1984_jardine et al

5/12/2018 1984_Jardine et al - slidepdf.com

http://slidepdf.com/reader/full/1984jardine-et-al 1/18

J A R D I N E ,R . J . , S Y M E S ,M. J . & BU RLAN D, . B . (1 9 8 4 ) . G io tech n iq u e 3 4 , No . 3 , 3 2 3 -34 0

The m easurem ent of soil stiffness in the

triaxial apparatus

R. J. JARDINE.* M. J. SYMES* and J. B. BURLAND*

This Paper describes a simple technique for accurately

measuring the mean local axial strains of triaxial sam-

ples over a central gauge length. The technique makes

use of an axial displacement gauge which is a develop-

ment of one devised by Burland & Symes (1982)

which makes use of electrolytic levels. The device can

resolve to less than 1 cm over a range of 15 mm, is

simple to mount on the specimen and is not damaged

when the sample is taken to failure. The results of

undrained triaxial tests are presented for a wide spec-

trum of soil types ranging from sands through intact,

reconstituted and remoulded low plasticity till, undis-

turbed London clay to intact unweathered chalk. The

test results show that conventional external measure-

ments of displacement contain errors which are fre-

quently so large that their use in the determination of

soil stiffness at working levels of stress is invalid. The

errors mainly result from tilting of the sample, bedding

at the end platens and the effects of compliance in the

apparatus. Although much more experimental work is

required before general conclusions can be drawn

about the small strain behaviour of soils the results

presented lead to some important observations on theundrained stiffness, linearity and yielding behaviour of

soils at small strains.

Cet article d&it une technique t&s simple pour mes-

urer de faGon prCcise les dkformations locales moyen-

nes d’tchantillons triaxiaux sur une jauge centrale. La

technique emploie une jauge de d&placement axial qui

reprksente une amelioration de celle invent&e par

Burland et Symes (1982) et qui utilise des niveaux

tlectrolytiques. L’appareil est sensible 2 moins de

1 pm sur une longueur de 15 mm. I1 est facile B

monter s u r l’tchantillon et reste intact m&me si

I’Cchantillon est dCtruit. Les rCsultats des tests triax-

iaux non-drain& sont prCsentCs pour une large gamme

de types de sol, commenqant par des sables, suivis de

moraines intactes de faible plasticitt reconstitukes et

remaniCes et de l’argile de Londres intacte jusqu’8 la

craie intacte non-altCrte par les intempkries. Les

rtsultats des tests montrent que les mesures conven-

tionnelles du d&placement cOrnportent des erreurs qui

sont souvent si considerables que les mesures sont ma1

adapt&es pour la d&termination de la rigidit du sol g

des niveaux operationnels de la contrainte. Les erreurs

proviennent principalement du basculement de

l’Cchantillon, de la liaison imparfaite au niveau des

plateaux terminaux et des effects du d&placement de

l’appareil.

Discussion on this Paper closes on 1 January 1985.

For further details see inside back cover.

* Imperial College of Science and Technology.

Bien que beaucoup de travail expCrimenta1

suppltmentaire soit nCcessaire afin de pouvoir tirer

des conclusions g&&ales au sujet du comportement

des sols sous des d&formations mineures, les r&hats

p&en& fournillent des observations importantes

concernant la rigidit dans 1’Ctat non-drain&, la

IinearitC et I’Ccoulement des sols sous des

d&formations mineures.

NOTATION

C

C”

El

F

KOL

LoLI

P’PO’

RI3

T

6

compliance of

(A,_+ 4&F

loading system =

undrained shear strength

undrained stiffness E,co.ol,-E,t 0.01%

strain, etc.

deviator force on sample

u~‘/u,’ at rest

E,(,,.l,/E,(o.o,, an index of linearity

length of sample

liquidity index

(a,’ + 2a,‘)/3 the mean effective stress

p’ at the start of the undrained test

relative density

(0,, - &&(& + &) tilt ratio

sample rotation

A, A,, AT, A,,, As, ARB, A,,, components of

measured deflexions (see Fig. 1)

corrected overall axial strain

larger local axial strain

smaller local axial strain

mean local axial strain

larger incremental rotation of electrolevel

(see Fig. 2(c))

smaller incremental rotation of electrolevel

(see Fig. 2(c))

vertical effective stresses

radial effective stress

INTRODUCTION

Accurate determination of soil stiffness is

difficult to achieve in routine laboratory testing.

Conventionally, the determination of the axial

stiffness of a triaxial sample is based on external

measurements of displacement which include a

number of extraneous movements. For example,the true soil strains developed in triaxial tests

can be masked by deflexions which originate in

the compliances of the loading system and load

measuring system. Such equipment compliance

323



324 JARDI NE, SYMFS AND BURLAND

errors add to a variety of sample bedding effects

to give a poor definition of the stress-strain

behaviour of the material under test, particularly

over the small strain range. Most triaxial tests

therefore tend to give apparent soil stiffnesses

far lower than those inferred from field be-

haviour.

The importance of such errors has long been

recognized and many diverse techniques have

been employed in attempts to improve strain

measurements. One solution has been to meas-

ure relative displacement between two reference

footings over a central length of a sample using

displacement transducers (e.g. Yuen, Lo, Palmer

& Leonards, 1978; Daramola, 1978; Brown,

Austin & Overy, 1980; Costa Filho, 1980).

Strictly these techniques are suitable only for

very small strain levels, since bulging of the

sample will cause the footings to rotate in later

stages of the test. Although important results

have been obtained with such techniques, they

are cumbersome and can suffer from jamming

and damage at large strains.

X-ray and optical methods have also been

used to follow reference points within the sam-

ple or on its membrane (Roscoe, Schofield &

Thurairajah, 1963; Arthur & Phillips, 1975).

However, the accuracy of these methods is

limited.

The resonant column apparatus offers a differ-

ent approach for the determination of the

dynamic stiffness of soils. The technique in-

volves the application of periodic small strain

perturbations to a sample as described by

Richart, Woods & Hall (1970). However, the

technique does not provide direct measurements

of the elemental behaviour of the soil under test,

since the states of stress and strain vary continu-

ously both with time and in their distributions

within the sample.

In summary present methods of soil strain

measurement have a number of serious limita-

tions. There is an urgent need for a simple but

precise method for the routine measurement of

the stress-strain behaviour of soil specimens

under controlled stress or strain paths, particu-

larly where the soil exhibits high stiffness at

small strains.

