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Analysis and Backcalculation Analysis and Backcalculation for Pavement Structuresfor Pavement Structures
Kunihito MatsuiKunihito MatsuiTokyo Denki University
No.16th ICPT July 20-23 2008 Sapporo Japan
1. Static Analysis1. Static Analysisyy
・・The Software GAMES is comparedThe Software GAMES is compared with BISARwith BISAR11--1. Cylindrical coordinates1. Cylindrical coordinates
The Software GAMES is comparedThe Software GAMES is compared with BISARwith BISAR11--2. Cartesian coordinates2. Cartesian coordinates
・・The uniform loads over a rectangular area and aThe uniform loads over a rectangular area and a
2 Dynamic Analysis2 Dynamic Analysis
・・The uniform loads over a rectangular area and a The uniform loads over a rectangular area and a circular area are comparedcircular area are compared
2. Dynamic Analysis2. Dynamic AnalysisWave propagation in viscoelasticWave propagation in viscoelastic multilayered mediamultilayered media
・・The responses from the solutions are comparedThe responses from the solutions are comparedwith the results of ADINA with the results of ADINA
3 B k l l i3 B k l l iDynamic backcalculationDynamic backcalculation
3. Backcalculation3. Backcalculation
No.26th ICPT July 20-23 2008 Sapporo Japan
1. Static Analysis1. Static Analysis in Cylindrical Coordinatesin Cylindrical Coordinatesyy yy
drθ
xO
1 ∂∂∂ σσττσ
The equilibrium equationsThe equilibrium equations
θτ zzrτzσ
θd ryθrdr
01=
−+
∂∂
+∂
∂+
∂∂
rzrrrrzrr θθ σστ
θτσ
021 ∂∂∂ rzr θθθθ ττστ
τ
rθτrσ
τ
θτ rdz
θσ
01+
∂+
∂+
∂ rzzzrz τσττ θ
0=+∂
+∂
+∂ rzrr
rzr θθθθ
θ
zθτ rzτz0=+
∂+
∂+
∂ rzrrrzzrz
θθ
StrainStrain--DisplacementDisplacement St iSt i StSt1;r r
u u v vr r r rθε γ
θ∂ ∂ ∂
= = + −∂ ∂ ∂
StrainStrain DisplacementDisplacement StrainStrain--StressStress
( )1 2(1 );r r z r rθ θ θνε σ νσ νσ γ τ+
= − − =1 1; z
u v w vr r r zw w u
θ θε γθ θ
∂ ∂ ∂= + = +
∂ ∂ ∂∂ ∂ ∂
( );r r z r rE Eθ θ θγ
( )1 2(1 );z r z zE Eθ θ θ θνε σ νσ νσ γ τ+
= − − =
No.1No.3
;z zrw w uz r z
ε γ∂ ∂ ∂= = +
∂ ∂ ∂ ( )1 2(1 );z z r zr zrE Eθνε σ νσ νσ γ τ+
= − − =
6th ICPT July 20-23 2008 Sapporo Japan
Uniformly distributed circular load
vertical + horizontal Vertical load Horizontal load loads
surfaceBase
Subgrade
6th ICPT July 20-23 2008 Sapporo Japan No.4
Features of GAMES
Pavement: Multilayer pavement system y ywith a possibility of interface slip.
Surface load: Multiple vertical and/or horizontal circular loads.horizontal circular loads.
Analysis: Multiple points of interest.Analysis: Multiple points of interest.
Response: Stresses, strains, andResponse: Stresses, strains, and displacements
6th ICPT July 20-23 2008 Sapporo Japan No.5
1. Static Analysis1. Static Analysisyy
2a = 30cmGAMES vs BISAR
Q = 49kN
2a 30cmθ = -30°
Xν = 0 35 Xθ = 30°
ν1 = 0.35 E1 = 2500MPa
Yν2 = 0.35 E2 = 280MPa
ν3 = 0.4 E3 = 50MPaZ
No.6
Z6th ICPT July 20-23 2008 Sapporo Japan
1. Static Analysis1. Static AnalysisyyGAMES vs BISAR
~ Distribution of horizontal displacement ux ~ Distribution of horizontal displacement, ux
0 01 0 02 0 03 0 04ux (cm)
010
0.01 0.02 0.03 0.04) 10
2030h
(cm
)
304050de
pth
GAMES5060
d BISAR
No.76th ICPT July 20-23 2008 Sapporo Japan
1. Static Analysis1. Static AnalysisyyGAMES vs BISAR
~ Distribution of horizontal Stress σx ~
-0 4 -0 2 0 0 2 0 4 0 6 0 8σ x (MPa)
Distribution of horizontal Stress, σx
010
-0.4 -0.2 0 0.2 0.4 0.6 0.8
1020(c
m)
3040ep
th (
GAMES405060
de GAMES
BISAR
No.8
60
6th ICPT July 20-23 2008 Sapporo Japan
