1975 Bishop Et Al

14
BISHOP, A. W. &WESLEY, L. D. (1975). G6otechnique 25, No. 4, 657-610. A hydraulic triaxial apparatus for controlled stress path testing A. W. BISHOP* and L. D. WESLEY* A simple and versatile hydraulically operated triaxial apparatus has been developed for stress path testing. The apparatus is described and the range of tests which can be performed is dis- cussed. These include both stress controlled and strain controlled tests. Some typical test results are presented and are used to illustrate the fact that under undrained conditions the deformation of the sample is a function only of the magnitude and sign of the stress difference, and is not otherwise influenced by the absolute magnitude of the total stress changes. The apparatus can be used with any convenient pressure control and recording system. A simple adaptation of the self-compensating mercury control system is illustrated. Un annareil triaxial simple et universe1 hydraulique, a &b-&C pour des es&s de traction. -L’appareil est decrit et la portCe des essais qui peuvent &tre r6ali&, est discutke. Ceux-ci comprennent des essais de traction contr8lte ainsi que des essais de deformation contrBlte. Quelques resultats d’essais typiques sont prCsentCs et utilisCs pour illustrer le fait que sous conditions non drainees la deformation de l’tchantillon est fonction seulement de l’impor- tance et du signe de la diffkrence des tractions, et qu’elle n’est pas autrement influencee par l’impor- tance absolue des changements de traction totale. L’appareil peut Etre utilise avec n’importe quel contrBle de pression convenable et de systtme d’enregistrement. Une adaptation simple du sys- t&me de contrBle de mercure & propre compensation est indiquee. The role of the triaxial test in the measurement of the strength and deformation characteristics of soil samples has been discussed in detail by Bishop and Henkel (1957, 1962). Though developments have continued in equipment for testing in plane strain (e.g. Wood, 1958; Cornforth, 1964; Bishop, 1966; Hambly and Roscoe 1969; Atkinson, 1973) and for indepen- dent stress or strain control (Lomize and Kryzhanovsky, 1967; Bishop, 1967; Green, 1969 and 1971; Hambly, 1969; Pearce, 1971), most triaxial tests on undisturbed samples are still limited to one system of loading, i.e. the cylindrical compression test, following one stress path, u3 (and u2) constant and u1 increasing. The reason for this limitation has been one of practical convenience, since the logical investigation of engineering applications (Bishop and Henkel, 1962; Lambe, 1967; Lewin and Burland, 1970; Lambe and Whitman, 1969) as well as the fundamental investigation of soil behaviour would suggest that other stress paths are of equal, if not greater importance, in particular for drained tests, and where deformation characteristics are under considerationl. There is thus a need for a simple form of triaxial apparatus in which the stress paths en- countered in engineering practice can be approximated to more readily than in the conven- tional equipment. This Paper describes a form of hydraulically loaded triaxial cell which satisfies the require- ments of both simplicity and versatility for samples in the low and medium strength range (with reference to the stress ranges encountered in civil engineering practice). Cylindrical samples can be tested in both axial compression and axial extension following a wide range of * Imperial College of Science and Technology, London. 1 Attention was drawn to this point by Bishop and Henkel (1957) p. 20.

Transcript of 1975 Bishop Et Al

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BISHOP, A. W. &WESLEY, L. D. (1975). G6otechnique 25, No. 4, 657-610.

A hydraulic triaxial apparatus for controlled stress path testing

A. W. BISHOP* and L. D. WESLEY*

A simple and versatile hydraulically operated triaxial apparatus has been developed for stress path testing. The apparatus is described and the range of tests which can be performed is dis- cussed. These include both stress controlled and strain controlled tests. Some typical test results are presented and are used to illustrate the fact that under undrained conditions the deformation of the sample is a function only of the magnitude and sign of the stress difference, and is not otherwise influenced by the absolute magnitude of the total stress changes. The apparatus can be used with any convenient pressure control and recording system. A simple adaptation of the self-compensating mercury control system is illustrated.