In this Paper a simple technique for accurately

measuring the mean local axial strains during

triaxial testing is described. Local axial strains

are taken as those developing over a central

gauge length of the sample. The origins of some

of the more significant strain measurement er-rors which develop in standard testing are ex-

amined and their magnitudes assessed using the

new techniques. Results of experiments per-

formed on a wide range of material are pre-

sented, and it is shown that, as expected, routine

tests which employ external measurements of

strain lead to apparent soil stiffnesses which are

much too low. For the purposes of this Paper

only undrained behaviour is considered, since

the no-volume change condition obviates the

need to measure radial strains. However, in tests

designed to investigate more general effective

stress behaviour the local measurement of radial

and axial strains is equally important. Symes &

Burland (1984) describe the use of proximity

transducers for radial strain determination and

Maswoswe (1984) describes the use of a high

accuracy, submersible, linear variable differen-

tial transformer (LVDT) for the same purpose

on 38 mm dia. triaxial samples.

AXIAL STRAIN ERRORS IN TRIAXIAL TESTS

In a conventional triaxial test there are several

sources of movement that develop during shear

testing which may give rise to an overestimate of

the axial strain. One such source is the com-

pliance of the loading system itself. For exam-

ple, the construction of a Bishop & Wesley

(1975) cell is such that the lower reference point

for the vertical displacement transducer is at-

tached to the ram while the upper reference

point is located on top of the cell, so that small

but nevertheless significant deflexions accumu-

late from the straining of the rolling Bellofram

diaphragms. For present purposes the sum of

such loading system deflexions will be termed

A,,. An internal load cell will also produce a

significant deflexion, which is termed A,.

The more important sources of error are il-

lustrated in Fig. 1. Some of the deflexions shown

in this figure may be quantified by careful calib-

ration, but large unaccountable errors remain

due to

(a) the difficulty of trimming a sample so that

the end faces are perpendicular to the verti-

cal axis of symmetry

(b) play in the connection between the load cell

and the sample top cap, and

(c) the inevitable ‘bedding down’ at the ends of

the sample, due to local surface ir-

regularities or voids.

In the testing of rock samples the importance

of such errors has long been recognized, and the

careful grinding of sample ends combined with

the use of ground cylindrical seated platens is

commonly specified (e.g. Vogler & Kovari,1978). The observation that many rocks fail in a

brittle fashion at axial strains of O-l% or less

has led to the specification of flatness limits of

+O.Ol mm and parallelism requirements of



MEASUREMENT OF SOIL STIFFNESS 325

around 3 minutes of arc for high quality sample

preparation. The preparation techniques em-

ployed for rock testing are unsuitable for most

soils, and it is probably not possible to approach

the same standards of sample regularity.

Recent work has demonstrated the rathersurprising finding that soils can be equally as

brittle as rocks and that an understanding of

their behaviour at levels of shear strain below

0.05% is very important (see Gens, 1982;

Simpson, O’Riordan & Croft, 1979). Indeed, it

is shown in this Paper that K. normally consoli-

dated clays may reach peak strength in the

triaxial apparatus at axial strains as low as

0.1%. Moreover, even when the behaviour is

not brittle, the strains prior to yield are usually

very small.

Measures can be taken to reduce the errorsimplicit in external strain measurement. The

results obtained from tests carried out on soil

which has been an&tropically consolidated to a

high level of mean effective stress suggest that

these procedures considerably reduce sample

bedding and tilting errors (see Gens, 1982). The

SHANSEP methods of testing soft clays can also

be expected to lead to significant improvements

in strain measurement. However, where swelling

stages are included in such tests tilting and other

errors may redevelop (Daramola, 1978).

Moreover, it is often desirable to obtain accu-rate strain measurements in tests which have not

involved anisotropic consolidation.

A more satisfactory approach is to make use

of local instrumentation which can be attached

to a central gauge length of a sample. Symes &

Burland (1984) have given a description of the

design of instruments which employ electrolytic

levels to measure combined horizontal shear

strain and axial strain in a hollow cylinder ap-

paratus. The same principles have been adapted

to develop a vertical displacement measuring

system for use in a 100 mm dia. triaxial ap-paratus (see Burland & Symes, 1982). This

Paper describes a further development and im-

provement of the earier devices which enables

mean axial strains to be determined to within a

range of +0.002% in triaxial stress path cells

designed for the testing of 38 mm dia. samples.

DESCRIBIION OF THE ELECIROLEVEL

GAUGES

Cooke & Price (1974) describe the use of

electrolytic liquid levels for the local measure-

ments of ground strains around test piles. Their

reliability, simplicity and accuracy make these

transducers attractive in a wide variety of appli-

cations, and by mounting the capsules in simple

mechanisms it is possible to develop a range of

reorientation

Samplecompression

Fig . 1. Sources o f em x in external s train measure-

me nts (+, is the larger of the two shins;

FL= (ELI + E&3

devices to measure axial, radial and shear strainsin laboratory tests (Symes & Burland, 1984).

The liquid level transducers consist of an

electrolyte sealed in a glass capsule. In the simp-

lest devices three coplanar electrodes protrude

into the capsule and are partially immersed in

the electrolyte. The impedance between the cen-

tral electrode and the outer ones varies as the

capsule is tilted. A variety of levels with differ-

ent sensitivities are commercially available.

The transducers employed in the triaxial

strain measurements were supplied by IF0 In-

ternational Ltd and have a working range of*lo”. The system was excited using a 5 V a.c.

power supply of 4 kHz frequency. The gains

were adjusted to give a *3 V full scale output

which was monitored to *O-l mV with typical

scatters of *0.2 mV. The levels are sensitive to

temperature and vibration and should be oper-

ated in still conditions which are temperature

controlled to within *3”C. Under such condi-

tions the gauges can be stable over periods of

weeks.

The principles of the new axial strain measur-

ing systems are essentially similar to those of the

earlier devices in that a hinged arrangement

converts displacements between two footings

mounted on the sample into a rotation of the

capsule, as shown in Fig. 2(a).



326 JARDINE, SYMES AND BURLAND

Stanless steel tubing

Hinges A and B(bl

Hinge C

IO

Fig. 2. (a) Conversion of axfal strain to rotation of

electrolevel capsule; (b) constructfon of electrolevel

gauges; (c) effects of tilting

The major difference between the instruments

described in this Paper and the earlier designs

lies in the geometrical configuration which per-

mits their use on 38 mm dia. samples. Fig. 2(b)

shows the construction of the new devices. In

addition to geometrical changes, the hingemechanisms have been improved by replacing

the original brass pivots with polylluorotet-

raethylene (PFTE) and by simplifying the con-

struction of the hinges themselves. The capsule

which protects the electrolytic level from the

action of pressure and water is constructed from

stainless steel, as are the tubular arms BC and

AC. The gauges are fully submersible and have

been tested at pressures of up to 1500 kPa. The

electrolevels are mounted in diametrically oppo-

site pairs on a sample using a rapidly curing

contact adhesive which bonds the brass footingsto the membrane. The gauges rely on the radial

effective stresses to anchor the footings to the

sample under test.