1. Static Analysis1. Static AnalysisyyGAMES vs BISAR
~ Distribution of Vertical Stress σz ~ Distribution of Vertical Stress, σz
0 0.05 0.1 0.15 0.2 0.25σ z (MPa)
0101020(c
m)
3040ep
th
GAMES4050
d GAMESBISAR
No.9
606th ICPT July 20-23 2008 Sapporo Japan
Interface Slip ModelsInterface Slip ModelsInterface Slip ModelsInterface Slip Models
{ }{ }1(1 ) ( ) (0) ( )i i ii r i r i rz iiu h u hβα α τ+− − =
* 1
1
1 1i i
i ii b
E Eν νβ +
+
⎛ ⎞+ += +⎜ ⎟
⎝ ⎠Model 1(GAMES) :
Model 2(BISAR) : * 12 i
ii b
Eνβ
⎛ ⎞+= ⎜ ⎟
⎝ ⎠
Model 3 : * 1
1
1 12 i i
i ii b
E Eν νβ +
+
⎛ ⎞⎛ ⎞+ += ⎜ ⎟⎜ ⎟
⎝ ⎠⎝ ⎠1i iE E +⎝ ⎠⎝ ⎠
0 1.0iα≤ < slip parameter
6th ICPT July 20-23 2008 Sapporo Japan No.10
GAMES vs BISAR (Interface slip)~ Distribution of radial displacement, u ~
u (cm)0.003 0.006 0.009 0.012 0.015
u (cm)0.003 0.006 0.009 0.012 0.015
0
10
)
0
10
m)
20
30pth
(cm
)
20
30dept
h (c
m
40
50
dep
GAMES(0) GAMES(0.2)
40
50d
BISAR(0) BISAR(0 2)50
60
( ) ( )
GAMES(0.5) GAMES(0.9)50
60
BISAR(0) BISAR(0.2)
BISAR(0.5) BISAR(0.9)
6th ICPT July 20-23 2008 Sapporo Japan No.11
GAMES vs BISAR (Interface slip)~ Distribution of vertical displacement, w ~
w (cm)0 045 0 065 0 085 0 105
w (cm)0 045 0 065 0 085 0 105
0
10
0.045 0.065 0.085 0.105
0
10
0.045 0.065 0.085 0.105
10
20
h (c
m)
10
20
pth
(cm
)
30
40dept
h 30
40de
p50
60
GAMES(0) GAMES(0.2)
GAMES(0.5) GAMES(0.9)50
60
BISAR(0) BISAR(0.2)
BISAR(0.5) BISAR(0.9)
6th ICPT July 20-23 2008 Sapporo Japan No.12
GAMES for Windows (graphics)F t~ Features ~
Language: Japanese / EnglishLanguage: Japanese / English
Unit of measurement: Load (kgf, kN), LengthUnit of measurement: Load (kgf, kN), Length (cm), Elastic modulus (kgf/cm2, MPa)
Input: Input of new parameters or import from existing fileexisting file
Output: analytical results and graphicsOutput: analytical results and graphics visualization (contour and color fill plots) of strainstrain
6th ICPT July 20-23 2008 Sapporo Japan No.13
Summary and recommendationsComputational accuracy of GAMES
Accuracy of GAMES is similar to and inAccuracy of GAMES is similar to and in some cases better than BISAR.
User interface and visualization processI ffi i i th f GAMESImproves efficiency in the use of GAMES and assists users to visualize distribution of pavement responses.
ApplicationApplicationGAMES can be used for analysis,
l ti d d i f tevaluation and design of pavements.6th ICPT July 20-23 2008 Sapporo Japan No.21
Dual Tire Footprints by SIM (Stress In Dual Tire Footprints by SIM (Stress In Motion)Motion)Motion)Motion)
(measured at CSIR, South Africa)(measured at CSIR, South Africa)
30 kN & 420 kPa inflation pressure
70 kN & 420 kPa inflation pressurep
6th ICPT July 20-23 2008 Sapporo Japan No.22
Contact pressure measured by SIM (provided by Prof. Morris De Beer)
6th ICPT July 20-23 2008 Sapporo Japan No.23
Contact pressure measured by SIM (provided by Prof. Morris De Beer)
6th ICPT July 20-23 2008 Sapporo Japan No.24
Contact pressure measured by SIM (provided by Prof. Morris De Beer)
6th ICPT July 20-23 2008 Sapporo Japan No.25
1. Static Analysis1. Static Analysis in the Cartesian Coordinatein the Cartesian Coordinatex
Oyy
σ
dx
x
y0=
∂∂
+∂
∂+
∂∂
zyxxzxyx ττσEquilibriumEquilibrium
zσ
yxτ
zyτ
τ
zxτyzτ
yσ
zdy
dz
0=∂
∂+
∂
∂+
∂
∂
zyxzyyxy τστ
∂∂∂ σττ y
xyτ dxx
xx ∂
∂+
σσxσ
xzτ
dyyyx
yx ∂∂
+τ
τ∂σ
dz
dxxxy
xy ∂
∂+
ττ
0=∂
∂+
∂∂
+∂
∂zyx
zyzxz σττ
u v w∂ ∂ ∂StrainStrain--displacementdisplacement
∂σ
dxxxz
xz ∂∂
+ττ
dzzzx
zx ∂∂
+ττ
y∂
∂τ
dyy
yy ∂
