asphalt pavement aging and temperature dependent ... pavement aging and temperature dependent...

Asphalt Pavement Aging and Temperature Asphalt Pavement Aging and Temperature Dependent Properties using a Functionally Dependent Properties using a Functionally

Graded Viscoelastic Model Graded Viscoelastic Model

Ph.D. Final ExamPh.D. Final Exam

Eshan V. Dave

June 5June 5thth 20092009

Department of Civil and Environmental EngineeringDepartment of Civil and Environmental Engineering

University University of Illinois at Urbanaof Illinois at Urbana--ChampaignChampaign

Sincere gratitude to:Sincere gratitude to:

William G. Buttlar

Glaucio H. Paulino

Harry H. Hilton

Phillip B. Blankenship

2

Phillip B. Blankenship

Hervé DiBenedetto

All colleagues and friends

AcknowledgementsAcknowledgements

NSF-GOALI Program: Project CMS 0219566

Koch Materials Company / SemMaterials L.P.

USDOT Nextrans Research Center

FHWA Pooled Fund Study: TPF-5(132)

3

Functionally Graded Viscoelastic Asphalt Functionally Graded Viscoelastic Asphalt Concrete ModelConcrete Model

Motivation and Introduction

Viscoelastic Characterization of Asphalt Concrete

Viscoelastic FGM Finite Elements

Correspondence Principle Based Analysis

4


Time Integration Analysis

Application Examples: Asphalt Pavement

Summary and Conclusions

Asphalt ConcreteAsphalt Concrete

Constituents: – Asphalt Binder

– Aggregates

Asphalt Binder: – Derived from Crude Oil

– Many times modified with polymers to enhance

5

– Many times modified with polymers to enhance properties

– Undergoes oxidative aging (stiffening) with time

Asphalt Concrete (Asphalt Mixture)– Large fraction produced as hot-mix asphalt (HMA)

– Most common form of pavement surfacing material (96% of pavement surface in United States)

MotivationMotivation

Cracking in Asphalt Concrete Pavements Cracking in Asphalt Concrete Pavements and Overlays:and Overlays:

Reflective crackingReflective cracking

Thermal crackingThermal cracking

Big Picture:Big Picture:–– Predict reflective and thermal cracking in asphalt Predict reflective and thermal cracking in asphalt

6

–– Predict reflective and thermal cracking in asphalt Predict reflective and thermal cracking in asphalt concrete pavementsconcrete pavements

–– Design pavements and overlays (with/without Design pavements and overlays (with/without interlayers) to prevent thermal/reflective crackinginterlayers) to prevent thermal/reflective cracking

MotivationMotivation: Progress in Recent Years: Progress in Recent Years

Significant improvements have been made towards accurate simulation of asphalt pavement systems:– Viscoelastic characterization and modeling

– Fracture energy measurements

– Cohesive zone fracture model

– Integrated studies

7

– Integrated studies

0

-15 -10 -5 0 5

Temperature (C)

Pavements are NonPavements are Non--Homogeneous StructuresHomogeneous Structures

Sources:1. Oxidative aging

2. Temperature dependence of material properties

3. Other sources (construction, additives etc.)

0

0 5 10 15 20

Complex Modulus, (GPa)Stiffness (GPa) Temperature (C)

0

10

20

30

40

50

60

70

80

Dep

th (

mm

)

9:00 AM

3:00 PM

6:00 PM

9:00 PM

12:00 AM

3:00 AM

0

50

100

150

200

250

300

350

400

Dep

th f

rom

Su

rfac

e (m

m)

Pavement Age=15years

8

Dep

th f

rom

Su

rface (

mm

)

Aging gradient generated using “Global

aging model” by Mirza and Witczak (1996)Temperature profiles generated using

“EICM” from AASHTO MEPDG (2002)

Asphalt Concrete is ViscoelasticAsphalt Concrete is Viscoelastic

Asphalt mixtures from US36 (near Cameron, MO)

9

Temperature = -20ºC

MotivationMotivation

Layered GradedE1

E2

E3

E(x)

Layered approach is the current state of practice– AASHTO MEPDG (Aging Gradient)

Simulation Approaches for Non-Homogeneous Structures

10

– AASHTO MEPDG (Aging Gradient)

Asphalt ConcreteE(t=t’, T(t’))