It should be noted that if the sample tilts

when loaded the output from each gauge is

made up of a strain component and a tilt com-

ponent, as shown in Fig. 2(c). Provided the

sample is homogeneous the mean axial strain is

given by half the sum of the outputs of a pair of

two diametrically opposed gauges and the tilt is

given by half the difference of the outputs. The

ability to detect sample tilt is a valuable featureof the gauge.

Jardine & Brooks (1984) have carried out

simultaneous measurements of surface strains

for chalk specimens using foil strain gauges

bonded to the sample and electrolevel gauges

mounted on the membrane. The experiments

showed that, over the considered strain range of

0.15 %, any relative movement between the

membrane and the sample could be neglected.

Moreover, Gens (1982) used an optical tech-

nique to demonstrate that the membrane only

moves in relation to the sample when largestrains are developed.

The resolution and range of the gauge have

been determined by a two-part procedure.

Firstly, routine calibrations were performed over

a displacement range of 15 mm by mounting two

opposing gauges on a micrometer winding frame

graduated to 0.01 mm. A typical displacement

voltage characteristic is presented in Fig. 3. A

third order polynomial regression analysis can

then be used to model the characteristic (with a

typical correlation coefficient of 0.999 99) within

the limits shown. To determine the resolution a

second stage of calibration was carried out by

mounting a high resolution, small travel, LVDT

on the central axis of the winding frame so that

the changes in output could be determined for



Table 1.

Name Material

North Sea clay

North Sea clay

North Sea clav

North Sea cla;

North Sea clay

North Sea clay

North Sea clay

North Sea clay

RMl North Sea clay

RM2 North Sea clay

HRSl Ham river sand

HRS2 Ham river sand

LCl London clay

LC2 London clay

Cl Upper Chalk 1

c2 Upper Chalk Intact


Rl

R1.4

R2

R4

R8

11

I2

13

Reconstituted

Reconstituted

Reconstituted

Reconstituted

Reconstituted

Intact

Intact

Intact

Remoulded

LI=O.18

Remoulded

LI=O.O9

Pluviated

R, = 0.149

Pluviated

R, = 0.848

intact

intact

intact

types. Unbonded low plasticity clays are materi-

als which may be expected to demonstrate many

of the features incorporated into critical state

descriptions of soil behaviour (Schofield &

Wroth, 1968) where stiffness would be princi-

pally conditioned by the initial stresses and pre-

consolidation stress level. The London clay sam-

ples were considered to be typical of weathered

lower London clay, which is a weakly bonded

material that can develop a reorientated fabric

on thin shear bands after failure, and thus, when

tested, often displays a number of characteristics

which diverge from the predictions of critical

state soil models (see Lupini, Skinner & Vau-

ghan, 1981). The Ham river sand is a uniformly

graded, angular sand in which stiffness could be

expected to be mainly related to its mode of

deposition, initial stress and density. In contrast

the intact, unfissured, chalk used for tests Cl

and C2 was a strongly cemented material in

which bond type and strength might be expected

to dominate the stress-strain behaviour.

EXPERIMENTAL RESULTS

Reconstituted samples of low plasticity clay

The effective stress paths followed by the

reconstituted samples Rl, R1.4, R2, R4 and R8

Sample Consolidation

preparation details

K,, (see Fig. 6)

K, (see Fig. 6)

K, (see Fig. 6)

K, (see Fig. 6)

K,, (see Fig. 6)

Lightly overconsolidated

in situ, then sampled

As above, reconsolidated

‘field stresses’

Heavily overconsolidated

in field. Swelled back

after sampling

Not consolidated

Not consolidated

Isotropically 4

consolidated

Isotropically 1

consolidated

Overconsolidated in situ -

then sampledAs above -

Cut from quarry face -

isotropically consolidated

As above -

OCR PObefore (initial):

shearing kPa

1.0

1.4

2.05

3.73

7.4

-1.1

267

206

158

106

65

474

El.1

>50

-

508

46

10

43

132

404

226

199

345

363

during undrained shear are presented in Fig. 6,

together with the deduced contours of de-

veloped axial strain (the strain shown in this

figure is the average strain from diametrically

opposite pairs of electrolevels). From Fig. 6 two

important observations can be made.

First, the effective stress paths followed by the

tests were initially both nearly vertical and

straight. However, in each case there was a

certain stress level where the paths sharply de-

viated and then travelled on to failure. The

latter portions of the effective stress paths were

taken as representing the post-yield portion of

each test. In every test yield was approached

after the development of only very small strains.

Test Rl reached peak deviator stress at an axial

strain of O.l%, and tests R1.4, R2, R4 and R8

all demonstrated sharp changes in stress path

direction at axial strains of less than 0.2%. It is

important to appreciate that for many practical

problems the working stresses will lie on the

vertical portions of the stress paths where the

strains are very small.

Second, the stress path for the normally con-

solidated sample Rl shows brittle behaviour

with a marked reduction in strength beyond

0.1% strain. Tests carried out by Gens (1980)

on another low plasticity clay showed similar



33 0 JARDI NE, SYMES AND BURLAND

1 2 5 -

( - - c o n t o u r s o f a x i a l S t r a i n%I

l o o -

1 5 0 2 0 0 2 5 0 3 0 0

( I T , ' + 3 ' ) / 2 , Pa

-251

Fig. 6. Nor th Sea day str ess paths for tests Rl, R2, R4. R8

behaviour. Small loops are apparent in the stress

paths for samples R1.4 and R2 close to failure.

If, instead of measuring pore pressures at the

base, a central piezometer probe had been used

(Hight, 1983) it is probable that these loops

would not have been observed.

Figure 7(a) shows the stress-strain charac-

teristics of the reconstituted samples of low plas-

ticity clay. Again it can be seen that the strains

over the initial range of stresses are exceedingly

small. In order to allow a meaningful analysis of

the initial stiff zone the strains have been replot-

ted to a logarithmic scale in Fig. 7(b). The latter

figure shows a remarkably consistent trend, with

the strain required to achieve peak strength

steadily increasing with OCR. The scatter in the

early stages of test R2 was caused by vibrations

from a nearby motor and demonstrates that the

new gauges perform best in a still environment.

In Fig. 7(c) the stiffness characteristics of the

samples are examined by plotting the nor-

malized secant modulus E J c , up to and includ-

ing peak deviator using the same strain axes.

