Fang-Ju Chou

1
Analysis of Flexible Overlay SystemsApplication
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
2
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

3
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).

4
Problem statement Cont.

• Current FAA Flexible OL Design Methodology
  Rollings (1988s)
• Assumptions used
• The environmental loading (i.e. temperature) is
  excluded.
• A 25 load transfer is assumed to present between
  slabs.
• 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.
5
Ongoing/Upcoming Research

• Expand 3D Parametric Study to Investigate
• Additional Pavement Configurations and Loading
  Conditions
• 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

6
Fracture Analysis J-integral
Compute Path Integral Around Various Contours
Estimate Stress Intensity Factors (KI and KII) at
Tip of an Inserted Crack (Length will be Varied)
7
Ph.D. Thesis of Fang-Ju Chou
Objectives

• To investigate how the following parameters
  affect the potential for joint RC in rehab.
  airfield pavements.
• Bonding condition between slabs CTB
• Load transfer between the underlying concrete
  slabs
• Subgrade support
• Structural condition (modulus value) of the
  underlying slabs

1. Introduce a robust reliable method (J-integral
   interaction-integral) to obtain accurate
   critical OL responses.
2. Understand the effect of temp. loading by
   introducing temp. gradients in models.
3. Identify critical loading conditions for rehab.
   airfield pavements subjected to thermo-mechanical
   loadings.

8
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.

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)
9
The J-Integral Path Independence

• A closed contour ?1 ?2 ?3 ?4

• On the crack faces (?3 and ?4 )
• n1 0 Assuming traction free ?ijnj 0
• No contributions to J-integral from segments ?3
  ?4
• J3 J4 0 J2 -J1

10
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)

J
Ks
G
11
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.

(at ? ?)

1. The finite element program ABAQUS uses the
   interaction integral method (Shih and Asaro,
   1988) to extract the individual stress intensity
   factor.
2. 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.
12
2D Model Description--Geometry Material

• 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 Colorado.

Note 1-inch 25.4 mm 1-psi 6.89 kPa
1 pci 271.5?103 N/m3
Hammons, M. I., 1998b, Validation of
three-dimensional finite element modeling
technique for jointed concrete airport pavements,
Transportation Research Record 1629.
13
2D Model Description--Loading
36 ft (10.97 m)

• 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)
• Each gear carries 47.5 loading
• 301,387.5 lb

Boeing 777-200
14
2D Model Description--Loading

• 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

4
Slab 3
1
Slab 2
Gear 1
Gear 2
55in
55in
57 in
57 in
240 in
432 in
16.32 in
6.82 in
225 in
225 in
Note Dimensions not drawn to scale
15
2D Model Description--Gear Loading Position

• not practical to investigate every possible gear
  position
• four selected positions have the greatest
  potential to induce the highest pavement
  responses under one gear

• Position A edge loading condition Position B
  joint loading condition
• Corner loading cond. (dash lines) cannot be
  considered in 2-D models, since the effect of the
  3rd dimension cannot be distinguished.

Modeled range
16
2D Model Description--Gear Loading Position

• 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

• Rehab. pavements subjected to Pos. AD modeled as
  2D pl-? condition.
• Joint discontinuity cannot be correctly modeled
  using 2D axisymmetric model

Modeled range
17
2D Model Description--Load Adjustment Factor (LAF)
One B777-200 wheel P 50231.25lb

1. Correct excessive wheel load need to adjust the
   applied load for pl-? models
2. 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.
3. For this 2-D rehab. pavement model of 5-inch OL
   under pl-? cond., the adjustment factor 0.697.
4. Reduced contact tire pressure p 69.7 ? q will
   be imposed on 2-D pl-? pavement models.
5. Limitations location, no. of wheel

Most simple, effective way
18
Results of Selected Loading Positions
Before inserting a sharp joint RC into OL, four
un-cracked rehab. models subjected to gear
loading positions AD are analyzed.
19
Results of Selected Loading Positions (Position A)
Tension
Comp.
Tensile Fields
PosA tensile fields are induced at the bottom of
OL above PCC joint
20
Results of Selected Loading Positions (Position C)
Tension
Comp.
Tensile Fields
PosC tensile fields are also induced at the
bottom of OL above PCC joint
21
Results of Selected Loading Positions (Position B)
Tension
Comp.
Compressive Zones
PosB compressive fields are present at the
bottom of OL above PCC joint
22
Results of Selected Loading Positions (Position D)
Tension
Comp.
Compressive Zones
PosD compressive fields are also present at the
bottom of OL above PCC joint
23
Inserting Joint RC

• Size of crack-tip element influences the accuracy
  of the numerical solution.
• two mesh types are used in the crack-tip region
  to ensure that a fine enough mesh has been
  applied around the crack-tip

