new generation aircraft flexible pavement design challenges
TRANSCRIPT
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NEW GENERATION AIRCRAFT
FLEXIBLE PAVEMENT DESIGN CHALLENGES
M. ThompsonU of IL @ Urbana-Champaign
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A380A380--800 (2006)800 (2006)--Gross Load 1.23 million lbsGross Load 1.23 million lbs
BOEINGBOEING--777 (1995)777 (1995)--Gross Load 632,000 lbsGross Load 632,000 lbs
NEW GENERATION AIRCRAFTNEW GENERATION AIRCRAFT
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20051.1B-747-400
21857.9B-777-300ER*
21555.8B-767-400
22553.4B-747-400ER
19762A-380*
22865.3A-340
PRESSURE(psi)
WHEEL LOAD(KIPS)
AIRCRAFT
* DUAL-TRIDEM
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787-8 Landing Gear Footprint
Preliminary Data
32 FT 2 IN(9.8 m) TYP
38 FT 1 IN (11.6 M)
74 FT 9 IN (22.8 M)
57.5 IN (1.5 M)
51 IN (1.3 M)
16KG/CM2TIRE PRESSURE221PSIMAIN GEAR
50X20.0R22/34PRINMAIN GEAR TIRE SIZE
KG/CM2TIRE PRESSUREPSINOSE GEAR
40x16.0R16/26PRINNOSE GEAR TIRE SIZE
216,817KILOGRAMSTAXI WEIGHT478,000POUNDSMAX DESIGN787-8UNITSCHARACTERISTI
CS
Preliminary Data
32 FT 2 IN(9.8 m) TYP
38 FT 1 IN (11.6 M)
74 FT 9 IN (22.8 M)
57.5 IN (1.5 M)
51 IN (1.3 M)
MTOW: 482 kips
MAIN GEAR TIRE LOAD: 55.5 kips
MAIN GEAR TIRES: 221 psi
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CBR-BASED DESIGN(COE / FAA AC No. 150/5320-6D)
BASED ON ESWL
Is ESWL Adequate for
Dual Tandem & Dual-Tridem ???
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Mechanistic-Based Pavement Design Concepts
for NEW GENEREATION AIRCRAFT
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Mechanistic-EmpiricalApproach
• Combines the practicality of empirical methods with the technical soundness of mechanistic solutions.
• Uses mechanistic analysis, to determine the pavement response to imposed loads…then applies “empirical” formulations (i.e. “transfer functions”) to determine the development of distress due to the load-induced pavement response.
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DESIRABLE M-E DESIGN FEATURES
“Technically Sound”“Technically Sound”“Understandable”“Understandable”“Minimum Inputs”“Minimum Inputs”
“User Friendly”“User Friendly”
M-E IMPLEMENTATION CONCERNS
Airport Agency ResourcesAirport Agency ResourcesInput Data Input Data
Transfer FunctionsTransfer FunctionsCalibration DataCalibration Data
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INPUTS• Materials Characterization
– Pavement Materials– Subgrade Soils
• Geometric Layout– Layer thicknesses
• Traffic– Load Levels– Loading Configurations– Number of repetitions
• Environmental– Temperature fluctuations
(daily, monthly)– Moisture conditions
STRUCTURAL MODEL• Linear or Non-linear Multilayered
Elastic models.
TRANSFER FUNCTIONS (FT)
FTCritical
Response
Pavement Distress
(i.e. Damage)
TRANSFER FUNCTIONS (FT)
FTCritical
Response
Pavement Distress
(i.e. Damage)
FINALDESIGN
DESIGNRELIABILITY
OBTAIN CRITICAL RESPONSES• Subgrade Deviator Stress (σD).• Top Subgrade Vertical Strain (εS).• Horizontal Strain (εAC) at the bottom of the
AC layer.
DESIGN ITERATIONS
And/Or
PAVEMENT PERFORMANCE• Cumulative development of distress
STA
RT
Mechanistic-Empirical Approach
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Mechanistic-Empirical Approach
AC Layer
Granular BaseLayer
Subgrade
εAC
SSR = σd / quεv
Determine theCritical Responses
εAC : AC FatigueSSR: Subgrade εp
εv : Pavement εp
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STRUCTURAL RESPONSES* STRESSES
* STRAINS
* DEFLECTIONS
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STRUCTURAL MODEL
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STRUCTURAL MODELSTRUCTURAL MODEL
SHOULD ACCOMMODATESHOULD ACCOMMODATE
“MATERIAL PROPERTIES”“MATERIAL PROPERTIES”
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Material Characterization
• Resilient Modulus• Pavement Materials:
+ Asphalt Concrete: Temperature, frequency.