∂+
σσ; ;x y z
u v wx y z
ε ε ε∂ ∂ ∂= = =
∂ ∂ ∂
; ;v u w v u wγ γ γ∂ ∂ ∂ ∂ ∂ ∂= + = + = + dz
zz
z ∂∂
+σσdy
yyz
yz ∂
∂+
ττ
dzzzy
zy ∂
∂+
ττ
; ;xy yz zxx y y z z xγ γ γ= + = + = +
∂ ∂ ∂ ∂ ∂ ∂
( )1 2(1 );x x y z xy xyE Eνε σ νσ νσ γ τ+
= − − =StrainStrain--stressstress ( )E E
( )1 2(1 );y y z x yz yzE Eνε σ νσ νσ γ τ+
= − − =
No.1( )1 2(1 );z z x y zx zxE E
νε σ νσ νσ γ τ+= − − =
6th ICPT July 20-23 2008 Sapporo Japan No.26
Method of SolutionMethod of SolutionMethod of SolutionMethod of Solution
NeuberNeuber--Papkovich RepresentationPapkovich Representation( )1u B xB yB zBλ μ+ ∂
= + +( )2 4 ( 2 )x x y zu B xB yB zBxμ μ λ μ
= − + ++ ∂
( )1 B B B Bλ μ+ ∂ ( )2 4 ( 2 )y x y zv B xB yB zBy
μμ μ λ μ
= − + ++ ∂
( )1 B B B Bλ μ+ ∂ ( )2 4 ( 2 )z x y zw B xB yB zBz
μμ μ λ μ
= − + ++ ∂
h2 2 2( , , ) ( , , ) ( , , ) 0x y zB x y z B x y z B x y z∇ = ∇ = ∇ =
where
( , , ) ( , , ) ( , , )x y zy y y
6th ICPT July 20-23 2008 Sapporo Japan No.27
1. Static Analysis 1. Static Analysis yyRectangular Area vs Circular Area
L6.0L6.0L3.0L4079.0
L8712.0L
Dimension of tire contact area(a) Actual Area (b) Equivalent Area
cm6.162 =b
Y
X6cm16cm1
cm2.332 =b
X・Dual tires ・Single tires
cm1.242 =a
b
Y
2cm2.401=A
a
2cm2.401=A
X
cm1.242 =a
b
aY
2cm4.8022 =A
X
cm3.11=r
Y
6cm16cm16cm1X
cm0.16=r
Y
X
No.28
2cm2.401=A2cm2.401=A2cm4.8022 =A
6th ICPT July 20-23 2008 Sapporo Japan
1. Static Analysis 1. Static Analysis yyRectangular Area vs Circular Area
X
kN49=zPLoading area
X2cm4.802=A
cm151 =h MPa50001 =E53.01 =ν
Young's modulusPoisson's ratio
cm151 =h MPa50001 =E53.01 =ν
Young's modulusPoisson's ratio
cm352 =hMPa4002 =EYoung's modulus
P i ' icm352 =hMPa4002 =EY Young's modulus
P i ' i
Bottom of first layer
cm352 =h 53.02 =νPoisson's ratiocm352 =h 53.02 =νPoisson's ratioTop of subgrade layer
Z
MPa603 =E40.03 =ν
Young's modulusPoisson's ratio
Z
MPa603 =E40.03 =ν
Young's modulusPoisson's ratio
No.29
ZZ
6th ICPT July 20-23 2008 Sapporo Japan
1. Static Analysis 1. Static Analysis cm6.162 =b
Y
X6cm16cm1
cm3.11=r
6cm16cm16cm1
X
yycm1.242 =a
b
Y
2cm2.401=A
a
2cm2.401=ALoading area Loading area
Y
2cm2.401=A2cm2.401=ALoading areaLoading area
~ Dual tires ~ Rectangular Area vs Circular Area
-250
ε120
140
-290
-270
n (×
10-6
)
Circular area(Dual)Rectangular area(Dual)
ε
zε
60
80
100
in (×
10-6
)
-330
-310
Stra
in0
20
40
60
Stra
i
εx (Circular area)εy (Circular area)εx (Rectangular area)εy (Rectangular area)
-350-30 -20 -10 0 10 20 30
Y (cm)
0-30 -20 -10 0 10 20 30
Y (cm)
εy (Rectangular area)
No.306th ICPT July 20-23 2008 Sapporo Japan
NonNon uniform Surface Loadinguniform Surface LoadingNonNon--uniform Surface Loadinguniform Surface Loading
b2 b2
Xa2
b2
Xa2
b2
ZY Z
Y
X directionY-direction
b2
X-direction
Xa2
b2
ZY
Z-direction6th ICPT July 20-23 2008 Sapporo Japan No.31
cm6.162 =b
X6cm16cm1
cm3.11=r
6cm16cm16cm1
X
Non-uniform
180
cm1.242 =a
b
Y
2cm2.401=A
a
2cm2.401=ALoading area Loading area
Y
2cm2.401=A2cm2.401=ALoading areaLoading area
loading
120
140
160
0-6)
40
60
80
100
Stra
in (×
1
εx(Rectangular area)εy(Rectangular area)
0
20
-30 -20 -10 0 10 20 30Y (cm)
εy(Rectangular area)εx(Circular area)εy(Circular area)
-260
-250
εz(Rectangular area)( i l )
-300
-290
-280
-270
n (×
10-6
)
εz(Circular area)
-340
-330
-320
-310
Stra
in
-350-30 -20 -10 0 10 20 30
Y (cm)
6th ICPT July 20-23 2008 Sapporo Japan No.32
2. Dynamic Analysis2. Dynamic Analysisy yy y
2∂∂
22--1. Axi1. Axi--symmetricsymmetric wave propagation analysiswave propagation analysis
2
2