Granular Base

Subgrade

Pavement Analysis and DesignPavement Analysis and DesignViscoelastic Lab Characterization:

(Chapter 3)

(a) Aging Levels

(b) Test Temperatures

Anticipated aging conditions

(based on distress type and

design life)

Pavement structure and

field conditions

Temperature distribution

0

10

20

30

Temperature

Depth

Viscoelastic FGM Properties

11

Viscoelastic FGM finite-element

method (Chapters 4 and 5)

(a) CP-Based Analysis

(b) Time-Integration Analysis

Pavement Analysis and Design:

(a) Study of critical responses (e.g. tensile strains at bottom of AC layer)

(b) Prediction of pavement performance

(c) Comparison of design alternatives (structure and/or materials)

Few examples shown in Chapter 6

30

40

50

60

70

80

9:00 AM

3:00 PM

6:00 PM

9:00 PM

12:00 AM

3:00 AM

Depth

ObjectivesObjectives

Develop efficient and accurate simulation scheme for asphalt concrete pavements

Viscoelastic characterization of asphalt concrete (Chapter 3)

Viscoelastic analysisa) Correspondence Principle (Chapter 4)

12

b) Time Integration Scheme (Chapter 5)

Account for:– Aging gradients

– Temperature dependent property gradients

Simulate asphalt concrete pavements and overlay systems (Chapter 6)




13






Viscoelastic CharacterizationViscoelastic Characterization

Asphalt concrete samples

Use of indirect tensile test (IDT), AASHTO-T322

Softer/Compliant Mixtures Crushing under loading head

14

Flattened IDT TestFlattened IDT Test

Increase contact area to prevent crushing under loading head

Viscoelastic solution to bi-axial loading

Results indicate flat IDT as a viable alternative to IDT

1x 10

-5

Regular

Flattened (α = 35o)

P

yIDT (AASHTO T322)

15

100

102

104

106

0

0.2

0.4

0.6

0.8

Reduced Time (sec)Reduced Time (sec)Reduced Time (sec)Reduced Time (sec)

Cre

ep

Co

mp

lain

ce

(1

/psi)

Cre

ep

Co

mp

lain

ce

(1

/psi)

Cre

ep

Co

mp

lain

ce

(1

/psi)

Cre

ep

Co

mp

lain

ce

(1

/psi)

Flattened (α = 35 )

Flattened (α = 50o)

R

αx

α=50º

Viscoelasticity: Commonly used models Viscoelasticity: Commonly used models for asphaltic materialsfor asphaltic materials

Could be classified as:– Prony series forms (Generalized models)

– Parabolic models

– Others

Prony series form: Generalized Maxwell Model

16

Prony series form: Generalized Maxwell Model

E1 E2 E3 Eh

η1 η2 η3 ηh

[ ]

i

i

i

h

i

ii

E

tExpEtE

ητ

τ

=

−=∑=1

/)(

Viscoelasticity: Constitutive modelsViscoelasticity: Constitutive models Parabolic Models:

– Huet-Sayegh Model (1965):

10,)(

:dashpot)dependent (time Unit Parabolic

<<= ktA

tkσ

εParabolicUnits

17

– 2S2P1D Model: Di Benedetto et al. (2005, 2007)

Other Models: Power law, sigmoidal etc.

Fewer parameters compared to generalized

models

Shared parameters between asphalt binders,

mastics and mixtures

Viscoelasticity: Prony Series ModelsViscoelasticity: Prony Series Models

Generalized Maxwell model is selected for the current study:– Applicability to asphaltic and other viscoelastic materials

– Flexibility w.r.t. fitting of experimental data

– Equivalence between compliance and relaxation

18

– Equivalence between compliance and relaxation forms

– Transformations are well established

– Compatibility with previous research (e.g. GOALI study, ABAQUS etc.)