+ Unbound Granular: “Stress hardening”.
• Subgrade Soils:+ Fine-grained soils: “Stress softening”
+ Granular: “Stress hardening”.
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Material CharacterizationAsphalt Concrete Modulus
* Temperature Dependent*Frequency Dependent
* Must consider in M-E Design!!!
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21/*17DEC
32/*27NOV
49/1,62042OCT
59/1,00051SEPT
69/61560AUG
72/53062JULY
66/71057JUNE
58/1,04550MAY
46/1,87039APRIL
33/*28MARCH
25/*21FEB
18/*15JAN
MMPT(F)/E (ksi)
MMAT(F)MONTH
CALGARYTemperature Data
MMPT @ 3–inch depth
For: f=10Hz* > 3,000 ksi
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“ICM”“ICM”
NCHRP 1NCHRP 1--37A37AENHANCED INTEGRATED ENHANCED INTEGRATED
CLIMATIC MODELCLIMATIC MODEL(Dempsey & Larson)(Dempsey & Larson)
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HIRSCH MODEL
“Hirsch Model for Estimating the Modulus of In-Place Asphalt Mixtures”
Christensen - Pellinen - BonaquistAAPT Journal - 2003
INPUTS VMA - VFA - Asphalt “Modulus”
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PREDICTIVE EQUATIONS: Modified Hirsch Model
1
*3000,200,4100
1)1(
000,10*3
1001000,200,4*
−
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
⋅+
−−+⎥
⎦
⎤⎢⎣
⎡⎟⎠
⎞⎜⎝
⎛ ⋅+⎟
⎠
⎞⎜⎝
⎛ −=binder
binder GVFAVMA
VMA
PcVMAVFAGVMAPcE
58.0
58.0
*3650
*320
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ ⋅+
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ ⋅+
=
VMA
GVFA
VMA
GVFA
Pcbinder
binder
IG*Ibinder
VMA
VFAvol. properties
dynamic modulus
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HIRSCH MODEL
+ G* INPUT (TEMP / FREQ) (ASPHALT MASTER CURVE)
+ G* COMPATIBLE WITH PG GRADE
+ VFA & VMA FROM MIX DESIGN
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G* master curve
1
10
100
1000
10000
100000
1000000
10000000
100000000
1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04
Frequency (Hz)
G* (
Pa)
master curve4.4°C21.1°C37.8°C54.5°C
PG 58-28
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GRANULAR MATERIALS
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FROM RADA & WITCZAK
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From Rada & Witczak
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UZAN MODEL (1985)UZAN MODEL (1985)
MMR = K1 ΘK2 (σd) K3
Θ =BULK STRESSΘ = σ1 + σ2 + σ3
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MMR = K1 ΘK2 (σd) K3
K1 & K2 MOST IMPORTANT !!K1 & K2 MOST IMPORTANT !!
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ERi (ksi) = 0.307 QU (psi) + 0.9
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MODULUS CLASSESFINE-GRAINED SOILS
SOIL ERi (ksi) Qu (psi) CBR
STIFF 12.3 33 8MEDIUM 7.7 23 5SOFT 3.0 13 2VERY SOFT 1.0 6 1
ERi (ksi) = 0.42 Qu (psi) - 2
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ESTIMATING ESTIMATING EERiRi
EERi Ri (OMC) = 4.46 + 0.098 (%C) + 0.119 (PI)(OMC) = 4.46 + 0.098 (%C) + 0.119 (PI)
EERiRi ((ksiksi) @ 95% T) @ 95% T--9999C C -- %Clay%Clay
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E – CBR RELATIONS
COE/FAA: E (psi) = 1,500 CBR
TRL/UK : E (psi) = 2,555 CBR0.64
(CBR: 2 -12)(TRL Report # 1132)
Deviator Stress = ????
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STRUCTURAL MODELS
• ELASTIC LAYER PROGRAMS
• FINITE ELEMENT PROGRAMS (2-D / 3-D)
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ELASTIC LAYER PROGRAMS
+ LINEAR ELASTIC MATERIALS
+ MODULUS CONSTANT WITHIN THE LAYER
+ NO FAILURE CRITERION
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Structural Models• Elastic Layered Programs (ELP)
– All materials linear elastic, homogenous, isotropic (newer versions are improved).
