Fang-Ju ChouFang-Ju Chouand and

William G. ButtlarWilliam G. ButtlarFAA COE Annual Review MeetingFAA COE Annual Review Meeting

October 7, 2004October 7, 2004

Department of Civil and Environmental EngineeringUniversity of Illinois at Urbana-Champaign

Analysis of Flexible Overlay Systems:

Application of Fracture Mechanics to Assess Reflective Cracking Potential in

Airfield Pavements

2

- Progress Since Last Review Meeting Development/Verification of Fracture

Mechanics tools for ABAQUS Application of Tools to Study Reflective

Cracking Mechanisms in AC Overlays Placed on PCC Pavements

- Current/Future Work

Outline

3

Problem statement - Review

Functions of Asphalt Overlays (OL): To restore smoothness, structure, and minimize

moisture infiltration on existing airfield pavements.

Problem: The new asphalt overlay often fails before achieving

its design life.

Cause: Reflective cracking (RC).

4

Problem statement ~ Cont.

Current FAA Flexible OL Design Methodology: Rollings (1988’s)

Assumptions used:

1. The environmental loading (i.e. temperature) is excluded.

2. A 25% load transfer is assumed to present between slabs.

3. Structural deterioration is assumed to start from underlying slabs. Reflective cracking (RC) will initiate when structural strength of

slabs is consumed completely. RC will grow upward at a rate of 1-inch per year.

However, joint RC often appears shortly after the construction especially in very cold climatic zones.

5

Ongoing/Upcoming Research• Expand 3D Parametric Study to Investigate:

– Additional Pavement Configurations and Loading Conditions

– Effect of Joint LTE on Critical Responses and Crack Propagation

• Development of Two Possible Methods to Consider Reflective Cracking Potential – Simpler than Crack Propagation Simulation– Less Sensitive to Singularity at Crack/Joint

6

Fracture Analysis: J-integral

Estimate Stress Intensity Factors (KI and KII) at Tip of an Inserted Crack (Length will be Varied)

Compute Path Integral Around Various Contours

7

Ph.D. Thesis of Fang-Ju Chou:

Objectives:

1. Introduce a robust & reliable method (J-integral & interaction-integral) to obtain accurate critical OL responses.

2. Understand the effect of temp. loading by introducing temp. gradients in models.

3. Identify critical loading conditions for rehab. airfield pavements subjected to thermo-mechanical loadings.

4. To investigate how the following parameters affect the potential for joint RC in rehab. airfield pavements. Bonding condition between slabs

& CTB Load transfer between the

underlying concrete slabs Subgrade support Structural condition (modulus

value) of the underlying slabs

8

Limitation of traditional FE modeling at joint

Limitation: The accuracy of the predicted critical OL responses immediately above

the PCC joint was highly dependent on the degree of mesh refinement around the joint.

FEA applied† on modeling of asphalt overlaid JCP.

†Kim and Buttlar (2002); Bozkurt and Buttlar (2002); Sherman (2003)

To seek reliable critical stress predictions, LEFM will be applied in an attempt to arrive at non-arbitrary critical overlay responses around a joint or crack.

Concrete Slab

Subgrade

CTB

AC Overlay

No. of Elements?

9

The J-Integral: Path IndependenceA closed contour = 1 + 2 + 3 + 4

4321

043211

1 JJJJdsnx

uWnJ jij

i

On the crack faces (3 and 4 )

n1 = 0 ; Assuming traction free: ijnj = 0

No contributions to J-integral from segments 3 & 4

J3 = J4 = 0; J2= -J1

12 1

11

1 dsnx

uWndsn

x

uWn jij

ijij

i

1 1

1 dsmx

uWm jij

i reverse the normal of segment 1;

new normal mj (points away from tip)

1 1

1 dsnx

uWn jij

i Rename mj = nj

J2

= J1J-integral is independent of the contour taken around the crack tip

1

2

3

4

nj

y

x

nj

mj

Crack faces

Elastic homogeneous material

10

Relation between J and GIntroduction Literature Review Principals of LEFM & Appl. 2D Pav. Model Model Appl. Summary

1. Rice (1968) showed that the J-integral is equivalent to the energy release rate (G) in elastic materials. (section 3.2.3)

J

G

Ks

For a linear elastic, isotropic material

(at = )2

2

'

2

'

2IIIIII K

E

K

E

KJ

For an elastic material

J = G

For a linear elastic, isotropic material

(at = )2

2

'

2

'

2IIIIII K

E

K

E

KG

Take Ks as critical stress predictions

Use J to quantify the propensity of joint RC

11

Extraction of Stress Intensity Factors

1. Numerically it is usually not straightforward to extract† K of each mode from a value of the J-integral for the mixed-mode problem.