– Availability of model parameters for variety of asphalt mixtures


Motivation and Introduction Viscoelastic Characterization of Asphalt Concrete


19

Correspondence Principle Based Analysis Time Integration Analysis Application Examples: Asphalt Pavement Summary and Conclusions

Viscoelasticity: BasicsViscoelasticity: Basics

Constitutive Relationship:

Model of Choice: Generalized Maxwell Model

( ) ( )( )

( )

'

'

'

' '

'

,, ,

:Stresses, , : Relaxation Modulus, : Strains

t t

t

x tx t C x dt

t

C x

εσ ξ ξ

σ ξ ε

=

=−∞

∂= −

∂∫

20

Time-Temperature Superposition

( ) ( )( )1

,N

h

h h

tC x t E x Exp

xτ=

= −

∑

( ) ( )'

0

Reduced Time, , , , '

t

x t a T x t dtξ = ∫

E1 E2 Eh

η1 η2 ηh

Relaxation Time, hh

hE

ητ =

Viscoelasticity: Correspondence PrincipleViscoelasticity: Correspondence Principle

Correspondence Principle (Elastic-Viscoelastic Analogy): “Equivalency between transformed (Laplace, Fourier etc.) viscoelastic and elasticity equations”

εσ

εσ

K

Gdd

3

2

=

=

εσ

εσ~~

3~

~~2~

K

Gdd

=

=

ElasticElastic Transformed ViscoelasticTransformed Viscoelastic

21

εσ K3= εσ ~~3~ K=

Extensively utilized to solve variety of nonhomogeneousviscoelastic problems: Hilton and Piechocki (1962): Shear center of non-homogeneous

viscoelastic beams

Mukherjee and Paulino (2003): Correspondence principle forviscoelastic FGMs

Graded Graded Finite ElementsFinite Elements

Graded Elements: Account for material non-homogeneity within elementsunlike conventional (homogeneous) elements

Lee and Erdogan (1995) and Santare and Lambros (2000)

– Direct Gaussian integration (properties sampled at integration points)

Kim and Paulino (2002)

Homogeneous Graded

Kim and Paulino (2002) – Generalized isoparametric formulation (GIF)

Paulino and Kim (2007) and Silva et al. (2007) further explored GIF graded elements– Proposed patch tests

– GIF elements should be preferred for multiphysics applications

Buttlar et al. (2006) demonstrated need of graded FE for asphalt pavements (elastic analysis)

22

Generalized Generalized IsoparametricIsoparametric Formulation (GIF)Formulation (GIF)

Material properties are sampled at the element nodes

Iso-parametric mapping provides material properties at integration points

Natural extension of the conventional isoparametricformulation

)),.(egPropertiesMaterial yΕ(x y

( ) [ ]0, 3 2E x y E Exp x y= −

23

x

y

z=E(x,y)x

(0,0)

ConventionalHomogeneous

GIF

( ) ( )1

Shape function corresponding to node,

Number of nodes per element

m

i ii

i

E t N E t

N i

m

=

=

=

=

∑

General FE General FE ImplementationImplementation

Variational Principle (Potential):

( ) ( )( ) ( )

( )( )

' '' '

''

''

''

' ''

'' ' ' ' ''

' ''

"

" ''

''

1,

2

,

Where, is Potential, are strains for body of volume ,

u

t t t t t

u

t t

t t

t

u

t tC x t t t dt dt d

t t

u tP x t t dt d

tσ

σ

ε εξ ξ

π ε

π= = −

Ω =−∞ =−∞

=

Ω =−∞

∂ ∂ = − − Ω ∂ ∂

∂− − Ω

∂

Ω

∫ ∫ ∫

∫ ∫

'

24

Stationarity forms the basis for problem description:

( ) ( )( ) ( )

( )( )

' '' '

''

''

''

' ''

'' ' ' ' ''

' ''

''

'' ''

''

,

, 0

u

t t t t t

u

t t

t t

t

t tC x t t t dt dt d

t t

u tP x t t dt d

tσ

σ

ε δεξ ξ

δ

δπ= = −

Ω =−∞ =−∞

=

Ω =−∞

∂ ∂ = − − Ω ∂ ∂

∂− − Ω =

∂

∫ ∫ ∫

∫ ∫

'

Where, is Potential, are strains for body of volume ,

is the prescribed traction

u

P

π ε Ω

on surface and is the corresponding displacementuσΩ

NonNon--Homogeneous Viscoelastic FEMHomogeneous Viscoelastic FEM

Equilibrium:

Solution approaches:1. Correspondence Principle (CP)

( )( ) ( ) ( ) ( )( )( )

( )'

' '

'

