RHEOLOGICAL MODEL AND RHEOMETER OF FRESH CONCRETE

* Zhuguo LI

In this study, the author proposed rheological models to describe the rehological behaviors of fresh concrete before and after yield, based on the

achievements of the author’s past study about the shear stress-shear strain, shear strain rate relationships. Three rheological property indexes (RPI) were

further suggested for fresh concrete, which are yield stress (shear failure limit stress), basic viscosity, and the shear stain rate under the yield stress

(hereafter called briefly thixotropy index), respectively. The basic viscosity and the thixotropy index are experimentally determined on basis of the shear

stress-shear strain rate relation that is measured when the mean particle contact angle of fresh concrete becomes zero. Furthermore, a ring shear

apparatus (named RSNS) was developed to measure the three rheological property indexes and the rheological constants (RCs) in the rheological

models. RSNS can measure the rheological performances of fresh concrete under a desired normal stress by either the stress-controlled test or the strain

rate-controlled test. Test methods for the RPI and the RCs based on the RSNS rheometer were discussed. Finally, an experiment was performed to

investigate the variation of the RPI and the RCs of high fluidity concrete with elapsed time.

Keywords : Fresh concrete, Rheological model, Rheological property index, Rheological constant, Rheometer

Tattersall G. H

1973 Two-point Workability Test 1)

(Coaxial Cylinder Rheometer, BML2))

(Parallel Plate Rheometer, BTRHEOM3))

(Impellers Rheometer, IBB4), Two-Point rheometer5))

(Vane-In-Cup Rheometer, ICAR rheometer6))7), 8)

9), 10), 11)

BTRHEOM ICAR

8), 12), 13)

( ) 14)

Tattersall Two-point

40

Associate Prof., Dept. of Information and Design Eng., Graduate School of Scienceand Eng., Yamaguchi University, Dr. Eng.

BASIC STUDY ON ESTIMATING STRENGTH OF CONCRETE BY UCI METHOD

Yohei INABA*, Toshikatsu ICHINOSE** and Tetsushi KANDA***

* Senior Research Engineer, Kajima Technical Research Institute of Technology, M. Eng. ** Prof., Nagoya Institute of Technology, D. Eng.

*** General Manager, Kajima Technical Research Institute, Ph. D

Concrete is the most important material to construct structures. One of the most important properties of concrete

is a compressive strength which is needed to control over the specified design standard strength after hardening. The compressive strength test is very important but generally tested objects are test pieces which molded cylinder, not structural concrete itself. The compressive strength of concrete is influenced by curing, the strength of test piece is different from that of structural concrete. The strength test is desirable to be tested in-situ.

One of the most popular strength tests for structural concrete is compressive strength test with boring core sampling. But this test is destructive, so the structure is damaged. Then desirable test is non-destructive. But the existing non-destructive tests have some problems about accuracy, strength range, etc.

It is necessary to investigate new strength test which has following 4 properties. 1) micro destructive, 2) testing in-situ, 3) easiness of calibrating, 4) capability of measuring the local area. The UCI (Ultrasonic Contact Impedance) method has these 4 properties, so basic study about UCI applying to concrete has developed.

UCI method has developed for metal materials in 1960’s to measure Vickers hardness automatically by electric device. UCI method is micro destructive, more accurate and applicable for high strength concrete with portable electric device. But UCI method has not be applied to concrete for many years, because of changing Young’s modulus with time. The UCI method needs Young’s modulus for estimating Vickers hardness, so Young’s modulus needs to be measured at the same time. But there is no method to measure Young’s modulus at the same time.

Improving the UCI method to estimate Young’s modulus and compressive strength is investigated and verified. The conclusions are below.

1. Because the young’s modulus of concrete is changing with age, it is necessary to measure the Young’s modulus of concrete at that age in order to estimate the strength of concrete by UCI method.

2. It is possible to estimate the young’s modulus by UCI method, using steel plate of 0.2mm thickness between material and Vickers diamond.

3. There is a high correlation between measured hardness and strength of concrete. 4. This modified UCI method has some possibility of being the micro-destructive in-situ testing for strength and

Young’s modulus of concrete.

