al.

(2004). The numerical sample had porosity of 1.5%,

aggregate percentage of 64.5%, and displacement

boundary conditions identical to the previous compression

models. The model parameters were the same as used

in the other compression simulations except m ¼ 0:04;cnc ¼ 0:04; cnt ¼ 0:02; ctt ¼ 0:01: Figure 13 illustrates the

evolving aggregate orientation vector diagrams in

the original configuration and at two different loading

steps of 1.5 and 3 mm. The overall load-deformation is

also shown. The evolving aggregate orientation results

indicate a slight decrease in the number of particles with

vertical-dominant long-axis orientation. Thus as expected

the vertical loading will compress the asphalt mass and

rotate aggregates to position the long-axis away from the

loading direction.

CONCLUSIONS

A micromechanical model has been used to simulate the

two-dimensional behavior of asphalt concrete samples

through the elastic, inelastic and failure loading range.

The aggregate-binder microstructure was simulated with

an equivalent finite element network that represented the

load-carrying behavior between adjacent aggregates in the

multiphase material. These network elements were

specially developed from an elasticity solution for

cemented particulates. Incorporating a damage mechanics

approach with this solution allowed the development of a

softening model capable of predicting typical global

inelastic and failure behaviors found in asphalt materials.

Particular microstructure parameters of asphalt

materials were identified and categorized for numerical

analysis. A series of model indirect tension and

compression samples were then generated with systematic

FIGURE 12 Indirect tension simulations with added small aggregates


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variation of particular microstructures. Test simulations

were conducted on these samples to determine the effect

of particular microstructural parameters on the material

response and damage evolution. These results provided

comparisons of the effects of microstructure on the overall

macro-response of the asphalt samples.

Numerical experiments included investigations on

aggregate orientation, shape, percentage and gradation,

and sample porosity. Aggregate orientation studies

on indirect tension samples indicated only slight variation

in the overall sample deformation behavior. Models with

higher aggregate shape aspect ratio and aggregate

percentage showed higher initial stiffness and larger

overall load carrying capacity. Porosity studies on both

indirect tension and compression samples indicated that

specimens with lower porosity resulted in higher load

carrying behavior. Simulation investigations on aggregate

gradation showed that indirect tension and compression

samples had higher initial stiffness and load carrying

behavior with added small or fine aggregates.

A compression simulation illustrated evolving aggregate

orientation during loading, and results showed a tendency

for the long-axis to move away from the loading direction.

In particular applications, some of the microstructural

measures are inter-related. For example, particle orienta-

tion and branch vector distributions are certainly related to

the compaction history of a sample or roadway. Such

dependencies, when combined with the difficulty in

FIGURE 13 Compression sample deformation and particle orientation distribution during different loading steps


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controlling the numerous microstructural parameters,

create a challenging task to establish an appropriate

numerical simulation study. The current two-dimensional

model is limited to the assumption of uniform

behavior through the thickness of the sample. Clearly

this assumption is not completely accurate and a three

dimensional extension of the model is underway.

Acknowledgements

The authors would like to acknowledge support from the

Transportation Center at the University of Rhode Island

under Grants 01-64 and 02-86, and to Cardi Construction

Corporation.

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Documents

Parametric Model Study of Microstructure Effects on Damage Behavior of Asphalt Samples