0

, 0 , ,

tj

ij j ij i

u tK x t u K x t t dt F x t

tξ ξ ξ

+

∂+ − =

∂∫

25

2. Time-Integration Schemes

Recursive Formulation

ã(s) is Laplace transform of a(t); s is transformation variable

0

( ) ( ) [ ]a s a t Exp st dt

∞

= −∫%

( ) ( ) ( ) ( )0 ,t

j iij

K x sK s u s F x s = % %%

NonNon--Homogeneous Viscoelastic FEMHomogeneous Viscoelastic FEM1. Correspondence Principle (CP)

Benefits:

– Solution does not require evaluation of hereditary integral

– Direct extension of elastic formulations

Limitations:

– Inverse transformations are computationally expensive

– Transform/Convolution should exist for material model and boundary conditions boundary conditions

2. Time-Integration Schemes (Recursive formulation)

Benefits:

– Fewer limitations on material model and boundary conditions

Limitations:

– Convergence studies are required to determine time step size

– Elaborate formulation and implementation

Both are explored in this dissertation

26






27





εσ

εσ

K

Gdd

3

2

=

=

εσ

εσ~~

3~

~~2~

K

Gdd

=

=

CPCP--Based Implementation (Ch. 4)Based Implementation (Ch. 4)

Define problem in time-domain (evaluate load vector ..

and stiffness matrix components and )

Perform Laplace transform to evaluate and ..

Solve linear system of equations to evaluate nodal

displacement,

( ),iF x t

( )0

ijK x ( )ij

K t

( ),i

F x s% ( ),t

ijK x s%

( )u s%

( ) ( ) ( ) ( )0 ,t

j iij

K x sK s u s F x s = % %%

Verification examples:1. Analytical solution (Creep extension shown here)

2. Comparison with commercial software28

displacement,

Perform inverse Laplace transforms to get

the solution,

Post-process to evaluate field quantities of interest

( )iu s%

( )iu t

Collocation is chosen as method of choice

2.5

3

3.5

4

4.5D

isp

lacem

en

t in

y D

irecti

on

(m

m)

t = 10 secVerification: Analytical SolutionVerification: Analytical Solution

Analytical Solution

FE Solution

y

x

E0(x)

( ) ( )( )

( ) [ ]

0

0

7

0

8

0

,

10 2 MPa

10 MPa.sec

2 mm

E xE x t E x Exp t

E x Exp x

u

η

η

= −

= −

=

=

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

x (mm)

Dis

pla

cem

en

t in

y D

irecti

on

(m

m)

t= 5 sec

t = 2 sec

t = 1 sec

29

0.7

0.8

0.9

1N

orm

alized

Rela

xati

on

Mo

du

lus, E

(t)/

E0

Verification with ABAQUS: Material GradationVerification with ABAQUS: Material Gradation

( ) ( )0P t P h t=

10-1

100

101

102

0.4

0.5

0.6

0.7

Time (sec)

No

rmalized

Rela

xati

on

Mo

du

lus, E

(t)/

E0

30

4

5

6

7

No

rmalized

Mid

-Sp

an

Defl

ecti

on

, u

(t)/

u0

6-Layer (ABAQUS)

12-Layer (ABAQUS)

9-Layer (ABAQUS)

Graded ViscoelasticPresent Approach

Commerical Software (ABAQUS)

Verification: Comparison with ABAQUSVerification: Comparison with ABAQUS

Present Approach FGMABAQUS Simulations Layered gradation

31

0 10 20 30 40 50 60 70 80 90 1001

2

3

4

Time (seconds)

No

rmalized

Mid

-Sp

an

Defl

ecti

on

, u

(t)/

u0

Homogeneous Viscoelastic(Averaged Properties)

6-Layer (ABAQUS)

FGM Average 6-Layer 9-Layer 12-Layer

Mesh Structures (1/5th span shown)


Motivation and Introduction Viscoelastic Characterization of Asphalt Concrete

Viscoelastic FGM Finite Elements Correspondence Principle Based Analysis Time Integration Analysis

32


Application Examples: Asphalt Pavement Summary and Conclusions

Time Integration Approach (Ch. 5)Time Integration Approach (Ch. 5)

Above could be solved sequentially using Newton-Cotes expansion (material history effect needs to be considered)

( ) ( ) ( )( )