【カテゴリーⅢ】�  日本建築学会構造系論文集 第80巻 第710号，527-537， 2015年4月J. Struct. Constr. Eng., AIJ, Vol. 80 No. 710, 527-537, Apr., 2015

フレッシュコンクリートのレオロジーモデルおよび試験方法に関する研究RHEOLOGICAL MODEL AND RHEOMETER OF FRESH CONCRETE

李 柱 国＊

Zhuguo LI

＊  山口大学大学院理工学研究科情報・デザイン工学系専攻 准教授・博士（工学）

Associate Prof., Dept. of Information and Design Eng., Graduate School of Science and Eng., Yamaguchi University, Dr. Eng.

─ 526 ─ ─ 527 ─

1 15)

16)

17

16)

( )

(2-1)16)

)fff

wn

t, t,

qtqtCcc

c

≤≤≤

−−⋅=−−⋅+

⋅+

⋅= ∞

(

)]exp(1[)]exp(1[1

232

6 γστ

τγ (2-1)

02 θφ +=cf

f3c

τθθ 0−

= 0Nc21

6 =

2

6

3228 ))((

ccc

Ccq wnτσ +

+= Cw2 =Nfwm cosθ,

232

6 1

wn Cccc

+⋅

+⋅

=∞ σττγ

(2-1)

γ

t γ

(s1)

γ (2-2)16)

)/exp()3(

)]exp(1[)(

)/(

1

327

12

32

2162sqccc

sq

ccCscc wn

ττττ

τσγ +

+−−+

+= (2-2)

τ (2-2) 1

2

γ τ

16)

( )

18)

(θ) θ (θf)

θ

(Λb)

(2-3) 1

θ16)

(Λa) (2-3) 2

f0ffa

0b

θθθ

cos/,sin/cos/

===

(2-3)

Time

Shea

r stra

in

Incremental stresses applied(

Yield stress exceeded

Shea

r stre

ssTime

Static yield stress( )

Dynamic yield stress( )

(a) (b) Time

Shea

r stra

in

Incremental stresses applied(

Yield stress exceeded

Shea

r stre

ssTime

Static yield stress( )

Dynamic yield stress( )

(a) (b)

─ 528 ─ ─ 529 ─

(2-3) 2

(2-4) 16)

γγκττ )](exp[*ff ttC −−⋅+= (2-4)

1)(* tan w

ttfnf Ce f ++= −⋅⋅− φθστ γκ

ccf

fN

kTENhC

)/exp(θ= , ]sin)tan([cos1 θφθθ −+= wmw NfC

(2-4) τ*fCw1

θ

θ Cw1θ θf

τ*f(2-4) 2 γ

C exp[-κγ(t-tf)] ( γ

(t-tf))

C

exp[-κγ(t-tf)]

(2-3) 2

Λa

θf(2-3) Λa (2-5)

fa θcos/0= (2-5)

(2-5) 16

(2-6)

) , ,(

]cos[tan

*

)(1)(

fffaf

ttf

wtt

fn

tt

eCe

f

f

>>>+=

+++= −−−⋅⋅−

γγγητ

γθ

ηφθστ γκγκ

(2-6)

η

cc

f

NkTENh

0

)/exp(cosθη = , ]cos[/ )( ftt

fa e −−= γκθηη

(2-6)

γ

ηa ( γ (t-tf))

η

(γa) (2-7)

(2-8)

2

22

222 2

)(21))((

21

ssstttts ffa

γγγ ==−−= (2-7)

γθ

ηφθστγκ

γκ

]cos[]tan[

22

22

2/12/

sf

ws

fne

Ce⋅−

⋅− +++= (2-8)

(2-9) 16)

1)tan( wfnf C++= φθστ (2-9)

(2-1) (2-2) (2-6)

2

19)

2(a) γ

τ

γf

2(b)

γ τ (Up-curve) τ γ

γ

τ (Down-curve)

θ γ t-tf))

θ =θf -κγ t-tf) θ

(2-6) (2-10) τ γ

γηττ φ += , 1tan wn C+= φστφ (2-10)

τφ

η η

τφ

τf (2-9)

Up-curve Down-curve

Up-curve Down-curve

(hysteresis loop)

( ) (2-6) (2-8)

(t) (s2) (σn)

─ 528 ─ ─ 529 ─

θ

θ γt

γt Down-curve τfγt

θ=θfθ γt

(2-6) γt (2-11)