The use of the secant modulus E , is not meant

to imply that the soil behaviour is strictly elastic,

and has merely been taken as a convenient

measure of soil stiffness.It is apparent that the initial stiffnesses ob-

tained using local instrumentation are very much

higher than the values commonly measured in

routine soil triaxial testing. The stress-strain be-

haviour is non-linear and at strain levels above

1.0% the ratio of E,/c, can be seen to fall to

more familiar levels. While the existence of high

initial stiffnesses has been postulated to explain

anomalies between observed and predicted field

behaviour (see Simpson et al., 1979) the results

given in Figs 6 and 7 demonstrate that labora-

tory tests are capable of revealing both the high

stiffness and the detailed nature of pre-yield

behaviour. The characteristic variation of stiff-

ness with strain is similar in all tests, but the

results from tests R1.4 and R2 demonstrate that

lightly overconsolidated clay shows a particularly

high normalized stiffness at low strain. The data

from tests Rl, R1.4, R2, R4 and R8 are sum-marized in Table 2. The column giving the times

to reach El = 0.1% strain gives a measure of

the differences between local and external strain

rates. In each case the local rate slowly in-

creased until, at large strains, it equalled 4.5%

per day. As discussed later, normal anisotropicconsolidation reduced many of the potential er-

rors in external strain measurement.

Intact samples of tow plasticity clay

The stress paths for tests 11, 12 and I3 are

given in Fig. 8(a) where the initial, post-sampling, effective mean stress for sample I1 is

represented by point A and the reconsolidation

effective stress path for sample 12 is given by the

broken line BC. The initial applied effective



MEASUREMEN T OF SOIL STIFFNESS 331

stress for sample 13 is represented by point D.

T h e axial strains which developed during shear

are indicated in the same figure, and details

of the sample’s initial conditions are given in

Table 1.

The observed errors in conventional overallmeasurements of strain are discussed in a later

i a$

section. However, it is of interest to compare the R4

externally and locally measured strains for test asa

11 since this test is typical of routine high quality 0 1 2 3 4

testing of intact samples. The comparison is(a)

shown in Fig. 8(b). It is apparent that the strains

deduced from external measurements of deflex-

ion, even though corrected for load cell and

apparatus compliance, give much larger strains

than the values measured locally on the sample.

Indeed the conventional measurements com-

pletely mask the initial stiff behaviour of theintact material. These errors are discussed more

fully later.

Referring again to Fig. 8(a), as was the case

for the reconstituted tests, all three intact sam-

ples demonstrate yield with a sharp deviation in

the effective stress path. The post-yield effective

stress path for the anisotropically consolidated

sample 12 differs markedly from that for the

comparable reconstituted sample Rl (see Fig. 6)

whereas the path followed by the heavily over-

consolidated sample 13 is similar to those fol-

lowed by R4 and R8. Ageing, bonding, sampl-ing, or macrofabric features could all be respon-

sible for such differences. With regard to the

strains, samples I2 and 13, like the reconstituted

samples, yielded at axial strains of 0.1% to

0.2%. In contrast, sample 11, which was tested

unconsolidated undrained, showed a less stiff

behaviour between the attainment of 0.1%

axial strain and the peak deviator condition.

The detailed stress-strain characteristics for

tests 11,12 and 13 are shown in Fig. 9 as plots of

(or’-u3’)/2 and EJc, against strain on semi-

logarithmic axes. A comparison between thestress-strain response of samples 11 and 12

shows that reconsolidation of 12 produced only a

slight change in stiffness. The values of EJc, for

11 and 12 fall within the limits of the stiffnesses

found from the reconstituted tests (see Fig.

7(b)). The EJc, curve for sample I3 can be seen

to lie below the band of stiffness values deter-

mined for 8 2 OCR 3 1.0 with reconstituted ma-

terial, but within a range that might be extrapo-

lated for highly overconsolidated samples.

Parameters from tests 11, 12 and 13 are given in

Table 2.The stress paths for the two experiments on

the remoulded samples RMl and RM2 are

shown in Fig. 8(a), as are the strain levels at

various stages of the tests. Although the samples

(‘4

3 2 0 0

F i g . 7. Tests Rl , R1.4, R2 , R4 and R8: (a)

stress-sti dat a; (b) stie ssstraia dat a; (c) StsIw ss

character is t ics

had not been preloaded, the shapes of the stress

paths and the pattern of strains are similar to

those given by the overconsolidated samples ofintact and reconstituted clay. The detailed

stress-strain and stiffness plots are given in Fig.

9 and may be seen to fall in the range extrapo-

lated for overconsolidated intact or reconsti-

tuted samples. Summary parameters for tests

RMl and RM2 are given in Table 2.

Tests on London clay, Ham river sand and

chalk

The intial conditions for the tests LCl and

LC2 (London clay), HRSl and HRS2 (Ham

river sand) and the two chalk tests Cl and C2are given in Table 1.

The stress paths followed during tests HRSl,

HRS2 and Cl and C2 are given in Fig. 10(a),

which also shows the strain levels at appropriate



332 JARLXNE, SYMES AND BURLAND

Table 2. summary f test results

T e s t c, :

k P a

E, @ 0.01 %:

k P a5 @J o.01 %

c,

3 @O.Ol% I ( “ . I ) t :

m in

R l 1 2 2 2 .22 x lo5 1 8 2 0 8 3 0 0 . 1 8 5 3 8R 1 . 4 1 2 2 4 .50 x lo5 3 6 9 0 2 1 8 0 0 . 2 7 0 4 9

R 2 1 0 8 3 5 9 x lo5 3 3 2 0 2 2 7 0 0 . 3 5 3 5 2

R 4 9 4 2 .26 x 1 0 ’ 2 4 0 0 2 1 3 0 0 . 3 8 6 6 5

R 8 6 7 1 .13x l o5 1690 1 7 4 0 0 . 4 0 7 1 0 5

1 1 2 5 5 5 .10x l o5 2000 1 0 8 0 0 . 3 3 3 1 0 0

I 2 2 7 5 7 .43 x lo5 2 7 0 0 1 4 6 0 0 . 1 8 7 5 9

1 3 1 7 3 9.4 x lo4 5 4 0 2 0 3 0 0 . 3 4 0 1 2 6

R M l 3 9 . 5 2.6 x lo4 6 6 0 2 4 3 0 0 . 3 3 1 1 5 6

R M 2 8 5 . 0 9.3 x lo4 1 0 9 0 2 1 8 0 0 . 2 7 8 7 2

H R S l 1 0 8 5 2 . 9 x 1 0 ’ 2 7 0 2 2 0 0 0 . 5 1 8 9 0

H R S 2 1 1 4 2 4.9 x lo5 4 3 0 1 2 1 0 0 .503 5 9

L C l 1 2 3 1 . 2 4 x l o5 1 0 1 0 5 5 0 0 .371 5 5

L C 2 1 0 0 1 .20 x lo5 1 2 0 0 6 0 0 0 .387 6 5

C l 1 3 5 0 5 .7 x l o6 4 2 2 0 1 5 5 0 0 0 .723* 510

c2 1 6 0 0 4.0 x lo6 2 5 0 0 1 1 0 0 0 0 .854* 587

* S i n c e b o t h s a m p l e s fa i l e d a t + < O . O l L w a s t a k e n h e r e a s E , ~ , . ,, ,I E , ~ O . O O , ~ .