tu
rzrrrzr
∂∂
=−
+∂
∂+
∂∂ θσστσ
2w∂∂∂ τστ2tw
rzrrzzrz
∂∂
=+∂
∂+
∂∂ τστ
1u u v v∂ ∂ ∂StrainStrain--DisplacementDisplacement
;
1 1;
r ru u v vr r r r
u v w v
θε γθ
ε γ
∂ ∂ ∂= = + −
∂ ∂ ∂∂ ∂ ∂
= + = +;
;
z
z zr
r r r zw w u
θ θε γθ θ
ε γ
= + = +∂ ∂ ∂
∂ ∂ ∂= = +
∂ ∂ ∂
No.34
;z zrz r zγ
∂ ∂ ∂
6th ICPT July 20-23 2008 Sapporo Japan
2 02 0
r ra b a aa a b a
σ εσ ε
+⎧ ⎫ ⎧ ⎫⎛ ⎞⎜ ⎟⎪ ⎪ ⎪ ⎪+⎪ ⎪ ⎪ ⎪⎜ ⎟
StressStress--StrainStrain2 0
2 0z z
a a b aE
a a a bθ θσ ε
σ ε
⎪ ⎪ ⎪ ⎪+⎪ ⎪ ⎪ ⎪⎜ ⎟=⎨ ⎬ ⎨ ⎬⎜ ⎟+⎪ ⎪ ⎪ ⎪⎜ ⎟⎪ ⎪ ⎪ ⎪0 0 0rz rzbτ γ⎜ ⎟⎪ ⎪ ⎪ ⎪⎝ ⎠⎩ ⎭ ⎩ ⎭
)21)(1(ν
=a)1(2
1+
=b)21)(1( νν −+ )1(2 ν+
FEM formulationFEM formulation
[ ]{ } [ ]{ } { }M z K z f+ =&&
⇓⇓[ ]{ } [ ]{ } [ ]{ } { }M z C z K z f+ + =&& &
[ ] [ ]C Kβ=6th ICPT July 20-23 2008 Sapporo Japan No.35
2. Dynamic Analysis2. Dynamic AnalysisE
y yy y
・・ Kelvin ModelKelvin Modelσ σ
F2 0
2 0r ra b a a
a a b adθ θ
σ εσ ε
+⎫ ⎧ ⎫⎛ ⎞⎜ ⎟⎪ ⎪ ⎪+⎪ ⎪ ⎪⎛ ⎞⎜ ⎟⎬ ⎨ ⎬2 0
0 0 0z z
Ea a a b
b
dFdt
θ θ
σ ετ γ
⎪ ⎪ ⎪⎛ ⎞⎜ ⎟= +⎬ ⎨ ⎬⎜ ⎟⎜ ⎟+⎝ ⎠⎪ ⎪ ⎪⎜ ⎟⎪ ⎪ ⎪⎝ ⎠⎩ ⎭ ⎩ ⎭0 0 0rz rzbτ γ⎪ ⎪ ⎪⎝ ⎠⎩ ⎭ ⎩ ⎭
)21)(1( ννν
−+=a
)1(21
ν+=b))(( )1(2 ν+
[ ]{ } [ ]{ } [ ]{ } { }M z C z K z f+ + =&& &[ ]{ } [ ]{ } [ ]{ } { }M z C z K z f+ + =
[ ] [ ] [ ] [ ];C F B K E B= =
No.37
[ ] [ ] [ ] [ ];C F B K E B= =
6th ICPT July 20-23 2008 Sapporo Japan
2. Dynamic Analysis2. Dynamic AnalysisWaveWave--PavePave, DynaDyna--Pave vs. ADINAPave vs. ADINA
y yy y
2 kN)20t(sin49 2 π=zPcm15=a (ms)400 ≤≤ t
RYong's modulus
cm151 =hMPa50001 =E
530Damping sMPa501 ⋅=F
3Poisson's rationcm151h 53.01 =ν
MPa4002 =EYong's modulus
Density 31 mkg2200=ρ
Damping sMPa42 ⋅=Fcm352 =h
2
53.02 =ν
g
Poisson's ration
p g
Density2
32 mkg2000=ρ
Z
MPa603 =E40.03 =ν
Yong's modulus
Poisson's ration 31 mkg1600=ρ
Damping
Density
sMPa6.03 ⋅=F
No.38
Z
6th ICPT July 20-23 2008 Sapporo Japan
2. Dynamic Analysis2. Dynamic Analysisy yy y
0 035 50
WaveWave--PavePave, DynaDyna--Pave vs. ADINAPave vs. ADINA
0.03
0.035
40
45
50D-0 (Wave-Pave)D-75 (Wave-Pave)D-150 (Wave-Pave)A A( 0)
0.02
0.025
m) 30
35
N)
ADINA(D-0)ADINA(D-75)ADINA(D-150)D-0 (Dyna-Pave)
0.01
0.015
Uz
(cm
20
25
Load
(kN
yD-75 (Dyna-Pave)D-150 (Dyna-Pave)LOAD
0
0.00510
15
-0.005
0
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20
5
No.39
Time (s)
6th ICPT July 20-23 2008 Sapporo Japan
SummarySummarySummarySummary
Dynamic analysis with Dynamic analysis with stiffness stiffness proportional dampingproportional damping is equivalent to is equivalent to p p p gp p p g qqdynamic analysis with dynamic analysis with the Kelvin modelthe Kelvin model
6th ICPT July 20-23 2008 Sapporo Japan No.40
2. Dynamic Analysis2. Dynamic Analysisy yy y・・ WaveWave--PavePave
kN)20t(sin49 2 π=P
R
kN)20t(sin49 πzPcm15=a (ms)400 ≤≤ t h3= 5m or ∞
Yong's modulusPoisson's ration
cm151 =hMPa50001 =E
53.01 =νDampingDensity
sMPa501 ⋅=F3
1 mkg2200=ρ
cm352 =hMPa4002 =E
53.02 =ν
Yong's modulus
Poisson's ration
Damping
Density
sMPa42 ⋅=F3
2 mkg2000=ρ
MPa603 =E40.03 =ν
Yong's modulus
Poisson's ration 31 mkg1600=ρ
Damping
Density
sMPa6.03 ⋅=F
3h
MPa100004 =E40.04 =ν
Yong's modulus
Poisson's ration 34 mkg1600=ρ
Damping
Density
sMPa1004 ⋅=F
No.41
Z
6th ICPT July 20-23 2008 Sapporo Japan
・・ WaveWave--PavePave uz ur
( t=0.01s )( )
0 0 001 0 002 0 003 0 004 0 005 0 0001 0 0 0001 0 0002 0 0003
Profile of Vertical displacement, uz Profile of horizontal displacement, ur
00 0.001 0.002 0.003 0.004 0.005
0-0.0001 0 0.0001 0.0002 0.0003
200
400
m)
200
400
m)
600
Z(cm
600
Z(cm
800h=∞h=5m
800 h=∞h=5m
1000 1000
6th ICPT July 20-23 2008 Sapporo Japan No.42
