Principal Investigators:
Jeffery Roesler, Ph.D., P.E.
Surendra Shah, Ph.D.
Fatigue and Fracture Behavior
of Airfield Concrete Slabs
Graduate Research Assistants:
Cristian Gaedicke, UIUC
David Ey, NWU
Urbana

Champaign, November 9
th
, 2005
Outline
Objectives
Experimental Design
Experimental Results
2

D Fatigue Model
Finite Element Analysis
Application of FEM Model
Fatigue Model Calibration
Fatigue Model Application
Summary
The Future
Cohesive Zone Model
Research Objectives
Predicting crack propagation and failure under
monotonic and fatigue loading
Can fracture behavior from small specimens predict crack
propagation on slabs.
Three point bending beam
(TPB)
Beam on elastic foundation
Slab on elastic foundation
Load
CMOD
Integrate full

scale experimental slab data and a 2

D
analytical fracture model (Kolluru, Popovics and Shah)
Check if the monotonic slab failure envelope controls the
fatigue cracking life of slabs as in small scale test
configuration.
Research Objectives
Fatigue load
Monotonic load
2

D Model
Load vs. CMOD curve
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CMOD (mm)
Load (kN)
Load vs. CMOD in 63 mm beam
0
0.5
1
1.5
2
2.5
0
0.002
0.004
0.006
0.008
0.01
CMOD (mm)
Load (kN)
Cycle 1
Cycle 1024
Load vs. CMOD for 63 mm depth beam
0
0.5
1
1.5
2
2.5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
CMOD (mm)
Load (kN)
Experimental Design
Simple supported beams:
2 beams, 1100 x 80 x 250 mm.
2 beams, 700 x 80 x 150 mm.
2 beams, 350 x 80 x 63 mm.
•
The beams have a notch in the
middle whose length is 1/3 of the
beam depth
.
Beams on clay subgrade:
2 beams, 1200 x 80 x 250 mm.
2 beams, 800 x 80 x 150 mm.
2 beams, 400 x 80 x 63 mm.
•
The beams have a notch in the middle whose
length is 1/3 of the beam depth.
Beam Tests
Experimental Design
Large

scale concrete slabs on clay
subgrade:
2 slabs, 2010 x 2010 x 64 mm.
4 slabs, 2130 x 2130 x 150 mm.
•
The load was applied on the edge through an
200 x 200 mm. steel plate.
•
The subgrade was a layer of low

plasticity
clay with a thickness of 200 mm.
Standard Paving
Concrete:
¾” limestone coarse crushed
aggregate, 100 mm slump and
Modulus of Rupture 650 psi at 28
days
Slab Tests
Concrete Mix
Experimental Results
Results on Beams
•
Full Load

CMOD curve.
•
Peak Load.
•
Critical Stress Intensity Factor (K
IC
) .
•
Critical CTOD (CTOD
c
).
•
Compliance for each load Cycle (C
i
).
Monotonic Load
Load vs CMOD in Simple Supported Beams
0
1
2
3
4
5
6
7
8
0
0.2
0.4
0.6
0.8
1
1.2
CMOD (mm)
Load (kN)
Load vs. CMOD Curve for Beams on Elastic Foundation
0
1
2
3
4
5
6
7
8
9
10
0
0.5
1
1.5
2
2.5
3
3.5
CMOD (mm)
Load (kN)
B63
B150
B250
Load vs. CMOD for Beam on Elastic Foundation
0
1
2
3
4
5
6
7
0
0.2
0.4
0.6
0.8
1
CMOD (mm)
Load (kN)
Compliance vs. load cycle
Beam FEM Setup
Small Beam
UIUC Testing
Monotonic Results and Crack Length
FSB 63
y = 0.0006x  0.008
R
2
= 0.9972
0
0.005
0.01
0.015
0.02
0.025
0.03
0
10
20
30
40
50
60
Crack length (mm)
Compliance
Peak Load
0
0.5
1
1.5
2
2.5
0
0.01
0.02
0.03
0.04
0.05
0.06
CMOD (mm)
Load (KN)
FSB 63B
FSB 63C
0
0.5
1
1.5
2
2.5
0
10
20
30
40
50
60
crack length (mm)
load (KN)
FSB 63b
FSB 63c
From FEM
From Testing
Experimental Results
Results on Beams
•
Load vs. CMOD curves
•
Compliance vs. number of
cycles
•
Peak Load.
•
Stress Intensity Factor (K
I
) .
•
Compliance for each load
Cycle (C
i
).
Fatigue Load in FSB
Load vs. CMOD Fatigue Cycles in 63 mm beam
0
0.5
1
1.5
2
2.5
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
CMOD (mm)
Load (kN)
Cycle 1
Cycle 1024
Cycle 10240
Cycle 45568
Experimental Results
Results on Slabs
•
Full Load

