1

By

Waleed Zeiada, Ph.D.

Civil, Environmental, and Sustainable Engineering

Tempe, AZ 85287‐5306

Fatigue Endurance Limits for

Perpetual Pavements

November 14, 2013

2

Outline Background

Research Statement and Objectives

Testing Plan and Design of Experiment

Endurance Limit (EL) Algorithm Development

Development of SR Models

Comparison of EL from Uniaxial and Beam Fatigue

Incorporating EL Methodology into AASHTOWare-ME

Conclusions, and Recommendations

3

Outline

Background

Research Statement and Objectives

Testing Plan and Design of Experiment

Endurance Limit (EL) Algorithm Development

Development of SR Models

Comparison of EL from Uniaxial and Beam Fatigue

Incorporating EL Methodology into AASHTOWare-ME

Conclusions, and Recommendations

4

Background

Fatigue

Perpetual

Pavement

Hot Mix

Asphalt

Endurance

Limit

5

HMA Fatigue Damage/Cracking

Description: Three different stages

Definition: A load associated damage due to repeated traffic loading.

Early Stage Final Stage Intermediate Stage

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Perpetual Pavements

Definition: Term used to describe a long lasting HMA

pavements.

At least 50 years

Full depth asphalt, 1960s

Three HMA layer system

Increases pavement

recycling

Cost savings

Environmental benefits.

7

Endurance Limit

Definition: Wöhler (1870)

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Does HMA Exhibit an Endurance Limit?

Monismith et al., 1970 Carpenter et al., 2003

HMA EL (Prowell et al., 2009):

Strain level yields 50 millions load repetitions until failure

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Perpetual Pavement Design Concept

Endurance Limit = 75 ms

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Outline

Background

Research Statement and Objectives

Testing Plan and Design of Experiment

Endurance Limit (EL) Algorithm Development

Development of SR Models

Comparison of EL from Uniaxial and Beam Fatigue

Incorporating EL Methodology into AASHTOWare-ME

Conclusions, and Recommendations

11

Research Problem Statement and objectives

The EL concept has not been totally implemented in

AASHTOWare Pavement ME Design software

No current methodology to consider the effect of the

environmental conditions, traffic condition, mix design,

and material properties together in the EL calculations

Develop an algorithm to determine EL that is compatible

with the AASHTOWare-ME software

12

New EL Definition

EL is a result of a balance of

damage caused by loading and

healing or damage recovery

that occurs during rest periods

T1 T3 T4 T5 T6 T2 A

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Outline

Background

Research Statement and Objectives

Testing Plan and Design of Experiment

Endurance Limit (EL) Algorithm Development

Development of SR Models

Comparison of EL from Uniaxial and Beam Fatigue

Incorporating EL Methodology into AASHTOWare-ME

Conclusions, and Recommendations

14

Factors Affecting Fatigue and EL

Factors Asphalt Content (%) Binder Grade

Air Voids (%) Aggregate Type

Temperature (oF) Filler Percent

Rest Period (seconds) Aggregate Gradation

Tensile Strain (μs) Test Type

10 Factors with 3 levels: 3^10 = 59049 tests

Three replicates: 69049 * 3 = 177147 tests

Assuming average of 10 hours per test

Total of 202 years

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Selected Factors

Factors No. of Levels

Asphalt Content, AC (%) 4.2, and 5.2

Air Voids, Va (%) 4.5, and 9.5

Temperature, T (oF) 40, 70, and 100

Rest Period, RP (seconds) 0, 5, 1, and 10

Tensile Strain, εt (μs) L, M, and H

Binder Type PG 58-28, 64-24, and 76-16

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Test Type

Uniaxial Fatigue Test Beam Fatigue Test

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Binder Type PG 58-28 PG 64-22 PG 76-16

Binder Content 4.2 5.2 4.2 5.2 4.2 5.2

Air Voids (%) 4.5 9.5 4.5 9.5 4.5 9.5 4.5 9.5 4.5 9.5 4.5 9.5

Temperature, F Tensile Strain Rest Period (sec)

40

L

0 U U U

1

5 U U U U

10

M

0 U U U

1 U

5 U U U

10 U

H

0 U

1 U

5 U

10

70

L

0 U U U

1

5 U U U

10 U

M

0 U U U

1 U

5 U U U U

10

H

0

1 U

5

10

100

L

0 U U U

1 U U

5 U U

10

M

0 U U U

1

5 U U U

10 U

H

0 U

1

5 U

10

Total Number of Combinations Beam Fatigue = 190 Uniaxial Fatigue = 51

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Outline

Background

Research Statement and Objectives

Testing Plan and Design of Experiment

Endurance Limit (EL) Algorithm Development

Development of SR Models

Comparison of EL from Uniaxial and Beam Fatigue

Incorporating EL Methodology into AASHTOWare-ME

Conclusions, and Recommendations

19

Healing of Micro-cracks

Test Without Rest Periods

Time

Strain

Test With Rest Periods

Time

Strain

0

0.2

0.4

0.6

0.8

1

1.2

0 5000 10000 15000 20000 25000

Sti

ffn

ess

Ra

tio

Number of Loading Cycles

Without Rest Period

With Rest Period

Healing

SR = 1.0, No Fatigue Damage

1-SR WRP

1-SR WORP

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Algorithm Development for HMA Endurance Limit Determination of Endurance Limit Using SR

