of Airfield Concrete Slabs

reelingripebeltUrban and Civil

Nov 15, 2013 (3 years and 11 months ago)

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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 = 1E-07x
2
- 1E-06x + 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=-1E-7x
2
+2.9E-4x
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 = 2E-06x + 0.0007
y = 5E-10x
2
- 9E-07x + 0.0014
0
0.0005
0.001
0.0015
0.002
0
400
800
1200
1600
2000
Crack length (mm)
KI/P (mm-3/2)
FEM-1
FEM-2
Lineal (FEM-1)
Polynomial (FEM-2)
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=-1E-7x
2
+2.9E-4x
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 = 1E-07x
2
- 1E-06x + 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