Testing and apparatusEssais et appareils

1 INTRODUCTION

In common with preceding symposia, i.e., IS-Hokkaido(Shibuya et al., 1994) and IS-Torino (Jamiolkowskiet al., 1999), the deformation behaviour of geomaterialsat relatively small strains was a centralized subject.Little attention was paid to the failure and post-failurebehaviour. It was an unintentional consequence thatreflected a worldwide trend in geotechnical researchin the ’90s. In cope with a warning to TC29 not to

become ‘exclusive club’ given by Professor MikeJamiolkowski at the occasion of Géotechnique Sym-posium in 1997, the term “pre-failure” was removedfrom the title of this Symposium (IS-Lyon’03). Reflect-ing this new policy of TC29, the contributed papers tothis symposium deal with not only the pre-failure butalso the post-failure behaviour of geomaterials.

Figure 1 shows a typical of stress-strain curve of soilelement when subjected to shearing in the laboratory.Pulse/vibration tests to obtain elastic or quasi-elastic

Deformation Characteristics of Geomaterials – Di Benedetto et al (eds)© 2005 Taylor & Francis Group, London, ISBN 04 1536 701 8

3

Recent developments in deformation and strength testing of geomaterials

S. ShibuyaGraduate School of Engineering, Hokkaido University, Sapporo, Japan

J. KosekiInstitute of Industrial Science, University of Tokyo, Tokyo, Japan

T. KawaguchiHakodate National College of Technology, Hakodate, Japan

ABSTRACT: Recent developments in equipments and techniques regarding deformation and strength testingof geomaterials in the laboratory are reviewed. The scope of strain measurement discussed in this keynote paperis wide, ranging from the elastic behaviour at very small strains to the generation of shear bands at large strainsbeyond failure. Some problems overlooked in characterising engineering properties of geomaterials in the lab-oratory are cited, and their countermeasures are discussed. Practical application of the laboratory test results isdiscussed with a limited number of case histories.

Hollow cylinder/ Simple shear

Pulse / Vibration tests

DSB / Triaxial UU / Vane

Peak Post-faliure(shear band boundary value problems)

Pre-failure(element)

Strain

G0

E0

Ring shear/ Cyclic DSB

Triaxial

IS-Hokkaido (’94), IS-Torino (’99)

IS-Lyon (2003)

Stress

Plane strain/ True triaxial

?

?

Figure 1. A typical of stress-strain curve of soil element when subjected to shearing in the laboratory.

stiffness, G0 or E0, at very small strains can techni-cally be performed at any stages. The interpretation ofthe result as the element may be appropriate over thepre-failure regime, but it is not so after the peak wherestrain localization (i.e., the development of shear bands)is usually seen.

In the current world-class standard of geotechnicallaboratories, the deformation behaviour over the wholepre-failure regime, including the elastic stiffness atvery small strains can successfully be observed in tri-axial test. Conversely, the scope of strain measurementseems inferior in HC/simple shear tests due to stress/strain non-uniformities in the specimens, but these testsenable us to examine more general behaviour such asanisotropy and the effects of principal stress rotation.Plane strain/true triaxial tests both using a rectangularspecimen provide an opportunity to examine thebehaviour of post-peak strain localization by using,for example, photo-image techniques.

This paper consists of two parts. In part I, recentdevelopments in measurement/control and data acqui-sition systems are reviewed. The scope of strain meas-urement discussed is wide, ranging from the elasticbehaviour at very small strains to the generation ofshear bands at large strains beyond failure. In Part II,practical implications of the laboratory test results arecited with a limited number of case histories.

2 PART I: RECENT DEVELOPMENTS IN MEASUREMENT, CONTROL AND DATA ACQUISITION

2.1 Servo-motor

Recently, the use of servo-motor has greatly enhancedthe capability of a variety of equipments in geotechnicalengineering laboratory. Figures 2 and 3 show two typesof servo-motor equipped for control of axial loadingpiston in triaxial apparatus. The AC servo-motor (seeFig.2) with a feature of zero-backlash is extensivelyin use for soil testing at University of Tokyo (Santuccide Magistris et al., 1999). As it can be seen in Fig.2,the loading system consists of a AC servo-motor withtwo gears. In this system, the motor always drives inone direction. Simultaneously, the upper gear is rotat-ing in one direction, whereas the lower gear is rotatingin the opposite direction. The movement of the loadingpiston can be switched from downwards to upwardswithout any backlash by using an electric clutch.

The direct-drive motor coupled with nearly zero-backlash reduction unit (see Fig.3) has been devel-oped at Hokkaido University (Shibuya and Mitachi,1997, Kawaguchi et al., 2002, Kawaguchi, 2002). Inthis system, ‘nearly-zero’backlash on reversal of load-ing direction can be achieved with the combination ofthe servo-motor, reduction unit and ballspline screw.

The control of axial loading can be fully automatedby using a personal computer. Furthermore, the load-ing system shows a distinct capability of achieving aminimum control for the axial displacement of 0.00015micrometer spanning over several orders of the rate ofaxial straining. Note that the resolution of axial dis-placement is equivalent to 1.5 � 10�9 of strain for asample with 10 cm high. On reversal of loading direc-tion, the system shows virtually zero backlash, thecharacteristic of which is vitally important to observethe hysteretic damping ratio of geomaterials under

4

To the loading piston of triaxial cell

18

17

16

15

5

8

6

3

47

910

11

13

12

1412

1. Speed-reduction gear boxes 2. Spur gear 3. Bevel gear A 4. Bevel gear B 5. Shaft 6. EMC(A)

8. EMB 9. Precision ball screw

11. Sheath 12. Guide linear-motion bearing 13. Linear-motion bearing 14. AC-Servo motor 15. Motor control unit 16. EMC switching system 17. Digital/Analog converter 18. Micro computer

EMC: Electro-magnetic clutchEMB: Electro-magnetic brake

(not to scale)

7. EMC(B)

10. No-backlash nut for precision ball screw

Upper gear(bevel gear A)

Ballspline screw

Lower gear(bevel gear B)

AC servo-motor

Figure 2. Axial loading system using AC servo-motor(Santucci de Magistris et al., 1999).

strictly controlled strain or stress with time (seeTatsuoka and Kohata, 1994). These characteristicswhen coupled with adequate instrumentation for theaxial strain measurement enables examination of geo-material response under strictly controlled rate ofaxial straining. The scope of tests that can be carriedout in MFT apparatus is wide, including K0–consoli-dation, cyclic and monotonic shear with constant aswell as altering rate of axial straining.

The direct drive motor has a function to give digitalinformation of the current positioning. Figure 4 showsthe axial strain from the servo-motor plotted againstthe comparable measurement using a proximity trans-ducer mounted at the top cap (Kawaguchi et al.,2002a). As seen in this figure, nearly one-to-one rela-tion is observed between these two measurements.Therefore, an external gage for the axial deformationmeasurement is no longer needed when this system isemployed. Also, it can be seen that the time lag onreversal of the loading direction is virtually nothing.

This feature of nearly zero-backlash enables us toprecisely measure, for example, the hysteretic damp-ing of geomaterials showing time-dependent stress-strain characteristics. Figure 5 shows the stress-straincurve of a clay sample subjected to complicated strainpath (Kawaguchi, 2002). It is successfully demon-strated that the elastic stiffness can be observed at anystage of shear by using this loading system.