7 r ( c. r ) c or r e s p o n d s t o t h e t i m e t a k e n t o d e v e l o p E , = O . l % i n e a c h t e s t . F o r a r a t e of s t r a i n o f

4 . 5 % p e r d a y t c O . i )w o u l d b e 3 2 m i n .

i n t e r v a l s . T h e s a n d e x p e r im e n t s showed a stiff

response to loading over the initial portions of

each test but the samples rapidly lost stiffness as

the stress paths approached the dilatant part of

their state boundary surface. After yield the

stress paths curved to the right and climbed thestate boundary surface until, at large strains,

peak strengths were developed. In both tests

failure was initiated by cavitation of the pore-

water, and neither sample achieved an un-

drained critical state condition.

The stress paths of the chalk tests Cl and C2

are compared in the same figure. The samples

showed stiff behaviour up to brittle failure at

a,’ - 03’ equal to 1331 kPa and 1620 kPa respec-tively. The failure strains for tests Cl and C2

were both around 0.075%. The post-failure

behaviour can be seen to be characterized by a

300-@’ = 30”

(Anal strams mdlcaled in %)

RM 2

60 0

(9’ + n3’)/2. kP a

(3 1

Fig. 8(a). Intact and remoulded stress paths for tests 11, I2, W, RMl and RM2



MEASUREMENT OF SOIL STIFFNESS 33 3

30 0

1Ultlmatec = 255 kPa

__ u __ -

Local measurements IELI

Overall corrected measurements (~2

Comparison of tuIcu calculaled from ~~ and E

100 FL, E /c E/ C ' .

% f&l FL Ir& ,”c

Apparent linear elasrlc modulus 0 005 2353

Eu = 4.8 X 10’ kPa, Eufcu = 188 0.01 2000

0.1 667 17 2

1.0 147 14 0

Fig. 8(b). Str ess-stra in data for test I1

(a l

2400

\\ Only test 12 athned\\

peak devtator at an

\ axial strain below 5%

Awal strain EC %

(b)

Fig. 9. (a) Str ess-stain data for tests 11,12,13, RM l

and R M2, (a) stiffness character istics for tests 11, I2,

13, RM l, RM2 and R2

progressive weake ning with the effective stresses

roughly following unloading paths.

The stress paths for tests LCl and LC 2 are

shown in Fig. 10(b). Both samples showed an

initially stiff response to loading which persisted

up to axial strains of around 0.1% . The stress

paths both deviated to the right after the attain-

ment of 1.0% axial strain u ntil peak strengths

were mobilized at strains of 4.5% and 3.5%

respectively. Both tests showed a steep post-

peak loss of strength, and examina tion of the

samples after testing showed that polished shear

surfaces had formed within the specimens. The

stress-strain and stiffness chara cteristic s for the

tests described in this section are summ arized in

Fig. 11 together with Fig. 12, which summ arizes

the results of all the tests repo rted in this Paper.

The plots demonstrate the following main

points.

(a)

(b)

The chalk samples showed brittle behaviour

with failure occurring at ~~2 0.075% . In

contrast, the London clay and sand samples

failed only after developing large strains.

The cha lk tests Cl and C2 gave the highest

normalized stiffnesses, which equalled thoseof the low plasticity clay at low strains but

exceeded them at strains above 0.0 1% . The

chalk samples also showed the most linear

behaviour.



334

1 6 0 0

1 2 0 0

1

$ 8 OC

a "

I

- g

4 o c

C

J ARDINE, SYMES AND BURLAND

20

m LC 2

%

N,c6 10

50

&y

0.7

K-4

0 . 2

0 1

0 0 7

0 . 0 2 z

0 ~ 0 0 4 0 . 0 1

0 . 0 0 2

1 7 5 200

(0,’ + 03’)/2 k P a

( 4

50

/fA 80

.’ O.

i:

o _ e L C l

04

0 2

i

0 . 1

0 0 5

0 0 2

n / , 1

1OU

‘t2 0

1 5 0

” “

250

(cl’ + 0,‘)/2: k P a

@I

300

Fig. 10. (a) Tests on chalk and Ham river sand: stress paths for HRSl, HRs2, Cl and C2; (b) stress pati fortests LCl and LC2 (axfaf strains: %)



MEASUREMENT OF SOIL STIF’F’NESS 335

3 0 0 .

0 0 1 0 1 1 0 1 0

( b )

Axia l s t ra in q : %

0 . 0 0 1 0 . 0 1 0 . 1 1

Ax , a l S t r a i n L %

WI

F i g . 11. (a) Stressstraio data for tests Cl and C2;

(b) s t res+stmfn data for tests HRSl and HRS2; (c )

stress-strafn data for tests LCl and LC2; (d) st itbws

character ist ics or tests Cl , C2, HRSl , HRS2, LCl

andLC2

5 0 0

4 0 0

3 0 0

" =

' 1UJ

2 0 0

1 0 0

C

O-

O-

O-

O- !

O-

O-I.01

Fig . 12. Summary of normafhd s _ e S

( c ) T h e London clay tests showed stiffness

characteristics which were similar to that of

heavily overconsolidated or remoulded, low

plasticity clay.

(d) The normalized stiffness characteristics for

the Ham river sand, experiments HRSl and

HRS2, form a lower bound to all the results,

continuing the trend demonstrated by the

dilatant samples of low plasticity clay in tests

RMl, RM2, 13 and R8.

The test results from all the experiments are

further summarized in Table 2.

INTERPRETATION

In the past most laboratory studies of the

stress-strain characteristics of soils have been

hampered by the errors that are inherent in

conventional triaxial testing, particularly for

overconsolidated soils, and comprehensivestudies of soil stiffness at low strains are rare.

The test programme on the low plasticity clay

provides a body of data which can be used for

evaluating the small strain undrained stress-

strain properties of that material. These proper-

ties may then be compared with the limited

number of results from the tests on the London

clay, the chalk and the Ham river sand in order

to highlight some of the factors influencing soil

stiffness. More detailed discussions of the small

strain behaviour of London clay and Ham river

sand are given by Costa Filho (1980) andDaramola (1978).

It is recognized that much more experimental

work is required using the new techniques be-

fore general conclusions can be drawn.



