Bishop Triaxial Test.pdf

n 11 (" .••.• \:••~:.~.\

THE MEASURE }!; I~' pF SOIL PROPERTIES THE TRIAXIAL TEST By

ALAN W. mSHOP, M.A., Ph.D. , A.l\1.I.C.E. Reader ill Suill\j ecllll1lir.< i" IIII' 1 Ili"ersily

imperial College oj Sciellce

WII)

'if

tOllc/OIl,

Tee/m olo!:.\'

AND

D. ] . lIE JKEL, B.Sc.(Eng.) , A.l\U.C.E. Lecturer ill ivil Etlgilleerill!! Imperial ol/eKe oj Sell' lIcr {/tld Teclu,o/ogy Unit·crsilY of L om}otl

LO ' DON

EDWARD ARNOLD (P BLISllER ) LTD

" '/

J

..., '. ::

"' L ~'

: • r

•

TIlE J\JE .-\S

RE!\lEl\'T OF SOl L PROI'EHT I ES I~

TIlE T IU .·\XI:\!. TEST

A. W. Bishop and D. J. Hell/~el I957 First published I957

-(

NB sst~ : . UP Regional c ~· .~ ~tbrary BaogalOi" ~ . ") r. _4

AccesC] OO

o

§17 ...... .. .

Made and prj"ted itl Great Britai" by William Clowes arId Sons, Limited, Londoll atld Beccles

CONTENTS l'aK.~ PREFA E PART I

PART II

VII

INTRODUCTlO 1. The Role of oil Testing 2. The Principlc of Effecti\'c Stress 3. The Pore-Pressure Parameters A and B 4. Types of Triaxial Test 5. The Application of the Triaxial Test to the:: Solution of Engineering Problems 6. General Remarks on the Advantages and Limitations of the Triaxial Test

1 2 5 8 21 26

PRINCIPAL FEATURES OF THE TRIAXIAL APPARATllS 33 1. Details of the Triaxial Cells for 1t-in. and 4-in. diameter Samples 2. Details of Apparatus for ontrolling the Cell Pressure 3. Details of Apparatus for Measuring Pore Pressure 4. Details of Apparatus for Measuring Volume hange 5. Details of Loading Systems 6. The Use of Side Drains

PART III

PART IV

33 44 52 63 74 81

STANDARD TESTS 1. Preparation of Samples 2. Undrained Tests 3. onsolidated-Undrained Tests 4. Drained Tests 5. Pore-Pressure and Dissipation Tests 6. Tests with No Lateral Strain (Ko-Tests)

106 122 131 140

SPECIAL TESTS

145

1. Drained Tests on Saturated lays with 0'1 Constant and 0'3 Decreasing 2. Undrained Tests on IJartly Saturated Soils with 0'] Constant and 0'3 Decreasing 3. Tests in which Failure is Cau ed by Increasing the Pore Pressure 4. Extension Tests 5. Anisotropic Consolidation 6. Measurement of the Pore-Pressure Ratio iJ under the ondition of Controlled Stress Ratio 7. Measurement of the Pore-Pressure Ratio iJ under Conditions Corresponding to Rapid Drawdown 8. onstant-Volume Tests 9. Tests to Determine the True ohesion and True Angle of Internal Friction v

83 83

94

145 147 149 152 156 160 161 ]63 164

~

CONTENTS

APPENDIX

1 Correction for Strength of Rubber Membrane and Drains

167

APPENDIX

2 Proving-Ring Characteristics

171

APPENDIX

3 Friction on the Loading Ram

174

APPENDIX

4 Rates of Testing

175

APPENDIX

5 Correction for Air Trapped between Sample and Rubber Membrane

179

BIBLIOGRAPHY

181

MANUFACTURERS OF EQUIPMENT

185

INDEX

187

CONVERSION FACTORS

190

PREFA E The part played by laboratory testing in the successful application of soil mechanics to civil engineering problems depends both on the uniformit of the natural strata and on the experience and skill of the engineer. In certain classes of problem, laboratory tests serve mainly to illustrate the principlcs on which a judgment may be based or to set broad limits to the probable behaviour of the soil. In many cases, however, the uniformity of the soil conditions or the importance of the project will justify a more accurate analysis, particularly if this is coupled with field measurement of the pore pressure- the factor most difficult to assess from laboratory data alone. Three classes of problem arc of particular note in this respect: (1) The design of water-retaining structures, such as earth dams and embankments, where failure could have catastrophic results, but where an overconservative design is very costly. (2) The examination of the long-term stability of cuts and natural slopes, where large-scale earth movements may involve adjacent engineering works and buildings. (3) The foundation of engineering works or buildings on deep clay strata. Current methods of stability and deformation analysis call for a range of test data which can be obtained conveniently only with the triaxial apparatus. This is due to the recognition of the advantages, in routine work as well as in research, of carrying out the analysis in terms of effective stresses and explicitly determined pore pressures. This book is therefore restricted to a treatment of the triaxial test alone, and of the ways of meeting the various problems which arise in its use in the laboratory. It cannot be repeated too often that the results are of practical significance only if the geology of the site is understood and if the samples are truly representative of the natural strata or fill, but it is outside the scope of the present tre'ltment to elaborate on this theme. The book is divided into four parts. In Part I the basic principles underlying strength and deformation measurement are briefly discussed in relation to the practical problems commonly encountered in soil mechanics. Part II contains descriptions of the principal features of the triaxial apparatus, including the porepressure, volume-change and load-measuring equipment. Part III presents the procedure for carrying out standard tests, which should be within the competence of a well-equipped laboratory carrying out either research or commercial testing. This section includes, for example, all the types of triaxial test likely to be called for by a consulting engineer dealing with soil problems. In Part IV special tests are described. These are likely to be encountered only in a research laboratory. In many cases these tests consist of an extension of the procedures described in Part III and do not require a detailed treatment. It is felt, however, that it may be of some value to indicate the range of tests which have been successfully performed in the triaxial apparatus and the additional problems entailed.

VllI

PREFACE

This book is not intended to serve as a manual. 1ts purpose is to explain the significant factors in the various types of triaxial test, and to draw attention to matters of practical detail which experience has shown to be important. The authors have drawn primarily on the experience of the Soil Mechanics Laboratory at Imperial College. This has becn done to simplify the presentation, and does not imply lack of regard for techniques and methods used elsewhere. It is obvious that there are many alternative solutions to the mechanical problems of testing. The confidence with which the present methods arc put forward is, however, strengthened by the extent to which they have been adopted by the commercial laboratories in Great Britain, and by a number of laboratories abroad. The authors wish to acknowledge their gratitude to Professor A. W. Skempton for his constant interest and encouragement. The decision to concentrate on the investigation of prob.lems of shear strength and stability was made by Professor Skempton when the Soil Mechanics Section was started in 1946. This decision has provided the opportunity not only for a detail ed study of the accurate measurement of shear strength characteristi(;s, but also for an examination of the relevance of the results to engineering practice. The authors also wish to express their apprc iation to Mr. K. L. Nash, Dr. R. E. Gibson and Mr. A. M. Fraser for reading and criticizing the manuscript; and to Miss . L. I lackcr and Miss P. Mimmack for preparing and checking the typescript. Imperial College 1957

A.W.E.

D.J. H.

THE MEASUREMENT OF SOIL PROPER TIE IN THE TRIAXIAL TEST PART]

IN T ROD UCT IO N 1. The Role of Soil Testing Gne authority after allother has simply evaded th e tash of experimental investiga tion by assuming that some of th e elements afferting the stability of earthwork are so uncertaill ill their operation as to justify their rejection . ... As a matter of fact, although these uncertain elements are lIeglected in investigations, engineers in designing, and stillmore contractors ill executing Y')orks, do 1I0t lIeglect them, nor could they do so without leading to u blametvorthy waste of mom')' in some instances, alld to a discreditable failure ill others. The result of the present Wa7lt of experimelltal data is the'll simply thaI. individual judgemellt has to be exercised in each instance without that aid from careful experimental investigation which in these times is enjoyed in almost every other brallch of ellgineering . ... Sir Benjamin Baker, 188 1: Thl' Actual Lateral Pressure of Eartlzworh.· Unfortunately, the research activitifS ill soil mechanics had one undesirable psychological effect. They divl'rted the attention of many illvestiKators alld teachers from the malllfold limitations imposed by 1Iature OIL the applicatioll of mathematics to problems ill earthwork ellgineering. As a consequen.ce, more and more emphasis has been placed on refinements in sampling alld testirlg and 01/ those very few problems that can be solved with accuracy. Yet, accurate solutions can be obtained ollly if the soil strata are practically homogelleous and contilluous ill horizolltal direcl.iolls . . . . On the overwhelming majority of jobs no more than all approximate forecast is needed, and If such a forecast callnot be made by simple means it canllot be made at all. Karl T erzaghi and Ralph Peck, 1948: Prcface to Soil MechCl1lics in Engineering Practice.

The civil engineer, in facing the practi cal problems raised by the use of the soil as a foundation and as a construction material, has frequently to strikc a balance between the need for a careful experimcntal investigation and th e need for simplicity in the means employed. His dccision will depend on his own experience and on thc magnitude, or novelty, of the particular problem. His difficulty in reaching a decision is often increased by lack of certainty as to what testing procedure is appropriate and practicable in each case. The use of accurate, and even elaborate, methods of testing requires no justification in the research laboratory. The extent to which these methods should be adopted in routine testing depends largely on whether or not they reduce the margin of uncertainty in design sufficiently to justify their cost. The answer is in many cases self-evident. In many less important cases, however, a wider issue is involved. The engineer'S own fund of empirical knowledge is • Full references are given in the Bibliography, p. 181. I-M.S.P.

THE TRIAXIAL TEST: PART I

made more certain in its future application if it is based on quantitative measurements of the relevant soil properties and of the subsequent performance of the actual structure. Valuable data may be obtained from straightforward as well as from difficult jobs. For the laboratory measurement of shear strength under controlled conditions of drainage, and of deformation characteristics (other than compressibility), the engineer is largely dependent on the triaxial test. The test may, however, be performed in various ways; and, in order to distinguish between the different types of test and relate them to the more common practical problems, it is necessary to make a brief survey of the basic factors controlling shear strength and deformation.

2. The Principle of Effective Stress The strength and deformation characteristics of soil are best understood by visualizing it as a compressible skeleton of solid particles enclosing voids which, in saturated soil, arc filled with water, or, in partly saturated soil, with both air and water. Shear stresses can of course be carried only by the skeleton of solid particles. On the other hand, the normal stress on any plane is, in general, the sum of two components- the stress carried by the solid particles and the pressure in the fluid in the void space. This, from the practical point of view, has two important consequences: l. In the relationship between normal stress ami volume change the controlling factor is not the total normal stress, but the difference between the total normal stress and the pressure of the fluid in the void space, termed the pore pressure. For an equal all-round change in stress, this is expressed quantitatively by the relationship : ~V

V where /j. V/V /j. /j.u c and

(7

= -Cc(~(1-~It)

(1)

denotes the change in volume per unit volume of soil , denotes th change in total normal stress, denotes the change in pore pressure denotes the compressibility of the soil skeleton, for the particular stress range considered.

The difference (1-U is termed the effective stress and denoted by the symbol It is important to note that equation (1) is valid whatever the contact area between the solid particles [Bishop and Eldin, 1950; Laughton, 1955J, though within the stress range encountered in engineering problems this area is likely to be small. This relationship may be illustrated by a conclusion of practical importance which follows directly from equation (1). A volume change will occur, without any change in the applied or total stress, if the pore pressure undergoes a change (Fig. 1). This is the primary cause of the long-term settlements of buildings founded on clay, in which the excess pore pressure set up during construction dissipates only at a slow rate. It is also the explanation of the additional settlements caused by ground water lowering, either for construction work or for water supply. 2. The shear strength of soils, as of all granular materials, is largely determined by the frictional forces arising during slip at the contacts between the soil particles. These are clearly a function of the component of normal stress carried by the solid skeleton rather than of the total normal stress. For practical (1 '.

3

(6)

(a)

- .6v

V

~----

(c)

Stage 11

Time

(d)

Time

(e) .60-' = .6cr- .6u

Time Time

(r)

- .c..v v

Fig. 1. The effect of pore-pressure dissipation on volume change (a) stress system applied to element; (b) relationship between decrease in volume, -!l VIV, and increase in effective stress !l a' ; (c) changes in total stres during test: stage I- increase in total stress !la under undrained conditions ; stage ll-dissipation of pore pressure under constant total stress ; (d) changes in pore pressure !lu; } (e) changes in effective stress !la'; in a fully satul'ated soil. (f) changes in volume, -!lVIV.

THE TRIAXIAL TEST : PART I

purposes the maximum resistance to shear on any plane ('Tj) is given by the expression: (2) 7"j = c'+(cr-u) tan rp' where c', denotes the apparent cohesion, } 10 . terms 0 f euee LX: t' . . lve s t ress r/> denotes the angle of shean.ng rpststallce, (] denotes the total pressure normal to the plane considered and, 11 denotes the pore pressure. In most engineering problems relating to stability, the magnitude of the total normal stress on a potential slip surface may be estimated with reasonable accuracy from considerations of statics. On the other hand the magnitude of the pore pressure is influenced by several factors, which are often incorrectly reproduced by conventional laboratory tests. (a) In the simplest case, that of stationary ground water, the magnitude of the pore pressure is determined by the position of the element of soil under consideration, relative to the ground water level. Where conditions approximate to steady seepage (for example, in natural slopes; and in cuts and earth dams after the influence of the pore-pressure changes during construction has died out) the pore pressure is obtained from the flow net corresponding to the known boundary conditions. The flow net may be computed or may be based on field observations of pore pressure. The pore pressure is thus an independent variable and its magnitude is not related to that of the total normal stress. The function of the triaxial test is simply to obtain the relationship between shear strength and effective normal stress. In soils of low permeability it may, however, take many years to establish a steady flow condition in the field. (b) More generally, a change either in the normal stress or in the shear stress carried by the solid keleton of the soil results in a tendency for a volume change to occur within the soil mass. Unless the conditions of drainage are such that the fluid in the pore space can be freely expelled, an excess pore pressure will temporarily result from the stress change. The rate at which this excess pore pressure will dissipate depends principally on the permeability of the soil, as reflected in its coefficient of consolidation. For thick clay strata and for impervious rolled fills the time required may be many years. During this period the pore pressure is a function of (i) the initial stress change, (ii) the coefficient of consolidation and (iii) the distance of the soil element from a surface at which drainage can occur. Cases falling into this category include:

i. The stressing of natural strata forming the foundation of a structure or of an earth daro. ii. The stressing of the compacted impervious fill of an earth dam during construction due to the weight of the superimposed layers. iii. The removal of the water load on the impervious fill of an earth dam due to rapid drawdowo. iv. The formation of slopes and cuttings in natural strata, in which porepressure changes result from the removal of the weight of the overlying soil. In such cases the laboratory test may be called 00 to provide data not only on the relationship between shear strength and effective stress, but also on the initial pore pressure set up by a change in stress.

INTROD CT I O

5

The use of the principle of effective stress in stability analysis thus involves two steps; first, the determination of the shear strength parameters c' and cp' and, second, the prediction of pore pressure at the most critical stage either of construction, operation or long-term stability. The pore pressure is the more difficult of the two to estimate with accuracy and for this reason field measurements of pore prt:s ure are made on many important engi neering works. The explicit determination of pore pressure may be avoided in the special case where the stress change likel y to cause failure is imposed under conditions which allow only negligible dissipation of the excess pore pressure to occur. The sample of soil is tested under undrained conditions and the shear stres at failure is expressed as a function of the total normal stress. The stability analysis is similarl y performed in terms of total stress. The relationship between the behaviour of soi l tested under undrained conditions and the strength characteristics expressed in terms of effective stress depends on the magnitude of the pore pressures set up in the test. To obtain a clear picture uf how the pore pressure responds to the different combinations of applied stress, the concept of pore pressllre parameters is found to be convenient [Skcmpton , 1954; Bishop, 1954 (a)]. This concept serves not only to explain the relationship between the different types of triaxial test, but also provide a basis for estimating the magnitude of the pore pressures to be encountered in practical problems.

3. The Pore-Pressure Parameter A and B The physical basis of the parameters is understood most easily by considering the simple case in which the compressible skeleton of soil particles behaves as an elastic.: isotropic.: material and the fluid in the pore space shows a linear relationship between volume change and stress. An increase in the three principal stresses of ~uJ' ~U2 and ~(J3 will result in a decrease in volume of -~ V (where V is the initial volume) and a consequent increase in pore pressure of l1u. The increases in the effecti ve stres es will be:

(3)

The decrease in vol ume of the soil skeleton is then AV

-u

= V '(1-2/L){A -E-

,

A

,

A

UUl +1..10'2 +1..10'3

'}

(4)

where E and /L are respectively Young's modulus and Poi son's ratio with respect to changes in effective stress. The decrease in volume of the soil keleton is almost entirely due to the decrease in vol ume of"the voids. If 11 is the initial porosity, and Cw the compressibility of the fluid in the pore space, this volume change is related to the pore-pressure change, if no drainage occurs, by the exp ression : (5)

It follows, therefore, that

n .Cw' ~u = 1~2/L{~O'l'+I1O'2'+I1O'a'}

(6)

6

THF. TRIAXIAL T ES T : PART I

The type of triaxial test most commonly used in research work and in routine testing is the cylindrical compression test, p. 9. In this test the stress changes are usually made in two stages: (i) an increase in the cell pressure resulting in an equal all-round change in stress and (ii) an increase in axial load resulting in a change in deviator stress. Under these conditions the changes in minor and intermediate principal stresses (6.O'a and 6.0'2 respectively) are both equal to the increase in cell pressure ; the increase in deviator stres is equal to 6.0'1-6.0'3' Putting 6.0'2 = 6.0'3, equations (3) and (6) lead to an expression for t:;.u which may be arranged into terms representing the change in cell pressure 6.0'3 and the subsequent change in deviator stress (~0'1-~O'a):

6.u

1

= I +n(CwfC}6.0'3+H~0'1-~0'8)}

(7)

where Cr = 3{ 1-2fL)fE, the compressibility of the soil skeleton. It is thus apparent that a change in pore pressure will in general result firstly from a change in all-round stress, and secondly from a change in deviator stress. In practice it has to be recognized that the volume change characteristics of the soil skeleton are non-linear, and that the principle of superposition is valid only under certain conditions. The value of Cru is a constant only in fully saturated soil. The corresponding changes in pore pressure arc thercfort: expressed in terms of two empirical parameters A and B, where (8)

For fully saturated soils the alue of CrQ-that of water alone- is so small that B = 1 to within the limits of experimental accuracy. The value of A depends very largely on whether the soil is normally consolidated or overconsolidated, and on the proportion of the failure stress applied [Skempton, 1954; H enkel, 1956]. This is illustrated by test results in Fig. 2. Values of A for typical undisturbed and remoulded soils are given in PART III , p. 117. In the case of partly saturated soil, the value of C r" is much hight:r, due to the presence of air in the pore space.4! The value of B is thus less than 1, but varies with the stress range. The value of B which applies during the application of the deviator stress (AO'l-6.0'3) is thus different from the value applying during the increase in all-round stress AO'3' For this reason it is often more convenient not to separate the terms of the product AB but to denote it by A and express equation (8) in the form:

6.u = B .AO's+A(AO'l- AO'a)

(9)

Where the purpose of the test is the accurate prediction of pore pressure at states of stress other than failure, the sequence of stress increments occurring in practice is followed more closely in the test by making simultaneous increases of both a] and as. The test result is presented in terms of the relationship between pore pressure and change in major principal stress, for the specified stress ratio, using the expression: (10) • urface tension results in pressure differences between the air and water omprtsmg the fluid phase, and a rigorous analysis requires a modified expression for effective stress. For soils in which the degree of saturation is high enough to lead to pore pressures of practical importance, the expression ,,' = is sufficiently accurate, Ii being taken as the pressure in the pore water.

,,-u

(a)

Normally_ consolidated Consolidation pressure · p

consoltdatlon pressure 'p over-consoltdatlOn ratto 8

OJ - Oj

OJ -Oj

0

(6)

0

AXial stram

fiU~V

AXial stram

+ t::.u

0

AXial stram

AXial strom

+10

(c)

A 0 ·5

OL-------------------+

AXial strain

AXlol stram· -0·5

(d)

+10

0 ·5

Ar o -0·5

'""

~

1

2

4

~ :--8

16

-

32

Ovef!.consoltdatlon ratio Fig. 2. The change in pore pressure during the application of the deviator stress; typical results for normally and over-consolidated clay samples (a) (b) (c) (d)

deviator stress, pore pressure change. and va lue of parameter A. plotted against axial strain; A,. the value of A at failure, plotted against over-consolidation ratio.

8

THE TRIAXIAL TEST: PART I

Practical examples of the use of this parameter are given elsewhere [Bishop , 1954- (a), 1955]. It should be noted that many practical problems approximate more closely to the condition of plane strain than to that of axial symmetry used in the standard triaxial test. Apparatus to give the condition of plan e strain with controlled conditions of drainage and with the measurement of pore pressure is seldom available.· Both c' and ' and the pore-pressure parameters will be influenced by the use of a modified value for the intermediate principal stress. The influence on the pore-pressure parameters for the idealized elasti c soil may be seen by substituting in equation (6) the plane strain condition:

(11) This leads to an expression for

~u:

(12)

where Cc = 2(1 +,..,.). (1-2,..,.)/E, which represents the volume change characteristic in plane strain under changes in a 1 and au. The pore-pressure parameters A and B corresponding to plane strain must therefore be expected to be somewhat different from those obtained by the standard triaxial test. There is little direct evidence of the magnitud e of this differen ce, which is only one of several factors influencing the relationship between laboratory measurements and the actual fi eld values of pore pressure and undrained strength. Another factor, difficult to reproduce in the triaxial apparatus, is the rotation of the planes of principal stress. In many practical problems of slope stability, earth pressure and foundation design , the principal directions of the components of the stress change made under undrained conditions do not correspond to those of the stresses under which the sample was consolidated. This limitation is usually ignored in applying the results of laboratory tests and affects the accuracy of the estimate of pore pressure and of undrained strength [Hansen and Gibson, 1949). Finally, it should be noted that it is the chaTlge in stress imposed under undrained conditions which determines the pore pressure set up and hence the value of 'T_r-the shear stress at which failure occurs btained in an undrained test. The initial state of stress before this change must be correctly represented in the test, if the relevant pore-pressure and strength values are to be measured. Results obtained from tests, in which the initial consolidation is under an equal all-round pressure, cannot therefore be applied directly to practical problems without making allowance for the probable stress ratio in the natural ground.

4. Types of Triaxial Test Ideally, the triaxial test should permit . independent control of the three principal stres es (Fig. 3), so that generalized state of stress can be examined, including the important special case corresponding to plane strain. However, the relatively high compressibility of the soil keleton and the magnitude of the shear strains required to cause failure lead to mechanical difficulties which make • The difficulties ar referred to in

PART

1, 4.

INTRODUCTIO

9

independent control too complicated for other than special research test.· The type of triaxial test most commonly used in research work and in routine testing is the cylindrical compression test. In this test, shown diagrammatically in Fig. 4, the cylindrical specimen is sealed in a water-tight ruhber membrane and enclosed in a cell in which it can be subjected to fluid pressure. A load applied axially, through a ram acting on CT,

~-

Fig . 3. Strca sy tern

/ the top cap, is used to control the deviator stress. L nder these conditions the axial stress is the major principal stress Gl; the intermediate and minor principal stresses (G z and Ga, respectively) are both equal to the cell pressure. t Connexions to the ends of the sample permit either the drainage of water and air from the voids in the soil or, alternati\'ely, the measurement of the pore pressure under conditions of no drainage. Generally the application of the all-round pressure and of the deviator stress form two separate stages of the test; tests are therefore classified according to the conditions of drainage obtaining during each stage:

i. Undrained tests. No drainage, and hence no dissipation of pore pressure, is permitted during the application of the all-round stress. 0 drainage is allowed during the application of the deviator stress. ii. Consolidated-undrained tests. Drainage is permitted during the application of the all-round stress, so that the sample is fully consolidated under this pressure. No drainage is allowed during the application of the deviator stress. iii. Drained tests.! Drainage is permitted throughout the test, so that full consolidation occurs under the all-round stress and no excess pore pressure is set up during the application of the deviator stress. • Kjellman (1936) and Buisson (1948) have experimented with apparatus of this type. A plane strain triaxial apparatus has recently been constructed at Imperial College. t Alternatively an extension test may be carried out by using a tension fitting between the ram and the top cap. In this case the axial stress is the minor principal stress 113, and the intermediate and major principal stresses (11. and 1110 respectivrly) are equal to the cell pressure. This procedure is less common. t In carrying out drained tests on soils of low permeability, sufficient time must be allowed for the excess pore pressure to dissipate. The rate of tcsting thus depends on the coefficient of consolidation of the soil and on the dimensions of the sample, but is usualJy slower than for undrained tests. lasses i , ii and iii are therefore sometimes referred to as quick, eomoNdated-quick and slow, tests respectively. As the rate of testing may also be varied to examine the influence of rate on the values of c' and .p', thi alternative terminology may lead to confusion.

)0

THE TRIAXIAL TEST: PART I

Axial load

! AII' t'elease valve _

Pressure gauge

Loading ram

Rubber

_ -Top cap ~~~~

_. - Porous disc -Flex/ble tube

Water-

-+

. - Sample enclosed in a rubber membt'cme

Rubber

_ . - Pot'ous disc ~ Sealing ring

\

~

To cell pt'essure control

n

/

~

_

\

,,-onnex/ons ,or vramage or pore pressure measurement

Fig. 4. Diagrammatic layout of the triaxial test

These classifications may be further qualified, for special tests, by indicating, for example, whether failure is caused by increasing 0"1 or by decreasing O"s' The state of stress during the consolidation stage may also be modified to give a principal stress ratio (Jl'/(J:/ greater than 1. The application of the triaxial test to the principal soil types will be considered under these classifications: (a) ndrained test on saturated cohesive soils. (b) Undrained test on partly saturated cohesive soils. (c) Consolidated-undrained test on saturated soils. (d) onsolidated-undrained test on partly saturated soils. (e) Drained test.

(a) Undrained test on saturated cohesive soils This test is carried out on undisturbed .samples of clay, silt and peat as a measure of the strength of the natural ground; and on remoulded samples of clay when measuring ensiti ity or carrying out model tests in the laboratory. The deviator stress at failure is found to be independent of the cell pressure (with the exception of fissured clays and compact silts at low cell pressure-). • Generally"," = 0 for fissured clays at cell pre ures above the overburden pressure . For silts the departure from the "'" = 0 condition is associated with dilatancy [Bishop and E ldin,1950) .

lNTROD

TlON

II

Fig. 5 shows the corresponding Mohr stress circles. If shear strength is expressed as a function of total normal stress by oulomb's empirical law : 'j

=

c,,+a tan /1

(13)

where e" denotes the apparent cohe ion }With respect to changes in total and CPu denotes the angle of sh ating resistance stress, then it follows that, in this particular case,

(14)

T

,Effect/lie stl'esses~!, 2 &3) \ ;'

/\¢' ",,---

",/

Fig. 5. Mohr stress circles for undrained tests on saturated cohesive soil The shear strength of the soi l, expressed as the apparent cohesion, is used in a stability analysis carried out in terms of total stress, which, for this type of soil, is known as the = 0 analysis [Skempton, 1948, (a) and (b)]. If the pore pressure is measured during the test the effective stresses at failure can be determined. It will be found that for saturated clays both the major principal effective stress aI' (= al-u) and the minor principal effective stress as' (= a3-u) are independent of the magnitude of the cell pressure applied. Hence only one effective stress circle (Fig. 5) is obtained from these tests and the shape of the failure envelope in terms of effective stress cannot be determined. Consolidated-undrained or drained tests are u ed for this latter purpose. Changes in pore pressure OCcur during the sampling and preparation of undisturbed samples as the result of the removal of the in-situ principal stresses, which are generally not equal. This fact, quite apart from any disturbance during this operation, leaves the sample with a modified stress history. Consequently the A-value, measured during the subsequent undrained test, is very different from the value in-situ under a similar change in shear tress. This has been discussed in more detail by Hansen and Gibson, 1949; and illustrated by laboratory tests, Bishop and Henkel, 1953 (a). For these reasons, pore-pressure measurements are not usually made during undrained tests on aturated samples. The failure stress is taken to be the maximum deviator stres which the sample can withstand. Where the stress train curve has a pronounced peak this value is unambiguous. In some soils which have softened after being heavily consolidated, and in remoulded soils, failure takes the form of plastic yield at a constant stress and occurs only after very large axial strains. Termination of the test at an arbitrary strain of 10% or even 20% may lead to an underestimate of strength.

THE TRIAXIAL TEST: PART I

12

(b) Undrained test on partly saturated cohesive soils The most common application of this test is to samples of earth-fill material which are compacted in the laboratory under specified conditions of water content and density. It is also applied to undisturbed samples of strata which are not fully saturated (for example, residual soils), and to samples cut from existing rolled fills or trial sections. In the latter cases the density change which may occur during the driving of a sampler must not be overlooked.

T (a)

T elL L 03

0;-

cr

(6)

Fig. 6. Mohr stress circles for undrained tests on partly saturated soil (8) total stresses,

(b) effective stresses .

The deviator stress at failure is found to increase with cell pressure. This increase becomes progressively smaller as the air in the voids is compressed and passes into solution, and ceases when the stresses are large enough to cause full aturation. The failure envelope expressed in terms of total stress is thus nonlinear Fig. 6 (a), and values of e" and
INTRODUCTION

13

The pore pressure recorded when the all-round pressure is applied • gives the value of the parameter B. The value of A is obtained from the pore-pressure change during the application of the deviator stress. Typical values are given in PART III, p. 106. In determining the values of c' and cp' in any test in which shear occurs under undrained conditions, a possible ambiguity arises about the state of stress to b The deviator stress and pore-pressure changes denoted by the term" failure occurring during an undrained test on a sample which tends to dilate when sheared arc illustrated in Fig. 7, (a) and (b). Values of c' and " almost equal to their maximum values, are found to be mobilized at quite a small fraction of the strain required to produce the maximum deviator stress. The increase in deviator stress occurring after this point is almost entirely the consequence of the drop in pore pressure- for example, from point (I) to point (2)- due to the tendency of the soil to dilate when sheared. It is therefore open to question whether stress circle (2) can be termed the state of stress at failure with any greater justification than some intermediate stress circle such as (I), Fig. 7 (c). The choice of the stress circle to be used to express the result of the test is of importance only since c' and ' decrease gradually after reaching their max.imum values. A prolonged drop in pore pressure will result in values of c' and 4>' based On the maximum deviator stress being slightly less than their peak values. The practical significance of this difference is usually negligible. It may be necessary, however, to examine the limiting values of c' and 4>' more closely in research investigations. Results of tests on a moraine, compacted abo 'e the optimum water content, which show this effect to a very marked extent, are illustrated in Fig. 8. A series of Mohr circles representing the states of stress at various strains is shown in Fig. 8 (b). I t will be seen that, for this soil, the stress circles for axial strains greater than 1% project outside the failure envelope obtained by the maximum deviator stress failure criterion (from results of the three tests shown in Fig. 8 (a)). For the circles which project furthest an upper limiting shear strength envelope can be drawn. In the special case of a soil in which c' is zero it follows immediately from the geometry of the Mohr diagram that the effective stress circle tangential to the limiting envelope also has the maximum principal stress ratio (11'/(13'. The circle can thus be identified directly from the tabulated results of the test. The use of the maximum principal stress ratio as the failure criterion is sometimes recommended, however, for cases in which c' is not zero [for example, by Holtz, 1947]. This results in the selection of a stress circle occurring slightly before the limiting envelope is attained. The consequent difference in c' and 4>' is small. There is some evidence that values of c' and 4>' obtained from the limiting envelope are in closest agreement with the results of drained tests, where no pore-pressure change occurs. However, the use of the stress circles corresponding to maximum deviator stress has the practical advantage of giving wider separation of the stress circles and thus a more clearly defined failure envelope in cases where the degree of saturation is high. This failure criterion will therefore be used unless otherwise stated. t fl.

• For practical purposes the change in pore pressure is expressed with respect to an assumed initilll pore pressure of zero in the unstressed sample. No error is involved if B is applied in practice on the same basis. For samples other than those having a low clay fraction or compacted wet of the optimum, appreciable negative pressures in fact occur in the pore water of the unstressed sample. t The same ambiguity arises in consolidated-undrained tests; comparative test results are given by Bishop and Eldin, 1953.

THE TRIAXIAL TEST: PART

r

(a)

01-0"3

Axial strain

(6)

03

"3 u.

u

A x fa / strain

(c)

Fig. 7. The variation of state of stress during an undrained test on a dilatant soil (a) deviator stress, nnd (b) pore pressure change, plotted against axial strain; (c) Mohr circles in terms of effective stress.

INTROD

TIO '

(0) 60 ~--~--~----~~

taper Sf{.

m4.nI-- -l---l-,LAr-=t:::::",._J

140

r

160

180

30

(6) 20

/b.per

sq In. 10

30

40

50

/ b. per sq.In. Fig. 8. Undrained tests on partly saturated soil (a) comparison of Mohr envelop s at maximum principal stress ratio and at maximum deviatior stress from tests I, II and III on compacted moraine, at different cell preSSUf(;!S . (b) states of stress for various strains during test I.

The fact that the values of c' and if) remain almost constant over a considerable range of strain can be used to advantage when onl y a limited amount of soil is available for testing or where the samples are very variable. tarting at a low cell pressure, the test is run in the ordinary way until the ratio of the effective stresses, a/las', reaches its peak value. The cell pressure is then increased to a higher value and the test continued until a new peak stress ratio is obtained. A test conducted in this way in three or four stages provides the necessary separation between the" failure" circles to define a satisfactory Mohr envelope. Examples of the use of the multi-stage test are given by Taylor (1951), Fleming (1952) and Lewis (1954). Some loss in accuracy in the measured c' and if) values may occur, and less information about the pore-pressure parameters is obtained than in the usual series of three or four separate tests. (c) Consolidated-undrained test on saturated soils This test is carried out on undisturbed samples of clay, ilt and peat; on remoulded samples of clay and silt; and on redeposited am pIes of cohesionless

16

THE THIAXIAL TEST: PAHT 1

soils such as sand and gravel. In the case of cohesionless soils the rubber membrane is supported by a rigid former while the sample is deposited under water within it. A small negative pore pressure is applied while the former is removed, to give the sample sufficient strength to stand unsupported until the cell pressure can be applied. In the standard test the sample is allowed to consolidate under a cell pressure of known magnitude (P), the three principal stresses thus being equal. Then the sample is sheared under undrained conditions by applying an axial load. As in the case of the undrained test (p. 10), the cell pressure at which the sample is sheared does not influence the strength (except of dilatant sands). The test result, in terms of total stresses, may thus be expressed as the value of CII' the apparent cohesion, oil< plotted against consolidation pressure p, Fig. 9 (b). For normally consolidated samples the ratio clI/p is found to be a constant, its value depending on the soil type. However, undrained triaxial tests and vane tests on strata existing in nature in a normally consolidated state lead to a lower estimate of the ratio cu/p than is found in samples consolidated under equal all-round pressure in the laboratory. The difference increases as the plasticity index decreases and may be attributed mainly to two causes: (i) A naturally deposited sediment is consolidated under conditions of no lateral displacement, and hence with a lateral effective stress considerably less than the vertical stress. The ratio of lateral effective stress to the vertical effective stress, termed the coefficient of earth pressure at rest, generally lies in the range 0·7-0·35, the lower values occurring in soils with a low pl3i:~ticity index. The reduction in the value of clI/p which results when samples are consolidated in the laboratory under this stress ratio, instead of under equal all-round pressure, may be as much as 50% and is illustrated by tests published elsewhere [Bishop and Henkel, 1953 (a) j Bishop and Eldin, 1953]. The theoretical basis of the difference is discussed by Hansen and Gibson (1949) and Skempton and Bishop (1954). (ii) Reconsolidation in the laboratory after the disturbance which is associated even with the most careful sampling leads to a slightly lower void ratio than would occur in nature. The value of the pore-pressure parameter A in particular is sensitive to the resulting modification in soil structure and this, in turn, leads to a higher undrained strength.t For these reasons the results of consolidated-undrained tests, expressed in terms of total stress, can be applied in practice only to a very limited extent. If the pore pressure is measured during the undrained stage of the test, the results can however be expressed in terms of effective stress. The values of c' and cp' thus obtained can be applied to a wider range of practical problems. In Fig. 9 the relationships between the total stress, pore pressure and effective stress characteristics are illustrated. The points a, band C represent normally consolidated samples j the point d represents an over-consolidated sample, the over-consolidation ratio being Ph/Pd' Fig. 9 (a). For normally consolidated samples the effective stress envelope, Fig. 9 (d), is a straight line with c' equal to zero, cp' depending on the type of soil. Over-consolidation results in an envelope lying a little above this straight line j a section of this envelope, over a specified • As before Cu = t( u, -us)" since rPu = 0 with respect to changes in total stress during undrained shear. . t In certain marine clays, the salinity of the pore-water has been reduced by leaching after the process of natural consolidation hos occurred. The ratio cu/p with respect to further consolidation of the leached strata is greatly in excess of the value occurring in the natural strata where consolidation preceded leaching. [Bjerrum and Rosenqvist, 1956.]

