Kim-2006.pdf

KSCE Journal of Civil Engineering

Vol. 10, No. 2 / March 2006

pp. 97~104

Highway Engineering

Vol. 10, No. 2 / March 2006 97

Viscoelastic Continuum Damage Finite Element Modeling of

Asphalt Pavements for Fatigue Cracking Evaluation

By Sungho Mun*, Murthy N. Guddati**, and Y. Richard Kim***

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Abstract

This paper documents the findings from the study of fatigue cracking mechanisms in asphalt pavements using the finite elementprogram (VECD-FEP++) that employs the viscoelastic continuum damage model for the asphalt layer and a nonlinear elastic modelfor unbound layers. Both bottom-up and top-down cracks are investigated by taking several important variables into account, such asasphalt layer thickness, layer stiffness, pressure distribution under loading, and load level applied on the pavement surface. Thecracking mechanisms in various pavement structures under different loading conditions are studied by monitoring a damage contour.Preferred conditions for top-down cracking were identified using the results from this parametric study. The conjoined damagecontours in thicker pavements suggest that the through-the-thickness crack may develop as the bottom-up and top-down crackspropagate simultaneously and coalesce together, supporting observations from field cores and raising the question of the validity oftraditional fatigue performance models that account for the growth of the bottom-up cracking only.

Keywords: viscoelasticity, Continuum damage, finite element modeling, asphalt fatigue cracking

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1. Introduction

A traditional approach to dealing with fatigue cracking in

asphalt pavements is based on the assumption that cracks initiate

at the bottom of the asphalt layer due to tensile stresses

developed from the flexure of the layer and propagate to the

pavement surface under repeated load applications (so-called

bottom-up cracking). However, recent field studies also suggest

that fatigue cracks can also initiate at the pavement surface and

propagate downward under traffic (so-called top-down cracking).

Myers et al. (2001) used linear elastic finite element analysis to

conclude that the major cause of top-down cracking is due to

tensile stresses resulting from the interaction between truck tires

and the pavement surface.

In order to accurately determine the initiation location and

cause of the fatigue cracking, it is imperative to use realistic

constitutive models for different pavement layers because the

cracking behavior of asphalt concrete is closely associated with

the stress-strain response of the material. In recent years, there

has been some success in developing a mechanistic constitutive

model of asphalt concrete. A series of experimental/analytical

studies by Kim et al. (1997), Daniel and Kim (2002), and

Chehab et al. (2002) has resulted in the viscoelastic continuum

damage (VECD) model that is based on the elastic-viscoelastic

correspondence principle using pseudo strain, continuum damage

mechanics, and time-temperature superposition principle with

growing damage. To take full advantage of this model’s strength,

the VECD model is implemented into the finite element code,

FEP++, developed by Guddati (2001). For aggregate base and

subgrade, the nonlinear stress-state dependent model is used.

The resulting VECD-FEP++ program is used in this study to

investigate the top-down and bottom-up cracking mechanisms in

various combinations of pavement structures, layer stiffnesses,

and loading conditions.

2. Viscoelastic Continuum Damage Model

Kim et al. (1997) developed a uniaxial viscoelastic continuum

damage model by applying the elastic-viscoelastic correspondence

principle based on pseudo strain to separate out the effects of

viscoelasticity and then employing internal state variables based

on the work potential theory to account for the damage evolution

under cyclic loading and the microdamage healing during rest

periods. From the verification study, it was found that the

constitutive model has the ability to accurately predict the stress-

strain behavior of asphalt concrete under varying loading rates,

random rest durations, multiple stress/strain levels, and different

modes of loading (controlled-stress versus controlled-strain). A

continued effort in refining this model resulted in the work by

Daniel and Kim (2002) in which a unique damage characteristic

curve between the normalized pseudo stiffness (C) and the

damage parameter (S) was discovered regardless of the applied

loading conditions (cyclic versus monotonic, amplitude/rate, and

frequency). This characteristic curve describes the reduction in

material integrity (C) as damage (S) grows in the asphalt concrete

specimen. In addition, Chehab et al. (2002) demonstrated that

*Member, Senior Researcher, HTTI, Korea Highway Corporation, Korea (Corresponding Author, E-mail: [email protected])

