JARDINE, R. J., SYMES, M. J. & BURLAND, J. B. (1984). Giotechnique 34, No. 3, 323-340

The measurement 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 the undrained 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 sur 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 KO

L

Lo LI

P’ PO’ RI3 T 6

compliance of (A,_+ 4&F

loading system =

undrained shear strength undrained stiffness E,co.ol,-E, at 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 JARDINE, 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 rather surprising 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 errors implicit 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

Sample compression

Fig. 1. Sources of emx in external strain measure- ments (+, is the larger of the two shins; FL = (ELI + E&3

devices to measure axial, radial and shear strains in 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 hinge mechanisms 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 footings to 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 feature of 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 large strains 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

MEASUREMENT OF SOIL STIFFNESS 329

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 sampled

As above - Cut from quarry face -

isotropically consolidated As above -

OCR PO before (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

330 JARDINE, SYMES AND BURLAND

125-

(- -contours of axial Strain %I

loo-

150 200 250 300

(IT,'+ 03')/2, kPa

-251

Fig. 6. North Sea day stress 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 EJc, 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 anisotropic consolidation 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

MEASUREMENT OF SOIL STIFFNESS 331

stress for sample 13 is represented by point D. The 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 overall measurements 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 the intact 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 the stress-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

3200

Fig. 7. Tests Rl, R1.4, R2, R4 and R8: (a) stress-sti data; (b) stiessstraia data; (c) StsIwss characteristics

had not been preloaded, the shapes of the stress paths and the pattern of strains are similar to those given by the overconsolidated samples of intact 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 C2 are 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 of test results

Test c,:

kPa

E, @ 0.01 %:

kPa 5 @Jo.01 % c,

3 @O.Ol % I :(“.I)t: min

Rl 122 2.22 x lo5 1820 830 0.185 38 R1.4 122 4.50 x lo5 3690 2 180 0.270 49 R2 108 359 x lo5 3320 2 270 0.353 52 R4 94 2.26 x 10’ 2400 2 130 0.386 65 R8 67 1.13x lo5 1690 1740 0.407 105 11 255 5.10x lo5 2000 1080 0.333 100 I2 275 7.43 x lo5 2700 1460 0.187 59 13 173 9.4 x lo4 540 2 030 0.340 126 RMl 39.5 2.6 x lo4 660 2 430 0.331 156 RM2 85.0 9.3 x lo4 1090 2 180 0.278 72 HRSl 1085 2.9 x 10’ 270 2 200 0.518 90 HRS2 1142 4.9 x lo5 430 1210 0.503 59 LCl 123 1.24x lo5 1010 550 0.371 55 LC2 100 1.20 x lo5 1200 600 0.387 65 Cl 1350 5.7 x lo6 4220 15 500 0.723* 510 c2 1600 4.0 x lo6 2500 11000 0.854* 587

* Since both samples failed at +<O.Ol L was taken here as E,~,.,,,IE,~O.OO,~. 7 r(c.r) corresponds to the time taken to develop E,=O.l % in each test. For a rate of strain of 4.5 % per day tcO.i) would be 32 min.

intervals. The sand experiments 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 the state 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 %)

RM2

600 (9’ + n3’)/2. kPa

(31

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

MEASUREMENT OF SOIL STIFFNESS 333

300

1 Ultlmatec = 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

0.1 667 172 1.0 147 140

Fig. 8(b). Stress-strain data for test I1

(al

2400

\ \ Only test 12 athned \ \

peak devtator at an

\ axial strain below 5%

Awal strain EC %

(b)

Fig. 9. (a) Stress-stain data for tests 11,12,13, RMl and RM2, (a) stiffness characteristics for tests 11, I2, 13, RMl, RM2 and R2

progressive weakening with the effective stresses roughly following unloading paths.

The stress paths for tests LCl and LC2 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 until peak strengths were mobilized at strains of 4.5% and 3.5% respectively. Both tests showed a steep post- peak loss of strength, and examination of the samples after testing showed that polished shear surfaces had formed within the specimens. The stress-strain and stiffness characteristics for the tests described in this section are summarized in Fig. 11 together with Fig. 12, which summarizes the results of all the tests reported 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 chalk tests Cl and C2 gave the highest normalized stiffnesses, which equalled those of 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

1600

1200

1

$ 8OC

a" I

-g

4oc

C

JARDINE, SYMES AND BURLAND

20

m LC2

%

N, c 6 10

50

&y 0.7 K o-4

0.2

01 007

0.02z

0~0040.01 0.002

175 200

(0,’ + 03’)/2 kPa

(4

50 /fA 80

.’ O .

i: o_eLCl

04

02

i

0.1

0 05

002 n /,1

1OU ‘t 120 150

” “,

250

(cl’ + 0,‘)/2: kPa

@I

300

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

MEASUREMENT OF SOIL STIF’F’NESS 335

300.

0 01 01 10 10 (b)

Axial strain q: %

0.001 0.01 0.1 1 Ax,al Strain EL %

WI

Fig. 11. (a) Stressstraio data for tests Cl and C2; (b) stres+stmfn data for tests HRSl and HRS2; (c) stress-strafn data for tests LCl and LC2; (d) stitbws characteristics for tests Cl, C2, HRSl, HRS2, LCl andLC2

500

400

300

"= '1 UJ

200

100

C

O-

O-

O-

O-!

O-

O- I.01

Fig. 12. Summary of normafhd s_eS

(c) The 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 comprehensive studies 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) and Daramola (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

12.

10.

8. unconsohdated

Mean axial strain EL: %

Fig. 13. Tests on low pldkfty clay: comparison 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 conventional 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 the maximum 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 ratios observed for tests on low plasticity day

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

samples*

0.005 2.0 2.1 0.01 1.5 1.7 0.05 0.9 2.6 0.1 0.4 2.8 1.0 0.1 0.9

T = (on - H&I(HL, + 0L2). * For parallel straining f3r1 = or and T = 0, and if 19r_~ is 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 bounded by 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 yield and 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 region lies 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 line behaviour 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

3000 Reconstituted

MLC2

- LCl c RM2

- RMl H RS2 HRSl I3-.

.

OCR

Fig. 15. summary of au tests

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 normalizing 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 EJc, 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 (EJc,),.,,, ranged between 540 and 3700 for the low plasticity clay and the normally 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 EJc, for a 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 et al. (1977) that, in comparable tests, the ratio EJc, is higher in ‘lean’ clays than in more plastic soils.

Although it is convenient to use the ratio EJc, 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, po’ 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

MEASUREMENT OF SOIL STIFFNESS 339

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

01 1 2 4 6 810 20 40 100

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.

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