( )0

', 0 , ' ' ,

'

tj

ij j ij i

u tK x u K x dt F x t

tξ ξ ξ

+

∂+ − =

∂∫

Alternatively, recursive formulation could be developed that requires only few previous solutions

33

( ) ( ) ( )( ) ( ) ( ) ( )

( ) ( ) ( )

11

11

1 1

1

2 0

,0

i n ij n ij n j

nj n ij ij n n

ij n m ij n m j m

m

F t K K u

u t K x KK K u t

ξ ξ ξ

ξ ξξ ξ ξ ξ

−−

−

− +=

− − − = + −

− − − − ∑

TimeTime--Integration Analysis (Ch. 5)Integration Analysis (Ch. 5)

Recursive Formulation (Yi and Hilton, 1994):

( )( ) ( )( ) ( )( ) ( ) ( )

( )( ) ( )( )( )

( )( ) ( ) ( )

( )( ) ( ) ( ) ( ) ( )( ) ( ) ( )( )

1 2

21

1

1 1 1

1

2 1

1 1 1 0 0 02

2, ,

2,

2, ,

me

ij ij n ij n j n i nh h hh

mne

ij ij n j n j nh hh ij h

ij n j n j n i ij j i n hh

K x v x t t v x t u t F tt

tK x Exp v x t u t u t

tx

v x t u t u t t u t v x t u t R tt

ξ

τ

=

− − −=

− − −

⋅ ∆ − = ∆

+ ⋅ − + ∆

− + ∆ − + + ∆

∑

∑ &

& &

Where,

34

( )( ) ( ) ( )( ) ( )( ) ( )( )

( )( ) ( ) ( )( ) ( )( ) ( )

( ) ( )( ) ( )( )

1

1 ' ' 2 1 ' '

0

' 2

1

'

1

, / ; , ,

/ ,

/

n n

n

t t

ij n ij ij n ijhh h ht

e

i n ij ij ij n j nh h h

ij j nh h

v x t Exp t x dt v x t v x t dt

R t K Exp t x v x t u t

Exp t x R t

ξ τ

ξ τ

ξ τ

−

−

−

= − =

= ⋅ − ⋅

+ −

∫ ∫

&&

Verification examples:1. Analytical solution (Stress relaxation shown here)

2. Comparison with commercial software

0.5

0.6

0.7

0.8

0.9S

tress in

y D

irecti

on

(M

Pa)

Analytical Solution

Step = 0.1 sec

Step = 0.2 sec

Step = 0.5 sec

Step = 1 sec

y

E0(x)

u0( ) ( )

( )

( ) ( )

0

0

7

0

8

,

10 2 MPa

10 MPa.sec

E xE x t E x Exp t

E x Exp x

η

η

= −

=

=

=

Verification: Analytical SolutionVerification: Analytical SolutionAnalytical Solution

Step = 0.1 sec

Step = 0.2 sec

Step = 0.5 sec

Step = 1 sec

10-1

100

101

102

0

0.1

0.2

0.3

0.4

time (sec)

Str

ess in

y D

irecti

on

(M

Pa)

35

x

E0(x)

u0

0 2 mmu =

Verification: Comparison with ABAQUSVerification: Comparison with ABAQUS

Temperature Dependent Property Gradient– ABAQUS Simulations: Using layered gradation

– Temperature distribution

-10

-8

-6

-4

-23( ) y

T y e= −

TEMPERATURE INPUT

36

10

-20

-18

-16

-14

-12

-10

-20-15-10-500

0.2

0.4

0.6

0.8

1

Temperature (deg. C)

He

igh

t (m

m)

-20-15-10-500

0.2

0.4

0.6

0.8

1

Temperature (deg. C)

He

igh

t (m

m)

TEMPERATURE INPUT

Solid Line: FGM (Present Approach)

Dashed Line: Layered Approx. (ABAQUS)

6 Layers 9 Layers

0.5

0.6

0.7

0.8

0.9

1

No

rma

lize

d R

ela

xa

tio

n M

od

ulu

s,

E(t

)/E

0Material BehaviorMaterial Behavior

-20 -15 -10 -5 00

1

2

3

4

Lo

g S

hif

t F

ac

tor,

aT

10-1

100

101

102

0

0.1

0.2

0.3

0.4

0.5

Reduced Time

No

rma

lize

d R

ela

xa

tio

n M

od

ulu

s,

E(t

)/E

0

37

Ref. Temperature = -20 C

-20 -15 -10 -5 0Temperature (deg. C)