0.4

0.6

0.8

1.0

1.2

0 5000 10000 15000 20000

Sti

ffn

es

s R

ati

o

Loading Cycles, N

5.2AC%, 9.5Va%, 112.5 με, 5 sec RP

5.2AC%, 9.5Va%, 155 με, 5 sec RP

At endurance limit, SR = 1.0

0.4

0.6

0.8

1

10 100 1000

Sti

ffn

ess

Rati

o

Tensile Strain, μs

EL = 80 μs

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Outline

Background

Research Statement and Objectives

Testing Plan and Design of Experiment

Endurance Limit (EL) Algorithm Development

Development of SR Models

Comparison of EL from Uniaxial and Beam Fatigue

Incorporating EL Methodology into AASHTOWare-ME

Conclusions, and Recommendations

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First Generation SR Model

SR = f (T, AC, Va, εt , RP, BT, and N)

AC = Asphalt content, %

Va = Air voids, %

εt = Tensile Strain, μs

T = Temperature, oF

RP = Rest period, sec

BT = Binder Type

N = Number of cycles

0.90

0.92

0.94

0.96

0.98

1.00

0 5000 10000 15000 20000 25000

Sti

ffn

ess

Ra

tio

Number of Loading Cycles

N = 5,000

N = 20,000

N = 15,000

N = 10,000

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First Generation SR Model Form of First Generation SR Model

Effect of Rest Period

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4 5 6 7 8 9 10 11

PS

R

RP, Second

PSR = a + b * Tanh (c * RP)

a, b, and c are regression coefficients

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First Generation SR Model

R2adj = 0.979

SR = 0.1564774 + (0.00079*BT) + (0.070059744*AC) +

(0.00393*Va) +(0.10095*RP) - (1.268*10-7 *Nf) - (0.0024676 *T)

- (0.0001677*BT*AC) + (3.29961x10-5 *BT*RP) + (3.488*10-

6 *BT*T) + (0.00794848*AC*RP) - (0.0042225*Va*RP) +

(0.0006044*AC*T) - (0.0001035*Va*T) - (2.889*10-8*RP*Nf) +

(2.9191*10-9 *Nf*T) - (0.0025*RP*T) - (3.97*10-7 *BT2) -

(1.20135*10-5*T2) + (8.434*10-8 *BT2*AC) - (2.8756*10-

8 *BT2*RP) + (1.9558*10-6 *AC*T2) + (6.6137*10-7 *Va*T2) -

(1.582*10-11 *Nf*T2) + (1.262x10-5 *RP*T2) - (1.176*10-6

*Va*RP*T2) + (3.124*10-12 *Nf*RP*T2) - (7.4*10-7 *BT*AC*T)

+ (3.92*10-7 *BT*RP*T) + (0.00013185 *Va*RP*T) + (2.19 * 10-

9 *Nf*RP*T)

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EL Values From First Generation SR Model

0.7

0.8

0.9

1.0

10.0 100.0 1000.0

SR

Tensile Strain, εt

4.5 Va% - 5.2 AC%

9.5 Va% - 5.2 AC%

4.5 Va% - 4.2 AC%

9.5 Va% - 4.2 AC%

PG 64-22

70⁰F

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EL Values From First Generation SR Model

0

50

100

150

200

250

3004.2

AC

-9.5

Va

4.2

AC

-4.5

Va

5.2

AC

-9.5

Va

5.2

AC

-4.5

Va

4.2

AC

-9.5

Va

4.2

AC

-4.5

Va

5.2

AC

-9.5

Va

5.2

AC

-4.5

Va

4.2

AC

-9.5

Va

4.2

AC

-4.5

Va

5.2

AC

-9.5

Va

5.2

AC

-4.5

Va

Endura

nce L

imit, ms

PG 76-16 PG 64-22 PG 58-28

40 ⁰F 100 ⁰F 70 ⁰F

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Second Generation PSR Model

SR = f (Eo, εt , RP, and N)

SR=2.0844-0.1386*log(Eo)-

0.4846*log(et)-0.2012*log(N)+

1.4103*tanh(0.8471*RP)+0.0320

*log(Eo)*log(et)-0.0954*log(Eo)

*tanh(0.7154*RP)-

0.4746*log(et)*tanh(0.6574*RP)

+0.0041*log(N)