・・ WaveWave--PavePave uz ur
( t=0.02s )
0 001 0 0005 0 0 0005 0 001 0 0015 0 0020 0 005 0 01 0 015 0 02 0 025
( )
Profile of Vertical displacement, uz Profile of horizontal displacement, ur
0-0.001 -0.0005 0 0.0005 0.001 0.0015 0.002
00 0.005 0.01 0.015 0.02 0.025
200
400
m)
200
400
m)
600
Z(cm
h=∞
600
Z(cm
800
h=∞h=5m800 h=∞
h=5m
10001000
6th ICPT July 20-23 2008 Sapporo Japan No.43
・・ WaveWave--PavePave uz ur
( t=0.03s )( )
0 0 005 0 01 0 015 0 02 0 025 0 03 0 035 0 002 0 001 0 0 001 0 002 0 003
Profile of Vertical displacement, uz Profile of horizontal displacement, ur
00 0.005 0.01 0.015 0.02 0.025 0.03 0.035
0-0.002 -0.001 0 0.001 0.002 0.003
200
400(cm
)
200
400cm)
600
Z(
600Z(
ch=∞
800 h=∞h=5m
800
h ∞
h=5m
1000 1000
6th ICPT July 20-23 2008 Sapporo Japan No.44
・・ WaveWave--PavePave uz ur
( t=0.04s )( )
0 0 005 0 01 0 015 0 02 0 025 0 001 0 0005 0 0 0005 0 001 0 0015 0 002
Profile of Vertical displacement, uz Profile of horizontal displacement, ur
00 0.005 0.01 0.015 0.02 0.025
0-0.001 -0.0005 0 0.0005 0.001 0.0015 0.002
200
400cm)
200
400
cm)
600
Z(c
600
Z(c
800 h=∞h=5m
800h=∞h=5m
1000 1000
6th ICPT July 20-23 2008 Sapporo Japan No.45
・・ WaveWave--PavePave uz ur
( t=0.05s )( )
0 0 003 0 006 0 009 0 012 0 0004 0 0002 0 0 0002 0 0004 0 0006 0 0008
Profile of Vertical displacement, uz Profile of horizontal displacement, ur
00 0.003 0.006 0.009 0.012
0-0.0004 -0.0002 0 0.0002 0.0004 0.0006 0.0008
200
400
m)
200
400m)
600
Z(cm
600
Z(c
800h=∞h=5m
800h=∞h=5m
1000 1000
6th ICPT July 20-23 2008 Sapporo Japan No.46
・・ WaveWave--PavePave uz ur
( t=0.06s )( )
0 0 001 0 002 0 003 0 004 0 005 0 0001 0 0 0001 0 0002 0 0003 0 0004
Profile of Vertical displacement, uz Profile of horizontal displacement, ur
00 0.001 0.002 0.003 0.004 0.005
0-0.0001 0 0.0001 0.0002 0.0003 0.0004
200
400
m)
200
400
m)
600
Z(cm
600
Z(cm
800h=∞h=5m
800 h=∞h=5m
1000 1000
6th ICPT July 20-23 2008 Sapporo Japan No.47
・・ WaveWave--PavePave uz ur
( t=0.07s )( )
0 002 0 001 0 0 001 0 002 0 003 0 0002 0 0001 0 0 0001 0 0002
Profile of Vertical displacement, uz Profile of horizontal displacement, ur
0-0.002 -0.001 0 0.001 0.002 0.003
0-0.0002 -0.0001 0 0.0001 0.0002
200
400m)
200
400m)
600
Z(cm
600
Z(cm
800 h=∞h=5m
800h=∞h=5m
1000 1000
6th ICPT July 20-23 2008 Sapporo Japan No.48
・・ WaveWave--PavePave uz ur
( t=0.08s )( )
0 0015 0 001 0 0005 0 0 0005 0 001 0 0015 0 0003 0 0002 0 0001 0 0 0001 0 0002
Profile of Vertical displacement, uz Profile of horizontal displacement, ur
0-0.0015 -0.001 -0.0005 0 0.0005 0.001 0.0015
0-0.0003 -0.0002 -0.0001 0 0.0001 0.0002
200
400cm)
200
400m)
600
Z(c
h=∞h=5m
600
Z(cm
800 800h=∞h=5m
1000 1000
6th ICPT July 20-23 2008 Sapporo Japan No.49
・・ WaveWave--PavePave uz ur
( t=0.09s )( )
0 0015 0 001 0 0005 0 0 0005 0 001 0 0015 0 0003 0 0002 0 0001 0 0 0001
Profile of Vertical displacement, uz Profile of horizontal displacement, ur
0-0.0015 -0.001 -0.0005 0 0.0005 0.001 0.0015
0
200
-0.0003 -0.0002 -0.0001 0 0.0001
200
400m)
200
400
cm)
600
Z(c
600
Z(c
800 h=∞h=5m
800 h=∞h=5m
1000 1000
6th ICPT July 20-23 2008 Sapporo Japan No.50
・・ WaveWave--PavePave uz ur
( t=0.10s )( )
0 0015 0 001 0 0005 0 0 0005 0 001 0 0015 0 00015 0 0001 0 00005 0 0 00005 0 0001
Profile of Vertical displacement, uz Profile of horizontal displacement, ur
0-0.0015 -0.001 -0.0005 0 0.0005 0.001 0.0015
0-0.00015 -0.0001 -0.00005 0 0.00005 0.0001
200
400
m)
200
400
m)
600
Z(cm
600
Z(cm
800h=∞h=5m
800h=∞h=5m