Un annareil triaxial simple et universe1 hydraulique, a &b-&C pour des es&s de traction. -L’appareil est decrit et la portCe des essais qui peuvent &tre r6ali&, est discutke. Ceux-ci comprennent des essais de traction contr8lte ainsi que des essais de deformation contrBlte. Quelques resultats d’essais typiques sont prCsentCs et utilisCs pour illustrer le fait que sous conditions non drainees la deformation de l’tchantillon est fonction seulement de l’impor- tance et du signe de la diffkrence des tractions, et qu’elle n’est pas autrement influencee par l’impor- tance absolue des changements de traction totale. L’appareil peut Etre utilise avec n’importe quel contrBle de pression convenable et de systtme d’enregistrement. Une adaptation simple du sys- t&me de contrBle de mercure & propre compensation est indiquee.

The role of the triaxial test in the measurement of the strength and deformation characteristics of soil samples has been discussed in detail by Bishop and Henkel (1957, 1962). Though developments have continued in equipment for testing in plane strain (e.g. Wood, 1958; Cornforth, 1964; Bishop, 1966; Hambly and Roscoe 1969; Atkinson, 1973) and for indepen- dent stress or strain control (Lomize and Kryzhanovsky, 1967; Bishop, 1967; Green, 1969 and 1971; Hambly, 1969; Pearce, 1971), most triaxial tests on undisturbed samples are still limited to one system of loading, i.e. the cylindrical compression test, following one stress path, u3 (and u2) constant and u1 increasing.

The reason for this limitation has been one of practical convenience, since the logical investigation of engineering applications (Bishop and Henkel, 1962; Lambe, 1967; Lewin and Burland, 1970; Lambe and Whitman, 1969) as well as the fundamental investigation of soil behaviour would suggest that other stress paths are of equal, if not greater importance, in particular for drained tests, and where deformation characteristics are under considerationl.

There is thus a need for a simple form of triaxial apparatus in which the stress paths en- countered in engineering practice can be approximated to more readily than in the conven- tional equipment.

This Paper describes a form of hydraulically loaded triaxial cell which satisfies the require- ments of both simplicity and versatility for samples in the low and medium strength range (with reference to the stress ranges encountered in civil engineering practice). Cylindrical samples can be tested in both axial compression and axial extension following a wide range of

* Imperial College of Science and Technology, London. 1 Attention was drawn to this point by Bishop and Henkel (1957) p. 20.

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658 A. W. BISHOP AND L. D. WESLEY

,,Axial screw adjustment

c Bellofram seal /

7 / C / / / / / /

r-

Bellofram seal

i

Hollow ram linking

Linearmorion bearing

Crosshead for displacement meawremcnt

Drainage and

pare-prerrurc lead

Pressure chamber Loading pressure

Base

Fig. 1. Diagrammatic layout of the apparatus

stress paths, subject only to the condition that the total and effective stresses remain positive (relative to atmospheric pressure) at the end caps. Tests can be carried out either at controlled rate of loading or controlled rate of strain.

The design is based on experience gained at Imperial College through the use of the ‘Bello- fram’ rolling seal as a loading device2 in creep tests (Lovenbury, 1969; Davies, 1975) and in plane strain tests (Atkinson, 1973). The particular configuration, that of mounting the sample on the top of the loading ram, was used as early as 1934 by Jtirgenson (who attributed the design to Gilboy) and more recently by Atkinson (1973). The advantages of this arrangement are discussed in subsequent paragraphs.

DESCRIPTION OF THE APPARATUS The new apparatus is shown diagrammatically in Fig. 1. A cross-sectional scale view is

shown in Fig. 2 and a photograph in Fig. 3. The upper part is similar to a conventional triaxial cell except that the vertical load in a compression test is applied by moving the sample pedestal upwards from below and pushing the top cap against a stationary load cell, which records the load.

The pedestal is mounted at the top of a loading ram, at the bottom end of which is a piston and pressure chamber. Bellofram rolling seals are used to retain the cell fluid and the ram travels up and down in a ‘Rotolin’ linear bearing. The axial load is applied to the sample by increasing the pressure in the bottom pressure chamber.

a Its use. as a seal for the loading ram is described by Warlam (1960) and a pressure generating device- by Ko and Scott (1967).

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TRIAXIAL APPARATUS FOR CONTROLLED STRESS PATH TESTING 659

Adjusting nut to raise.

