        Vs !"#$%&'

()*!"+,+-./012 Vs
3  4567849:8;)<=>?@1)

ABCD9:EFGBHI8JKLMN
OPQ+-()*CR

100
Percentage finer by weight (%)

1. S)(;)lmno()*pqr
sft`G()n)

Kariwa sand3
ρs = 2.72g/cm
emax = 1.007
emi n= 0.610

Toyoura sand3
ρ s = 2.65g/cm
emax= 0.990
emin= 0.597

60
40
200TUVWXYZ2B3[\]!^_`abcdbefghAiCDj80

1E-30.01

0.1
Grain size, D (mm)kF110Fig. 1 3CWXY

uvG(]GB!

^wxGC./012WXYZ29:
100

Mixture Intermediate soil

oB*nSC
C

2. pqr

3C}3A+

&GBoB*
 K0 XzGB6

./012 Vs zfBCb?>bCBE ) z!"
BE !"CWXYZ2 RL BC¡¢£G¤¥!"oB*pqr§¨RC©ª«¯°±²³3C¦

Percentage finer by weight (%)

CTUVWXYZ2yz{|C}"~ρ s = 2.715g/cm

803Fc = 31.2%S c = 68.8%
G c = 0.0%60

Hirokawa soil3
ρ s = 2.734g/cm
F c = 38.1%
S c = 37.8%
G c = 24.1%

40
2001E-30.01

0.1
1Grain size, D (mm)Fig. 2

10¬S)(WXY­®AoB´µiwxGBRC¯°R)¶FGB*·BC-+R!^¸¹f
BCº»¼/½6G(¾¿ÀR HA ÁÂdbÃ6ÄÅ¸ 7:3ÆÇGBÈCÆ^3 Table. 2 Ôf*(1) !"F)BÚ!ÛÚ!ÛÜÝÞ;ß 60mmC

àÏ 100mm3Mbáâã100äÇ©É6)CÊ¼/½6G(ËÌ6120mm ©¼¡¸ 5%å2jæGBçCèÍÎ!^G(F)B*-+»ÏÐÑÒÓéF)Bê~ëtÝ5 ìètµo(CR!^3 Fig. 1 CÍÎ!^3 Fig. 2 Ôf*ízÉî¸nµïáGB*3.  3.1 BE pqr

3CRÕ6./012 Vs B

 BE !"oB*!"ÖhC·B×ØoB!"Ù?)(R!^3 Table. 1CÍÎ!

(2) !"3Ú!ÛïáçCðñóô(Ú!Û-100kPa òõö÷øùø1.5 úÉGBçCÚ!Ûû+¡üýþFG(¡Y
*¡çCàð¡)CàU)B+CP3 Ø

Yß.CBE PfzGB*nSC!"

ß.(Ú!ÛTable. 1  BE DrOCR / σv’K0

OCR=1.0σv’=0154
OCR=1.5σv’=0231154
OCR=2.0σv’=0308154
OCR  Dr=40%
OCR  Dr=40%
OCR 
OCR 3P

ftr=20kHz  sin  1 F)( Vs z

e

40

0.833

0.473

60
75
44
70

0.754
0.695
0.832
0.729

0.440
0.404

oB*Vs 3(1)µG()*     Vs =L                (1)tLÞb?É(mm)CtÞúÉ(msec)

A*./0úÉzÝ3 T.D.ÝwFG(SiCb?É L 3 BE ûÉ ”tip-to-tip” Ý C . / 0    ú É  tTable. 2 BE 

Gc /Gmaxe

0.0 / 2.0

0.978

17.5 /
9.5

0.808- / 0.850.603

0.406

OCR / σv’

K03”start-to-start”ÝwFG(æG()* Table. 1 Sµ Table. 2 S)( σv’43CK0 !"µo(,+-B K0 4µiC¤¥!"S)( p’=100kPa!àð"#f!"Ù?