ηφφθσ

ηττ

γ φ ]tan)[tan()( −+=

−= fnf

t (2-11)

τfη γt

3

τf η

γt

τf

τf γt σn

2.55kPa σn

( 2350kg/ m3)

15cm

τf γt (2-9) (2-11)

(2-9) Cw1 σn

τf (2-9)

2 Cw1 1 σn

c2 c6, c3 c6, c8, Cw1, η φ θf κ

BTRHEOM

Hu 20) BTRHEOM (rheometer)

3

(blade)

2

8 29cm( 75cm)20), 21) 8cm

BTRHEOM

BTRHEOM

γγf

τ

τf

γγf

τ

τf

τ

τf

η

γ

τφ

: Up-

curv

e

: Dow

n-curv

e

1tan wn C+= φστφ 1)tan( wfnf C++= θφστ

γt

τ

τf

η

γγ

τφ

: Up-

curv

e

: Dow

n-curv

e

1tan wn C+= φστφ 1)tan( wfnf C++= θφστ

γtγt

─ 530 ─ ─ 531 ─

Hu

BTRHEOM 2

( CEMAGREF-IMG

LAFARGE)

BTRHEOM

10 BTRHEOM

CEMAGREF-IMG LAFARGE20) BTRHEOM

0.2 rev/s

Ring shear test

ASTM

ASTM D7608-10 ASTM D6467 - 13 BTRHEOM

BTRHEOM

4

RSNS(Ring Shear under Normal Stress)

4 RSNS (blade)

30mm 3mm

30mm

250mm

30mm

340mm

3mm

28mm

2cm

2

(a) RSNS 3

156mm 30m

m

28mm

250mm

156mm 30m

m

28mm

250mm

(b) RSNS

RSNS

─ 530 ─ ─ 531 ─

BTRHEOM

RSNS

(156mm) BTRHEOM (100mm)

(

)

4

5

r

γ γ (3-1)

hr

180ϕπγ = ,

hr

180πγ = (3-1)

γm γm(3-2)

hRR

m 360)( 21 ϕπγ += ,

hRR

m 360)( 21 += πγ (3-2)

(Γ) (3-3)

τm (3-4)

=2

1

22R

Rdrr τπ (3-3)

)(23

31

32 RRm

m−

=π

τ (3-4)

(progressive failure) 23

23), 24), 25)

(

)

23)

24)

23)

(shear band)23) 6

26)

24)

R1/R2 0.5

RSNS

RSNS

(3-5)

h

( :

: )

)180/( hrϕπγ = R1

R2

)(γτ f=

)(γτ f=r

γγγγm

mτ

γγγγ

γγγγ

τ

τ

mτ

h

( :

: )

)180/( hrϕπγ = R1

R2

)(γτ f=

)(γτ f=r

γγγγm

mτ

γγγγ

γγγγ

τ

τ

mτ

─ 532 ─ ─ 533 ─

ρσ )21(8.9 hhtn +⋅= (3-5)

(3-6)

(3-7)

)(/)(2

)2

(8.9 21

22

2

RRRPAmhh umca

tn−

−−+++⋅=

πρσ (3-6)

)(2

)2

(8.9 21

22 RR

PAmhh catn

−+

++⋅=π

ρσ (3-7)

(2-1) (3-8)

6

322)/(c

ccCwn τγ

στ +=

+ (3-8)

Cw2 σn

Cw2 (3-8) (3-9)

τ σ γ τ

c2/c6 c3/c6

τγστ

6

3

6

2/cc

ccn += (3-9)

Cw2 (2-1)

(3-10) (x<1 ln(1+x) x)

qt−=−∞

)lnln(γγ (3-10)

(3-10) q

c8

c2/c6, c3/c6 c8 (2-1)

( )

(1.0~3.0N m)

(0.5~1.5deg./s)

(

5deg./s

(3-2) (3-4)

τm γm γm

τm γm τm γm τf

γf (τm/σn)/γm τ ( )

(3-9) c3/c6

(τm/σn)/γm c2/c6

ln(-ln(γm/γm ) t

( ) (3-10) q

τ σn c2/c6 c3/c6 c8

(2-6) (2-9) (3-11)

γθ

ηφθφθσττ γκγκ

]cos[)tan(tan )(

)(

f

ftt

ff

ttfnf

ee −−

−⋅⋅− ++−+=−

(3-11)

x tanx x

(3-11) 2

(3-11)