./

(d)

T

Effective normal stress

0-'

Fig. 9. Consolidated-undrained tests on saturated soil (n) (b) (c) (d) 2-M.S.P.

water content. undrained strength. and value of At. plotted against consolidation pressure p; Mohr envelope in terms of effective stress.

18

THE TRIAXIAL TEST; PART I

stress range, being represented with sufficient accuracy by a slightly modified value of f and a cohesion intercept c'. The most marked effect of over-consolidation is, however, on the value of A, which, with increasing over-consolidation ratio, drops from a value typically about J at failure to values in the negative range. These low A-values are, in turn, largely responsible for the high undrained strength values resulting from over-consolidation (compare point d, Fig. 9 (b) , with point a). Values of c' and cp' are usually based on the effecti ve stress circles corresponding to maximum deviator stress. In tests on over-con olidated clay samples and on samples of sand the limiting values of c' and f may occur at an intermediate stage, as explained in the previous section. Here again the difference is of importance only in research investigations, a typical result for sands being an underestimate of cp' by about 2 0. (d) Consolidated-undrained test on partly saturated soils This test may be called for in the determination of c' and f on undisturbed samples or on compacted samples of earth fill, in particular when the degree of saturation is not low enough to result in a sufficient range of strengths in the undrained test to define a satisfactory failure envelope. It may also be used to examine the effect on c' and f of flooding foundation strata and earth-fill materials, and indicates the magnitude of the accompanying volume change. Flooding, even for a period of months under an appreciable hydraLllic gradient, does not produce full saturation in the laboratory. Hence in all such tests the strength, measured during the undrained stage of the test, is not independent of changes in cell pressure at this stage, and cannot be expressed simply by a value of Cit as in the case of a saturated soil. A total stress analysis is thus quite impracticable. The values of the effective stresses at failure are obtained from measurement of the pore pressure, and values of c' and cp' are thus determined. (e) Drained test Drained tests are carried out on soil samples of all types either undisturbed, remoulded, compacted or redeposited. The samples may be either full y or partly saturated. ohesionless materials such as sand, gravel and rock-fill are often tested dryas it simplifies laboratory procedure. This may, however, lead to a slight over-estimate of the value of f in some cases. Tests on sugar, grain, etc., for silo design are also performed under normal "air-dried" conditions. In the standard test consolidation takes place under an equal all-round pressure, and the sample is then sheared by increasing the axial load at a sufficiently slow rate to prevent any build-up of excess pore pressure. The minor principal stress as' at failure is thus equal to p, the consolidation pressure; the major principal stress ai' is the axial stress. Since the pore pressure is zero, the effective stresses are equal to the applied stresses, and the strength envelope in terms of effective stress is obtained directly from the stress circles at failure, Fig. 10. The values of c' and tj/ obtained from drained tests are often denoted Cd and CPd respectively. The drained test also provides inform.ation on the volume changes which accompany the application of the all-round pressure and the deviator stress, and on the stress- strain characteristics of the soil.

An appreciation of the relationship between the results of the different types • See also p. 26 ; kempton and Bishop, 1950; and Bishop, 1952.

INTROD UCTlO

(a)

T

Normally consolidated

0-'

(6)

Over-consolidated

0-'

OJ

=p

Fig. 10. Mohr stress circles for drained tests (a) on normall y consolidated sam ples, and (h) on over-consolidated samples.

of test is essential to their correct application in practice. The theoretical background is discussed elsewhere [Skempton and Bishop, 1954]. The application of the results to the principal classes of stabi lity analysis is outlined in PART I, 5, p.21. Two general conclusions about the interrelationship of the test results may, however, be kept in mind in both stability and deformation problems: (1) For a given sample of soil, the shear strength parameters c' and cf/ are almost independent of the type of test used to measure them, with the following qualifications: (a) For normally consolidated clays the values of c' and if>' obtained from consolidated-undrained tests with pore-pressure measurement and from drained tests are, for practical purposes, identical provided comparable rates of testing are used. (b) For heavily over-consolidated clays and for sands (except in a very loose state) the drained test will lead to slightly higher values of c' and 4>', due to the work done by the increase in volume of the sample during hear and to the smaller strain at failure. (c) For some compacted fills and other partly saturated samples, the value of c' will be reduced if an increase in water content occurs in the consolidated-undrained or drained test.

THE TRIAXIAL TEST: PART I

20

(2) In contrast, deformation and volume-change characteristics in drained tests, and pore-pressure and undrained strength characteristics in consolidatedundrained tests, are largely controlled by the sequence and sign of the stress changes. This may be illustrated by two examples. In Fig. 11, the stress-strain and volume-change characteristics are compared for two samples of loose sand, consolidated with zero lateral strain. Fig. 11 (a) represents failure with (71

Stress

(OJ)o t--_____ (T.;....,

Fa/lure with OJ mcreasing

oa

Failure with Oi decreaSing

(O])o=Ko(Oj)o t-------__;!,..._

°o~--~~-----~ Ax/al strain

(]

oO!---A"-X-IO-I'-s-tro-in--

Axial strain

or----~~~~-----~

(6) (0)

Fig. 1 t . Drained tests on loose sand, consolidated with zero lateral strain (3) failure with a, increasing, and (b) failure with a. decreas in~.

increasing, as in the standard test. Fig. 11 (b) represents failure with (7s decreasing and (71 constant, as in the active earth pressure case. The marked difference in strain and volume change at failure will be seen. In Fig. 12 a comparison is made between the undrained and drained strength of two identical samples of clay, normally consolidated under the same all-round pressure p. In Fig. 12 (a) the samples are failed by increasing (711 (73 remaining equal to p. The drained strength is, in this case, greater than the undrained, the slope of the consolidated-undrained failure envelope (denoted by the angle c/>tu) being about one-half that of the effective stress envelope. This is the standard case usually illustrated, and corresponds to passive earth pressure conditions. However, if failure occurs with (7s decreasing and (7] constant (and equal to p), as in the active earth pressure condition, the undrained strength remains unchanged, but the drained strength is grea;Iy reduced, Fig. 12 (b). For most soils the total stress envelope for this condition leads to a value of c/>
INTROD UCT IO N

21

The value of r/>cu obtained from the standard test will therefore be seen to be of limited application . in practice. In many slope stability problems which approximate more closely to the active earth pressure ca e, it gives a quite misleading impression of the strength changes occurring when passage of time permits the drained condition to be established.

7

0/.. Increasm9_g;

Fal/llre

Dramed test. / - - -- / effectIVe stresses

(a)

_.... ·....-rI/JCLl

I,

(OJ

(b) 7

leu

I

OJ =p

&cu

Fat/tire by" decreasmg.2j c- u test.- toto/stresses

./

/

c- u test .- effective stresses '--~_""r- Drained test,effective

stresses

\ \

_~')Cti

-p

(U)cu' negatIVe

Fig. 12. Comparison between drained and undrained strengths of samples of normally consolidated clay (a) failure by increasing (1" and (b) fa ilure by decreasing " •.

5. The Application of the Tr iaxial Test to the Solution of Engineering Problems Much of the work carried out with the triaxial apparatus has been directed towards the basic understanding of soil properties rather than to the immed iate solution of engineering problems. In this section a brief indication will be given of the types of triaxial test used in the main classes of engineering problem ininvolving stability analysis.· The problems may be di vided into two main classes in which [I] the pore pressure is independent of the magnitude of the total stresses acting in the soil; and [n ] the pore pressure depends on the magnitude of the stresses acting in the soil and on the time which has elapsed since their application. • A detailed discussion of the theoretical background and field evidence supporting the various methods is in course of preparation .

22

THE TRIAXIAL TEST: PA RT J

[I) Analyses in which pore pressure is an independent variable 1. L07lg-term stability of slopes, earth fills and earth retaining structures The anal ysis is carried out in terms of effecti ve stress using the values of c' and ' may alternatively be taken from consolidatedundrained tests in which pore-pressure measurements are made. The numerical difference is generally insignificant. (ii) In stiff-fissured and weathered clays the value of c' found to correspond to equilibrium in the field (from the analysis of slip failures) is somewhat less than that obtained in laboratory tests on samples other than those taken from the actual failure zone [Henkel, 1957]. The value of c' is in any case not large (in London Clay, for example, about 250 lbjsq. ft) and in design work based on samples from undisturbed ground it is prudent to ensure a factor of safety· of at least 1·0 for the lower limiting value of c' = O. (iii) The values of c' and ,p' quoted for rolled earth fills are often obtained from undrained tests carried out at the placement water content. Subsequwt changes in both water content and volume occur due to the action of atmospheric moisture and impounded water. In fills placed on the dry side of the optimum water content, particularl y if poorly compacted, the value of c' may drop almost to zero, ' for the calculation of long-term stability of embankments or dams should be based on • T he most genera l definition of factor of safety against complete failure, which call be applied irrespective of the shape of th e fai lure surface, is expressed in terms of th e proportion of the measured shear strength that must be mobilized to just maintain limiting equilibrium. In the effective stress anal ysis the shear strength is thus: 'T

c' tan rP' = p+(o-u)--p

The value of F , in the analysis of a given problem, is usuall y obtained by assuming limitin g equilibrium along a trial slip su rface (generall y the arc of a circle in section), balancing the forces and solving for F . The value of u is taken either from a flow net, from field mea surements of pore pressure or from R ca lculation bused on stress chan ge and coefficient of consolidation, depend ing on the type of problem. The valu e of u is determined from the equilibrium of the soil mass above the fa ilure su.rfuce. Its distribution along the fai lure surface is influenced by statica lly indeterminate forces within th e soil mass, but their values have little influ ence on the actua l value of F , provided they satisfy the overall condition of equilibrium and correspond to statically possible states of stress [Bishop, 1955, and Kenney, 1956J. In problems where the disturbing forces are primarily the weight of the soil mass itself or of water impounded to a known limit and where plastic eq uilibrium exists in at least part of the soil mass, a satisfactory alternative d efinition is difficult to find, though the subject continues to arouse interest [for example, Taylor, 1948 (a); Bishop , 1952 ; The Proceedings of the onference on the Stabilit:>: of Earth Slopes, tockholm, 1954J. t This volume change, when resulting from the action of impounded water, may lead to cracking and failure by piping, irrespective of the theoretical stability against shear failure [for example, Sherard, 1953J.

INTRODUCTION

23

tests with full opportunity for softening in the appropriate stress rang', or alternatively c' should be put equal to zero for this condition. (iv) Total stress methods are sometimes applied to the analysis of existing slopes in which the pore pressure has reached its long-term equilibrium value. The undrained strength c" of undisturbed samples from the slope is used in the analysis. This is difficult to justify theoretically, and in practice gives the correct value of factor of safety only in special circumstances. For slopes in which shear failure is occurring the value of P, based on this method, is found to vary from about 5 in heavily over-consolidated clays, to about 0'7 in some sensitive normally consolidated clays. For other normally consolidated or lightly overconsolidated clays a value of ]'O±O'1 has been found on a number of 0 casions and has led to unjustified assumptions about the general validity of this approach [examples of the use of this method and of its attendant errors are given by Henkel and kempton, 1955; evaldson, 1956; Bjerrum and Kjaernsli, 1957]. 2. Stability of slopes of sand or gravel subject to the drawdowlI of impoullded waler In relatively pervious soils of low com pre sibi lity the distribution of pore pressure on drawdown is controlled by the rate of drainage of pore water from the soil. ince volume changes in the pore space of the soil are negligible, this condition is represented by a series of flow nets with a moving boundary [Terzaghi, 1943; Reinius, 1948]. The flo"v pattern is a function of the ratio of drawdown rate to permeability, and the values taken from the appropriate flow net are used in the stability analysis. This case is of practical importance where the operation of hydro-electric schemes subjects fill, normalJy considered as free draining, to very high rates of drawdown. [The results are summarized by Bishop, 1%7 (a)]. The values of c' and 4' used in the analysis arc taken from drained tests or consolidated-undrained tests with the measurement of pore pressure.

[II) Analyses in which pore pressure is a function of stress change 1. Inilial stability of the foundation of {l structure or embankment on saturated clay; the initial stability of an open cut or sheet piled excavatiml made ill clay; the initial stability agai1l.ft bottom-heave of a deep excavatiOtI in clay

The analysis is carried out in terms of total stress using the value of Cu obtained from undrained tests on undisturbed samples. Since the soil is saturated, cf>u = 0, and the analysis is usually referred to by this description. The undrained test· is applicable in these cases since the stress change likely to lead to failure occurs under undrained conditions, unless the drainage paths are short or the construction operation extended over several seasons. The overall effect, in the cf> = 0 analysis, of the departure from plane strain in the test and the rotation of the stress directions in the actual problem appears to be small. Field records indicate that, with uniform strata, an accuracy of 'Within ± 15 % may be expected in the estimate of factor of safety [Cooling and Golder, 1942; Skempton and Golder, 1948; Bjerrum and Eide, J956; etc.]. The following comments may be made: (i) As an alternative procedure it is sometimes recommended tbat the samples should be reconsolidated under an all-round pressure equal to the overburden pressure before carrying out the undrained stage of the test. The use of a consolidated-undrained test in this way results in an over-estimate I)f the strength, • The in-situ measurement of undrained strength with the vane teat may also be used in these cases.

24

THE TRIAXIAL

TEST:

PART I

the difference being particularly large in soils of low plasticity index. The reasons for this difference are discussed in PART I, 'I, p. 16. (ii) Sampling disturbance is more marked in its effect on the undrained strength c" than on the values of c' and 4>'. Particular care must be taken in the case of sensitive soils. 2. Stability of the clay foundation of an embankment or dam where rate of construction permits partial consolidation The analysis is carried out in terms of effective stress using the values of c' and ' obtained from drained tests or consolidated-undrained tests with the measurement of porc pressure. The rate of consolidation or of pore-pressure dissipation is measured either in the oedometer or in the triaxial apparatus. The magnitude of the initial porc pressure is controlled not only by the vertical stress due to the weight of the embankment but also by the shear stress set up beneath it. The value of A nel:essary for this calculation is obtained from the consolidated-undrained test. [The method is discussed by Bishop, 1952; its application in practice is described by Skempton and Bishop, 1955.] The estimate of the rate of dissipation of pore pressure in stratified alluvial deposits is the factor most subject to error, and field measurements of pore pressure during construction are most desirable in important works of this kind. 3. Stability of impervious rolled fill The analysis is carried out in terms of effective stress using the ~alues of c' and ' obtained from undrained tests with measurement of pore pressure. The estimate of pore pressure is based on the values of the pore-pressure parameters obtained from these tests or from special tests in which the major and minor principal stresses arc increased simultaneously to approximate to the actual stress condition in the embankment [Bishop, 1954 (a)). The rate of dissipation of pore pressure is obtained from tests in the triaxial apparatus in which the rate of decrease of pore pressure is measured at one end of the sample while drainage is permitted from the other end. Attention is drawn to the following points : (i) In samples of earth fill compacted at water contents well above the optimum value, the degree of saturation is often high and the value of the porepressure parameter B may lie between 0'8 and 1·0. A series of undrained tests at different cell pressures may thus not result in a sufficient range of effective stresses to define a satisfactory failure envelope. A series of consolidatedundrained tests with pore-pressure measurement is then used. (ii) The value of the initial pore pressure may alternatively be computed from the compressibility of the soil, measured under drained conditions in the oedometer, and from its initial porosity and degree of saturation [Hili, 1948]. The value obtained corresponds to that measured in the undrained test using a stress ratio giving no lateral yield (PART III, p. 140). The latter test is much quicker, but requires a little more skill. More recent work [Hilf, 1956] indicates that the assumptions on which the indirect method is based may lead to significant errors in the calculated pore pressure, particularly in soils having a high clay fraction and compacted at, or on the dry side of, the optimum water content. (iii) The principal limitation in accuracy arises from the difficulty of predicting the placement conditions of water content-and density which will be obtained in the field, and of reproducing them in the laboratory. It is prudent to run several series of tests at different water content within the tolerance likely to be forced on the engineer by borrow pit or climatic conditions. This indicates

INTRODUCTION

25

the possible limits within which the shear strength and pore-pressure parameters are likely to vary. In general it is found that r/>, is almost unchanged by variations in water ontent. The value of c· drops rapidly with increase in water content, though in large dams this factor may represent only a small proportion of the total shearing resistance on deep slip surfaces. The most abrupt change is in the value of excess pore pressure, which in certain soils may be doubled by a 1% increase in water content. In such cases refinements in the state of stress used in the pore pressure test may be only of academic interest. Unless climatic conditions are favourable the designer will be more concerned with precautions to deal with possible high excess pressure, based either on controlled dissipation or on a restricted impervious zone [for example, Bishop, 1957 (a)). An additional difficulty arises in reproducing field conditions in the laboratory with rolled fill materials containing stones. With 4-in. diameter test specimens the maximum particle is usually restricted to the i-in. sieve size, or in special cases, the :i·-in. size. The coarser fraction of the natural material which is omitted from tests on moraine, till, boulder clay, etc., has a significant effect particularly on the relationship between water content and density obtained for a given amount of compaction. The values of density and water content of the all-in material, corresponding to the laboratory values of the < ~-in. material, can be calculated by assuming that the stones merely act as displacers [ .S.B.R., 1951; R.R.L., J 952]. Experimental evidence indicates that this method is only an approximation, particularly with regard to the density correlation. The resulting uncertainty again applies mainly to the magnitude of the pore pressure. Field measurements of pore pressure are therefore recommended in most important rolled fills. (iv) The results of the undrained test may be expressed in terms of the total stress parameters CII and '" and then used in a total stress analysis. The value of the excess pore pressure is implicit in the resulting values of CII and ,pit; but, since it is not evaIuated separateIy, the implied pore pressure cannot be checked against field measurements during construction. Allowance for partial dissipation of pore pressure cannot readily be made in this type of analysis.

4. The stability of impervious Tolled fill, and of natuTal slopes or Cllts in clay, subject to rapid drawdown The analysis is performed in terms of effective stress using the values of C· and ' measured in consolidated-undrained tests in which full opportunity has been given for saturation to occur. The pore pressure after drawdown is calculated from the consequent stress change using a value of B obtained from a special test. In this test the sample is allowed to saturate and consolidate under the principal stress ratio obtaining before drawdown, and is then subjected to the appropriate stress change under undrained conditions. Alternatively the value of 13 = 1 is taken, a theoretical safe working value which appears to be justified by field data. [The basis of the pore pressure calculation is described by Bishop, 1954 (a).] Attention is drawn to the following points: (i) Except in saturated natural strata and soils placed rather wetter than the optimum water content, or subjected to very high stresses, the overaU effect of consolidation and saturation is a drop in c', the value of rp' remaining almost unchanged. The value of c' is found to be controUed almost entirely by the water content at which the test is run, independent of the type of test, provided the same compactive effort has been used. Hence, if an accurate estimate can be

THE TRIAXIAL TE T: PART t

made of the final water content after saturation of the fill, c' can be obtained from the results of series either of undrained, consolidated-undrained or drained tests, using interpolation to obtain a series of stress circles with the same water content at failure. (ii) Even if de-aired water is passed through a partly saturated sample under a small hydraulic gradient for a month or more, full saturation is not achieved . The measured value of B is therefore rather less than may be expected in the field. The residual pore pressure after drawdown is therefore likely to be overestimated on this basis. (iii) Incomplete saturation will also mean that unique values of Ceu and cp(U wiU only be obtained if no change in cell pressure is made after the consolidation stage, before the sample is sheared [Skempton and Bishop, 1950]. This limitation does not apply in practice, where failure in fact occur under reducing average stresses (which, since B < I, will result in a lower strength than is indicated by the conventional consolidated-undrained test). The use of a total stress analysis based on parameters measured in this test is th refore open to serious criticism. A further criticism of this approach, which applies to fully saturated samples, is based on the fact that in the standard test consolidation takes place under an equal all-round pressure, and the pore pressure is thus a function of the total shear stress applied, instead of merely the increase in shear on the removal of the support due to the water. The resulting error may lead either to an underestimate or over-estimate of factor of safety depending on the soil type [Bishop, 1952].

6. General Remarks on the Advantages and Limitations of the Triaxial Test The outstanding advantages of the triaxial test are the control of drainage conditions and the possibility of the measurement of pore pressure. No other strength test combining these two features has yet been developed to a stage of practical utility. Failure to appreciate the significance of excess pore pressure in strength measurement has been perhaps the greatest single factor in the late development of Soil Mechanics as a systematic branch of Civil Engineering. This may in part be attributed to the use of the direct shear test, which dates back to Collin (1846). It is of interest to note that the first indication of the significance of pore pressure came, not from direct shear tests, but from tests made by Osborne Reynolds in 1886, using a rubber bag full of saturated sand, compressed between two plattens and connected to a manometer which measured the pore pressure. Oshorne Reynolds noted the high undrained strength which resulted from the negative pore pressure set up by dilatancy (a value of -13 Ib/sq. in. was measured) and the loss in strength on allowing atmosph ric pressure to be set up again in the pore spacc-a result which is now found to throw light, for example, on the softening of stiff clays subjected to shear [Bishop and Henkel, 1953 (a)]. Terzaghi was, however. the first to appreciate the significance in engineering practice of pore pressure in fine-grain soils, and originated the application of the triaxial test under controlled conditions of dJ:ainage [Terzaghi, 1932]. The first triaxial tests on clay with the measurement of pore pre sure were carried out by Rendulic (1937). Except for the use of the h ar box for measuring drained strength and volume change characteristi s [for example, Casagrande, 1936; H vorslev, 1937; Gibson,

INTHODUCTIO

1953], the triaxial apparatus has been used in most basic rese::arch work on shearstrength and pore-pressure characteristics. ]t is being applied increasingly to the solution of practical problems. The triaxial test carried out on a cylindrical sample between rigid end plates is subject to severallirnitations, to which attention is fr quently drawn, in general terms, in current publications. To maintain a sense of perspective it is necessary to obtain direct field evidence of the overall error in applying test results in actual ca es. Case records [collected, for example, by Skempton and Golder (1948), Bjerrum and Eide (1956), and Se::valdson (1956)] suggest that the overall error using strength values expressed either as undrained strength or in terms of effective stress may be less than lO o~ , provided the type of analysis u ed is relevant to the conditions of drainage in the actual problem. Several of the limitations have been referred to in earlier paragraphs, pp. 8, 9. A detailed discussion is outside the scope of this book, but the important factors may bl:! briefly summarized:

[I] Jnfluence of the value of the intermediate principal stress. [II] Change in principal stress directions. [lII) Influence of e::nd restraint. [IV] Duration of test. [1] Influence of the value of the intermediate principal stress. In the cylindrical compression test the intermediate principal stress a2 is equal to the minor principal stress as. In many practical problems approximating to plane strain the valye of a2 will be higher than as. This will influence both c ' and ' may be expected to be:: slightly higher in plane strain, by about ItOfor c/>' = 20 0 and 5° for c/>' = 35 ° [Bishop, 1954 (b)]. Thert: is, as yet, little conclusive experimental evidence on this point"" or on the porepressure changes in plane strain. Results from the other special case, the extension test, in which a2 = al , indicates values of A for saturated soils greatly in excess of those measured in the compression test. The effect on c/>' appears to be small but to vary with soil type. Final conclusions are difficult to draw from the present experimental evidence [Taylor, 1941; Habib, 1953; Bishop and Eldin, 1953; Parry, 1956].

[II] Change in principal stress directio7ls. In the cylindrical compression test the principal planes arc fixed in relation to the axis of the specimen. This restriction is unimportant in problems involving active or passive pressure in zones with a horizontal boundary, but in problems where the direction of the major principal stress changes steadily under the applied stresses this restriction limits the accuracy with which pore pressure can be predicted. In soils which . are laminated as a result of over-consolidation or method of compaction, or varved as a result of the manner of deposition, the values of c' • Torsion shear tests by Habib (1953) appear to show this tendency. The aCCUl"acy with which the rubber correction and cross-sectional area at failure can be assessed is, however, a limitation to accuracy in this type of test. The results of shear box tests are open to various interpretations [Hill, 1950], and improved forms of direct sheM test [Kjellman, 1951 ; Roscoe, 1953] have not solved both the theoretical and practical problems of the plane nrain tcst.

28

THE TRIAXIAL TEST: PART I

and ' will be influenced by the inclination of the plane on which the maximum shear stress occurs. Experimental information on the magnitude of this effect is limited. The effect can be examined by cutting the test specimen with its axis inclined so that the failure surface can follow the natural planes of weakness [for example, Bishop, 1948). The value of c' is the parameter likely to be most affected by laminations in over-consolidated strata. [III) Influence of erld restraint. Friction between the ends of the specimen and the rigid end caps necessary to transmit the axial load restricts lateral deformation adjacent to these surfaces. This lc::ads to a departure from the condition of uniform stress and strain. The effects may be considered under three heads: (i) Strength characteristics. (ii) Volume change characteristics. (iii) Pore-pressure characteristics. (i) Strength characteristics. Tests have been carried out using special end fittings to eliminate end restraint [Taylor, 1941), and also using samples having different ratios of length to diameter. These indicate that no significant error occurs in the strength measurement, provided that the ratio of length to cliametcr is about 2. The permissible range depends on the soil type and on the freedom of movement of the top cap, since long samples may fail by buckling. A range of from It to 2t diameters is usually atisfactory. The deviator stress is calculated in these circumstances on the basis of the average cross-sectional area, Fig. 1}.

-Dol

Initially Leng&h Volume Cross -sectional area

At axial stroin 60,0

to +lJ.l vo+6v

to vo

a. . 1+ ~.%o (average) o

1+Ll.Yz

o

Fig. 13. The effect of train on the average cross-sectional area of a test specimen

lNTRODUCT10

Let a o denote the initial cross-section area, Lo the initial length, and Vo the initial volume. Then, if a is the average cross-sectional area after a change t:.1 in length and t1 V in volume, it follows that ( J.Ij) I.e. a -

-

l+t:. V /Vo Vo 1+t:.lllo . 10

In the compression test the axial strain this expression may be written as

a = a o·

=

£

(16)

-j.lllo, and, since Vollo = ao,

l+~V/Vo

1_

(17)

£

In undrained tests on saturated soils ~ V is zero and hence the actual area is a function only of axial strain. In all other test a knowledge of L\ V is necessary for the accurate dssessment of cross-sectional area. In the latter stages of compression tests in which displacement continues on a single rupture surface this expression ceases to be applicable. imilarly, in extension tests, a rapid departure from the calculated area occurs as local "necking" begins. For tests concerned primarily with the measurement of strength at Jarge strains it is necessary to usc alternative equipment such as the torsion shear apparatus [for example, H vorslev, 1939]. The control of drainage and the measurement of pore pressure is. however. difficult in this apparatus. (ii) Volume change characteristics. If both 01 and (73 are increased simultaneousiy throughout a drained test so that no lateral yield occurs (as in the

(a)

)

(

)

I (6)

Fig. 14. The effect of end restraint on the deformation of a test specimen (a) under cell pressure only. and (b) on subsequent application of deviator stress.

Ko-test,

PART III, 6 , p. 140), then no shear is mobilized acros the ends of the sample, and the axial strain and volume change are uniform throughout its length. However, in the standard test, the cell pressure is generally applied first, and the decrease in diameter which accompanies the reduction in volume is resisted locally by end restraint, Fig. 14 (a). As the deviator stress is applied the diameter tends to increase, and this again is opposed by end restraint. The sample thus adopts the shape shown in Fig. 14 (b).

THE TRIAXIAL TEST: PART I

Non-uniformity of volume change and axial strain becomes noticeable at large strains in loose sand [for example, Shockley, 1953]. In dense sands, however, failure occurs at small strains; but both for sands and for heavily overconsolidated clays in which failure is accompanied by an increase in volume it appears that the significant volume changes are often confined to narrow zones adjacent to a limited number of slip planes. These cannot be studied on the basis of overall volume change measurements alone, even if end restraint were wholly eliminated. For sands it should be noted, however, that the non-uniformity of the void ratio at failure has little influence on the consistency of the strength results, expressed in terms of effective stress, provided they are correlated on the basis of the initial porosity (or voi d ratio) at which the sample was prepared [for example, Bishop and Eldin, 1953]. The practical application of deformation characteristics measured in drain ed tests is generally limited to small strains wherc end restraint is not of importance. (iii) Pore-pressure characteristics. Just as in the drained test non-uniformity of volume change may occur, so in the undrained test non-uniformity of pore pressure is likely to result from end restraint. Where this non-uniformity is of appreciable magnitudc it leads to a migration of pore water whi ch can be detected by a series of accurate water content measurements made at different I vels in the sample. The extent to which this readjustment occurs depenus on the permeability of the sample, its dimensions and thc rate of testing. This has led to two alternative approaches to the measurcment of pore pressure. Where the primary purpose of the test is to measure strength characteristics in terms of effective tress, it is advantageous, on grounds both of simplicity and reliability, to run the test at such a rate that the pore pressure is uniform throughout the sample. The pore pressure can thus be measured from a saturated porous disc at its base. Some modification of the value of the pore-pressure parameter A will, however, result from the process of equali zation. Alternatively, a local measurement of pore pressure may be made by inserting a porous probe into the sample in the anticipated failure zone [Taylor, 1944, 1948 (b)] . This requires greater skill, and is difficult to apply to samples containing tones or to sensitive clays. If the test is performed fast enough to ensure no redistribution of pore pressure, the pore pressure measuring apparatus may not respond sufficiently rapidly to indicate the full value of the pore-pressure change. For silts and sands the rate of testing requ ired to minimise redistribution would be excessive, and the significance of A would thus depend on the type of soil being tested. For these reasons the simpler test is to be preferred for most purposes·. [IV] Duration of test. The duration of test commonly used in the trialtial apparatus and the parameters by which the results are expressed are open to criticism on the grounds that they take no account of the phenomena of creep in soils [for example, Geuze, 1953]. As the criticism i usually based on the results of undrained tests, it is necessary to separate the factors involved. The application of a shear stress to a saturated sample will result, under undrained conditions, in an excess pore pressure. Failure conditions in a consolidated-undrained test on a normally consolidated clay are represented in Fig. 15 (a) by an excess pore pressure u • Initial non-uniformity of pore pressure may 0 cur in both natural and compacted samples. In stiff-fissured clays localized pore-pressure changes may occur during shear in zones not adjacent to a probe. In both cases effective stress parameters based on the equilibrium pore pre sure nre more reliable.

lNTHOD UCT JO

31

T

a-

OJ u

(0)

1

>. .... 0..

e -.i-

.t:J "'I 0

;J~ 0 l) \() ....l .... V'I ~ c:: 0 8) .... C'/.l V 0

(O;-Oj)f

t/)

CQ

log. time to failure

Z

--' ~

C

0

'bi)

...

~

OIl

" r.1f

~

~

sand clay

ton¢'

log. time to failure

(6) Fig. 15. The effect of duration of test on undrained strength (8) Mohr circles at fallure for a consolidatcd-undmined test on a normally consolidated clay, (b) variation in measured strength with time to failure .

and an effective stress circle tangential to a failure envelope defined by the angle cp', c' being zero. If a second sample consolidated under the same conditions is tested at a much lower rate of testing, it is found that the undrained strength (0'1-0'3) is lower and that cp' has also decreased a little, Fig. 15 (b). The drop in cp' is negligible for sands, but may amount in some clays to about 5% decrease in tan cf/ for each increase of X 10 in the duration of the test.· • The scatter of test results on natural samples makes this difficult to detect in practice. Tests on remoulded soil are often quoted but probably over-estimate this effect.

N

~

~ ; 0

~

c

0

,

Vl

g <:

32

THE TRIAXIAL TEST: PART 1

The undrained strength is, however, controlled also by the value of the pore pressure u. The relationship between pore pressure and deviator stress is probably not independent of the rate of testing, but its average value, and hence the measured strength, is influenced by the amount of redistribution within the sample. The extent to which creep characteristics determined in undrained tests in the laboratory can be applied in practice is therefore limited. Two factors must be borne in mind in assessing evidence of actual failures in clay strata attributed to creep. The initial "undrained" porc pressure does not necessarily represent the most critical condition. Local redistribution of pore pressure over relatively short distances or in seams of higher permeability may lead to a gradual increase in the average pore pressure before drainage begins to be effective [Terzaghi and Peck, 1948; Ward, Penman and Gibson, 1955J. Secondly, in the case of over-consolidated clays, in which shear may result in a drop in pore pressure under undrained conditions, delayed failure may in fact be the consequence of the increase in pore pressure which occurs with passage of time as equilibrium ground water conditions are re-established. For long-tcrm stability problems in which the solution is based on effective stress parameters and on calculated or observed pore pressures, the drained test normally used is performed in a time varying from t to 3 days depending on soil type. The theoretical difference, due to the difference in time scales, between the laboratory value of tan rp' and the value applying in practical problems is unlikely to exceed 20 % . However, failure usually occurs at the time of the seasonal rise in ground water level and this tends to reduce the difference in time scale. In the intermediate class of problem, such as the construction of embankments and earth dams, the critical pore-pressure will usually occur within the construction period or during drawdown, and the difference in time scale is therefore smaller. While the margin of error can obviously be reduced by using slower testing rates in the laboratory, the practice is likely to continue of using the minimum rates consistent with obtaining either full drainage in drained tests or accurate measurement of pore pressure in undrained tests. This error is to some extent balanced by the effect of the intermediate principal stress and by the use of a two-dimensional stability analysis. The analysis of full-scale failures shows satisfactory agreement with shear parameters measured at the rates mentioned above. The routine undrained test on undisturbed samples is often performed in about 10 minutes. The direct use of these results in the total stress analysis involves a greater number of compensating factors, as both c' and rp' an the pore-pressure change determine the final result. Current practice in this respect is justified largely on empirical grounds.

PART II

PRINCIPAL FEATURES OF TIlE TRIAXIA APPARATUS 1. Details of the Triaxial Cells for It-In. and 4-In. Diameter Samples The form of triaxial test most commonly used in routine testing and in research work is the cylindrical compression t("st, and it is for this test that the usual triaxial cell is primarily designed. It may also bc used for stud ying volumechange and pore-pressure characteristics and li ssipati on rates under all-round pressure; and, with minor modifications, it may be used for axial extension tests. The cell consists of three principal components- the base, which forms the pedestal on which the samplt: rests and incorporates the various pressure connexions; the removable cylinder and top cap, which enclose the sample and enable fluid pressure to be applied; and the loading ram, which appli es the deviator stress to the samp le. The c~ll for It-in. diameter samples. The l1-in. diamt:ter specimen is the generally accepted standard in Great Britain for testing soi ls frec from stones. It enables the sampling and testing equipment to be kept to convenient dimensions. Where 4-in. diameter undisturbed samples arc obtained, three 11-in. diameter samples can be cut from anyone layer, which greatly facilitates the investigation of the shear characteristics of strata having a rapid variation in trength in the vertical direction. For clays a sample height of 3 in. i usually adopted; for sands this is sometimes increased to 31 in. The dimensions of the eell itself are designed to allow plenty of space around a sample of this size for special fittings to the loading cap, flexible drainage connexions, etc. Details arc given in Fig. 16. The principal features to be noted are: (1) (2) (3) (4) (5)

The base. The removable cylinder and top cap. The loading ram. Loading caps. Rubber membrane.

(1) The base is machined from a single bronze forging or casting. If a casting is used, there is a possibility of leakage due to porosity, and it is a useful precaution in this case to impregnate the base with a thermosetting resin. The base is usually plated. Provision for three pressure connexions is maLle: (i) The connexion for filling the cell with the fluid, usually water, to apply the all-round pressure. This connexion also serves to empty the cell at the end of the test and should therefore be made sufficiently large for rapid emptying.

3-M .S•P .

THE TRIAXIAL TEST: PART II

34

Stainless steel ram, lz"d/a,

Bronze top cap. 0/1 fil/er with

A II' release valve

Dowty Bonded Seal

~---t-r Seating coned 120

%,"dla. stainless steel tiC. bars, 3 spaced at 120° "

,~ Odla, sample

enclosed in rubber membrane --1-1-+-+--

.. I' "

. .