The servo motors with distinctive features of high-precision of displacement control and zero-backlashmay be employed for a variety of purposes. Figure 6shows a large-scale true triaxial apparatus in whichthe lateral load or lateral displacement, hence �y or �ycan precisely be controlled by using the servo motorsystem (AnhDan and Koseki, 2003). When the ball-screw driven by the AC servo motor moves up anddown, the loading wedges also move vertically, whichin turn triggers horizontal movement of the lateral load-ing plate. Figure 7 shows the results of test on Toyoura

5

Direct-drive motor('nearly-zero' backlash)

Ballspline screw('nearly-zero' backlash)

Drive Unit

Serial Port

1.

2. 3.

4.

5. 6.

7.

8.9.

10.

11.

1. Manual handle2. Direct-drive motor3. Output-flange of motor4. Input section of revolution to reduction unit5. Reduction unit6. Output section of reduced revolution to ball screw nut7. Ballspline screw8. Ball screw nut9. Thrust-angular bearing10. Spline nut11. Piston rod

Reduction unit('nearly-zero' backlash)

PersonalComputer

Figure 3. Axial loading system using direct-drive motor(Shibuya and Mitachi, 1997, Kawaguchi, 2002).

0 0.1 0.2 0.3 0.40

0.1

0.2

0.3

0.4

0 0.1 0.2 0.3 0.40

10

20

30

40

50

Axial strain calculated by position of motor (%)

Axi

al s

trai

n m

easu

red

with

pro

xim

eter

(%

)0.98

NSF clay

p'c = 300 kPaCD test

dεa/dt = 0.0002 (%/min)

1

q (k

Pa)

εa (%)

0 10 20 30 40 50 60 70 80

–0.005

0

0.005

17 18 19 20

0.0045

0.005

Time (sec.)

Axi

al s

trai

n m

easu

red

with

pro

xim

eter

(%

)

Frequency0.013 (Hz)

Top cap

Proximity

Time (sec.)

ε a (

%)

transducer

Figure 4. Axial strain from the servo-motor plotted againstthe comparable measurement using a proximity transducermounted at the top cap (Kawaguchi et al., 2002).

sand in the true triaxial apparatus (AnhDan, 2001). Itis demonstrated that the elastic Young’s modulus inthe vertical (z) direction was measured by changing �zwhile the stress in horizontal (y) direction was main-tained at a constant value. Similarly, the elastic Young’smodulus in y-direction was successfully measured byfollowing similar techniques. It seems this systemenables us to measure the small-strain stiffnessanisotropy from the direct measurement of stress-strainrelationship.

The direct-drive motor is employed in direct shearbox (DSB) apparatus, in which the horizontal dis-placement of the lower box against the fixed upperbox can be controlled cyclically without any time lag onreversal of the loading direction. Figure 8 shows theresults from a cyclic test (Mitachi et al., 2003). In thistest on clay, the horizontal displacement was appliedin a cyclic manner with a single amplitude of displace-ment of 6 mm. As seen in this figure, the shear stresson the horizontal plane gradually decreased as thecumulative displacement increased in value to reachthe residual state. The envelopes associated with fullysoftened state and the residual state were successfullyobtained in a series of tests with different consolida-tion pressures.

Figure 9 shows another example for the use ofservo motor. In this torsional shear apparatus, a coupleof direct-drive motors are employed for generatingthe axial load and the torque (Yamashita and Suzuki,1999a). Figure 10 shows the results of undrained cyclictest performed in this set of apparatus. When theloose sample of Toyoura sand was subjected to cyclicapplication of shear strain, the ratio of shear stress to

6

0 0.02 0.04 0.06 0.08 0.1 0.120

2

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 1 1.2 1.40

0.02

0.04

0.06

0.08

0.1

Axial strain, εa (%)

Dev

iato

r str

ess,

q (k

Pa)

NSF clay

p' = 30 (kPa)

OCR = 10

K = 1.0

0.18

1

Axi

al s

trai

n, ε

a (%

)

Time (min.)

1

–0.18

Figure 5. Stress-strain curve of a clay sample subjected tocomplicated strain path (Kawaguchi, 2002).

Loadingwedge

Loadingwedge

Loadingplate

Ball screw

Device for controllinglateral displacement byrotating ball screw

EMB:Electro-magnetic brakeEMC:Electro-magnetic clutch

AC servo-motor

EMC

(Unit : mm)

Bearing

Top plate

Load cell

Top cap

Universal joint fortransmitting torque

Observation window(4@ φ90)

Reaction plate

High-stiffnesspre-pressurized bearing

Roller bearing Roller bearing

Ball screw

Pre-pressurized nutLoading wedge

Tie

rod

(4@

φ60

)

C

DF

GE

A

B

E

Pedestal

Specimen(X=220,Y=250,Z=500)

Pneumaticcylinder forcounter-balancing

Loading platewith slanted back face

0 100 200 300 400 500(mm)

Sta

inle

ss-s

teel

cel

l (in

ner

φ 7

00,t2

0)

Load

ing

shaf

t (φ

50)

Base plate

Figure 6. A large-scale true triaxial testing apparatus (AnhDan and Koseki, 2003).

7

400 500 600 700 800 90042

44

46

48

50

52

0

2

4

6

8

10(a) Toyoura sand

Vertical small cyclic loadingat σx= 49 kPa

qz

qy

q z=

σz-

σ x (

kPa)

q y=

σy-

σ x (

kPa)

Time (sec)

q z=

σz-

σ x (

kPa)

q y=

σy-

σ x (

kPa)

42

44

46

48

50

52

850 900 950 1000 1050 1100 1150 12000

2

4

6

8

10(a)

qy

qz

Time (sec)

Toyoura sandHorizontal small cyclic loadingat σx= 49 kPa

q z=

σz-

σ x (

kPa)

0.021 0.022 0.023 0.024 0.02542

44

46

48

50

52(b)

Toyoura sandVertical small cyclicloading at σx=49 kPa

εz (%) (by LDTs)

q z=

σz-

σ x (

kPa)

εz (%) (by LDTs)-0.006 -0.005 -0.004 -0.003 -0.0020

2

4

6

8

10b)

Toyoura sandHorizontal small cyclicloading at σx=49 kPa

Figure 7. Typical results by applying small amplitude cyclic loading in vertical and horizontal directions (AnhDan, 2001).

0 100 200 300 4000

50

100

150

200

Shea

r str

ess,

τ (k

Pa)

Yubari clay

Vertical stress, σv (kPa)

c's = 18.0 (kPa) φ's = 20.7 (deg.)c'r = 14.4 (kPa) φ'r = 11.3 (deg.)

–6 –4 –2 0 2 4 6–200

–100

0

100

200

Horizontal displacement, δ (mm)

Shea

r st

ress

, τ (

kPa)

Yubari clayσ'v = 325 kPa

no. of cycles: 3dδ/dt = 0.02 mm/min

0 10 20 30 40 50 60 700

50

100

150

Horizontal displacement, Σδ (mm)

Shea

r str

ess,

|τ| (

kPa)

Yubari clayno. of cycles: 3σ'v = 325 kPa

τp

τr

τr:

τs:

τs = 133.7

τr = 73.9

Pneumaticcylinder

Dial gauge(vertical disp.)

