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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.