Diiplacement

Rods to activate dial gauge and transducer for strain measurement*

Hole ac centre of loading ram to cake pore-pressure leads

Inlet to apply pressure

Fig. 2. Cross-section of the apparatus for 3 in. x 1% in. (76 x 38 mm) samples

The loading ram has a cross-arm attached to it which moves up and down in wide slots in a ‘spacer’ which connects the bearing housing to the lower pressure chamber. The cross-arm supports two vertical rods which pass through clearance holes in the cell base and deflect the dial gauges (or displacement transducers) mounted on the top of the cell. These gauges thus record the movement of the ram from which the axial strain in the sample is determined.3 One vertical rod would actually be sufficient but two were used to keep the ram balanced and to enable both a dial gauge and transducer to be mounted at the same time.

The drainage and pore-pressure leads from the sample pedestal are taken down the centre of the loading ram and out through slots in the spacer. Provision is made for drainage leads from the top cap should these be required.

Very many alternative arrangements were considered before arriving at this design. It may seem more logical to load the sample from above as in a conventional test, but the arrangement with the load applied from below has several advantages. Setting up the sample is very simple, as in a conventional apparatus, but no corrections are required for loading ram weight. The upper part of the cell which is removed for mounting or dismantling the sample remains light in weight and easy to handle. The weight of the ram and the sample acts against the lower Bellofram seal and maintains a positive pressure in the pressure chamber so that there is no danger of damaging the rolling seal by turning it inside out. There is some danger of this occurring when the load is applied from above (as in the earlier creep cells) as the weight of the piston pulls down on the Bellofram instead of acting against it.

3 A small correction has to be made for the deformation of the load cell.

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660 A. W. BISHOP AND L. D. WESLEY

The use of two Bellofram seals perhaps requires some explanation since it would be possible to use only one seal to separate the cell fluid from the pressure chamber fluid, as is done in the creep cells at present in use at Imperial College.

The two seals have the following advantages. First, strain measurements can be made externally by means of the cross-arm arrangement attached to the ram between the seals. Second, extension tests (i.e. tests in which the horizontal stress is greater than the vertical stress) are possible as the pressure in the pressure chamber can be made less than the cell pressure. Third, the linear bearing is not submerged in cell or loading chamber fluid so that the use of oil to protect the Rotolin bearing in either of these is unnecessary.

Extension tests are made possible by attaching a small device4 to the load cell which, on partial rotation, connects it to the sample top cap. Extension tests with plain end caps are however only possible if a cell pressure is applied, the magnitude of which is a function of the strength of the sample.

It should be noted that the apparatus is self-contained; it requires no loading frame and is quite portable. It is equally well suited to both stress controlled and strain controlled loading.

To operate the cell auxiliary equipment is required in the form of two controllable pressure sources (for controlled stress tests) or a controlled pressure source and a constant rate of flow source (for axial-strain controlled tests). As will be shown later, the self-compensating mercury control (Bishop and Henkel, 1962, Figs 28 and 29 and Bishop et al., 1973, Fig. 1) and the screw control cylinder (Bishop and Henkel, 1962, Figs 28 and 35) can be readily adapted for these two functions.

The test may be run either undrained or consolidated undrained with or without pore- pressure measurement; or drained, either to atmospheric pressure or against a constant or varied back pressure, the last two cases requiring a third pressure control unit.

The two Bellofram seals in the apparatus are identical and have an effective area of 29.4 cm2, which is slightly greater than 2.5 times the sample area of 11.4 cm2. The merits of this arrange- ment are discussed in the next section.

OPERATION OF THE APPARATUS

The operator using the apparatus will generally desire to vary a, (the axial stress) and a, (the radial stress)5 in some controlled manner and measure the resulting deformation of the sample and the pore-pressure response or volume change. However, the two pressures which can be controlled directly are the cell pressure (up) and the pressure in the lower pressure chamber (p). The value of u& is dependent on both or and p and the key to the operation of the apparatus is the relationship between u,, up and p. This relationship is obtained by con- sidering the equilibrium of the loading ram and it is easily shown that

u*=p;+u, l-5 -5 . . . . . . . . t )

where A is the sample area, at the relevant stage of the test, a is the Bellofram seal area and W is the weight of the loading ram.