• 2D “Axi-symmetric” Non-linear Finite Element:– Can incorporate a wide range of material models,
more specifically “Stress dependent” models.– Results for Single Wheel Loads (in theory)
• 3D Non-Linear Finite Element:– Same as 2D but can apply Multiple Wheel Loads.
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Structural Models: ILLIPAVE
• Analysis for Single Wheel Load (SWL)…Uses superposition to extend results to MWL.
• “Stress dependent” material models for Coarse and Fine Grained soils.
• Mohr-Coulomb Failure criteria.• 32-bit application, run-time ~5-30 sec for
typical pavement geometry.• Up to 7000 elements can be used.• User-friendly GUI input software for Windows.
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ILLI-PAVE: 2D FEM
Surface
Base
Subgrade
Subbase
AxisOf
Revolution
Surface
Base
Subgrade
Subbase
AxisOf
RevolutionSurface
Base
Subbase
Subgrade
Results for Single Wheel LoadsResults for Single Wheel Loads
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Structural Models: 2D FE• 3D Non-linear FEMs are very inefficient even
with computing power today…
• Consider the possibility of using 2D Non-linear FEMs with superposition to extend the single wheel results to multiple wheel.
• Must validate the Principle of Superposition for“Engineering” purposes.
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ILLIPAVE MODEL
* “Stress dependent” material models for Granular Materials and Fine Grained soils.
*Mohr-Coulomb Failure Criteria.* Analysis for Single Wheel Load (SWL)* SUPERPOSITION to extend results to
MWL.
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MULTIPLE WHEEL SOLUTION
Chou & Ledbetter (1973)MWHGL TESTS @ WES
SUPERPOSITION WORKS for
FLEXIBLE PAVEMENTS !!
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SUPERPOSITION Studies USCOE Study 1973 (Examples…)
Section #1 Section #2
-0.05
0
0.05
0.10
0.15
0.20
0.25
0.30 4 6 1080 2
-0.02
0.02
0.04
0.06
0.08
0
4 6 1080 2Ver
tical
def
lect
ion,
10-3
inch
es
Offset, FT
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SUPERPOSITION Studies USCOE Study 1973 (Examples…)
Section #1 Section #2
-404 6 1080
-20
0
20
40
60
80
2-20
0
20
40
60
80
Ver
tical
Stre
ss, l
b/in
2
Offset, FT4 6 1080 2
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Horizontal Stress(Radial or Tangential)
0.0
5.0
10.0
15.0
20.0
25.0
30.0
0.0 5.0 10.0 15.0 20.0 25.0 30.0
Superposed Response, psi
Act
ual R
espo
nse,
psi
Rebound Response
Vertical Stress
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0Superposed Response, psi
Actu
al R
espo
nse,
psi Rebound Response
Vertical Stress
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0Superposed Response, psi
Actu
al R
espo
nse,
psi Rebound Response
Vertical Stress
0.0
10.0
20.0
30.0
40.0
50.0
0.0 10.0 20.0 30.0 40.0 50.0Superposed Response, psi
Actu
al R
espo
nse,
psi Rebound Response
Horizontal Stress(Radial or Tangential)
0.0
5.0
10.0
15.0
20.0
0.0 5.0 10.0 15.0 20.0
Superposed Response, psi
Act
ual R
espo
nse,
psi
Rebound Response
Horizontal Stress(Radial or Tangential)
0.0
5.0
10.0
15.0
20.0
0.0 5.0 10.0 15.0 20.0
Superposed Response, psiA
ctua
l Res
pons
e, p
si
Rebound Response
MFC Section HFS Section HFC Section
Equality Line
Upper/Lower Bounds(2-psi or 10%)
FAA NAPTF Study FAA NAPTF Study 2001 2001 –– UofUof ILILFAA Airport Technology Transfer Conference FAA Airport Technology Transfer Conference -- 20022002
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SOLUTION FOR MULTIPLE WHEELSILLI-PAVE + Superposition