1000 1000
6th ICPT July 20-23 2008 Sapporo Japan No.51
・・ WaveWave--PavePave uz ur
( t=0.20s )( )
0 0001 0 00005 0 0 00005 0 0001 0 000015 0 00001 0 000005 0 0 000005
Profile of Vertical displacement, uz Profile of horizontal displacement, ur
0-0.0001 -0.00005 0 0.00005 0.0001
0-0.000015 -0.00001 -0.000005 0 0.000005
200
400
m)
200
400m)
600
Z(cm
600
Z(cm
h800
h=∞h=5m
800h=∞h=5m
1000 1000
6th ICPT July 20-23 2008 Sapporo Japan No.52
Dynamic BackcalculationD-BALM (FEM)
W BALM( W P )W-BALM( Wave-Pave)
BALM: Static Backcalculation
No.53
BackcalculationBackcalculationBackcalculationBackcalculationO
{ }2
1 ( ) ( )1 ( ) ( )L NtJ d∑ ∑∫ Xl l
Objective Function
{ }1 ( ) ( ) 0
1 1
1 ( ) ( , )2
ti it
iJ u t z t dt
LN = == −∑ ∑∫ Xl l
l
L : Number of tests
()izl ()l
L : Number of tests
N : Number of sensors
( )iu l Measured deflection at sensor i at th test( )l
X Vector of unknown parametersp
( layer modulus and layer damping)
( 0, 1)t t Time interval of deflection matching( 0, 1)t t Time interval of deflection matching
6th ICPT July 20-23 2008 Sapporo Japan No.54
National Institute for Land and Infrastructure National Institute for Land and Infrastructure Management (NILIM) in JapanManagement (NILIM) in Japan
Same Size as Landing Gear of B747-400Max. Running Speed : 5km/hM L d 1200kNMax. Load : 1200kN
6th ICPT July 20-23 2008 Sapporo Japan No.55
Experimental Pavements (Plan)Experimental Pavements (Plan)
6th ICPT July 20-23 2008 Sapporo Japan No.56
Experimental Pavements (Section)Experimental Pavements (Section)
6th ICPT July 20-23 2008 Sapporo Japan No.57
Accelerated Loading TestAccelerated Loading TestTest ConditionTest ConditionRunning Speed : 5km/hLoad : 910kNLoad Repetition : 10,000 times
Measurement ItemDynamic Vertical DisplacementDynamic Soil Pressure
Laser Displacement Metersp
Aircraft Load Simulator
6th ICPT July 20-23 2008 Sapporo Japan No.58
Backcalculated Results E1&C1Backcalculated Results E1&C1Backcalculated Results E1&C1Backcalculated Results E1&C1
8000
10000
12000
MPa
)
Section ASection B
2000
4000
6000
Mod
ulus
(M
0
0 50 100
200
500
1000
2000
3000
5000
(bef
ore)
5000
(afte
r)
7000
1000
0
No. of Load repetitions90 Section A
40
50
60
70
80
ng (M
Pa ・s)
Section ASection B
0
10
20
30
40
0 50 00 00 00 00 00 00 ) ) 00 0
Dam
pin
5 10 20 50 100
200
300
5000
(bef
ore)
5000
(afte
r)
700
1000
No. of Load repetitions
6th ICPT July 20-23 2008 Sapporo Japan No.59
Backcalculated Results E2&C2Backcalculated Results E2&C2Backcalculated Results E2&C2Backcalculated Results E2&C2250 Section A
100
150
200
ulus
(MPa
)
Section B
0
50
100
0 50 100
200
500
000
000
000
re)
er)
000 00
Mod
u
1 2 5 10 20 30
5000
(bef
or
5000
(afte 70 100
No. of load repetitions
1.8 Section A
0.8
1.0
1.2
1.4
1.6
ng (M
Pa ・s)
Section B
0.0
0.2
0.4
0.6
0 50 00 200
500
000
000
000
re)
er)
000 00
Dam
pi
1 2 5 10 20 30
5000
(bef
or
5000
(afte 70 100
No.of load repetitions
No.60
Backcalculated Results E3&C3Backcalculated Results E3&C3Backcalculated Results E3&C3Backcalculated Results E3&C3
50
60
70
80
(MPa
)
Section ASection B
10
20
30
40
Mod
ulus
(
0
0 50 100
200
500
1000
2000
3000
5000
(bef
ore)
5000
(afte
r)
7000
1000
0
No. of load repetitions0.3 Section A
0.2
ing
(MPa ・
s)
Section B
0.0
0.1
0 50 100
200
500
000
000
000
re)
er)
000
000
Dam
pi
2 5 10 20 30
5000
(bef
or
5000
(afte 70 100
No. of load repetitions
6th ICPT July 20-23 2008 Sapporo Japan No.61
Incorporated Administrative Agency Incorporated Administrative Agency Public Works Research InstitutePublic Works Research Institute