Equation (1) is correct whether us is greater or less than ul. although, of course, u& can only be made less than a, by attaching the sample top cap to the load cell. For any particular test it is easy to determine from eqn (1) the way in which the pressure p must be varied in relation to u, in order to produce a required stress path. To do this it is easier if eqn (1) is written in terms of stress change

* Similar in principle to the bayonet catch illustrated by Bishop and Henkel (1962), Fig. 109. 5 This nomenclature is used to avoid confusion when the principal stress directions are interchanged during the course of a test.

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662 A. W. BISHOP AND L. D. WESLEY

Consolidation or swelling under various stress ratios not leading to failure This may be considered under four subheadings, as set out in the following.

Equal all roundpressure. Here K= 1 in eqn (6) and Ap=Aur’, i.e.

Ap = Au, if u is constant , . . . . . * (7) In fact Ap automatically adjusts itself to equal Au, if the cell pressure is applied with the valve to the loading pressure chamber closed and the sample cap not in contact with the load cell. Anisotropic consolidation. Here K,, <Kc K,, where Kf, and K,, represent the effective stress ratios at failure in axial compression and axial extension respectively. These limiting states represent the active and passive cases for a vertical sample taken beneath a horizontal ground surface. These stress paths may be used in reconsolidating an undisturbed sample to the assumed (or measured) in situ effective stresses, before testing under either undrained or drained conditions. Two examples are given in Fig. 4, for undisturbed samples of an alluvial clay with W,= 54, W,= 25 and a natural water content of 51%.

Two points of interest may be noted. The starting point in each test represents the effective stress retained by the pore-water tension u, in the unconfined sample after the stress release and disturbance involved in the operations of sampling and sample preparation. In fully saturated samples of clay under low and medium stresses the initial values of ug’ and a,’ will be closely equal to - u,.

Ladd and Lambe (1963) have taken the ratio - us/uV’, where uV’ is the in situ vertical effective stress, as an index of disturbance (which includes moisture content redistribution within the core or block sample). Data from laboratory tests simulating the release of shear stress on sampling presented by Bishop and Henkel(1953), Skempton and Sowa (1963) and Ladd and Lambe (1963) suggest the values of -~,/a~’ would lie in the range 0.35 - 0.75 for normally or lightly overconsolidated samples in the absence of sampling disturbance. Field data presented by Ladd and Lambe suggest that a drop of 80% below the value for ‘perfect sampling’ is typical for current sampling procedures in normally and lightly overconsolidated soils. The range would thus be O-07-O-15, depending on plasticity.

The present tests were on block samples and give values of - ~,/a,’ of 0.50 (sample A) and 0.11 (sample B). The better block samples are thus clearly much less disturbed than Ladd and Lambe’s ‘average sample’.

The stress paths chosen to recover the estimated in situ effective stresses are illustrated in Fig. 4 and consist of an increase in a,’ (ul ’ in this case) at constant or’ (a,‘) to achieve the estimated value of K,,, followed by further consolidation at a constant value of K equal to K,,. These two stress paths are given, respectively, by

up’ constant and Ap = $ Aua’ . . . . . . . (8)

and by

Ap = Au,’ [l+t(;-1)] . . . . . . . .

Although this value of K approximates to the best estimate of K,, it is of interest to note that the lateral strain (calculated from the volume change and axial strain) does not quite equal zero, as the stresses in the sample are below the preconsolidation stresses.

For controlled effective stress ratio consolidation it is necessary to apply the stress changes slowly to avoid significant excess pore-pressures building up. The accuracy with which the stress paths can be followed using the simple mechanical adaption of the self-compensating mercury control is illustrated by Fig. 4.

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TRIAXIAL APPARATUS FOR CONTROLLED STRESS PATH TESTING 663

IO -

5-

Ok 0

v,‘: IcNd

Fig. 4. Stress paths followed in consolidating samples to in situ effective stresses

K,,-consolidation. In this case the lateral strain is monitored either indirectly from the volume change and axial strain, or directly from a lateral strain indicator such as that illustrated by Bishop and Henkel (1962), Figs 47 and 48. The ratio of the increases in da, and da, during consolidation, or of the decreases during swelling, is then continuously adjusted to maintain zero lateral strain.