2. The finite element program ABAQUS uses the interaction integral method (Shih and Asaro, 1988) to extract the individual stress intensity factor.

3. The interaction integral method of homogeneous, isotropic, and linear elastic materials is introduced in section 3.3.1.

(at = )2

2

'

2

'

2IIIIII K

E

K

E

KJ

† AB

AQ

US

user

s m

anua

l, 20

03, H

ibbi

tt, K

arls

son

and

Sore

nsen

, Inc

., P

awtu

cket

, Rho

de I

slan

d.

12

2D Model Description--Geometry & Material

• Purpose: analyze a typical pavement section of an airport that serves Boeing 777 aircraft

• The selected model geometry and pavement cross sections are based on the structure and geometric info.† of un-doweled sections of runway 34R/16L at DIA in Colorado.

Concrete Slabs

ECTB = 2,000 ksi; CTB = 0.20

k = 200 pciSubgrade

CTB

18 in

8 in

AC Overlay 5 in EAC = 200 ksi; AC = 0.350.5 in0.2 in

EPCC = 4,000 ksiPCC = 0.15

Cross sectionNote: 1-inch = 25.4 mm; 1-psi = 6.89 kPa; 1 pci = 271.5103 N/m3

Traffic Direction

Transverse Joint = 0.5in

Longitudinal Joint = 0.5in

240 in

225 in

Top view CL

†Hammons, M. I., 1998b, Validation of three-dimensional finite element modeling technique for jointed concrete airport pavements, Transportation Research Record 1629.

13

36 ft (10.97 m)

Boeing 777-200

2D Model Description--Loading57 in 57 in

21.82 in

13.64 in

55in

One Boeing-777 200 aircraft:

• 2 dual-tridem main gears

• Gear width = 36 ft

• main gear (6 wheels; 215 psi)

• Gross weight = 634,500 lbs (287,800 kg)

• Each gear carries 47.5% loading

= 301,387.5 lb

14

• Boeing777-200: larger gear width (36 ft = 432 in)

• The 2nd gear is about 2 slabs away from 1st gear

• Assumption: the distance between gears is large enough such that interactions may be neglected for the study of the OL responses

57 in

55in

225 in

Gear 1

6.82 in

225 in

240 in

432 in

57 in

16.32 in

Note: Dimensions not drawn to scale

Gear 255in

1 Slab 2 Slab 3 4

2D Model Description--Loading

15

2D Model Description--Gear Loading Position• not practical to investigate

every possible gear position

• four selected positions: have the greatest potential to induce the highest pavement responses under one gear

Position AAC OverlayConcreteSlab

CTB

Subgrade2-D pavement cross-section (Cut A-A)

AC

Ove

rlay

Con

cret

e S

lab

CT

B

Sub

grad

e

Mod

eled

ra

nge

2-D pavement cross-section (Cut B-B)

Pos

itio

n B

• Position A: edge loading condition; Position B: joint loading condition

• Corner loading cond. (dash lines) cannot be considered in 2-D models, since the effect of the 3rd dimension cannot be distinguished.

Cut A-A

Cut

B-

B

Pos. A

Pos. BCorner

Top

vie

w

Modeled range

16

2D Model Description--Gear Loading Position

The other two positions:

• Position C: selected to study the case where the gear is centered over the joint to maximize bending stresses in the OL

• Position D: also has the potential to induce higher bending stresses in an OL

Position CAC OverlayConcreteSlab

CTB

Subgrade2-D pavement cross-section (Cut C-C)

AC

Ove

rlay

Con

cret

e S

lab

CT

B

Sub

grad

e

Mod

eled

ra

nge

2-D pavement cross-section (Cut D-D)

Pos

itio

n DCut

D-

D

Pos. C

Pos. D

Top

vie

wCut C-C

R

ehab

. pav

emen

ts s

ubje

cted

to

Pos

. A~D

mod

eled

as

2D p

l-

cond

itio

n.