ILLIILLI--PAVEPAVE++
SuperpositionSuperposition
( ) ( )( ) ( )
( )
αττ
αττ
αασστ
σσ
ασασσ
ασασσ
cos
sin
cossin
cossin
sincos
22
22
⋅=
⋅=
⋅⋅−=
=
⋅+⋅=
⋅+⋅=
rzxz
rzyz
ttrrxy
zzzz
ttrryy
ttrrxx
α
r σrr, σtt, σzz, τrz
X
Y
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Mechanistic-Empirical Approach
AC Layer
Granular BaseLayer
Subgrade
εAC
SSR = σd / quεv
Determine theCritical Responses
εAC : AC FatigueSSR: Subgrade εp
εv : Pavement εp
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CONCEPTS FOR DEVELOPING A M-E BASED ACN PROCEDURE
FOR NEW GENERATION AIRCRAFT2006 ISAP
Quebec City, Canada
Thompson & Gomez-Ramirez (U of IL)
Gervais & Roginski(Boeing)
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20051.1B-747-400(REF)
21857.9B-777-300ER*
21555.8B-767-400
22553.4B-747-400ER
19762A-380*
22865.3A-340
PRESSURE(psi)
WHEEL LOAD(KIPS)
AIRCRAFT
* DUAL-TRIDEM
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ICAO Subgrade
" Representative" CBR QU (psi) ERi (ksi)
A 15 68 21
B 10 45 15
C 6 27 9
D 3 14 5
ICAO SUBGRADESC = QU/2 PHI = 0°
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GRANULAR LAYERS
TGRAN = BASE + SUBBASE
MR (psi) = 5,000 (THETA)0.5
C = 0 PHI = 45°
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10 -507.5 - 10A (CBR-15)15-505A (CBR-15)15-607.5 -10B (CBR-1020-605B (CBR-10)20-705C (CBR-6)30-705C (CBR-6)
40-1007.5 & 10D (CBR-3)50-1005D (CBR-3)
GRANULAR(INCHES)
AC(INCHES)
ICAOSUBGRADE
PAVEMENT PARAMETERS
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SINGLE WHEEL RESPONSES* Surface Def. (0-72 ins)
* AC Surface Strain* AC Base Strain
* GB Dev. Stress (top/middle)* Subgrade Dev. Stress
(Top / 1&2 Radii)* Subgrade Vertical Strain
(Top / 1&2 Radii)
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MULTIPLE WHEEL RESPONSES(GRID: 1/4 Dual & 1/4 Axle)
* Max. Surface Def. * Max. AC Surface Strain
* Max. AC Base Strain* Max. GB Dev. Stress (top/middle)
* Max. Subgrade Dev. Stress(Top / 1&2 Radii)
* Max. Subgrade Vertical Strain(Top / 1&2 Radii)
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ILLIPAVE Analysis Results-1
26 -132 -1
52
-124
-126 -133
-161
-121
-180-160-140-120-100-80-60-40-20
0A340M A340B A380M A380W B747-
400ERB767-400 B777-300 B747-400
Aircraft Type
Def
lect
ion,
mils
MLG--Surface DMax
AC Surface Thickness: 10-in -- Modulus: 500-ksiGB Thickness: 40-in -- SG Eri: 5-ksi
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ILLIPAVE Analysis Results-1
26 -132 -1
52
-124
-126 -133
-161
-121
-180-160-140-120-100-80-60-40-20
0A340M A340B A380M A380W B747-
400ERB767-400 B777-300 B747-400
Aircraft Type
Def
lect
ion,
mils
MLG--Surface DMax
AC Surface Thickness: 10-in -- Modulus: 500-ksiGB Thickness: 40-in -- SG Eri: 5-ksi
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ILLIPAVE Analysis Results47
4
470
443
442
433
435
423
406
360
380
400
420
440
460
480
A340M A340B A380M A380W B747-400ER
B767-400 B777-300 B747-400
Aircraft Type
Mic
rost
rain
MLG--Max AC Surface Strain
AC Surface Thickness: 10-in -- Modulus: 500-ksiGB Thickness: 40-in -- SG Eri: 5-ksi
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ILLIPAVE Analysis Results7.
6
8.2
8.0
7.8
8.5
8.9 9.
0
8.2
6.5
7
7.5
8
8.5
9
9.5
A340M A340B A380M A380W B747-400ER
B767-400 B777-300 B747-400
Aircraft Type
Stre
ss, p
si
MLG--Deviator Stress @ Top of Subgrade Layer
AC Surface Thickness: 10-in -- Modulus: 500-ksiGB Thickness: 40-in -- SG Eri: 5-ksi
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ILLIPAVE Analysis Results0.
54
0.59
0.57
0.56
0.61
0.63 0.