Universal jointLoad cell

Load cell

Shear box

Linear roller way

Direct-drive motor

'

Figure 8. Direct shear box (DSB) apparatus with results from a cyclic test (Mitachi et al., 2003).

the isotropic consolidation stress gradually decreasedinvolved with the steady accumulation of excess porepressure. It seems the value of this system in simulatingin-situ shear strain history regarding sand liquefaction.

2.2 Local strain measurement

Figure 11 shows a triaxial specimen whose axial defor-mation was measured by using a couple of proximitytransducers. The metal targets are pinned into the sam-ple so that potential error due to slipping between thetarget and the rubber membrane and also between therubber membrane and the soil specimen may be min-imized (refer to Lo Presti et al., 2000). We have foundthat this type of slipping may take place in tests onsoft clay and also on stiff geomaterials like soft rocks.

Local deformation transducer (LDT) developed byGoto et al. (1991) is now widely used in geotechnicallaboratories. Figure 12 shows a hollow cylinder (HC)specimen on the surface of which three LDTs are

mounted to form a triangle in shape. In addition, ahorizontal LDT is mounted on the inner wall. In thisconfiguration, four components of strains; i.e., verti-cal strain (�z), circumferential strain (��), radial strain(�r) and shear strain (�z�) can be measured simultane-ously (HongNam and Koseki, 2003). Figure 13 showsthe results of such measurements (HongNam, 2004).The shear modulus Gz� was measured by cyclically

8

Figure 9. Torsional shear apparatus equipped with a cou-ple of direct-drive motors for generating the axial load andthe torque (Yamashita and Suzuki, 1999a).

Figure 10. Results of undrained cyclic test performed in thetorsional shear apparatus (Yamashita and Suzuki, 1999b).

Figure 11. A triaxial specimen whose axial deformationwas measured by using a couple of proximity transducers.

applying the shear stress on the horizontal plane. Onthe other hand, Young’s modulus Ez, together with thePoisson’s ratio, vz� was measured through observationof the response of vertical and circumferential strainswhen �z was cyclically changed.

Figure 14 shows a true triaxial apparatus in which‘true’ plane strain conditions were achieved by main-taining the normal strain �y, when locally measured byLDTs, zero throughout the test (Maqbool and Koseki,

2003). This methodology is termed here as activecontrol in contrast to the conventional passive control,in which the plane strain conditions may not be satis-fied owing to the effects of bedding error between therigid platen and the membrane. In the test performedon coarse-grained gravel, there observed significantdifference in the stress-strain behaviour. In the con-ventional test, the �y observed was as much as 1.5%,resulting in the stress-strain response similar to triaxialcompression at an early stage of testing. Conversely,the stress-strain relationship in the active test exhib-ited stiffer and stronger response as compared to theconventional test. As well demonstrated in Fig.14, weshould be careful enough about the fact that ‘true planestrain’ conditions for the small-strain behaviour in par-ticular are difficult to be achieved when a rigid bound-ary with lubrication is employed. The use of local strainmeasurement coupled with a deformation control sys-tem may be needed for performing this kind of test.

Local strain measurement shows the value in observ-ing strain localization. Strain localization is of interestin two cases; i.e., to give insights into non-uniformstrain (or stress) distribution of granular materials andnatural cohesive soils and into the development ofshear band(s) at large strains. Table 1 shows innovativetechniques developed for observing localized or dis-crete deformation of soil specimen in the laboratory.

Figure 15 shows a high-rigidity plane strain appara-tus for testing stiff geomaterials (Salas-Monge et al.,2003). The confining plate is made of well-polished3 cm-thick transparent Plexiglas. As can be seen, aseries of dots are marked on the membrane mountedon the plane of zero strains. Figure 16 shows shear-strain contours of cement-treated sandy soil at fourstages of cyclic shear in compression. As it can beseen, the development of strain localization of thisstiff geomaterial may be readily visualized in a digitalform. The pictures analyzed were taken by a digitalcamera with a resolution of about 3 megapixels thatwas available in a market.

2.3 Elastic wave velocity measurement

Elasticity refers to materials’ property involved withno energy dissipation for any closed stress cycle. It isirrelevant whether the stress-strain relationship is lin-ear or non-linear. In addition, the elastic propertiesought to be time-independent, for example, the stiff-ness must not be influenced by the rate of stressing orstraining.

Quasi-elastic geomaterial properties may be definedfor the behaviour at small strains because of the above-mentioned strain (or stress) history with time. Forexample, the stress-strain response at extremely smallstrains is quasi-elastic in respect that it shows a hys-teretic loop implying a small amount of energy loss, butthe stiffness is unaffected by the rate of shearing over

9

GS8 GS6

16cm

20cm

30cm

GS7 GS5

GS5,GS6GS1

SET1GS3

GS7,GS8

SET2

GS2

GS3 GS1

GS2

Fz

GS4

T

GS4

P-LDT

SET1

Hinge*

Conicalhole

Pin

HTPB strip

*glued on the surface of specimen

45°

Figure 12. Pin-type triangular LDTs employed for hollowcylinder specimen (HongNam and Koseki, 2003, HongNam,2004).

10

30 40 50 60 70 8090100 200 300 400 50030

40

5060708090

200

300

400

500

m=0.45

Toyoura sand

0.2295 0.2300 0.2305 0.2310 0.2315 0.2320 0.2325

197.5

198.0

198.5

199.0

199.5

200.0

200.5

11

ε θ (%

) at

out

er s

urfa

ce

Eeq=103.6 MPa

Vertical loading at σz=200 kPa, τzθ=60 kPa

σ z (k

Pa)

εz (%)

-0.2160

-0.2158

-0.2156

-0.2154

-0.2152

-0.2150

-0.2148

νzθ=0.45

Toyoura sand

-0.003 -0.002 -0.001 0.000 0.001 0.002

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1

Torsional loading at σz =200 kPa, τz =60 kPa

Geq=34.6 MPa

τ zθ (

kPa)

γzθ(%) at radius of (Do+Di)/2

Toyoura sand

30 40 50 60 70 80 90100 200 300 400 50030

40

5060708090

100

200

300

400

500

σ'θ=200 kPa, τzθ = 0 kPa σ'θ=200 kPa, τzθ = -35 kPa σ'θ=200 kPa, τzθ = 35 kPa

σ'θ=200 kPa, τzθ =0kPa σ'θ=200 kPa, τzθ =-35kPa σ'θ=200 kPa, τzθ =35kPa

σ'θ=100 kPa, τzθ =0kPa σ'θ=100 kPa, τzθ =-25kPa σ'θ=100 kPa, τzθ =25kPa

σ'θ=100 kPa, τzθ = 0 kPa σ'θ=100 kPa, τzθ = -25 kPa σ'θ=100 kPa, τzθ = 25 kPa

Test 9

n=0.49Gzθ

/f(e)

(M

Pa)

Ez

/f(e)

(M

Pa)

[σ'z.σ'θ]0.5

(kPa) σ'z (kPa)

Toyoura sand

f(e) = (2.17 e)2 / (1+e) f(e) = (2.17 e)

2 / (1+e)

IC (τzθ =0) IC (τzθ =0)

100

Figure 13. Typical results by applying small amplitude cyclic loading in vertical and torsional directions (HongNam, 2004).

Figure 14. Plane strain compression tests on Chiba gravel under passive and active controls (Maqbool and Koseki, 2003).

normal range encountered in geotechnical engineering(Tatsuoka and Shibuya, 1992, Shibuya et al., 1992).