Jo

int d

isco

ntin

uity

can

not b

e co

rrec

tly

mod

eled

usi

ng 2

D

axis

ymm

etri

c m

odel

Modeled range

17

2D Model Description--Load Adjustment Factor (LAF)One B777-200 wheel P = 50231.25lb2D axisymmetric model: circular loading

q = 215 psi

CTB

Concrete Slabs

Overlay

240 in

σX1= -119.1 psi

CL r = 8.624 in

CTB

Concrete Slabs

Overlay

q =215 psi

240 in

17.248 in

σX2=-170.8 psi

2D pl- model: strip loading

1. Correct excessive wheel load: need to adjust the applied load for pl- models

2. LAF: obtained by reducing the q of the 2-D pl- model until the horiz. stress prediction at the bottom of the asphalt OL matches the 2-D axisymmetric prediction.

3. For this 2-D rehab. pavement model of 5-inch OL under pl- cond., the adjustment factor = 0.697.

4. Reduced contact tire pressure p = 69.7% q will be imposed on 2-D pl- pavement models.

5. Limitations: location, no. of wheel

Mos

t sim

ple,

eff

ectiv

e w

ay

18

Results of Selected Loading Positions

Bef

ore

inse

rtin

g a

shar

p jo

int R

C in

to O

L, f

our

un-c

rack

ed r

ehab

. mod

els

subj

ecte

d to

ge

ar lo

adin

g po

sitio

ns A

~D a

re a

naly

zed.

Position A (Cut A-A) Long. Joint

Overlay

Concrete Slabs

CTB225 in

Position C (Cut C-C)Long. Joint

Overlay

Concrete Slabs

CTB225 in

Position B (Cut B-B)

Overlay

Concrete Slabs

CTB

240 in

Trans. Joint Position D (Cut D-D)

Overlay

Concrete Slabs

CTB

240 in

Trans. Joint

19

Ten

sion

Com

p.

Pos

A: t

ensi

le f

ield

s ar

e in

duce

d at

the

botto

m o

f O

L a

bove

PC

C

join

t

Results of Selected Loading Positions (Position A)

20

Results of Selected Loading Positions (Position C)

Ten

sion

Com

p.

Pos

C: t

ensi

le f

ield

s ar

e al

so

indu

ced

at th

e bo

ttom

of

OL

ab

ove

PC

C jo

int

21

Results of Selected Loading Positions (Position B)

Ten

sion

Com

p.

Pos

B: c

ompr

essi

ve f

ield

s ar

e pr

esen

t at t

he b

otto

m o

f O

L

abov

e P

CC

join

t

22

Ten

sion

Com

p.

Pos

D: c

ompr

essi

ve f

ield

s ar

e al

so p

rese

nt a

t the

bot

tom

of

OL

ab

ove

PC

C jo

int

Results of Selected Loading Positions (Position D)

23

Inserting Joint RC

Contour No.8

Coarse crack-tip mesh

Contour No.2

0.025”ℓ

Crack Faces

8

Contour No.5

Contour No.9

0.025”

Fine crack-tip mesh

Crack Faces24

005.0"5"025.0)( ACh 0015.0"5"0075.0)( ACh

ℓ4

C2C1

B2B1

y, v

x, u

r

ℓ

Cra

ck-t

ip e

lem

ent

(Sin

gula

r E

lem

ent)

Si

ze o

f cr

ack-

tip

elem

ent i

nflu

ence

s th

e ac

cura

cy o

f th

e nu

mer

ical

sol

utio

n.

tw

o m

esh

type

s ar

e us

ed in

the

crac

k-ti

p re

gion

to e

nsur

e th

at a

fin

e en

ough

mes

h ha

s be

en a

ppli

ed a

roun

d th

e cr

ack-

tip

24

Fracture Model Verification

1. Shih et al. (1976) proposed a disp. correction technique (DCT) to calculate (KI)s using the disp. responses of a singular element

2. Ingraffea and Manu (1980) generalized this approach for mixed-mode stress fields at the crack-tip.

3. Showed that the ℓ/a ratio had a pronounce effect on the evaluation of Ks. (note: a = crack length)

4. Using DCT, we can calculate the separate (KI)s & (KII)s in a mixed-mode problem based on the displacements of crack flank nodes of singular elements

1122 4421

2CBCBIK

1122 4421

2CBCBII uuuuK

u =

the

slid

ing

disp

. at t

he c

rack

fla

nk n

odes

= th

e op

enin

g di

sp. a

t the

cra

ck f

lank

nod

es

ℓ4

C2

C1

B2

B1

y, v

x, u

r

ℓ

Cra

ck-t

ip e

lem

ent

(Sin

gula

r E

lem

ent)