64
0.59
0.480.500.520.540.560.580.600.620.640.66
A340M A340B A380M A380W B747-400ER
B767-400 B777-300 B747-400
Aircraft Type
SSR
MLG--Subgrade Stress Ratio (SSR)
AC Surface Thickness: 10-in -- Modulus: 500-ksiGB Thickness: 40-in -- SG Eri: 5-ksi
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ILLIPAVE Analysis Results-9
74
-111
4
-105
7
-973
-104
9 -111
5
-112
8
-998
-1150
-1100
-1050
-1000
-950
-900
-850A340M A340B A380M A380W B747-
400ERB767-400 B777-300 B747-400
Aircraft Type
Mic
rost
rain
MLG--Vertical Strain @ Top of Subgrade Layer
AC Surface Thickness: 10-in -- Modulus: 500-ksiGB Thickness: 40-in -- SG Eri: 5-ksi
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ILLIPAVE Analysis Results1.
03 1.09
1.25
1.02 1.04 1.
10
1.32
1.00
1.17
1.16
1.09
1.09
1.07
1.07
1.04
1.00
0
0.2
0.4
0.6
0.8
1
1.2
1.4
A340M A340B A380M A380W B747-400ER B767-400ER B777-300ER B747-400Aircraft Type
Rat
io W
RT
B74
7-40
0
MLG--Surface DMax MLG--Max AC Surface Strain
AC Surface Thickness: 10-in -- Modulus: 500-ksiGB Thickness: 40-in -- SG Eri: 5-ksi
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ILLIPAVE Analysis Results0.
93 1.00
0.98
0.95 1.
03 1.08 1.10
1.00
0.98
1.12
1.06
0.98 1.
05 1.12
1.13
1.00
0
0.2
0.4
0.6
0.8
1
1.2
A340M A340B A380M A380W B747-400ER B767-400ER B777-300ER B747-400Aircraft Type
Rat
io W
RT
B74
7-40
0
MLG--Deviator Stress @ Top of Subgrade LayerMLG--Vertical Strain @ Top of Subgrade Layer
AC Surface Thickness: 10-in -- Modulus: 500-ksiGB Thickness: 40-in -- SG Eri: 5-ksi
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TRANSFER FUNCTIONS(RESPONSES – DISTRESS)
CRITICAL FACTORS!!!
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FLEXIBLE PAVEMENT DISTRESSES
• HMA FATIGUE
• RUTTING:
+ HMA (MATL. SELECTION / MIX DESIGN)
+ GRANULAR BASE/SUBBASE
+ SUBGRADE
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SUBGRADE TRANSFER FUNCTIONS
•SUBGRADE VERTICAL STRAIN
•SUBGRADE STRESS RATIO (SSR)(SSR= DEV STRESS / QU)
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VERTICAL STRAIN CRITERIA εε= L (1/N)m
0.40.2531.5*10-2TRL/1132 (85%)
0.251.8*10-295%0.252.1*10-285%0.252.8*10-250%
SHELL0.50.2231.05*10-2AIRD (INS)mLAGENCY
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WES / TOWNSEND & CHISOLM / 1976
Vicksburg ”BUCKSHOT CLAY”
(CH)
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Transfer Functions:Subgrade Rutting-
Vertical Strain Design Criteria1.5
1.0
0.90.8
0.7
0.61,000 2,000 5,000 10,000 20,000VE
RTI
CA
L C
OM
PRES
SIVE
ST
RA
IN A
T TO
PO
F SU
BG
RA
DE,
εv
10-3
ANNUAL STRAIN REPETITIONS
(20 YEAR LIFE)
EESS = 30,000 PSI= 30,000 PSI
15,00015,000
9,0009,000
3,0003,000
COE / FAA LEDFAA
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FAAFAA SUBGRADE STRAIN CRITERIA
(Revised)
C = (0.004 / εv )8.1 Coverages < 12,100
C = (0.002428 / εv )14.21 Coverages > 12,100
C - Coverages
εv - Subgrade Vertical Compressive Strain
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Transfer Functions:Subgrade Rutting-SSR
Influence of SSR on Permanent Deformation
0.00
0.02
0.04
0.06
0.08
1 201 401 601 801 1001
Load Applications
Perm
anen
t Str
ain
1.00 SSR
0.75
0.50
0.25
qu = 28 psiγd = 98 pcfw = 26 %
UNSTABLE!!!UNSTABLE!!!
