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Analysis of Flexible Overlay Systems: Application of Fracture Mechanics to Assess Reflective Cracking Potential in Airfi

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### 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

- 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

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).

Problem statement - Review

Current FAA Flexible OL Design Methodology: Rollings (1988’s)

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.

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

Compute Path Integral Around Various Contours

Estimate Stress Intensity Factors (KI and KII) at Tip of an Inserted Crack (Length will be Varied)

Introduce a robust & reliable method (J-integral & interaction-integral) to obtain accurate critical OL responses.

Understand the effect of temp. loading by introducing temp. gradients in models.

Identify critical loading conditions for rehab. airfield pavements subjected to thermo-mechanical loadings.

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

Ph.D. Thesis of Fang-Ju Chou:

Objectives:

AC Overlay

Concrete Slab

CTB

Subgrade

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)

nj

1

mj

4

nj

Crack faces

3

y

Elastic homogeneous material

x

J2

reverse the normal of segment 1;

new normal mj (points away from tip)

Renamemj=nj

=

J1

J-integral is independent of the contour taken around the crack tip

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

For a linear elastic, isotropic material

(at = )

Take Ks as critical stress predictions

Use J to quantify the propensity of joint RC

J = G

(at = )

For an elastic material

For a linear elastic, isotropic material

Introduction

Literature Review

2D Pav. Model

Model Appl.

Summary

Relation between J and G

- 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

Extraction of Stress Intensity Factors

- 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 = )

- 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.

225 in

Traffic Direction

240 in

Transverse Joint = 0.5in

Longitudinal Joint = 0.5in

Cross section

EAC = 200 ksi; AC = 0.35

AC Overlay

5 in

0.5 in

EPCC = 4,000 ksi

PCC = 0.15

Concrete

Slabs

18 in

0.2 in

ECTB = 2,000 ksi; CTB = 0.20

CTB

8 in

Subgrade

k = 200 pci

C

L

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 = 271.5103 N/m3

†Hammons, M. I., 1998b, Validation of three-dimensional finite element modeling technique for jointed concrete airport pavements, Transportation Research Record 1629.

57 in

55in

13.64 in

21.82 in

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

- 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

Position B

Cut B-B

Corner

Pos. B

Modeled range

AC Overlay

Pos. A

Cut A-A

Concrete Slab

CTB

Subgrade

Position A

AC Overlay

2-D pavement cross-section (Cut B-B)

Concrete

Slab

CTB

2-D pavement cross-section(Cut A-A)

Subgrade

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

Cut D-D

Position D

Pos. D

Modeled range

Pos. C

AC Overlay

Cut C-C

Concrete Slab

CTB

Subgrade

Position C

AC Overlay

2-D pavement cross-section (Cut D-D)

Concrete

Slab

CTB

2-D pavement cross-section(Cut C-C)

Subgrade

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. A~D modeled as 2D pl- condition.
- Joint discontinuity cannot be correctly modeled using 2D axisymmetric model

Modeled range

Correct excessive wheel load: need to adjust the applied load for pl- 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- cond., the adjustment factor = 0.697.

Reduced contact tire pressure p = 69.7% q will be imposed on 2-D pl- pavement models.

Limitations: location, no. of wheel

2D axisymmetric model: circular loading

r = 8.624 in

q = 215 psi

Overlay

σX1= -119.1 psi

Concrete Slabs

240 in

CTB

2D pl- model: strip loading

17.248 in

q =215 psi

Overlay

σX2=-170.8 psi

Concrete Slabs

240 in

CTB

C

L

2D Model Description--Load Adjustment Factor (LAF)

One B777-200 wheel P = 50231.25lb

Most simple, effective way

Trans. Joint

Overlay

Concrete Slabs

Position A(Cut A-A)

Long. Joint

240 in

CTB

Overlay

Position C(Cut C-C)

Concrete Slabs

Long. Joint

225 in

CTB

Overlay

Concrete Slabs

225 in

CTB

Position D(Cut D-D)

Trans. Joint

Overlay

Concrete Slabs

240 in

CTB

Results of Selected Loading Positions

Before inserting a sharp joint RC into OL, four un-cracked rehab. models subjected to gear loading positions A~D are analyzed.

Results of Selected Loading Positions (Position A)

Tension

Comp.

Tensile Fields

PosA: tensile fields are induced at the bottom of OL above PCC joint

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

Results of Selected Loading Positions (Position B)

Tension

Comp.

Compressive Zones

PosB: compressive fields are present at the bottom of OL above PCC joint

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

Crack-tip element

(Singular Element)

r

C2

B2

x, u

C1

B1

ℓ

4

ℓ

8

24

Coarse crack-tip mesh

Fine crack-tip mesh

Contour No.8

Contour No.9

0.025”

ℓ

0.025”

Contour No.5

Contour No.2

Crack Faces

Crack Faces

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

Crack-tip element

(Singular Element)

r

C2

B2

Crack faces

x, u

C1

B1

ℓ

4

ℓ

u = the sliding disp. at the crack flank nodes

= the opening disp. at the crack flank nodes

Fracture Model Verification

- 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 mixed-mode 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 mixed-mode problem based on the displacements of crack flank nodes of singular elements

E = 200 ksi

= 0.35

v

2a

u

10"

u

v

Deformation scale factor = 15.0

2c = 10"

22

Right crack tip

Deformation scale factor = 27.5

Left crack tip

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

- 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(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

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

- Supplying the disp. responses of the crack flank nodes computed via ABAQUS, the reference Ks using DCT are obtained for both crack tips.
- 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.

Results of Selected Loading Positions

- 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
- 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 = 113.46”

x = 189.51”

x = 34.57”

x = 0”

Fine & coarse mesh employed

AC Overlay

5 in

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

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

Stable J-value of fine mesh begins

Stable J-value of coarse mesh begins

last available contour or contour far away from the crack-tip

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.

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

- 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.

Application 1 (Traffic vs. Combined Loadings)

Three loading scenarios

Aircraft loading position 7 only

Aircraft loading position 7& Temperature loading (TPCC=-23F)

Aircraft loading position 7& Temperature loading (TPCC=-15.3F)

Position 7

113.46-in

47.2F

40F

TAC=-1.5F/in

TAC=-1.5F/in

Overlay=5”; AC=1.3888910-5 1/F

54.7F

47.5F

TPCC=-0.85F/in

Concrete slabs=18” PCC=5.510-6 1/F

TPCC=-1.25F/in

Longitudinal Joint

225 in

70F

70F

CTB=8”; CTB=7.510-6 1/F

70F

70F

Subgrade

Introduction

Literature Review

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.

Application 1 (Traffic vs. Combined Loadings)

- Under the combined loadings, the predicted J-value is much bigger than the one induced by aircraft loading only.
- 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.

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.

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

- 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 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.
- Field Verification

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