336 JARDINE, SYMES AND RURLAND

1 2 .

1 0 .

8 . u n c o n s o h d a t e d

Mean a x i a l t r a i n L :%

F i g . 13. Tests on low pldkfty clay: compar ison of

internal and external corrected strain measurements

Nevertheiess, the results obtained are suffi-

ciently encouraging to warrant a preliminary

discussion since a number of important observa-

tions can be made from the data presented in

the previous sections. To develop these points

the discussion is divided into three main parts

(a) an analysis of the strain errors implicit in

conventional triaxial testing, which will be

based on comparisons between observed

differences between the external and inter-

nal measurements of strain

(b) general features of the observed soil be-

haviour at small strains

(c) a discussion of the choice of parameters for

the comparison and normalization of the

experimental data.

Errors in conven tional stiffness measurements

Figure 1 shows that the overall measured

deflexion in a triaxial test is given by

A=AL+AT+ABT+AS+AeB+A,,, (1)

Calibration of the load cell and ram characteris-

tics for the apparatus used in this testing pro-

gramme showed that their combined compliance

c could be taken, approximately, as c =

5.4 x 10e4, where c = (A,+ A,,,)/F mm /N and

F is the deviator force in newtons. Clearly such

deflexions are most important for strong ma-

terials, so that in tests Cl and C2, for example,

c was around SO times larger than the com-

pliance of the samples themselves.

The significance of the remaining terms in

equation (1) may be assessed from Fig. 13 in

which the local measurements of axial strain, Ed,

are plotted against the ratio E,/E~ for all the

tests on the low plasticity clay (E, is the external

strain corrected for the compliance of the load

cell and ram). Four main conclusions can be

drawn as follows.

(a)

(b)

(cl

(4

For normally, anisotropically, consolidated

samples the corrected strain, E,, is close in

magnitude to the mean local strain.

For overconsolidated samples (e.g. R2, R4,

R8) the agreement between local and over-

all corrected measurements is far less satis-

factory.

The difficulties in obtaining accurate load

cell stiffness calibrations can lead to overes-

timates of the stiffness and thus produce

values of FJQ_ less than unity.

For unconsolidated tests on intact or re-

moulded samples the disagreement between

local and external corrected measurements

is most severe, and E, can be an order of

magnitude greater than Ed..

The last observation is emphasized in Fig. 8(b)

(referred to previously) in which the locally and

externally measured strains are plotted against

shear stress for test Il. The bedding and other

errors implicit in the corrected strain E, give the

illusion of nearly linear straining up to about

0.6% axial strain, while the central portion of

the sample was behaving in a much stiffer and

less linear way. The initial slope of the apparent

stress-strain line corresponds to E,/c,- 190,

which is more than 12 times smaller than themaximum secant EJc, deduced from the local

strain measurements at 0.05% strain.

In general the strains measured by each pair

of electrolevels during a test were dissimilar

until the average local strain exceeded 0.1%.

This can be explained by non-parallelism of the

sample ends, differential bedding and top cap

movements. It should be noted that if the non-

parallelism of the ends were to cause the sample

to tilt when loaded, then the apparent strains

measured by the electrolevel gauges would

equally overestimate the larger local strain .sr.,and underestimate the smaller strain E~.~.Al-

though a number of dual axis gauges would be

required to describe fully the tilt experienced by

a sample the mean axial strain can be computed

from the data given by a pair of gauges as

cc = (E,., + ~&/2. A measure of tilt in relation to

axial strain is given by the ratio (or., - &,)/(e,, +

f&) = T the tilt ratio. The maximum values ob-

served for this ratio at various mean strains are

summarized in Table 3. The results show that

the tilting action can be considerable and that

the use of paired local displacement gauges is

essential if the stress-strain behaviour below

e,_ = 0.1% is to be observed. For the remoulded

samples a ball seating was used and this accen-

tuated tilting, particularly at large strains.



MEASUREhJENT OF SOIL STIFFNESS

Table 3. Maximum tilt ra tios observed for tests on low plasticity day

Mean axial strain eL: % Tilt ratio T for intact Tilt ratioand reconstituted samples* T for remoulded

samples*

0.005 2.0 2.10.01 1.5 1.70.05 0.9 2.60.1 0.4 2.81.0 0.1 0.9

T = (on - H&I(HL, + 0L2).* For parallel straining f3r1= or and T = 0, and if 19r_~s negative T can exceed unity.

337

Summarizing, it is found that even the most

careful calibration of the load cell and ram

deflexions is not sufficient to allow external

measurements to be used to define the stress-

strain characteristics of a soil accurately. Fea-tures such as bedding of the end platens and

tilting of the sample can lead to serious under-

estimation of soil stiffness. The electrolevel de-

vices described earlier in this Paper offer a sim-

ple means of circumventing the errors which

invalidate the measurement of soil stiffness in

conventional triaxial tests.

Small srrain behaviour

It has been shown that the region of stress

space within which the tested soils exhibit very

stiff undrained behaviour is generally boundedby the 0.1% axial strain contour. Such a low

strain region is shown in Fig. 14 for a number of

samples which have all been consolidated, under

K. conditions, to the same maximum stresses

before unloading to various overconsolidation

ratios prior to undrained compression (see also

Fig. 6). The 0.1% contour coincides with the

yield point for OCR= 1 but lies below it for

OCR>l. The 0.1% strain contour shown in

Fig. 14 is not strictly a yield locus since drained

effective stress paths parallel to, but beneath, it

(e.g. along the swelling line) could involve yieldand large strains. Specimens undergoing differ-

ent stress history and/or modes of deposition

prior to undrained testing will usually have

different low strain regions. For example, for

specimen 11, which was sampled and tested un-

consolidated undrained, the small strain regionlies well below the region observed by shearing

from the K0 swelling line (see Figs 6 and 8).

However, it is evident from Figs 6 and 14 that

the small strain region for undrained compres-

sion can be extensive and the stress paths for

many engineering problems will be within this

region.

For ease of comparison and presentation, the

initial undrained stress-strain characteristics

may be represented by the following two in-

dexes relating to stiffness and linearity.

(a)

(b)

Stiffness is given by the undrained secant

modulus at 0.01% axial strain, E,o.o,,. It

may be expressed non-dimensionally as

(E,/c,)~.,,,, (E,lp~)o.ol, etc., as discussed in

the next section.

An index of linearity is defined as L =

E,(,,.,JE,(,,.,,,, where EUo.,, is the undrained

secant modulus at 0.1% strain. Straight line

behaviour then gives L = 1.0, and if the

modulus decreases with strain L < 1.0.