In the case of an undisturbed sample the stress ratio KO (= u,‘/u,‘) will only approach that for a normally consolidated soil when the preconsolidation stresses have been substantially exceeded and consolidation is proceeding approximately along the ‘virgin’ p-e curve. The initially low KO value for an undisturbed sample of London Clay is illustrated by test results plotted by Bishop et al. (1965). Generalized stress path. With the use of a more sophisticated control system, the stress path during consolidation or swelling can be made to follow any path between any two points lying within the section of stress space bounded by failure in axial compression on the one hand and failure in axial extension on the other, subject only to the limitation of no negative effective stress at the contact with the end caps and to the safe working pressures of Bellofram seal and triaxial cell. Negative values of ua’ at the mid-section of the sample may be obtained by reducing the cross-sectional area over the central portion of the cylindrical specimen and using a dumb-bell shaped sample as described by Bishop and Garga (1969).

Undrained stress changes leading to failure Mechanically these tests fall into two simple classes, as follows: tests in which a, (the cell

pressure) is held constant and u, increased or decreased to cause failure; these are the conven- tional forms of compression and extension test, and only involve increasing or decreasing p, which is related to us by the expression

Ap=tAo, . . . . . . . . . . (9)

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664 A. W. BLSHOP AND L. D. WESLEY

Fig. 5. Effective

0, + cr qa ‘+ my’ and - : kN,m’

2 2

and total stress paths for undrained compression and extension tests

and tests in which CT, is held constant and (TV is decreased or increased to cause failure in com- pression or extension respectively; in this case the relationship betweenp and ur is given by the expression

Llp=da, 1-f . . . . . . . . . c 1

Thus to maintain U& constant the value of p must be varied by an almost fixed proportion of the change in uy, the variation being due to changes in cross-sectional area A with axial strain as the test proceeds. These are small in undisturbed samples failing at small axial strains, but involve systematic adjustments in the ratio dp/do, if an accurate stress path is required.

While more generalized stress paths may approximate more closely to those encountered in the field, it may be shown theoretically that, for saturated soils in which B is closely equal to unity6, it is only the sign and magnitude of the component (T, - gI. which determines the effective stress path and thus the deformation and failure of the sample. The shape of the total stress path under undrained conditions is in other respects irrelevant.

This is demonstrated by the total and effective stress paths presented in Fig. 5 and by the stress-strain curves given in Fig. 6. Four samples a-d cut from the same block were con- solidated to the same estimated values of in situ effective stress, corresponding to a K0 value of 0.56. Samples a and b were then brought to failure in compression, a with (TV constant and u, increasing and b with ug constant and ul. decreasing. Samples c and d were brought to failure in extension, c with u, constant and u, decreasing, and d with ua. constant and a, increasing.

It will be seen that the undrained compression tests a and b (~~--a, positive) have almost identical effective stress paths and stress-strain curves. The undrained extension tests c and d

6 Where B = AU/AU for equal changes in all three principal stresses under undrained conditions.

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TRMXIAL APPARATUS FOR CGNTROLLED STRESS PATH TESTING 665

30 Test I C, constant C, Increasing

Test b Q conrtant c3 decreasing

25

Fig. 6. Stress-strain curves for undrained compression and extension tests on normally consolidated clay starting from field effective stresses

(a, - or negative at failure) likewise have almost identical effective stress paths and stress-strain curves, whilst for each pair of tests the total stress paths are radically different.

It is of interest to note that strength is not uniquely related to void ratio, which should be the same for each sample, but that in extension the strength is only 60% of the strength in com- pression. The corresponding value for the Drammen clay reported by Berre and Bjerrum (1973) is 40%.

Drained stress changes leading to failure In contrast to the behaviour under undrained conditions, equal increments of the three

principal stresses do result in significant strains under drained conditions. If the soil sample has developed an anisotropic structure (as will be the general case in undisturbed samples) these strains will not necessarily be equal, and if the principal axes of the stress changes do not coincide with the axes to which anisotropy is referred, then coincidence of stress and strain direction cannot be expected even at small strains.

The most realistic simulation of effective stress path and of sample orientation is therefore desirable in making a prediction of deformation, volume change or strength. The limitations of the cylindrical compression or extension test are of course apparent when dealing with problems in which axial symmetry is absent, but the relative magnitudes of a number of limiting cases can usefully be examined. With the present apparatus failure may be approached with any combination of do, and d(a, - a,).

As a simple example of a test of this type, the sample may be brought to failure with the mean principal effective stress held constant.