G($zGB*3.2  !

 pqr

3CRÕ6WXYZ2 RL B¡¢£G¤¥!"oB*!"Ö

hC·B×ØoB!"Ù?)(R!^3(1) R!^Ú!Û3C%&¼¡¸ w=5%jæGBçCët

Table. 410 ìèt*Ýµo(ízÉî¸nOCR Dre

OCR406075
440.833
0.754
0.695
0.832

1.0 2.0
1.0
1.0
1.0 2.0
Gc / GmaxeOCR



0.0 / 2.0
17.5 / 9.5

0.978
0.808

1.0 1.52.0
1.0 1.52.0

 


- / 0.85

0.603

1.0 2.0

 ·BCÍÎ!^Ú!Û3C+Ç5»2jæGB
-.GCíz

0.450



µïáGB*!^ φ5×12.5cm ,á'?()OCR  Gc =0.0%

Table. 3 Table. 3CÍÎ!^3 Table. 4 Ôf*òÝF)( φ5×12.5cm '?()

0.485



OCR=1.0σv’=0152
OCR=1.5σv’=0228152
OCR=2.0σv’=0305152Éî¸nµèt10 ìèt/0ëtÝ

ïáGB*

Gc=17.5%Ù?

CËÌ6(2) 3CÊÆ.fµ>b1b23?L4b56

 2)¡¢£G¤¥!"3CEÄòÈÚ

7ß.&!ÛF+ùø¡¡GC?GHI¦ð

~

Cφ4.8×12.5cm 89GBÚ!ÛuG(CÐ¡GB 425µm !^ 1mm :G(d>?

p’=50kPa X

J 200kPa K 1.5 úÉ"#f;<IÛ~=?@Af*Ý*ÝïáGB*nSC¡CåBBÚ!Û3>b1bC.fn<@+nXDo()

Ú!ÛYLQß.CÉî:B>0.96 GBçCízðM*)CNOÈ¥12 0.1%/minC%&?G¦ð p’=100kPaG()*oB*nSCå¢£G./0f*Ý
3 3t ÝPQiúÉRzfGB*IÙ?S()()G()*·BC¢£3¥ DA=5%GBTUW

G"#åXYGBÈnG!"VfGB*
ß+C¸ OCR  1 !")(3Cízð)oBçC¡ÅzXXGBTU¡W#

Shear wave velocity, Vs (m/sec)

300

¡ÅI

4.1 Vs - σv’20015050100150200250300

X§¨RF)B BE !" Vs  σv’9Fig. 3 BE 

B Vs 3 σv’300

AiCbc3 Dr µ+MG)]oB*·BC

Fig. 4 3 Fig. 3 d¥Éî¸ e Veô(cfgGBÈA*ZµiCÉî¸¾ß<n_h Vs Ó9~i<no(SiCÉî¸5Éî¸i¾möf

Toyoura sandD ri =40%
D ri =60%
D ri =75%

250

200

1500.650

!"`o+È Vs 3àðSµÉî¸Fig. 4 BE XYZ2 RL 3C¥*c DA=5%S¢£zqG()*ZµiCVs i<n_h RL Èi<nbc3rôÈCyclic stress ratio to cause DA=5.0%in 20 cycllic loadings, RN=2 0 ( σ d/2 σc')RL 9: Fig. 5 Ôf*nSCpqrS)(WC!^st5 OCR u)µv+i!"# Vs $ e %&Toyoura sand
OCR = 1.0
OCR = 2.0
Kariwa sand
OCR = 1.0
OCR = 2.0
Hirokawa soil
OCR = 1.0
OCR = 1.5
OCR = 2.0
Mixture Intermediate soil
OCR = 1.0
OCR = 2.0

0.3

0.2

0.10.0<CVs +aq~ RL yzG(G·Cni050

100150
Shear wave velocity, Vs (m/sec)

200250Fig. 5 '( Vs $ RL %&w2x)yn* OCR=1.0 R!^

0.850

0.4

oB BE !"Sµ¢£G¤¥!