STABLE BehaviorSTABLE Behavior
BejaranoBejarano & Thompson (2001)& Thompson (2001)DuPontDuPont ClayClay
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Transfer Functions:Subgrade Rutting-SSR
Permanent Deformation vs. SSR
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.00 0.25 0.50 0.75 1.00Subgrade Stress Ratio
p afte
r N=1
000
20.0% CSSC23.0%24.5%23.0% DPC26.0%28.5%30.5%
BejaranoBejarano & Thompson (2001)& Thompson (2001)
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SUBGRADE RUTTING ALGORITHM
LOG εP = A + b (LOG N)
εP = ANb
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“Development of a Simplified M-E Design Procedure for Low-Volume Flexible Roads”
Zhao & DennisUniversity of ArkansasTRR # 1989 – Vol. 1
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Subgrade Stress Ratio (SSR) / A
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Subgrade Stress Ratio (SSR) / b
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Transfer Functions:Subgrade Rutting-SSR
Damage Potential… Low/Acceptable Limited High SSR… 0.5 / 0.6 0.6 to 0.75 > 0.75
SSR General GuidelinesSSR General Guidelines
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GRANULAR LAYER RUTTING
* COE – NOT A CRITERION* FAA / LEDFAA - NOT A CRITERION
INDIRECT ACCOMODATION: MINIMUM HMA SURFACE THICKNESS
STABILIZED BASE - > 100 KIPS
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GRANULAR BASE
• Minimum HMA Surface ThicknessFAA
4-5 ins. / Critical3-4 ins. / Noncritical
(Base CBR - 80)
• S. African “F”
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South African Mechanistic Approach
Stress Based Safety Factor FMaterial Shear Strength / Shear Stress
F = [σ3 ∗ φterm + cterm] / [σ1 - σ3]where:
φterm = [tan2(45 + φ/2) - 1]cterm = 2 * C * tan(45 + φ/2)φ - friction angle, degreesC - cohesion, psi
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GRANULAR BASE RATIO
FOR PHI = 45° & C = 0
F = DEV. STRESS / 4.8 * SIG 3
DECREASED “F”: MORE RUTTING
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HMA FATIGUE(TRADITIONAL)
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HMA FATIGUE CRACKING
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LEDFAA – HMA FATIGUE
LOG C = 2.68 – (5*LOG ε) - (2.665*LOG EHMA)
C – COVERAGES TO FAILURE
ε - HMA STRAIN @ BOTTOM OF P401 HMA SURFACE
EHMA – HMA MODULUS (200 ksi)
Heukelom & Klomp – AAPT (1964)
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AASHTO TP 8-94
Standard Test Method for Determination of
the Fatigue Life of Compacted HMA
Subjected to Repeated Flexural Bending
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FATIGUE DESIGN• Tensile Strain at Bottom of Asphalt• Tensile Strain in Flexural Beam Test
Other Configurations
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FATIGUE TESTING
• Tensile Strain in Flexural Beam Test– Other Configurations
– 10 Hz Haversine Load, 20o C, Controlled Strain
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STIFFNESS CURVE
2000
3000
4000
5000
6000
7000
8000
0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07 2.5E+07 3.0E+07 3.5E+07 4.0E+07
Number of Load Cycles
Stiff
ness
, mPa
Failure
FAILURE: 50% Reduction
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LABORATORY ALGORITHM
0.00001
0.0001
0.001
0.01
1.0E+02 1.0E+04 1.0E+06 1.0E+08 1.0E+10
Load Repetitions
Tens
ile S
trai
n
K1 = InterceptK2 = Slope
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FATIGUE ALGORITHMS
Nf = K1(1/ε)K2
Nf = K1 (1/ε)K2 (1/E*)K3
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AC FATIGUE
LOG N
LOG
εA
CN = K1(1/εAC)K2
K2’>K2
K2’
K2K2
K1
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HMA FATIGUE @ UIUCCarpenter - Ghuzlan - Shen
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IDOT HMA FATIGUE DATA SUMMARY
84 MIXES
N = K1 (1/ ε)K2
Minimum K2: 3.5
90% K2: 4.0
Average K2: 4.5
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OTHER STUDIES
0
1
2
3
4
5
6
7
-16 -14 -12 -10 -8 -6 -4 -2 0
Lo g (K1)
K2
U of IllinoisMaupin Resu ltsMyr eF HWAF innLinear (U of Illinois)Linear (Maupin Resu lts)Linear (Myr e)Linear (F H WA)
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K – n RELATIONS
Myre / Norway NTH (1992)LOG K1 = (1.332 – K2) / 0.306
U of IL / IDOT HMAsCarpenter – et al
LOG K1 = (1.178 – K2) / 0.329
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0.710.490.330.23250
7.13.82.01.1150
160.660.022.48.4**
75
K24.5
k24.0
K23.5
K23.0
HMA STRAIN
*
N = K1(1/HMA STRAIN)K2
* Micro-strain **Mreps
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NO “UNIQUE”
THERE IS
HMA FATIGUE ALGORITHM !!!!