Seismic tests involved with the measurement of shearbody wave velocity, Vs, manifests the quasi-elasticshear modulus, G, the estimate of which is based on;

(1)

where �t denotes bulk density of soil.The bender element (BE) that is designated for

measuring G, is handy, inexpensive and durable. The

instrument suits well for measuring Vs in the laboratory(Shirley and Hampton, 1977, Dyvik and Madshus,1985). In fact, the BE has been plugged into a fewtesting devices such as consolidometer (Jamiolkowski

et al., 1994, Shibuya et al., 1995, Kawaguchi et al.,2001 among others), triaxial apparatus (Tanizawa et al., 1994, Viggiani and Atkinson, 1995, Jovi�ic′ et al.,1996, Kuwano and Jardine, 1997 among others), andalso applied to in-situ measurement of Gf (Nishio andKatsura, 1994). Strength as well as G can be measuredsimultaneously when used in shear devices such asdirect shear box and triaxial devices.

Figure 17 shows a simple consolidometerequipped with a pair of BEs (Shibuya et al., 1997a).Figures 18 and 19 show similar cases of direct shear

11

Table 1. Innovative techniques for localized deformation.

Image analysis (e.g., PIV) Frost & Yang, 2003Bowman & Soga, 2003Kobayashi & Fukagawa, 2003

Laser aided tomography Matsushima et al., 2003(LAT) Konagai et al., 1992CCD sensor Kishi & Tani, 2003Digital microscope Towhata & Lin, 2003X-ray CT method Otani et al., 2000

Figure 15. High-rigidity plane strain apparatus for testingstiff geomaterials (Salas-Monge et al., 2003).

15

10

5

0

15

10

5

0

LDT2

LDT1

6cm8cm

16cm

Shear band

0200

400

600

800

1000

12001400

1600

1800

2000

0.0 0.5 1.0

6

54321

(b) LDT2

Axial strain, ε1 (%) LDT2D

evia

tor

stre

ss, q

= σ

1-σ 3

(kP

a)

0

200

400600

800

1000

12001400

16001800

2000

6

54321

(a) LDT1Dev

iato

r st

ress

, q =

σ1-

σ 3 (k

Pa)

4. After 15cycles

5. After 20cycles γmax (%)

γmax (%)3. After 10cycles

2. After 5cycles

Figure 16. Shear-strain contours of cement-treated sandysoil at four stages of cyclic shear (Salas-Monge et al.,2003).

box apparatus and triaxial apparatus (Hwang et al.,1998), respectively.

In the consolidometer developed at HokkaidoUniversity (see Fig.17), a disk-shaped soil specimenof nominal dimensions 60 mm in diameter and 20 mmhigh undergoes 1D consolidation. It features by extracapabilities of

i) measurement of �h as well as �v,ii) back air pressure application,iii) pore pressure monitoring at the base, andiv) dual measurement of �v at the base and over the

apparatus,

The measurement of two principal stresses enablesus to determine K0-value of the clay sample.

Application of back air pressure enhances the degreeof saturation in the sample, which in turn improvesaccuracy of void ratio determination, hence e-log��vcurve on reconsolidation.

An unsolved issue regarding the BE test is how todetermine the correct travel time of the shear wave.Near field (NF) effects are a real nuisance whichmakes it difficult (Salinero et al., 1986, Kawaguchi et al., 2001 among others). Yet, no international con-sensus has been made on this issue. Therefore, TC29has organized international parallel test on BE testand the latest information regarding BE test is available on the official website of TC29(http://www.jiban.or.jp/e/tc29/index.htm, 2003).

Anisotropy of elastic stiffness is an interest forpractical engineers when they interpret the result ofin-situ seismic survey performed using differentmethods such as cross-hole and down-hole methods(for example, Butcher and Powell, 1995). Anisotropyin shear modulus can also be measured using BEs(refer to Jamiolkowski et al., 1994, Fioravante, 2000among others). Figure 20 shows a triaxial specimenof Toyoura sand in which the shear wave velocity ismeasured using three sets of BEs (Yamashita et al.,2003). A set of BEs mounted on top cap and thepedestal enables us to measure shear wave velocitywith the wave propagating in the vertical directioninvolved with the soil grain movement in the horizon-tal direction, VH. Similarly, the velocities associatedwith HV and HH shear can be measured with other twosets of BEs. Figure 21 shows the results of such meas-urements on Toyoura sand and a volcanic ash, sug-gesting that GHH is slightly larger than GVH (� GHV).

12

Figure 17. A consolidometer equipped with a pair of BEs(Shibuya et al., 1997a).

Figure 18. Direct shear box apparatus equipped with BEs.

Figure 19. Triaxial apparatus equipped with BEs (Hwanget al., 1998).

Soil ‘structure’ may be estimated by knowing thequasi-elastic stiffness. Figure 22 shows the relation-ship between void ratio, e, and the elastic shear mod-ulus, G when subjected to 1D compression. Thetriangular symbol refers to the behaviour of reconsti-tuted clay, whereas the comparable results of two nat-ural samples, each recompressed to in-situ geostaticstresses, are shown using squares (Li et al., 2003). Asit can be seen in this figure, the ‘structure’ of the agednatural samples may be evaluated quantitatively bymetastability index, MI(G), which refers to the differ-ence of void ratio between the non-structured recon-stituted sample and the natural sample at a common G(Shibuya, 2000).

Figure 23 shows the measurement of P-S wavevelocities (AnhDan et al., 2002). In this system, amulti-piezo-ceramic unit, which is more powerfulthan a single bender, is employed as the trigger togenerate not only S-wave but also P-wave. The P andS wave velocities are measured using accelerometersmounted on the lateral surface of the specimen. Thissystem seems most suitable for the elastic wavevelocity measurement of large size soil specimen.

It is well known that in tests on coarse-grained soilor soft rocks, the elastic wave velocity measurementundergoes the effects of sample heterogeneity (forexample, refer to Tatsuoka and Shibuya, 1992). Asillustrated in Figure 24, the stiffness from the stress-strain curve in the laboratory refers to the overalldeformation behaviour, whereas the elastic wavemeasurement reflects predominantly on those of thestiff part (Tanaka et al., 1994).

Figure 25 shows the ratio of the equivalent elasticwave velocity from static test to the measured velocityfrom dynamic test plotted against the ratio of the meangrain diameter to the half of wave length (Tanaka et al.,2000, AnhDan et al., 2002, Maqbool et al., 2004).

As it can be seen, the ratio using both S and P wavestends to decrease as the wave length graduallyapproaches to the grain size. The results strongly sug-gest that we should use the wave length, say roughly1,000 times or more, the D50 of the soil specimen inorder to obtain the overall elastic stiffness on average.

13

VH

HV HH

VH

HV HH

BEBE

Figure 20. Triaxial specimen of Toyoura sand in which theshear wave velocity is measured using three sets of BEs(Yamashita et al., 2003).

Figure 21. Results of BE tests on Toyoura sand and a vol-canic ash (Yamashita et al., 2003).