**Assistant Professor, Campus Box 7908, Department of Civil, Construction & Environmental Engineering, North Carolina State University, Raleigh, NC,

U.S.A. (E-mail: [email protected])

***Professor, Campus Box 7908, Department of Civil, Construction & Environmental Engineering, North Carolina State University, Raleigh, NC, U.S.A.

(E-mail: [email protected])

Sungho Mun, Murthy N. Guddati, and Y. Richard Kim

98 KSCE Journal of Civil Engineering

the time-temperature superposition principle is valid not only in

the linear viscoelastic state, but also with growing damage. This

finding allows the prediction of mixture responses at various

temperatures from laboratory testing at a single temperature. The

damage characteristic curve and the time-temperature super-

position principle with growing damage are the foundations of

the VECD model employed in this study.

The major contribution of the VECD model is the significant

reduction in testing requirements for the determination of input

parameters. The model allows the prediction of the material’s

behavior at any temperature from a test result obtained from a

single temperature and the time-temperature shift factors

obtained from temperature sweep complex modulus tests, as

long as the viscoplastic response is minimal in the stress-strain

behavior (i.e., low to intermediate temperature and intermediate

to fast loading rates). That is, one can perform a simple strength

test at a single temperature and dynamic modulus tests at

multiple temperatures and predict the cyclic fatigue life of the

mix under different testing conditions (i.e., load amplitudes and

frequencies, loading time, and temperatures).

More detailed descriptions of the VECD model can be found

in (Kim et al., 1997, Daniel and Kim, 2002, and Mun, 2003). The

finite element implementation of the VECD model was verified

using the uniaxial tension test results (Mun, 2003).

3. Structures, Material Properties, and LoadingConditions

In this study, the VECD-FEP++ program is used to investigate

the effects of asphalt layer thickness, layer stiffness, contact

pressure distribution, and load level on the stresses and fatigue

cracking mechanisms in aggregate base pavements. Combinations

of these variables are selected so that the effects of individual

variables on stress and damage states can be evaluated separately

and effectively. Values selected for each variable are summarized

in Table 1.

Only one base thickness of 50 cm and infinite subgrade was

selected for this study. The Prony series constants and a damage

function, shown in Table 1, were obtained from the experimental

study by Chehab et al. (2002) in which the Maryland Superpave

12.5 mm mix was tested in uniaxial tension. The base and

subgrade material parameters of the nonlinear universal model

Table 1. Layer thicknesses and properties selected in this study

Pavement Layer Thickness (cm)(Poisson’s Ratio)

Material Parameter**

Asphalt Concrete7.6, 17.8, 30.5

(0.30)

AC I AC II

Relaxation Time,

m

Prony Coefficients,Em (kPa)

Relaxation Time,

m

Prony Coefficients,Em (kPa)

0.02 4908141.9 0.02 1258989.3

0.2 5735749.4 0.2 2214693.3

2 4955029.9 2 3621321.1

20 2956638.2 20 5136030.7

200 1261172.2 200 5729228.2

2000 446992.8 2000 4459729.9

20000 157584.1 20000 2317303.2

E : 58269.0 kPa E : 155243.0 kPa

Damage Function:

Base50

(0.35)

Type k1 k2 k3

Stiff 5764.0 0.420 -0.240

Weak 354.0 0.484 -0.403

SubgradeInfinite(0.40)

Type k1 k2

Stiff 474.0 -0.366

Weak 771.0 -0.169

Type k1 k2

Combination Type of Base Type of Subgrade

Modulus SS Stiff Stiff

Modulus SW Stiff Weak

Modulus WS Weak Stiff

Modulus WW Weak Weak

**

where E , m, and Em are infinite relaxation modulus, relaxation time, and Prony coefficients, respectively.