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HMA ENDURANCE LIMIT
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Monismith & McLean
“Technology of Thick Lift Construction: Structural Design Considerations”
1972 AAPT Proceedings
70 Micro-Strain Endurance Limit!!
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Michael Nunn“Long-Life Flexible Pavements”
8th ISAP ConferenceSeattle, WA - 1997
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M32
M32CORE
TRL
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Longitudinal
crack in
M1
TRL
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LOW STRAIN TESTING
10
100
1000
10000
1.E+00 1.E+05 1.E+10 1.E+15 1.E+20 1.E+25 1.E+30 1.E+35 1.E+40
Load Repetitions, E50
Flex
ural
Stra
in, m
icro
stra
in
70 Micro Strain Limit
21 Mixes Tested for Endurance Limit
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HMA FATIGUE
N (LOG)
ε AC
(LO
G)
N = K1 (1 / εAC)K2
70 µε
ENDURANCE LIMIT
PERPETUAL PAVEMENT
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FATIGUE ENDURANCE LIMIT
0.00001
0.0001
0.001
0.01
1.0E+02 1.0E+04 1.0E+06 1.0E+08 1.0E+10
Load Repetitions
Tens
ile S
train
K1 = InterceptK2 = Slope
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FATIGUE ENDURANCE LIMIT
• Damage and Healing Concepts and Test Data Support a Strain Limit Below Which Fatigue Damage Does Not Accumulate
• Strain Limit Is Not The Same for All HMAs.
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FATIGUE ENDURANCE LIMITIDOT DATA
NEVER < 70 micro-strain!!!
GENERALLY: 70 –100 micro-strain
MAY BE > 100 micro-strain
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EFFECT OF REST PERIODS
SMALL REST PERIODS BETWEEN STRAIN REPETITIONS SIGNIFICANTLY
INCREASES HMA FATIGUE LIFE
IDOT HMA5 SECONDS: 10 X
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OVERLOADING
• HMA CAN SUSTAIN “SPORADIC OVERLOADS” AND RETURN TO “ENDURANCE LIMIT” PERFORMANCE
• SUBSEQUENT HMA STRAIN REPETITIONS < ENDURANCE LIMIT:
“DO NOT COUNT”
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NAPTF – PAVEMENT RUTTING
NAPTF TEST SECTIONS
75 FEET LONG60 FEET WIDE
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“As-Built” NAPTF Test Sections
AC Surface (P-401)
Granular Base(P-209)
LOW StrengthSubgrade
Granular Subbase(P-154)
5 in.
7.75 in.
36.4 in.
LFCLFC
Subgrade=94.7 in.
AC Surface (P-401)
Granular Base(P-209)
LOW StrengthSubgrade
Granular Subbase(P-154)
5 in.
7.75 in.
36.4 in.
LFCLFC
Subgrade=94.7 in.
AC Surface (P-401)
Granular Base(P-209)
MEDIUM StrengthSubgrade
Granular Subbase(P-154)
5.1 in.
7.9 in.
12.1 in.
MFCMFC
Subgrade=94.8 in.
AC Surface (P-401)
Granular Base(P-209)
MEDIUM StrengthSubgrade
Granular Subbase(P-154)
5.1 in.
7.9 in.
12.1 in.
MFCMFC
Subgrade=94.8 in.
AC Surface (P-401)
Asphalt Stab. Base(P-401)
LOW StrengthSubgrade
Granular Subbase(P-209)
5 in.
4.9 in.
29.6 in.
LFSLFS
Subgrade=104.5 in.
AC Surface (P-401)
Asphalt Stab. Base(P-401)
LOW StrengthSubgrade
Granular Subbase(P-209)
5 in.
4.9 in.
29.6 in.
LFSLFS
Subgrade=104.5 in.
AC Surface (P-401)
MEDIUM StrengthSubgrade
Granular Subbase(P-209)
5 in.
4.9 in.
8.5 in.
Asphalt Stab. Base(P-401)
Subgrade=101.6 in.