2

2.5

3

3.5N

orm

ali

ze

d M

id-S

pa

n D

efl

ec

tio

n

12 Layer(converges with Analytical Solution)

Dashed Line: ABAQUS®

Solid Line: Present approach

(Overlaps with present approach)

Present Approach FGMABAQUS Simulations Layered gradation

38

0 20 40 60 80 1000

0.5

1

1.5

Time (sec)

No

rma

lize

d M

id-S

pa

n D

efl

ec

tio

n

3 Layer

6 Layer

9 Layer

FGM 6-Layer 9-Layer 12-Layer

Mesh Structures (1/5th span shown)






39





Pavement Analysis and DesignPavement Analysis and DesignViscoelastic Lab Characterization:

(Chapter 3)

(a) Aging Levels

(b) Test Temperatures

Anticipated aging conditions

(based on distress type and

design life)

Pavement structure and

field conditions

Temperature distribution

0

10

20

30

Temperature

Depth

Viscoelastic FGM Properties

40

Viscoelastic FGM finite-element

method (Chapters 4 and 5)

(a) CP-Based Analysis

(b) Time-Integration Analysis

Pavement Analysis and Design:

(a) Study of critical responses (e.g. tensile strains at bottom of AC layer)

(b) Prediction of pavement performance

(c) Comparison of design alternatives (structure and/or materials)

Few examples shown in Chapter 6

30

40

50

60

70

80

9:00 AM

3:00 PM

6:00 PM

9:00 PM

12:00 AM

3:00 AM

Depth

ExampleExample--1: Full Depth AC Pavement1: Full Depth AC Pavement Based on I-155, Lincoln IL

Single Tire load simulated (up to 1000 sec loading time)

Aged material properties (Apeagyei et al., 2008)

Surface of AC: Long term aged

Bottom of AC: Short term aged

Surface Course (38.1 mm)2.5x 10

5

41

y

x0, Bottom

75150

225300

372, Top

10010

110210

310410

51060

0.5

1

1.5

2

Height of AC Layer (mm)Reduced Time (sec)

Rela

xati

on

Mo

d.

(MP

a)

Base Course (337 mm)

Stabilized Subgrade

(304-mm, E =138 MPa )

Subgrade

(E = 35 MPa )

ExampleExample--1: FEM 1: FEM DiscretizationDiscretization

Coarse Mesh Fine Mesh

6 Layers

Two mesh refinement levels

Coarse mesh: Graded and Homogeneous simulations

Fine Mesh: Layered simulations

42

72150 DOFs 129060 DOFs

6 Layers

16 Layers

0, Bottom75

150225

300372, Top

10010

110210

310410

51060

0.5

1

1.5

2

2.5x 10

5

Height of AC Layer (mm)Reduced Time (sec)

Rela

xati

on

Mo

d.

(MP

a)

ExampleExample--1: Simulation Results1: Simulation Results

Material Distributions:

FGM

Layered

Aged

Unaged

Pavement Responses:

Tensile strain at bottom of asphalt layer (to

43

Tensile strain at bottom of asphalt layer (to

investigate cracking and fatigue)

Shear strain at wheel edge (longitudinal

cracking/rutting)

Comparison of FGM and Layered predictions

Compressive strain at interface of asphalt layers

14

16

18

20

22P

eak S

train

in

x-x

Dir

ecti

on

(x10

-6m

m/m

m)

FGM

Layered Gradation

Aged (Homogeneous)

Unaged (Homogeneous)

ExampleExample--1: Strain at Bottom of AC1: Strain at Bottom of AC

10-1

100

101

102

103

6

8

10

12

14

Time (second)

Peak S

train

in

x-x

Dir

ecti

on

(x10

44

x

y

AC LayersStrain in x-x Dir.