24
Fracture Model Verification

1. Shih et al. (1976) proposed a disp. correction
   technique (DCT) to calculate (KI)s using the
   disp. responses of a singular element
2. Ingraffea and Manu (1980) generalized this
   approach for mixed-mode stress fields at the
   crack-tip.
3. Showed that the l/a ratio had a pronounce effect
   on the evaluation of Ks. (note a crack length)
4. Using DCT, we can calculate the separate (KI)s
   (KII)s in a mixed-mode problem based on the
   displacements of crack flank nodes of singular
   elements

25
Verification of Reference Sol. (using DCT) v.s.
Analytical Sol.

1. To confirm the accuracy of predicting Ks using
   DCT, a flat plate with an angled crack is modeled
   under pl-? cond. with unit thickness.
2. The closed form solutions for Mode I and Mode II
   stress intensity factors at either crack-tip are

KI(0) Mode I stress intensity factor (? 0) a
half of the crack width c half of the plate
width
2a 3.873093344E-02
? tan-1(0.5)
Note drawing not to scale
26
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.

27
Results of Selected Loading Positions

1. 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
2. In addition to loading positions 1 and 2 (same as
   positions A and C), 9 gear loading positions are
   also analyzed for rehabilitated pavements with an
   initial sharp joint RC of 0.5 or 2.5.

Pos1 (PosC)
Pos2 (PosA)
Pos7
Pos11
x 189.51
x 34.57
x 113.46
x 0
Fine coarse mesh employed
5 in
AC Overlay
Crack Length 0.5 or 2.5
0.5 in
4.5 in
18 in
Concrete Slab
13.5 in
0.2 in
225 in
8 in
CTB
Subgrade
225 in
225 in
Pavement geometry not drawn to scale
28
Determination of Critical Loading Situation
(Traffic Loading Only)
Eleven traffic loading positions (gear loading
positions 1 to 11)
Two lengths of joint RC (0.5-in and 2.5-in)
Two mesh types (fine coarse at the crack-tip
region)
44 Sets of Numerical Results
29
Determination of Critical Loading Situation
(Aircraft Loading Only)

• 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.

30
(Aircraft Loading Only)
Mode I SIFs vs. 2 a/hAC ratios -- 11 positions --
Fine coarse meshes
Reduced contact tire pressure 69.7 ? 215 psi

• Tensile mode I SIFs are predicted starting from
  loading position 6, where the center of B777 main
  gear is at least 93.45 away from the PCC joint.
• Both mesh types give about the same predictions
  of mode I SIFs

31
Comparison of Results

• Castell et al. (2000) applied LEFM for flexible
  pavement systems and modeled the fatigue crack
  growth using FRANC2D and FRANC2D/L.
• 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
  distributed wheel loads are applied above a crack.

32
Application 1 (Traffic vs. Combined Loadings)
Three loading scenarios Aircraft loading
position 7 only Aircraft loading position 7
Temperature loading (?TPCC-23?F) Aircraft
loading position 7 Temperature loading
(?TPCC-15.3?F)
Position 7
113.46-in
47.2?F
40?F
?TAC-1.5?F/in
?TAC-1.5?F/in
Overlay5 ?AC1.38889?10-5 1/?F
54.7?F
47.5?F
?TPCC-0.85?F/in
Concrete slabs18 ?PCC5.5?10-6 1/?F
?TPCC-1.25?F/in
Longitudinal Joint
225 in
70?F
70?F
CTB8 ?CTB7.5?10-6 1/?F
70?F
70?F
Subgrade
33
Introduction
Literature Review
Principals of LEFM Appl.
2D Pav. Model
Model Appl.
Summary
Num. mode I and mode II SIFs a/hAC 0.1 and 0.5

• 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
• 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.

34
Application 1 (Traffic vs. Combined Loadings)

1. Under the combined loadings, the predicted
   J-value is much bigger than the one induced by
   aircraft loading only.
2. The critical loading condition of this 2-D
   rehabilitated pavement (i.e. 5-inch 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.

35
Recent Findings

• Based on the findings of this study, the
  following conclusions can be drawn
• 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.
• 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
  2.5-inch.
• Whereas, for un-cracked asphalt OLs, highly
  localized horiz. tension was found to exist in
  the asphalt OL just above the PCC joint.
• Temperature cycling appears to be a major
  contributor to joint reflective cracking.

36
Research Products

1. UIUC Ph.D Thesis Fang-Ju Chou October 1, 2004.
   
2. FAA COE Report Fall, 2004.
3. Conference, Journal Papers In preparation.
4. Models, models, models!

37
Current and Future Work

1. 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.
2. 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.
3. 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.
4. Modeling limitations must be addressed. The
   move to 3D, crack propagation modeling in
   composite pavements subjected to
   thermo-mechanical loading pushes the limits of
   current FEA capabilities. Modeling
   simplifications and advances in numerical
   modeling efficiencies are needed.
5. Field Verification

38
Thank you!