#### Transcript Slide 1

Analysis of Flexible Overlay Systems:
Application of Fracture Mechanics to
Assess Reflective Cracking Potential in
Airfield Pavements
Fang-Ju Chou
and
William G. Buttlar
FAA COE Annual Review Meeting
October 7, 2004
Department of Civil and Environmental Engineering
University of Illinois at Urbana-Champaign
Outline
- Progress Since Last Review Meeting


Development/Verification of Fracture
Mechanics tools for ABAQUS
Application of Tools to Study Reflective
Cracking Mechanisms in AC Overlays Placed
on PCC Pavements
- Current/Future Work
2
Problem statement - Review
Functions of Asphalt Overlays (OL):
 To restore smoothness, structure, and minimize
moisture infiltration on existing airfield pavements.
Problem:
 The new asphalt overlay often fails before achieving
its design life.
Cause: Reflective cracking (RC).
3
Problem statement ~ Cont.
Current FAA Flexible OL Design Methodology: Rollings (1988’s)
Assumptions used:
2. A 25% load transfer is assumed to present between slabs.
3. Structural deterioration is assumed to start from underlying slabs.
 Reflective cracking (RC) will initiate when structural strength of
slabs is consumed completely.
 RC will grow upward at a rate of 1-inch per year.
However, joint RC often appears shortly after the
construction especially in very cold climatic zones.
4
Ongoing/Upcoming Research
• Expand 3D Parametric Study to Investigate:
– Effect of Joint LTE on Critical Responses and
Crack Propagation
• Development of Two Possible Methods to
Consider Reflective Cracking Potential
– Simpler than Crack Propagation Simulation
– Less Sensitive to Singularity at Crack/Joint
5
Fracture Analysis: J-integral
Estimate Stress Intensity
Factors (KI and KII) at Tip
of an Inserted Crack
(Length will be Varied)
Compute Path
Integral Around
Various Contours
6
Ph.D. Thesis of Fang-Ju Chou:
Objectives:
1. Introduce a robust & reliable 4. To investigate how the
following parameters affect the
method (J-integral &
potential for joint RC in rehab.
interaction-integral) to obtain
airfield pavements.
accurate critical OL responses.
 Bonding condition between slabs
2. Understand the effect of temp.
& CTB
underlying concrete slabs
conditions for rehab. airfield
 Structural condition (modulus
pavements subjected to
value) of the underlying slabs
7
Limitation of traditional FE modeling at joint
FEA  applied† on modeling of asphalt overlaid JCP.
Limitation:

The accuracy of the predicted critical OL responses immediately above
the PCC joint was highly dependent on the degree of mesh refinement
around the joint.
No. of Elements?
AC Overlay
Concrete Slab
CTB
To seek reliable critical stress predictions, LEFM will be applied in an attempt
to arrive at non-arbitrary critical overlay responses around a joint or crack.
†Kim
and Buttlar (2002); Bozkurt and Buttlar (2002); Sherman (2003)
8
The J-Integral: Path Independence
2
A closed contour = 1 + 2 + 3 + 4
J 


ui

Wn


n

 1 x ij j ds  J1  J 2  J 3  J 4  0
1

1 2 3 4 
4
Crack faces
On the crack faces (3 and 4 )
n1 = 0 ; Assuming traction free: ijnj = 0
y
No contributions to J-integral from segments 3 & 4
J3 = J4 = 0; J2= -J1




