Eisa RahmaniMasoud K. Darabi

Eyad A. MasadDallas N. Little

Rashid K. Abu Al-Rub

Constitutive Modeling of Oxidative Aging Effects on Damage Response of Asphalt Concrete

Petersen Asphalt Research Conference and P3 Symposium, Laramie, WYJuly 2014

Acknowledge funding by:Qatar National Research Foundation

Asphalt Research Consortium through FHWA

Overview

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Mechanical loading

Air voids

Major products:Carbonyl, C=OSulfoxides, S=O

Stiffer & More Brittle

Oxidative Aging Constitutive Relationship• Physically-Based Aging Variable• Oxygen content and temperature

dependent

Coupling to Mechanical Behavior

through PANDA

Calibration & Validation• Experiments• Computations

Pavement Performance Simulations

( ) 21 1 ( )kkadA A f Tdt

θ= Γ −

k1 controls the oxygen content effect

k2 controls the aging history effect

Oxidative Aging Constitutive Relationship

expCAdCA Er Pdt RT

αβ − = =

• Carbonyl Formation Rate:

• Oxidative Aging Constitutive Relationship:

Aging variable, accounts for property change caused by oxidative aging

Aging Fluidity parameter Normalized oxygen content

History dependent term

Thermal coupling term

3

(Abu Al-Rub et al. 2013)

(Rahmani et al. 2014, under review)

(Liu M. et al. 1996)

• Identifying “Aging variable” using Dynamic Modulus Test

Calibration

4

Test Specimens

Mixing and preparation

Superpave Gyratory

Compactor

Aggregate Limestone

Binder PG 67-22

Air void Content 7.0 ± 0.5

Max Agg. Size 19.0 mm

Aging Temperature Room @ 60˚C

15.2 cm

10 cm

ARC Mix #1, Test conducted by TAMU

2

2

(1 )

(1 )

kaged unagedn n

kaged unagedn n

D A D

Aλ λ

= −

= −

5

( )1

1 exp N

t tn n

n

D D λψ=

∆ = − − ∑

Compliance termsRetardation times

Calibration

( ) ( )( )

2

20 21

1[ / ( 1 )] 1

k unagedNnunaged

aged k unagedn

A DD D

Aω

ω λ

−′ = +

− +∑

( ) ( ) ( )( )

2 2

2 21

[ / ( 1 )]( 1 )[ / ( 1 )] 1

k kunaged unagedNn n

aged k unagedn

A A DD

Aω λ

ωω λ

− −′′ =

− +∑

• Storage compliance

• Loss compliance

Transient Compliance of Aged Material:

Interconversion Relationships:

( ) ( )20 0 1 0

tt ijve tij ij

d gg D g D d

d

ττ

ψ ψ σε σ τ

τ−

= + ∆∫Nonlinear Viscoelasticity:Schapery, 1969

Prediction of Aging-Viscoelastic Response

6

Axi

al S

tress

Time

• Repeated Creep-Recovery at Various Stress Level

Axi

al S

train

Time

Loading Unloading

Irrecoverable Strain

Viscoelastic Recovery

Prediction of Aging-Viscoelastic Response

7

• Repeated Creep-Recovery at Various Stress Level

Test No. Temperature (˚C)Aging

ConditionAir Void

Percentage

Loading Time -Unloading Time

(sec)

Confinement Stress (kPa)

1

40

Unaged

7% 0.4 - 30 1383 months2

6 months3

4

55

Unaged

7% 0.4 - 30 1383 months5

6 6 months

ARC Mix #1, Test conducted by TAMU

Prediction of Aging-Viscoelastic Response

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Comparisons of Recovered Viscoelastic Strain for Aged Asphalt Concrete

6-month aged @ 55˚C

3-month aged @ 40˚C

3-month aged @ 55˚C

6-month aged @ 40˚C

• Some of the Capabilities of PANDA in Constitutive Modeling:

Oxidative aging

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Aging-Viscoelastic-Viscodamage Response Prediction

Nonlinear Viscoelasticity

Viscodamage

Schapery, 1969

Darabi et al. 2013

• PANDA References:1. Abu Al-Rub et al. 2010, “A micro-damage healing model that improves prediction of fatigue life in asphalt mixes”.2. Abu Al-Rub et al. 2011, “A unified continuum damage mechanics model for predicting the mechanical response of asphalt mixtures and pavements”.3. Darabi et al. 2011, “A thermo-viscoelastic-viscoplastic-viscodamage constitutive model for asphaltic materials”.4. Darabi et al. 2012, “A continuum damage mechanics framework for modeling micro-damage healing”.5. Darabi et al. 2012, “A modified viscoplastic model to predict the permanent deformation of asphaltic materials under cyclic-compression loading at

high temperatures”.6. Darabi et al. 2013, “Cyclic Hardening-Relaxation Viscoplasticity Model for Asphalt Concrete Materials”.7. Shakiba et al. 2013, “Continuum Coupled Moisture-Mechanical Damage Model for Asphalt Concrete”.