2.4 Friction on rigid interface

The last topic in Part I is the effects of friction onrigid interface in the laboratory test. When soil movesrelative to the rigid wall, friction force develops at theinterface. Error in the �v measurement due to the wallfriction has been found quite significant in conven-tional testing devices in which soil specimen is con-fined in a rigid box or ring (Shibuya et al., 1997b).Like the consolidometer already shown in Fig.17, thevertical load at the base, Wlower as well as the measure-ment at the top, Wupper should therefore be measuredby which the effect of wall friction is properlyaccounted for. Averaged �v in consolidometer test maybe given by

(2)

where A stands for cross-section area of specimen.Figure 26 shows the relationship between void

ratio e and ��v of Osaka Bay clay (Li et al., 2004) The� value refers to the slope of NC line in terms of e-��vrelationship. The effect of interface friction acting onthe lateral surface of the specimen was significant forthe ��v measurement. The conventional measurementat the top grossly overestimated the ��v as comparedto the average of the upper and lower measurementsin compression, and vice versa in swelling. As seen inFigure 27, the conventional ��v measurement yieldedthe well-known design value of the overconsolidationratio (OCR) of 1.2, whereas the OCR value from theaveraged ��v yielded approximately unity. Accordingly,we have chosen the averaged vertical stress in order to

14

4 6 8 10 20 401.00

1.20

1.40

1.60

1.80

2.00

Voi

d ra

tio, e

Elastic shear modulus, G (MPa)

S(R)

S(U)

S(L)

GBE Geq

GBE Geq

Geq

–ν

–µ

–µ

–µ

ν = 0.29µ = 0.080∆ = 2.13

1

1

1

1MI (G)

Reconstitutedsample

In-situsamples

Singapore clay

Figure 22. Relationship between void ratio and elasticshear modulus of Singapore clay when subjected to 1D com-pression (Li et al., 2003).

L1

L2

L3

Trigger

H

Triggers

Receiver

Trigger

Receivers

Figure 23. Measurement of P-S wave velocities in verticaland horizontal directions (AnhDan et al., 2002).

Figure 24. Effects of sample heterogeneity (modified fromTanaka et al., 1994).

Figure 25. Effects of particle size and wave length on ratioof equivalent elastic wave velocities by static and dynamicmeasurements (modified from Tanaka et al., 2000, AnhDanet al., 2002, Maqbool et al., 2004).

determine the yield stress, hence the OCR value. Weshould be more careful about the effects of interfacefriction even in conventional oedometer test using aspecimen of merely 2 cm high.

The effects of interface friction of a rectangularspecimen are demonstrated in Figure 28 by conducting

a small-scale true triaxial test on a rubber dummy(Hayano, 2001). In case where two interfaces are notlubricated, three normal strains exhibited values dif-ferent to each other when subjected to isotropic stressapplication. The divergence virtually diminished whenthe two surfaces are both lubricated. The results

15

102 1031.6

1.8

2.0

2.2

Voi

d ra

tio, e

Effective vertical stress, σ'v(kPa)

σ'v(in–situ)=320kPa

: upper: lower: average

1 1

–λ

–κ

yielding

Osaka Bay clay

Figure 26. Relationship between e and �‘v of Osaka Bayclay in CRS test (Li et al., 2004).

Figure 28. Small-scale true triaxial test on rubber dummy (Hayano, 2001).

0 500 10000

500

1000

Con

solid

atio

n yi

eld

stre

ss,

p c (

kPa)

Effective overburden pressure, σ'v(in–situ) (kPa)

:average

:upper:lower

Osaka Bay clay

OCR1.0OCR1.1

OCR1.2

Figure 27. Determination of OCR of Osaka Bay clay inCRS test (Li et al., 2004).

strongly suggest the need for lubrication on the rigidsoil to metal interface in laboratory element test.

3 PART II: APPLICATION IN ENGINEERINGPRACTICE

3.1 Introduction

In Part II, four cases all regarding the application ofdeformation and strength test results in engineeringpractice will be described separately. These are;

i) deformation of soft clay ground in deep excava-tion,

ii) lateral subgrade reaction of large foundation,iii) earth pressure at high seismic loading, andiv) seismic stability of fill dam.

Figure 29 shows Geo-cow illustrated by Shibuyaet al. (2001). The original concept described byShibuya et al. (2001) was to distinguish the differencebetween the reconstituted specimens for hamburgerand natural soils for fillet with effects of ageing,anisotropy, and so on. However, in this paper, Geo-cow is meant to distinguish the difference in theextents how we make use of laboratory test results.“Hamburger” stands for the tests that are performedfrequently in practice, such as unconfined compres-sion test to evaluate qu and E50 values, which areemployed in the conventional design of earth struc-tures and foundations. On the other hand, “fillet”stands for the tests that are not frequently performedin practice, but provide detailed data on the strengthand deformation properties.

All of the four case histories described in thispart II can be classified as “fillet”, since they arebased on the results of elaborated laboratory tests.Some of them employ the detailed test results directlyin the project, while the others employ the relevanttest results in order to develop rational design proce-dures reflecting the actual behavior of natural soils.

3.2 Deformation of soft clay ground in deep excavation

In the preceding conference in Torino, Simpson (2000)has drawn our attention to a couple of engineeringneeds. One is the technical need for a good model ofsoil behavior in the range of strain of engineering sig-nificance, generally 0.001% to 0.1%. The other is thepragmatic need for rapid analysis, and especially formore rapid testing methods, notably for clays.

In this section, a case history in Thailand on deepexcavation in soft clay with concrete diaphragm wallis described with a particular attention paid to theground deformation behind the diaphragm wall. Assummarized in Table 2, there have been several

empirical proposals how we should select the soilstiffness employed for FE analysis. For embankmentloading, the use of several hundreds or tens times ofundrained shear strength su has been proposed for theequivalent Young’s modulus. For excavation works,on the other hand, much higher factors have been pro-posed by Bowels (1988) and Hock (1997) for the con-version from su, or the use of half of the small strainstiffness Emax obtained by in-situ seismic survey hasbeen proposed by Simpson (2000).

Figure 30 shows the variations of secant Young’smodulus normalized using su and Emax with axialstrain, that were obtained in undrained triaxial com-pression test on normally consolidated clays collectedfrom worldwide (Temma et al., 2000, 2001). In thepresent case history, the ground strains behind thediaphragm wall was on the order of 0.1%, which is

16

Figure 29. Geo-cow (Shibuya et al., 2001).

Table 2. Elastic deformation modulus employed for FEanalysis in the past.

E � �Su Author

Embankment loading analysisEu � 200–500Su Bjerrum (1964)E� 70–250SuFVS Balasubramaniam et al.

(1981)Eu � 15–40SuFVS Bergado et al. (1990) (Back-

calculation)Excavation works analysisEu � 200–500Su Bowels (1988)Eu � 280–500Su Hock (1997) (soft clay)Eu � 1200–1600Su Hock (1997) (stiff clay)E� � E�max/2 Simpson (2000)

consistent with the proposals by Simpson and Hock.Similar strain level has been also reported by Ou et al.(2000) for deep excavation with diaphragm wall inTaipei, Taiwan. It should be pointed out that the axialstrain associated with E � Emax/2 corresponds to a nar-row range from 0.03% to 0.3%. The use of E � Emax/2,therefore, matches well the ground strains of soft claybehind diaphragm wall induced by deep excavation.Note also that the Esec/su value corresponding to theaxial strain of 0.1% ranges from 200 to 400.