ui
ui
 Wn1  x1  ij n j ds   Wn1  x1  ij n j ds
2
1
J2


ui
  Wm1 
 ij m j ds
x1

1 


ui

  Wn1 
 ij n j ds
x1
1 

=
J1
1
nj
nj
mj
3
x
Elastic homogeneous material
reverse the normal of segment 1;
new normal mj (points away from tip)
Rename mj = nj
J-integral is independent of the contour taken around the
crack tip
9
Introduction Literature Review Principals of LEFM & Appl. 2D Pav. Model Model Appl. Summary
Relation between J and G
1.
Rice (1968) showed that the J-integral is equivalent to the energy release
rate (G) in elastic materials. (section 3.2.3)
For a linear elastic, isotropic material
K I2 K II2 K III2
J '  ' 
(at  = )
E
E
2
Use J to quantify the
propensity of joint RC
J
Ks
J=G
For an elastic material
G
Take Ks as critical stress
predictions
2
K I2 K II2 K III
G '  ' 
(at  = )
E
E
2
For a linear elastic, isotropic material
10
Extraction of Stress Intensity Factors
1.
Numerically it is usually not straightforward to extract† K of each mode from a
value of the J-integral for the mixed-mode problem.
K I2 K II2 K III2
J '  ' 
(at  = )
E
E
2
2.
3.
The finite element program ABAQUS uses the interaction integral method
(Shih and Asaro, 1988) to extract the individual stress intensity factor.
The interaction integral method of homogeneous, isotropic, and linear elastic
materials is introduced in section 3.3.1.
†
ABAQUS users manual, 2003, Hibbitt, Karlsson and Sorensen, Inc., Pawtucket, Rhode Island.
11
2D Model Description--Geometry & Material
CL
Top view
• Purpose: analyze a typical
pavement section of an airport
that serves Boeing 777 aircraft
• The selected model geometry and
pavement cross sections are based
on the structure and geometric
info.† of un-doweled sections of
runway 34R/16L at DIA in
225 in
240 in
Traffic
Direction
Transverse
Joint = 0.5in
Longitudinal
Joint = 0.5in
Note: 1-inch = 25.4 mm; 1-psi = 6.89 kPa;
1 pci = 271.5103 N/m3
†Hammons,
M. I., 1998b, Validation of threedimensional finite element modeling technique
for jointed concrete airport pavements,
Transportation Research Record 1629.
Cross section
AC Overlay
Concrete
Slabs
CTB
5 in EAC = 200 ksi; AC = 0.35
0.5 in
E = 4,000 ksi
18 in PCC
PCC = 0.15
0.2 in
8 in ECTB = 2,000 ksi; CTB = 0.20
k = 200 pci
12
57 in
57 in
55in
13.64 in
36 ft (10.97 m)
21.82 in
One Boeing-777 200 aircraft:
• 2 dual-tridem main gears
• Gear width = 36 ft
• main gear (6 wheels; 215 psi)
• Gross weight = 634,500 lbs (287,800 kg)
= 301,387.5 lb
Boeing 777-200
13
• Boeing777-200: larger gear width (36 ft = 432 in)
• The 2nd gear is about 2 slabs away from 1st gear
• Assumption: the distance between gears is large enough such that
interactions may be neglected for the study of the OL responses
1
Gear 1
55in
240 in
4
Slab 3
Slab 2
Gear 2
55in
57 in
57 in
432 in
16.32 in
6.82 in
225 in
Note: Dimensions not drawn to scale
225 in
14
Modeled range
Pos. B
Position A
AC Overlay
Concrete
Slab
CTB
Modeled range
Cut A-A
CTB
Pos. A
Concrete Slab
•
condition; Position B: joint
lines) cannot be considered
in 2-D models, since the
effect of the 3rd dimension
cannot be distinguished.
Corner
AC Overlay
•
Top view
Position B
•
not practical to investigate
every possible gear position
four selected positions: have
the greatest potential to
induce the highest pavement
responses under one gear
Cut B-B
•
2-D pavement crosssection (Cut B-B)
2-D pavement crosssection (Cut A-A)
15
Pos. D
Position C
AC Overlay
Concrete
Slab
CTB
CTB
Rehab. pavements subjected
to Pos. A~D modeled as 2D pl condition.
Concrete Slab
AC Overlay
Pos. C
Cut C-C
Joint discontinuity cannot be
correctly modeled using 2D
axisymmetric model
Modeled range
Top view
Cut D-D
The other two positions:
• Position C: selected to study
the case where the gear is
centered over the joint to
maximize bending stresses in
the OL
• Position D: also has the
potential to induce higher
bending stresses in an OL
Position D
2-D pavement crosssection (Cut D-D)
Modeled range
2-D pavement crosssection (Cut C-C)
16
One B777-200 wheel P = 50231.25lb
1.
2.
3.
4.
5.
models
LAF: obtained by reducing the q of
the 2-D pl- model until the horiz.
stress prediction at the bottom of
the asphalt OL matches the 2-D
axisymmetric prediction.
For this 2-D rehab. pavement
model of 5-inch OL under pl-
0.697.
Reduced contact tire pressure p =
69.7%  q will be imposed on 2-D
pl- pavement models.
Limitations: location, no. of wheel
Most simple, effective way
CL
r = 8.624 in
q = 215 psi
σX1= -119.1 psi
Overlay
Concrete Slabs
240 in
CTB
17.248 in
q =215 psi
Overlay
σX2=-170.8 psi
Concrete Slabs
240 in
CTB
17
Before inserting a sharp joint RC into OL, four un-cracked rehab. models subjected to
Position A (Cut A-A)
Long. Joint
Overlay
Concrete Slabs
225 in
CTB
Concrete Slabs
225 in
CTB
Trans. Joint
Overlay
Concrete Slabs
Long. Joint
Overlay
CTB
Position B (Cut B-B)
Position C (Cut C-C)
Position D (Cut D-D)
Trans. Joint
Overlay
240 in
Concrete Slabs
240 in
CTB
18
Tension
Comp.
PosA: tensile fields are induced
at the bottom of OL above PCC
joint
19
Tension
Comp.
PosC: tensile fields are also
induced at the bottom of OL
above PCC joint
20
Tension
Comp.
PosB: compressive fields are
present at the bottom of OL
above PCC joint
21
Tension
Comp.
PosD: compressive fields are
also present at the bottom of OL
above PCC joint
22
Inserting Joint RC
Crack-tip element
Size of crack-tip element influences the accuracy of the
numerical solution.
(Singular Element)
C2
C1
two mesh types are used in the crack-tip region to ensure
that a fine enough mesh has been applied around the crack-tip
y, v

