11

DEVELOPMENT OF NEW STRESSANALYSIS AND THICKNESSDESIGN PROCEDURES FOR

JOINTED CONCRETEPAVEMENTS

Sixth Int �il Purdue Conference onConcrete Pavement

Y. H. Lee, S. T. Yen, C. T. Lee,J. H. Bair , Y. M. LeeTamkang University

Taiwan, R.O.C.

• Develop an Alternative StressEstimation Procedure

• Validate ILLI-SLAB Program �as Applicability• Modify PCA Stress Analysis & Thickness

Design Procedure• Develop a User-friendly TKUPAV Program

for Automatic Stress Calc. & Thickness Design• Applicable to Metric & English Systems

OBJECTIVES

RESEARCH APPROACH

• Westergaard �es Closed-Form Solutions• Effects of Curling & Warping• ILLI-SLAB Solutions and Its Applicability• Identification of Mechanistic Variables• Development of Stress Prediction Models• Modified PCA Stress Analysis and

Thickness Design Procedure• Development & Verification of

TKUPAV Program

CLOSED-FORM SOLUTIONS /ILLI-SLAB F. E. MODEL

• Westergaard/ Bradburyu Loading Onlyu Thermal Curlingu Loading Plus Curling

• ILLI-SLAB F. E. Modelu Dimensional Analysisu Identification of Mechanistic Variables

EFFECTS OF CURLING &WARPING

• Thermal Curling Stress(Positive ∆T => Additional Stress)

• Moisture Warping Stress(Negative ∆M => Stress Reduction)(But Not Easy to Measure)

• Suggest to Include the Effect of Positive ∆T

ILLI-SLAB Program• Originally Developed by Tabatabaie , 1977• Continuously Revised by Wong, Conroyd ,

Ioannides , 1980-1985• Included Curling Analysis by Korovesis ,

1986-1989• Re-Compiled by Lee, 1995

(Microsoft FORTRAN PowerStation)

22

RESULTS OF ACTUAL FIELDMEASUREMENTS

• Arlington Road Testu Edge Stress (Curling Only)

• AASHO Road Testu Edge Stress (Loading + Curling)

• Taiwan �as Second Northern Highwayu Corner Stress (Loading + Curling)

• Compared to ILLI-SLAB Results• Validated Its Applicability

Arlington Road Test

Measured Stress, psi

ILLI

-SLA

B S

tress

, p

si

0

100

200

300

400

0 100 200 300 400

REF: Lee 1993

AASHO Road Test

Measured Stress, psi

ILLI

-SLA

B S

tress

, p

si

0

100

200

300

400

500

600

0 100 200 300 400 500 600

REF: Lee 1993

Traffic

X

X

X

X

X

X

C72

C70

C71

X

X

X

Unbonded

Taiwan �as Second Northern Highway

10�0PCC6�C LCB

Taiwan �as Second Northern Highway

0

20

40

60

80

100

0 20 40 60 80 100

Measured Stress, psi

ILLI

-SLA

B S

tress

, p

si

Identification of Mechanistic Variables(Loading Only)

σ δhP

kP

qP

f a L W s t D AGGk

hhefft

2 2 2

0

1

2

, ,

, , , , , , ,

l l

l l l l l l l

=

finite

finite

L

W

33

t Convert to a Single-Wheel(Single-Axle) LoadDual-WheelTandem-AxleTridem -Axle

Effect of Wheel and Axle Spacing

ts

Identification of Mechanistic Variables(Loading + Curling)

σ δ

α γ

Eh qh

k

f a T L W hk

Phk

, ,

, , , , ,

l l

l l l l l

2 2

2

2 4

=

∆

finite

finite

L

W ∆T

DEVELOPMENT OF STRESSPREDICTION MODELS

• Factorial F.E. Runs Based on theDimensionless Mechanistic Variables

• Two-Step Modeling Approachu Projection Pursuit Regression (PPR)u Piece-wise Linear Regression

• S-PLUS Statistical Package• Lee & Darter (TRR 1449)

Proposed Stress Prediction Models(Edge, Corner, Interior)

σ σ σ

σ

σ α

cr w 1 2 3 4 5 T cR R R R R + R

Prediction Models

= ⋅ ⋅ ⋅ ⋅ ⋅ ⋅

= ×

= ×

=

w

c

T

P

hf

a

E T fW

R R R

2 1

2

1 5

12

( )

( )

~ ,

l

l∆

MODIFIED PCA STRESS ANALYSIS& THICKNESS DESIGN

PROCEDURESl Review PCA Thickness Design Procedure

u Equivalent Stress Calculationu Fatigue Analysis

l PCA� s Simplifications and Limitationsl Modified Equivalent Stress Calculationl Modified PCA Fatigue Analysis & Thickness

Design Procedures

PCA THICKNESS DESIGN

l J-SLAB Program (Edge Stress)l Equivalent Stress Calculationsl Fatigue Analysis (& Erosion Analysis)

l But Did NOT Consider Curling Stressl PCAPAV Program

DnNr

i

ii

m=

=∑

1

h

44

PCA�Cs Equivalent Stress Calculation

σeqeM

hf f f f

Me f k

= • • • •

=

62 1 2 3 4

( , )l (in English System)SA/NS , TA/NS , SA/WS , TA/WS

PCA�Cs Fatigue Analysis

log N . . SR SR .