c=20 Ø0.800

B*"`oµiBC./012 Vs WXYZ2G"#Ø

0.750
Void ratio, e4.2 )*+,-. Vs /0123. RL 4$%
 p’=100kPa

0.700

n]-()Ci¾p+ß-()

45098Z)Ôß-B*aj~ Vs 3C6kl3)

Shear wave velocity, Vs (m/sec)

 Vs ^Å3_`az

400!"# Vs $ σv’%&[Ðf\)[ÐG()]*àð σv’350

Vertical stress, σ v' (kPa)Vs - e $%&'(: Fig. 3 Ôf*Zµi BE !"Toyoura sand(D ri=40%)(D ri=60%)(D ri=75%)¢£G./0YfGB*4. "#250

oB BE !"µi,+-B

Vs  e 9: Fig. 6 C¢£G¤¥!"µi,+-BWXYZ2ÒÓ Fig. 7 Ôf*Fig. 1 ÔfµR!^»Ï3z()CVs - e 9:§¨RC¯°R

3AuGCWXYZ

2ÒÓ3D9:{|G()*µo(CR!^)Sst6+ 5Ao(ÈbcI<u}~fÝµC!^abc

dbeíz!"}g
*AÎô+-0.35

Case OCR = 1.0
Toyoura sandKariwa sand

200

150
0.650

0.7000.750

0.800

Case OCR = 1.0
Toyoura sand (D r = 40%)
Kariwa sand (D r= 44%)

0.30
Cyclic stress ratio, σ d / 2σc 'Shear wave velocity, Vs (m/sec)

250

0.850

0.25

0.20

0.15

0.10

Void ratio, eFig. 6  Vs - e %&)*

0.05

c=20

1Fig. 7 +,-./

4.3 56789: Vs ; RL <=>?@

4.2 `oµiCVs +aq~ RL yzfC

3CTUVµi]GB!^wxG(C!"µi,+-B Vs S4nÉî¸Úy(ïáG(WXY!"w2;Îô*GGn+CTUV Vs ½
H3Cðyzf3[{|250A*

3C

Aµo(C!^ Vs 5 RL 150
0.650

0.700

0.750

0.800

0.850

Void ratio, eFig. 8 012345678 Vs $ e %&8)(f*§¨R BE !"`oµi,+-B Vs Éî¸ e0.4

È OCRàÓ=)GCSÉî¸nuoB Vs +-oB*

Iwasaki & Tatsuoka4)3º»¼·n)»ÏoBRÝ!"

B./0 γ=10-6

./08 G0 (2)µÔG()*   G0 = 900F (e)σ v ' 0.2 σ h ' 0.2         (2)CG0Þ./08(kgf/cm2)Cσv’ÞHI¥*cð(kgf/cm )Cσh’ÞHI*cð(kgf/cm )CF(e)Þ
2Éî¸9Cyclic stress ratio to cause DA=5.0%
in 20 cycllic loadings, RN=2 0 ( σ d/2 σc ')9: Fig. 8 Ôf*ZµiCOCR [Ðf)*200hµ56`fjC}~fyÝ1000

Toyoura sand (σ v' ᄎ 150kPa)
OCR = 1.0
OCR = 1.5
OCR = 2.0pqr
Shear wave velocity, Vs (m/sec)w2ynoB*D!Ûñ

10100
Number of cycles to liquefaction, cToyoura sand
OCR = 1.0
OCR = 2.0

0.3

0.2

0.1

0.0
0.650

0.700

0.750
Void ratio, e

0.800

0.850

Fig. 9 012345678 RL $ e %&2A* -µi9:(2)3CG0 Éî¸kl9G()CG0 56`f Vs -+OCR È56()oB* C§¨R¢£G¤¥!"`oµi,+-B
RL  e 9: Fig. 9 Ôf*ZµiCOCR=2.0 3

