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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
6
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)
8
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
9
Perpetual Pavement Design Concept
Endurance Limit = 75 ms
10
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
13
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
15
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
16
Test Type
Uniaxial Fatigue Test Beam Fatigue Test
17
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
18
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
20
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
21
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
22
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
23
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
24
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)
25
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
26
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
27
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
28
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
29
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
30
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
32
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
33
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
35
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
36
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
38
Recommendations Field calibration is needed
Consider other types of aggregates, and mixes such
as warm mix asphalt, asphalt rubber, and polymer
modified mixtures
39
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
40
Questions!