B2
B1
r
x, u
ℓ
4
ℓ
8
Coarse crack-tip mesh
Contour No.8
ℓ
24
Fine crack-tip mesh
Contour No.9
0.025”
0.025”
Contour No.5
Contour No.2
Crack Faces
( hAC )  0.025" 5"  0.005
Crack Faces
( hAC )  0.0075" 5"  0.0015
23
Fracture Model Verification
1.
2.
3.
4.
Shih et al. (1976) proposed a disp.
correction technique (DCT) to
calculate (KI)s using the disp.
responses of a singular element
Ingraffea and Manu (1980)
generalized this approach for mixedmode stress fields at the crack-tip.
Showed that the ℓ/a ratio had a
pronounce effect on the evaluation
of Ks. (note: a = crack length)
Using DCT, we can calculate the
separate (KI)s & (KII)s in a mixedmode problem based on the
displacements of crack flank nodes
of singular elements
y, v
Crack-tip element
(Singular Element)
Crack faces

C2
B2
C1
B1
r
x, u
ℓ
4
ℓ
2
 1
2
K II 
 1
KI 

2
4B 2  C 2   4B1  C1 

2
4uB 2  uC 2   4uB1  uC1 
u = the sliding disp. at the crack flank nodes
 = the opening disp. at the crack flank nodes
24
Verification of Reference Sol. (using DCT) v.s. Analytical Sol.
1.
2.
To confirm the accuracy of predicting Ks using DCT, a flat plate with an angled
crack is modeled under pl- cond. with unit thickness.
The closed form solutions for Mode I and Mode II stress intensity factors at
either crack-tip are:
KI  KI (0) cos 
2
KII  KI (0) cos sin 
=1000 psi
KI(0) = Mode I stress intensity factor ( =0)
a = half of the crack width
c = half of the plate width
Deformation scale factor = 15.0
E = 200 ksi
 = 0.35
2a
22
v