Civil Engineering Research Institute for Cold Region Civil Engineering Research Institute for Cold Region (CERI)(CERI)
6th ICPT July 20-23 2008 Sapporo Japan No.62
CERI Field Test SiteCERI Field Test SiteCERI Field Test SiteCERI Field Test SiteWakkanaiWakkanai
6th ICPT July 20-23 2008 Sapporo Japan No.63
City of WakkanaiCity of WakkanaiCity of WakkanaiCity of Wakkanai
6th ICPT July 20-23 2008 Sapporo Japan No.64
Pavement Cross SectionsPavement Cross Sections注意:各工区の舗装厚は、ひずみセンサー設置位置における数値である。
P=1870 実試験施工区間延長 L=436.5m
4工区 5工区 6工区 7工区 交差点 3工区 2工区 1工区L=80.0 L=80.0 L=80.0 L=80.0 L=10.0 L=30.0 L=6.5 L=30.0 L=10.0 L=30.0
TA法による設計 多層弾性理論 TA法による設計 多層弾性理論 多層弾性理論 多層弾性理論(3年設計) 多層弾性理論20年設計 20年設計 20年設計 20年設計 25年設計 TA法による設計4年設計 1年設計信頼性90% 信頼性90% 信頼性90% 信頼性90% 信頼性50% 信頼性50% 信頼性50%
Sec.No.7 Sec.No.3 Sec.No.2Sec.No.4 Sec.No.1Sec.No.5 Sec.No.6
信頼性90% 信頼性90% 信頼性90% 信頼性90% 信頼性50% 信頼性50% 信頼性50%
表層 表層 表層 表層中間層 中間層 中間層 中間層
アスファルト安定処理 基層 基層 基層密粒度アスコン アスファルト安定処理 アスファルト安定処理
アスファルト安定処理 アスファルト安定処理
表層表層密粒度アスコン アスファルト安定処理
表層
路盤(40mm級) 路盤(40mm級) 路盤(40mm級) 路盤(40mm級) 路盤(40mm級) 路盤(40mm級) 路盤(40mm級)
路床 路床 路床 路床路床 路床路床 路床
路床基盤(ベットロック)
As層厚(cm) 16.0 23.0 32.3 32.5 11.1 10.7 10.3路盤厚(cm) 100.0 62.6 52.7 51.5 70.9 77.3 72.7路床路床厚(cm) 275.0 200.0 154.0 140.0 190.0 210.0 210.0ベットロック舗装厚 116.0 85.6 85.0 84.0 82.0 88.0 83.0
測点 P=1870~1950 P=2080~2160 P=2160~2240 P=2240~2320P=2483.5~2493.5 P=2493.5~2523.5
P=2523.5~2530 P=2530~2560
P=2560~2570 P=2570~2600
延長 L=80 L=80 L=80 L=80 L=10 L=30 L=6 5 L=30 L=10 L=30
岩盤(風化泥岩)
延長 L=80 L=80 L=80 L=80 L=10 L=30 L=6.5 L=30 L=10 L=30
※As層厚および路盤厚は、㈱ウオールナットさんの実測値を使用した。 ただし、センサー設置位置は路盤上部が多少下がっていると 予想して、路線調査におけるセンサー設置測点の舗装厚から、センサー位置JustにおけるAs層厚を差し引いたものを路盤厚とした。※路床厚は調査で測定できなかったことから、従来どおり地質断面図から推定した。
6th ICPT July 20-23 2008 Sapporo Japan No.65
FWD TestFWD TestFWD TestFWD Test
National highway 238 (test site)
6th ICPT July 20-23 2008 Sapporo Japan No.66
Truck Loading TestTruck Loading TestTruck Loading TestTruck Loading Test
6th ICPT July 20-23 2008 Sapporo Japan No.67
Position of FWD Loading PlatePosition of FWD Loading Plate
Loading plate
6th ICPT July 20-23 2008 Sapporo Japan No.68
9,000 40
5,000
6,000
7,000
8,000
s (M
Pa) June
AugustNovember
25
30
35
(MPa・
s)
June AugustNovember
1,000
2,000
3,000
4,000
Mod
ulus
5
10
15
20
Dam
ping
0
1,000
P1 P1+30 P1+60 P2 P2+30 P2+600
P1 P1+30 P1+60 P2 P2+30 P2+60
140
160
180
200
a)
JuneAugust November
0.80
1.00
s)
June AugustNovember
60
80
100
120
Mod
ulus
(MPa November
0.40
0.60
Dam
ping
(MPa・ November
0
20
40
P1 P1+30 P1+60 P2 P2+30 P2+600.00
0.20
P1 P1+30 P1+60 P2 P2+30 P2+60
6th ICPT July 20-23 2008 Sapporo Japan No.69
120
140
160
180
200
MPa
)
JuneAugust November
0 60
0.80
1.00
Pa・ s
)
June AugustNovember
40
60
80
100
120
Mod
ulus
(M
0 20
0.40
0.60
Dam
ping
(MP
0
20
40
P1 P1+30 P1+60 P2 P2+30 P2+600.00
0.20
P1 P1+30 P1+60 P2 P2+30 P2+60
1,200
1,400JuneAugust N b
8
9
10June August
600
800
1,000
Mod
ulus
(MPa
) November
4
5
6
7
ampi
ng (M
Pa・
s) November
0
200
400
P1 P1+30 P1+60 P2 P2+30 P2+60
M
0
1
2
3
P1 P1+30 P1+60 P2 P2+30 P2+60
Da
P1 P1+30 P1+60 P2 P2+30 P2+60 P1 P1+30 P1+60 P2 P2+30 P2+60
No.70
0.03
0.04
0.05
ions
(cm
)
D-0(ADINA) D-30(ADINA)
D-60(ADINA) D-90(ADINA)
D-150(ADINA) D-0(FWD)
D-30(FWD) D-60(FWD)
D 90(FWD) D 150(FWD)
Back-Calculation
0
0.01
0.02
Surfa
ce d
efle
cti D-90(FWD) D-150(FWD)
June 2006-0.01
0
0 0.01 0.02 0.03 0.04 0.05 0.06Time(s)
S
250ADINA
June 2006
100
150
200
ε r×1
0-6
Measuring strainstrainMesasured