Figure 31 shows cross-section of deep excavationwith diaphragm wall for the construction of subwaytunnels in Bangkok by open-cut method. The con-crete diaphragm walls were pre-installed to a depth of39 m, and deep excavation was afterwards carried outin soft and stiff clays down to a depth of 22 m(Tamrakar et al., 2001). Instrumentations were apiezometer, two series of inclinometers set along thewall axis and the borehole located at a horizontal dis-tance of 17 m from the diaphragm wall, and a series ofmarkers for monitoring ground settlement.

Figure 32 shows the stratigraphy with representa-tive profiles of OCR, compression and swell indices,� and , and geostatic stresses and pore pressures.

Figure 33 shows the results of a series of undrainedtriaxial compression tests on undisturbed clay speci-mens retrieved from several depths. Although thesmall strain stiffness values vary with depth, thedegradation curves of the normalized stiffness werealmost similar to each other.

By considering the proposal by Simpson, half of thesmall strain stiffness corresponding to the strain level ofabout 0.1% was employed in the numerical simulationof the full scale behavior using an equivalent-linearelastic approach. In addition, Kovacevic et al. (2003)has performed a non-linear elastic analysis using amodel called the small strain stiffness or SSS model.The results of boundary values predicted using thesetwo kinds of analysis are compared in Figures 34 and 35.The horizontal deformation of the diaphragm wallwas compared at several excavation stages (see Fig.34).From a practical point of view, the result from equiv-alent-linear analysis presented using dash lines wasnot bad, while the deformation profile could be bettercaptured by the non-linear analysis shown in solidlines assuming full moment connection between theroof slab and the diaphragm wall. Similarly, the non-linear analysis using a small-strain stiffness (SSS)model could better capture the ground settlement pro-file than the linear analysis (see Fig.35), suggestingan importance of using proper soil stiffness consider-ing its strain level and stress state dependencies.

3.3 Lateral subgrade reaction of large foundation

Nowadays, the size of foundations is becoming larger and larger, including those of cast-in-place

17

Figure 30. Normalized secant Young’s modulus of normallyconsolidated clays (Temma et al., 2000, 2001).

39m

22.1m

Ground levelWeathered clay

Soft clay

Stiff clay

Roof slab

Retail slab

Concourse slab

Base slab

25m

DW

Center line (CL)

Vibrating piezometerat 18.3m from CLand at 11.6m depth

Inclinometer at 17mdistance from DW

Ground settlement markersInclinometer in DW

Sand

Figure 31. Cross-section of deep excavation with diaphragmwall in Bangkok (Tamrakar et al., 2001).

Figure 32. Soil profiles for deep excavation work inBangkok (Tamrakar et al., 2001).

reinforced-concrete piles, diaphragm wall founda-tions, and well foundations.

When such large foundations are constructed in anidealized linear-elastic ground, the coefficient of sub-grade reaction that is used to compute their displace-ment should be reduced with the increase in the sizeof foundations. However, the actual ground is not linearelastic. Thus, in order to investigate the scale effectson the horizontal subgrade reactions, a series of in-situlateral loading tests was conducted by using a part of well foundation having a diameter of 2.5 m con-structed in a clayey gravel deposit, while changing thewidth of the loading plate between 0.5 and 2.0 m, asschematically shown in Figure 36 (Ogata et al., 1999).

Figure 37 shows the result of triaxial compressiontests on undisturbed specimens retrieved from thesite. Based on this result, the stress-strain relationshipwas modeled in a non-linear elastic form by consider-ing the dependency of initial stiffness, the peakstrength on the confining stress, and the dependencyof tangential stiffness on the shear stress level. Asshown in Figure 38, a 3-D non-linear elastic analysiswith this model could simulate the in-situ lateralloading test result reasonably. It can also be seen thatthe other predictions largely underestimated the sub-grade reaction, which were obtained based on

18

Figure 33. Undrained triaxial compression test results onundisturbed clay specimens (Shibuya et al., 2001).

-5 -4 -3 -2 -1 0 1Horizontal displacements (cm)

10

20

30

40

Dep

th (m

)

Legend:MeasuredPredicted (E'max/2)Predicted (SSS, springs)Predicted (SSS, slabs)

-5 -4 -3 -2 -1 0 1Horizontal displacements (cm)

10

20

30

40

Dep

th(m

)

-5 -4 -3 -2 -1 0 1

10

20

30

40

Dep

th (m

) -5 -4 -3 -2 -1 0 1

10

20

30

40

Dep

th(m

)

(a) 2nd stage of excavation- Roof slab

(b) 3rd stage of excavation- Retail slab

(c) 4th stage of excavation- Concourse slab

(d) 5th stage of excavation- Base slab

Figure 34. Horizontal deformation of diaphragm wall atfour excavation stages (Kovacevic et al., 2003).

0 10 20 30 40 50 60Distance from CL (m)

-4

-3

-2

-1

0

Legend:MeasuredPredicted (E'max/2)Predicted (SSS, springs)Predicted (SSS, slabs)

0 10 20 30 40 50 60Distance from CL (m)

-4

-3

-2

-1

0

0 10 20 30 40 50 60

-4

-3

-2

-1

00 10 20 30 40 50 60

-4

-3

-2

-1

0

(a) 2nd stage of excavation- Roof slab

(b) 3rd stage of excavation- Retail slab

(c) 4th stage of excavation- Concourse slab

(d) 5th stage of excavation- Base slab

Sett

lem

ents

(cm

)Se

ttle

men

ts (c

m)

Figure 35. Ground surface settlement at four excavationstages (Kovacevic et al., 2003).

conventional designs with linear-elastic approach, inwhich the stiffness was converted from the results ofa bore-hole loading test, the SPT N-value and the secantYoung’s modulus in a triaxial compression test definedat a shear stress level equal to half of the peak state.

Figure 39 compares the load-displacement curvesobtained by using loading plates having a width of 0.5and 2.0 m, respectively. The 3-D non-linear elasticanalysis could capture reasonably the scale effectsseen in the observations.

This analysis was applied to predict the behavior ofwell foundations each having a diameter of 1, 2.5 and5 m (Koseki et al., 2001). Three different soil properties

were assigned based on relevant triaxial test results.Figure 40 shows the scale effects on the coefficientsof horizontal subgrade reaction, defined at a displace-ment of 1 cm and normalized with the value at adiameter of 1 m. Although such formulation with thepower n equal to minus three quarters has beenemployed in the conventional design of highwaybridges in Japan (e.g., JRA, 1994), its correction forlarge foundations with less scale effects has beenintroduced by the Japan Highway Public Corporationbased on such results considering the dependencies ofsoil stiffness on strain level and stress states.

19

Loadingplate

φ = 2.5 m

G.L.-5m

G.L.-10m

L

Lining

Jack

Jack

Section

Case2

Case1

Case3

Case1,2:B=0.5mCase3:B=1.0mCase4:B=2.0mB: Loading widthB/L=2(All cases)

B Case4

Loadingplate

Plan

Figure 36. A schematic diagram of in-situ lateral loadingtests (Ogata et al., 1999).

0 5 10 150

500

1000

1500

2000G.L.-10mq=σv – σh

98kPa

49kPa

196kPa

392kPa

σh=490kPa

Dev

iato

r st

ress

, q (

kPa)

Axial strain, εv (%)

0.0 0.5 1.0 1.50

100

200

300

400

500

ExternalLDT

Figure 37. Drained triaxial compression test results onundisturbed gravel specimens (Ogata et al., 1999).