CMOD curve.
•
Peak Load.
•
Compliance for each load Cycle
(C
i
).
Monotonic Load
≈ 5 mm
Load vs CMOD for 150 mm slabs
0
20
40
60
80
100
120
140
0
0.2
0.4
0.6
0.8
1
1.2
1.4
CMOD (mm)
Load (kN) ...
Edge notch Specimen A
Edge notch Specimen B
Unnnotched (Estimated CMOD)
Load vs CMOD for 63 mm depth slabs
0
10
20
30
40
50
60
0
0.2
0.4
0.6
0.8
1
1.2
CMOD (mm)
Load (kN)...
1/3 depth notch
Edge notch
Experimental Results
Results on Slabs
Fatigue Load
Compliance vs. number of Cycles
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
Number of Cycles
Compliance (mm/kN)
U1
L2
U2
L3
•
Load vs. CMOD curves
•
Compliance vs. number of cycles
•
Peak Load.
•
Stress Intensity Factor (K
I
) .
•
Compliance for each load Cycle (C
i
).
Crack Length vs Number of Cycles (T2 slab)
0
15
30
45
60
0
10000
20000
30000
40000
50000
60000
Number of Cycles
Crack Length (mm)…...
2

D Fatigue Model
2

D Fatigue Model
t
w
C
w
a
g
sa
E
i
2
0
2
1
)
/
(
6
t
w
C
w
a
g
sa
E
loop
u
eff
c
2
)
#
(
2
2
)
/
(
6
(Kolluru, Popovics and Shah, 2000)
2
1
E
E
P
max
CMOD
P
*
C
i
*
C
(loop)
P
min
*Secant compliance
C
u
(1)
P
c
CMOD
P
C
i
½ P
c
C
u
(2)
C
u
(3)
P
c
a
eff
P
O’
a
0
O
P
c
a
eff
P
a
0
P
max
a
\
failure
P
min
Relation between load and effective
crack length a
eff
is obtained !!
Monotonic Test of TPB
Fatigue Test of TPB
P
c
a
eff
P
O’
a
0
O
P
max
A
B
C
D
a
\
failure
s
a
t
w
2

D Fatigue Model
2

D Fatigue Model
O’

O: no crack growth, linear
part of the load

CMOD curve.
O

B: Crack Deceleration Stage,
Stable crack growth, nonlinear
part of the load

CMOD curve
until peak load.
B

D: Crack Acceleration Stage
Post peak load

CMOD.
Where:
C
1
, n
1
, C
2
, n
2
are constants
D
a = incremental crack growth between
D
N
D
N
= incremental number of cycles
D
K
I
=stress intensity factor amplitude of a load cycle
a
P
c
a
P
O’
a
0
O
P
max
A
B
C
D
a
\
failure
a
\
crit
Log
(D
a/
D
N)
a
0
O
B
C
D
a
\
failure
a
\
crit