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666 A. W. BISHOP AND L. D. WESLEY

Wine/, variator A

Fig. 7. Differential hydraulic stress path control

Thus

or Au;+Au;+Aa,’ = 0

Au,’ = -$Aa,’ . . . . , . . . * (11) The value of K in eqn (4) is then -3 and eqn (6) becomes

. . . . . . . - (12)

An axial compression test would thus be run with u,’ decreasing and with p increasing, unless u/A is greater than 3, which is not the case in the present apparatus. For an extension test with constant mean principal effective stress Au,’ would be positive, and Ap negative, with the same qualification.

PRESSURE CONTROL SYSTEM The apparatus has been designed to suit any available pressure control system which can

continously vary pressure in a predetermined manner. Currently at Imperial College a variable speed differential drive has been connected to the standard self-compensating mercury control

Table 1

Parameter

p (maximum working pressure) PllllU a A0

0, (maximum working pressure) 0, rnlll W (including sample)

Value

345 Ib/in.2 (2380 kN/m2) 0 4.56 in.z (29.4 cm”) l-77 in.3 (11.4 cm”). The actual value of A may lie on either side of this value due to consolidation or swelling, compression or extension 150 lb/in2 (1034 kN/m2) 0 Approximately 9 lb (40 N)

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TRIAXIAL APPARATUS FOR CONTROLLED STRESS PATH TESTING 667

mm/h in/h

cv014°

0.334-

Deflexion: mm 0.4 016 I I

Load A :

, ~o~Q-~~o-~~~~~--o-~- strain rate -.O---O--- 2 . .

cell prerrure = 500 kN/m’

Deflexion: in.

Fig. 8. Strain rate and load plotted against deflexion in ‘constant rate of strain’ test

units (Bishop and Henkel, 1962, Figs 28 and 29). This system has been described by Bishop et al. (1973) and is illustrated in Fig. 7.

A small electric motor driving through ‘Kopp’ Variators and miniature gear boxes is con- nected to the winch drums of two mercury control systems with shafts fitted with universal joints. Kopp Variator A permits a smooth overall control of the time rates of both stress increments. Kopp Variator B can be used to make fine adjustments to the value dp/do, as the test proceeds, either to correct for changes in the cross-sectional area A or to modify otherwise the stress path.

The major changes in rate of loading necessary when changing from undrained to drained tests, or when changing from one type of stress path to another, are obtained by selecting appropriate gear boxes and change wheels.

A more flexible computer controlled system is being introduced but is justified only for research purposes or if a large number of units can be simultaneously controlled and logged.

STRAIN CONTROLLED TESTS

Cylindrical compression tests with constant rate of axial strain are likely to continue to form the type of triaxial test most frequently used for routine testing. This type of test can be conveniently run by connecting the loading pressure chamber to a standard control cylinder with a screw-controlled piston (first introduced to operate the null-indicator in undrained pore-pressure measurement by Bishop and Eldin, 1950). The screw is then rotated by one of the drive shafts of the control unit described in the preceding section.

This system gives a remarkably constant strain rate under a varying load, as is shown in Fig. 8. Some initial care is required to free the fluid system from air bubbles. Mechanical details of the control cylinder are given by Bishop and Henkel(1962), Fig. 35.

RANGE AND PERFORMANCE OF APPARATUS

The apparatus was primarily designed for tests on soils of low and medium strength in the low and medium stress range. Even so the apparatus can handle quite a wide range of values of up and ua, the accuracy of the stress paths and stress observations depending mainly on the control and measurement systems used.

It will be seen from eqn (1) that the value of o, depends on p, the pressure in the lower pressure chamber, on the area ratio u/A, where a is the effective area of the Bellofram seal and

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668 A. W. BISHOP AND L. D. WESLEY

kNIm2 lb/in?

Maximum wwking prerrure of Bellofram seal of pressure chamber

Working pressure of Pcrrpex cylinder of

Iwo

-Iwo

-20w -&+ji-$ lb/in?

500 loo0 kN/m’

Fig. 9. Stress limits for hydraulically operated triaxial cell

A the cross-sectional area of the sample, on the value of q and to a minor extent on the weight of the loading ram and sample (IV). In the present design these parameters have the values shown in Table 1.