(3-12)

)1( )( fttfnf e −⋅⋅−−=− γκθσττ (3-12)

x <1 ln(1+x) x (3-12)

(3-13)

)()lnln( ffn

f tt −⋅⋅−=−

− γκθσ

ττ (3-13)

(3-13) ln{-ln[ τf -τ σnθf]} (t-tf)

κ

γ(t-tf)

(2-6) (3-14) τ σn

φ

)(tan 1 γηφστ ++= wn C (3-14)

5deg./s

4

1(5deg./s)

2

─ 532 ─ ─ 533 ─

2

(5deg./s)

45deg./s 3

3

4

(5deg./s)

4 0MPa, 0.3MPa, 0.5MPa,

0.7MPa

(2-6)

1) τm γm 2(b)

Down-curve η

2) τ m σn ( )

φ Cw1

ηγ

3) τ f σn φ, Cw1 (2-9)

θf

4) (3-13) ln{-ln[ τf

-τ σnθf]} γ(t-tf) ( ) κ

100mm 1

AE

60 120

1

RSNS 3

7

τm γm

7

τm γm 2

τf

γf τm γm 8

τf γm

τf γf 9

τf γf

(τ/σn)/γ t (

)

c2/c6 c3/c6 9

γ

γ/γ ( γ, γ

)

q c8 ( 9 )

9

c2/c6 c3/c6 c8

τm

γm 2 ( 60 )

10

27)

(kg/m3) W/C s/a

(%) W C S ( )

G ( )

SP(C×%) (kg/m3)

0.38 44.6 165 434 748 980 1.5** 0min.: Sf. = 70 60min.: Sf. = 45, Sl. = 22 120min.: Sf. = 30, Sl. = 16 2330 W/C W C S G s/a Sl (cm) Sf. (cm) SP

AE

0.35

0.45

0.55

0.65

0.50 0.60 0.70 0.80(kPa)

0.00

0.02

0.04

0.06

0.50 0.60 0.70 0.80(kPa)

(1/s

)

γγγγm ττττm γγγγm ττττm

─ 534 ─ ─ 535 ─

Down-curve

( )

γt ( 11 )

φ Cw1

( 11 )

ln{-ln[ τf -τ σnθf]} γ(t-tf) ( )

κ ( 11 )

11

φ, θf γt η Cw1

κ η

(2-1) (2-6)

γt

τf, φ, θf, γt, c2/c6, c3/c6 γf c8

η, Cw1

κ η, Cw1

τ (Pa)

τ m

τf , Pa

τφ

γ

1.37

0.66

1.25

0.480.41 0.40

0.07 0.090.02

0.34

0.500.59

0.33

0.780.70

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0min. 60min. 120min.

(kPa)

c8c3/c6c2/c6

0.00

0.20

0.40

0.60

0.80

1.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00kPa)

1/

γγγγm ττττm

0.56 0.480.47 0.190.210.00

12.11

6.28

8.28

10.90

8.30

12.75

1.89 1.89

0.76

3.323.94

0.020.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

0min. 60min. 120min.

(kPa s)Cw1

k

─ 534 ─ ─ 535 ─

γm

γf

t

tf

γ

γm

γ

σn

G

ηb (s-1)

ηa (s-1)

fwm

θ0

θf

φ

Λb

Λa

Λ0

Λf

Λc

k (1.3808 10-16erg/deg.)

B (6.626 10-27erg s)

s1 (N/s)

s2 ( ) (s-2)

κ

Cw1

Cw2

η

ηa

h (m)

ht (m)

R1 (m)

R2 (m)

Γ

Γu (N m)

r (m)

Ω deg./s

ϕ (deg)

ρ (kg/m3)

ma (N)

P (MPa)

Ac (mm2)

Γm (N m)

1) Tattersall G. H. The rational of a Two-Point workability test, Magazine of Concrete Research, Vol.25, No.84, pp.169-172, 1973

2) Wallevik O.H., and Gjorv, O.E. Development of a Coaxial Cylinder Viscometer for Fresh Concrete, Proc. of the RILEM Colloquium, Hanover, pp. 213-224, 1990.10