-

1

Perspex cylinder 4"o.D x3~' [D. and 7" in length

'

. .

,"

".

.

,' .

... .. ..,': .. . '. ' . "

0

' , '

", , '

4 radio/grooves, f16/1 wide x 112" in depth Rubber 0 "ings

!J1l'dio, studs.

asfoced ot 120, with wlngnvts

IonneK/on to pressure suppty, f'orce fJ't; or screwed & sweoted Bronze bose

Dettlilof' drainage connexion to top of'sample Fig. ] 6. The triaxial ccII for I i -in. diameter samples

PRINCIPAL FEATURES OF THE TRIAXIAL APPARATU. 3S (ii) The connexion with the base of the sample. This provides for drainage in a drained test, and for pore-pressure measurement in undrained or consolidated-undrained tests. For undrained tests made without th measurement of pore pressure th connexion is capped at its outer end, and the sample is placed on a Perspex disc instead of on a porous disc. Four shall ow radial grooves in the top of the pedestal communicate with the base of the porous disc in drained or pore-pressure tests. The disc should be inert, robust and accurately flat. The material u ed for vitrified grinding wheels meets these requirements, and may be obtained in various gradings. Discs i in. in thickness made of material, whose particle size lies between the 80- and lOO-B.S. sieves, are satisfa tory for most tests on sand or clay."

(iii) The connexion with the top cap of the sample. This is used only if it is necessary to pass water through the sample during the test (to saturate it or to measure permeability); or in a dissipation test when the coefficient of consolidation is determined by measuring the rate of decrease in pore pressurt! at the base of the sample while drainagt! is permitted from its upper end. Such tests arc more commonly p rformed in the larger cell, but, when they are required on It-in. diameter samples, a I-mm J.D . polythene tube is run from the loading cap, through a soft rubber col lar in the gland in the base of the cell, and connected to a J O-c.c. burette or graduated tube. The cell is then supported on three short spa ers whi le bnder test (Fig. 17). (2) The removable cylinder a1ld lOp cap. A transparent Perspex cylinder is used, which facilitates the setting up of the test and enables the mode of lailure to be observed. train observations can also be made optically. The 4 in.diameter cylinder used is in. in wall thickness and is normally taken up to a pressure of 150 Ibjsq. in. The only failure of which the authors are aware, in seamless tubing of this size, occurred under about 5 times this pressure with repeated loading. The cylinder is permanently fitted between O-rings as seals; the only joint to be made during testing is between the lower brass collar and an O-ring set in the base of the cell. For this the hand tightening of three wi ng nuts is sufficient. The top cap, to which the cylinder is fixed, i a bronze casting, and the central boss forms the bush through which the stainless-steel ram slides. An air release valve is fitted, and there is also an oil filler hole for adding oil before long duration tests. The cap has a raised edge to cateh any leakage from the bush during the test. A short pillar to carry the arm for the axial strain indicator is screwed to the end of one of the three tie bars. (3) The loading ram poses the mechanical problem of how to combine minimum friction and leakage with a ram stiff enough to carry a wide range of axial loads and with a travel sufficient to permit large strains. A number of solutions of varying complexity have been adopted. For the small triaxial cell the method adopted at Imperial College is to use a t-in. diameter ground stainless steel ram running in a lapped or honed bronze bush and lubricated with oil or grease. No packing or sealing rings are used. With the clearance normally used (0-0003 in.) the ram, if wiped clcan of oil, fall freely through the bush, and if oiled, falls slowly under its own weight.

*

• A list of manufacturers of specialized materials is given on p. 185.

THE TRIAXIAL TEST : PART II

Fig. 17. The triaxial cell for 1 ~-in. diameter samples (with drainage connexion to loading cap in place)

Leakage is controlled in short duration tests (up to about half an hour) by applying a film of thin grease or oil to the ram immediately before testing. For tests of longer duration, the cell is filled with water to within about t in. of the top, and the remaining space filled with machine oil, which floats on the water. The viscosity of the oil reduces leaka e past the ram to negligible proportions, and tests of several days duration can be run on one charging of oil. Efficient lubrication of the ram is also ensured. A discu sion of possible errors due to friction is given in Appendix 3, p. 174. For tests run at a constant rate of strain it is generally sufficient to obtain a zero reading on the proving ring with the testing machine running at the specified rate of strain, but with the ram out of contact with the top of the sample. The tam is fitted with an adjustable collar (Fig. 18) as a stop to prevent it from being blown out of the cell when not in position in a testing machine. The cell can thus be used a an independent unit during the consolidation stage of the test, and transferred to the machine on a flexible pressure lead only when the a ialload is to be applied. rubber O-ring is recessed into the top of the collar

PRl

IPA!. FEATURE S Of" THE TRIAXIAL APPARAT US

37

_0 ring Brass collar rO.D.

Spacer 7,

/I

~2

-%" OD.

I

long

Fig. 18. The adjustable collar for the !-in. diameter loading ram and forms a complete seaJ again t leakage under the action of the upward thrust on the ram. (4-) Loadi7lg caps. The load from the ram is transmitted to the sample by various alternative types of loading cap. Several types are shown in Fig. ) 9. For undrained tests a plain disc of Perspex may be used, Fig. 19 (a) , with a central coned seating in its upper surface to take a -i-in. diameter stainless-steel ball, which registers in a conical seating in the end of the ram. This en ures that the load is applied centrally and allows some freedom of movement to the top of the sample during the test. Lack of axial alignment will be automatically corrected in the early stages of loading, by the action of the coned seating in the ram. This may lead to a rather uncertain start to the stress-strain curve under small loads. Where the deformation characteristics are of importance a halved steel ball and flat-ended ram are used, Fig. 19 (b). More care should be taken in this case in truing the ends of the sample and centring it, as any initial lack of alignment persists throughout the test. In consolidated-undrained or drained te t8 the volume changes in the initial stage of consolidation under an all-round pressure may, if large, lead to lack of alignment in samples which are not of completely uniform compressibility. This may be avoided by using the cap illustrated in Fig. 19 (c). The tubular projection above the cap is a loose sliding fit on the ram, and serves as a guide during

THE TRIAXIAL TEST: PART 11

consolidation. Before the cell is assembled the collar on the ram is adjusted 0 that the lower end of the ram will project down into this guide, without making contact with the steel ball. Alignment is then maintained as the sample decreases in length under the action of the all-round pressure. To apply the axial load the end of the ram is brought into contact with the ball in the usual way.

-

I,"J '

7;! a/a. rom

~ ''dio. stainless

steel boll cut inholf

(6)

(0)

J{' dlo. sto/n~.::.es:..:s'--__--t

steel boll Perspex d..:_:is:..c:;_ _ :--...""'~~~~"\. "\. ,..-----''2 "dio.

(c)

i'..

(d)

Annulargroove 1f6"wide and tl'deep

Fig. 19 . Loading caps for 1t -in. diameter samples The frictional force on this guide is usually small, but the zero reading of the proving ring should be checked with the ram out of contact with it (by raising the ram at the end of the loading stage, for example). A convenient method of mea uring ax ial deformation during the consolidation stage is with a vernier telescope focused on the top of the steel ball, and the guide is slotted to make the ball visible. This method is limited to research tests. When drainage from the top of the sample is required a 1-mm I.D. polythene tube is fitted to a special loading cap which has a groove machined on its base, Fig. 19 (d). This tube pas es through the gl~d in the base of the cell. (5) Rubber membralle. The ample is enclosed in a thin rubber tube or membrane 5- 6 in. in length which may be obtained commercially or made in the laboratory from self-vulcanizing latex. The membrane should apply the minimum restraint to the sample consi tent with providing a reliable barrier to

l'RIN IPAL FEATURE

OF TIlE TRIAXIAL APPARATl lS

39

leakage. The thickness is usually 0·01 in., or Ie s for pecial test on soft cia . The correction which must be made to the observed strength to allow for the action of th rubber is discussed in Appendix I, p. 167. For the It-in. diameter specimen it may be of the order of a 0·6 Ibl q. in. correction to the compression strength with a commercial membrane. The rubber membrane is sealed against the smooth surface of the loading cap and of the pedestal by rubber O-rings under tension , sprung into place from the end of a metal tube. For a It-in. dia. cap a soft grade ring, of It-in. inside diameter when unstretched, is used. One ring at each end is suffi ient if the surfaces are clean and the membrane is a close fit. but it is generally a useful precaution to use several rings, particularly in long-duration tests. Leakage sometime occurs due to pin hole in the rubber, a defect occasionally found in new membranes, but more usually arising aft r r peated use . Rubber membranes should be carefu lly checked b holding them, stretched, against a bright light. After use, when they shou ld be washed to remove traces of oil, they may be checked by inflating with water. Ruhhers should be stored dry, and in the dark, after dusting with French halk . They tend to harden with age and should be discarded when this occurs. In long-duration tests the permeability of the rubber itself be omes of importance. This has little infl uence on the correct measurement of the state of effective stress in the sample, but results in misleading volume-change or porepressure characteristics. The permeability of the membrane to air is many times greater than to water. For this reason water containing dissolved air should not be used in the cell in tests lasting more than half an hour. Membranes from various sources appear to vary considerably and should be checked occasionally by repla~ing the sample with a rigid cylinder of porous vitrified material and measurlng the flow thro.lgh the membrane. 1£ de-aired water is used, the leakage through a good quality membrane may generall y be neglected. The membrane wi ll absorb water and soften during prolonged immersion. Special precautions appear to be necessary, however, only if the test lasts more than two weeks. These include the use of two rubbers, if the cel l pressure is high. The cell for 4-in. diameter samples. For compacted amples this cell permits the use of the same compaction equipment as is used for the standard compaction test (B.S. 1377). Soil with a maximum grain size of i in. may thus be tested, although satisfactory test specimens are more readlly obtained if the limit is placed at the i-in. sieve size. The height of the test specimen is usually 8 in. The cell is also used to test undisturbed samples taken in the 4-in. diameter sampler. This procedure is used with stony soils from which smaller specimens could not be prepared. It is also used for the accurate measurement of deformation properties, for dissipation tests and tests such as the measurement of coefficient of earth pressure at rest. The principal features of the 4-in. cell are illustrated in Figs. 20 and 21. It differs in design from the small cell mainly owing to the much greater forces involved, and to the desirability of keeping the height as small as possible to permit its use in a general purpose testing machine. (1) The base is supported by the platform of the testing machine only over its central area, so that the tie bars and the pressure connection from the top of the sample can pass through the base without obstruction. A porous djsc i in. in thickness of vitrified grinding wheel material (of the same grading as for the small

40

THE TR I AX IAL TEST: PART 11

Ife -Inf'orcmg bonds of'resin-bonded gloss fibre. /"wlde and Of 'ln t hickness stoinless tie bol's.6 s9uolly spaced

Ollta,l 01 silct/on at entry of' cmm. bortl polythene conneKlon tc tcp of somp/s.

Fig. 20. T he triaxial c 11 for 4-in. diameter samples

PRINCIPAL FEATURE

OF THE TRIAXIAL

PPARAT S

cell) is placed beneath the sampl in drained tests or undrained tc ts with por pressure measurement. (2) The removable cylinder alld top cap. It has usually been necc sary to use a cylinder fabricated from sheet Per pex, i in. being the normal thickness. The butt joint is a source of weakness and is liable to fatigue fai lure. The cells for high pressure tests are th refore reinforced with circumferential band" In the testing of partly saturated soils, in which the "olum changes have to be deduced

Fig. 21. The triaxial cell for 4-in. diameter samples (with drainage connexion to loading cap in place)

TH E TRrAXIAI. TEST: pl\R 'r II

from the volume of water entering or leaving the cell during thc test, this reinforcement has the advantage of greatly reducing the correction necessary to allow for the elasticity of the cell itself. These volume change characteristics are described in more detail in Section 4, p. 65. Originally, stainless-steel bands were used. Thc fastenings present a difficulty, and slip and bedding at the contact with the Perspex cylinder lead to an erratic relationship between pressure and volume change. More recently resin-bonded glass fibre has been used. As this is wound on circumferentially and bonded in-situ no bedding or slip occurs. The material has a high tensile strength (about 100,000 Ibjsq. in.) and a high Young's modulus (about 6,000,000 lbjs q. in.).

Filler Valve 011-

-

- -1+

Water . . . . . . ............

PreSSUf'e

4 atersIIPpiy Trom pf'essllre system

Perspex cylmder 211/'D. & IS/In length, wIth

scale.

Contfii-;;:to top of triaxial cell

Fig. 22. The system for supplying oil under pressure to loading ram

Four bands 1 in. in width and 0'1 in. in thickness are used. A typical pressurevolume change calibration is given in Fig. 40, p. 66. In order to reduce the load on the collar at the lower end of the cylinder, the six tie bars extend through it and through the base. The seal is made with the O-ring set in the base by tightening the nuts on the lower ends of the tie bars. The bronze top cap is domed, primarily to reduce the bending stresses. Its shape also facilitates the removal of trapped air, which otherwise limits the accuracy of volume measurements based on the volume of water in the cell. In order to restrict the space occupied by the oil supply for the ram, the oil is retained in a Perspex collar fitted to the lower end of the bronze bush. This is fed by a polythene tube passing through a gland in the cap, and can be recharged, if neces ary, while the cell is under pressure. A simple system for supplying oil under pressure in known quantities is illustrated in Fig. 22. As appreciable leakage would limit the accuracy of volume measurements, castor oil of relatively high viscosity is u ed; this has the added advantage that, being a vegetable oil,

PRIN · IPAI. FEATURES OF THE TR1AXIAl. APPAR T Ufi

43 it does not damage the rubber membrane if accidentally brought into contact with it. For routine undrained tests in which volume ob ervations arc not made, a film of grease or oil on the ram suffices. The pillar for the axial strain indicator is screwed on to the projecting cnd of one of the tie bars. (3) The loading ram. Owing to the relatively short unsupported length of the ram a i-in. diameter ground stainless-steel rod has proved to be satisfactory for an axial load of up to 6000 lb, which represents a deviator stress of about 500 Ib/sq. in. The ram is fitted with a collar, and either a hemispherical or Aat end piece as required (Fig. 23). Friction is discussed in Appendix 3, p. 174.

Lower end of'rom %" In diameter "/(ubber 0 ring Co/lor

Dralnoge connexlon when reqtllred, 2 mm. bore

polythene tube

Flats for

11:."

·L~~~~~J....LI (6) Stainless steel throughollt Fig. 23. Loading cap for 4-in . dia. samples and fittings for

~-in .

dia . ram .

(4) Loadillg caps. A deep rimmed stainless-steel cap is normally used, owing to the high local load applied by the ram (Fig. 23). A 2-mm bore polythene tube is fitted, when necessary, to provide a drainage connexion. Thi tune passes through a gland in the base of the cell and is fitted with a valve. Consolidated-undrained or drained tests on compressible soil arc generally carried out only in the small cell. A loading-cap guide has therefore not been required on the large cell. With compacted samples less trouble with alignment is encountered in any case. (5) Rubber membrane. For the 4-in. dia. samples a membrane 0·01 ·015 in. in thickness is used , about 12 in. in length. Owing to the larger cross-section of the sample, the rubber correction is relatively smaller, and is often neglected. Typical values are given in Appendix I, p. 167. The rubber membrane is sealed against the cap and pedestal by rubber 0rings in tension. Rings of unstretched internal diameter of 3t in. are generally used. When the drainage lead is connected to the loading cap a split ring is necessary to place these rubber sealing rings in position.

THE TRIAXIAL TEST: PART 11

2. Details of Apparatus for Controlling the Cell Pressure In the three most common types of triaxial compression test, the cell pressure is held constant throughout each stage of the test. The duration of the routine undrained compression test is about 10 minutes, if pore-pressure measurements arc not required. If pore-pressure measurements are required, however, the total duration of the test may be from 1 to 8 hours depending on the soil type and on the accuracy called for. The consolidation stage of a consolidated-undrained test may take as much as 3 days in a soil of low permeability, and it is important that variations in cell pressure should be avoided during this period. Similarly, the consolidation and the shearing stages of a drained test may each take up to 3 days. For certain speciaJ tests a constant cell pressure may be r quired for a period of several weeks or even months. The maintenance, with sufficient accuracy, of a constant pressure over long periods presents considerable difficulty, and a number of different methods have been tried. The authors have experimented with several of the principal methods at present in usc, and as none of them has pro cd to be satisfactory for accurate work, the self-compensating mercury control has been developed [Bishop and Henkel, 1953 (b)]. Although relatively expensive, it is a simple and reliable method, and the apparatus is easy to construct. Its use will be assumed in the subsequent treatment of testing procedure. Before describing it in detail, a brief outline of some of the alternative methods will be given. (1) The use of an air reservoir. The simplest method is to have an air reservoir, of large capacity compared with possible volume changes in the sample or leakage from the cell. The air acts on the surface of the water supply to the cell and is itself supplied either by a motor-driven compressor or by a tyre-pump. A typical layout is illustrated in Fig. 24. The air supply passes through a reducing valve A and its admission to the reservoir is controlled by the valve D. The blow-off valve C permits the reduction of pressure, either when making fine adjustments to its magnitude, or at the end of a test. If a high-pressure water supply is available, this can be used to compress the air, in place of an air pump, by using the layout illustrated in Fig. 25. Here water supplied through the valve A traps air in the space above its surface. As more water is admitted the air is compressed and the pressure increases. This enables the cell to be filled, and, after the closing of the air release valve I, the pressure may be built up to the required value. Pressure is reduced by opening the waste valve B, which should be large enough to permit the reservoir to empty rapidly at the end of the test. The principal difficulties with either layout are pressure variations due to changes in temperature after scaling-off the reservoir, to the solubility of air in water, and to loss of air due to small leaks. In addition, the water in the cell is likely to contain dissolved air. This may cause errors in volume change or pore-pressure value owing to the relatively high permeability with respect to air of the rubber membrane enclosing the sample. (2) The use of a reducing valve as the pressure control. An adjustable reducing valve can it elf be used as the constant pressure control. Commercial valves of the spring-loaded diaphragm type have been used with varying degrees of success, particularly on short duration tests. Their principal disadvantage

PRINCIPAL FEATU RE

OF THE TRIAXIAL APPARAT S

45

Pressure gauge Water

Water C

D

D

E

From compressor Reducmg valve Air

--

Water

A

B

, Fig. 24. The use of a compr ssed air supply for co ntrolling cell pressure

Water supplY Waste

Fig. 25 . The use of a high-pressure wuter supply for controlling cell pressure

from the soil testing pOint of view, is their tendency to hUllt. Repeated fluctuations in pressure, even if small, are mo t undesirable. Mechanical troubles due to condensation, oil carried from the compressor, and dust also occur and an air filter is necessary. As an air bleed is required, several tests run simultaneously make a heavy demand on the compressor. On the other hand, their successful use has been reported [Spencer, 1954J and they arc installed in a number of commercial laboratories. (3) The loaded ram. This is, in effect, a small hydraulic accumulator in which a dead load applied to a ram is used to maintain constant pressure. Friction, leakage and limited volum tri c capacity are the principal difficulties. The first two difficulties can be met by using oil as the fluid and by rotating the ram continuously. This is not convenient fur routine work. An alternative method is adopted by the Non IVegian Geotechnical Institute, in which a small precision made ram and cylinder are set truly verti cal by a three-screw adjustment. This, combined with the use of oil as the fluid, largely eliminates friction. The limited capacity remains a seriou practical objection , especially when large samples are to be tested. A i-in. diameter ram requires more than a 3-in. travel to displace a volume of 1 cu. in., which represents a volume change of only 1 % in a standard 4-in. diameter sample, quite apart from any loss of fluid due to leakage. (4) The self-compe nsating m e rcury control. The principle of the selfcompensating mercury control is illustrated in Fig. 26 (a). The pressure of the water in the triaxial cell results from the difference in level between the mercury surfaces in two small cylinders- connected by a thin flexible pressure tubewhich form, in effect, the two limbs of a manometer.

THE TRIAXIAL TEST: PART 11

Pressure gouge

Fig. 26. The principle of the self-compensating mercury control

1£ hI and liz are the initial levels of the two mercury surfaces, and h3 is the level of the sample, measured above the same datum, then the water pressure at the level hs is a, where: (18) and y", denotes the density of mercury. and Y." denotes the density of water. When a volume decrease occurs in the sample due to consolidation, or jf leakage takes place past the loading ram, water will be lost from cylinder No.2 and the mercury level in this cylinder will rise a distance ~1z2' A corresponding drop in level wiJl occur in cylinder No.1, and, if the cylinders are the same in diameter, it follows that: (19) If both cylinders remained stationary, Fig. 24 (b), the cell pressure would change to C7+~a, where: a+~a = (hJ -Ah-hz-Ah)Ym+(h 2 +Ah-ha)yw (20) that is, (21) ~a = -(2Y",-Yw)Ah Since the value of Ah is likely to be of the order of at least 1 in. in a longduration test, the resulting pressure drop would be about 2 in. of mercury or 1 lb/sq. in. , which is inadmissible-especia)ly where the cell pressure (as is often the case) is a low as 5 or 10 Ib/sq. in. If, however, the level of the upper cylin~er is raised by a distance Al, Fig. 26 (b), the value of a+~C7 becomes:

a+Aa = (h 1 +Al-Ah-h z-Ah)Ym+(h z+Ah-ha}yw

(22)

that is, (23)

PRINCIPAL FEATURES OF THE TR I AX I AL APPARATU _

Zero pressure change can be ensured by choosing that is,

II

value of .).1 so that

M = (2 _Yru)~h

~a

47 = 0,

(24)

y",

Since the drop in mercury level, D..h, in the upper cylinder reduces its weight, the cylinder can be made to adjust its own level automatically if it is hung on a spring of the appropriate stiffness. The decrease in weight due to a drop in mercury level j.h is A. YIII' ~Ir, where A is the cross-sectional area of the cylinder. The shortening of the spring, D..l, must correspond to this reduction in weight, and also allow for the additional length !:ll of the fl exible tube fill ed with mercury 'which is lifted from the floor. If W is the weight of unit length of this tubing, then the necessary spring stiffness is K lb/inch extension, where:

K.D..l

= A.Ym.D..Ir- W.D..l

(25)

From equation (:!4) it therefore follows that:

K=A.Ym '2

1

(

-Yr. y",

-W

(26)

In a typical apparatus the internal diameter of the cylinders is 2·5 in. Hence: Cross -sectional area, A Density of mercury Density of water Weight of flexibl e tubing+mercury P~VinYI -ChIOrid e, 3 mm internal]

[

dis. x

I

= 4'91 sq. in . = 0'489 Ib/eu. in.} = 0'036 lb/cu. in .

=

20° C

at

0'006 lb/in .

. . (

mm wa ll thickness .

.

Thus K

0'489

.

= 4·91 X 2_1/13'6-0'006 = !·24Ib/m .

-

This represents a spring of convenient dimensions, and indicates that for practical purposes the weight of the flexible tubing may be neglected.

Pract£cal Deta£ls The practical application of this principle is illustrated in Figs. 27 and 28, and the components are shown in Fig. 29. The spring carrying the upper cylinder is hung from a sliding bracket, which runs the full height of the laboratory on a vertical aluminium rail. With the height available in the present laboratory at Imperial College this gives a pressure range of 0-72 Ibjsq. in., and the bracket may be set to give any required pressure within this range by a ratchet winch which raises the bracket on a thin flexible steel wire. (For higher pressures, the pair of adjustable cylinders are placed in series with a pair pre-set at 72 Ib jsq. in., by closing the valve G} and opening the valves G 2 and G s in the layout illustrated in Fig. 28, and pressures in the range 72- 144 lbjsq . in. are obtained.) The basic layout of the pressure system is illustrated in Fig. 27, and the procedure for routine testing is as follows: (1) The mercury control is checked to see that the mercury is mainly in cylinder No.1. The position of the mercury can be adjusted by opening valves Dl and G 1 and admitting water from the supply valve BI . (2) Valve Al is opened and cylinder No.1 is raised until the required pressure is shown on the pressure gauge.

THE TRIAXIAL TEST : PART If

Reservoi Ratchet winch

I

Screw control Flexible tube (PVC)

o

Fig. 27. The basic layout of st!lf-compensating mercury contro l

- Manometer

Reservoir. Flex/ble tf/be(P.V,C)

Ratchet

winch

Fig. 28 , The layout of the self-compensating mercury control with extended pressure range

PRINCIPAL FEATURES OF THE TRIAXIAL APPARATU

49

T(J8E CONNECTION

Topped 48.A

"FIXED" (JPPER CYLINDER

LOWER CYLINDER WINCH fRAME

WINCH DR(J'" & RATCHET

Inches SCALES :

Assembly 0

1 it

3 4-

5 6

Inches Detul/ O ___' _ _Z~__3

Fig. 29. Details of self-compensating mercury control

4-M •S•P •

50

THE TRIAXIAL TEST: PART 1 J

(3) Valve G 1 is closed, and valves Bl and E are opened to admit water to the triaxial cell. "" The air valve I on the triaxial cell is opened to release trapped air. The rate of filling is reduced when the cell is almost full, and valve Bl is closed when water begins to flow from the air release valve I , which is then closed. (4) The water in the cell is then adjusted to the required pressuret by opening valve C and displacing water with a screw-controlled piston.! Valve G l is then opened and valve is closed. There is a considerable initial intake of water due to the elastic expansion of the Perspex cylinder of the triaxial cell and to the immediate compression of the sampl e if the soil is not fully saturated. By the use of the procedure outlined above, water is not drained from the mercury control by these initial volume changes. The control can thus be used for tests on 4-i n. diameter samples in the large cell, as well as for those on It -in. diameter samples, without increasing the capacity of the cylinders. If the volume change or leakage in a long-term test is more than the capacity of the control (about 12 cu. in.), mercury may be returned to the upper cy linder, while the test is in progress, by the following methods. (i) The cell is isolated for a few minutes by closing valve E, while water is admitted under pressure through valve C, using the screw-con trol (or air-reservoir system) . This is the simplest method, but may lead to a small temporary pressure change if rapid volume change or appreciable leakage is occurring. (ii) Valve Dl is closed and valve C opened; and the required pressure reading is obtained with the screw-control (or air-reservoir system). Valve Dl is re-opened, and the pressure is maintained by manual control while cylinder No. 1 is temporarily lowered a few inches to allow the necessary quantity of mercury to flo back. ylinder No. 1 is then returned to its original level and valve C is closed. At the completion of the tests valve G 1 is closed and the pressure is dropped to atmospheric by opening valve Bs. Valve Al is closed to protect the pressure gauge, and with valves 1 and B2 open and Ba cl osed, the cell is emptied by the suction main. To prevent air, and the oil from the ram, entering the pressure control and volume-measuring systems, valve B2 should be closed while the cell still contains some water, the residue being drained from tbe hose connexion at the bas of the cell. Several practi cal requirements have to be satisfied by the equipment, and the ways in which these have been met are given below. (a) The val ves must be completely free from leakage, and whether they are open or closed should be obvious at a glance. Klinger "sleeve-packed " cocks have been found to satisfy these requirements and size A.B.lO has been used for all the principal valves. " (b) A very flexible light-weight tube is necessary for the adjustable pair of cylinders. Polyvinyl-chloride tubing, 3 mm in internal diameter and 1 rom • For tests in which an accurate measurement is to be made of eith er pore pressure or volume change, the use of de-aired water is necessary. The air may be removed by subjecting the water reservoir to a \'acuum with a small laboratory water ejector. t This operation is often performed by connectin g valve C to 8n air-reservoir system of the type illustrated in Fig. 24. A certa in amount of water containing dissolved air may then enter the cell, unles special precautions are taken. t The screw-controlled piston works in a I t-in. dia . cylinder with a 5-in. travel, using a rubber O-ring to eliminate leakage. It is descri bed in detail in Fig. 35, page 57. II The manufacturers of components are listed on p . 185.

PRINCIPAL FEATURES OF THE TRIAXIAL APPARATU

Sf

wall thickness, has proved satisfactory since it coil down without difficult on the floor. The pre-set cylinders are connected with polythene tubing 2 mm in internal diameter and 1 mm wall thickness which is less flexible but can withstand higher pressures. Any further reduction in the bore of the tube is however, found to reduce the rate of equaliza tion of the mercury levels to an inconvenient extent. The other features are illustrated in Fig. 29 and include: 1. Simple mountings to provide for fine adjustment of the effective length of the spring. 2. Connex ions for the pressure tubing which avoid contact between mercury and any metal components. • 3. The adjustable bracket and ratchet winch. The apparatus has now been tn ust: for about 7 years. it has proved to be entirely free from hUlIting. and the va riation in pressure during a test is generall y too small to be detected by a pressure gauge, the maximum being about O· J Ib/sq. in. It is in fact u ed as a convenient method of direct calibration of the commercial Bourdon-tube pressure gauges. Very little maintenance has been required. Each triaxial machine is provided with three sets of pressure-control eq uipment so that three samples can be consolidated simultaneously under three different cell pressures. This minimi zes the time required for carrying out consolidated-undrained or drained tests. By means of the valvt!s D J • D2 and D s, the three sets use the same pressure gauge, and pressure and suction mains, etc., as illustrated in Fig. 28. Continuous variation of th.e cell pressure is called for in certain tests. Thcst! are generally of the controlled strain type, and include tests in which the cell pressure is adjusted so that no lateral yield occurs during compression (the K otest, PART JII , p. 140), and those in which the cell pressure is adjusted so that no volume change occurs during shear (tht: constant-volume test, PART IV,

p.163). The most convenient and sensitive method of continuous manual pressurecontrol is to use the screw-operated piston (with valves. Al , • Dl and E open). Of the details illustrated in Fig. 35. the fine pitch screw thread and large hand wheel are particularly important under the higher pressures (75- 150 Ibjsq. in.). Alternatively, manual adjustment of the self-compensating mercury control may be used. The measurement of cell pressure is usually made with a Bourdon-tube type of pressure gauge. It is important to calibrate this instrument in-situ , before any tests are performed, with an accurate pressure gauge tester, and to re-check at fairl y frequent intervals. A rotating ram with dead weights may be used, but direct measurement of the mercu ry levels in the pressure control provides a simple alternative. For low pressure work a mercury manometer, calibrated directly in pounds per square inch, should be part of the standard equipment (connected at valve A2 ill Fig. 28). The heights of the two mercury columns in the manometer can be converted directly into pressure readings by the use of equation (18) and (21). In Fig. 30 the heights of the two mercury surfaces are hI and h2above any convenient datum, and h.s is the height of the mid-point of the sample. Then, from equation (18).

u = (h1 - h2 )y",-(ha- h2 )yw

THE TRIAXIAL TEST: PART IT

Water

Mercury

Fig. 30. Calibration of mercury rnanomt!ter

If the heights are expressed in illches, and the pressure in pounds per square inch, then, at 20° C. If the two limbs of the manometer are of the same internal diameter, it follows from equation (21) that the change in mercury level in either limb, per pound per square inch change in pressure, is

2XO'48~-O.036 in.

Ah = = 1,062 in.

The accurate measurement of celJ pressure is particularly important when the effective stresses are small. This occurs in drained tests under small cell pressures, and in undrained tests when the difference between the cell pressure and the pore pressure is small.

3. Details of Apparatus for Measuring Pore Pressure The usual laboratory methods of measuring pressure-the mercury manometer and the pressure gauge of the Bourdon-tube type-cannot be applied directly to the measurement of pore pres ure. in a small sample of soil, owing to the volume of pore water which would have to flow from the sample to cause the instrument to register. This amounts, for example, to 0,0]3 cu. in. for each pound per square inch rise in pressure for an t-in. bore manometer; for a sensitive Bourdon gauge (total range 150 Ib/sq. in.) the volume change averages 0'025 cu. in. per lb/sq. in. over th range 5- 15 Ib/sq. in.

PRINCIPAL FEATURES

F THE TRIAXIAL APPARAT

53

This flo w of pore water has two undesirable results. I t modifies the actual magnitude of the pore pressure existing in the test specimen, whi h it is the purpose of the apparatus to measure; this is particularly important in soils of low compressibility. In addition, in soils of low permeability, the fl w of por water leads to a serious lag in the attainment of a steady reading on the pre sure gauge or manometer. These difficulties can be minimized by the use of a diaphragm gauge in which the deflections are small and are measured by electric strain gauges [for exampl ,

Pressure gouge d ----j"""",___

Flexible copper tllbe filled with water /

Bloss capillary tllbe

II

I

\

Screw control e Fig. 31. N ull method of pore pressure measurement; original arrangement

Plantema, 1953). They can be entirely avoided, however, by the use of a null method of pressure measurement (such as that used by Rendulic, 1937] which has many advantages for general laboratory use. The form in whi ch the null method wa originally used at Imperial ollege is shown diagrammatically in Fig. 31. T he pore-pressure connexion at the ba e of the triaxial cell is connected through valve a to one limb b of a small bore glass -tube by a water-filled tube. To the other limb c is connected a pressure gauge d and a small water-filled cyLinder e, from which water can be displaced by a screw-controlled piston. The lower part of the -tube is filled with mercury. This can be levelled before a test by opening valve I, which remains closed during the measurement of pore pressure.

THE TRIAXIAL TEST: PART 11

54

An increase in pore pressure in the sample will tend to depress the mercury in the limb b of the U-tube. This can be immediately balanced by adjusting the piston .in the cylinder e to increase the pressure in the limb c by an equal amount, which is registered on the pressure gauge d. The only flow of pore water which can occur results from the elastic deformation of the tube connecting the cell to the limb h, which is negligible for most practical purposes, or from the compression of air bubbles inadvertently trapped in the system between the base of the sample and the mercury surface in the limb b.

Water To pressure gauge and screw control

Valve a Flex/ble copper tube Fig. 32. Modified null indicator for pore pressure measurement (diagrammatic) Trapped air bubbles are, in fact, the principal hazard in making accurate measurements of pore pressure. To facilitate their elimination from the system, and to avoid the problem of alignment in fitting a glass -tube into rigid mountings, the -tube was soon replaced by a single straight section of glass capil lary tube dipping into an enclosed trough of mercury as shown in Fig. 32 [Bishop and Eldin, 1950J. The de-airing ope"ration has been further simplified by making it possible to withdraw the mercury trough below the level of the capillary tube while circulating water through the system. Some details of the present apparatus are shown in Figs. 33, 34, 35 and 36. The elimination of even the slighte t leak is also of great importance.

P R INC IP AL FEATU RE

OF THE TRIAX I AL APPA HATll S

S5

h6" bore x)8

II0.0. annealed copper t(lbe soldered mto connecto{' Dowty Bonded Seal ~/IO.

::i!!R\O Enlarged detail of connector

o ring In

V groove

Supporting bracket - - - - -- ...... nuts

Stainless steel (Jpper body - - - -Soft rubber washer with I mm. 0. 0. hypodermic needle inserted thro(Jgh it _:__----ttsftF'~ Stainless steel tube with window cut as shown and fitted with paper scale ----~rA' }1J '(//0. brass or stainless steel piston fitted with {'(lbber 0 rings Copper washer

I mm. bore glass tube 10 mm. 0. O. and 6~" in length

$pft rubber washer with fmm O.D hypodermic needle inserted through it St(linless steel lower body_ _ _ __

Knurled nut for lowermg mercuIY trough

/

Polythene tube connexlon to g(l(Jge (lnd control C':)'/Inder

Fig. 33 . Details of the null indicator used at ImpeJ'ial College

56

THE TRIAXIAL TEST: PART 11

The principal features are: (1) Pressure connexion from the triaxial

cell. (2) Valves.

(3) The upper body. (4) Glass tube and end seals. (5) The lower body. (J) Pressure connexion from the triaxial eell. Annealed copper tubing i in. 0.0. and i tJ in. 1.0. is generally used, to minimize volume changes under pressure. To give freedom of movement a length about 9 ft is coiled into a helix. Occasional contact with mercury appears to have little effcct on its uscful lifcsomc has been in usc for eight years. The type of end connexion illustrated in Fig. 33 has proved to be trouble-free. (2) Valves. Valves a and f should be entirely free from leakage and not displace water when operated. The commercial sleeve-packed plug-cock satisfies these requirements in practice, but it should bc lubricated and adjusted before usc. The standard end fittings are, however, not convenient for the detachable valve at the base af the cell. The small piston valve illustrated in Fig. 33 is generally used for valve a. (3) The upper body is preferably made of stainless stecl to avoid rust and deterioration through chance contact with mercury. (4) GLass tube and end seals. A section of I-mm-bore glass tubing, outside diameter about 10 mm, is ground .flat at each end, and sealed in by axial compression between two soft rubber washers, through each of which Fig. 34. The null indicator a short length of I-rom 0.0. stainless steel tubing (hypodermic needle) is inserted. At the lower end it is this section of stainless tubing which extends below the mercury surface. The I-rom-bore glass tubing gives adequate sensitivity and minimizes capillary effects. (5) The lower body is connected to the upper body by an internally threaded tube, which enables the seals on the glass tube to be adjusted. It contains a cylindrical chamber, into the lower end of which the mercury trough is sealed by two rubber O-rings. The trough may be raised or lowered by a knurled nut running on the screw thread on the outside of the chamber. The upper part of the chamber, which is filled with water, is connected to the pressure gauge and control cylinder and is designed to avoid the trapping of air bubbles. The chamber and th mercury trough are made of stainless steel. The mercury level in the capillary tube is observed through a window cut in the threaded tube, which is provided with a paper scale.