E t E Em

m 1=

M

exp t– m+=

Viscoelastic Continuum Damage Finite Element Modeling of Asphalt Pavements for Fatigue Cracking Evaluation

Vol. 10, No. 2 / March 2006 99

that were used are found in Santha (1994) and Garg et al. (1998).

A moving load was represented by the haversine load with

peak magnitudes of 20 and 40 kN. A loading duration of 0.03 sec

and a rest period of 0.97 sec were selected. For a tire-pavement

contact pressure distribution on the pavement surface, both

uniform and nonuniform contact pressure distributions were

studied. The uniform contact pressure has been used most widely

for pavement response evaluation. However, recent studies

(Sebaaly and Tabatabaee, 1993, Groenendijk et al., 1997, and

Miradi et al., 1997) have revealed that the contact pressure is

nonuniform and that the effect of the nonuniform distribution of

the contact pressure is crucial in actual pavement response

computation. For the nonuniform tire pressure, the tire pressure

measured by Sebaaly (1992) and Siddharthan et al. (2002) was

selected for this study.

4. Investigation of Macrocrack Initiation Mecha-nisms

The research performed in this study focuses on investigating

the fatigue failure mechanism(s) of top-down and bottom-up

cracking modes by monitoring the state of stresses and structural

damage. One unique feature of the VECD-FEP++ program is its

ability to determine the amount of damage in the asphalt layer as

the number of loading cycles increases. The amount of damage

is represented by a damage parameter calculated from the VECD

model.

This feature of the VECD-FEP++ program is quite different

from typical finite element analysis based on fracture mechanics,

such as the studies done by Jenq et al. (1991, 1993) and Myers et

al. (2001). In their studies, an artificial crack was introduced

before the load was applied and critical stresses that contribute

most to the macrocrack propagation were identified. In this

study, the approach allows the investigation of the location and

mechanisms of microcracks without any initialized artificial

cracks in the pavement structure.

The pavement structure is modeled by an axisymmetric finite

element model. Fig. 1(a) shows radial stress-strain curves at the

bottom of the asphalt concrete layer under nonuniform contact

pressure in the cyclic mode. The hysteresis loops shifted to the

right side, demonstrating the increase of radial strain in tension

as the damage in the asphalt layer increases. Fig. 1(b) presents

Fig. 1. VECD-FEP++ Analysis of a Pavement with Thick Asphalt Layer Thickness: (a) Cyclic Hysteresis Behavior; (b) Damage Contours

at Different Cycles



the damage contours at different numbers of cycles. It is noted

that the intensity of damage increases as the number of cycles

increases.

In Fig. 1(b), significant damage is found at the pavement

surface near the load center where the compressive stress is the

greatest. In the current formulation of the VECD-FEP++

program, the damage parameter is calculated from the absolute

value of stresses. Therefore, the damage observed at the

pavement surface around the load center is the damage

computed from the compressive stress and, therefore, should be

ignored as an error. This error can be corrected by assigning the

damage value of zero when the stress is in compression.

It was found that the comparison of stress and damage

contours at the peak load of the 1,000th cycle yields similar

conclusions to those made from longer cycles. For this paper,

therefore, stress and damage contours at the peak load of the

1,000th cycle are used for comparison. Fig. 2 to Fig. 6 show the

contours of damage and stresses for all the pavement structures

and loading conditions selected in this study. Fig. 2 to Fig. 5 were

generated using the soft asphalt stiffness (i.e., AC I) only, and the

effect of asphalt layer stiffness is shown in Fig. 6.

4.1. Effect of Asphalt Layer Thicknesses

The level of damage is found greatly affected by the asphalt

layer thickness. In Fig. 2, the damage value decreases signi-

ficantly as the asphalt layer thickness increases. For example, the

increase of the asphalt layer thickness from 7.6 to 17.8 cm results

in the decrease in the damage level by about 60 times, as seen in

the comparison between the maximum values of the contour

legends shown in Fig. 2.