Cra

ck f

aces

25

Verification of Reference Sol. (using DCT) v.s. Analytical Sol.1. To confirm the accuracy of predicting Ks using DCT, a flat plate with an angled

crack is modeled under pl- cond. with unit thickness.2. The closed form solutions for Mode I and Mode II stress intensity factors at

either crack-tip are:

2)0( cosII KK

sincos)0(III KK

KI(0

) =

Mod

e I

stre

ss in

tens

ity

fact

or (

=0)

a =

hal

f of

the

crac

k w

idth

c =

hal

f of

the

plat

e w

idth

2a = 3.873093344E-02

=1000 psi

10"

2a

2c = 10"

uv

uv

E = 200 ksi = 0.35

= tan-1(0.5) Note: drawing not to scale

4107321.1"5/"0086605.0/ c

Deformation scale factor = 15.0

Deformation scale factor = 27.5

Right crack tip

Left crack tip22

26

Verification of Reference Sol. (using DCT) v.s. Analytical Sol.

Predicted Stress Intensity Factors (K I and K II) using DCT versus

Analytical Solutions

204.03

102.01

198.48

99.24

195.34

97.67

0

50

100

150

200

250

Str

ess

Inte

nsi

ty F

acto

rs (

KI

& K

II),

psi

DCT_Prediction_Left Analytical Sol. DCT_Prediction_Right

K I K II

1.S

uppl

ying

the

disp

. res

pons

es o

f th

e cr

ack

flan

k no

des

com

pute

d vi

a A

BA

QU

S,

the

refe

renc

e K

s us

ing

DC

T a

re o

btai

ned

for

both

cra

ck ti

ps.

2.R

efer

ence

Ks

com

pare

wel

l with

the

anal

ytic

al s

olut

ions

for

bot

h cr

ack

tips

with

th

e er

ror

perc

enta

ges

of 1

.58%

and

2.8

% f

or th

e ri

ght a

nd le

ft c

rack

tip.

27

Results of Selected Loading Positions1. Magnitudes of stress predictions immediately above the PCC joint are influenced by

the degree of mesh refinement around the joint; not recommended to be taken as critical pavement responses directly

2. In addition to loading positions 1 and 2 (same as positions A and C), 9 gear loading positions are also analyzed for rehabilitated pavements with an initial sharp joint RC of 0.5” or 2.5”.

x = 189.51”Fine & coarse mesh employed

Pos1(PosC)

5 in

18 in

8 in

0.5 in

0.2 in

4.5 in

13.5 in

Subgrade

225 in 225 in

Crack Length = 0.5” or 2.5”AC Overlay

Concrete Slab

CTB

†Pavement geometry not drawn to scale

x = 0” x = 34.57” x = 113.46”

Pos2 (PosA)

Pos7 Pos11

225 in

28

Position 7

Determination of Critical Loading Situation (Traffic Loading Only)

Ele

ven

traf

fic

load

ing

posi

tions

(gea

r lo

adin

g po

sitio

ns 1

to 1

1)

Tw

o le

ngth

s of

join

t RC

(0.5

-in

and

2.5-

in)

Tw

o m

esh

type

s

(fin

e &

coa

rse

at th

e cr

ack-

tip r

egio

n)

44 S

ets

of N

umer

ical

Res

ults

29

Determination of Critical Loading Situation (Aircraft Loading Only)

• Sta

biliz

ed J

-val

ue is

obt

aine

d w

hen

the

inte

gral

is e

valu

ated

a f

ew c

onto

urs

away

fro

m th

e cr

ack

tip

• J-v

alue

of

the

firs

t con

tour

is le

ast a

ccur

ate

and

shou

ld n

ever

be

used

in th

e es

timat

ion.

• The

acc

urac

y of

the

num

eric

al J

-val

ue e

vent

ually

deg

rade

s du

e to

the

rela

tivel

y po

or m

esh

reso

lutio

n in

reg

ions

far

aw

ay f

rom

the

crac

k-tip

.

Loading Position 7 with (a/hAC)=0.1

1.2485E-01

1.2490E-01

1.2495E-01

1.2500E-01

1.2505E-01

1.2510E-01

1.2515E-01

1 3 5 7 9 11 13 15 17 19 21 23

Contour No.