Underlying Layers

70

80

90

100

110P

eak S

hear

Str

ain

(x10

-6m

m/m

m)

FGM

Layered Gradation

Aged (Homogeneous)

Unaged (Homogeneous)

ExampleExample--1: Peak Shear Strain1: Peak Shear Strain

10-1

100

101

102

103

20

30

40

50

60

Time (second)

Peak S

hear

Str

ain

(x10

45

x

y

AC Layers Shear Strain

Underlying Layers

340

345H

eig

ht

of

the A

C L

ayer

(mm

)

FGM

Layered Gradation

Aged Properties (Homogeneous)

Surface Course

ExampleExample--1: FGM vs. Layered1: FGM vs. Layered

-35 -30 -25 -20 -15330

335

Strain in y-y Direction (x10-6

mm/mm)

Heig

ht

of

the A

C L

ayer

(mm

)

Binder Course

46

~ 20% Jump

x

y

AC Layers

Strain in y-y Dir.

Underlying Layers

Example 2: Graded InterfaceExample 2: Graded Interface

Pavement: LA34, Monroe LA

Two simulation scenario

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Two simulation scenario

1. Step interface 2. Graded interface

Surface Course

RCRI

PCC

Subgrade

z

X

47-mm

24-mm

120-mm

240-mm

Step Interface

Graded Interface

Material PropertiesMaterial Properties

10-1

100

101

102

103

0

1

2

3x 10

4

Time (sec)

Re

lax

ati

on

Mo

d.

(MP

a)

RCRIRCRIRCRIRCRI

Surface CourseSurface CourseSurface CourseSurface Course (PG70-16, 19-mm Superpave mix) (PG70-16, 19-mm Superpave mix) (PG70-16, 19-mm Superpave mix) (PG70-16, 19-mm Superpave mix)

Graded Interface Step Interface

(Interlayer)

Top

Bottom

10-1

100

101

102

103

0

1

2

3x 10

4

Interface WidthReduced Time (sec)

Re

lax

ati

on

Mo

du

lus

(M

Pa

)

Top

Bottom

10-1

100

101

102

103

0

1

2

3x 10

4

Interface WidthReduced Time (sec)

Re

lax

ati

on

Mo

du

lus

(M

Pa

)

48

2

2.5

3

3.5

4

Str

ess in

x-x

Dir

ecti

on

(M

Pa)

Step Interface, Surface Mix

Step Interface, Average

Peak Tensile Stress in OverlayPeak Tensile Stress in Overlay

Overlay

Interlayer

0 100 200 300 400 500 600 700 800-0.5

0

0.5

1

1.5

Time (sec)

Str

ess in

x-x

Dir

ecti

on

(M

Pa)

Graded InterfaceStep Interface, RCRI

~ 30%

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SummarySummary

Viscoelastic graded finite elements using GIF are proposed

Correspondence principle based formulation is developed and implemented

Recursive formulation is utilized for time-integration analysis

Verifications are performed by comparison of present

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Verifications are performed by comparison of present approaches with:– Analytical solutions

– Commercial software (ABAQUS)

Asphalt pavement systems are simulated:– Aged pavement conditions

– Graded interfaces

ConclusionsConclusions

Aging and temperature dependent property gradients should be considered in simulation of asphalt pavements

Non-homogeneous viscoelastic analyses procedures presented here are suitable and preferred for simulation of asphalt pavement systemssystems

Proposed procedures yield greater accuracy and efficiency over conventional approaches

Layered gradation approach can yield significant errors

– Most pronounced errors are at layer interfaces in the stress and strain quantities.

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Conclusions (cont.)Conclusions (cont.)

Interface between asphalt concrete layers can be realistically simulated using the procedures discussed in the current dissertation

When using the layered approach, averaging at layer interfaces may lead to significantly different predictions as compared to the FGM approach

– The difference is usually exaggerated with time – The difference is usually exaggerated with time when a significant viscoelastic gradation is present

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Other Applications and Future ExtensionsOther Applications and Future Extensions

Applications and ExtensionsApplications and Extensions

Transition Layers CharacteristicsMicromechanical Predictions

Graded Viscoelastic + Stress Dependent Model

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Applications and ExtensionsApplications and Extensions

Design of Viscoelastic

FGMs

( , )E x t

Analysis of graded viscoelastic materials:• Metals at high temperature• Polymers• Geotechnical materials• PCC/FRC• Biomaterials• Food industry

Other material models:• 2S2P1D• Power law etc.

ABAQUS UMAT Subroutine

Thank you for your attention!!Thank you for your attention!!

E1 E2 EN

τ1 τ2 τN

Questions??Questions??

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asphalt pavement aging and temperature dependent ... pavement aging and temperature dependent...

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