3

5

7
# cycles
a
a
0
a
\
crit
a
\
failure
N
f
0.4N
f
B
C
1
0
1
)
(
n
a
a
C
N
a
D
D
2
2
)
(
n
K
C
N
a
I
D
D
D
Finite Element Analysis
FEM Mesh
Computation of the Stress
Intensity Factor & C
i
(a)
a
c
b
d
e
f
Element

1
Element

2
E
lement

4
Element

3
Y, v
X, u
a
D
a
D
a
D
O’
F
c
O
)
(
2
1
)
(
2
1
0
0
d
c
e
a
d
c
c
a
I
v
v
F
a
v
v
F
a
G
Lim
Lim
D
D
D
D
An indirect method was used to calculate
K
I
, called “Modified Crack Closure Integral
Method. (Rybicki and Kanninen, 1977)
Normal equations for TPB Beams are not
applicable.
FEM Modelation is required.
CMOD vs. Crack Length
Compliance vs. Crack Length
Finite Element Analysis
Relation between Crack length, Compliance and
CMOD
The CMOD increases its value with the
increase of the Crack Length.
y = 1E07x
2
 1E06x + 1.0228
0
0.3
0.6
0.9
1.2
1.5
1.8
0
400
800
1200
1600
2000
Crack length (mm)
Normalized compliance
FEM
Poly. (FEM)
0
0.05
0.1
0.15
0.2
0.25
0
500
1000
1500
2000
Crack length (mm)
CMOD (mm)
FEM
Poly. (FEM)
y=1E7x
2
+2.9E4x
The normalized compliance at the midslab
edge predicted using the FEM model
shows a quadratic behavior.
Finite Element Analysis
Relation between Stress
Intensity Factor and Crack
Length
Relation between CMOD
and Crack Length
y = 2E06x + 0.0007
y = 5E10x
2
 9E07x + 0.0014
0
0.0005
0.001
0.0015
0.002
0
400
800
1200
1600
2000
Crack length (mm)
KI/P (mm3/2)
FEM1
FEM2
Lineal (FEM1)
Polynomial (FEM2)
0
0.05
0.1
0.15
0.2
0.25
0
500
1000
1500
2000
Crack length (mm)
CMOD (mm)
FEM
Poly. (FEM)
y=1E7x
2
+2.9E4x
Application of FEM Model
Step 1: Experimental Relation between CMOD
and the Displacement
CMOD vs Displacement
y = 0.0005x
3
 0.0037x
2
+ 0.0123x
R
2
= 0.9851
0
0.04
0.08
0.12
0.16
0.2
0
2
4
6
8
10
Displacement (mm)
CMOD (mm)
Experimental relation
between CMOD
measurements and
displacement.
Load vs CMOD Curve
0
20
40
60
80
100
120
140
0
0.2
0.4
0.6
0.8
1
1.2
1.4
CMOD (mm)
Load (kN)
Edge notch Specimen A
Edge notch Specimen B
Unnnotched (Estimated CMOD)
Step 2: Determination of the Load vs. CMOD curves
The relation
between CMOD
and displace