The most important observation from Fig. 2 is the change in

the location of crack initiation as a function of the asphalt layer

thickness. When the thinnest layer is modeled in Fig. 2, the

severe damage is found at the bottom of the layer with negligible

damage at the top of the asphalt layer. As the asphalt layer

becomes thicker, damage right under the tire edge starts to

emerge, in addition to that at the bottom of the asphalt layer. In

the thickest asphalt layer case, the intensity of damage under the

tire edge is as high as that at the bottom of the asphalt layer. This

result can be attributed to the increased localization of punching

shear stresses in thicker pavements under the edge of the load.

The different cracking mechanisms between thin and thick

asphalt layers can be seen more effectively when Fig. 1(b) and

Fig. 3 are compared. In Fig. 3, for the thin asphalt layer, the

damage evolution is governed mostly by the damage that started

from the bottom of the asphalt layer. However, in Fig. 1(b), for

the thick asphalt layer, damage initiates from both the bottom of

the asphalt layer and right under the tire edge, and propagates

simultaneously to form a conjoined damage contour. This

conjoined damage contour, shown in Fig. 1(b) and Fig. 2 for the

Fig. 2. Damage Contours in Varying Asphalt Layer Thicknesses Under Nonuniform 40 kN Load for: (a) MODULUS SS; (b) MODULUS SW;

(c) MODULUS WS; (d) MODULUS WW


Vol. 10, No. 2 / March 2006 101

Fig. 3. Damage Evolution in the Thin Asphalt Layer

Fig. 4. Damage Contours in Varying Asphalt Layer Thicknesses Under Uniform 40 kN Load for: (a) MODULUS SS; (b) MODULUS SW; (c)

MODULUS WS; (d) MODULUS WW



medium and thick asphalt pavements, supports the findings from

field studies of top-down cracking (Gerritsen et al., 1987); that is,

the top-down cracks are found in asphalt pavements with an

asphalt layer thicker than 25 to 30 cm.

Also, the conjoined damage contour suggests that the through-

the-thickness crack may develop as these bottom-up and top-

down microcracks propagate further and coalesce together.

Gerritsen et al. (1987) reported that they found field cores with

top-down cracking for about 10 cm, about 5 cm with no cracking

at all, and about 10 cm bottom-up cracking in the same core. The

conjoined damage contour in Fig. 1(b) and Fig. 2 explains the

reason behind this observation. This finding clearly demonstrates

the problem associated with the traditional approach to fatigue

performance prediction in which the tensile strain at the bottom

of the asphalt layer is related to the fatigue life of the pavement.

This approach cannot account for the additional crack growth

from the top of the pavement and, therefore, overestimates the

fatigue life of the pavement.

4.2. Effect of Contact Pressure Distributions

Sebaaly (1992) presented the nonuniform contact pressure

distribution measured from a moving surface load. Fig. 2 and

Fig. 4 show the results from the nonuniform and uniform contact

pressures, respectively. One observation that can be made from

the comparison of the figures is that the nonuniform pressure

distribution results in a greater amount of damage in all the cases.

For example, Fig. 2, with the nonuniform contact pressure,

shows greater damage than Fig. 4 with the uniform contact

pressure when the values of the contour legends are compared.

This difference suggests that the pavement responses, calculated

in the traditional way of treating the tire pressure as uniform,

may underestimate the actual damage in the field and thereby

overestimate the pavement service life. Also, it needs to be noted

that the propensity of top-down cracking becomes greater under

nonuniform pressure than under uniform pressure. This

observation supports findings from laboratory tests conducted by

Groenendijk et al. (1997) and Miradi et al. (1997) who showed

that a nonuniform load causes large stresses at the pavement

surface. Fig. 6 presents the medium thick asphalt layer cases for

uniform and nonuniform pressures and clearly shows the same

observation.