3) de Larrard F., and Hu C., et al A new rheometer for soft-to-fluid fresh concrete, ACI Materials Journal, Vol.94, No.3, pp.234-243, 1997

4) Beaupre D., and Mindness S. Rheology of fresh shotcrete, Proc. of Special Concretes: Workability and Mixing (Scotland), pp. 225-235, 1994

5) Tattersall G.H., and Bloomer S.J. Further development of the Two-Point test for workability and extension of its range, Magazine of Concrete Research, No. 31, pp. 202-210, 1979

6) Koehler E.P., and Fowler D.W. Development of a portable rheometer for fresh portland cement concrete, Report of International Center for Aggregates Research, The University of Texas at Austin (No.: ICAR105-3F), pp.57-176, 2004

7) Ukraincik V. Study on fresh concrete flow curves, Cement and Concrete Research, Vol.10, pp. 203-212, 1980.3

8) , , No.421, pp.1-10, 1991.3

9) , , Vol.30, pp.270-273, 1976

10) ,

, No.462, pp.1-10, 1994.8 11)

, , No.578/V-37, pp.19-29, 1997.11 12) F. de Larrrd, C. F. Ferraris, and T. Sedran Fresh concrete : a Herschel-Bukley

material, Material and Structure, Vol.31, No.211, pp.494- 498, 1998 13) Nicolas Roussel A thixotropy model for fresh fluid concretes: Theory, validation

and applications, Cement and Concrete Research, Vol.36, pp.1797-1806, 2006 14) ,

, No.501, pp.11-20, 1988.11 15) Koehler E.P., and Fowler D.W. Development of a portable rheometer for fresh

portland cement concrete, Report of International Center for Aggregates Research, The University of Texas at Austin (No.: ICAR105-3F), pp.57-176, 2004

16) , , Vol.77, No.679, pp.982-001, 2013.5

17) , , Vol.33, No.2,

pp.124-130, 2011.7 18) , , pp.27-375, 1990 19)

, , Vol.75, No.653, pp.1173-1180, 2010.7 20) C. Hu, and F. D. Larrard, et al Validation of BTRHEOM, the new rheometer

for solid-to-fluid concrete, Materials and Structure, Vol.29, pp.620-631, 1996. 21) Hu, C. Rhdologie des b&ons fluides' (Rheology of fluid concretes), Ph. D.

thesis of ENPC, l~tudes et P, echerches des LPC, S&ie ouvrages d'art, 1995 22) Coussot, P. R.hdologie des boues et laves torrentielles-]~tudes de dispersions et

suspensions concentr&s, Th~se de doctorat de l'Institut National Polytechnique de Grenoble, et l~tudes du CEMAGREF, S&ie Montagne, No. 5, p. 418, 1993

23) Abouzar Sadrekarimi, and Scott M. Olson A new ring shear device to measure the large displacement shearing behavior of sands, Geotechnical Testing Journal, Vol. 32, No.3, pp.1-12, 2011.9

24) Stark T. D., and Contreras I. A. Constant volume ring shear apparatus, Geotechnical Testing Journal, Vol.19, No.1, pp.3-11, 1996

25) Neal R. Iverson, Robert W. Baker, and Thomas S. Hooyer A ring-shear device for the study of till deformation: tests on tills with contrasting clay contents, Quaternary Science Reviews, Vol.16, pp.1057-1066, 1997

26) Osano S. N. Direct shear box and ring shear test comparison:why does internal angle of friction vary, ICASTOR Journal of Engineering. Vol. 5, No. 2, pp.77-93, 2009

27) ,

, p.94, 2001.

─ 536 ─ ─ 537 ─

RHEOLOGICAL MODEL AND RHEOMETER OF FRESH CONCRETE

Zhuguo LI*

* Associate Prof., Dept. of Information and Design Eng., Graduate School of Science & Eng.,

Yamaguchi University, Dr. Eng.

For improving the efficiency of concrete construction and ensuring the construction quality of concrete component with individual geometry and reinforcing bar arrangement, optimization of the workability of fresh concrete is necessary and possible, according to component’s structural formation and construction method. The study on the rheological model that can express the complex rheological behaviors of various fresh concrete, including non-linearity, dilatancy, vertical pressure-dependence, and loading time-dependence, etc., is very important and urgent for realizing the workability design based on numerical flow simulation.

