asphalt pavement aging and temperature dependent ... pavement aging and temperature dependent...
TRANSCRIPT
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
Correspondence Principle Based Analysis
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)
Functionally Graded Viscoelastic Asphalt Functionally Graded Viscoelastic Asphalt Concrete ModelConcrete Model
Motivation and Introduction
Viscoelastic Characterization of Asphalt Concrete
13
Viscoelastic FGM Finite Elements
Correspondence Principle Based Analysis
Time Integration Analysis
Application Examples: Asphalt Pavement
Summary and Conclusions
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
Functionally Graded Viscoelastic Asphalt Functionally Graded Viscoelastic Asphalt Concrete ModelConcrete Model
Motivation and Introduction Viscoelastic Characterization of Asphalt Concrete
Viscoelastic FGM Finite Elements
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
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
27
Correspondence Principle Based Analysis
Time Integration Analysis
Application Examples: Asphalt Pavement
Summary and Conclusions
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)
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 Time Integration Analysis
32
Time Integration Analysis
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)
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
39
Correspondence Principle Based Analysis
Time Integration Analysis
Application Examples: Asphalt Pavement
Summary and Conclusions
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
47
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%
49
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
50
Correspondence Principle Based Analysis
Time Integration Analysis
Application Examples: Asphalt Pavement
Summary and Conclusions
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
51
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.
52
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
53
Other Applications and Future ExtensionsOther Applications and Future Extensions
Applications and ExtensionsApplications and Extensions
Transition Layers CharacteristicsMicromechanical Predictions
Graded Viscoelastic + Stress Dependent Model
54
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??
55