0.0 0.5 1.0 1.5 2.00

5

10

15

20

FEMCs=88.2MN/m3

k=P/δ

k=k0(B/30)-3/4

k0=1/30αEE :EBHLT,E50,ESPT

ESPT=137.3MPa,α=1

E50=68.4MPa,α=4

EBHLT=135.0MPa,α=4

Measured

G.L.-10mB=0.5m,B/L=2

Ave

rage

con

tact

pre

ssur

e, p

h (M

Pa)

Horizontal displacement, δh (cm)

Figure 38. Comparison of in-situ lateral loading testresults with its simulations (Ogata et al., 1999).

0.00 0.01 0.02 0.030

5

10

B : Width of loading plate(m)Cs: Tangential stiffness of joint element at interface between lining and subsoil(MN/m3)

G.L.-5mB/L=2

Measured(B=0.5)Measured(B=0.5)Measured(B=2.0)FEM(B=0.5,Cs=88.2)FEM(B=0.5,Cs=0)FEM(B=2.0,Cs=88.2)FEM(B=2.0,Cs=0)

Ave

rage

con

tact

pre

ssur

e, p

h (M

Pa)

Normalized horizontal displacement, δh/√ (B�L)

Figure 39. Comparison of in-situ lateral loading testresults with results from FE analysis. (Ogata et al., 1999).

3.4 Earth pressure at high seismic loading

Figure 41 shows a retaining wall structure for railwaythat was damaged by the 1995 Hyogoken-nanbuearthquake (Tatsuoka et al., 1996). Before this earth-quake, relatively low soil strength values, such as an internal friction angle of 30 degrees, have beenemployed on the assumption of relatively low designloads in the seismic design of retaining walls in Japan(e.g., JRA, 1987). However, if a well-compactedbackfill material undergoes shearing under planestrain conditions, which is typical boundary condi-tions for retaining walls with a sufficient length in thelongitudinal direction, it can exhibit a peak strengththat may approach to as large as 50 degrees.

After the Hyogoken-nanbu earthquake, it wasattempted in Japan to establish a rational design pro-cedure to evaluate stability of retaining walls at highseismic loading, typically more than 0.5 g. Undersuch a high design seismic load, a rational design wasnot possible without taking advantage of the highpeak strength of the backfill. At the same time, it wasalso required to consider the effects of strain softening

from peak to residual strengths as typically shown inFigure 42 (Koseki et al., 2003).

Figure 43 shows a force equilibrium assumed inthe original Mononobe-Okabe method (Mononobe andMatsuo, 1929; Okabe, 1924), which has been employedin many of the conventional seismic designs in whichseismic earth pressures are estimated for design. Thismethod is an extended version of the Coulomb’s earthpressure theory, where the effects of pseudo-staticseismic forces in both the horizontal and verticaldirections were considered.

20

Prototype behaviorof well foundationwith B=1, 2.5, 5 m

n=-1

n=-1/2

n=-3/4

1 100.1

1

3D FEM SimulationSoftrockGravelClayey GravelB0=1m

k/k0=(B/B0)n

δ=1cm constant

Normalized loading width, B/B0

Nor

mal

ized

hor

izon

tal s

ubgr

ade

reac

tion,

k/k

0

Conventional designfor highways in Japan

δ

10m

BSoftrock Sedimentary

mudstonedeposit

Gravel

Clayeygravel

Crushed sandstone (Fc=2%)

Pleistocenedeposit(Fc=10-20%)

Figure 40. Scale effects on coefficients of horizontal sub-grade reaction (Koseki et al., 2001).

Figure 41. Damage to gravity type retaining wall by the1995 Hyogoken-nambu earthquake (Tatsuoka et al., 1996).

0 2 4 6 80

2

4

6

8

10

φres = 45.4°

φpeak = 51.7°

Direction of σ1measured frombedding plane

δ = 90°

Toyoura sand, σ3 = 9.8 kPa

Case 5 (eo=0.644)

Prin

cipa

l str

ess

ratio

, R =

σ1/

σ 3

Axial strain, ε1 (%)

Figure 42. Drained plane strain compression test results ondense sand (Koseki et al., 2003).

It should be noted that, in this method, the mobi-lized strength of backfill along the potential failureplane (or shear band) is assumed to be constant anddistributed uniformly.

Figure 44a shows a relationship between the coef-ficient of active earth pressure and the horizontalseismic coefficient. When the original Mononobe-Okabe method is applied with a relatively low �value, the coefficient of active earth pressurebecomes extremely large. As shown in Figure 44b, italso induces unrealistically small value of �, definedas the angle between the shear band and the horizontaldirection.

On the other hand, when considering the strainsoftening behavior of well-compacted backfill asmentioned before, the use of the original Mononobe-Okabe method with a high � value corresponding to thepeak strength is obviously less conservative. Therefore,a modified version of the Mononobe-Okabe methodhas been developed and adopted in some designcodes in Japan. In this modified version, the locationof shear band in the backfill is determined by usingthe peak strength. After the formation of the shearband, the strength mobilized on the shear band willdrop from the peak to the residual state, while theother region will remain to potentially mobilize thepeak strength (Koseki et al., 1998).

The modified version can yield reasonable valuesof the coefficient of active earth pressure and theangle �. A typical example is shown in this figurewith the peak and residual � values set equal to 50and 35 degrees, respectively. Referring to the relevantlaboratory test results, the peak and residual � valuesto be used in the design of railway retaining walls inJapan (RTRI, 1997 and 1999) are assigned as shownin Table 3. Thus, proper use of soil strength consider-ing strain softening behavior from peak to residualstates and associated shear band formation has beenimplemented in practice.

Since the modified version yields a step-wise changein the coefficient of active earth pressure, it was furthersimplified by approximating it with a linear functionas shown in Figure 45 and adopted in the design codeof highway bridge abutments in Japan (JRA, 2002).

3.5 Seismic stability of fill dam

As is the case with retaining walls, a relatively lowsoil strength has been used in the conventional seis-mic design of fill dams in Japan. In order to urge damconstruction projects in a cost-effective manner, it isrequired to establish a rational design procedure withwhich the earthquake-induced displacement of filldams may be properly evaluated. In this section, amodified Newmark’s sliding block method consideringthe strain-softening properties of coarse materialsalong shear band is introduced.

The rock material used for constructing rockfilldam is coarse. In order to investigate the shear banding

21

Retainingwall

Backfillsoil

Failure plane (or zone)

kvW

kvWkhW

khWWR

Pa

Pa

WR

H

L

α

δ

β

φψ

θ

Force polygonfor soil wedge

Figure 43. Force equilibrium assumed in Mononobe-Okabe method (modified from Koseki et al., 1998).

Modified MO (50°/35°)

MO (50°)

MO (50°)

MO (35°)

MO (35°)

1.0

0.8

0.6

0.4

0.2

0.0

60

40

20

00.0 0.2 0.4 0.6 0.8 1.0

kh

ψ (d

eg)

Coe

ffici

ent o

f act

ive

eart

hpr

essu

re, K

EA

(φpeak = 50, φres = 35, δ = 0)

(a)

(b)

Modified MO (50°/35°)

Figure 44. Comparison of original and modifiedMononobe-Okabe methods (RTRI, 1999).

Table 3. Peak and residual strengths assigned for modifiedMononobe-Okabe method (RTRI, 1999).