PRIN lPAL FEATURE

OF THE THIAXIAL APPARATUS

57

The unit is mounted on a bracket by tightening a nut on the threaded stem of the upper body, and forms a robust fitting for routine use. The principal features of the control cylinder, Fig. 35, are: (1) The cylinder. (2) The brass piston. (3) The stainless-steel piston rod.

(1) The cyl£nder of hard-drawn brass tubing 11 in. J.D. and i in. thickness is screwed and sweated on to a brass base. This is suitable for pre sures of up to 150 lb/sq. in.

4.,.spex handwheel 8 Ndia. & ~6"thickness with semiCircular notches ~" R.spaced every 30 °

Brass cap - - - - - -

Set screws-------+

Screwed collar

Brass cylinder IeJ,-"I.D. )( /}:/o.D. & 6}z"in length - Screwed & sweated. /

Force fit or screwed &sweot ed

Connector - - ~~~~>7.i~;;~~~~~~~~-Connector

Fig. 35. Details of the control cylinder

58

TlIE TRIAXIAL TE T: PART JI

(2) The brass piston is fitted with a rubber O-ring. The thrust on the end of the screwed piston rod is carried by a deep groove ball race to avoid back-lash. Commercial rubber sealing rings give a smooth-running and leak-proof seal, essential to the performance of the apparatus. (3) The stainless-steel pistol! rod with 26 threads per in. passes through a brass nut which forms the cap to the cylinder. The screwed rod is turned by an 8-in.-dia. Perspex handwheel , and has a total travel of 5 in.

h

Fig. 36. Layout of apparatus for measuring pore pressure The complete layout of the apparatus is shown diagrammatically in Fig. 36 and illustrated in Fig. 37. It will be noted that in addition to the pressure gauge (0- 150 lb/sq. in. in gradations of lIb/sq. in.) a mercury manometer is fitted. This is used (i) for negative pore pressures, (ii) for the accu rate measurement of low positive pore pressures, and (iii) for checking the zero error of the pressure gauge. It is calibrated directly in pound per square inch units. Failure to close the isolating valve 111 when passing into the high-pressure range appears to be sufficiently frequent to justify fitting a mercury trap at the top of the manometer I The graduated tube h connected to the valve f is used for determining the gauge and manometer readings corresponding to zero pore pressure. In the case of fully saturated samples this graduated tube can also be used to measure volume change during the consolidation stage of tests in which drainage is permitted through the ba e of th specimen. This procedure is not permissible with partly saturated samples as it results in the accumulation of air in the connexions u ed for the measurement of pore pressure during the undrained stag of the tests. De-airing arid cLeani7lg apparat.us. In a new apparatus, or one not used for some time, small bubbles of air or other gas tend to adhere to the inside of the various tubes and fittings. The procedure for removing them is outlined below: (1) The mercury trough g i screwed to the lower limit of it travel, so that

PRIN IPAL FEATURE

OF THE TRIAXIAL APPARAT

Fig. 37. The apparatu for measuring pore pres ure

59

60

THE TRIAXIAL TEST; PART II

the connexion to the lower end of the glass capillary tube no longer dips below the mercury surface. Water may then be freely circulated through the system without carrying mercury away from the trough. (2) The triaxial cell is disconnected, and the end of the copper tube immersed in a dish of freshly boiled water with the valve a open. A rubber tube connected to a vacuum line operated by a water ejector is fitted to the tube II, and with the valves f, k and 7l open, and I, m and j shut, water is drawn through the system while the piston is screwed in and out. Rapid opening and closing of valve a at this stage facilitates the removal of air from the valve itself. The vacuum lead may then be transferred to valve j; with this valve open and valve f shut the process may be repeated. Alternatively, valve a can be closed and water may be drawn in through valve f from the tube h. Finally, with valves f and j closed and valve a open, water may be forced out under pressure through the copper tube. (3) To check that the system is now air-free, valve a is closed and valves f and I are opened (valves k and 11 being open and valve j shut). The mercury trough g is screwed into its upper position. As this operation displaces water, the mercury may rise up the capillary tube unless the control cylinder e is screwed back at the same time. The control cylinder is then screwed in until mercury rises to a convenient level in the capillary tube. The pressure gauge d indicates an initial reading. (4) The valvef is now closed and the pressure increased by scre\\ing in the control cylinder. A further rise in the mercury level in the capillary tube indicates either expansion of the apparatus, compression of air bubbles still remaining between the mercury surface and valves a and f, or leakage. If the control is adjusted to maintain constant pressure on the gauge d, steady creep of the mercury level indicates leakage, provided the apparatus has been allowed to cool before checking. A large rise which is not fully reversible generally indicates air bubbles, which pass into solution at higher pressures. fully reversible rise in level of less than t in. per 100 IbJsq. in. rise in pressure 0 leakage at should readily be achieved; with some units it is as low as 0,3 in. all can be tolerated. The rise of t-in. corresponds to 6'} X 10- 6 cu. in. per IbJsq. in., and in a few special tests where greater accuracy is required, the zero line used in the null method is raised progressively with increase in pressure to allow for this deflection. Fllr routine tests this is not necessary. This elaborate de-airing procedure is seldom necessary once the apparatus is in regular use. It is generall y sufficient to check the system prior to each test by a momentary increase in pressure, and, if necessary, to pass cold de-aired water through it by using the screw control. Two other minor practical points may be of interest. Occasionally the balance becomes insensitive due to dirt or grease lodging in the capillary tube. This can be corrected, if need be during a test, by closing valve a and lowering the pressure in the unit to zero. Valve f is opened, the mercury drawn back into the trough, which is then lowered. With the pressure gauge isolated by valve I, warm domestic detergent- followed by cold de-aired water- is drawn in through h by suction at j. After re-checking, the unit may be put back into operation. If the mercury is dirty it may appear in the capillary tube as a discontinuous series of beads with water between; and a sensitive balance will be difficult to obtain, if a meniscus is located in the lower section of small-bore stainless tube. This may also be remedied by sucking detergent slowly through the apparatus as in the previous paragraph, but using the screw control to create the suction,

PRINCIPAL FEAtURES OF THE TRIAXIAL APPARATU

61

and retaining the mercury trough in the upper position, so that the detergent bubbles through the mercury. The apparatus is finally flushed with clean water as above. Alternatively, the mercury trough may be removed and refilled with clean mercury.

Calibration. It is seldom convenient to set the pressure gauge exactly at the same level as the sample in the testing machine. This, in addition to the difference in level between the mercury surfaces in the capillary tube and in the trough, necessitates the use of a zero pore-pressure reading on both the pressure gauge and the manometer. It is, in fact, of some practical ad\'antage to maintain a considerable difference in mercury levels, as this ensures that the pressur gauge i normally under a small positi"e pressure, eycn if placed at eye level. To obtain the zero reading, after th apparatus has bcen checked for trapp d air, val\'e f is opened (after reducing the pressure to zero) and the graduated tube II. adjusted so that the level of the water in it corresponds to the mid-height of the sample under test. The screw-control is adjusted to bring the mercury level in the capillary tube to a convenient height, which is marked, and the pressure gauge and manometer readings are noted. These are the zero readings corresponding to atmospheric pressure at the mid -height of the sample, and all changes in pore pressure are measured with reference to them. The zero readings obviously depend on the mercury level chosen. In general this level is chosen to give a whole number on the pressure gauge scale; the manometer scale is then adjusted to read zero for this level, so that no correction is necessary. Provided the level of the pecimen being tested remains approximately constant (a 3-in. change in l'.:veJ represents an error of approximately 0'1 IbJsq. in .), the zero settings should remain constant. The few seconds taken to check them before each test are, however, well justified, as they will indicate the presence of air in the manometer, drift in the calibration of the pressure gauge or los of mercury from the system. The methods of calibrating the pressure gauge and manometer are discussed on p. 51. One additional point is of importance when both cell pressure and pore pressure are large and the effective stress, which is the difference between them, has to be known accurately. A direct calibration of the pore-pressure system against the cell-pressure gauge may bc made by connecting up to a triaxial cell full of water but without a test specimen. The pressure read on the pore-pressure system is thus equal to the cell pressure. The use of this direct calibration minimizes the error which might otherwis be introduced into the small difference of two large quantities. Connexion to triaxial cell. It is also important that air should not be trapped within the base of the triaxial cell, and that the connexion between the cell and the copper tube should be absolutely free from leakage. When coned brass fittings are used for this connexion, the likelihood of leakage can be reduced by rotating the coned parts to and fro, with the nut drawn up, before finally tightening. This serves to bed the two surfaces together. With the small cell (for It-in. dia. samples), this connexion can be made before de-airing the apparatus. The base of the cell is then submerged in a deep tray of hot water before carrying out the de-airing operation described above. Mter de-airing, water appearing at the orifice in the central pedestal should be free from bubbles when it is run baek from the burette h with the valve a open. As a more rigorous check the orifice may be ealed with a tapered plug and the change in the mercury level noted when the pressure is raised.

62

THE TRTAXIAL TE ST: PART II

In the case of a consolidated-undrained test on a saturated clay sample it is often convenient to connect a burette directly to the base connexion of the triaxial cell for measuring volume changes during consolidation or swelling i and to connect the pore-pressure equipment only when required during the shear test stage. It is then sufficient to immerse the base of the cell in a tray of cold de-aired water while interchanging the connexions. As a precaution against a bubble of air, or gas, having lodged in the passage between the base of the sample and the connector, a piece of small diameter (1 mm J.D. X 2 mm O.D.) polythene tubing connected to the suction line may be passed up this passage while the cell base is immersed. This circulates water through the passage and removes the bubbles. In the case of the large cell (for 4-in. dia. samples), a similar technique may be applied, though for many routine tests on partly saturated soils it is sufficient simply to run water back from the pore-pressure apparatus through the base of the cell and to check freedom from air bubbles at the orifice in the pedestal. Owing to the large volume of the sample and large base area communicating with the pore-pressure apparatus, the last trace of air is of much less significance than in the case of the small samples. The porous disc placed on the pedestal beneath the sample must also be free from air. This is achieved by boiling the disc under a vacuum and keeping it under water until required. General observations. The pore pressure can be measured with an accuracy of 0'1 lb/sq. in. if the capillary tube is reasonably clean, the limiting factor usually being the calibration of the pressure gauge and manometer. The accuracy of the no-flow condition depends on the effectiveness of the de-airing technique, and on the ~ operator's ability to maintain the mercury surface at a constant level during the test. The technique for dc-airing is soon acquired and the number of tests performed in this manner now runs into thousands, including research and commercial laboratories. The maintenance of a constant mercury level presents no difficulty while the changes in pore pressure are due to hanges in shear stress and occur smoothly and regularly. Difficulty may, however, arise during the raising or lowering of the cell pressure if this is done too rapidly or erratically. A very simple remedy is to exercise more careful control over the rate of pressure change. A mistake generally made at least once by every operator is to forget to shut off thc apparatus at the valve a before "blowing off" the cell pressure at the end of a test. The sudden drop in pore pressure usually results in the mercury thread travelling the fu ll length of the copper helix and appearing at the base of the sample. While the pore-pressure apparatus is in operation, it requires the attention of an operator; this raises the obvious que tion of the possibility of using a servomechanism. uch a method has in fact been used successfully by the Delft, oil Mechanics Laboratory (1948), and Penman (1953). A decision to use this method will, however, depend on several factors. While important pore-pressure changes are occurring the operator will in any case have to be in attendance to observe and record them. When the rate of change of pore pressure becomes slow, intermittent attention from an operator attending to several machines is sufficient, as the screw-control forms a stable system of control i alternatively the apparatus may be shut off at the valve a except when readings are required . The latter procedure, which is used for ~issipation tests lasting up to everal days, means that the valve a must be a

PRINCIPAL FEATURES OF THE TRIAXIAL AI'PAHATL' 5

plug or piston valve which operates without displacing water. If a long peri d elapses between readings, the control is adjustt:d to th t: estimated n e\~ \'Il lu f the pore pressure, and the valve opened with care, to p rmit the balance to b ' achieved. With a large sample of high permeability Or containing many air voids, a sudden jump in the mercury level can occur if the t:sti mate is poor, and for this rt:ason a long capillary tube is used in the pore-pres ure apparatus (Fig. 33). A servo-mechanism does offer some advantage in this respect, though it is rather lim!ted unless all the rele va nt readings are also taken au tomati cally. It also requires more daborate maintenan ce and introdu cs the problem of Il!lIltiTlg. Several other systems are also used, and it is diffi ult to make 1I fair assessment without actually u sing them. In the apparatus developed by D. W. Taylor (1944) the surface between water and air in a capillary tube is u ed as the indicator for the null method. This necessitates the use of compressed air for maintaining the balan ce, which is inhercntl y a less stahle system. The U .S. Bureau of Reclamati on use a method in \\'hi eh the pressure on a thin metal diaphragm is balanced by compressed air, the poi nt of balance hei ng indicated electrically [Hami lton, 1939J. This leads to some departure from the no flow condition each time the balanct: is ma':ie, as sufficie;:nt movement has to occur at the diaphragm to bn:ak an electri c contact. Pu blished results are mainly from large samples, in which the importance of this efft:ct is to some extent reduced. In general the presence of a diaphragm increast:s the difficulty of freeing the system from air. Finally, whatever method is ust:d, it is important to note that the result of diffuential thermal expansion in the water and the fittings enclosing it may cause a departurt: from the no-flow condition greatt:r than tht: elastic deformation of the apparatus. This is not of practical importance in ordinary tests, but may ha ve to be taken into account in research work.

4. D e tails of Apparatus for M e as uring Volume Ch a n ge A change in cell pressure or in axial load generally results in a change in the volume of the sample. ] n the parti cular case of an undrain t:d t<:st on a fully saturated sample this volume change is negligible from the engi neeri ng point of view, owing to the low compressi bility of rhe water in the pore space (= 3'4 xl 0- 6 per Ibjsq. in.) and of the material forming th soil particles (of the order 1 X 10- 7 -2 X 10- 7 per Ibjsq. in .). I n undrained tests on partly saturated samples, and in consolidatedundrained or drained tests, volume changes occur. For over-consolidated or compacted soils these volu me changes may amount to 5% or 10 0 " of the initial volume; but in normally consolidated or loose soils, vol ume changes of up to 25 % or more may be encountered . The measurement of the e volume changes is of importance both in determining the compressibility of the sample and in calculatin g the actual cross-sectional area of the sample at failure, on which the stress values are based . The three principal methods in use are based on (a) the volume of fluid entering the cell to compensate for the change in volume of the ample, (b) the volume of fluid expelled from the pore space of the soil, and (c) the direct measurement of the change in length and diameter of the sample. (1) Volume changes in undrained te 18. In saturated samples the volume chan ge is assumed to be zero and no direct measurements are taken.

THE TRIAXIAL TE ST : PART II

- - Transparent

Water

cylinder

Flexible tube

(polythene) ~

--II

(a)

II

FromceJlpl'essvl'e

K,

LI

co~ =:lE~=:::!.!==::::J!==::!.~==To=t,:!!!!!/ cell

(6) Fig. 38. Apparatus for measuring volume change under pressure (a) Measuring unit.

(b) Valve system for reversing flow .

In partly saturated soils a volume change occurs due to the compressibility and solubility in water of the air or other gas in the pore space. This is measured by observing the quantity of water entering or leaving the cell as the cell pressure and axia1 load are changed. To make this observation it is necessary to measure the displacement of a free surface between the water supply to the cell and some

PRIN '(PAL FEAf lJ HE

OF TilE TRIAXIAL APPARAT US

other fluid. Such a urface is provided, for example, by the boundary between the water and mercury in the lower cylinder of th constant PI' ssure ontrol (Fig. 27). In practice a small diameter cylinder is preferable, to give greater accuracy in the volume readings, and a special measuring unit is used, Fig. 38 (
5-

M •. P.

66

THE TRIAXIAL TE T: PART J!

volume change characteristics of the cell can be measured with the cell filled with water only. A typical calibration of a cell with a Perspex cylinder and four fibreglass bands is given in F ig. 40 (a). Variations in the torque used to tighten down the fixing nuts can introd uce an error into this calibration, which should be checked from time to time.·

40

~ I..l

,

~

30

~ ~

~ c:

20

¥".

.~

t.'j

§

~

10

4.l

/.

o~

°

~

~

20

V

~

~

~

.A I"'"

~

Iii"""

V

60

40

80

100

Cell pl"8SSure .' 16 per sq. in. (a)

Cell pressure =.10 /b persq. in. I

20

40

60

80

100

Time : hours

(6) Fig. 40. Relationship between pressure and volume change for a triaxial cell for 4-in . diameter samples (a) Expansion of ccli plotted against cell pressure. (b) Expansion of cell at constant cell press ure plotted against time.

(2) D uring the loading of the sample water is displaced by the movement of the ram into the cell. This correction !s added to the observed decrease in volume and amounts to a,.. 11[, where a, is the cross-sectional area of the ram and I1Z the movement. • The measuring cylinder itself is subject to a small expansion under increasing pressure. Part of thjs error is automatically compensated for in deducting the cell calibration. The remainder can be neglected in practice.

PRINCIPAL FEATURE

OF THE TRIAXIAL APPARATU

There are several possible sources of error to be guarded a amst in this method of volume measurement. Variable amounts of air may be trapped inside the top cap of the cell, and lead to deviations from the cell calibration curve. This error is minimized by allowing water to run from both the air release valve and the oil filler valve as the cell is filled, until freedom from bubbles is observed. A second source of error lies in the air trapped between the sample and the rubber membrane enclosing it. Even with careful handling thc >rror i seldom less than 0·2 ~~ of the total volum> of the sample. This is a typt: of bedding error" which disappears under higher pressures. \\,ith partly saturated samples it is not permissible to remove tht: air by flushing with water, and this technique in any ease only serves to introduce an equally uncertain quantity of water. However, if the pore pressure is measured during the test, the volume of trapped air can be calculated from the relationship between I'olume change and pore pressure (Appendix 5, p. 179). This can be done for each test, or, for simplicity, a standard average correction can be used for 'the particular type of rubber membrane and method of fitting in use. In tests of long duration, in particular, additional errors may occur due to: II

(a) Differential tht:rmal expansion within the measuring system. An error of 0·1 (~~ of the initial volume of tht: sample per degree entigrade can occur. Measurements shou ld be taken as far as possible at a constant temperature. (h) Leakage of the lubricating oil around the ram. Thi is generally negligible except in high pressure tests, hut can be checked by measuring the oil in the collecting groove. (c) Creep in the Perspex cylinder of the triaxial cell. The magnitud of this error is illustrated in Fig. 40 (b). (d) Leakage through the rubber membrane. With air-free water in the cell this error is negligible in tests lasting under 8 hours (unless the membrane is faulty). For longer periods the error is likely to be less than 0·02 ° ~ of the initial volume of the sample per day, but this sh uld be checked for the type of membrane used. Although the list of possible errors is formidable in the standard undrained tests, which are completed in several hours, the volumt: changes during shear are obtained with considerable accuracy (to within 0·1 % of the initial volume of the sample). Jt is only the initial volume change at low cell pressures which is likely to present difficulty. This is illustrated in Fig. 41 by a comparison of the volume change measured by this apparatus with that calculated from direct strain measurement, for the case of zero lateral yield, described below. (2) Volume c h a nges in drained tests . With a fully saturated sample, a volume change can only occur under the action of the cell pressure or of an axial load if water is permitted to drain from the sample. The volume of water expelled is a direct measure of the volume change, and may be measured in a burette (Fig. 42). A 10-c.c. burette is suitable for the standard It-in. diameter sample and a 1oo-c.c. burette for the 4-in. diameter sample. With cohesive soil an initial error, on first applying the cell pressure, is again difficult to avoid, due to air trapped between the rubber membrane and the sample. As this air may also result in erratic readings at later stages of the test if it pas es into the connexion to the burette, it is often removed by flushing water up through the space between the sample and the membrane before sealing the membrane to the top cap. Although most of this surplus water is removed by lowering the burette a few feet below the level of the ceU to et

68

THE TRIAXIAL TEST: PART If

S

::::: ~

.....~

.

4

~

."/

~

" II)

~I~ I

,. " ,...

,:~

~

c:..._ ()

2 ~ .....

."

"I.:)

§

~

::os

,.

<:).

~

~

~

~

3

"I.:)

N

~

,

.,. ,. ""

I

It-~

"

,.• "

"

/

C) ~

~

~

/

"

I

2

5

3

-6v 0/

V /0 Ca/cu/ate.d {'rom strain measurement

Fig. 41. omparison between measured volume changes and those calculated from the measurement of axial strain under conditions of ze ro lateral yield (no correction made for trapped air)

10ec. burette

" C/omp -

Fig. 42 . Method of measuring the volume change of fu lly aturated samples

PRINCIPAL FEATURES OF THE TRIAXIAL APPARAT

up a small suction pres ure, some initial error remains. Thi error can be estimated from the change in water content during the test, which provi les an independent measure of total volume change in II fully saturated soil.. Alternatively a sufficient positiv pressure is maintained in the pore-water to drive the air into solution, the required effcctive stress being obtained by using a higher cell pressure. This necessitates the use of a volume indi ator working under pressure as described above. For the ac urate measurement of small Perspex corer

ploU! cemented /1/

pOSition

Woodell fi'ame

- -Valves Fig. 43 . The volume change indicator used with J 4-in. diameter samples when working under pressure volume changes under these conditions an alternative dcsign is used, consisting. in principle, of a calibrated U-tube, partly filled with mercury, one limb of which is connected to the drainage lead from the sample, the other limb being connected to the constant pressure system. The l.'-tube, shaped a an arc of a circle, i free to rotate about its centre. The displacement of the mercury, as a volume change occurs, thus causes the U-tube to tilt and mai ntain equal pressures in the two limbs. In its practical form (Figs. 43 and 44), the U-tube is an annular groove milled in a Perspex disc, sealed with a covering ring bonded in place. Free rotation is ensured by two small baJl-races on the spindl e, and the use of flexible smallbore polythene tubing for the connexions. Drainage from partly saturated soils results in a mixture of air and water reaching the burette. To measure the volumes of both fluid phases, two burettes may be used (Fig. 45). The inverted burette measures the ga volume and the second burette indicates the total volume change. The water levels should be equalized before taking a reading. This is not a very accurate measure of the volume change of the sample owing to compressibility and capillary effects in • - AVV = I

wl- WIG' , where WI+ 1 •

V, denotes initial volume,

w, denotes initial water content, rUf

and

denotes final water content

G. denotes specific gravity of soil grains.

THE TnIAXIAL TEST: PART IT

Fig. 44. The volume change indicator for small volume changes under pressure thc air bubbles in the sample, and owing to displact!ment by air of water from the porous disc at the base of the specimen. The method described on p. 64 is generally more reliable for drained tests on partly saturated soils. In tests on dry sand and other cohesion less materials accurate volume change measurements may be made with the constant pressure air system illustrated in Fig. 46. Atmospheric pressure is maintained in the pore space and in the measuring syst m by changing the level of the mercury in the burette so ao to keep a constant reading on the oil manometer. The overall volume of air in the ystem is thus constant and the mercury level in the burette thus gives a direct reading of volume change in the sample. (3) Volume changes based on the direct measurement of strain. The direct measurement of strain in the three principal directions presents some difficulty in the case of soils. Suitable indicators are diffi ult to fix owing to the low strength of the sample ; and, owing to the non-uniform strains resulting from end restraint, measurement at a number of points would be required to give the 0 erall volume change.

PR(N (PAL FEATURES OF TilE TRIAXIAL APPARATU S

H

/

Fig. 45. Measurement of the volumes of both air and water expelled from a partly saturated sample

Ail'

Burette y

w Fig. 46. Constant pressure air system used to measure volume changes in dry samples

72

TilE 'J'HIAXIAL TE ST : PART 11

Perspex

Elevation of' Hing.!!.. Spring-loaded hinge ,..----Polished hinge -pin

BrazedJomt

<)1 ,

Pivot

\

,

Plan Craduated perspe.K tube

r'mm. bore

Section of Pad .r",

'!r"r

0''''0

I

Screw adjustment Thin rubber or polythene diaphroqm enclosing mercury

@ o

0

Elevation with diaphragm removed

Develof!_ed SectIon of /,!dicator

Fig, 47. The lateral strain indicator for use with 4-il1. diameter samples

PRIN IPAL FEA 'll' flE S OF THE TRIAXIAL APPA flATtI

73

1n two special cases, howel'er, the direct measurement of strain may be used in calculating volume change. (a) nder an equal all -round pressure the three principal strains are eq ual if the soil is isotropic. Yolume changes during the consolidation stage can therefore be obtained directl y from the measu rement of the axia l strain alone, \l'hi h can readily be obtained with a I'erni r telescope reading between the ball on the top cap of the sample and a convenient n:ferencc point on the cell. 1n saturated soi ls lack of isotropy can be checked by comparing th · difference between the initial and final water contents with th e volume change obtained . for srn:dl strains, by multipl ying the axial strain by 3. The error due to end restrai nt is small in specimens haying th e usual rati o of length to diam ter. This provides an accurate 'heck on long-term consoli dation haracteristic;;, th e measurement of which mig ht otherwi se be masked hy passage of wa ter through the rubber membrane. (b) l lnder conditions of zero lateral strain there is no shear on the surfaces of the sample in contact with the rigid end caps and a constant ross-section is thUR maintained. A single lateral strain indicator is then suffi cient, and an accurate measurement of the volume change can he obtained from the axial compression of the sample . The state of stress under ze ro late ral strai n corresponds to the ('arlh pressllre at resl condition and is thus of fundamental int<.:rest . Th e lateral strain indicator u sed with 4-in. diameter samples is illustrated in Figs. 47 and 4 . The relative mo\'ement of tll'O cun'cd metal pads which bear

Fig. 48 . The lateral strain indicator for use with 4-in. diameter samples

74

THE TRIAXIAL TE T; PART II

lightly on the surface of the sample is magnified x 2 by the hinged ring which embraces the sample and is imparted to a diaphragm enclosing a small quantity of mercury. This movement is magnified by the small bore of the calibrated transparent tube in which the free surface of the mercury moves. Changes in diameter of 1 X 10- 3 inches can be readily observed. During a test the axial load is slowly increased and the cell pressure is adjusted by the screw-controlled piston to maintain zero lateral yield. This test provides a very accurate measure of volume change and is limited only by the small bedding errors at the end caps. A practical precaution, which has to be taken, is to avoid trapped air in the space enclosing the mercury, which would compress and lead to a false change in mercury level under increasing ceJl pressure. Air can be removed under a vacuum , and checked, either by the fall in level when the vacuum is released, or by testing a dummy specimen of a rigid material. For accurate work a frequent recheck is justified, as with some rubber membranes bubbles tend to reappear. 41<

5. Details of Loading Systems Current methods of applying the axial load to the sample are influenced both by the requirements of the test and the need for mechanical simplicity. Two classes of procedure may be broadly distingui shed- controlled rate of strai1l and controlled stress. For routine tests and for the more common research tests the use of controlled rate of strain has many advantages and is generally accepted. The rate of strain at failure is accurately known and the influence of rheological factors on the observed strength can thus be taken into account. The shape of the stress- strain curve beyond the point of maximU'm stress can also be observed. The duration of the test can be predicted with reasonable accuracy, which, from the practical point of view, is important in planning the testing programme. The loading system may consist either of a screw jack operated by an electric motor and gear box; or of a hydraulic ram operated by an oil pump. The screw-operated system offers the more positive control of the rate of strain, particularly under the lower rates of strain used in drained tests and in some porepressure tests. In addition, manual control of the screw jack offers the most sensitive way of making fine adj ustments. One of the general purpose machines (6000-lb capacity) used at Imperial College for tests on It-in., or 4-in., diameter samples is shown diagrammatically in Fig. 49. In Figs. 50 and 51 its use with the two sizes of cell is illustrated. The platform on which the cell rests is raised by a screw with a pitch of 5 threads per inch. The rotating nut which drives the screw is operated through a worm reduction gear of 100; 1 ratio either by a handwheel or, through a clutch, by an electric motor and gear box. For rapid adjustment the key is withdrawn from one of the three alternative key-ways on the screw, which is then rotated by a knurled collar. The full travel is 6 in. The drive from the gear box, which is rubber mounted, is taken through a rubbcr V-belt to eliminate vibration (this also gives a margin of safety against overload). A i-h.p. geared induction motor unit is fitted to the gear box, givi ng a basic range of speeds of 60 r.p.m. to 0'0192 r.p.m. in intervals of X A further

t.

• This may be due to a surface tension effect at the sharp corners of the space enclosing th mercury. It is avoided by de-airing the apparatus with water in this space, before displacing it with mercury.

Two J;"steel plotes

75

.... Screw for heIght ocfJlIstment

~i

@

: Hemispherical

1------1

I

seating f'or proving ring Adjllstable between 16"ond 28"

C:::::::;::;:;:==:l Plotf'orm to toke cells for either

'1 "dla. or 4 "dlo somples

- Key Steel table covered wIth neoprene 4Nm tlllckness Worm drIVe - Clutch

/

Operating screw with trovel of 6 inches

~ Rubber V- belt drIVe from multi- speed geor mounted separately on rubber.

bOK,

8"x6"x 35Ib/f't. rolled steeljoist, bolted to wall

Fig. 49. The 6000-lb capacity general purpose testing machine

THE TRIAXIAL TEST: PART II

Fig. SO. Arrangement of triaxial ccli and p'l"oving ring in te ting machine: undrained test on 1!-in. diamt!ter sampl

1'"1

(, IPA L FEATURE

OF T il E TRIAXI

L AI'PARAT S

77

Fig. 5), Arrangement of triaxial ell and proving ring in testing machine : undrained test on 4-in . diameter sample. ( ote: guid bars fitted to the top cap of cell used in tests with high axial loads)

THE TRIAXIAL TEST: PART II

adjustment can be made by alternative pairs of fixed-centre change wheels, giving ratios of 2: 1, 3 :2, 1: 1, 2: 3, 1: 2. For a ample 3 in. in length this corresponds to a range of rates of strain from 10% per minute to 0·0008 % per minute. The load is measured by a high-tensile steel proving ring placed between the top of the ram in the triaxial cell and the head of the testing machine. An adjustable screw in the head of the machine permits the use of the two cell sizes, and a collar at the lower end of the screw supports the proving ring when the cell is removed. The selection of a proving ring of suitable load capacity and sensitivity is discussed in Appendix 2, p. 171. Axial strain is measured, in the case of the large cell, by a 2-in. travel dial gauge calibrated in nho-in. divisions. This is fixed to an arm clamped to the top of the loading ram, and registers with an adjustable arm fitted to a pillar screwed to the top of the cell. In the ca of the small cell, a ] -in. travel dial gauge is used, and is generally fitted to the lower mounting of the proving ring (see Figs. 50 and 51). Exact control of the rate of strain is limited by the deformation of the proving ring itself, though during plastic failure at constant stress this effect is, of course, negligible. In estimating the duration of a test with a sensitive proving ring on a stiff sample this effect must, however, be taken into account. The accuracy of the measurement of strain is limited by any bedding occurring between the sample and the loading cap, and the loading cap and the ram. Most of the bedding bctween the sample and cap will occur prior to the application of the axial load, duc to the action of the ccli pressure. Bedding errors at the end of the ram are largely avoided if a halved stcel ball and flat ended ram are used, as described in Section 1, pp. 37 and 4-3. In the large cell the elastic compression of the ram amounts to about 3 X 10- 3 inches under maximum load. If tRC cell pressure is changed while the axial strain is being measured, the movement of the gauge pillar due to deformation of the cell will require an additional correction of about 5 X 10- 3 inches for a pressure change of 100 Ib/sq. in. These corrections are only made for special tests, and are negligible for the small cell. Stress-controlled tests are generally performed by the addition of a series of increments of dead load to the ram. As failure is approached prolonged creep will occur under ea h load increm nt, and the operator is faced with the difficulty of determining when non-terminating creep may be considered to have begun. In addition, the rate of strain at failure is difficult to estimate, and for these reasons this method is avoided for routine tests, particularly if pore-pressure measurements are to be made. In special tests concerned with deformation and volume change under stress combinations not leading to failure, or where failure is caused by reducing the cell pressure progressively, dead loading can be used to advantage. The simplest method is the use of a light-weight hanger (Fig. 52). Except at low cell pressures a hanger system made of duralumin is less in weight than the reaction required to balance the upward force on the ram due to the action of the cell pressure, and no special counterbalancing system is required. The hanger illustrated weighs 4·1 lb, and can carry a maximum load of at least 300 lb. Strain readings are in this ca e taken with a dial gauge supported by an arm clamped to the ram. . Stres -controlled tests on 4-in. diameter samples are carried out by maintaining the required load on the proving ring with manual adjustment to the screw jack. The frequency with which such tests are called for does not justify the use of the more elaborate dead load system necessary for loads of several tons.

79

Fig. 52. The use of light-weight hanger for applying dead load: drained test on It-in . diameter sample

80

THE TR I AXIAL TEST: PA RT I t

Where <.: onsolidation under an anisotropic stress system is requ ired in the low load range, however, the upper adjustable screw is repl aced by a spindle sliding on ball bearings, carrying on its upper end a short beam with two hangers (Fig. 53 ). Owing to the change in cross-sectional area of thc sample resulting from both axial strain and volume change, the maintenance of an accurately constant stress requires continuous adjustment of the ve rtical load as deformati on proceeds. For constant volume tests thi s can be achieved automatically by a simple linkage, as in the constant stress rheometer [ affyn, 1944J. In general, the va riation in area

Fig. 53. The u e of beam for the anisotropic consolidation of a 4-in. diameter sample in the testing machine

81

PRI NC IPA L FEA T URES OF T il E TRI AX I AL APP AR AT S

during an increment of stress is neglected, if the change in strai n is small ; or, if greater accuracy is required, small wt:ights can be added to the dead load . ontinuous adjustment of the sere\\' jil ck is limited to tests of relatively short duration (for research test of up to about 6 hours) . The pecial problems raised by the appli cation of tran iC!nt or pulsating I ads are outside the scope of this book . The increased drag and inertia forces on the ram at high rates of strain will necessitate the use of e1ectri 'al load measuring devices within th e cell [as descri bed, for example, hy asagrande and hannon, 1948 (a )). The rapid movcment of the ram into the cell may also result in a surge in cell pres ure unless special precautiong are taken.

6. The U e of Side Drain If drainage during the consolidati on stage of the test is restricted to th . end surfaces of th e samplc, the time required for full dissipati on of the pore pressure is too long for routine tests on soi ls of lo\\' permeability. The use of a continuous porous j acket enclosing th e sample has been tri ed in the past [fo r example, by Jurgenson , 1934) . The effect of its strength on the measured deviator stress is very considerable, and for this reaso n a se ri es of drainage strips is preferal Ie, though less effi cient from the consolidation point of ,·ie\\,.

Ftlter papel' Cllt away

b ~------~/~ /+r '\~\--------~-~ f7' 1\

Tr-r- - -

r- r- ,.-

3~'

II

-+-- - '- 'T

I~----------------

:- ' - -

4 k" ~ ----------------~

Fig. 54. Details of side drains u ed with t ! -in . diameter samples For compression tests on It-in . diameter samples the jacket is cut with a razor from a single piece of filter paper (Fig. 54). Th e paper should be of a type which does not soften in water (for example, Whatman's No. 54). It is soaked in water before being wrapped round the sample, and is placed so as to overlap the porous disc at each end (Fig. 55). The time required for 95 % con olidation is reduced to one-tenth of the time with double end drainage, and the need for a top drainage connexion is eliminated. The effect on deviator stress is still significant, especially at low cell pressures. pecial tests should be run to calibrate the type of drain used . F or typical 6 -M. S.P.

82

THE TRIAXIAL TEST: PART II

Fig. 55. ], ilter paper drain in position on n-in. diameter sample

conditions it leads to an increase in- mea ured deviator stress of about 2 lb/sq . in. For 4-in. diameter samples the error is proportionately Jess. Where failure is to b caused by extension, a spiral of filter paper is wound round the sample to minimize the effect on strength, and the correction is usually neglected. As hown by the data given in PART III, pp. 112 and 127, this brings consolidated-undrained and drained tests on to a time scale which is practicable for routine purposes. The equalization of pore pre ure within an undrained specimen is al 0 greatly accelerated by the use of the filter strips, and they should be used where there is any doubt about the accurate measurement of pore pressure in soils of low permeability.