10"
u
Right crack tip
u
v
2c = 10"
Deformation scale
factor = 27.5
2a = 3.873093344E-02
 = tan-1(0.5) Note: drawing not to scale
Left crack tip
 / c  0.0086605" / 5"  1.7321104
25
Verification of Reference Sol. (using DCT) v.s. Analytical Sol.
1.
Supplying the disp. responses of the crack flank nodes computed via ABAQUS,
the reference Ks using DCT are obtained for both crack tips.
2.
Reference Ks compare well with the analytical solutions for both crack tips with
the error percentages of 1.58% and 2.8 % for the right and left crack tip.
Predicted Stress Intensity Factors (K I and K II) using DCT versus
Analytical Solutions
Stress Intensity Factors (KI & KII), psi
250
200
204.03 198.48
195.34
150
102.01
99.24
100
97.67
50
0
KI
DCT_Prediction_Left
KII
Analytical Sol.
DCT_Prediction_Right
26
1.
2.
Magnitudes of stress predictions immediately above the PCC joint are influenced by
the degree of mesh refinement around the joint; not recommended to be taken as
critical pavement responses directly
positions are also analyzed for rehabilitated pavements with an initial sharp joint RC
Pos1
Pos2
Pos7
of 0.5” or 2.5”.
Pos11
(PosC) (PosA)
x = 0” x = 34.57”
x = 113.46”
x = 189.51”
Fine & coarse mesh employed
AC Overlay
5 in
Crack Length = 0.5” or 2.5”
0.5 in
Concrete Slab
18 in
0.2 in
CTB
4.5 in
13.5 in
225 in
8 in
225 in
†Pavement geometry not drawn to scale
225 in
27
Position 7
Two lengths of joint RC
Two mesh types
(0.5-in and 2.5-in)
(fine & coarse at the crack-tip region)
44 Sets of Numerical Results
28
•Stabilized J-value is obtained when the integral is evaluated a few contours away from the crack tip
•J-value of the first contour is least accurate and should never be used in the estimation.
•The accuracy of the numerical J-value eventually degrades due to the relatively poor mesh resolution
in regions far away from the crack-tip.
1.2515E-01
Stable J-value of fine mesh begins
J-value (lb/in)
1.2510E-01
1.2505E-01
Stable J-value of coarse mesh begins
last available contour or contour
far away from the crack-tip
1.2500E-01
1.2495E-01
1.2490E-01
1.2485E-01
1
†
3
5
7
The B777 gear is 113.46" away from the joint
9
11
13
15
17
19
21
23
Contour No.
Fine_mesh
Coarse_mesh
29
Pos11
PosC
Mode I SIFs vs. 2 a/hAC
ratios
400
0.5
)
300
Stress Intensity Factor, KI (psi-in
200
-- 11 positions
-- Fine & coarse meshes
Reduced contact tire pressure
= 69.7%  215 psi
100
0
-50
-25
0
25
50
75
100
125
150
175
200
225
-100
Crack-tip mesh
-200
Ring8
-300
-400
Pos11
Ring5
PosC
-600
400
Distance from joint (inch)
300
Stress Intensity Factor, KI (psi-in
0.5
)
a/hAC =0.5
200
100
0
-50
-25
0
25
50
75
100
125
150
175
200
-100
Crack-tip mesh
-200
Ring
-300
-400
Ring2
-500
-600
Distance from joint (inch)
a/h AC=0.5
a/hAC =0.1
225
a/h AC=0.1
Tensile mode I SIFs are
predicted starting from
center of B777 main gear is
at least 93.45” away from
the PCC joint.
Both mesh types give
of mode I SIFs
30
Comparison of Results
1.
Castell et al. (2000) applied LEFM for flexible pavement systems and modeled the
fatigue crack growth using FRANC2D and FRANC2D/L.
2.
A distributed wheel load of 10,000 lb with a 100 psi contact tire pressure was applied
above the crack. A compressive KI was found to exist at the crack tip.

Differences: conventional FP: softer material below surface; Rehab. pavement: much
stiffer slabs below surface.