�peak �res

Well-graded sand 55° 40°Sand/Gravel 50° 35°Poorly-graded sand 45° 30°Clay 45° 45°

properties of such coarse geomaterials, a series oflarge scale plane compression tests was conducted byOkuyama et al. (2003) on a variety of samples havingdifferent grading curves. Figure 46 shows a typicalformation of shear band, obtained for an Andesite-originsample with a mean diameter of 2.5 mm. By analyzingsuch image data, the shear displacement along shearband was evaluated. In this case, the thickness of theshear band was about 15 mm, and a clear strain-soft-ening behavior was observed as shown in this stress-strain relationship.

Figure 47 shows a summary for the tested sampleson the normalized relationship between the post-peak

drop of the principal stress ratio and the increment of shear displacement along the shear band from thepeak state. At the peak and residual states, the norma-lized principal stress ratios are defined to be unity andzero, respectively. By normalizing the increment ofshear displacement along the shear band with themean diameter powered by 0.66, rather a unique rela-tionship could be obtained among different testresults. A trial computation of earthquake-induceddisplacement of a rockfill dam was conducted usingthis normalized relationship.

Figure 48 shows a cross-section of a rockfill damhaving a height of 100 m that was analyzed byOkuyama et al. (2003). An input earthquake motionhaving a maximum amplitude of about 0.5 g wasemployed for its earthquake response analysis. Apseudo-static stability analysis was conducted using thedynamic response. Since the computed factor of safetywas always larger than unity, the dynamic response wasincreased by a factor of 1.7. As a result, when the largestpeak strengths of each material are used in the stabilityanalysis, the critical failure plane to yield a factor ofsafety equal to unity was obtained as shown in Fig.48.

By assuming that strain softening takes placealong the critical failure plane, cumulative shear dis-placements under four different peak strength condi-tions corresponding to different degrees of compactionwere computed based on the Newmark’s sliding blockmethod, which was modified to accommodate the

22

57cm

us : shear disp.along shear band

Figure 46. Shear band observed in large-scale plane straincompression test (Okuyama et al., 2003).

Figure 47. A summary of strain softening properties ofwell-graded materials (Okuyama et al., 2003).

Figure 48. Dam model (Okuyama et al., 2003)

0 0.5 10

1

2modified

M–O

kh

KEA

δ

Present

Linear function

Figure 45. Simplification of modified Mononobe-Okabemethod (JRA, 2002).

strain softening behavior. It was also assumed that theresidual strength of each material is constant irre-spective of the different peak strengths, and the strainsoftening property was assumed to follow the nor-malized relationship as mentioned before.

As shown in Figure 49, when the largest peakstrengths corresponding to a case with heavy com-paction were used, the computed shear displacementalong the failure plane was 27 mm, and the mobilizedshear resistance did not drop down to the residualstate. On the other hand, when the mobilized shearresistance was assumed to be equal to the residualstate from the beginning, as is the case with the con-ventional approach, the shear displacement accumu-lated up to 203 mm. Such a difference suggests animportance of considering the strain softening behav-ior that depends on the degree of compaction and theparticle size.

4 CONCLUDING REMARKS

The contents of Part I: Recent developments in control/measurement/data acquisition can be summa-rized as follows;

Servo-motors for control

i) The use of servo-motor featured with ‘zero’ back-lash and variable speed enables us to achieve full-automation and high-precision of testing, and alsoenhances the scope of testing to be performed(e.g., monotonic/cyclic loadings, elastic stiffnessat small strains to residual strength at largestrains, strain rate/acceleration effects, etc.).

ii) Such servo-motors may be facilitated in variouslaboratory machines with various purposes (e.g.,the control of cell pressure, loading plate, etc.)

Local strain measurement (LSM)

i) Dual-measurement with two independent prox-imity transducers is compatible to mono-gaugemeasurement such as LDT.

ii) The hinge (or target) of clip gauge like LDT (or ofproximity transducer) should be glued on themembrane (or pinned into the sample) in tests onstiff (or soft) geomaterials.

iii) ‘True plane-strain’ test can exclusively be carriedout by maintaining zero strain with LSM.

iv) Stiffness anisotropy at small strains can be inves-tigated in true triaxial apparatus with LSM.

v) The LSM should be employed in hollow cylindertesting, since the effects of end restraint are significant.

vi) Innovative techniques (e.g., LAT, PIV) are nowavailable so as to observe strain localization ofnot only a rectangular specimen but also a cylin-drical specimen in shape.

Elastic wave velocity measurement

i) Bender element when designated to generate S-wave is suitable for measuring quasi-elastic shearmodulus of relatively small sample of soft soils.

ii) Determination of correct travel time is still anunsolved issue involved in bender test. An inter-national round-robin test as to the measurementof elastic shear wave by benders is now underwayto provide an insight into it.

iii) An piezo-ceramic vibrator may be mounted ontop cap to generate P-S waves, and the velocitiesmay be measured on the lateral surface of thespecimen by using accelerometers. This system issuitable for large sample of geomaterials.

iv) Some of important characteristics such as structure,anisotropy, sample disturbance, etc. may be under-stood by measuring quasi-elastic soil properties.

Friction on soil/metal interface

i) The effects of interface friction are significant evenin oedometer test on soft clay using a standardspecimen of 2 cm in height. The conventionalmeasurement of vertical load grossly overesti-mates the stress at yielding, which in turn bringsabout a considerable overestimate of OCR value.

ii) Lubricated ends are needed to achieve reasonablestress/strain uniformities in true triaxial test usinga rectangular specimen.

The contents of Part II: application in engineeringpractice may suggest the following;

Engineering needs for deformation/strength testingof geomaterialsThere are a variety of engineering needs for applica-tion of deformation and strength test results, such as

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Figure 49. Computed shear displacement along criticalfailure plane (Okuyama et al., 2003)

excavation works in urban areas, design of large-scalestructures or foundations, and seismic design againstlarge earthquakes. In order to meet these needs, con-ventional approaches based on stability analysis usingconservative soil strength, or deformation analysisusing conservative soil stiffness may not work.

Use of proper soil stiffnessThe use of proper soil stiffness considering its strainlevel dependency and stress state dependency in thedeformation analysis is vitally important. If the strainlevel can be predicted in advance, a linear elasticanalysis using a well-chosen stiffness would be ofpractical value. If not, however, non-linear elastic orelasto-plastic approaches considering these factorswould be more appropriate.

Use of proper soil strengthIn addition, use of proper soil strength consideringstrain softening from peak to residual states, accom-panied by shear banding or strain localization, isrequired in establishing rational design proceduresagainst large earthquake loads.

It should be noted that, relevant laboratory tests incombination with proper in-situ tests can reveal allthese important soil properties mentioned in the above.

ACKNOWLEDGEMENTS

A lot of people as shown below kindly supported us inpreparing this paper; Prof. Tatsuoka, F. (Univ. ofTokyo), Prof. Mitachi, T. (Hokkaido Univ.), Prof.Miura, S. (Hokkaido Univ.), Dr. Yamashita, S.(Kitami Institute of Technology), Mr. Sato, T. (IIS,Univ. of Tokyo), Dr. Hayano, K. (Port and AirportResearch Institute), Dr. Fukuda, F. (Hokkaido Univ.),Dr. Li, D.J. (Hokkaido Univ.), Dr. AnhDan, L.Q.(Univ. of Notre Dam) and Dr. HongNam, N. andMr. Maqbool, S. (IIS, Univ. of Tokyo).

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