PART III

TA

DARD TE T

1. Preparation of Sample (1) Undisturbed samples of clay, silt and peat. The selection. preparation and testing of undisturbed samples in the laboratory form only one stage in a complete site investigation, and cannot be considered in isolation. The factors to be taken into account in planning a site inve~tigation and in selecti ng the sampling equipment arc discussed in detail c1stwherc [for example, by Terzaghi and Peck, 1948; Hvorslev, 1949; Harding, 1949 and 1952]. The laboratory programme should be carried out, or closely supervised, by an engineer familiar with these fa tors, with the geology of the site and with the type of stability or deformation analysis in which the results are to be applied. The engineer's responsibilities will include the selection of representative sections of the available cores for the different types of test, and tht assessment of the degree of disturbance to which the \'arious parts of each core have been subje<;J:ed. No sample, either hand-cut in a shaft or taken from a boring with a coring tool, is completely free from disturbance. The operation is accompanied by a release of stress and also by a shear strain, since the vertical and horizontal stresses in- itu are generally not equal. The ohje t of good field and laboratory technique is to minimize further changes in hear strain, and eliminate changes in water content- either absorption of free wattr in the borehole, in stiff-fissured clays in particular, or drying out in transit and during sample preparation. Considerable judgment and experience arc necessa ry in recognizing when the degree of disturbance is such that tests performcd on the sam pit would be misleading. everal broad rules are, however. found to apply. Deformation characteristics (i.e. the shape of the stress-strain cu rve and the compressibi lity) are particularly subject to error as a result of even slight disturbance. ndrained strength is subject to significant error after rathtr greater disturbance. The effective stress parameters c' and 4' are least affected by disturbance. ensitivity to disturbance is usuall y expressed in terms of the loss of undrained strength. It is most marked in normally consolidated soils, particularly those of low plasticity index. The Scandinavian quick-clays are the most extreme example of sensitivity, and special sampling and laboratory technique are required [for example, Andresen et at., 1957]. However, for normally consolidated strata, the well-established correlation between the ratio cli/p and plasticity index [ kempton, 1948 (c) and 1957 ; Bjerrum, 1954 (a)] enables a rapid check to be made on any loss in undrained strength due to disturbance. This correlation is illustrated in Fig. 68, p. 98. Over-consolidated strata are less affected by disturbance. As a result, however, un atisfactory ampling and laboratory technique may pass undetected until a comparison is made with the results of field measurements. Undisturbed samples for routine tests are u ually obtain d with a sampling tool from borings and are trimmed to size in the laboratory. In Great Britain the standard core is 4 in. in diameter and, if the soil is free from stones, three

THE TRIAXIAL TEST: PART III

It-in. diameter samples can be cut from anyone layer, a feature which facilitates the investigation of variable alluvial strata. The simplest method of preparing the samples, in soil of low or moderate sensitivity, is to jack out a 4-in. length of the core into a sharpened tube of 4-in. internal diameter, clamped so that its cutting edge is about i in. from the end of the core barrel in which the sample bas been taken. The faces of the 4-in. section are trimmed flat, and three thin-walled cutters are jacked into it (Fig. 56). The cutters are usually of polished brass tube, 11 in. in internal diameter, 0'03

Fig. 56. Pr paration of thr eli-in. diamet r samples from 4-in. diameter core

STANDARD TESTS

5

in. in thickness and 6 in. in length, sharpened on the outside to give a constant bore. The cutters are lubri cated. Jf 0 'casional stones 0 'cur in the soil, a 4-in. wooden spacer is placed on top of ea 'h cutter. Any cutter m 'eting an obstruction can then be abandoned by remoying the spacer above it. To trim the sample to length (usually 3 in.), it is pushed out with a loose-fitting wooden dolly so that about t in. projects first from one end of the cutter, wher ' it is trimmed off square, and then from the other, where it is also trimmed off. To prevent a flash forming a close fitting metal disc is pia ed on the end of the doll ' and :I disc of filter paper is interposed to facilitate removal of the disc and subsequent handling. 1t is obvious that some additional disturbance occurs during this operation. Correlation with field mt:asurements and also with tests on 4-in. diameter samples indicates that a signifi ant error occurs in general only in the shape of the strcssstrain curve. This method has the advantage that it can bt:: used with case on fissured clays and on sandy strata or residual soils possessing almost no oht::sion. It al 0 minimizes drying out. With cutters 0'0625 in. in thickness samples have ~ee n prepared from soil having an undrained compression strength of up to 150 Ib /sq. in. A number of alternative methods an: in use. Published data on their influence on the measured soil properties is, however, Fig. 57. Use of wire saw and framt: rather limited. Method include the use for preparing a sample of sensitive of cutters with freedom for lateral disclay placement of the clay, the soi l lathe and mitre box [for example, sterberg, 1948; Lambc, 1951]. A method used with success on the Scandinavian quick-clays is illustrated in Fig. 57-. The sample is cut from a section of the undisturbed c re held between two plattens which can be rotated, so that a series of thin slices Can be removed with a wire saw and frame. Before placing the sample in the triaxial .cell its weight is recorded (to 0') gram), and its length and diameter are measured. For routine tests the diameter is taken to be that of the cutter where thi is used, but a direct measurement should be made in accurate work. Tests on 4-in. diameter samples are sometimes made with stony soi ls such as boulder clay and with chalk; or in making special tudies of the deformation characteristics of clay. A section of the core, which usually lightly exceeds 4 in. in diameter owing to the internal clearance of the sampler, is jacked into a cutter 4 in. in internal diameter and 8 in. in length, clamped about in. from thc end of the sample tube (Fig. 58). Thi trims the core to size and enables the ends to be squared. A clearance of about 1 ~~ is allowed in ide tbe cutting edge to minimize adhesion. The diameter of the core is sub equently checked at several levels with a dial gauge indicator (Fig. 59).

t

• Publi hed by permission of the Director of the

orwegian

eotechnicol Institute.

86

THE TRIAXIAL TEST: PART III

Fig. 58. Trimming of 4-in . diameter undisturbed sample of day

Fig. 59. Dial gaug indicator for measuring diameter of samples

STAN DARD TE TS

7

amples of boulder clay arc often badly scor d a a result of a stone atching on the cutting edge of the sampler. uch samples may b patched with remoulded soil. Owing to the low sensitivity little loss in accuracy results. Partly saturated soils present an additional difficulty, as the use of a sampler, and of a cutter in the laboratory, may lead to a change in ,'olume. Unless block samples arc taken in the field and haped with a wire saw or trimmer, compressibility results must be treated with reserve. (2) Remoulded samples. Sensitivity is expressed numerically as th ratio of the undisturbed strength of the soil to its remoulded strength, both being measured under undrained condition . When the sensitivi ty of the sample is to be measured, it is therefore necessary to rcmould the sampl e fully without change in water content and to form anoth r cylindri cal specimen. A water content specimen should be taken from t he sampl e before this is done. It is then simplest to remould the sample rapidly with the fingers and repack it with the thumb in about i-in. layers in a It-in. diameter tuhe against the end of a doll y, which is progressively mo ved back down th e tube. Removal of the sample is facilitated by a film of oil on the surface of the tube, and by a paper disc on the end of the doll y. The ends arc trimmed as dtscrihcd on p. 85. After the test the water content is again measured. If any changc is noted a correction can be made from a plot of ,"vater content against the logarithm of the un drai ned strength of the remoulded soil. In the ca e of sensitive soils, th e remoulded strength is often insufficient for a cylindrical sample to be formed; a vane test may thcn be used [the laboratory apparatus is described by kempton and Bishop, 1950]. Where the preparation of the remoulded sample forms tht starti ng point for a rcsearch investigati on involvi ng subsequent consolidati on, the same procedure may be followed. In this case care to maintain uniformity and to avoid trapped air is of greater importance. (3) Compacted samples. To facilitate correlation with the standard compaction test and to enabl e a wide range of particle sizes to be included in the sample, 4-in. diameter samples are usually prepared. A three-part split mould 8 in . long is used. This fits the base and coll ar of the mould for the Proctor or British tandard compaction test (Fig. 60). Jacking out of partly saturated samples from a tube leads to a change in density; this is avoided by using a split mould. Even with very adhe ive soils the sample can be stripped by standing it on a 4-in . diamettr block and maintaining a mall but steady force parallel to the axis on each section in turn. The mould may also be lightly oiled to facilitate stripping. In the standard compaction test the mould is 4'6 in. in height and the sample is compacted in three equal layers. The B-in. sample may be prepared by using 6 layers to make a sample double the length of th e standard mould and trimming back. As, however, the three layers of the standard test add up to about 4·9 in. to allow for levelling, an equally close approximation to equal work per unit volume is obtained by using 5 layers to give a height of 4'9 X 5/3 = 8'2 in. Even with equal work per unit volume the height of the sample ha.'! a slight influence on the density obtained, but this is not of much practical significance. tones up to the i-in. sieve size may be included in the sample; in special case a t -in. limit is sometimes used. The dimensions of the sample should be measured after the mould is removed, as some samples, particularly those compacted at water contents above the optimum, shorten by 1- 2% and increase in diameter on release from the mould.

88

TIl E 'I'HI AX IAL TE ST: PAnT III

... VJ

0.

~ '"

"0

~

u

'"0.

E

8

S1' ANDARD l'E 1'S

Fig. 61. Preparation of a aturated cohe ion Ie s sample 4 in. in diameter

THE TRIAXIAL TEST: PART III

The water content of the compacted sample cannot be assumed to be equal to that of the batch of soil from which it is prepared. An appreciable error may result, particularly in wet samples. The water content is more accurately determined from the water content measurements made at the end of the test, corrected for the difference between the weights of the sample measured at the beginning and end of the test. (4) Saturated cohesionless samples. In order to make a sand specimen for use in the triaxial test it is necessary to use a former which will maintain the required specimen shape until effective stresses of sufficient magnitude to make the sample self-supporting can be applied. For samples of 4 in. diameter the split mould used in the preparation of compacted samples can be readily adapted (Fig. 61). A suitable former for preparing samples of It in. diameter is shown in Fig. 62. It consists of a split

Metalor plostic spilt mO/Jld----+-D (Jx T200segments)

Base of' cell for' 1z"dia. samples Fig. 62. The split former for 1 i-in. diameter samples mould of 1·52 in. internal diameter, which enclo es the rubber membrane, and is clamped to the base of the cell. The lower sealing rings are accommodated in a groove. Complete saturation is extremely difficult to ensure if the sample is placed dry and subsequently flooded. Means employed to facilitate saturation include the use of a more oluble gas such as ammonia to displace the air before passing water through the sample [Waterways Experiment tation, 1950; Casagrande and Wilson, 1951J. Control of effective tress ~uring this operation is difficult, and there is also some evidence that a modified value of cp' is obtained in sand whose structure is established and subjected to stress before flooding. These difficulties can be avoided by depositing the sand under water using an apparatus such as that illustrated in Fig. 63. The base of the cell i de-aired and connected either to the pore-pressure apparatus for the consolidated-undrained

STANDA RD

n:

T

G/ossrod

Fig. 63. The preparation of a saturated sample of cohesionles soil , It-in . dia.

THE TUIAXIAL TEST: PART III

test, or through a valve to the burette for the drained test. The rubber membrane is sealed to the pedestal by two O-rings and the split former is clamped in position. The upper ring (I) is placed inside the top of the rubber membrane and is held with the clamp (2) before placing the funnel (3) and rubber bung in position. The membrane and funn el are then fill ed with de-aired water ; the pres ure due to the head of water holds the rubber membrane against the inside of the former. Sufficient sand to fill the former is weighed out and saturated by mixing in a beaker with enough watt:r just to cover the sand . The mixture is boiled under a vacuum to remove trapped air, and is then placed with a spoon in the funnel, the stopper (4) being in position. To minimize segregation the sample is built up by allowing a continuous rapid flow into th e former. The funnel and stopper are then removed. To increase its density the sample may be compacted by vibration . After the surface of the sample has been It:velled, a porous disc is placed on it to retain the sand and a Perspex loading cap is gently lowered into position. Rubber O-rings arc used to seal the membrane to the cap. A small negative pore pressure is applied to give the sample rigidity, by lowering the burette after opening valve a l in the drained test, Fig. 85 (in the consolidated-undrained test valves a and f are opened, Fig. 73). The suction required depends on the size of sample and density. For samples 1t in. in diameter and 3t in. in height, a value of -0-3 Ib/sq. in. is usually sufficient. For samples 4 in. X 8 in . a value of -0-8 Ib/sq. in . is generall y used. Consolidation under this effective stress occurs almost at once, and is indicated by the change in water level in the burette. As this results in a slight shortening of the sample, the diameter of the upper porous stone should be reduced so that it can enter the top of the former without difficulty; otherwise a neck may form in the sample. The split mould is then removed and the height and diameter of the sample are measured ; the measured thickness of the membrane being deducted to obtain the actual volume of the sample. ince this volume measurement is used to determine the initial porosity, it is convenient to use a standardized suction pressure to facilitate comparison of test results. (5) Dry cohesionless samples_ The direct practical application of tests on dry materials is usually limited to silo design, where grain, sugar, fertilizer, etc., are handled in an "air dried" state. Dry sand is, however, widely used for model tests in the laboratory, and detailed measurements of its strength and deformation properties are then required. A split former is used as for saturated samples, but since there is no water pressure to press the membrane in contact with the former, the correct initial size of the membrane is more important. Suction between the former and the membrane may be used [Penman , 1953]. Loose samples are placed by running the material in continuously and rapidly from a funnel using a constant height of drop. D ens samples can be obtained by subsequent vibration. Alternatively the material, particularly if uniform, can be poured at a slower rate, using a larger drop. Homogeneous sample of a wide range of den ity can be obtained by this means [for example, Kolbu zewski, 1948]. The sample can be tamped in thin layers, though this may lead to holes in the rubber membrane. The slight tickiness of raw ugar prevents the use of pouring. Satisfactory samples may be prepared if the sugar is plated in thin layers and pressed out by a disc, equal in diameter to the sample, weighted to correspond to a column of about 4 in. of sugar. After the sample has been levelled, capped and sealed, suction is applied to

· TANDARD TEST.

93

give the sample sufficient strength to stand while the dimen ions are measured and the cell assembled. The volume changes, in the case of small sample , arc usually measured by the constant pressure air system (Fig. 46, p. 71). This apparatus may also be u cd to maintain the initial suction and to measure the volume fthe "oids in th sample. Suction is created by using the control cylindcr U' to I wer the mercury level in the burette y. The pressure is indicated by the difference in mercury level between the burette and the open limb x.

0,

Fill. 64. The layout of the apparatus for undrained tests on 1~-in . tliameter

samples: without measurement of pore pressure The volume of voids can be deduced from the relationship between volume change in the air system and pressure change, using Boyle's law. This is preferably done at a stage of the test when the sample has been consolidated and a small increase in air pressure will not effect its volume significantly. The valve z to the oi l manometer is closed. The change in level in the burette y gives the volume change in the air i:1 V consequent on an increase in pressure i:1p, indicated by the difference in mercury levels. If Vo is the initial volume of air in the sample and in the apparatu , and Po atmospheric pressure, it follows that:

(27) The volume of the apparatus i measured in the same way by sealing off the pedestal. The difference gives the volume of voids in the sample at tllat particular stress j the initial volume i determined from the volume change up to that point.

THE TRIAXIAL TEST : PART III

2. Undrained Tests The standard undrained test is a compression test performed under constant cell pressure. This means that the minor principal stress <73 is maintained at a constant value while failure results from the increase in the major principal stress <71' It may be performed with or without the measurement of pore pressure, depending on the type of soil to be tested and on the type of analysis in which the result is to be used.

(1) Undrained test without measurement of pore pressure. The test in this form is usually restricted to fully saturated samples of cohesive soils, either undisturbed or remoulded. Specimens of 1-!- in. diameter are generally used. A typical layout of the apparatus is shown in Fig. 64. The weight, diameter and length of the sample are noted, and it is then placed on a Perspex disc about t in. thick on the central pedestal of the cell. A Perspex cap is placed on top. A rubber membrane is placed inside a 3t-in. length of thin-walled brass tubing of about It in. internal diameter and is turned back over the ends (Fig. 65). Suction applied to the space between the membrane and the brass tube (either with the mouth or a vacuum line) expands the membrane to a convenient size to slip over the sample without touching it. The suction is released so that the membrane contracts on to the sample, and its ends are slipped off the membrane stretcher (a dusting of French chalk on the rubber facilitates this). Two rubber O-rings are then stretched over the end of the brass tuue, which is held over the sample again while a ring is rolled off with th e fingers, to grip the membrane against the lower Perspex disc and the loading cap, successively. A stainless-steel ball is placed in the seating on the cap, and the axial alignment is checked. The upper part of the cell is carefully placed over the sample, the ram being lifted to the upper limit of its travel while this is being done, and the three-wing nuts are tightened evenly with the fingers. The cell may now be filled with water from the main supply·, with valves Bl , Dl and E open and the air release valve I on the cell ,llso open, the other valves being closed. The rate of filling should be reduced when the cell is almost full and valve B} shut when water begins to flow from the air release valve 1. Valves E and I are then closed, and the pressure supply adjusted to the required ceU pressure. With the constant pressure control illustrated in Fig. 64, the mgst reliable method is first to open valves A}, Dl and G 1 , and set the upper cylinder to give the required pressure (the mercury should be mainly in the upper cylinder- this adjustment may be made before raising the pressure by running in additional water at valve B1). Valve G 1 is then closed and valve C opened. After adjusting the control cylinder to bring the gauge back to zero pressure, valve E is opened and the cell pressure raised by the control cylind r to the required gauge reading. Valve G 1 is re-opened and valve C closed, leaving the pressure to be maintained by the mercury control. The loading platform of the testing machine is then raised to bring the ram close to the loading cap. With the ram about t in. above the sample, the motor drive is started at the rate to be used during the test and the dial gaug on the proving ring is set to zero. This automatically compensates for • The cell is usually placed in position in the testing machine before the cell pressure is appli d, so that the proving ring retains the ram in place. If the cell pressure is applied lit lin earlier stage, the adjustable collar (Fig. 18) should be used to retain the ram.

STA

DARD TE T

9S

Iding cap

Rubber membrane

- ,---

..

"

. ... Solderedjoint

',,1. " ,,' '2 in, "

3 7.'1f

'

,

:,' : diamete'l" :' .. .'.-

,' ,' , 'sr:rmple', ,: ~' ,: ",.:, •••

•

-

.

-l

" ...

,

."

t

I

'

,

'

I

"

. ." . .' . . .

,-

,

•

•

,

: I

•• •

,

I

~)

Flexihle tuhe for applYing suction

,

,

/

"

• •

I

'

"

...

,

Fig, 65 The membrane stetcher for It -in, diameter samples the upward thrust on the ram due to the fluid pressure in the cell, and for any frictional drag, The motor drive is then stopped and the hand adjustment used to bring the ram in contact with the top of the sample. Contact is indicated by the dial gauge on the proving ring. The strain dial gauge is now set to zero by adjusting the movable arm on the pillar, and the test commenced using the motor drive. The rate of strain and the frequency of th e readings will depend on the purpose of the test. Routine tests are generally performed at 1% strain per minute. A rate of 2% per minute is sometimes used, but is the highest rate convenient for accurate booking of the readings. A dial gauge reading in rtoo-in. divisions is used to indicate strain, and at the end of each 10 division interval a reading on the load dial is taken. This represents an interval of 0'3% axial strain. After 6% strain the frequency may be decreased to 20 division intervals, and later to every 50 divisions when the rate of change of load is small.

TIlE TRIAXIAL TE T: PART HI

For special tests, or with samples showi ng unusual stres train characteristics, the frequency of the readings will req uire modification. As the need for this is often apparent only after the test is completed, it is better to record more reactings than are usually required, and evaluate only those necessary to define the stress- strai n curve accurately. The test is continued until the deviator stress (1) - (13 remains constan t or begins to fall, indicating that failure has occurred. T his is generally shown by a drop in the load gauge reading. However, with samples which yield at constant stress (plastic failure), the load will continue to rise slightly with axia l strain owing to the increased cross-sectional area to which this leads. Evaluation of a few readings will indicate whether plastic fai lure is occurring. The strain required for failure varies with soil type, consolidation history and degree of disturbance. In undisturbed samples of normally consoli dated clay, and in some over-consolidated clays of high strength, failure may occur at 2- 5';/0 strain. f20

12

I I'\...-Jdlsturbl

10

/ "'" '-I

.~ 8 IS. ._,

~

~

~ I

I()()

!}_ndistul'bed

a -a3

I

Pl =29 w. c.' TO

6

~

4

2

20

/,!,,!!!ulded

V--5

0 0

10

15

30 SMot'SttYSS'

(0)

w,c.·26

/

o o

Ax/{:II strain 1. Normally consolidated cloy

a -66 Pl ·Z6

/ /

40

I:)

l,;'

l""-

/

Z

8

6

AXial stroin % Heavily over-consolidated clay

LFissured London Cloy : averoge of 5/ tests l~pp/~:JKlmate JvelYlge o~et'6vl'tlul Pl'Usvt'; Insltv

mlbpersr;.1n

20

---;?

---- ----

~

V 10

/'

l\

20

30

-

:x (

IX\

v 40

i\

50

60

~

~

TO

80

---

1\

90

Total normal stress : Ib per sq. in.

(6) Fig. 66. Undrained tests tress-strain curves from undrained tests on normally and over-consoljdated clays . (b) Mohr envelope, in terms of total stress, for undrajned tests on saturated fissured clay ("'" =:= 0°). (0)

100

TANDARD TEST

97

In boulder clays and in remoulded samples, failure strains of up t 30 0 0 rna be encountered. The strain at which slip surfa es first appear should be noted. If the unloading curve is required the motor may be reversed. L1sing a reduced rate of strain, rcadings are taken under decreasing load, at small strain intervals, after which the zero reading with the ram moving in the reverse dire tion may b checked. For routine tests this is not called (or, and the sample is unloaded rapidly by the hand adj ustment. To reduce the cell pressure, valve G 1 is closed (to isolate the mercury control) and valve Bn is opened. Valves Be and I are then opened and valve Bj closed, so that the water runs to waste down the suction line without setting up a negative pressure in the cell. The top of the ell is r moved, the loading cap is dried, and the rubber stripped from the sample. The sample is reweighed, the mode of failure sketched and the inclination of any slip planes measured; and at least two moisture ontent specimens are taken. From the pro\'ing ring cali bration (Appendix 2, p. 17 I) and the corrected area the deviator stress (1J - (19 can be calculated, and the rubber correction (Appendix 1, p. 167) is subtracted. Typical results are shown in Figs. 66 and 67. Points to be noted are: (a) 1 he change in both strength and dt:formation characteristics on remoulding an undisturbed sample of normally consolidated clay.

Shear strength /b per sq. ft .

0

o

5

500

o o

1000

T

%.

10

5

10

a -eo Pi - U

15

.,

oL)

~ 15 I

~

20

~ 71 "'0'3 25

,J()

.

~::s

~::s'" ~

20

25

~

~ ~

~

Shear strength/b per sq. 7't. 500

1000

-

1500

2000

(if'Ol,ln(/

~

2500

.toter ..J..

level

\.

. .-

~f:~ \

1

30

'S

35

40 4s

. 1,\

Normally consolioateo clo/

~ 35 t::l 40

1 45

Heavily over-consolidated clay

~) ~) Fig. 67. Typical strength-depth profiles for (a) normally consolidated clay, (b) for over-consolidated clay

7-

M .S.P .

98

THE TRIAXIAL TEST: PART III

(b) The fact that 4>" = 0 when the results are plotted with respect to total stress on the Mohr diagram. (c) The characteristic change in strength with depth (and thus with consolidation pressure) encountered in normally consolidated clay strata. (d) A typical strength profi le in over-consolidated clay strata. For normally consolidated clays the ratio of the undrained shear strength to the vertical effective stress under which it was consolidated in the field shows a close correlation with the plasticity index, illustrated in Fig. 68. This correlation is now confirmed by sufficient field evidence to require that any tcst result not conforming with it should be re-examined, in respect both of laboratory and sa mpling techniques. 0 ,9

+ Gosport o GIY1hg.mOlltll

--

08

~Ftn$

-

07

o

KopJn!

I)

HtlC.rYlew N Z.

o Horten • Sh.llhoyen • TiI(Jur,Y

0 ,6 f--

'.

(~)

l-

0 ·5

RIO

.Ol'Omman • Monglo Nd

S.fempt:lJfl (19+8) Skempt:lJfl (19+8) SkefTIPton {1948} I(jellmon (I"" <M1m) Newland 1IIIIely(19~1) Hansen (19S0) SlwnptQn I H."k.1 (195J) Sk.mptonJH."kel (1953) SIlYo (19S3) 8/errum (195'" 8/orrum (1954)

-

1-

~V' •

02

-:::

o

o

10

(~}. 0.".OOO31(P.:!__

I

30

40

SO

___\_._ Cu • s~arst,.t(1gt" at a depth Wh8N .ftect/Ye ol'tJr(JvtV/4I> prossuro is e.t;vol to p

lB~o

20

- - 1-

'j....-

~ -

: ~~~I

0'3

0 ,1

1--I - - I - - 1-

__, ... / 001

w

ro

PlostlClty

'-

-

\ - - I- - I-- I - -

~

~

~

~

~

~-

m

~

Index

Fig. 68 . The relationship between (culp) and Plasticity Index (PI) for normall y consolidated clays (After Skempton, 1957)

(2) Undrained test with measurement of pore pressure. This test is used principally in testing compacted sample of fill materials. Due to the presence of air voids, an increase in celt pressure under undrained conditions leads to a decrease in volume and an increase in effective stress. The stress circles obtained from a series of tests at different cell pressures thus enable a failure envelope in terms of effective stress to be plotted if the pore pressure is measured. Compacted samples of 4 in. diameter are generally used, and the test will therefore be considered as taking place in the large cell. When partly saturated undisturbed samples of cohesive soil are encountered- this seldom OCcurs in temperate climates except near the surface-a similar test may be performed in the small cell. The complete layout of the apparatus including the volume measuring unit is shown diagrammatically in Fig. 69. The absence of air in the base of the cell is checked by running water through from the burette h with valves a and f open, and noting freedom from bubbles. The pore-pressure apparatus is then checked by observing the change in mercury level, with valves a and f closed, on raising the pressure with the control cylinder t. Its zero is checked as described in PART II, p. 61. A saturated porous disc is weighed and then slid on to the pedestal

TANDARD TESTS

99

100

THE TRIAXIAL TEST: PART III

(the disc should be kept under water after de-airing by boiling or by a vacuum). The sample is weighed, its dimensions noted,4I and it is then transferred to the pedestal. t A cap witho ut a drainage connection is placed on top, the rubber membrane is placed in position with a membrane stretcher, and two rubber O-rings are sprung into position at each end. The top of the cell is lowered into position with the ram lifted! to the upper limit of its travel, and the six nuts are evenly tightened. With valves D 1 , E, J, H and I open, water is run in through the main at valve B1 . When water runs from H and I, valves Bl and E are closed, about 2 cu. in. of castor oil are run in through H from the oil pressure supply, and the valves H and I are closed. The sample is now ready to test. After the pressure system has been adjusted as described in section (1), p. 94, the control cylinder is brought to zero pressure with the valves C and Ai open (and the manometer valve A2 for low-pressure tests). Valve E is then opened; valvcs K J and L J are opened and valve J closed to bring the volume measuring device into operation. Its zero reading is noted and the cell pressure raised by the control cylinder. When a value has been reached sufficient to ensure a positive pore pressure (a cell pressure of 3- 5 lb/sq. in. typically in soils having a low clay fraction), valve a is opened to bring the pore-pressure apparatus into operation. This valve should be opened slowly, the control cylinder e being adjusted to keep the mercury indicator constant. The cell pressure is now increased steadily to the required valuc, the porepressure control being adjusted continuously. Valve G 1 is then opened al'Jd valve C closed, leaving the mercury control to maintain the cell pressure. Some time may elapse before the volume change and pore-pressur readings reach equilibrium, as a result both of creep in the soil structure !lnd initial nonuniformities of pore pressure.§ Half an hour is generally a sufficient wait for ordinary tests. The pore-pressure and volume readings are noted , and the loading platform raised to bring the proving ring in contact with the ram. The motor drivc is started in order to obtain the zero setting on the load dial gauge, the final adjustment to bring the ram in contact with the sample being made by hand. The volume reading is again taken, the difference from the previous value being due to the displacement of the ram, and th zero of the strain dial is set. The motor drive is now started , and the pore-pressure control adjusted as necessary. A 2-in. travel dial gauge reading in 0100 in. divisions is used to measure deformation. Readings of the load dial, pore-pressure and volume gauges are taken at intervals of 20 divisions, 40 divisions and 100 divisions progressively as the rate of stress change decrease. This is facilitated by the fact that it is generally desirable to run the test relatively slowly in order to ensure uniformity of pore pressure throughout the sample. • With some samples, particularly wet amples wh ich tend to deform in handling, the dimensions are sometimes measured after placing the specimen on the pedestal. With dry samples. however, it is important that the minimum time should elapse tween placing the specimen on the saturated porous disc and applying the cell pressure, in order to reduce the tendency of the soil to absorh water from the disc. t If the soil is of low permeability a top porous disc is also used and a set of t-in. wide strips of filter paper are placed vertically at I-inch centres around the sample, overlapping the porous discs at each end. t The adjustable arm used for the strain measurement erves as a convenient stop for this purpose. § In soils not having a high degree of satura.tion. the pore pressures, though small and not so important fr m the engineering point of view, undergo rather erratic changes if left for a prolonged period. A nwnber of factors. such as temperature fluctuations, redistribution of moisture within the macrostructure, etc., may be involved.

TA

DARD TE 1'S

101

The factors co~tr~lIing t?e rate of strain necessary to ensure uniformity of pore pr.essure ar.e mdlcated III PART 1, p. 30. Typical values arc given in Table I I~ relation to sOIl type and to permeability. It is not convenient to lise a testing time of less than one hour, unless two operators are available, even when the permeability permhs a higher rate of strain. On the other hand, even with soils of low permeability, the lise of filter strips to accelerate equalization of pore pressure permits a testing time seldom exceeding 6 hours. The slower rates TABLE

1

Typical testing rates for undrained tests with measurement of pore pressure on compacted soi ls I

Type of soil

Permeability: Coefficiellt I Rail' of etll. PI'] sec. of collsoli- : a:.:ial .1Ira i" : • I 0 dation : o per 1111n . 2 e1ll . per sec.

I 1

Moraint:

Bould er clay Boulder clay and residual clay

1 X 10- 4 to 1 X 10- 6 1 X 10-

6

to

1 X 10-

7

1 X 10 -

7

to

1 X 10-"

2 X 10-

1

0·08

2 X 102xl0 to 2 X 10-

2

0 ·08 with filter strips

3

2 X 10- 3 to 1 X 10-'

AbOt,1' Below Optillllllll optimum water cOl/fell f [vafl'r cOl/fellf

I

I

to 2

Appro., ·. tillle tu failure : hOllrs

I 0with ·08-0 ·04 .filter I

1

1

21

11

3

2-4

4-8

stnps

I

present little practical difficulty as the operator can supervise several tests, or compute the stress and pore-pressure values while the test is in progress. orne experience in estimating the probable failure strain is useful in choosing the appropriate rate of strain at which to set the gear box. Failure strain varies both with compaction moisture content and with cell pressure. Typical values arc given in Table 2. The test is usually terminated when the maximum deviator stress has clearly been reached. The pore-pressure apparatus is then isolated by closing valve 0, and the volume gauge is shut off by closing valves Kl and L!, and opening valve J. The axial load is removed with the hand control- the number of complete revolutions made by the load dial can be confirmed at this stage- and the zero rechecked if desired. The pressure control and gauges are isolated by closing valves G l , Al and As. When emptying the cell it is convenjent to blow off the oil first by opening valve H. After drawing off the bulk of the water with valves B2 and I open, valve Bs is closed and the remainder drained from the hose connexion at the base of the cell, to prevent the possibility of air and oil entering the volume measuring system. The membrane is rolled down from the sample, which is then reweighed. The weight of the porous djsc is also checked as this will indicate the extent of

102

THE TRIAXTAl TEST: PART III

90 /'"

80

60

/

50

/6 pel'

J

40 30 20

10

-

~ l- (o;-03)

70

sq. in.

~

t

I

-_ ~

,

1i l'

')2 u-,{

--_ -

/'

5 '0

--

0;' '1/,

3·0 703 2 '0

J

5

+ 40

4- ·0

10

Axial strain .%

~I

.1 1

15

I.

vag = 301b pel' sq.In .

30 U

20

16 pel'

sq. in

10

V

~ r--.....

0

-10

.6vo

I

'r--.-r--

T

1 ·01----I---I----l--

'I

t--

'i

"20%

I

--j..,,""""' 4 - - + - - 1 - - - I

v-lo 0~~--~~--4-~--~--~~

Fig. 70. Typical result of an undrained test on a compacted fill material

STANDARD TE T TABLE

103

2

Variation of failure strain with compaction water content and with cell pressure: undrained tests on ompacted cohesive soil Material

I

Clay Optimum Optimum Water Arial strain aT failur(, for gi,'m frac tion dry COtltellt cell pressur" (strail1 at 0/1 os' wat" < 0'002: content : density: as tested: max. ill parNlth esl:s): 01 0 mm.% Iblm. ft ,0 % '0

a, =

0, =

Us =

15Ib/sq.ill. 30 Ib/sq. ill . 60 Ib/sq. ill.

Moraine

Boulder clay

2

12'2

10

9'5

120

Residual

clay

21

I

16'0

111

I

(3,)

4!

(4)

21 (2) 4 (3) 11 (3t)

8'5 10'5

3 (2,) 6';' (4) 17 (3.,)

14' 5 16.0 18'0

8 (6) 10 (St) 9 (5) s~ (5~) 18t (3';') 16~ (3~)

9'5

130

4

10'2 12'2 14'2

16

('4)

41 (4) 8-!- (li) 14

(5)

61 (6) 6';' (5,) 17-!- (5) 9 (8.,) 11 (6) 16, (5) 11

(11 )

I 19t 9t cst) (3t)

water absorption by the sample. The mode of failure is sketched and the inclination of any slip surfaces is measured. At least three moisture content samples should be taken. For an accurate stress calculation the area correction must be based on the actual volume at each stage of the test·, as explained in PART 1, p. 28. Many routine tests are conducted without the measurement of volume change, and the correction is based on the initial volume of the specimen. The error will depend on the degree of saturation and will vary with cell pressure. It usually results in an underestimate of the deviator stress not exceeding 3(}o in soi ls of low compressibility. T he proving ring calibration is used to determine the deviator stress. The rubber correction is usually negligible. The correction for filter strips, jf used, is about 0'5 Ib/sq. in. at failure, and is deducted from the deviator stress (see Ap pendix 1, p. 167). Typical results are shown in Figs. 70, 71 and 72. In Fig. 70 are plotted the stress- strain, pore-pressure and volume-change characteristics of a compacted fill material , as obtained from a single test. In Fig. 71 a typical Mohr envelope is given. Provided the samples are accurately of the same water content, the results will lie close to a straight line envelope with little scatter. If difficulty arises in maintaining consistent water contents, the results may be expressed as plots of (0'1- 0'3)' and (Ja'), against water con· tent for a number of tests at each ceJl pressure, and the Mohr envelope for the required water content obtained by interpolation (Fig. 72). Val ues of " and ¢> ' obtained from tests on typical soils are given in Table 3. Attention is drawn to the effect on the value of c' of small changes in water content. Some typical values of Band AJ are given in Table 4 . • The reduction in cross-sectional area during the application of the cell pressure may be calculated from the volume change by making the assumption of iS0tropic strain during this stage. Changes in cross-section during shear are calculated from equation (I 7).

104

THE TRIAXIAL TEST: PART II! 125

lrL

.!i: ~100

~

~

~

75

~

~

~

<5i

Rj 50

r

/'7

25

{ :Col1

~rsq. m

Z5

~

...........

I \ N

'" 1\

\

1\

i',.

Glen Shiro Moraine compacted at optimum water content

-........

I--

./

A. ~j

c'. 7·2 16

o

v

V

~,= 36~I ~

f'-

\

~

m

m

~

~

~

,

~

m

£f'f'ectlve normal stress cr' - /6 per sq. tn.