ments allows to
estimate the
CMOD for the
unnotched
specimen
Application of FEM Model
Step 3: Estimation of the Crack Length
The crack length is
estimated using
this modified
equation from the
FEM model and the
CMOD
CMOD vs. Crack Length
y = 231084x
3
 32098x
2
+ 3357.4x
R
2
= 0.9622
0
200
400
600
800
1000
1200
1400
1600
0
0.05
0.1
0.15
0.2
0.25
CMOD (mm)
Crack Length (mm)…..
Application of FEM Model
Step 4: Estimation of the Normalized
Compliance (FEM)
Normalized Compliance vs Crack Length
y = 1E07x
2
 1E06x + 1.0228
R
2
= 0.9018
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
0
500
1000
1500
2000
Crack Length, a (mm)
Normalized Compliance
Application of FEM Model
The normalized
compliance
obtained from the
FEM Model for
different crack
length is multiplied
by the experimental
initial compliance
Step 5: Experimental Compliance vs. Crack
Length curves
Compliance vs Crack Length
0
0.00025
0.0005
0.00075
0.001
0.00125
0.0015
0
250
500
750
1000
1250
1500
1750
2000
Crack Length, a (mm)
Compliance (mm/kN)
Edge notch Specimen A
Edge notch Specimen B
Unnnotched (Estimated CMOD)
Application of FEM Model
Fatigue Model Calibration
Compliance vs Number of Cycles
0
0.0001
0.0002
0.0003
0.0004
0.0005
0
10000
20000
30000
40000
50000
60000
Number of Cycles
Compliance (mm/kN)..
Step 1: The Compliance is measured for each
fatigue load cycle of slab T2
Fatigue Model Calibration
Step 2: The Crack length is obtained for each
cycle using the FEM Model for slab T2.
Crack Length vs Number of Cycles
0
0.4
0.8
1.2
1.6
2
0
10000
20000
30000
40000
50000
60000
Number of Cycles
Crack Length (mm)log scale …….
Fatigue Model Calibration
Step 3: The Critical Crack a
crit
is Critical Number
of Cycles N
crit
is obtained for slab T2.
Crack Length vs Number of Cycles
0
15
30
45
60
0
10000
20000
30000
40000
50000
60000
Number of Cycles
Crack Length (mm)
a
crit
= 41 mm
N
crit
= 25000
This point of
critical crack
length is a
point of
inflexion in the
curve
Fatigue Model Calibration
Crack Growth Rate vs Crack Length
3.5
3
2.5
2
1.5
1
0.5
0
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Crack Length, a (mm)
Log (
D
a/
D
N)
a
crit
= 41 mm
25
.
12
)
(
)
(
0
1
1
0
1
D
D
a
a
C
n
a
a
C
N
a
657
.
6
)
(
*
)
(
2
2
2
D
D
D
D
I
I
K
C
n
K
C
N
a
Step 4: The two sections of the model are
calibrated
Different fatigue
equations apply
for crack length
bigger or smaller
than a
crit
•
Log C
2
=

15.0
•
Log C
1
= 17.6
25
.
12
)
(
)
(
0
1
1
0
1
D
D
a
a
C
n
a
a
C
N
a
25
.
12
)
(
)
(
1
0
1
1
0
1
D
D
a
a
C
n
a
a
C
a
N
da
a
a
C
n
a
a
C
N
crit
a
a
0
25
.
12
)
(
)
(
1
0
1
1
0
1
1
Fatigue Model Application
Estimation of N
1
N
1
is he required number of cycles to achieve a
crit
This fatigue equation allows to predict crack propagation for
any number of cycles N<N
1
If we have an unnotched slab, a
0
= 0
0
1
0
1
1
0
1
25
.
12
)
(
)
(
a
dN
a
a
C
n
a
a
C
a
N
•
Log C
1
= 17.6
657
.
6
)
(
*
)
(
2
2
2
D
D
D
D
I
I
K
C
n
K
C
N
a
657
.
6
)
(
*
)
(
1
2
2
2
D
D
D
D
I
I
K
C
n
K
C
a
N
da
K
C
n
K
C
N
failure
crit
a
a
I
I
D
D
657
.
6
)
(
*
)
(
1
2
2
2
2
000
,
61
2
1
N
N
N
TOTAL
Fatigue Model Application
Estimation of N
2
N
2
is he required number of cycles to achieve a
failure
This fatigue equation allows to predict crack propagation for
any number of cycles N
1
<N<N
2
crit
N
N
I
I
a
dN
K
C
n
K
C
a
D
D
1
2
2
2
657
.
6
)
(
*
)
(
•
Log C
2
=