J-v

alu

e (

lb/i

n)

Fine_mesh Coarse_mesh

† The B777 gear is 113.46" away from the joint

Stable J-value of coarse mesh beginslast available contour or contour far away from the crack-tip

Stable J-value of fine mesh begins

30

(Air

craf

t Loa

ding

Onl

y)

T

ensi

le m

ode

I S

IFs

are

pred

icte

d st

artin

g fr

om

load

ing

posi

tion

6, w

here

the

cent

er o

f B

777

mai

n ge

ar is

at

leas

t 93.

45”

away

fro

m

the

PC

C jo

int.

B

oth

mes

h ty

pes

give

ab

out t

he s

ame

pred

ictio

ns

of m

ode

I S

IFs

Red

uced

con

tact

tire

pre

ssur

e

= 6

9.7%

2

15 p

si

KI vs. 11 Loading Positions (Fine Mesh)

-600

-500

-400

-300

-200

-100

0

100

200

300

400

-50 -25 0 25 50 75 100 125 150 175 200 225

Distance from joint (inch)S

tre

ss

Inte

ns

ity

Fa

cto

r, K

I (p

si-

in0.

5)

a/h =0.5 a/h =0.1AC

PosC

Pos11

AC

Ring5

Ring8Crack-tip mesh

KI vs. 11 Loading Positions (Coarse Mesh)

-600

-500

-400

-300

-200

-100

0

100

200

300

400

-50 -25 0 25 50 75 100 125 150 175 200 225

Distance from joint (inch)

Str

es

s In

ten

sit

y F

ac

tor,

KI (

ps

i-in

0.5)

a/h =0.5 a/h =0.1AC AC

PosC

Pos11

Ring2

RingCrack-tip mesh

Mod

e I

SIF

s vs

. 2 a

/hA

C

ratio

s

-- 1

1 po

sitio

ns

-- F

ine

& c

oars

e m

eshe

s

31

1.C

aste

ll e

t al.

(200

0) a

ppli

ed L

EF

M f

or f

lexi

ble

pave

men

t sys

tem

s an

d m

odel

ed th

e fa

tigu

e cr

ack

grow

th u

sing

FR

AN

C2D

and

FR

AN

C2D

/L.

2.A

dis

trib

uted

whe

el lo

ad o

f 10

,000

lb w

ith

a 10

0 ps

i con

tact

tire

pre

ssur

e w

as a

ppli

ed

abov

e th

e cr

ack.

A c

ompr

essi

ve K

I was

fou

nd to

exi

st a

t the

cra

ck ti

p.

D

iffe

renc

es: c

onve

ntio

nal F

P: s

ofte

r m

ater

ial b

elow

sur

face

; Reh

ab. p

avem

ent:

muc

h st

iffe

r sl

abs

belo

w s

urfa

ce.

H

oriz

. Str

ess

dist

ribu

tion

wou

ld n

ot f

ollo

w th

e si

mil

ar tr

ends

.

Comparison of Results

Stu

dy o

f C

aste

ll et

al.

agre

es

with

the

pres

ent w

ork:

T

he c

ompr

essi

ve s

tres

ses

can

be p

redi

cted

at t

he c

rack

-tip

for

2-D

pav

emen

t mod

els

whe

n di

stri

bute

d w

heel

load

s ar

e ap

plie

d ab

ove

a cr

ack.

32

Application 1 (Traffic vs. Combined Loadings)

Thr

ee lo

adin

g sc

enar

ios

Air

craf

t loa

ding

pos

ition

7 o

nly

Air

craf

t loa

ding

pos

ition

7 &

Tem

pera

ture

load

ing

(T

PC

C=

-23

F)

Air

craf

t loa

ding

pos

ition

7 &

Tem

pera

ture

load

ing

(T

PC

C=

-15.

3F

)225 in

Longitudinal Joint

Overlay=5”; AC=1.3888910-5 1/F

Concrete slabs=18” PCC=5.510-6 1/F

CTB=8”; CTB=7.510-6 1/F70F

70F

47.5F

40F

TPCC=-1.25F/inTPCC=-0.85F/in

Subgrade

113.46-in

70F

70F

54.7F

47.2F

TAC=-1.5F/in TAC=-1.5F/in

Position 7

33

Introduction Literature Review Principals of LEFM & Appl. 2D Pav. Model Model Appl. Summary

Predicted K II versus Two Crack Lengths

-14.2

13.4

-146.40

53.14

-104

43.85

-200

-150

-100

-50

0

50

100

Str

ess

Inte

nsi

ty F

acto

r, K

II (

psi

-in

0.5)

Aircraft loading only T = -23 F T = -15.3 F

a/hAC=0.1 a/hAC=0.5

PCC PCC

th

e pr

edic

ted

mod

e I

SIF

is

rais

ed d

ram

atic

ally

fro

m 1

68.3

ps

i-in

0.5 t

o 16

69 p

si-i

n0.5 o

r 22

60

psi-

in0.