4.3. Effect of Load Levels

Damage contours under 20 kN loading are plotted in Fig. 5 for

the nonuniform and uniform contact pressures, respectively.

Compared to the damage contours in Fig. 2 and Fig. 4 for the 40

kN load, the magnitude of damage is dramatically reduced for

thin pavements due to the reduction of the load. Comparing the

values of contour legends for the thin asphalt layer cases in Fig. 2

to Fig. 5 reveals that a reduction in the load level by a factor of

two results in the reduction in the damage by more than five

times, regardless of structures, contract pressure distribution, or

layer properties.

One major use of the damage values calculated from different

load levels is the development of the Equivalent Axle Load

Factor (EALF). Traditionally, the damage under a load was

either represented by critical pavement responses or calculated

by performance equations. Using the damage computed from the

VECD-FEP++ program, one can directly determine the damage

ratios of different load levels and, therefore, EALFs.

4.4. Effect of Base and Subgrade Moduli

The effect of base and subgrade moduli can be evaluated by

comparing four subfigures under each response parameter in

each figure. First of all, it is found in and Fig. 4 that the effect of

the subgrade modulus on damage states is much less than the

effect of the base modulus. Regarding the crack initiation

location, the weaker base and/or weaker subgrade increases the

intensity of damage under the tire edge and, therefore, the

propensity of top-down cracking. In the thickest asphalt layer,

Fig. 5. Damage Contours in the Thin Asphalt Layer Under Nonuniform and Uniform 20 kN Load for: (a) MODULUS SS; (b) MODULUS SW;

(c) MODULUS WS; (d) MODULUS WW


Vol. 10, No. 2 / March 2006 103

the weaker base resulted in more damage in general, but this

trend was more evident in the damage under the tire edge.

4.5. Effect of Asphalt Layer Stiffness

Fig. 6 presents the damage contours calculated using two

asphalt layer stiffnesses (AC I and AC II in Table 1) under both

nonuniform and uniform pressure distributions. It can be

concluded from this figure that the damage under the tire edge

becomes slightly greater as the stiffness of the asphalt layer

increases. This observation may become important when the

aging of the asphalt layer is considered. It is known that aging is

more severe at the top portion of the asphalt layer. The stiffening

effect of aging, therefore, makes the top portion of the asphalt

layer stiffer than the rest of the layer, which in turn increases the

tendency of top-down cracking.

5. Conclusions

It is demonstrated that the VECD-FEP++ program, with a

damage characteristic curve determined from a single monotonic

test and the time-temperature shift factor determined from the

complex modulus test, may be used to study the cracking

mechanisms of asphalt pavements. The findings from this study

show the effect of various pavement and load factors on

pavement responses as well as damage in the asphalt layer. It was

found that the propensity of top-down cracking increases as: (1)

the asphalt layer becomes thicker; (2) the contact pressure

becomes nonuniform; (3) base and/or subgrade become less stiff;

and (4) the asphalt layer becomes stiffer.

The conjoined damage contours in thicker pavements suggest

that the through-the-thickness crack may develop as these

Fig. 6. Damage Contours in the Medium Thick Asphalt Layer: (a) Nonuniform Pressure and AC I Stiffness; (b) Nonuniform Pressure and

AC II Stiffness; (c) Uniform Pressure and AC I Stiffness; (d) Uniform Pressure and AC II Stiffness.



bottom-up and top-down cracks propagate simultaneously and

coalesce together. This observation raises a serious question of

the validity of the traditional fatigue performance prediction

approach in which only the tensile strain at the bottom of the

asphalt layer is considered in predicting the fatigue life of asphalt

pavements.

6. References

Chehab, G.R., Kim, Y.R., Schapery, R.A., Witczak, M.W., and

Bonaquist, R. (2002). “Time-temperature superposition principle for

asphalt concrete mixtures with growing damage in tension.” Journal

of Association of Asphalt Paving Technologists, Vol. 71, pp. 559-

593.