Horiz. Stress distribution would not follow the similar trends.
Study of Castell et al. agrees
with the present work:
 The compressive stresses can
be predicted at the crack-tip for
2-D pavement models when
applied above a crack.
31
113.46-in
Position 7
47.2F
Overlay=5”; AC=1.3888910-5 1/F
TAC=-1.5F/in
40F
TAC=-1.5F/in
54.7F
Concrete slabs=18”
PCC=5.510-6 1/F
225 in
TPCC=-0.85F/in
Longitudinal
Joint
47.5F
TPCC=-1.25F/in
70F
70F
70F
70F
CTB=8”; CTB=7.510-6 1/F
32
& Appl.K 2D
Introduction Literature Review Principals of LEFM Predicted
Pav. Model Model Appl. Summary
versus Two Crack Lengths
I
2500
Num. mode I and mode II
SIFs
a/hAC = 0.1 and 0.5
Stress Intensity Factor, KI (psi-in
0.5
)
2260
2000
1811
1669
1351
1500
1000
500
168.3
168.1
0
a/hAC=0.1
Predicted K II versus Two Crack Lengths
a/hAC=0.5
 TPCC= -23  F
 T PCC = -15.3  F
Stress Intensity Factor, KII (psi-in
0.5
)
100
53.14
50
43.85
13.4
0
-14.2
-50
The predicted mode II SIF is
also raised from 14.2 psi-in0.5 to
104 psi-in0.5 or 146.4 psi-in0.5
depending on TPCC.
-100
-104
-150
the predicted mode I SIF is
raised dramatically from 168.3
psi-in0.5 to 1669 psi-in0.5 or 2260
psi-in0.5 depending on TPCC
-146.40
-200
a/hAC=0.1
a/hAC=0.5
 T PCC = -23  F
 TPCC = -15.3  F
33
1.
Under the combined loadings, the predicted J-value is much bigger than the one
2.
asphalt overlay on the rigid pavement) is the aircraft loading position 7 plus
negative temperature gradients. The bigger the negative temperature differential
through the underlying concrete slabs, the higher the predicted mode I SIF.
Predicted J-value versus Two Crack Lengths
25
22.50
J-value , (lb/in)
20
14.41
15
12.26
10
8.018
5
0.1251
0.1247
0
a/hAC=0.1
a/hAC=0.5
 TPCC = -23  F
TPCC = -15.3  F
34
Recent Findings
Based on the findings of this study, the following conclusions can be drawn:
1.
By applying LEFM on modeling of rehab. airfield pavement, reliable critical
OL responses (i.e., the J-value, and stress intensity factors at a crack-tip) can
be obtained.
2.
For the OL system considered in this study, which involved a 5-inch thick
asphalt OL placed on a typical jointed concrete airfield pavement system
serving the Boeing 777 aircraft, gear loads applied in the vicinity of the PCC
joint were found to induce horiz. compressive stress at the RC tip for all load
positions considered. The crack lengths studied ranged from 0.5-inch to 2.5inch.
3.
Whereas, for un-cracked asphalt OLs, highly localized horiz. tension was
found to exist in the asphalt OL just above the PCC joint.
4.
Temperature cycling appears to be a major contributor to joint reflective
cracking.
35
Research Products
1.
2.
3.
4.
UIUC Ph.D Thesis – Fang-Ju Chou: October 1, 2004.
FAA COE Report – Fall, 2004.
Conference, Journal Papers – In preparation.
Models, models, models!
36
Current and Future Work
1.
2.
3.
4.
5.
To better simulate the behavior of asphalt OLs, an advanced material model
that accounts for the viscoelastic behavior of the asphalt concrete can be
implemented in the FEA. However, a thorough understanding of a nonlinear
fracture mechanics will be required to properly interpret the modeling results.
The use of actual temperature profiles versus the critical OL responses are
recommended. This analysis should be conducted in conjunction with the
implementation of a viscoelastic constitutive model for the asphalt OL.
By inserting appropriate interface elements such as cohesive elements
immediately above the PCC joint, a more realistic simulation of crack
initiation and propagation can be obtained.
Modeling limitations must be addressed. The move to 3D, crack propagation