MFSMFS
AC Surface (P-401)
MEDIUM StrengthSubgrade
Granular Subbase(P-209)
5 in.
4.9 in.
8.5 in.
Asphalt Stab. Base(P-401)
Subgrade=101.6 in.
MFSMFS
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NAPTF Traffic Test ProgramN
30 ft.
12.8 ft.
0 ft.
-12.8 ft.
-30 ft.
B747
C/L
Wheel Load: 45,000 lbs
Tire Pressure: 188 psi
Traffic Speed: 5 mph
B777
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NAPTF Traffic Wander
0
-7 ft.-12.8 ft.-19 ft. 7 ft. 12.8 ft. 19 ft.
Trac
k #-
1
Trac
k #1
Trac
k #2
Trac
k #3
Trac
k #4
Trac
k #
-2
Trac
k #
-3
Trac
k #
-4
Trac
k #-
1
Trac
k #0
Trac
k #1
Trac
k #2
Trac
k #3
Trac
k #4
Trac
k #
-2
Trac
k #
-3
Trac
k #
-4
9.8 in.
B777 WANDER AREA B747 WANDER AREA
B77
7Tr
ack
#0
B74
7
66 Passes(33 East, 33 West)
σ = 30.5 in.
C/L
N
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NAPTF “Failure” Criteria
• “At least 1 inch surface upheaval adjacent to the traffic lane” (USCOE MWHGL tests)
• This is considered to reflect structural or shearing failure in the subgrade
• 1 inch surface upheaval may be accompanied by a 0.5-inch rut depth or rut depths in excess of 3 inches
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High Severity Rutting
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Number of Passes to “Failure”
MFC 12,952* - 12,952
MFS 19,869* - 19,869
LFC 19,950 24,145 44,095*
LFS 19,939 24,749 44,688*
NAPTF Test
Section
* - "Failure" achieved
45,000-lb Wheel Load
65,000-lb Wheel Load Total
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Max Rut Depths at “Failure”
B777 B747 B777 B747 B777 B747
MFC 3.4 3.1 - - 3.4 3.1
MFS 3.5 1.0 - - 3.5 1.0
LFC 0.7 0.9 2.5 2.2 3.2 3.1
LFS 0.5 0.4 1.6 1.7 2.1 2.1
Total RD (in.)NAPTF Test
Section
RD under 45,000-lb Wheel Load (in.)
RD Under 65,000-lb Wheel Load (in.)
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0
1,000
2,000
3,000
4,000
5,000
0 2000 4000 6000 8000 10000 12000 14000Number of Load Repetitions (N)
Rut
Dep
th (m
ils)
B777-SEB747-SEB777-TSPB747-TSP
RD Vs N – MFC1
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0
1,000
2,000
3,000
4,000
5,000
0 10,000 20,000 30,000 40,000 50,000 60,000Number of Load Repetitions (N)
Rut
Dep
th (m
ils)
B777-SEB747-SEB777-TSPB747-TSP
RD Vs N – LFC1
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RD Vs N – LFS1
0
1,000
2,000
3,000
4,000
5,000
0 10,000 20,000 30,000 40,000 50,000 60,000Number of Load Repetitions (N)
Rut
Dep
th (m
ils)
B777-SEB747-SEB777-TSPB747-TSP
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N to Reach Specific RDLow Strength Sections
Medium Strength Sections
B777 B747 B777 B747 B777 B747 B777 B747
250 28 516 28 531 10,743 12,442 28 28
500 5,008 8,083 7,791 8,723 20,068 20,642 15,111 515
1000 21,612 21,414 21,084 22,759 22,888 26,153 21,488 21,488
LFS2Rut Depth (mils)
LFC1 LFC2 LFS1
B777 B747 B777 B747 B777 B747 B777 B747
250 28 28 28 28 - 28 28 5,295
500 299 133 133 133 - 10,529 5,373 7,513
1000 3,343 1,193 1,193 1,448 - 19,869 12,440 15,108
Rut Depth (mils)
MFC1 MFC2 MFS1 MFS2
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Conclusions
• Max RD at “failure” higher for conventional sections compared to stabilized sections
• More passes at higher wheel loads was required by L sections to reach “failure” compared to M sections
• N required by B777 and B747 gears to reach 1-inch RD were similar
• B777 RDs and B747 RDs do not differ significantly
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M-E DESIGN TOOLS ARE:
“AVAILABLE” AND
“TECHNOLOGICALLY ADEQUATE”
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IT IS TIME TO:
“MOVE ON”