Fig. 71. Mohr envelope for undrained tests on a compacted fill material TABLE 3 Values of the shear strength parameters c' and f from undrained tests with pore-pressure measurement

Material

Clay Optimum Optimum Wat er IractiQ11 dry content as water < 0'002 content: density: tested : mm: %, lb /cu . It % %

CohesiOI1 c' : Ib/sq . It

A ngle .Jj .~Ju:ari/lg

resistance

rf/: degrees

Moraine

<1

8'S'

131

6'8 8'8 10'2

890 750 115

42 44 41

Moraine

2

12'2

120

9'6 12'2 14'8

1440 980 0

36 37 36

Boulder clay

4

7'8

135

6'8 7'8 8'8

1300 980 270

38 38 37

Boulder clay

10

9'5

130

9-5

1440

33

Boulder clay

19

10'7

126

8'8 10'7 12'4

2350 1660 490

27 24 28

Residual cla~

25

47-0

72

48-2

1200

31

Residual clay

44

23 -0

98

20'0 23-0 25-0

2590 2260 620

24 21 24

The eoropnetiv effort used in sample preparation approximated in all cases to that used in the standard compaction test . amples 4 inches in diameter and 8 inches in height were used cept where indicated by an asterisk ._

STA

401----1---1---1- -

-

DARD TESi

lOS

-

k:_03 '" 3016 per sq. in.

lVo/(Jesof

1---01---"""""', ~rl~l 20

-"3': 15/b per sq. 111. '-

!~~,;; I----I--

-l---

10

-

po- ;.. - 0 -

I----l- -

"

-

-

-

12

-

-

JOjI}f

i"

e -'-,,-

-

-~ .- f -

Q

-

- f-..-Q- - - -

-

-

13

Water content %

Fig, 72 , Variation with water content of d'viator stress and minor principal effective stress at failure for a compacted fill material

THE TRTAXTAL TEST: PART III

106

TABLE 4

Values of the pore-pressure parameters B and AI from undrained tests with pore-pressure measurement Clay fraction < 0,002

Optimum

Optimum

water content :

mm: %

%

dr)' density : [blell . ft

Moraine

<1

8'8

131

6'8 8'8 10'2

0'06 -0'01 0'26 -0,03 0'90 - 0,28

Moraine

2

12'2

120

11'7 13'0 14'5

0,02 -0·01 0'23 -0'04 0'46 - 0,15

Boulder clay

10

9'5

130

8'5 9'5 10'5

0·04 +0'01 0'26 -0,03 0'54 -0 '1 3

Boulder clay

19

10'7

126

8'8 10'7 12'4

0'03 +0'01 0'27 +0'09 0'69 -0'15

Residual clay .

20

27'5

94

26'0 27 'S 31'S

0 '05 +0'05 0'05 +0'07 0'14 +0'27

Residual clay .

44

23 '0

98

20'0 23 '0 25,0

0 '03 0'16 0'36

Material

.

Wafer content as tested:

B

Al

%

+0'02 +0'14 +0'06

The compactive effort used in sample preparation approximated in all cases to that used in the standard compaclio1l test. Samples 4 inches in diameter and 8 inches in height were tested.

3. Consolidated-Undrained Tests The standard consolidated-undrained test is a compression test in which the soil specimen is first consolidated under an aU-round pressure in the triaxial cell before failure is brought about by increasing the major principal stres , Ul' It may be performed with or without the measurement of pore pressure, although for most applications the measurement of pore pressure is desirable. In the field consolidation of the soil generally occurs under conditions in which the major and minor principal stresses are not equal; for example, under Ko conditions in level ground, or under the particular stres system obtaining in a slope. For a full investigation of these cases it is necessary to consolidate the specimens under stress ratios similar to those occurring in the field and the use of anisotropic consolidation will be considered in PART IV, p. 156. (1) Tests on saturated sands with measurement of pore water pressure. amples of aturated sand are prepared as indicated in PART III, 1, p. 90, and in this section the test is described from the point where the specimen of

STANDARD TE TS

107

sand, enclosed in the rubber membrane, is standing on the base of the cell with a small negative pore pressure maintained by the lowered burett.e to give it rigidity. In addition, it will be assumed that the standard cell for It-in. diameter samples is used. The top of the cell is first lowered into position, with the ram lifted to its fullest extent, and the three wing nuts are evenl y tightened. The pressure supply is connected to the cell and with valves BI , Dl and E open (see Fig. 73) water is run in from the main until the cell is nearly full. Oil is then introdu 'd at plug Z (for a short duration test of only a ft\\' hours about l in. of oil i neces ary). After the oil has been put in, the plug is replaced, and the last of the air in the cell is forced out of the air valve r by allowing a little more water to enter the cell. Care should be taken to limit the rate of flo\\' of the water as there may be (l surge of pressure as the la t of the air leaves the air valve and oil starts to escape. The air valve is left open until no further flow of water into the lowered burette h occurs and the sample may then be considered to be consolidated under the head of water measured from thc top water levcl of the cell to the level in the burette. After closing the air \'alve I the cell pressure is raiseu by opening valve C, forcing watcr from the control cylinder on the pressure side into the cell ; and at the same time the burette II is raised until its water level is at the midheight of the sample. When the required cell pressure is reached, the mercury control, which has been preset to the desin:d cell pressure, is conne ted into the circuit by opening valve G 1 . Valve C is then closed. The sample is allowed to come to equilibrium under the cell pressure and the volume change indicated by the burette is noted. Before closing valveI. the zero reading of the pore-pressure apparatus is checked. A final check on the completeness of eonsoljdation is given by the fact that. provided the cell pressure is constant, there should be no tendency for the pore pressure to rise, after valve I is closed and before the sample is loaded. When dense sands, which show marked dilatancy, arc tested, large deerea es in pore pressure may accompany the application of the deviator stress and the pore pressure may fall sufficiently for cavitation to take place in the pore-pressure system [Bishop and Eldin, ] 950]. nder these conditions the constant volume state cannot be maintained and the test is best carried out by having a large positive pressure in the pore water immediately prior to this stage of the test. This can be most easily achieved after consolidation is completed and valve I is closed, by raising the cell pressure under undrained conditions. J n a saturated material the increase in cell pressure is accompanied by an equal increase in pore pressure and the effective stresses do not change during this process. The table of the testing machine is raised to bring the proving ring into contact with the ram and, with the motor drive running at the chosen rate, the zero reading on the load dial gaugc is noted. The ram is finally brought into contact with the sample using the hand control and the zero of the strain dial is set. The compression test may now be started and the pore-pressure control is adjusted when necessary to maintain the no volume change condition. Deformation is measured by a dial gauge reading in -nh>o--in. divisions, and readings of the load dial and pore pressure are made at intervals of 5 divisions in the early stages of the tcst. increasing progressively to 50 division intervals as the stress-strain curve flattens. As sands are very permeable, no pore-pressure lag will occur, and the rate of testing chosen will depend only on the convenience of taking readings. A time to failure of about one hour is commonly adopted. nJess special studies of the behaviour of the material under large deformations are being made the test is

THE TRIAXIAL TEST: PART III

108

...c ., .,E..., ;:l II)

.,'" E

.....

-5 .~

.,'"

0.

E

'"'"

....... G.)

I1J

~

:.0

.S, ..... c

0

21

'"

~

G.)

....

;:l

'"'" ."";c

.. .,... ""c, ... "" G.)

G.)

0-

;:l

~

:"9'"

"0

'"0c

. u

.B

..'"

::l

~

'"0-0'"

G.)

-5

... 0

....

::l 0

>,

GO;

tJ::5I

~

~

I

~

.

~

..c: E-< M

r--

t>O

li.;

0

00

ST ANDARD TESTS

109

stopped when a maximum deviator stre s has been reached. The pore-pr ssur apparatus is then isolated by closing valve 0, the axial load is remov d using the hand control, the zero of the load dial being checked in th process. The mer ury pressure control is then isolated by closing valve GlI and the c II pressure is reduced to atmospheric pressure by opening valve Bs. With valves AJ and A2 shut most of the water from the cell is allowed to flow down th suction line. To prevent oil from entering th valve system, the remaining water is allowed to drain from the hose connexion at the ba e of the cclI. Typical results are shown in Fig. 74 (1I) for a very loose sand and Fig. 74 (b) for a denser sample (n denotes initial porosity). The stress- strain and porepressure change characteristics are given for samples consolidated at the same cell pressure. The Mohr envelope for a series of tests on loose sand is shown in Fig. 75.

(2) Tests on saturated clays with measurement of pore water pressure. (i) C011so1idotioll with drainage to atmosph('ric pressure Before preparing the samples as described in Section 1, p. ):\1, a I D-c.c. burette is connected to the pore-pressure outlet on the base of the cell through a piston valve. The ".. hole system is then dc-aired and filled with water. This may be accomplished by inverting the cell base in a dish of de-aired water and applying suction to the open end of the burette. Rapid opening and closing of the valve facilitates the removal of any hubbies which may lodge in the cell base or in the valve. When no furth er bubbles are observed in the burette the vah'e is shut and the suction line is removed. A little water is allowed to flow back from the burette to cover the pedestal. A saturated porous disc is slid on to the top of the pedestal." The sample of clay is placed on the p.orous disc; and, if required to accelerate consolidation, filter paper drains which have been saturated with water are placed in position round the specimen. Th e rubber membrane is placed over the sample using the membrane stretcher and the lower part of the membran is scaled to the pedestal with two O-rings. In order to remove as much air as possible from between the rubber membrane and the specimen, the rubher membrane is gently stroked in an upward direction hefore the upper porous disc and the Perspex loading cap, Fig. 19 (c), are placed in position and sealed with two more O-rings. In soft clays, where little swelling would take place during the setting up time, water may be allowed to run from the burette up between the membrane and the sample to facilitate the removal of air before the loading cap is scaled. This procedure is, however, not recommended for stiff clays where rapid surface softening may occur. For accurate work on these clays the specimens should be consolidated with a back pressure in the pore water so that any air remaining may be dissolved. This technique will be considered later. In those cases where water has been used to assist de-airing in setting up the sample, the burette is lowered so that a few inches of negative water head can be applied to the sample and the valve a1 (sec Fig. 76) is opened to draw any excess water away from the sample and to ensure that the specimen is sitting firmly on the pedestal. After a few minutes the valve is sh ut and the burette is returned to a convenient position on the bench. The cell is assembled, care being taken with the alignment of the top of the " If the top of the pedestal is at all greasy th water wi ll not wet the ':"ctaJ and air will be trapped when the porous disc is slid into position. Commercial detergent may be used to clean the metal.

IlO

OJ -03 Ib per

sq. in. 0

(a)

0

5

10

15

20

25

Ax/al strain %

s::'0r-±;+; I r; I !

o0

5

10

15

20

25

Axial strain % 20u

failu1,e 160

0; -03

v

120

Ib per

sq. in. 80

4o

(b)

o

V

o

/

/ s

/

V

/

k-:"'::

n ", 43'0%

.

10

15

20

25

,]0

35

Axial st rain.% + 40

o

-

""'"~ 5

~

10

...._

:----!'----

15.

20

Ax/al strain %

.-l 25

30

Fig. 74. Consolidated-undrained tests on 'atul'ated sand. Deviator stress and pore pressure plotted against axial strain (a) for a very 100 e sand, (b) for a denser sand

35

STA

DARD TE T

tIl

~4 c::;..

'"to.

~30r---~r----1~---i-----t--~~----~~--;r----~~__'

:::: I

"'ZO'~----~----+-----~~--'r-----+-----+-----4

~ ~ ..,

~ W ~----~~~+---~+-~~+-----~----~----~----~~--~ II)

~ 40

50

60

70

80

Normal stress - /b persq.in. Fig. 75. Mohr en velope in terms of effecti\'~ stress for consolidatedundrained tests on l oos~ sand

Fig. 76. The layout of the apparatus for the consolidation of 1 i-in. diameter saturated sampJes

1I2

THE TRIAXIAL TEST: PART II J

cell as the ram is inserted into the guide in the loading cap. De-aired water is run into the cell from the main supply with the air release valve I open until the cell is nearly full. About i in. depth of oil is then introduced into the cell at the plug Z. Any remaining air i expelled through the air valve by admitting more water. The cell pressure is raised to the desired value using the screw control and the mercury pressure system is then brought into operation. The water level in the burette is adjusted to a suitable height to allow the decrease or increase in volume of the sample to be measured. (If the change in height of the specimen during consolidation is to be measured the distance between the ball in the sample cap and the ram is observed with a vernier telescope.) The val ve a1 is opened and if required the change in volume with time is recorded by a series of suitably spaced readings." Consolidation is compl eted when no significant movement of the water level in the burette occurs. For the compression test the cell must be transferred to the testing machine and the pore-pressure systemt must be connected to the base of th e cell . In order to make the pore-pressure connexion without trapping any air, the cell is placed in a tray containing water standing to a depth of about It inch es. The valve a} and the volume measuring burette are removed as a unit. With the burette h standing so that its water level is slightl y above the water level in the tray and with valve f open, a little water is allowed to flow from the porepressure apparatus through valve a before it is connected to the base of the cd l. The layout is then as shown in Fig. 73. The cell is placed on the loading platform of the testing machine and the proving ring brought into contact with the ram. The burette h is adjusted so that its water level is at the mid-height of the specimen and the zero reading of the pore-pressure apparatus is checked before closing valve f. When a large negative change in pore pressure is expected to dcvf'lop as the deviator stress is applied, the cell pressure- should be raised at this stage by an amount at least equal to the anticipated drop in pore pressure. The initial pore pressure will then be high enough to prevent the occurrence of any substantial negative values. With the motor drive running, the zero reading of the proving ring is recorded. The ram is brought into contact with the loading cap of the sample by the hand control and the zero of the strain indicating dial is set using the adjustable arm. The test is then started. Readings of the proving ring dial and the pore pressure are taken at intervals until a peak deviator stress is reached. The sample is deformed at the rate necessary for the accurate measurement of pore water pressure. In practi ce it has been found that in the more common clays a testing time of 4 to 6 hours is sufficient. After failure has been reached the pore-pressure system is isolated by closing valve Q. The sample is unloaded by hand and the proving ring zero is checked. The cell pressure is now reduced and the water and oil removed from the cell. The top of the cell is taken off and surplus water is wiped from the loading cap. The O-rings and cap are then removed and the rubber stripped from the sample. After removing the filter paper drains and end discs the sample is weighed; and two or three slices about i in. in thickness taken from various parts of the specimen are then used to find the water content. From the difference between the initial and final weights and water contents • If the volume changes are large, it may be necessary to remove water from the burette during the consolidation process to prevent the bu.rette overflowing . t The pore-pressure apparatus should be checked to see that it is free from air before starting this sUlge of the test.

TANDARO TESTS

113

the volume and cross-sectional area of the sample after con.olidation can b determined (using either the assumption of isotropic strain or the a.x ial strain obtained by optical measurement), Changes in cro s-section during shear are calculated from equation (17). The deviator stress is determ ined using the pro\'ing ring calibration. Corrections to the calculated stresses are made to allow for the effects of the drains and rubber membrane as indicated in Appendix 1, p. 167. (ii) COllsolidating against a back pressure When it is not possible to de-air the space between the rubber membrane and the sample, the consolidation stage may be carried out with the pore pressure at an elevated value so that the air will be dissol ved. 1n order to make the necessary observations of volume change during consolidation, the apparatlls illustrated in Fig. 43 is used . The procedure for carrying out the test is very similar to that described above and Fig. 77 shows the general arrangement of the apparatus. After the ell has been filled with water and th oil added both the cell pressure and the prcssur on the drainage side are raised before "alve Q 1 is opened. The difference between these two pressures gives the cffective stress under which the specimen is to be consolidated. In practice a back pressure of about 30 Ib/sq . in. is usually sufficient to dissol ve all the air. Another difference in test procedure is required when the fully consolidated sample is to be connected to the pore-pressure measuring sy tem. Valve 01 must be closed and left in place on the cell base while the volume measuring equipment is removed. The connexion to the pore-pressure apparatus is made by joining valve a to valve a1 under water. Before valves a1 and a arc opened the pore pressure must be adjusted to the same value as the back pressure under which the specimen has been consolidated. The test may then proceed as before. (iii) Over-consolidation of specimens Over-consolidated clays may be produced in the laboratory by first consolidating the specimen under a particular effecti ve stress and then allowing it to swell under a reduced value of effectiv e stress. The test procedure is simi lar to that already described for the initial consolidation process; but, when this is completed, valve 01 (Fig. 76) should be closed while the cell pressure is adjusted to the reduced value. On opening valve 01 the swelling pro ess is initiated and readings of volume change against time may be taken. If there is any likelihood of air having collected in the pedestal during the consolidation period it should be removed, as described in PART II , p. 62, before swelling is permitted. Heavy over-consolidation will normally lead to the development of negative pore pressures in the undrained test; and swelling under a reduced effective stress may, with advantage, be carried out using a back pre sure in the pore water, as described above.

Typical results Typical results obtained in consolidated-undrained tests on normally consolidated clays are shown in Fig. 78. The ratio A f between the change in pore pressure during shear and the deviator stress at failure is usually fairly cia e to unity. A set of Mohr circles for a series of tests with different consolidation pressures are shown in Fig. 79 in terms of both total and effective stresses. The magnitude of the pore pressures set up when over-consolidated clay are tested depends greatly on the degree of over-consolidation [Henkel, ] 956J. Typical results for a fairly heavily over-consolidated specimen are shown in 8- M.S.P.

'filE TRIAXIAL -rE T : PART III

TA

DARD TE TS

20

fotl"{e ./

.~ 15

v-

I

..,ti-. ~

~ 70

I

...c:::,

........

.........

b'" I

5

I:)

-.....:...

o

o

5

10

15

20

25

Axial strain %

20

.~ ti-.

15

.., ~

~ 10 ~ :::,

<J

5

o

--/ II

o

17'

5

10

+ -0:;=30/6

persq.in.

15

20

2S

Axial strain %

Fig. 78. A consolidated-undrained test on a normally consolidated clay sam pi deviator stress and pore-pressure change plotted against strain

Fig. 80 where a decrease in pore pressure has occurred by the time failure is reached. The Mohr envelope for a serie of tests on an over-consolidated clay will in general have a cohesion intercept and results in terms of both total and effective stresses are shown in Fig. 81. An overall picture of the effects of over-consolidation on the pore-pressure changes during shear is given in Fig. 82. Here the value of A at failure is plotted against the over-consolidation ratio (Pt,/Pd in Fig. 9 a). The results shown are for samples of both Weald Clay (LL 43, PL 18) and London Clay (LL 78, PL 26) prepared in the laboratory and consoHdated under equal all-round pressure. orne typical values for other clays are given in Table 5.

_1--7' < r Ii 20 40

--

~

b ~~

1/'\ (

60

80

f.--

-

l-

~o

19'cu s /3

"-

V

"'- II \ \ 100

120

ltW

160

\

\ zoo

180

Tota l stress - /6 per sq.in.

~

....-1

k rrt 20

L ~

ft1\ If 40

.......

60

r-= ..... L.

~

h¢!_z) -

p :

'"

\

80

1\ 100

140

120

Effective stress - /6 per sq. ffl. F ig. 79. Mohr envelopes in terms of both total and effective stresses for consolidated-undrained tests on normally consolidated clay samples 15

fallure~

II

/

V

5

V--

/

+--

10

/5

20

25

30

AXial stroin % +5

03- 51b per Sft in. 1..,..--.......,

~ 5

~

10

~

15 .

Axial strain .%

20

f

25

30

Fig. 80. A consolidated-undrained test on a heavily over-consolidated clay sample; deviator stress and pore-pressure changes plotted against strain

STA N D ARD T EST

--

0

10 Ccu=Slh ~rslfln.

~

{~ ~1\

o

20

I

~(

"'J'...

......::. t:?"

.. i7"""-

~

~

..........

V

i\

I

\'

40

·\~~. '5°

X I-1\ '" \ \

0

~

.

II

80

60

100

\

120

140

Total stresses - 16 per S(I- in.

so

.......

,

10

c '= ,·316 perS'l.ii;:-

~ °Vi rtl i\ 20

f 7/

v( ~ 40

7

(

'"

\

1\ 80

stresses~/b

........

'\

'\

60

EFFective

~

\

-

t-....

-::z......

~

~Lo

.L.

"\ 1\

100

120

/4{)

per sq. in.

Fig. 81. Mohr envelopes in terms of both total and effecti ve stresses for conso lidated-undrained tests on over-consolidated clay sample

T ABLE

5

T ypical value of AI for various soil types: from consolidated-undrained tests

I Plasticit),

Type of S oil

Normally consolidated

m arin e clay; undisturbed London clay: remoulded Weald clay; remoulded alluvial sandy clay: undisturbed loose sand dense sand

{ W"ld d.y, =di' Mb, d Over-consolidated

.

Weald clay; remoulded , over-consolidation ratio = 8 . London clay; remoulded , over-consolidation ratio = 8 .

Index

Va lue of AI

60 52 25

+1-3 +0-97 + 0 -94

-

18

-

+0-47 + 0'08 -0-32

c. 25

-0 -62

25

-0 -22

52

-0 -11

lIS 1'0

\

'8

(a)

\,

Weald Cloy

1\

'4

.\

~

""

o

'" " ~

l'-..

- ·2

I'-. r-..

-· 4

- ·6

~ I;---; • r-•

,.5

1

2

3

4 5 6 7 8910

15

20

30

40

Overconsolidation Ratio

·8

~

\

(b)

·6

London Clay

\

'i

~'\

'2

o

l"- i'- ......,

-·2

-·4

~~ ~

r..r--- •

•

•

1

"5

2

345678910

IS

20

30

40

Overconsolidation Ratio Fig. 82. The effect of over-consolidation on the value of the pore-pre sure parameter A at failure: (a) Weald clay (b) London clay

STA

DARD T£ T

119

(3) Partly saturated soils. Consolidated-undrained tests on partly saturat d soils may be divided into two main categorie : (i) tests in whic h water is circulated through the specimen befor appl ing the deviator stress, in order to investigate the effects of soft ning du to saturation. (ii) tests in which the pore pressure set up by the consolidating pressure is simply allowed to dissipate before the compression tc t starts;

The tests are usually carried out on 4-in. diameter specimens and the implest layout of the apparatus for the first type of test is shown diagrammatically in Fig.83. J nstead of the pore-pressure connexion, used in undr, in d tests, a 100-c.e. burette 171 is connected to the base of the ample through valve a l • Dc-aired water is run from the burette until water emerging through the pedestal is free of air bubbles. The sample is then set up and the cell assembled as des ribed for the undrained tests, with the addition of a connexi n to permit drainage from the top of the ~~mp le into another JOO-c.c. burette The cell pressure is raised to the required value, the volume changc in the specimen under undrained conditions being obtained by measuring the volume of water flowing into the cell and applying the appropriate co.rections for ell expansion. ~T hen the volume changes associated with the increase in cell pressure have ceased, valve a2 is opened and the pore pres ure is allowed to dissipate. In general both air and water will he expelled from the specimen and , if measurement of hoth are required, the apparatus shown in Fig. 45 is us d. The most accurate reading for the total volume change will, howcyer, be given by the volume of water flowing into the cell. \Vhen consolidation is completed , water is allowed to flow upwards through the specimen by raising burette h] and lowering burette /7 2 so that the water level in them are an equal distance above and below the mid-height of the specimen. Owing to the low permeability of many compacted material, equilibrium may take many days to achieve, but for practical purposes two or three days flow usually produces a sufficient inc rea e in water content to give a satisfactory indication of the effects of softening. When it is considered that sufficient time has elapsed for softening to occur, valves aJ and a2 are closed and the pore-pressure apparatus is c nnected to valve at. Time is allowed for the pore-pressure differences, associated with the hydraulic gradient in the sample, to equalize before commencing the shear test. The increase in the degree of saturation may be estimated if the cell pressure is raised and the accompanying increase in pore pressure measured. An increase in cell pressure before the compression test commences is, in any case, de irable if dilatant materials are being tested. In Fig. 84 a comparison is made between the failure envelopes obtained from undrained tests and from consolidated-undrained tests in which softening has been permitted. The decrease in the value of c' will be noted. The second type of test is called for in the determination of c' and 1>' wher the degree of saturation is not low enough to result in a sufficient range of strengths in the undrained test to define a failure envelope. The base of the sample is connected directly to the pore-pressure apparatu instead of to the burette hi' The layout is then similar to that used for pore-pressure and dissipation tests (Fig. 96). The setting up of the sample- and the initial stages of the test foUow the

"2'

• In soils of low permeability filter-paper strip are u ed to accelerate consolidation .

120

THE TRIAXIAL TEST: PART III

oS

-1:::'"

'"

-0 ~

.. ~

....

::l

os

~

til

>.

t

~

....0. 0

.,'"

Q.

~

.,'"....

ti

o~ c: 'OJ

-0

'
.....0

C

o~

~

....

E ~

til

-0 C

os

c

·3os ~

-0 '"c 0

u

.,

-5

....

.s 2'" ....~

~

0. 0.

.,os ..c

........0 ....

::l

~

..s., ..c

E-<

~

M 00

bC

~

STANDARD TE 1'S

121

procedure described for undrained tests on page 98. After the cell pressure has been raised and the readings of pore pressure and volume change taken, the pore-pressure apparatus is isolated by losing valve a j • Val e au is then upened and the pore pressure is allowed to dissipate.

20

40

60

100

80

120

140

160

180

Normal stress-Ib per sq. in. (0)

20

40

60

80

100

120

14()

160

180

Normal stress-/b per sq. in.

(6) Fig. 84. Comparison between th Mohr envelopes (or a compacted clay obtained (a) in undrained tests, and (b) in consolidated-undrained tests in which softening has been permitted

When consolidation is completed, valve a2 is closed, and valve a1 is opened to recOnnect the pore-pressure apparatus. The compression test then proceeds as described on p. 100 for undrained tests. If considerable dilatancy is expected the cell pressure should be raised immediately prior to the shear stage to give an initial po itive pressure in the pore water.

THE THIAXIAL TE ST: PAnT III

122

4. Drained Tests The standard drained test is a compression test in which the sample is first consolidated under an equal all-round pressure, and i then cau ed to fail by increasing the axial stress under conditions of full drainage. The rate of loading or deformation is so arranged that negligible excess pore pressure is present in the specimen at any time during the application of the axial load and particularly at failure. o

IOcc.bllf'e

Fig. 85. The layout of the apparatus for drained tests on H-in. diameter samples As the exce s pore pressure i negligible the cell pressure and the applied major principal stress are both effective stresses, and this test thus gives a direct measurement of the effective stress parameters. The test is usually carried out at a constant rate of stram, but may also be performed by applying the axial load in increments. The sample preparation and the initial consolidation of the specimens is carried out in exactly the same way as has already been described for consolidatedundramed tests. When the samples are expected to dilate during shear, more satisfactory results are obtamed by having a back pressure in the pore water unless the samples are fully saturated. This IS because air may accumulate in the vertical portion of thc drainage channel inside thc pedestal and thc air lock so formed may prevent the sp cimen sucking in water during dilation . In these circumstanccs the pressure in the pore water may fall below atmospheric pre sure and the applied stresses will no longer be effective stres es.

TANDARD TESTS

1 2)

[1] Tests on saturated sands !he specimens .are prepared as described on p. 90, the ba e of the sample bemg connected dIrectly through valve G) to a burette (Fig. 85). The assembly of the cell and the consolidation stage follows the proc dure for the consolidated-undrained test de crihed on p. 106. When consolidation is complete the ram is brought into contact with the loading cap in the usual way the compression test is started and volume hanges are read from the burette: 120

faJll/1e

100

0;- 03

(

/ ~

......._

80

80

r--. r--

/rOJ-03 60

16 per 59 In 60

16 p.r sqm 40

03 ~ 30 ·6/6 persq Ifl

n • 397.

40

20

o

5

10

15

Axial strain %

+6

+4

+2

6,,;{. Vo

•

a r-"

/

v

/

V

v

20

10

15

AXial strom % (a)

persq ffI

5

/0

/5

20

25

AXial strom %

25

v

~;'NJ ~

5

03 · 30·6/6

n . 45'6 7-

II

o

20

I I

20

5

II I

m n m Axialstrom %

H

25

(b)

Fig. 86. Drained tests on saturated sand : deviator stress and volume change plotted against strain for (a) dense sand , (b) loose sand As sands are free draining the duration of the test is governed by tbe necessity of being able to take accurate readings of load and volume change. A test time of about 1 hour is suitable. Typical test results for loose and dense sands are given in Fig. 86 and the corresponding Mohr envelopes are shown in Fig. 87.

[2] Tests on saturated clays The setting up of the specimen and the initial consolidation is (,.ll rried out as described for consolidated-undrained tests. Where increases in volume are expected to accompany the shearing process, as in the case of heavily overconsolidated specimens, the initial consolidation and the compression test should be carried out with a back pressure in the pore water, if there is any doubt about the completeness of saturation.

TIlE TRIAXIAL TEST: PART III

124

80 .~

It 60

"..,

~

~ 40 I

,

'"'"

S '"~

20

\

III

t5

,

\

I

40

60

80

120

140

Normal stress-Ib per sq. In. Fig. 87. Mohr envelopes for drained tests on both loose and dense sands

(i) Ch.oice of deformation rate Owing to the low permeability of clays, drained tests on these materials must be carried out slowly if the condition of negligible excess pore pressure is to be satisfied. The effects of incomplete pore-pressure dissipation may be illustrated by considering the two extremes of undrained and fully drained tests. In Fig. 88 the Mohr circle at failure for both tests have been drawn for a clay normally consolidated under a pressure p. In the undrained test a pore pressure 6..u, almost equal to the deviator stres§ (O'l- 0'3), is set up and the effective stress circle is displaced to the left by the amount 6..11. If the pore pressure set up is allowed to dissipate during the test the measured strength will increase, with the effective stres circle at failure moving to the right, until at full dissipation the minor

Normal stress Fig. 88. Mohr stress circles for both drained and undrained tests on samples consolidated under the same all-round pressure p principal effective stress will be p. The measured strength will be a linear function of the excess pore pressure at failure. The relationship between the undrained strength, the fully drained strength and the strength with partial dissipation of excess pore pressure may therefore be written as: (0'1- O's)/

=

(0'1-0'3)"+

OJ[( 0'1- O'S)d-( 0'1- O'S)..] .

(28)

STANDA RD TEST

where (<71- (73)'

= measured

strength at any degree of dissipation at failure

(<71- (73)" = undrained strength (0, = 0), (<7 1- (73)J = fully drained strt!ngrh (01 = 1)

and

0 "

Of = the average degree of dissipat ion at fai lure.

Although ~uitable rates f.or. carrying out drained tests ma ' be found by a process of tnal and error, It IS useful to be able to calculate in advan e the approximate time required for these tests. The theory of consolidation has been ~pplied to this problem [Gibson and Henkel, 1954J. It JS £do~ndh thfat the average degree of dissipation at failure, 01' may be expresse tn t e orm:

(29) where h = ! the height of the sample, ct ' = coefficient of consolid ation, tI = time to failure and '1 = 3 factor depending upon drainage conditions at the sample boundari s. The values of 1) for various conditions of drainage arc given in Table 6. In the case of radial drainage it has been assumed that the sample height is twice the diameter. TABLE

6

Draillage COllditions

Drainage from one end on ly " both ends " radial boundary onl y " both ends and radial boundary

0'75 3'0 32'0 35'0

A comparison between this theory and the results of drained tests (Appendix 4, p. 175) shows that a theoretical degree of dissipation of 95 ° 0 is sufficient to ensure a negligible error in the measured strength. The requisite time to failure for a test may then be written as

h2 tf

=

1)clJ' 0'05

20h2

=

(30)

1)c"

The consolidation stage, prior to the shear test, may be u ed to find the coefficient of consolidation. A number of methods of calculating the coefficient of consolidation from the measured relationships between volume change and time are available. For simplicity, however, the fact may be used that the initial portion of the plot of volume change against , I t is a straight line for all drainage conditions. If this straight line portion is produced to cut the line representing 100% consolidation, the time intercept of this point, (1 100), may be expressed for the various drainage conditions as shown in Table 7. From these expressions for t 100 the value of elJ may readily be calculated. In order to illustrate the method of calculation. the measured relationship between volume change and t. for the consolidation of a remoulded specimen of Weald Clay (LL 43 , PL 18) is shown in Fig. 89. The intercept of the straight line portion produced gives t100 = 107 min.

126

THE TRIAXIAL TE T: PART HI TABLE

7

Drainage conditions

t 100

t 100

(II = 2R) Tfh 2

-Ct)

Drainage from one end only

"

"

"

"

"

Tf II -" 4ct) Tf R "16ct)

Tf fJ 2 M Ct)

Tf1z 2[ 1 ] 4ct) (1 +2h/ R) 2

-100cv

both ends

"

radial boundary only both ends boundary

and

where 2/t R and

radial

o 2

4

6

Av ccs 8

10

40

so

J

I

60

Weald Clay

\ \ l

~ T

~

-, \

l/fioo

14

30

1\

\ 12

I

= height of sample = radius of sample.

It Inmlns. 20

10

Tfh ~

""

~ -

~ t ,00 • .'~ mlns. _ I--.

Fig. 89. Relationship between th volume change ann vtime for a sample of (:lay during consolidation under an all round pressure (radial and end drainage)

STA ' DARD 1'E 1'5

12 7

In this test filter-paper drains were used and drainage took pia e from both the ends and the radial bou11dary of the specimen. The specimen had a ratio of height to diameter of two and a mean height of 2'9 in. The coefficient of consolidation is therefore found from the expression

.".112

ctJ

= 100/

""X } '45 2

100

= 100x 107 = 6'2x 10-~ sq. in·/min.

This value of CtJ is now substituted in equation (30) with 1] = 35 and the value of 211 after consolidation of 2'8 in. The time to failure is therefore: If

20x }'4 2 = 35(6'2x 10--4)

=

•

1800 mlO.

In order to chose a suitable rate of deformation to bring about failure in the calculated time:: it is also necessary to know, at least approximately, the failure strain. Failure strains depend on both the type of clay and its consolidation history. A'S a guide to estimating the:: failure strain typical values are given in Tablt: 8, based on the results of experience in the testing of clays. TABLE

8

LL

PL

Failure straill I)u

Tim e to /oilllrl': hOl/rs

34 34 18 27 18

24 24 20 4-6 4-8 4-8

46 50

{ Lond" Lias Weald boulder

103 116 28 80 56 43 30

15

4-6

Remoulded Normally {London Weald consolidated Over-consol.idation {London Weald ratio of 4 Over-consolidation { London Weald ratio of 24

78 43 78 43 78 43

26 18 2b 18 26 18

22 20

Type of clay

Ulldisturbed

NonnalJy consolidated Heavily over-consolidated

{ estuar~n e estuarme alluvial

24

11 14 5

7

10

30 25 8 8 48 30 48 30 24 8

I

For the normally consolidated Weald Clay considered above the time to failure is found to be 1800 min. With an estimated failure strain of 20% on a specimen 2'8 in. in length, this leads to a calculated rate:: of strain of 3 X 10--4 in·/min.· Testing times used in tests on some typical clays are also given in Table 8. (ii) Compression test procedure After the initial consolidation is completed, and the choice of testing rate has been made, the cell is placed in the testing machine. The burette should be • For a more precise estimate of rates allowance should be made for the probable deformation of the proving ring by the time failure is reached.

THE TRIAXIAL TEST: PART III

128

placed so that the water level in it is at the mid-height of the sample and is adjusted from time to time to compensate for the ftow of water that takes place. • After the proving ring zero has been noted, the ram is brought into contact with the loading cap and the motor is started. Readings of proving ring deformation and volume cbange are made at convenient strain intervals until failure occurs. In order to prevent any swelling of the sample following the removal of the axial load and the lowering of the cell pressure valve a1 should be closed as soon as the motor is stopped (see Fig. 85). The sample is removed as described before, its weight is recorded and its moisture content measured. From these final readings of weight and water content the volume at the end of the test may be calculated. The burette readings give the change in volume during the test and the strain dial gives the change in height, thus enabling the cross-sectional area at any time to be calculated. Typical results of tests on normally and over-consolidated clays are given in Fig. 90. 40 JO

OJ-a;

20

16 per S'l. /11

10

I /

/ I

v-

til/lure

0"3 - 51b

per sq 111 10

IT,- Oj 16 per ..q.ln

5

OJ = 30/6 p.r sq.ll1.