N.

SR .. SR .

N SR .

SR = /S =

f

f

.

f

c

= − × ≥

=−

< <

= ≤

11 737 12 077 0 55

4 25770 4325

0 45 0 55

0 45

3 268

Unlimited

, N Allowable Load Repetitionsf σ

LIMITATIONS OF PCA THICKNESSDESIGN PROCEDURE

λ Did NOT Consider Curling Stressesλ Limited to Fixed Gear Configurationsλ Only Applicable to English System

PCA�Cs Simplifications & Limitations

• Fixed Slab Size:L=180 in., W=144 in.

• Fixed Gear Configurations: a=4.72 in., t=50 in., s=12 in.(Axle Width D=72 in.)

• Fixed Material Properties:E=4 Mpsi, µ=0.15, AGG=25,000 psi

t

s

W

L

Modified Equivalent StressCalculation (I)

()

σ σ

σeq w 1 2 3 4 5

T c 3 4

R R R R R

+ R f f

= ⋅ ⋅ ⋅ ⋅ ⋅

⋅ ⋅ ⋅

Modified Equivalent StressCalculation (II)

σ

σ α

w

c

T

Ph

fa

E T fW

R R R

= ×

= ×

=

2 1

2

1 5

12

( )

( )

~ ,

l

l∆

Prediction Models

55

Modified PCA Stress Analysis &Thickness Design Procedures (I)

• Calculate Expected Load Repetitions (ni)

• Calculate Modified Equivalent Stress (σeq)σeq = σcr * f3 * f4

u Loading Onlyu Loading + Curling (∆T>0)

• Calculate Stress Ratio (σeq /Sc)

Modified PCA Stress Analysis &Thickness Design Procedures (II)

• Determine Max. Allowable LoadRepetitions (Ni)

• Check Cumulated Fatigue DamageΣ (ni/Ni) < 100%

• Repeat Previous Steps, If Necessary

DnNr

i

ii

m=

=∑

1

h

DEVELOPMENT OF TKUPAVPROGRAM

• Using Visual Basic Program (Ver. 4.0)• Highly User-Friendly Interfaces• Basic Features of TKUPAV Program

u Different Slab Size, Axle Configurations,Material Properties, TemperatureDifferentials

u Metric and English Systemsu English & Chinese Versions

TKUPAV Example Input Screens

TKUPAV Example Input Screens TKUPAV PROGRAMVALIDATION

• Comparing the Results of PCAPAV,TKUPAV, and a Spreadsheet Program

• Equivalent Stress Calculationsu TKUPAV / PCAPAV

• Fatigue Analysisu Loading Onlyu Loading + Day-time Curling

66

A Case Study for Validation

Single Axle Tandem AxleLoad,kips

Axles/1000Trucks

Load,kips

Axles/1000Trucks

30 0.58 52 1.96�� �� �� ��12 168.85 16 124.69

Basic Assumptions: Same as PCA Method

Comparison of Equivalent Stress(TKUPAV / PCAPAV)

0

200

400

600

800

0 200 400 600 800

PCA

TKU

PAV

(in psi)

Fatigue Analysis for Loading Only

Fatigue (%)AxleLoad PCAPAV TKUPAV

Single 61.4 70.5Tandem 2.0 0.9Sum = 63.4 71.4

Fatigue Analysis for Loading +Day-time Curling

TKUPAV Fatigue (%)AxleLoad 90% Load

Only10% Load +

CurlingTotal

Single 63.4 128.9 192.3Tandem 0.8 9.8 10.7Sum = 64.2 138.8 203.0

DISCUSSIONS• Followed Similar Approach Adopted by

NCHRP 1-26 Projectu ILLI-CONC Program for Edge Stress Only

• Resolved the Dimensional Analysis Issue forLoading + Curling Condition

• Provided More Complete Treatmentu Edge, Corner, and Interior Stress Analysis

• ESAR Concept Was Replaced by StressReduction Adjustment Factors (R �es =0~1)

CONCLUSIONS ANDRECOMMENDATIONS (I)

• Validated ILLI- SLAB�Ls Applicability• Developed an Alternative Procedure

for Critical Stress Estimationu Edge, Corner, & Interior L+C Stress

• Modified PCA�Ps Equivalent StressCalculation & Fatigue Analysis

• Developed a Highly User-FriendlyTKUPAV Program

77

CONCLUSIONS ANDRECOMMENDATIONS (II)

• Expanded PCA Thickness Design for:u Different Slab Size, Axle Configurations, Material

Properties, Temperature Differentialsu Metric and English Systems

• Validated the TKUPAV Program• Illustrated the Effect of Loading +

Curling Should be Considered• Further Verifications & Trial Applications

ACKNOWLEDGMENTS

• Research Sponsored by National ScienceCouncil, Taiwan, R.O.C.• NSC83-0410-E032-009• NSC84-2211-E032-022• NSC84-2211-E032-008• NSC85-2211-E032-010

THANKS FOR YOURATTENTION!

Y. H. Lee, J. H. Bair , C. T. Lee,S.T. Yen, Y. M. LeeTamkang University

Taiwan R.O.C.