These values give an upper limit AB to u, in Fig. 9, and a lower limit EF which lies in the tensile stress range for all values of op. It will thus be seen that the apparatus can in principle fail a sample with an unconfined compression strength of over 800 lb/in2 (5516 kN/m2) or a confined stress difference of almost 500 lb/in.2 (3448 kN/m2) at a cell pressure of 150 lb/in.2 (1034 kN/m2).

In extension a maximum stress difference (a,-~~) of 150 lb/in.2 may be applied, if the maxi- mum cell pressure is used and zero adhesion at the end caps assumed. The apparatus is, of course, capable of substantial negative values of (T, if suitable end-grips are used, but these are associated with positive values of up, the line EF representing the limit of the apparatus.

In terms of effective stress the limiting state lines for values of #J’ of 20”, 30”, 40” all lie within the capacity of the cell in compression (Fig. 9), except for 4’ = 40” when associated with a high value of u,’ (or with a large value of c’ and a slightly lower value of u,‘).

Extension tests on samples having significant values of c’ may imply negative values of Us’. While a value of u,’ of almost - 100 lb/in.2 (690 kN/m2) could be obtained by a suitable combination of u= and back pressure in the sample, it would involve the use of end-grips to transmit it to the sample. The limited amount of data on the tensile behaviour of soils (Conlon, 1966; Bishop and Garga, 1969) suggests the maximum tensile stress which could be

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TRLGUAL APPARATUS FOR CONTROLLED STRESS PATH TESTING 669

sustained by an undisturbed soil sample is relatively small. This can be obtained more readily by the use of dumb-bell shaped samples, which are in effect held against the end- caps by a component of the cell pressure. The negative value of ua’ in the central section (where the cross-sectional area is reduced) is associated with a positive value of u,‘, their re- lative values depending, in the limit, on the area ratio selected for the sample (Bishop and Garga, 1969).

The apparatus has been applied only to a limited number of the possible stress paths to date. With the simple control system (without feed-back) the typical paths (b and d in Fig. 5) may ‘wander’ by about 1 kN/m2. The accuracy of measurement is, of course, limited only by the sensitivity of the load cell, pressure gauges and transducers currently in use.

It is of interest to note that calibration tests indicate that the ‘frictional’ force involved in moving the Rotolin bearing and unrolling and rolling up the two Bellofram seals amounts to about 2 N. This is estimated from the differences obtained from calibrations with the ram moving up and with the ram moving down, which amount to a force averaging O-95 lb (4.2 N). This is equivalent to an axial stress difference of 0.54 lb/in.2 (3.7 kN/m2) and must be taken into account in planning the pressure path if feed-back from the load cell is not used.

ACKNOWLEDGEMENTS

The apparatus was developed as part of a programme of research into the influence of stress path on soil behaviour supported by grants from the Science Research Council. Advantage was taken of earlier experience gained with Bellofram seals and Rotolin bearings by Dr H. T. Lovenbury, Dr J. Atkinson and Dr P. Davies. The load cell was designed by Dr A. E. Skinner.

The three prototypes currently in use were constructed at Imperial College by Mr Collin Gagg. Mr E. V. Harris has assisted with the preparation of the illustrations.

REFERENCES Atkinson, J.H. (1973). The deformation of undisturbed London Clay. PhD thesis, University of London. Berre, T. & Bjerrum, L. (1973). Shear strength of normally consolidated clays. Proc. 8th ht. Conf. Soil

Mech., Moscow 1.1, 39-49. Bishop, A. W. & Eldin, A. K. G. (1950). Undrained triaxial tests on saturated sands and their significance

in the general theory of shear strength. Giotechnique 2, No. 4, 13-32. Bishop, A. W. & Henkel, D. J. (1953). Pore pressure changes during shear in two undisturbed clays. Proc.

3rd Int. Conf. Soil Mech. Ziirich 1, 302-308. Bishop, A. W. & Henkel, D. J. (1957 & 1962). The measurement of soil properties in the triaxial test.

London : Edward Arnold. Bishop, A. W., Webb, D. L. &Skinner, A. E. (1965). Triaxial tests on soils at elevated cell pressures. Proc.

6th Znt. Conf. Soil Mech. 1, 170-174. Bishop, A. W. (1966). Sixth Rankine Lecture: The strength of soils as engineering materials. Ge’otechnique

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