Values of L are given in Table 2 and it can be

seen that every test departed from straight linebehaviour over its small strain range. In general,

Undrained

stress path

for OCR =

Undrained

1.0

Fig. 14. Schematic drawiog of upper bound to small strain range for

reconstftuted low plasticity day



338 JARDINE, SYMFS AND BUFUAND

Rl-4

R2

3000Reconstituted

ML C 2

- LClc RM2

- Ml

HRS2 HRSl I3-..

OC R

Fig. 15. summaryf autests

the values of L increased with overconsolidation

ratios, and test Rl (OCR= 1.0) showed the

smallest L value of 0.185. The two chalk speci-

mens showed almost linear behaviour.

Choice of parameter for n o r m a l i z i n g E ,

It is not, at present, common to carry out

triaxial tests to determine undrained stiffness for

purposes of practical design and analysis. Most

engineers rely on correlations between stiffness

and a related, but more readily obtained,

parameter. For example, Ladd, Foot, Ishihara,

Schlosser & Poulos (1977) presented stiffness

data from SHANSEP tests which are normalized

by c, plotted against OCR. In their plots E, was

determined over given proportions of shear

stress increment rather than the fixed strain

increments used in this work.The stiffness data given here in Figs 7(b), 9(b),

11(c) and 12 have also been normalized with

respect to the peak undrained shear strength.

Fig. 15 shows the curve of E J c , at 0.01% axial

strain against OCR for the reconstituted low

plasticity clay. Results from the other tests re-

ported here are shown as single points. The

stiffness of the normally consolidated sample Rl

is perhaps misleading as the initial behaviour is

probably controlled by the amount of time per-

mitted for secondary consolidation. However,

the data show that (EU/c,)o.Ol quickly increased

from the value at OCR = 1 to a maximum at an

OCR of about 1.4, and then steadily reduced

with increasing overconsolidation. Although the

stiffness given by the intact samples of the same

clay can be seen to follow approximately the

same relationship, the remoulded tests RMl and

RM2 give values which only correspond to the

most heavily overconsolidated reconstituted

samples. The ratio (EJ c,),.,,, ranged between

540 and 3700 for the low plasticity clay and thenormally consolidated tests Rl, I1 and I2 gave

values between 1800 and 2700.

The data for the comparative soils are also

given in Fig. 15 and show that the (E,/c,)~.~,

values for the chalk were similar to the max-

imum given by the North Sea clay. The London

clay results fell roughly in the mid-range but the

Ham river sand tests gave the smallest

(EJcJ,.,, values of all.

The data from the triaxial tests show that even

with fixed rate of displacement compression

tests there is a wide range in the ratio E J c , fora single clay. The undrained stiffness clearly

depends on strain level, stress history, method of

formation and, probably, strain rate. With other

soils mineralogy, grading, macrofabric and

cementation could produce different characteris-

tics. It has, for example, been suggested by Ladd

e t a l . (1977) that, in comparable tests, the ratio

E J c , is higher in ‘lean’ clays than in more

plastic soils.

Although it is convenient to use the ratio

E J c , to compare different soil types and initial

conditions, the parameter cannot be considered

to be fundamental since the undrained shear

strength also depends on rate, total stress path,

sample disturbance and soil macrofabric. In par-

ticular, the use of c, can be confusing in soils

which develop orientated, residual, structures in

thin shear zones.

The initial mean effective stress po’ acting in a

sample has been used as an alternative parame-

ter with which to normalize stiffness measure-

ments (see Atkinson, 1973; Wroth, 1971).

While the undrained shear strength depends on

the conditions of testing, pO’can be measured in

the laboratory without ambiguity. In the field,

however, p o’ will depend on KO and cannot be

calculated with such certainty.

Figure 16 shows the same data as Fig. 15, but

with the stiffness EUo.,,, normalized by pO’ in

place of c,. The pattern demonstrated by the

reconstituted low plasticity clay is familiar. The

normally consolidated tests again showed rela-

tively low normalized stiffnesses but the other

reconstituted, intact and remoulded results fall

within a far narrower scatter than the c, nor-

malized result, with (EJp,‘),,.,, lying between

1700 and 2400.

The results for the Ham river sand, perhaps

fortuitously, plot close to the curve for the re-

constituted North Sea clay, but the London clay




results fall distinctly below the full line. The

chalk tests produced very high (E,/p,‘),.,,, values

but since their stiffnesses are probably control-

led by bonding, rather than effective stress,

these values may be arbitrary.

From the experiments described in this Paper

normalization by p,,’ would appear to be prefer-

able for uncemented soils. The ratio Eu/po’ is

seen to be less dependent on method of forma-

tion and stress history than E,/c,, and an effec-

tive stress approach is likely to be more useful

when the small strain laboratory techniques are

applied to drained behaviour.

The work described here deals only with un-

drained stiffness in triaxial compression. It is

evident that investigations are required into the

more general behaviour of soils in the small

strain range, where accurate radial strain meas-

urements would be required, and that the in-

fluence of many parameters (including rate and

ageing effects) must also be assessed.

SUMMARY AND CONCLUSIONS

A new technique is described for the accurate

measurement of local axial strains on soil speci-

mens in the triaxial apparatus. The strains are

measured using an electrolytic level device

which is simple to use, resolves relative displace-

ments to less than 1 urn over a range of 15 mm

and is not damaged when the sample is taken to

failure.

The new technique was employed in a pro-

gramme of tests principally on a low plasticity

clay from the North Sea with additional com-

parative tests being conducted on Ham river

sand, London clay and intact chalk, thus cover-

ing a wide spectrum of soil types.

The test results show that conventional exter-

nal measurements of displacement contain er-

rors which frequently mask the initial stress-

strain characteristics of the soil and invalidate

their use in the determination of soil stiffness.

The errors in the external measurement of dis-

placement mainly result from tilting of the sam-

ple, bedding on the end platens and the effects

of compliance in the apparatus.

In every test the low plasticity clay showed

highly non-linear, but very stiff, initial be-

haviour. The attainment of 0.1% axial strain

generally coincided with a marked loss of stiff-

ness and could be taken as the limit to the small

strain range. Correlation with the undrained

effective stress paths shows that such a range

extends over the main part of stress space in

which soil would usually be considered elastic.

Such stiff initial behaviour is therefore likely to

be important in the analysis of many practical

problems.

3000r

c

13 +

RMl

RMZ

0 11 2 4 6 810 20 40 10 0

OCR

Fig. 16. Summary of all tests

The stiffness ratio (E,/c,)~.~~~ was shown to be

strongly dependent on OCR for the intact and

reconstituted samples. Lightly overconsolidated

conditions produced the highest values of the

ratio, and heavily overconsolidated and re-

moulded samples showed the lowest. The alter-

native non-dimensional ratio (E,/p,,‘),.,, was less

sensitive to OCR and method of formation.