Daniel, J.S. and Kim, Y.R. (2002) “Development of a simplified fatigue

test and analysis procedure using a viscoelastic continuum damage

model.” Journal of Association of Asphalt Paving Technologists,

Vol. 71, pp. 619-650.

Garg, N. and Thompson, M.R. (1998) Mechanistic-Empirical

Evaluation of the Mn/ROAD Low Volume Road Test Sections,

Illinois Cooperative Highway and Transportation Research Program

Report FHWA-IL-UI-262, Urbana, IL.

Gerritsen, A.H., Van Gurp, C.A.P.M., Van der Heide, J.P.J., Molenaar,

A.A.A., and Pronk, A.C. (1987). “Prediction and prevention of

surface cracking in asphalt pavements.” 6th International Conference

on Structural Design and Asphalt Pavements, The University of

Michigan, Ann Arbor, MI, pp. 378-391.

Guddati, M.N. (2001) FEP++: A Finite Element Program in C++,

Input Manual, Department of Civil Engineering, North Carolina

State University.

Groenendijk, J., Vogelzang, C.H., Molenaar, A.A.A., Mante, B.R. and

Dohmen, L.J.M. (1997). “Linear tracking response measurements:

determining effects of wheel-load configurations.” Transportation

Research Record 1570, TRB, National Research Council,

Washington, D.C., pp. 1-9.

Jenq, Y.S., and Perng, J.D. (1991). “Analysis of crack propagation in

asphalt concrete using cohesive crack model.” Transportation

Research Record 1317, TRB, National Research Council,

Washington, D.C., pp. 90-99.

Jenq, Y.S., Liaw, C.J., and Liu, P. (1993). “Analysis of crack resistance

of asphalt concrete overlays - A fracture mechanics approach.”

Transportation Research Record 1388, TRB, National Research

Council, Washington, D.C., pp. 160-166.

Kim, Y.R., Lee, H.J., and Little, D.N. (1997) “Fatigue characterization

of asphalt concrete using viscoelasticity and continuum damage

theory.” Journal of the Association of Asphalt Paving Technologists,

Vol. 66, pp. 520-569.

Miradi, A., Groenendijk, J., and Dohmen, L.J.M. (1997) “Crack

development in linear tracking test pavements from visual survey to

pixel analysis.” Transportation Research Record 1570, TRB,

National Research Council, Washington, D.C., pp. 48-54.

Mun, S. (2003). Nonlinear Finite Element Analysis of Pavements and

Its Application to Performance Evaluation. Ph.D. Dissertation,

Department of Civil Engineering, North Carolina State University,

2003.

Myers, L.A., Roque, R., and Birgisson, B. (2001). “Propagation

mechanisms for surface-initiated longitudinal wheel path cracks.”

Transportation Research Record 1778, TRB, National Research

Council, Washington, D.C., pp. 113-122.

Santha, B.L. (1994). “Resilient modulus of subgrade soils: Comparison

of two constitutive equations.” Transportation Research Board

1462, TRB, National Research Council, Washington D.C., pp. 79-

90.

Sebaaly, P.E. (1992). Dynamic Forces on Pavements: Summary of Tire

Testing Data. Report on FHWA Project DTFH 61-90-C-00084.

Sebaaly, P.E. and Tabatabaee, N. (1993). “Influence of vehicle speed on

dynamic loads and pavement response.” Transportation Research

Board 1410, TRB, National Research Council, Washington D.C.,

pp. 107-114.

Siddharthan, R.V., Krishnamenon, N., El-Mously, M., and Sebaaly, P E.

(2002). “Investigation of tire contact stress distributions on

pavement response.” Journal of Transportation Engineering, Vol.

128, No. 2, ASCE, pp. 136-144.

(Received September 8, 2005/Accepted February 8, 2006)

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