*log(Eo)+0.0557*log(N)*log(et)+

0.0689*log(N)*tanh(0.0259*RP)

R2adj = 0.891

BT, T, AC, Va were replaced by initial stiffness, Eo

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Second Generation SR Model

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

10 100 1000

SR

e, ms

Eo=50 ksi Eo=100 ksi Eo=200 ksi Eo=500 ksi

Eo=1000 ksi Eo=2000 ksi Eo=3000 ksi

RP = 5 sec, N

= 200,000

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EL from Second Generation SR Model

0

50

100

150

200

250

1 2 5 10 20

En

du

ran

ce L

imit, m

s

Rest Period, sec

Eo=3000 ksi Eo=2000 ksi Eo=1000 ksi Eo=500 ksi

Eo=200 ksi Eo=100 ksi Eo=50 ksi

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Outline

Background

Research Statement and Objectives

Testing Plan and Design of Experiment

Endurance Limit (EL) Algorithm Development

Development of SR Models

Comparison of EL from Uniaxial and Beam Fatigue

Incorporating EL Methodology into AASHTOWare-ME

Conclusions, and Recommendations

31

Beam Fatigue Versus Uniaxial Fatigue Tests

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 50000 100000 150000

Sti

ffn

ess

Rati

o

Number of Loading Cycles

Beam Fatigue

Uniaxial Fatigue

4.5 Va% - 4.2 AC%

100 Tensile με, 40 F(a)

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

0 2000 4000 6000 8000 10000 12000

Sti

ffn

ess R

ati

o

Number of Loading Cycles

Uniaxial Fatigue without RP

Uniaxial Fatigue with RP

Beam Fatigue without RP

Beam Fatigue with RP

4.5 Va% - 4.2 AC%

100 Tensile με, 40 F5 sec. RP

Uniaxial Fatigue

Healing

Beam Fatigue

Healing

Damage Comparison

Healing Comparison

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Uniaxial Fatigue Versus Beam Fatigue

y = 0.8986xR² = 0.9688

10

100

1000

10 100 1000

Un

iaxia

l F

ati

gu

e E

nd

ura

nce

Lim

it

Beam Fatigue Endurance Limit

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Outline

Background

Research Statement and Objectives

Testing Plan and Design of Experiment

Endurance Limit (EL) Algorithm Development

Development of SR Models

Comparison of EL from Uniaxial and Beam Fatigue

Incorporating EL Methodology into AASHTOWare-ME

Conclusions, and Recommendations

34

Incorporation of EL into AASHTOWare-ME 1. Calculation of Endurance Limit

SR = f (Eo ,et, N, and RP)

N = Number of cycles

N of 20,000 is recommended

RP= Rest Period (sec)

RP = t / ∑(NT)

Eo, Initial Stiffness (ksi)

1.0E+04

1.0E+05

1.0E+06

1.0E+07

1.0E+08

-10.00 -5.00 0.00 5.00 10.00

Dy

na

mic

Mo

du

lud

, E

* p

si

Log Reduced Frequency, Hz

Tensile Strain is equal to the

Endurance Limit at PSR = 1.0

et, Tensile Strain, μs

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Incorporation of EL into AASHTOWare-ME

2. Incorporation of EL into Fatigue Damage

Di= Σ (ni / Nfi)

D = Fatigue Damage

ni = Actual traffic for period i (Traffic Demand)

Nfi = Allowed Traffic in period i (Traffic Capacity)

If the calculated EL < the actual et, Damage is count

If the calculated EL ≥ the actual et, the Ni is infinity and

the Damage is zero

et

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Outline

Background

Research Statement and Objectives

Testing Plan and Design of Experiment

Endurance Limit (EL) Algorithm Development

Development of SR Models

Comparison of EL from Uniaxial and Beam Fatigue

Incorporating EL Methodology into AASHTOWare-ME

Conclusions, and Recommendations

37

Conclusions

HMA exhibits endurance limit

Mixtures using softer binders exhibit higher endurance

limits than mixtures using stiffer binders

High binder contents and low air voids produced the

high endurance limit values

Endurance limit values were higher at high

temperatures

The endurance limit values from the beam fatigue

exhibit similar trends compared to those of the uniaxial

fatigue test

The endurance limits obtained in this study can be

incorporated in the AASHTOWare-ME

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Recommendations Field calibration is needed

Consider other types of aggregates, and mixes such

as warm mix asphalt, asphalt rubber, and polymer

modified mixtures

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Acknowledgement NCHRP 944-A Project Panel

ASU Project Team and Lab Support:

Dr. Matthew Witczak

Dr. Michael Mamlouk

Dr. Kamil Kaloush

Dr. Mena Souliman

Mr. Peter Goguen, and Mr. Kenny Witczak

IPC:

Mr. Con Sinadinos, Mr. Alan Feeley, and Mr. Stephen

King

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Questions!