Analysis and Backcalculation for Pavement …Analysis and Backcalculation for Pavement Structures Kunihito MatsuiKunihito Matsui Tokyo Denki University 6th ICPT July 20-23 2008 Sapporo

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


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


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



~ 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



~ 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


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


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)


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)


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


GAMES for Windowst t i d~ start-up window ~


GAMES for Windowsi t i d~ input window ~




GAMES for Windowst t i d~ output window ~






GAMES for Windowst t i d~ output window ~


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


Contact pressure measured by SIM (provided by Prof. Morris De Beer)






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+= − − =


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


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


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


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


Z

MPa603 =E40.03 =ν


No.29

ZZ


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)


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)


Dynamic Analysis ofDynamic Analysis of Pavement Structure

No.33

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

∂ ∂ ∂


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= =


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


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)


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


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


Damping

Density

sMPa6.03 ⋅=F

3h

MPa100004 =E40.04 =ν

Yong's modulus


Damping

Density

sMPa1004 ⋅=F

No.41

Z


・・ 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



( 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

( )


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



( 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


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



( 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


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



( 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


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



( 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


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



( t=0.07s )( )

0 002 0 001 0 0 001 0 002 0 003 0 0002 0 0001 0 0 0001 0 0002


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



( 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


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



( 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


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



( 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


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



( t=0.20s )( )

0 0001 0 00005 0 0 00005 0 0001 0 000015 0 00001 0 000005 0 0 000005


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


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


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


Experimental Pavements (Plan)Experimental Pavements (Plan)


Experimental Pavements (Section)Experimental Pavements (Section)


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


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


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


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)


CERI Field Test SiteCERI Field Test SiteCERI Field Test SiteCERI Field Test SiteWakkanaiWakkanai


City of WakkanaiCity of WakkanaiCity of WakkanaiCity of Wakkanai


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。


FWD TestFWD TestFWD TestFWD Test

National highway 238 (test site)


Truck Loading TestTruck Loading TestTruck Loading TestTruck Loading Test


Position of FWD Loading PlatePosition of FWD Loading Plate

Loading plate


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


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-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-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


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


-400

-350-300


11月

0.02

0.025

0.03

0.035

ions

(cm




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


-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


-200

-150


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 !


Pavement ProfilesPavement ProfilesPavement ProfilesPavement Profiles⎞⎛ 20⎟⎠⎞

⎜⎝⎛ −

×= 2020680.0

1 103026)(t

tf

)62.4(04.02 101000,30)( ++

= ttf101+



~ 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



X

cm0.16=r

X

yycm1.242 =a

b

aY

2cm4.8022 =ALoading area

Y


~ 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


X

cm6.162 =b

X6cm16cm1

yycm1.242 =a

b

aY


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)


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


Documents

Analysis and Backcalculation for Pavement …Analysis and Backcalculation for Pavement Structures Kunihito MatsuiKunihito Matsui Tokyo Denki University 6th ICPT July 20-23 2008 Sapporo