-50
0
50
0 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 08 0 09 0 1
ε
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Time(s)
0
50
100
250
-200
-150
-100
-50
ε z×1
0-6
ADINAMeasuring strainstrainMesasured
-350
-300
-250
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1Time(s)6th ICPT July 20-23 2008 Sapporo Japan No.71
8月
0 03
0.04
0.05
0.06
ions
(cm
D-0(ADINA) D-30(ADINA)
D-60(ADINA) D-90(ADINA)
D-150(ADINA) D-0(FWD)
D-30(FWD) D-60(FWD)
D 90(FWD) D 150(FWD)
0
0.01
0.02
0.03
Surf
ace
defle
cti D-90(FWD) D-150(FWD)
August 2006-0.02
-0.01
0 0.01 0.02 0.03 0.04 0.05 0.06Time(s)
S
3 0
400
200
250
300
350
ε r×10
-6
ADINAMeasuring strainstrainMesasured
0
50
100
150ε
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Time(s)
050
100
-250
-200-150
-100
-50
ε z×1
0-6
ADINAMeasuring strainstrainMesasured
-400
-350-300
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1Time(s)6th ICPT July 20-23 2008 Sapporo Japan No.72
11月
0.02
0.025
0.03
0.035
ions
(cm
D-0(ADINA) D-30(ADINA)
D-60(ADINA) D-90(ADINA)
D-150(ADINA) D-0(FWD)
D-30(FWD) D-60(FWD)
D 90(FWD) D 150(FWD)November 2006
0
0.005
0.01
0.015
Surf
ace
defle
cti D-90(FWD) D-150(FWD)November 2006
-0.01
-0.005
0 0.01 0.02 0.03 0.04 0.05 0.06Time(s)
S
140
60
80
100
120
×10-6
ADINAMeasuring strainstrainMesasured
-20
0
20
40ε r×
200 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Time(s)
0
50
-100
-50
ε z×1
0-6
ADINAMeasuring strainstrainMesasured
-200
-150
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1Time(s)6th ICPT July 20-23 2008 Sapporo Japan No.73
Questions ?Questions ?GAMES can be downloaded from
htt // t i l b l / i
http://www.jsce.or.jp/committee/pavement/downloads/
http://matsui.labo.googlepages.com/games_win.eng
Thank you !Thank you !Thank you !Thank you !
6th ICPT July 20-23 2008 Sapporo Japan
Pavement ProfilesPavement ProfilesPavement ProfilesPavement Profiles⎞⎛ 20⎟⎠⎞
⎜⎝⎛ −
×= 2020680.0
1 103026)(t
tf
)62.4(04.02 101000,30)( ++
= ttf101+
6th ICPT July 20-23 2008 Sapporo Japan
1. Static Analysis1. Static AnalysisyyGAMES vs BISAR
~ Distribution of shearing stress txz ~ Distribution of shearing stress, txz
τxz (MPa)
0-0.6 -0.4 -0.2 0 0.2 0.4
1020(c
m)
3040ep
th (
GAMES5060
de GAMES
BISAR
No.9
60
6th ICPT July 20-23 2008 Sapporo Japan
1. Static Analysis 1. Static Analysis cm2.332 =b
X
cm0.16=r
X
yycm1.242 =a
b
aY
2cm4.8022 =ALoading area
Y
2cm4.8022 =ALoading area
~ Single tires ~ Rectangular Area vs Circular Area
cm4.8022A
g
150
200
100
×10
-6)
50
Stra
in (
εx (Cylindrical)εy (Cylindrical)
-50
0 εx (Cartesian)εy (Cartesian)
No.16
50-30 -20 -10 0 10 20 30
Y (cm)6th ICPT July 20-23 2008 Sapporo Japan
1. Static Analysis 1. Static Analysis cm2.332 =b
X
cm6.162 =b
X6cm16cm1
yycm1.242 =a
b
aY
2cm4.8022 =ALoading area
cm1.242 =a
b
Y
2cm2401=A
a
2cm2401=ALoading area Loading area
-250
Rectangular Area vs Circular Area~ Distribution of Vertical strain, εz ~
cm2.401=Acm2.401A
-270
-250
Cylindrical(Dual tires)Cylindrical(Single tires)
i ( l i )
-310
-290
(×10
-6) Cartesian(Dual tires)
Cartesian(Single tires)
-350
-330
Stra
in
-390
-370
No.17
-30 -20 -10 0 10 20 30Y (cm)
6th ICPT July 20-23 2008 Sapporo Japan
Back-calculation700 Back calculation
600 D0
Measured Calculated
400
500n
(μm
)
300
400
flect
ion
100
200 D2500
Def
0 10 20 30 40 500
100
Dynamic Back-calculation using FWD Deflection Data
0 10 20 30 40 50Time (msec)
Dynamic Back calculation using FWD Deflection Data
6th ICPT July 20-23 2008 Sapporo Japan