15.0
Summary
Currently, empirical fatigue curves don't
consider crack propagation. Fracture
mechanics approach has clear advantages to
predict crack propagation.
Monotonic tests are failure envelope for
fatigue.
Mechanics of model work but model
coefficients need to be improved.
A Cohesive Zone Model has greater potential
to give a more conceptual and accurate
solution to cracking in concrete pavements
Tasks Remaining
Fatigue crack growth prediction of beams on
elastic foundation (NWU)
Complete model calibration on remaining slabs
Several load (stress) ratios
Tridem vs. single pulse crack growth rates
Write final report
Current Model Limitations
Crack propagation assumed to be full

depth
crack across slab
pre

defined crack shape
Need geometric correction factors for all
expected slab sizes, configurations, support
conditions
Need further validation/calibration with other
materials and load levels
•
Size Effect Method (SEM)
•
Two

Parameter Fracture Model (TPFM)
–
Equivalent elastic crack model
–
Two size

independent fracture parameters : K
I
and CTOD
c
Bazant ZP, Kazemi MT. 1990, Determination of fracture energy, process zone length and brittleness
number from size effect, with application to rock and concrete,
International Journal of Fracture
, 44,
111

131.
Jenq, Y. and Shah, S.P. 1985, Two parameter fracture model for concrete,
Journal of Engineering
Mechanics
, 111, 1227

1241.
Quasi

brittle
0
1
t
N
B f
D D
Strength Theory
LEFM
log
D
1
2
log
N
►
Energy concept
►
Equivalent elastic crack model
►
Two size

independent fracture
parameters: G
f
and c
f
Fracture Mechanics Size Effect
What is the Cohesive
Zone Model?
Modeling approach that defines cohesive
stresses around the tip of a crack
w
f
w
t
f
Traction

free macrocrack
Bridging zone
Microcrack zone
Cohesive stresses are related to
the crack opening width (w)
Crack will propagate, when
= f
t
How can it be applied to
rigid pavements?
The cohesive stresses are defined by a cohesive
law that can be calculated for a given concrete
F f
G G
f
G
t
f
w
f
w
1
w
t
f
Concrete properties
Cohesive law
1
u
1
v
2
v
2
u
3
u
3
v
4
u
4
v
t
w
n
w
Cohesive
Finite Element
Cohesive Elements are
located in Slab FEM model
Cohesive
Elements
Why is CZM better for
fracture?
The potential to predict slab behavior under
monotonic and fatigue load
F f
G G
f
G
t
f
w
f
w
1
w
t
f
The cohesive relation is a MATERIAL
PROPERTY
Predict fatigue using a cohesive relation
that is sensitive to applied cycles,
overloads, stress ratio, load history.
Allows to simulate real loads
Cohesive laws
Cohesive
Finite Element
Monotonic and Fatigue
Slab behavior
Cohesive
Elements
Load vs CMOD for 63 mm depth slabs
0
10
20
30
40
50
60
0
0.2
0.4
0.6
0.8
1
1.2
CMOD (mm)
Load (kN)...
1/3 depth notch
Edge notch
Compliance vs. number of Cycles
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
Number of Cycles
Compliance (mm/kN)
U1
L2
U2
L3
Proposed Ideas
Laboratory Testing and Modeling of Separated
(Unbonded) Concrete Overlays
Advanced Concrete Fracture Characterization
and Modeling for Rigid Pavement Systems
Laboratory Testing and Modeling of
Separated Concrete Overlays
Concrete Overlay
h
ol
Existing Concrete
Pavement
h
e
Bond
Breaker

Asphalt Concrete Bond Breaker ~ 2”
Laboratory Testing and Modeling of
Separated Concrete Overlays
New PCC
Old PCC
AC Interlayer
Rigid Support
New PCC
Old PCC
AC Interlayer
Support
Cohesive elements
Advanced Concrete Fracture
Characterization and Modeling for Rigid
Pavement Systems
F f
G G
f
G
t
f
w
f
w
1
w
t
f
Concrete properties
Cohesive law
1
u
1
v
2
v
2
u
3
u
3
v
4
u
4
v
t
w
n
w
Cohesive
Finite Element
Cohesive Elements are
located in Slab FEM model
Cohesive
Elements
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