1  G   ? @  n )  C OCR  I o  µ i

0.4

(OCR = 2.0)
 RL Cyclic stress ratio to cause DA=5.0%
in 20 cycllic loadings, RN=2 0 ( σ d/2 σc ')Shear wave velocity, Vs (m/sec)

250

BÚ!ÛWXYZ2cfg

Vs = 200m/s

200
(OCR = 1.0)
e1 = 0.737

150
0.650

0.700

e2 = 0.790

0.750

0.800

0.3

RL = 0.208

0.850



0.2


(OCR = 1.0)

0.1

e2 = 0.790

e1 = 0.737
0.00.650

Void ratio, e(OCR = 2.0)

0.700

0.750
Void ratio, e

0.800

0.850

Fig. 10 9:;<=)>?@! RL ABCD

Fig. 11 9:;<=)>?@! RL ABCD

E"# Vs - e %&F

E"# RL - e %&F

OCR=1.0 ÒÓµiÈ*cfgß-()*fCFig. 11 ¦§n*3Ce1=0.737

+]µCOCR WXYZ2OCR=1.0_`MG<no()

fCVsCRL ÈD-½ÐD3e 37n)[µiPG()]*C VsCRL óô56å2]*·iCÎôCVs +yzGBÉî¸C¨z~Éî¸)
S)(C¢£G¤¥!"}G(ÈCzÅ~JKfghAÎô+-*56Î©GBWXYZ2yz{|5. ABCDEFGH'I0123.4JK)

C4B

11 þFG(BTUV·-(<CÚ!ÛïáúètµiÉîW!"µi,+-B Vs µA*}«gcGC

ïFGBGÎô+-Cñ]GB!^wxf*

Fig. 10 S)(COCR=2.0 £ñ3C

B Vs=200m/s3+n)*Fig. 10  e1=0.737C¢£G¤¥!"*ñïáGBÚ!ÛÉî¸ e1=0.737 3CðÚ!Û3C_`M}Éî¸ e2=0.790 3u¬­ïáf()

n*WXYyÝ´F89f3Ciµ¶n¬uG(·¸ACpÝµ-vC;Kn[\]!^wxn<CRL ;)¥Fig. 11 µiCe1=0.737 ¢£G¤¥!"`oC

6. "LS?

@n)BC±n?@²ÑÄh[{³w2A*a*C}

A-vC

Îô+-*oBÈno()*RL =0.208ÈnX

º»10%°20%å2¼/½!^íz Vs nÉî¸Ú!ÛïáG¤G()BC}n!

 GGn+C-+®¯fB3CÅ¡zf*nSCp¢3TUV

¸jæf3ªG<Cµn6^ïáf3CðjæfGn)µiCWXYZ2yGB) Vs g§¨RA* ËÌ65ÆÇ©É6µº» 30%¼µo(f*uvnA·ô( Fig. 10  Fig.

XYZ2Cp}~Ýµihµyyzpqr

BCXH¹A*3CTUV+,+-B Vs F)(CWXYZ2 RL yzfÝ}~oB*w2µ)yzBlmn56)()CoB*
1.

Vs  e 9:µiCSÉî¸2.

Vs È[ÐfoB*RL  e 9:µiCSÉî¸

3.

È OCR È OCR RL È[ÐfoB*

BC)§¨R Vs +¨z~Éî¸ºG(CWXYZ2 RL yz

{|8ÔGB*4.

»6ÕuG(C·B¬nh

½n<uG(È¼}")CÝ´Ffgh

A*MNOP1)

GHIJKLMNOKPQRSTUVWXYZ!
[(\;]'^_K2.(\;]'K($`aK2)

3)

4)('bcdKVol.33KNo.8Kpp. 65-77K1985.
SeSfTUg+,-Kpp.36-37K1991

International Parallel Test on the Measurement ofGmax Using Bender Elements Organized by TC-29

Iwasaki, T., Tatsuoka, F. and Takagi, Y.: Shear Moduli ofSands Undear Cyclic Torsional Shear Loading, , Soils andFoundations,Vol.18, No.1, pp. 39-56, 1978.