Effect of Aging on Viscodamage Evolution Function:

( )0

, 0q

kvdeff

Y kY

φ ε

= Γ <

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Aging-Viscoelastic-Viscodamage Response Prediction

1σσφ

=−

Nominal (damaged) Configuration

∆ ∆

Effective (undamaged) Configuration

Remove damages

(Darabi et al. 2013)

Effective Stress:

Normalized damage force

Effective Strain

Damage Density

∆

t

σ

ε

Age

unaged agedφ φ<

• Cyclic Crosshead-Controlled Test

LVDTs

Loading rod

11

0

300

600

900

1200

1500

0 0.25 0.5 0.75 1

Stra

in (m

icros

train

)Time (sec)

Applied strain at the end platesMeasured strain at the LVDTs

Average strain at the end platesMeasured strain at LVDTs

Aging-Viscoelastic-Viscodamage Response Prediction

Test No.

Aging condition Temperature Average initial on-

specimen micro-strainLoading frequency

(cycle/sec)

1 3 months5˚C

10810

2 3 months 102

3 6 months5˚C

10610

4 6 months 105ARC Mix #1, Test conducted by NC State University

3-month aged

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Aging-Viscoelastic-Viscodamage Response Prediction

• Predictions of Stress Response:

(Strain Amplitude= 108 micro strain) (Strain Amplitude= 102 micro strain)

6-month aged

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Aging-Viscoelastic-Viscodamage Response Prediction

• Predictions of Stress Response:

(Strain Amplitude= 107 micro strain) (Strain Amplitude= 105 micro strain)

• Quantifying Effective Oxygen Diffusivity

3D microstructure of asphalt concrete

Aggregates

Non-diffusible

BinderAir voids

Super diffusible

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You et al. 2012

Pavement Performance Simulations

Experimentally determined

VF = 82% VF = 7% VF = 11%

• Framework:

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θ=1

L

θ(t)

• Oxygen Diffusion Simulation

2effD

tθ θ∂= ∇

∂Fick’s second law:

Normalized Oxygen Content, θ

Pavement Performance Simulations

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Pavement Performance Simulations

Experimental results from Han and Glover (2011)

Type of MaterialExperimental

ResultsComputational

Results

Binder 3.82 – 22.81 11.16

Matrix(with fine aggregates up to 25% VF)

3.11 – 19.87 7.93

Full Mixture N.A. 3.33

• Computational and Experimental Results for Oxygen Diffusivity at Intermediate to High Temperatures

Units in mm2/day

• Objective:Investigate the effect of oxidative aging on damage performance of a 2D pavement structure

• Contact Area = 0.0715 m2

• Wheel load = 71 (kN)• Contact pressure = 993 (kPa)

• From: Transportation Pooled Fund Study TPF-5(019) and SPR-2(174) Accelerated Pavement Testing of Crumb Rubber Modified Asphalt Pavements

500 mm

150 mm

100 mm

• Pulse loading(axisymmetric model)

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Pavement Performance Simulations

Oxygen content

12 months

30 months

60 months

120 months

Aging variable

θ

18

A

100 mm

Pavement Performance Simulations

Unaged 6 months

12 months 30 months

60 months 120 months

Damage evolution 8000 loading cycles, loading time=0.1 sec, rest period=0.4 sec

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ɸ

Pavement Performance Simulations

• The oxidative aging constitutive relationship was presented.

• The effects of oxidation is incorporated by the physically-based aging variable.

Summary and Conclusions

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• A straight-forward procedure was introduced to identify material properties.

• The proposed constitutive modeling of aging is capable of predicting the viscoelastic and time-dependent damage response of laboratory conducted tests.

• The presented computational framework is used to investigate the effect of different constituents on oxidative aging susceptibility of asphalt concrete. This will provide a tool to design more aging-resistible pavements.

• Further validation of aging-mechanical constitutive model

• Incorporate the healing effect into oxidative aging studies

• Thermodynamic framework for oxidative aging constitutive modeling

• Thorough investigation of asphalt layer geometry and material properties on fatigue response of aged pavements

Ongoing Research

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Acknowledge Funding by:

• Qatar National Research Fund (QNRF)• The Asphalt Research Consortium –The US Federal Highway Administration

Special Thanks to:

Dr. David H. AllenDr. Charles J. GloverDr. Emad Kassem

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Thanks For Your Attention