The quantitatively experimental investigation on the rheological properties of fresh concrete is very difficult because present rheometers are originally designed for only measuring yield value and plastic viscosity. For this reason, the author developed a microscopic approach in the past study16), in which fresh concrete is considered as a viscous particle assembly containing water, the mean particle contact angle θ is introduced to express the particles’ interlocking degree that increases in the viscous elastic-plastic state but decreases in the failure state, and the micro strain of fresh concrete arises from the movement of the sliding particles occurring in probability. Using this microscopic approach, the author has further investigated quantitatively the relationships between shear stress (τ ) and shear strain (γ), shear strain rate γ before and after yield, respectively16), 19).

In this study, the author further modeled the rheological properties of fresh concrete based on the achievements of the past studies mentioned just above. The shear deformation model before yield is shown in Eq.(2-1). With increasing the τ and loading time (t), the γincreases, but the greater the normal stress (σ ), the smaller the γ The diagram of the shear deformation model is shown in Fig.2 (a). After yield, because the shear deformation speeds up, viscous resistance is yielded and thus results in a continuous increase of shear stress. Eq. (2-2) shows the γ -τ relationship before yield. With increasing the τ till to the yield stress (τf) the γ firstly increases before suspension limit, then decreases and approaches to zero at the time point of rupture, as shown in Fig.2 (b). The τf is shown in Eq. (2-9) that indicates that it depends on the σn and mean particle contact angle (θf) at the time point of yield, besides mean inter-particle frictional angle (φ) The shear resistance model after yield was proposed as shown in Eq. (2-6) that consists of the particle-characteristic resistance portion (the first and the second term in the right side of the equation) resulting from the particle fabric, and the viscous resistance portion (the third term). The first term and the apparent viscosity (ηa) decease with the increase in shear deformation after yield, thus the increase of the γ with the τ speeds up, as shown in Fig.2 (b). Based on the proposed rheological models, three rheological property indexes (RPI) were suggested for fresh concrete’s evaluation and quality control, which are τf basic viscosity (η) and thixotropy index (γt) respectively. The η and γt are the viscosity and shear strain rate under a shear stress equal to the τf when the θ is near to zero

For measuring the RPI and the rheological constants (RCs) in Eq. (2-1) and Eq. (2-6), a ring shear apparatus was developed, named RSNS rheometer, as shown in Fig.4, which is able to increase shear stress by torque-controlled method or by rotation speed-controlled method. The σ is changed by two air cylinders driven by a compressor. The upper blade can’ t rotate, but the lower blade is driven by an electric motor. The central standstill axis of RSNS is a rod-shaped vibrator that is also used for compacting fresh concrete sample. Mean shear strain, mean strain rate, mean shear stress, and the σ are calculated by Eq. (3-2). Eq.(3-4), and Eq. (3-7), respectively.

Then, the test methods of the RPI and RCs were discussed in case of using the RSNS rheometer. Before yield, q and c8 are measured by keeping the torque unchanged, according to Eq. (3-10) and Eq. (2-1). And the τ-γ relationship curve is gotten by increasing the torque at a very small rate for determining the τf as well as c2/c6 and c3/c6 according to Eq.(3-9). After yield, based on the down-curve (straight line) of the flow curve measured by reducing the rotation speed of the lower blade, Eq. (2-10) is obtained, the η and γt are thus determined. When calculating the γt the shear stress used is equal to the τf And using the result of the τ σn relationship, which is measured at a very small shear rate under different pressures of air cylinders, the φ and Cw1 are determined according to the Eq. (3-14). Furthermore, the θf is calculated by substituting the values of τf σn, φ, and Cw1 into Eq. (2-9). Finally, based on the measuring results of shear stress on the condition that the γ is very small constant, the rheological constant κ is determined, using the relationship shown in Eq. (3-13).

Using the above test methods, variation of the RPI and RCs of high fluidity concrete with elapsed time were investigated. The experimental results of the RPI and RCs are shown in Fig. 9 and Fig.11.

（2014 年 7 月 7 日原稿受理，2014 年 12 月 22 日採用決定）

RHEOLOGICAL MODEL AND RHEOMETER OF FRESH CONCRETE

Zhuguo LI＊

＊ Associate Prof., Dept. of Information and Design Eng., Graduate School of Science and Eng., Yamaguchi University, Dr. Eng.

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