.1 allure

/'

-

-

1/

5

10

1 15

1-

20

25

Axial strom % 5

10

15

Ax/al stl'Oin;:

20

~zf1f11 o

IS

_j_

5

(0

IS

20

Axial strain % Normally consolidated

25

+4

.. 2 6 vo/ Vo 10

o

i 25

-2

-

o

_J-? 5

v

10

--IS

ZO

AXIal straIn % Over- consolidated

zs

Fig. 90. Drained tests at constant rate of strain. Deviator stress and volume change plotted against strain for nom1ally consolidated and over-consolidated samples of clay (iii) The use of dead loads Although there are certain advantages in carrying out drained tests at constant rate of strain, it requires the use of the testing machine for long periods. It is often useful therefore to carry out these tests using dead loading. Satisfactory results can be achicved provided that the loads are applied in small increments and sufficient time is allowed between increments for dissipation of pore pressure. Tests on London and Weald Clay have shown that increments of approximately 10% of the estimated total failure load may be applied twice a day in the early stages of the test. As failure is approached the stress increments should be reduced so that a reliable determination of the failure trength may be made. A typical test result obtained using this method is given in Fig. 91. • When a back pressure is used, the volume changes are measured with the apparatus illustrated in Fig. 43, p. 69.

STANDARD TE T S

12 9

(3) Partly saturated material As in the case of other triaxial tests on partly saturated material drained t sts • are usuall y earried out using 4-in. diameter specimens. The initial procedure of setting up the sample and a sembling the cell i similar to that employed in the consolidated-undrained tests, the top of the sampl > 25 l"-

20

15

16 per>

r

_r--

r--,7

r-

0";-03

t-!....-

1/

II

sq.in. 10

5

5

10

15

20

Axial strain ,% +

1 · 0r-------r---...,....---~--~

_I·OL-_ _....L_ _--L _ _ _..L-_ _-l 20 5 fO 15

o

Axial strain %

Fig. 91. Drained test llsing dead loading. Deviator stress and volume change plotted against strain for an over-consolidated sample of clay being connected to burette 112 through valve a2' Fig. 83. The volume changes which occur in both the consolidation and sheari ng stages of the drained test are obtained by measuring the volume of water flowing into the cell as de cribed in PART II , Section 4, p. 63. After the cell pressure has been raised, valve a2 is opened and, when significant volume changes cease, the ample is taken to be fully consolidated. Although the relationships between degree of consolidation and time determined for saturated soils to not strictly apply to partly saturated soils, a rough estimate of

9-

M .. P .

THE TRIAXIAL TEST: PART I1J

13° 250

~

200

I

750

01- iT3 Ib per sq. in.

I

100

I

50

oa

2

4-

Axiol strom %

6

8

Or------r-----.------~----_,

~r-

- ,r------+~~~+_----_+------~

D.v 0/

Vo

-r---l--

/0 -2~----~----~------~----~ 2 4 6 8

o

AXiol strain %

Fig. 92. Results of a drained test on compacted boulder clay. Deviator stress and volume change plotted against strain can be made by using the best fit that can be obtained between the measured and theoretical curves. The time required for the test is then calculated as described above. In practice the times necessary for testing most rolled fill materials lie between 4 and 8 hours if side drains are used. Typical results of a drained test are given in Fig. 92 which shows the stress, strain and volume change relationships for a boulder clay compacted at optimum water content. In Fig. 93 the results of a series of tests at different consolidation pressures are plotted in the form of Mohr circles and the failure envelope, giving the values of c' and 1/>', is shown. Cv

(4) Tests on dry materials When dry materials are tested under drained conditions using samples It in. in diameter, the constant pressure air system is used for measuring volume

STANDARD TE T

13 1

changes. In tests on 4-in. dian:eter samples the volume changes are usually measured by the flow of water mto the cell u ing the apparatus illustrat d in Fig. 38 . . The g~neral ar~ang~ment of the apparatus for tests on samples It in. in dJameter IS shown In Fig. 94. The sample is prepared as de crib cd on p. 92. and a small suction (about 0'3 IbJsq. in.) is maintained while the cell is a sembled. 200·r-----~----,_----._----~----~----~----_

.~

~~O r-----~------~----~--~~---­

." ~

c:u 1::1..
(100r-----~------_t~~~~------~----~~----~----~

! ."

~ 50r------+.~~~+-----~­

c:u

~

O~L-~~-L~~----~----~------L-----~--~

100

!50

200

250

300

350

Normal stress-Ib persqin. Fig. 93. Mohr envelope for drained tests on compacted boulder clay After filling the cell with water, the cell pressure is increased while the suction is reduced at the same rate until the air in the porc space is again at atmospheric pressure, as indicated by the mercury levels in x and y. Valve z is then opened to bring the sensitive oil manometer into operation. The specimen is further consolidated by rai ing the cell pre sure, the control cylinder being used to keep the oil at the same level in each limb of the manometer. Any change recorded in the level of the mercury in burette y then indicate the change in volume. The shearing process is carried out as described above; readings of the proving ring deformation and volume change being taken at convenient intervals of strain. A typical failure envelope obtained from drained tests on raw sugar is shown in Fig. 95.

5. Pore.Pressure and Dissipation Tests The triaxial cell may be used. without a testing machine, to study the buildup of pore pressure due to a stress change under undrained conditions. and the subsequent rate of dissipation of pore pre sure when drainage i permitted from one end of the sample. For purpo es of ettlement analysis the necessary data about compressibility and rate of consolidation is usually obtained from the volume changes in the oedometer test. However, under certain conditions the direct measurement of the pore-pressure changes is to be preferred. esp cially

13 2

THE TRIAXIAL TEST: PART III

when the data is to be applied to an estimate of stability, These conditions are: (1) In partly saturated samples, either of natural strata or of compacted fill, the test gives the initial pore pressure set up , which is in general not equal to the applied stress, and the volume change under undrained condition, The subsequent dissipation stage gives the coefficient of consolidation with an accuracy

-;

'C

co'"

E

..>.

-c

.....0

VJ
0.

E

~

...''""

~

'" E '"

~

d

'j

.....' c:

0

II

'"

~

-c c:'"

'; ... -c

...

.£ VJ

3

...'"

'0.0." '"

-£'"

...... 0

~ 0

>,

~

-=t-<'"

~

..f 0bi>

~

which cannot be obtained in the oedometer owing to the difficulty of fitting the observed and theoretical time-settlement curves when air voids are present. (2) In stiff soil where the volume changes ar very small and in stony soils from which a sample for the oedometer of sufficiently low ratio of thickness to diameter cannot be prepared, the triaxial test gives a more reliable measurement of dissipation rate and volume change.

133

STANDARD TIl. T

(3) When required, a direct measurement of permeability can be made at a value. of the pore pressure .corresponding to field conditions. This is of importance. m partly saturated sOIls, whe.re the degree of aturation is greatly increa ed at hIgher pore pressures. ElevatIOn of the pore pressure can in fact be conveniently used to produce full saturation in samples in which it cannOl be achieved by prolonged flooding. 3

-

5

/'"

0

5

~

0

Av7

s

V

vr

5

10

V

V /'" - 17 ~

( {\ 15

20

- 1- -

~ -

2S

v= ! -.

~

--..

L{.J

30

-......

-

--

~

l\

f\

35

\

40

4S

50

-

1\

SS

\

60

Normal stress - 16 per sq. In Fig. 95. Mohr envelope for drained tests on raw sligar

The test is usually carried out on 4-in. diameter samples. A sample height of 8 in. is used where the coefficient of onsolidation is high; a height of 4- in . being used for soils of low permeability, to reduce the duration of the test. ndisturbed samples of clays of high plasticity may be tested in the small cell , a minimum sample height of It in. bcing used. The test procedure follows that for the undrained test with pore-pressure measurement (p. 98); with the addition of a saturated porous disc on lOp of the sample and a de-aired drainage connexion to tbe loading cap. No side drains are used. If drainage is to be permitted to atmospheric pressure, the connexion is taken to a burette (a twin burette is used for partly saturated soils). The layout is illustrated in Fig. 96. ]f a back pressure is to be applied during the dissipation stage, the alternative volume measuring devices described in PART II, ecti n 4, p. 63, are ubstituted for the burette. After the sample has been prepared and the cell a embled the zeros of the volume-change and pore-pressure devices are checked. With the drainage valve a2 clo ed the cell pressure is increased in several steps to tlle required value. the volume change and pore pressure being read after each step when the values have become steady. Where an accurate estimate of volume change is being made, the relation between pore pressure and volume change during the intermediate steps permits the determination of the initial volume of air trapped between the rubber membrane and the sample (Appendix 5). From the ratio of pore-pressure change to cell-pressure change values of the parameter Bare obtained. This stage of the test also gives the relationship between volume change and effective stress under undrained conditions. The drainage valve a2 i then opened, and readings are taken of pore pressure,

134

THE TRIAXIAL TEST: PART In

ST ANDARD TE STS

135 sample volume and expelled water (and also of expelled air in partly saturated soils). As in the standard consolidation test the time intervals are chosen to suit the rate of dissipation of pore pressure, and should approximate to equal increments on a logarithmic scale. As the initial and final pore pressures are known the percentage dissipation of pore pressure can be plotted without waiting for consolidation to terminate, and a rapid determination of the coefficient of consolidation can thus be made. The accuracy of the B value measured in a subsequent undrained stage is, however, influenced by the completeness of the preceding consolidation stage. Typical results are illustrated in Figs. 97, 98 and 99. In Fig. 97 (a) pore pressure is plotted against cell pressur for a three stage test. The value of B is closely related to the initial degree of saturation, which, in compacted soils, is controll ed by the placement water content. The criti cal effect of a small change in water content near the optimum value i illustrated in Fig. 97 (b). The effect on the B value of dis ipation of pore pressure in the preceding stage of loading is of importance in earth dam construction and is shown in Fig. 97 (a). A marked decrease in the magnitude of the pore pressure set up by a given change in stress is usually found [Bishop, 1957]. In Fig. 98 (a) the percentage dissi pation i ~ plotted against the logarithm of time t for a sample of a typical compacted fill. In Fig. 98 (b) the theoretical relationship is plotted between percentage dissipation and logarithm of time factor T; the numerical values being given in Table 9. This relationship assumes TABLE

9

The relationship between time factor T and percentage dissipation of pore pressure at lower surface of sample drained from upper surface T

% dissipation

T

% dissipatiOIl

0 0 '05 0-10 0'15 0'20 0'30 0'40 0'50

0 0'3 5-1 13'5 22'8 39'3 52'4 62'8

0'60 0'70 0-80 0'90 1'00 1-20 1'40 2'00

71'0 77-2 82-2 86 '0 89'2 93'4 96'0 99'1

an incompressible fluid in the void space. For soils of sufficientl y high degree of saturation to show large pore pressures the shape of the observed curve does not depart to any important extent from the theoretical relationship, though the observed curve becomes flatter as the degree of saturation decreases. The value of c the coefficient of consolidation, is obtained by fitting the two ,JI d" . curves over the range of pore pressure required, the value at 5001 10 lSSlpation being quoted unless otherwise specified. The time factor T is c"t/W, where H is the drainage path and hence the height of the sample. It follows, therefore, that c" = (T/t)H2, and hence for a fit at 50% dissipation we have

(31)

13 6

THE THIA 'X IAl- T ES T: PART III

60

/

/1

I.

)

0

W(Jtercontent ~ opt. +2 · 5%

/

50

.~

/.

1-. ti- 40

..,

/.

,.cr;" /. " ,,; / "l/dlssIPatlon of

~

~

~ ~~I--'

30

I

~ '"'" tt:l
~

C(

/.

/

t..

t:l

~.

-;' ,

pore pressure

20

/

/.V ,

0\(1

~

~~ I

/ O·~ \O~ /.

10

~# eO

1/'lof 10

~or(J1 30

40

~dr(J' I j (LIn diSSIpatIon

j

v,r'

50

~

~ (OCIo,ng L

10(.1

0,(1

;0

I/dissipation

60

70

80

90

Totol stress - Ib per sf/. in.

(a)

/'

-

-

/

/"

/

~

/

v

V:

9

~ OPtlinU, WfJtercrtMt

,

i

10

11

Water content %

12

13

(6) Fig. 97. Pore-pressur and dissipation test on compacted boulder clay (a) C hanges in pore pressure during a thre · stage diss ipation test. (b) Variation in the initial value of B with the water content at which the soil is compacted .

The value of 1'& 0 is 0'38 (from Fig. 98 (b), the time tso is obtained from the plot of percentage di sipation again t the logarithm of time and H is the sample height (corrected for decrease in length due to volume change). orne typical values of e" for undi turbed and compacted samples are given in Table 10.

TAN'DARD TE 1'5

IJ7 In . F.i~. 99 a typical compressibility result is given. In general the compressibility .~easured under equal alJ-round stress is greater than that measured ~nder conditions ~f no lateral strain, as in th oedometer. The diiferen c is least 10 .normally consolid~ted clays, but i.s greater in over-consolidated and compllcted sOils. In sands the \ olu me change 111 the oedometer is about 60 1' 0 of that in th e

I(), 000

10

80ultierchy comporl:ed at (/ WtlW

--

~

~

l-

contMt ofopllmllm + 2 5 % ~// pre.sSVI'e .30·0 /b pi:!' $9111.

T

/nlt/(//fJO"fJprt.fJ'VI't!·RNllJper.f1/ln lIelghtol'St1mp/~ · 3 ·9111 C""RxIO- lcm' p6Psoc

(0)

li"me factor T

Fig. 98. Dissipation test (a) Percentage dissipation of por pressure plotted against the logarithm of time for a sample of bou lder clay compacted 2! Ou above the optimum water content. (b) Theoretical relationship between percentage dissipation of pore preS8ure at base of sample and logarithm of time factor T.

triaxial cell for the same pressure. This relationship is discu ed more fully elsewhere [Skempton and Bishop, 1954J . For this reason the porc-pres ure ratio Jj is lower and the value of,v is higher if measured under conditions of no lateral yield. In the case of the pore-pressure ratio the difference is of practical importance in earth dam design and the alternative te t described in the following section m ay be used. Mter completing the consolidation stages of the test it i usual to reduce the effective stress in the sample before removing it from the cell, so that it will

THE TRIAXIAL TEST: PART 111

not swell and absorb extra water during this operation. This is done by applying a back pressure to the drainage lead of about 90% of the final cell pressure. The volume of water flowing in may be measured with the volume device, and the rate of build up of pore pressure (which is much faster than the dissipation rate) TABLE

10

Typical values of the coefficient of consolidation ctl from dissipation tests (Total stress increment 0- 30 Ib per sq. in .)

Typ e of soil

Clay fraction < 0-002 : mm %

Optimum water content:

%

Optimum dry dPnsit)l: lbl cll. it

<1

9-5

129

7'8

134

Water content as tested:

Value of cv :

%

em. 21 sec_

9-1 10-4 8'4 9'3 10-4 10-7 13'5 28-2 33'0 16'1 19-8

1-2 1-8xlO- 2 1'9 X 10- 2 3 '7x10 - a 2'9 X 10- 3 7-6 X 10- ' 4'3 X 10- ' 6'6 X 10- ' 8-6 X 10- 5 2-7 X 10- 2 1-9x10- 1

14-9 26-3

3-6x10- ' 2-9x10- s

Compacted-

Moraine

I

Boulder clay

4

Boulder clay

10

9'5

130

Boulder clay

19

10'7

126

Residual clay

20

27-5

94

Residual clay

21

16'0

111

-

-

I

Undis turbed Boulder clay Residual clay

c. 19 31

-

• The compactive effort used in sample preparation approximated in all cases to that used in the standard eompactioll test.

Effective stress - / b per Sf1. in. 20

r.::J

o

40

60

80

too

end ofundrained stage end of'dissipation stage

Fig_ 99_ Volume change in dissipation test plotted against effective stress at each stagc: compacted moraine

STANDARD TBSTS

139

is also measured. The cell pressure IS . fi na II y decreased under undrained COIlditions. The sample is wei~he~ on removal from the cell, and several sp cimen for water-content determmatlOn are taken. The test itself presen~ no s?ecial difficulty. Two points may, however, be noted. If the laboratory IS subject to temperature fluctuation the accurac of

r .. "

..

~

:,w"-r

~" dl(.l. bolt -+-+1;i i! ,

II

II

Perspex

Fig. 100. Indicator used in measuring axial strain during consolidation under equal all round pr ssure the volume measurements may not be satisfactory. In this case, and in any accurate determination of smail strains, the length changes may also be measured . In the small cell the seamless Perspex tube is sufficiently true for this to be done optically with a vernier telescope. In the large cell the loading ram is used, its lower end being fitted with a sensitive indicator (Fig. 100) to show contact with the cap without any significant load. Secondly, in clay fill materials compacted at low moisture contents the pore pressure tends to be erratic, as indicated on

p.100. The accuracy of the estimate of coefficient of consolidation in partly saturated soils can be increased by limiting the dissipation stage to the range of porepressure values which will apply in practice. Drainage is in this case permitted against a specified back pressure maintained by a constant-pressure system. The direct measurement of permeability is made, at low values of pore pressure, by connecting a burette on a flexible lead to each end of the sample and maintaining a constant head by periodic adjustment in level (as in Fig. 83). At high pressures a constant-pressure system is used at each end of the sample. The cylinders of the mercury-type pressure control are fitted with a scale and

THE TRIAXIAL TE ST: PART III

used to record the volume of water flowing, Fig. 101. If the permeability is very Iowa volume-measuring apparatus .is interposed at one end. Test results show that, for compacted fill materials, the value of the coefficient of permeability, calculated from the coefficient of onsolidation and the volume change in the dissipation test, is in satisfactory agreement with the direct measurement of permeability.

Fig. 101. Use of the self-compensating mercury control for the measurement of volume change

6. Tests with No Lateral Strain (Ko-Tests)

It is sometimes of practicru importance, as well as of research intercst, to carry out triaxial tests under conditions of zero lateral strain. Tests of two types are performed: (i) ndrained tests on partly saturated samples, either of natural strata or of compacted fill, are carried out to provide a direct measurement of the pore-

TANDARD TE T

14 1

pressure ratio f) f~r this condition of lateral restraint. The measurement of pore pressure also provIdes values of the ratio of the effective principal stresses corresponding to this condition and hence values of KQ' the coefficient of earth pressure at rest (defined as (1s' /(11' for zero lateral strain). This test gives a very accurate measurement of m, .. the compressihility in one-dimensional consolidation. Since no flow of pore water occurs, an equili brium pressure is rapid ly established in the pore space, even in soils of low permeability, irrespective of the dimensions of the sample. amples 8 in. in height can therefore be used and thi permits accurate measurement of th axial strain and minimizes the effect of bedding errors. The range of effecti\'e stress is, of course, limited to that causing a volume change equal to the initial volum of free air. (ii) Drained tests on saturated, partly saturated or dry samples are carried out to obtain values of Ko and mv' Since manual control of the lateral pressure has so far been used, these tests have been limited to the more permeable soils by the time required to ensure full dissipation of pore pressure. Tests of this type are of particular value in soils of very low compressi hility, such as dense sand, ..."here results arc otherwise difficult to obtain with accuracy. (a) Undrained Ko-lests 011 partly saturated samples Sample preparation and assembly of the apparatus foll ow the procedure for the undrained test with pore-pressure measurement (p. 98), with two additional features. Firstly, a flat end is used on the ram, together with a halved steel ball in the seating in the top cap. This minimizes bedding errors. Secondly, the lateral strain indicator is placed in position at the mid-height of the sample before assembling the upper part of the cell. The zeros of the pore-pre sure, volume-change and load gauges arc noted. With the ram just in contact with the sample the testing machine i started, and the cell pressure is increased manually either with a control cylinder or by raising one cell of tbe mercury control, so as to maintain ze ro lateral strain as shown by the indicator. Readings of axial strain, load , pore pressure and volume change are taken at convenient intervals. The maximum strain can be calculated in advance from the percentage of air voids. This determines the frequency of the intermediate readings. The rate of testing is chosen to avoid any lag in the pore-pressure readings and to reduce, as far as is practicable, the rate effect on the compressibility. A duration of from 3 to 6 hours is generally used, depending on the soil type. As full saturation is approached, the increase in cell pres ure necessary to maintain zero lateral strain rapidly increases. The test is terminated at this point and the load removed by reversing the testing machine. As the load is reduced, the ratio (13'/0'1' gradually increases to unity, Fig. 102 (b). To maintain no lateral yield for stresses below this point it is necessary for the vertical effective stress to be less than the lateral effective stress. To satisfy this requirement a tension fitting can be used on the end of the ram, Fig. 110, but this is done only in special tests. On removal from the apparatus the sample is again weighed and specimens are taken for moisture content determination. Cn Fig. 102 typical results are given. The increase in P?re pressure is ~Iotted against total major principal stress in Fig. 102 (a), and IS co~pa~ed wlt~ the higher values obtained under equal all-round pressure as deSCribed III ectlOn 5, p. 137. In Fig. 102 (b) the lateral effective stre.s 0'3' is ~Iotted agains~ the vertical effective stress 0'/. OJ) firs~ loading, thls approXllllates to a linear

THE TRIAXIAL TEST: PART III

142

80

.~ ~

,

">

60

~ :!:! I

:::s ~

~

40

:s

~

Test with 03 - OJ ~ .....

~

~

20

~

~

~

---

~

_.-

~

~

V

,/

V

-Ko-test ~~

20

I

40

60

80

100

/20

140

160

180

Total mojor principol stress Of - Ib pel' sq. in . (a)

20

40

60 _

80

100

120

Eff'ectlve mqjor principal stress OJ' - 16 per SfI. in.

(b) /20

~

~I~

2

I

4

(a)

Fig. 102. Undrained Ko-test on a sample of moraine compacted at a water content 1'5% above the optimum (values from a test on a similar sample under equal a11round pressure shown for comparison) (a) Pore pressure plotted against total major principal stress . (b) Effective minor principal stress plotted against effective major principal stress. (c) Relationship between volume change and .effective major principal stress.

T ANDARD TE T5

relationship, particularly if the stress range is large compared with the pre tress resulting from compaction. On unloading, the value of us' decreases relatively slowly at first and the stress ratio (Ts'lul' becomes equal to 1 at a pint in the lower stress range; below this point the vertical effective stress is less than the lateral effective stress. Values of Ko obtained during the loading cycle depend on the soil type, and range between about 0'35 for compacted moraine and 0·65 for a clay fill. Typical values are given in Table 11. TABLE

11

The coefficient of earth pressure at rest Ko: average values on first loading Maten:al

Clay fraction < 0·002

% Moraine, compacted Boulder clay, compacted Residual clay, compacted Boulder clay, compacted Residual clay, compacted Sandy clay, undisturbcd Clay, rcmoulded Loose sand, saturated Dense sand , saturated Raw sugar, dry Loose lead shot , dry

1

Activity

PI "0

0·44 0·44 0·59 1·55

15 25

0·90 0·60

-

-

-

Value of

Undrained Und rained Undrained Undrained Undrained

0·36 0·43 0·42 0·56 0'66

Drained Drained Drained Drajned Drained Drained

0·43 0·70 0·46 0·37 0'50 0'44

K0

clay

10 21 19 20

-

Type of test

-

-

In Fig. 102 (c) the relationship between volume change and effective stress is shown , and this illustrates the lower compressibility measured under conditions of zero lateral yield.

(b) Drained Ko-tests on soils or granular materials of all types Sample preparation and assembly of the apparatus follow the procedure for the drained test (as described in Section 4, p. J22), with the two additional features mentioned above. In cohesion less samples an initial effective stress is required to give the necessary rigidity during assembly. As this is produced by the suction pressure (of 0'3-0'8 lb/sq . in. in magnitude), the initial condition represents all-round consolidation under this stress. The val ue of Ko is therefore taken from the ratio of the subsequent changes in effective stress, flu3'/flu)', made under conditions of zero lateral yield. The rate of testing is chosen to permit sufficient time to control and record the strains accurately, to reduce rate effects on the compressibility and to ensure dissipation of the pore pressure. Even wi th sands or dry granular materials in which excess pore pressure presents no difficulty a testing time of less than 3 hours is not usually found convenient. In soils of lower permeability the testing time is based on that used in ordinary drained tests, and side drains are employed when necessary. The range of effective stress employed is Limited only by the capacity of the testing machine, and in particular of the cell, which usually restricts ua' to 150 lb/sq. in.

THE TRIAXIAL TEST: PART III

The results obtained are in general si milar to thosc of the undrained Ko-test, exprcssed in terms of effecti ve stress, as illustrated in Figs. 102 (b) and (c), though the stress range is greatcr. For eohesionless materials the ratio of t::.u3' / t::.(Jl' is almost constant over a wide range of stress on first loading. Some typical values of Ko are given in Tablc 11. It will be noted that in the undrained test two measurements of volume change may be obtained, (a) from the axial strain observation and (b) from the flow of water into the cell. In the drained test the volume of fluid expelled from the sample gives a third value. The axial strain measurement gives thc most accurate value of volume change and is all that is required in routine tests. The other values are, howevcr, of interest in research as their agreement with the axial strain val ue is an indication of their reliability as means of volume measurement (for example, see Fig. 41,

p.68). T he fact that the expclled fluid must be equal in volume to thc axial compression multiplied by the initial cross-sectional area of the sample if no lateral yield occurs, has been used as an alternative basis for the Ko-test [Bishop, 1950; Bishop and Eldin , 1953]. The cell pressure is controlled so that the burette reading maintains the calculated relationship with the axial strain dial. This method is readily applicable to small samples in which the drainage paths are short, but is less sensitive than the method described above, particularly in soils of low compressibility. In calcu lating the axial stress from the proving ring readings allowance must be made for the change in the thrust resulting from the action of fluid pressure on the end of the ram. If

(73

denotes cell pressure,

a denotes cross-sectional area of sample, Or denotes cross-sectional area of ram and P denotes axilliload indicated on the proving ring, then

(32)

PART IV

SPECIAL TE TS 1. Drained Tests on Saturated Clays with Decr easing

01

Constant and

0

3

In problems involving the long-term stabilit of slopes and retaining walls the stress change which leads to failure is primaril y a decrea_e in the lateral pressure. The laboratory test which most closely reproduces the fi 'Id conditions is one in which the axial stress is kept constant and failure is brought about by reducing the cell pressure. Constant ratc! of strain tests in which a j is kept constant require onti nual attention over the whole period of the test. In soils of low permeability drained tests may last several days and thty arc therefore usually carried out with str'ss control. A dead load applied by means of a hanger is used to maintain a constant axial stress as the cell pressure is decreased in steps. In order to calculate the change in dead load necessary to compensate for a change in cell pressure, the following equation is used: at =

where W it HI, W ar and a

denotes denotes denotes denotes denotes

the the the the the

W,,+W,+W-a,a3 +as a

(33)

weight of the hanger, weight of the ram, dead load on the hanger, area of the ram area of the sample at any time.

With aj kept constant and equal to he cell pressure (aa)o immediately prior to the shear stage, the dead load on the hanger may be expressed as

W = (as)oa-(W,,+ Wr)+aa(a-a r) .

(34)

The value of a may be calculated at any stage from the sample dimensions immediately prior to the shear stage, the axial strain and the volume change, as shown in PART I, 6, p. 28. The relevant equation (/7) is:

1 +~VJVo

a = Go --r=;- -

In practice it is not convenient to maintain a j exactl y constant at every point of the test as a continues to change after each increment of loading. However, provided a reasonable estimate of the average value of a for each increment is made, no serious errors will arise. It is desirable that the weight of the hanger should Dot exceed that of the first increment of axial load. A suitable hanger, made of duralumin. for use with 1t-in. diameter specimens is shown in Fig. 52. This hanger has a total weight of 4·1 Ib, but the lower portion may be detached to give a load of only 1·5 lb. The sample is prepared in the same manner as for the standard drained test and the lO-c.c. burette is again used to measure vol ume changes. When consolidation is complete the change in height of the specimen is measured optically IO-M.S.P.

THE TRIAXIAL TEST: PART IV

and the cross-sectional area is calculated. The weight necessary to maintain Ul constant under the first change in cell pressure is determined. With just sufficient weight on the ram to counterbalance the upward force due to the cell pressure the ram is brought into contact with the loading cap, and the strain dial zero is set. The strain dial is carried on a duraJumin arm fixed to the ram and registers on an arm attached to the top of the cell, Fig. 103.

Fig. 103. Method of measuring strain in dead load tests The valve E connecting the mercury pressure control to the cell, shown in the layout diagram for drained tests, Fig. 85, is shut and the mercury control adjusted to give the cell pressure for the first load increment. The valve is then opened and at the same time the additional weights necessary to keep Ul constant a added to those which just balanced the initial cell pressure. Readings of the strain and volume change are taken at intervals after the application of the load. When the rate of deformation and volume change become small the sample area is again calculated, an estimate of likely changes under the next increment is made and the new dead load for the next change in cell pressure is calculated. The procedure of shutting off the cell pressure, adjusting the mercury control and adding the new weights as the cell is. reconnected to the mercury control is then repeated. Not more than about 10% of the estimated deviator stress at failure is usually applied at a time, but a failure is approached the stress increments should be small so that a reliable determination of the failure strength may be made.

SPECIAL TESTS

The strain and volume change during each increment are plotted on a tim scale as the test proceeds, so that an estimate may be made of how far the consolidation or swelling process has advanced. Although complete consolidation under each load increment is desirable, little error in the mea ured strength i found to result from reducing the loading intervals so that the overall duration of the test is about equal to that of the constant rate of strain test described on

p.123. Steady deformation of the specimen under the last stress increment indicates when failure has been reached. The valve a1leading to the burett is then shut, and the hanger and weights removed. The sample is taken out of the cell and .its final weight and water content are determined. Typical stress-strain and volume change cur\, S for a test on a normally consolidated clay are shown in Fig. 104 (a) while similar results for a heavily overconsolidated clay are shown in Fig. 104 (b).

2. Undrained Tests on Partly Saturated Soils with and Os Decreasing

OJ

Constant

On fully saturated materials, undrained tests with (1) constant and I1s decreasing give exactly the same results in terms of effective stress as the standard undrained test where a3 is kept constant and a1 is increased. This special test is therefore usually confined to partly saturated materials where significant differences in the effective stresses can occur. In common with the other types of undrained test, this test can be completed in a day and is run at constant rate of strain, using a proving ring to measure axial loads. The cell pressure is adjusted so that the axial stress is k pt constant. The way in which the cell pressure must be changed during the test is determined from the following expression for I1j : 0']

=

N8+ Wr-arag + a

(3.5)

l1a

where N denotes the proving ring factor expressed in load per division , Il denotes the proving ring deflection in divisions from zero load, Wr denotes the weight of the ram, a r denotes the area of the ram and a denotes the area of the sample at any time. The condition for 0'1 to be constant and equal to the initial cell prcssure (11,)0 is more conveniently expressed by the equation : 0'3

N8+ Wr ]

= [(0'3)0- - a-

[

]

]

I-arIa

(36)

The value of a at any time will depend not only on the area of the sample at the start of the test but also on the axial deformation and any volume change that may occur in the partly saturated soil. This is calculated as shown in the previous section. In order to determine rapidly the value of aa required to keep 0'1 constant at any stage in the test it is often useful to preparc a series of curves relating all the variables, once the area and height after the raising of the cell pressure are known. If the rate of testing is low, the necessary calculations can, however, be made as the test proceeds.

THE TRIAXIAL TEST: PART IV

40

30

/ I

OJ -03 20

/bper

CV

.,;;17 0; test= 60lb persq.in.

1/

sq. In. 10

°0

2

6

8

10

12

10

12

AXial strain %

~v~]r 0

.4

2

I4 -

I6

I

8

Axial strain % Fig. 104 (a). Drained tests with Ul constant and U3 decreasing. Deviator stress and volume change plotted against strain for normally consolidated clay

An example of the type of curve required is shown in Fig. 105 where the relationship between the change in 8 and the change in as is plotted against strain for different volume changes. A slide rule is used to give the actual value of as at any particular point in the test. Four-inch diameter samples arc prepared in the usual way, as described for undrained tests on partly saturated soils, and the cell pressure is raised to the desired level. When the volume-change and pore-pressure readings have reached equilibrium the calculations necessary to relate the proving ring readings and as are made and the test can be started. The ram is brought into contact with the loading cap. After the strain dial has been set the motor is started at a suitable slow rate and the cell pressure is adjusted in accordance with the calculations. Readings of the proving ring dial, the pore pressure, vol ume change and axial deformation are taken at regular interval. When the peak deviator stress is attained, i.e. when the cell pressure has reached a minimum value, the test is stopped. The equipment for measuring pore pressure and volume change is isolated, the axial load is taken off and the sample is removed from the cell. It is then weighed and its moisture content is determined.

P ECIAL TE T

4 ·0

v if

3D

q- O]

1.j.9

-

+--

oa test =sib pel'sq.In. Q3max=!20Ibpersq.1n.

2·0

Ib per

sq. in. 1'0

o o

2

4

6

8

10

12

8

10

12

AXial strain % +6

~

+4

/

/j, v 0/

Vo

V--

/0 +2

o

:/

o

2

4

6

Axial strain % Fig. 104 (b). Drained tests with 0', constant and 0'3 decreasing. D eviator stress and volume change plotted against strai n for heavily over-consolidated clay

3. Tests in which Failure is Caused by Increasing the Pore Pressure In certain problems in the stability of embankments, slopes and earth retaining structures, failure is most likely to result from an increase in pore pre sure under conditions of almost constant total stress. Tests to simulate this condition are therefore of both practical and research interest. Tests have been carried out on sand in which there is no significant lag in the equalization of pore pressure throughout the sample, and also, with suitable modifications, on soils of low permeability. The preparation of the sample and a sembly of the apparatus follow that for

150

THE TRIAXIAL TEST: PART IV 0 ~4r-----'------'------.------r-----'----~

0 '14o,!;------7.5:-------,,:t:o;-------:/.I;:5-----::!2~0-----2':f5:=-------:::'30

Axial strain % Fig. 105. Drained test with al constant and aa decreasing : constant rate of strain. Typical relationship between change in as and change in deflection of proving ring plotted against strain

a drained test, except that the base of the sample is connected to the control cylinder of the pore-pressure apparatus (Fig. 106). The required initial stresses are established under drained conditions by increasing the cell pressure and applying an axial load with the testing machine, drainage being permitted through the loading cap· to burette h2• For t:arth pressure studies the condition of zero lateral yield may be adhered to during this stage of the test (as described in PART III, 6, p. 140). Failure is then brought about by increasing the pore pressure with 0"1 and O"s held constant. Constant lateral pressure O"u is maintained by the mercury controL Constant 0"1 is most easily maintained by running the testing machine so as to give a constant rate of axial compression, and increasing the pore pressure manually by the control cylinder so as to maintain on the proving ring a load corresponding to constant 0"1' This load varies slightly during the test since the diameter of the specimen increases. The average cross-sectional area is calculated from the axial compression and volume change, and the load calculated from the relationship given in equation (35). The test is therefore run sufficiently slowly for the necessary calculation to be made from time to time. A typical result for loose sand is given in Fig. 107. The relatively small strain required to mobilize the full shear strength will be noted, together with the marked reduction in the decrease in volume 'during shear (cf. Fig. 86 (b». For clays the procedure is modified by the time taken for a uniform pore • Drainage from the base of th sample is used in the case of fully saturated cohesionles8 soils. to simplify the fitting of the loading cap.

SPE tAL TESTS

...

41 ::l

::! ~

Q.

..

41

8. 41

-5 till

.S

rJ

~ u

.S ;:... ..0

] ~

r!

.!l

e -=:Ii ..cu :E l::

.S !l

~

.

~

...~ ~

Q. Q.
41

-5 .... 0 :l

~

.!'!

41

-'= E-<

8.... e.O

i;i; I

~

~

THE TRIAXIAL TEST: PART IV

250

5

ra) 200

I' -

OJ

I---

.-.I

__

4

OJ

_-- ----- ----- \P-~I

----

--3

.-

I

03

15 2

50

......;:, ~

lJ

£,3

If

o

." 'I>

I~ r-

o

~ l:)

z

4

6

8

10

12

14

o

Axial strain %

+ '5

(6) fl.v 0/ 0

Vo

/0

1'- '5

o

2

4

6

----

L.----

8

-

10

f.--

12

14

Axial strain 10 Fig. 107. Test on saturated loose sand in which failure is caused by increasing the pore pressure: (a) major and minor principal effective stress, principal stress ratio and (b) volume change plotted against strain pressure to be established throughout the sample, and the use of a dead load system as in PART IV, 1, p. 145, is more convenient. Failure is brought about by increasing the pore pressure in small steps with the mercury control, the overall testing time being similar to that of the drained test.

4. Extension Tests In some investigations (for example, the heave of the bottom of an excavation) it is necessary to examine the behaviour of soils in axial extension and tests of this type require that an upward force be applied to the cap at the upper end of the sample.