5 dep

endi

ng o

n T

PCC

T

he p

redi

cted

mod

e II

SIF

is

also

rai

sed

from

14.

2 ps

i-in

0.5 t

o 10

4 ps

i-in

0.5 o

r 14

6.4

psi-

in0.

5 de

pend

ing

on

TPC

C.

Predicted K I versus Two Crack Lengths

168.3 168.1

16691811

2260

1351

0

500

1000

1500

2000

2500

Str

ess

Inte

nsi

ty F

acto

r, K

I (p

si-i

n0.

5)

Aircraft loading only T = -23 F T = -15.3 F

a/hAC=0.1 a/hAC=0.5

PCC PCC

Num

. mod

e I

and

mod

e II

S

IFs

a/h A

C =

0.1

and

0.5

34

Predicted J-value versus Two Crack Lengths

0.1251 0.1247

22.50

14.41

12.26

8.018

0

5

10

15

20

25

J-va

lue

, (l

b/i

n)

Aircraft loading only T = -23 F T = -15.3 F

a/hAC=0.1 a/hAC=0.5

PCC PCC

1.U

nder

the

com

bine

d lo

adin

gs, t

he p

redi

cted

J-v

alue

is m

uch

bigg

er th

an th

e on

e in

duce

d by

air

craf

t loa

ding

onl

y.

2.T

he c

ritic

al lo

adin

g co

nditi

on o

f th

is 2

-D r

ehab

ilita

ted

pave

men

t (i.e

. 5-i

nch

asph

alt o

verl

ay o

n th

e ri

gid

pave

men

t) is

the

airc

raft

load

ing

posi

tion

7 pl

us

nega

tive

tem

pera

ture

gra

dien

ts. T

he b

igge

r th

e ne

gativ

e te

mpe

ratu

re d

iffe

rent

ial

thro

ugh

the

unde

rlyi

ng c

oncr

ete

slab

s, th

e hi

gher

the

pred

icte

d m

ode

I S

IF.

Application 1 (Traffic vs. Combined Loadings)

35

Rec

ent F

indi

ngs

Based on the findings of this study, the following conclusions can be drawn:

1. By applying LEFM on modeling of rehab. airfield pavement, reliable critical OL responses (i.e., the J-value, and stress intensity factors at a crack-tip) can be obtained.

2. For the OL system considered in this study, which involved a 5-inch thick asphalt OL placed on a typical jointed concrete airfield pavement system serving the Boeing 777 aircraft, gear loads applied in the vicinity of the PCC joint were found to induce horiz. compressive stress at the RC tip for all load positions considered. The crack lengths studied ranged from 0.5-inch to 2.5-inch.

3. Whereas, for un-cracked asphalt OLs, highly localized horiz. tension was found to exist in the asphalt OL just above the PCC joint.

4. Temperature cycling appears to be a major contributor to joint reflective cracking.

36

Res

earc

h P

rodu

cts

1. UIUC Ph.D Thesis – Fang-Ju Chou: October 1, 2004.

2. FAA COE Report – Fall, 2004.

3. Conference, Journal Papers – In preparation.

4. Models, models, models!

37

Cur

rent

and

Fut

ure

Wor

k

1. To better simulate the behavior of asphalt OLs, an advanced material model that accounts for the viscoelastic behavior of the asphalt concrete can be implemented in the FEA. However, a thorough understanding of a nonlinear fracture mechanics will be required to properly interpret the modeling results.

2. The use of actual temperature profiles versus the critical OL responses are recommended. This analysis should be conducted in conjunction with the implementation of a viscoelastic constitutive model for the asphalt OL.

3. By inserting appropriate interface elements such as cohesive elements immediately above the PCC joint, a more realistic simulation of crack initiation and propagation can be obtained.

4. Modeling limitations must be addressed. The move to 3D, crack propagation modeling in composite pavements subjected to thermo-mechanical loading pushes the limits of current FEA capabilities. Modeling simplifications and advances in numerical modeling efficiencies are needed.

5. Field Verification

Thank you!