Normally consolidated samples of intact and

reconstituted samples of the low plasticity clay

showed the least linear initial behaviour, and

gave values of L = (= Euo.,,/E,~,.,,,,) which were

lower than 0.2. Although linearity steadily in-

creased with overconsolidation ratio the largest

value of L recorded for the clay was 0.407.

The limited number of comparative tests on

other materials shows that the small strain

characteristics of the low plasticity clay are not

unique. The values of (E,/c,)~.~,~ and (Eu/p,,‘)o.cll

for specimens of chalk, sand and London clay

exceeded the results obtained in conventional

tests, and in each case the small strain behaviour

was non linear. The cemented chalk samples

showed both the highest normalized stiffness

and the nearest approximation to linear stress-

strain behaviour.

In summary, the techniques described in this

Paper make it possible to detect, simply and

reliably, mean local axial strains in triaxial tests

with a resolution of approximately 0.001%. In

the first programme of tests using the new

equipment observations have been made of the

undrained stress-strain characteristics of soils

which, without local strain measurements, could

only be inferred from field measurements. Al-

though more research is required into the fac-

tors controlling the stiffness of soils, finite ele-

ment analyses have been carried out using con-

stitutive models based on the experimental data,

as described by Jardine, Potts, Fourie & Burland



340 JARDINE, SYMES AND BUFUAND

(1984), which demonstrate that the initial small

strain characteristics of a soil are of great impor-

tance in the analysis of engineering problems

and the interpretation of in situ tests.

ACKNOWLEDGEMENTS

The samples of low plasticity clay from the

North Sea were provided by BP International

Ltd and the Authors are grateful to h4r W. J.

Rigden for his interest in the work and his per-

mission to publish the results. Thanks are also due

to Dr J. H. Atkinson for his helpful comments.

The Authors wish to acknowledge the impor-

tance of the contribution to this topic of Dr P.

R. Vaughan, who supervised the first small

strain studies conducted by Dr L. C. Costa Filho

and Dr 0. B. Daramola at Imperial College, and

also to thank their colleagues who have gener-

ously donated time and practical help to the

work described. Mr P. Smith and Mr N. Brooks

both provided particularly valuable contribu-

tions to the work, which was funded by the

Marine Technology Directorate of the Science

and Engineering Research Council.

REFERENCES

Arthur, J. R. F. & Phillips, A. B. (1975). Homogene-

ous and layered sand in triaxial compression.

Giotechnique 25, No. 4, 799-1815.

Atkinson, J. H. (1973). The deformation of undisturbedLondon clay. PhD thesis, University of London.

Bishop, A. W. & Wesley, L. D. (1975). A hydraulic

triaxial apparatus for controlled stress path testing.

Gt?oorech&ue 25, No. 4, 657-670.

Brown. S. F.. Austin. G. & Overv. R. (19801. An

instrumented triaxial cell for cyc& loading of clay.

ASK%4 Geotech. Test. J. 3, No. 4, 145-152.

Brooks, N. J. (1983). The settlement of foundations on

chalk. MSc thesis, University of London.

Burland, J. B. & Symes, M. (1982). A simple axial

displacement gauge for use in the triaxial ap-

paratus. Giotechnique 32, 1, 62-65.

Cooke, R. W. & Price G. (1974). Horizontal in-clinometers for the measurement of vertical dis-

placement in the soil around experimental founda-

tions. Field instrumentation in georechnical en-

gineering, pp 112-125. Butterworths: London.

Costa Filho, L. M. (1980). A laboratory inuestigation

of the small strain behaviour of London clay. PhD

thesis, University of London.

Daramola, 0. (1978). The influence of stress history on

the deformation of sand. PhD thesis, University of

London.

Gens, A. (1980). Discussion: Design parameters for

soft clays. F’roc. 7th Eur. Conf. Soil Mech., Brigh-

ton, 1979 4, 25-26.

Gens, A. (1982). Stress-strain and strength characteris-

tics of a low plasticity clay. PhD thesis, University

of London.Hight, D. W. (1983). Simple piezometer probe for the

routine measurement of pore water pressure in

triaxial tests on saturated soils. Gkotechnique 32,4,

315-322.

Jardine, R. J. & Brooks, N. J. (1984). The use of a

new axial displacement gauge for the determina-

tion of rock stiffness. In preparation.

Jardine, R. J., Potts, D. M., Fourie, A. & Burland, J.

B. (1984). The importance of small strain be-

haviour in the analysis of soil structure interaction.

In preparation.

Ladd, C. C., Foot, R., Ishihara, K., Schlosser, F. &

Poulos, H. G. (1977). Stress deformation and

strength characteristics. Proc. 9th Int. Conf. Soil

Mech., Tokyo 3, 293-305.

Lupini, J. F., Skinner, A. E. & Vaughan, P. R. (1981).

The drained residual strength of cohesive soils.

GPotechnique 31, No. 2, 181-213.

Maswoswe, J. (1984). PhD thesis, University of Lon-

don. In preparation.

Richart, F. E., Woods, J. D. & Hall, J. R. 1970.

Vibrations of soils and foundations. New Jersey:

Prentice-Hall.

Roscoe, K. H., Schofield, A. N. & Thurairajah, A.

(1963). An evaluation of test data for selecting a

yield criterion for soils. Prcc. Symp. Laboratory

Shear Testing, ASTM STP 361, 111-128.Schofield, A. N. & Wroth, C. P. (1968). Critical state

soil mechanics. London: McGraw Hill.

Simpson, B., O’Riordan, N. J. & Croft, 0. D. (1979).

A computer model for the analysis of ground

movements in London clay. Gkotechnique 29, No.

2, 149-175.

Symes, M. J. & Burland, J. B. (1984). The determina-

tion of local displacements on soil samples. ASTM

Geotech. Test. J. In press.

Vogler, U. W. & Kovari, K. (1978). Suggested

methods for determining the strength of rock ma-

terials in triaxial compression. Int. J. Rock Me&

Min. Sci. Geomech.Abstr. 15, o.

, 47-51.Wroth, C. P. (1971). Some aspects of the elastic

behaviour of over-consolidated clay. Stress-strain

behaviour of soils. Proceedings of the Roscoe

Memorial Symposium, 347-361. Cambridge:

Foulis.

Yuen, C. M. K., Lo, K. Y., Palmer, J. H. L. &

Leonards, G. A. (1978). A new apparatus for

measuring the principal strains in anisotropic clays.

ASTM Geotech. Test. J. 1, o. 1. 4-34.

1984_jardine et al

Documents

axial stiffness

strain measurements

stressstrain behaviour

dplacement axial

axial displacement gauge

sample u

small strain range

burland symes