Apparatus Details of the loading caps and rams used for extension tests in the cell for It-in. diameter sampl s are shown in Figs. 108 and 109. The arrangement shown in

SPEC IAL TESTS

Fig. 108 may be used where the ~pward load to be applied is relatively small. The cap has a short length of i-In. dIameter brass rod screwed into it and the projecting end, which is threaded, locates in a i~-in. diameter hole bor~d in the bottom of the r~. This hole acts as a guide during the consolidation pro ·css. Before the extension test starts the ram is lowered until the threaded rod reaches the tapped upper portion of the hole in the ram, and the ram is rotated to engage the thread.

Durall/min

loading

cap \..

~---!.I ...J..,,_

II

_'

1+

t:-_~

Fig. 108. Loading cap for ex nsion tests on It-in . diameter samples (t-in. diameter ram)

When the upward force to be applied is large, or when carrying out drained extension tests with dead loading, the It-in. diameter ram shown in Fig. 109 is used. With this arrangement the cell pressure is utilized to apply the necessary upward force on the specimen. A bayonet catch is screwed into the cap at the top of the specimen; and when the extension test is to be started, the catch is pushed through the slotted plate mounted on the bottom of the It-in. diameter ram, and engaged by rotating the ram through 90 °. Tensile forces may also be applied when using the cell for 4-in. diameter samples. For these tests the bali jointed loading cap, shown in Fig. 110, has been developed. The threaded rod projecting from the ball is screwed into the bottom of the i-in. diameter ram used in this cell. This type of fitting enables a smooth transition from compression to tension to be made without any backlash. This is required, for example, in the tests where the values of Ko on unloading are being investigated. The load capacity of thi fitting is, however, sufficient only for relatively small values of deviator stress. Except with the arrangement illustrated in Fig. 109, where extension is caused by the action of the cell pressure itself, provision must b made to transmit the tensile force by clamping the base of the cell to the screw jack.

THE TRIAXIAL TEST: PART IV

154

Lower end of ram

slotted plate

r-44 y L ____

Stainless steel

L_ - -. r '

~

I.

II

" II

II II

Ll __ ..L!

II

Loading cap ---

I,

II

..

II

II

I.! _ _.ll

Fig. 109. Loading cap and slotted plate for extension tests on it-in. diameter samples (It-in . diameter ram)

Test procedure Undrained, consolidated-undrained or drained extension tests may all be carried out using the apparatus described above. The initial sample preparation is the same as for the corresponding compression tests, but the special loading caps must be used. When the 1t-in. diameter ram is used, care must be taken to see that an adequate reaction is available to prevent the ram being blown out of the cell when the cell pressure is applied. The clamp illustrated in Fig. 111 may be used during the consolidation process. If an undrained test is to be carried out, the cell Clay be placed directly in the testing machine and the proving ring used to provide the necessary reaction. When the clamp is used, sufficient load should be applied to the top of the ram to balance the force due to the cell pressure, before the clamp is released. In all cases the force on the ram, due to the cell pressure, should be balanced either by dead loads or by a proving ring before the connexion between the ram and top cap is made. When tests are carried out at a constant cell pressure, constant rate of strain may conveniently be used. The motor is set to the appropriate rate and readings of the proving ring dial and the volume change or pore pressure are taken at suitable intervals of strain.

ISS

SPEC I AL TESTS

Lower end of ram

threaded

Locating pin

_Bronze or stamless steelboll I I "

~~~~~__~~________~__J /r

Fig. 110. Loading cap for extension tests on 4-in . diameter samples Undrained tests with increasing cell pressure and constant axial stres , which can be completed in a day, may also be made at constant rate of strain. The cell pressure must be varied in accordance with the proving ring dial and strain dial readings to ensure that a constant axial stress is maintained as indicated by equation (36).

THE TRIAXIAL TEST: PART TV

Clamp

Top of cell

Sample Perspex cylinder

Fig. 111. Clamp for securing the 1t-in. diameter ram during consolidation of the sample under equal all-round pressure When drained tests at constant axial stress are made on soils of low permeability it is more convenient to use dead loading, as the constant rate of strain test needs continuous attention. The load necessary on the hanger for each value of the cell pressure may be calculated from equation (34). Two typical results from this class of test are illustrated in Figs. 112 and 113. In the drained test on a normally consolidated clay, shown in Fig. 112, a decrease in the axial stress is accompanied by a decrease in volume. In the corresponding undrained test (Fig. 113) a decrease in the axial stress results in an increase in pore pre sure.

5. Anisotropic Consolidation The stress conditions under which consolidation occurs in most practical problems do not approximate to equal all-round pressure. The consolidation of natural strata under their own weight o~curs under conditions of no lateral yield, for which the stress ratio a3' lal' is equal to the coefficient of earth pressure at rest, Ko· In a rolled fill dam or beneath a foundation, where some lateral yield may occur, smaller values of the ratio as' Ial' may obtain. Anisotropic consolidation is therefore of importance both in studying the undrained strength of

157

PECtAL TEST.

.

30

2

01 =CT2

-

5\

\

~

~~

---

failure

~

i""--

-

~03

5

°07-------2~------~4-------~6-------~8-------~m----~ -~ Axial strain %

e:;' Ir-----=::::::-li~-r---I

"'--1t "'-------' 1 1

O~------2~------~4-------~6-------~8-------~'0------~~

Axial strain ,% Fig. 112. Drained extension test on a normally consolidated clay. Axial stress and volume change plotted against strain (171 = 17, = 30 lb per sq. in .)

consolidated samples, and in examining the deformation and volume change characteristics during consolidation. The Ko-test, described in PART III , 6, p. 140, represents the special case of anisotropic consolidation with no lateral yield and may be followed by shear under either undrained or drained conditions. The method of con olidation adopted when other stress ratios are applied will depend upon the speed with which the excess pore pressure is able to dissipate in the soil under test. For relatively free draining materials, in which the consolidation and shear stages can be completed in a day, it is convenient to carry out the test at a constant rate of strain. The axial stress on the sample at any time can be determined

THE TRIAXIAL TEST: PART IV

from the load on the proving ring and the cell pressure is then adjusted by means of the control cylinder to maintain the required ratio between the principal stresses. The relationship between the principal stresses and the applied load may be expressed, as shown on p. 147, by the equation : 0'1

=

N8+ W r -a,0'3+ a

0'3

OJ = CT2

30

25

20

\

'"

1b1"re

I'---.-.._

CT~

.-

. 5

-2

-4

-6

-8

- 10

- 12

-10

- 12

Axial strain % +5

..1-

/

~

(7

-2

- 4

-6

-8

Axial strain.% Fig. 113. Consolidated-undrained extension test on a normally consolidated clay. Axial stress and pore pressure plotted against strain (111 = 111 = 30 Ib per sq. in.)

SPECIAL TESTS

159 Where consolidation is to be carried out at a constant principal tress ratio the relationship may be rewritten: (37)

where f3 =

C11/(13'

B~fore ~tarting the test a series of curves is prepared showing the numerical relationship bet~een C1s and 8 with increasing strain, for various possible volume

changes. A tYPical set of curves is shown in Fig. J 14.

0·13,----,-----,-----r-----.-----.....---

10

15

20

25

30

AXial stl'Oin % Fig. 114. Anisotropic consolidation at constant rate of strain with constant principal stress ratio. Typical relationship between cell prt!ssure and deflection of proving rin g plotted against strain

The specimen is set up in the usual way with provision for drainage into a burette; the cell is filled with water and oil is added. The ram is brought into contact with the loading cap. A suitable rate of strain is chosen and the motor is started. The cell pressure is adjusted with the control cylinder so that the calculated stress path, as shown by the curves, is followed. When the specimen has been consolidated to the desired maximum tress, the sample may be tested in any way required. At low cell pressures, where the weight of the ram is not counterbalanced by the cell pressure, the ram is held against the proving ring by 3. pair of small tension springs. . For soils in which the excess pore pressure dissipates slowly, dead loading is used for the consolidation process. The load required on the hanger during

160

Tl'IE TRIAXIAL TEST: PART IV

each increment in cell pressure, to maintain the ratio f3 between the major and minor principal stresses, may be calculated from the following equation: W=

aa.a(f3-1+ ~)-(W,,+ W,)

(38)

Mter the initial sample preparation the cell is filled with water and the oil is added. The valve E leading from the mercury control to the cell is shut while the pressure is adjusted, and is opened when the increment of load is added to the hanger. When consolidation is complete, any subsequent test will generally be carried out under a dead loading system. However, special arrangements may be made for the maintenance of the consolidation load if it is required to transfer the cell to the testing machine.

6. Measurement of the Pore-Pressure Ratio jj under the Condition of Controlled Stress Ratio The magnitude of the pore pressure set up under undrained conditions in a partly saturated soil is influenced by the sequence in which the stresses are applied. In practice the major and minor principal stresses change simul. taneously. This process can be simulated in the triaxial apparatus, and any specified stress path can be followed. One special case has alreaJy been described (PART III, 6, p . 140) in which the stress ratio corresponding to zero lateral yield is maintained. During the construction of an embankment the average principal stress ratio is likely to lie between the value corresponding to zero lateral yield (the case of a uniform layer of infinite extent)-and the value corresponding to the minimum factor of safety acceptable to the designer. The difference between these effective stress ratios is not large. A test may be run at constant factor of safety F by following the stress path illustrated in Fig. 115. The Mohr envelope, in terms of effective stress, is found from tests on samples at the appropriate water content and degree of compaction, and is represented by,' and
PE IAL TE T

M

¢'

T (0)

CT'

(6)

03' Fig. 11 S. Consolidation with constant factor of saf

ty

(a) Mohr envelope for fai lure and envelope to be followed in test with constant factor of safety F. (b) Relationship between (0"1 -us) nod u.' for constant factor of saft·ty.

7. Measurement of the Pore-Pressure Ratio B under Conditions Corresponding to Rapid Drawdown For a typical element of the upstream slope of an earth dam, drawdown of impounded water results in a decrease in both major and minor total principal stresses, accompanied by an increase in deviator stress. The porc-pressure change under undrained conditions can therefore be obtained only from a test which reproduces, at least approximately, these stress changes. The state of stress in the element before drawdown is determined by the changes in total stress and pore pressure occurring during construction and impounding. The sequence of the stress changes made during the test is designed to simulate this stress history as closely as is practicable. As an approximation the average total major principal stress may be taken as the weight of the column of soil and water above the element. The average shear stress may be calculated from a critical slip circle passing through the element. These stre ses are calculated for the three cases (a) end of construction (b) reservoir full and (c) drawdown. The sample preparation and assembly of the apparatus follow the procedure for the pore-pressure test (p. 131). The sequence of operations performed in II-M.S.P.

16z

THE TRIAXIAL TEST: PART IV

the test is illustrated diagrammatically in Fig. 116 (b), and consists of the following stages: (1) The cell pressure is increased to correspond to the major principal total stress on the element of soil at the end of construction, and the pore pressure is measured under undrained conditions. This stage gives the value of B on loading. (Anisotropic consolidation is not introduced until a later stage of the test to minimize the leakage of oil around the ram during the long period required to achieve sufficient saturation in stage (5).)

ill

(a )

so

l7j I I

1.1

I

u

MOI'OJne. compacted at

I

I water GYJl'ltent oi'apunTl.lm+iMJ{, :

I

I

-

I AtXXvafl.l8ofB . A.I. . fl2

I

AQj

I

-'*""" 2 I

:

I

I

I

-"- 3 --.. 4

I ..

_.,._ 5 t

6

i

70

'(6)

Fig. 116. Measurement of the pore-pressure ratio B under conditions corresponding to rapid drawdown : (a) Changes in water leve l at upstream slope. (b) Total stress and pore-pressure changes in triaxial apparatus.

(2) Drainage is allowed from the connexion at the top of the sample and the value of Cv may be determined from the rate of dissipation of pore pressure. (3) The pore pressure is then raised, by applying a back pressure to the drainage connexion, to a value corresponding to water level I in Fig. 116 (a). The back pressure is applied with the mercury control, and equalization of pore pressure is indicated by the pore-pressure apparatus. The ceLl pressure is maintained at a constant value during this stage. (4) Both the total stresses and the pore pressure are increased simultaneously by equal amounts corresponding to impounding to top water level (level II in Fig. 116 (a)). This is achieved by raising the cell pressure and back pressure by equal amounts in a series of small steps, equalization of pore pressure being indicated by the pore-pressure apparatus. In this stage it is assumed that there is no lag in the establishment of the equilibrium value of pore pressure under field conditions. . (5) The pore-pressure apparatus is disconnected, and a constant-pressure water supply is connected to the base of the sample through a volume gauge. To avoid a drop in pore pressure during this operation, valve a 1 remains fixed to the base of the cell. De-aired water is then passed through the sample

SPECIAL TESTS

under a sm.all difference i~ head f?r a su~ci~nt period to giv the degree of In pra.ctl~e. ThIs IS difficult to as ess accurately; Incomplete saturatIon, however, IS likely to lead to a conservative timate of residual pore pressure after drawdown. The permeability may b obtained by direct measurement at this stage. (6) The value of 0'8 is then reduced to correspond to the estimated state of anisotropic stress with the reservoir full, the val ues of 0'1 and of pore pressure remaining ~nchange~. ~o do this, the adjustment screw above the proving ring of the testing machme IS replaced by a rod running in a frictionle guide as illustrated in Fig. 53, p. 80. A dead load is applied to the top of the provin ring, by means of a. hanger, to maintain constant 0'1 while (13 (the cell pressure) is reduced to the calculated value. (7) The pore-pressure apparatus is reconnected to the ba of the sample and the upper connexion is closed. For simplicity the stress changes under undrained conditions, corresponding to drawdown, are made in two stages: ~aturation hkely t~ occur

(a) Both total principal stresses are reduced by an amount equal to the decrease in water pressure on drawing down from level lIto level I which corresponds to the overall decrtase in major total principal stress. From the measured pore-pressure change the value of B on unloading may be determined. (b) The minor principal stress is further decreased to correspond to the increase in shear stress, resulting from the lowering of the impounded water from level II to level TIL The major principal stress 0'1 is maintained at a constant value by manual operation of the testing machine, a stop above the proving ring permitting loads in excess of the dead load to be applied. The line XX represents the final state of stress in the slope. The overall porepressure ratio for drawdown , E, is equal to fj,u/fj,u I as indIcated in Fig. ) 16 (b). The decrease in O's is generally continued far enough to define a failure circle in terms of effective stress. Typical results are given elsewhere [Bishop, 1954J. From the e results it is clear that the change in shear stress on drawdown is an important factor in reducing the value of the residual pore pressure.

8. Constant-Volume Tests In the standard consolidated-undrained test on a fully saturated sample the volume change during shear is equal to zero. Difficulty is sometimes en~u_n­ tered in ensuring that the sample is fully saturated. Due to the compressIbility of the air in the voids, a volume change may occur during shear and, in consequence, the measured values of strength and pore pressure are subject to error. These errors can be avoided by running this stage of the test as a constant-volume test [described by Taylor, 1939]. In this procedure the volume is held constant during shear by varying the cell pressure throughout this stage of the test 80 as to maintain a constant pore pressure under conditions of no drainage. The changes in the effective stresses during shear a~ constan.t volu~e are thus given directly by the change in cell pressure and the Ifl~rease m deVIator stress. The change in the force on the ram due to the change lD cell pressure must be allowed for in calculating the deviator stress. The sample preparation and assembly of the cell foll~w ~e proce?ure for the consolidated-undrained test (p. 106). When the consolidatIon stage IS complete,

THE TRIAXIAL TEST: PART IV

control of the cell pressure is transferred from the mercury system to the control cylinder, after the latter has been adjusted to the consolidation pressure (by opening valves C and D] and closing valve G 1 in Fig. 73). The axial load is applied at a constant rate of strain, and the cell pressure is continuously adjusted so that the mercury level in the pore-pressure apparatus remains unchanged, the pore-pressure gauge reading being maintained at zero. This testing technique may also be applied to undrained tests on undisturbed samples. It has the advantage that it minimizes the effects of air trapped in the apparatus, but, in samples that tend to dilate on being sheared, air trapped in the system may nevertheless lead to serious errors due to capillary effects at the base of the specimen. The procedure and computations are more difficult than for the standard test.

9. Tests to Determine the True Cohesion and True Angle of Internal Friction According to the hypothesis put forward by Hvorslev (1937) the shearing strength, T / , of a saturated clay may be expressed as (39)

where c., the true cohesion, is a function of water constant only, r7n ' is the effective normal stress on the failure plane and cf>. is the true angle of internal friction. In order to separate the two components of the shear strength it is necessary to compare the results of tests in which the specimens have the same water content at failure but significantly different effective stresses. These conditions may usually be achieved jf a series of tests on normally and over-consolidated specimens are carried out. The values of strength and effective stress for tests having the same water content at failure may be found by interpolation. Either drained tests or consolidated-undrained tests with pore-pressure measurement may be used in the determination of the true cohesion and true angle of internal friction. If a consistent approach is to be maintained, allowance must be made for thc effect of the rate of volume change at failure on the strength measured in the drained test. Gibson (1953) has suggested a modification to Hvorslev's parameters, which were determined directly from drained test results. The symbols Cr and tPr are used to denote the true cohesion and angle of internal friction after an energy correction [Bishop, 1950] has been applied to the drained test results. These modified parameters are derived directly from consolidated-undrained tests, where no volume change at failure occurs. In a clay with a low plasticity index, even heavy over-consolidation does not give sufficient separation between the Mohr circles (for normally and overconsolidated samples at the same water content) to allow an accurate determination of Cr and cf>r to be made. Bjerrum (1954) has suggested that, for remoulded clays, better results can be obtained if samples are remoulded at different initial water contents before consolidation. A series of test results for determining the true cohesion and true angle of internal friction from drained tests are shown in Fig. 117 (a) and a similar set for consolidated-undrained tests in Fig. 117 (b). It has also been shown by Hvorslev that the true cohesion at any water content w is directly proportional to the equivalent consolidation pressure Pt. In the

SPE I AI. TE T 23

22'1- --1--

, I

- - t -..___+------l-I-

19

I

~) 18j--1---t-+-r--~'--~~~~-+j___i______l__J

90

~O

'\

38

36

:" "

~

~

34

~

,

"

,I

~r

JO

...... I

. .: ~ < II

I'

,

, I

-,

~

o, ~ C I r

Cr

(jJ

.-

r-[

I i ~--rs ~r

!

I

,

T

I

-- ' ~V ",

1

~r 0

I~

I:::;.;;?'"

20

30

40

~

SO

-

I

I t

I

+

rI

I

I

,,

I

"'~1,........... -I

...,.....

:

r

fIT

10

I

-r l-~ --

I

I I

10

1-

r

,,

20

.J

........"::, ...

,,

I

30

I

~

~.

120

I/O

London Cloy Undramed tests I -

normally consolldoted

I I ><...._a;fI, ovef\.consol!doted

,

:/

,

28

cr,;

~

I

I

~u

(b)

I

100

I 60

70

80

!}O

--I-

I I

I

IDa

110

120

Nor mol stress-It; p er s(/. In.

Fig. 11 7. T est results fo r determining the true cohesion and true angle of internal friction. Relationship between water content and major principal effective stress at failure together with correspondin g Mohr circles for (a) drained tests on Weald clay, (b) undrained tests on London clay

166

THE TRIAXIAL TEST: PART IV

triaxial test p. is taken as the all-round consolidation pressure which produces this particular water content w in a normally consolidated sample. Advantage may be taken of this fact to make a dimensionless plot of the results so that satisfactory average values of the parameters may be obtained. The basic shear strength equation may be rewritten in terms of the principal effective stresses as follows: (O'}- O's)j _ c, cos ,+ 0'3' sin CPr (40) 2p. p.(1-sin CPr) where (at - a')j denotes the deviator stress at failure and au' denotes the minor principal effective stress at failure. The ratio (0'1- O'a)j/2p. is plotted against O's'/P. and the best fitting straight line is drawn through the points. The slope of the line is sin cp,(l-sin CPr) and the intercept is c, cos 4>,lp.(l-sin 4>r). An example of this type of plot is given in Fig. 118. The application of the basic parameters c, and CPr in the theory of shear strength is illustrated by Skempton and Bishop (1954). 0 ·4

~y 0·3

/

L "". 0 ·7

/4 • 0 '2

/ yo .

0 ·3

0 ·4

o·s

0 ·6

OJ!Pe Fig. 118. Method of plotting test results to determine average values of the true angle of internal friction and of the ratio of true cohesion to equivalent consolidation pressure

APPENDIX 1 Correction for Strength of Rubber Membrane and Drains . Restraints are imposed on the specimen by the rubber membrane enclosing It and by the filter paper drainage strips used in certain tests on clay and a correction to the measured stresses has to be made. '

(1) Rubber membrane correction (i) Plastic failu.re. Experiments have heen carried out [Henkel and Gilbert, 1952] to investigate the effect of the rubber membrane on the measured strength of triaxjal specimens of It in. diameter. The correction was first determined directly by a comparison between the undrained strengths of remould d samples measured with and without a ruhber membrane. These sample failed by symmetrical bulging and not on a si ngle shear plane. A method of calculating the correction from the properties of the rubber membrane was then developed and this gave results in substantial agreement with the measured values. This method was based on the following assumptions : (1) that the membrane, when held against the sample by the ceU pressure, was , capable of taking compression; (2) that the sample deforms as a right cylinder.

Since the Poisson's ratio of rubber is almost exactly one-half, it follows that in undrained tests no hoop tension is induced in the membrane. The correction is therefore applied to the axial stress and not to the lateral pres ure. If (u1 - us)", is the measured compression strength, then the actual compression strength (u1 - U3) of the sample wi ll be given by: (ul-uS) = (u1-ua )'"

7TD.M .£ a

(41)

where a denotes the corrected area of the sample at axial strain ~, D denotes the initial diameter of the sample and M denotes the compression modulus of the rubber membrane, per unjt width .

u,

=

a

=

ao

(42)

where a o is the initial cross-sectional area of the specimen. The compression modulus M cannot be measured directly on a thin membrane but its value may reasonably be assumed to be similar to that meas~red i~ exte.nsion. With the arrangement shown in Fig. 119, a circumferential strip 1 m. wide is used to find the extension modulus M. French chalk on me contact face between the glass rods and me ru~ber serves to :educe fri~ion.. . The samples used in the tests failed at approXlmately 15 Yo axial stram and .the measured corrections, corresponding to this strain, have been plotted agaJnst extension modulus in Fig. 120. Three different thlcknesses of rubber membrane

168

THE TRIAXIAL TEST: APPENDIX

1

were used and the calculated corrections have also been plotted. For the standard membrane, 0'008 in. thick, the correction is 0'6 IbJsq. in. at 15 % axial strain. The rubber correction is usually fairly small compared with the compression strength of natural clays and the simplified calculation method outlined above is sufficiently accurate for most purposes.

finch wide circumferential strip of rubber membrane

Mean length ofmemhrane = 2(l-d-Zt) + 7T(d+t)

=¥

Load per inch Extension modulus M - load per inch strom -

Scale pan and weights

tW Fig. 119. The apparatus for measuring the extension modulus of the rubber membrnne (length measurement made with vernier telescope) For 4-in. diameter samples a rubber membrane 0'01 in. in thickness is often used and the value of M determined experimentally is about 2·0 lb/in. The calculated relationship between rubber correction and axial strain is shown in Fig. 121. The correction is clearly very small an.d is usually neglected. Altbough the corrections have been determined from tbe results of undrained tests, experience has shown that they may be applied to drained tests with little error. (ii) Failure Ott a sitlgle shear platte. Where failure on a single shear plane occurs, the behaviour of the rubber membrane i more complex than in the case of

Extension modulus -16 per inch Fig. 120. The relationship between extension modulus and rubb r membrane ~orrection at 15 per cent. axial strain: observed and calculated values

O·4.-------r-----r----,----,

5

10

15

20

AXial strain % Fig. 121.

The vanatton in rubber membrane correction with axial strain : calculated values for 4-in. diameter samples

THE TRIAXIAL TEST: APPENDIX

1

plastic failure. No satisfactory analysis has so far been possible but the limited experimental evidence suggests that the correction increases slightly with cell pressure and, at the same strain, may be considerably larger than for plastic failure. However, as failure on a single shear plane usually occurs at a comparatively small strain, the actual correction at failure is generally of the same order as the 0'6 lb/sq. in. applied to plastic failures at 15 % strain. (2) Drain corrections The restraint imposed by the filter paper drains is of much greater significance and is more difficult to estimate accurately than that of the rubber membrane alone. If it were not for the overriding necessity of completing consolidation on clays of low permeability in a reasonable time, it would be desirable to do without drains. The type of drain used for It-in. diameter samples tested in compression is shown in Fig. 54, while for the 4-in. diameter samples filter paper strips i-in. in width are placed in contact with the specimen, spaced at I-in. centres. In each case approximately half the surface of the sample is covered by the drains. Whatman's No. 54 filter paper is used as it has a high permeability and retains its strength sufficiently to be removed easily from the specimen after the test. (i) Plastic failure. A series of tests carried out on 1i-in. diameter specimens, with and without drains, has shown that at failure, which occurred at 15 % axial strain , a total correction of approximately 2 Jb/sq. in. has to be applied to the compression strength to allow for both rubber membrane and drains. Observations on the behaviour of the drains show that, under small strains, the sample, the rubber membrane and the drain act as a unit. After about 2- 3% strain buckling occurs in t~e drains and a series of ridges becomes visible. 1 he correction builds up quickly with strain and, in practice, the correction of 2 Ib/sq. in. should be applied at strains above about 2% .'" For cell pressures below about Sib/sq. in. slip between the drains and the sample occurs, and the combined correction for membrane and drains falls below 2 lb/sq. in. However, due to the complexity of the factors involved the precise magnitude of the correction under particular conditions can be found only by comparative tests. No direct experimental evidence on the correction necessary for the drains on the 4-in. diameter specimen is available but, assuming the same mechanism and u~ing the data from the tests on the It-in. diameter samples, the magnitude of the correction can be calculated. The proportion of the circumference of the sample covered by the drains is the same for the two specimen sizes and the stiffness of the paper used is the same. The correction to the stresses for the drains alone will therefore be proporti nal to the ratio between the circumference of the samples and their areas. For the 4-in. diameter pecimen the correction will be

1'4 X \5Ib/sq. in. = 0'5 Ib/sq. in. As the 4-in. diameter samples are normally used in testing compacted or partly saturated materials which have a high strength, the correction will in most cases be unimportant. • This is in conflict with earlier results reported by Henkel and Gilbert, 1952, when it was thought that the drain correction increased with strain in a similar manner to the rubber correction.

CORRECTION FOR

TRE

GTH OF R BBER MEMBRA

E A D DRAI

S

Failure on a single shear plane The drain .correction ~o ~e applied to 1t-in. diameter samples when failure occurs On a smgle plane IS ?If!icult to determine with any accuracy. The experime~tal data suggest~ /that It I~ dep~ndent on strain, but, at the relativel small stram~ o! about 4-5. / 0' at w~lch fadures of this type usually occur, no serious ~rror IS Introduced If a comblOed membrane and drain correction of 2 Ib/sq. in. IS used.

APPENDIX 2

Proving Ring Characteristic . For design purposes the maximum safe load and the sensitivity of proving rIngs may be calculated using the theory of thin rings. For a load, P, applied at the opposite ends of a diameter, the maximum moment, M, can be shown to be:

M=Pr 1T

(43)

where r is the mean radius of the ring. The neutral axis is assumed to lie in the middle of the ring section and for a ring of rectangular cross section the maximum fibre stress, I, is given by:

6Pr

1= 1Tbl2

(44)

where t is the thickness and b the width of the ring. The deflection 0 under the load P may be expressed as: 0=

Pr3(~_~) = 0'149 Pr3 El 4- 1T El

(45)

where E is the modulus of elasticity of the ring material I is the moment of inertia of the ring section . and For a ring of thickness t and width b th moment of inertia i bt 3 / 12 and the expression for the deflection reduces to: 8 - l'79Pr3 (46) - Ebt3 In order to obtain high sensitivity, consistent with high load capacity, proving rings are usually made from high tensile steel with a safe working stress of at least 50 tons or 112,000 lb/sq. in. For normal laboratory use, rings with outside diameters of 6-7 in. have been found satisfactory. The way in which the maximum load and sensitivity change with ring thickness is shown in Fig. 122. In the calculations E is taken as 30 xl 0 8 lb/sq. in., the maximum fibre stres a 112,000 lb/sq. in., and a ring 1 of in. width is assumed. A dial gauge reading to 10000 in. is used to indicate the ring deflection and the sen itivity has been expressed as 10-4 in./lb. . With increasing ring thickness the sensitivity decreases much more rapIdly than the load capacity increases, and there are thus theoretical advantages in having wide rings. The advantage of increased sensitivity for the same ultimate

THE TRIAXIA L TEST: APPENDIX

2

so

50,000

7"0.0. ~

II

(;;:

:::,

()

10

~~~nSltiVitY

6 0 .0.\

10,000

~

to.

CI)

~

\

\

6-C .0.

....I . . . . . . .

\

f'I

CI)

'\ \. [\

13 .~

'It I

~

"" .... ~

'\ \

~ 'i;: ......

.... ~7

}:'

1

~ ......

~

'/

f'I (;;:

1000 '\..

"

'/

~

'\..

//

/1 0"

o

Maximum Load

v

\.

'/

"-,

""- ~~ '.

"

0 ·'

0 ·2

p.O.

0 ·3

0'4

"',

"-

o·s

100 0'6

Ring thickness - inches Fig. 122. Proving ring characteristics : the variation in maximum load and sensitivity with ring thickness for proving rings 6 in. and 7 in. outside diameter made of high tensile steel (values given are for rings 1 in. wide) load is, however, offset by the difficulty of making satisfactory end mountings. In practice, therefore, proving rings of 6-7 in. diameter are usually made about 1 in. wide but in special cases the width may be increased to 2 in. The calculated sensitivities of rings are not sufficiently accurate for load measurement and all ring should be calibrated against an accurate stand.ard. I t is found that the stress- strain relationships are, in general, not linear and there is also a certain amount of hysteresis. Fig. 123 shows a typical calibration for a 7-in. O.D. high-tensile ring, 1 in. wide, with a thickness of 0,145 in. The position of the calibration curve, for unloading, depends on the maximum load reached in the test. The curve for unloading from the maximum ring capacity indicates the greatest difference that occurs. A more unsatisfactory feature of the calibration curve is the way in which rapid changes in sensitivity occur where the load is less than about t of the maximum. In calculating axial load it is common practice to use as a zero value the reading obtained as the ram is being pushed into the cell against the cell pressure alone, and to work from the standard calibration curve shown in Fig. 123. If a significant error is to be avoided when a sensitive ring is used and the

PROVtNG Rt

C CHARACTERtSTt

173

initial ram load is an appreciable part of the capacity of the ring, a calibration curve based on the deflections from this initial reading should be constructed. Alternatively the total deflection, from the zero used in the calibration test , should be measured, the corresponding load found and the initial load due to 8 ·4~

/~~

Unloading

V

,,\

~p

Vtoading

f--

/~V

(\

'-....,..;'

~v

-

"V

7'6

o

500

fOOD

1500

2000

1-

2500

3000

Proving ring deflection - lO-4inches Fig. 123. Calibration curve for 7-in. diameter proving ring 0'145 in . thick and 1 in. wide the force exerted by the piston should then be subtracted to give the load on the sample. In any case the possible error should be checked before an y simplified calibration curve is used to calculate axial loads. In order to measure accurately the wide range of strengths encountered in practice, proving rings of various load capacitie are required . The range of proving rings given in Table 12 is suitable for most triaxial tests. TABLE

12

Outside Thickness : itl. diameter:

Material

Width : tn.

11I.

Mild steel. High tensile steel II

"

II

II

II

II

II

II

"

7 7 7

6 6

0'100 0·145 0·231 0'339 0·339

1 I

1 1 2

Approx . Maximum load: lb

S ensitivity: 10- ' itt. p er lb

50 300 1000 3000 6000

20 8 1·9 ()O38 0'19

I I

APPENDIX 3 Friction on the Loading Ram In most of the triaxial test equipment in common use the axial load applied to the specimen is measured outside the cell and the load is transmitted to the specimen by a ram passing through a bush in the top of the cell. If there is any friction in this bush, errors will arise when the axial stress in the specimen is calculated. In order to reduce or eliminate ram friction, ball bushings, rotating rams or rotating bushings have been used. Other methods have also been developed whereby the loads are measured inside the cell [for example, by Taylor, 1943; and Casagrande, 1948]. All these methods of overcoming ram friction lead to additional complications in the apparatus. In order to see the problem in perspective it is useful to examine the magnitude of the errors involved. Provided the ram and bushing are smooth and have adequate clearance between them, friction can arise only as a result of lateral forces which push the ram against the bushing. Lateral forces on the ram can arise either from external causes, if the proving ring or other loading system does not apply a strictly axial load, or from non-uniform deformation of the test specimen itself. Proper design of the testing machine and alignment of the triaxial cell can eliminate lateral forces due to external causes; but those due to non-uniform deformation of the sample cannot be avoided. 2 '0

~

V

o0

V 1

/

V 3

V

~

V

,./"

4

5

Axial stroln %

6

7

8

9

Fig. 124. The error in axial10ad measurement due to ram friction: variation with axial strain in a typical test on a 4-in. diameter sample Theoretical studies and tests by Haus ler- indicate that, in a well designed cell, the friction should not exceed about 1:2% of the axial load, provided oily lubricants are used. Warlam,· in a study of methods of loading used in triaxial tests, concluded that the friction using a i-in. diameter ram would lie between - These data are summarized in the 1947 Progress Report on Triaxial SIlJ!ar Research, published by the Waterways Experiment tation, Vicksburg.

175

FRI TION ON THE LOADINC RAM

1 % and 3% of the axial load for most of the loading range. It might, ho\ ever, ~xcee~ 3% at very small loads. A limited number of tests at Imperial ollege, m which the load has been measured both with and without rotation of the bushing or ram,.indicate that the errors normally lie between about 10 0' and 30', 0 . ~ here no rotatIOn IS used. In the particular case where a specimen fails on a smgle plane, large lateral forces may be induced, and the error may rise to about 5 % of the axial load. Even when this is not the case, tests indicate that the error in the load measurement increases with axial strain , as illustrated in Fig. 124. For a most commercial testing and also for a good deal of research work , the simplicity of the apparatus is more important than the elimination of errors of the magnitudes mentioned above. A nominal correction can be made wh re necessary. In some cases, however, additional accuracy is requir d and under these conditions a rotating bushing appears to be the simple t satisfactory way of reducing friction . Rotation of the piston itself can transmit tor ional stresse to the specimen which may alter the stress system sufficiently to nuJlify, to a large extent, the increased accuracy in the measurement of axial load.

APPENDIX 4-

Rates of Testing (1) Drained tests- constant rate of strain A method of calculating a suitable rate of straiJ) for carrying out drained tests to ensure adequate dissipation of excess pore pressure has been described in the section on drained test procedure. In order to iJlustrate the effect of rate on the measured compression strength some typical results are given here. F igs. 125 (a), (b) and (c) show the results of series of drained tests on normally consolidated specimens of remoulded Weald Clay, London Clay and Kaolinite. The fuJI lines represent the average test results, while the dotted line show the theoretical results calculated from equations (28) and (29): ( eT1- eTa),

=

(eT1- eT3)"

+ 0,[(

(11- eTS)d- (Ul-

eTa),,]

and

h2 'T}c"t,

OJ= 1 - Although the degree of dissipation of pore pressure increases with time, the test results show that the strength increases only up to a certain maximum value, after which a gradual reduction occurs. The changes in strength up to the maximum value agree reasonably well with the theory. It is fo~n~ th~t the maximum corresponds to a theoretical ~egree of po~e-pressure dISSipatIOn. of about 95 % and this has been used to prOVIde the workmg rule for the calculatIon of sujtable times to failure in drained tests given on p. ] 25. The gradual decrease in strength with increasing time to failur~ which occurs after this point is the result of the small viscous component present 10 the strength of clays. From the available drained test results it would appear that a tenfold increase in the time to failure results in a decrease of strength of only about 5%. In Fig. 126 the results of drained tests on a heavily over-consolidated. sample of remoulded Weald Clay are shown. In the undrained te t a large negative pore

THE TRIAXIAL TEST ; APPENDIX

50

40

l-

,~ I:)..

~ 30

.?

~

~ ..

~~

_-

':::'

J,,~J-

4

,1..1 1,111

Weald Clay(retnoII. l1eo') i - f-+-

r{;c~a:: t-- -

-

I

l-

i

20

1

'r+-Uno'IYJlneo' strength

l:)

03 ~ 3016 ptrsq,ln ,

I

I

80%

~ 10

95%

90%

97'S%

1rt,i~essure TSiproi

alao

10,000

1,000

nme to failure - minutes

40

l

Lohdon Cia) (t.emouldb) -~_J+test results

-

f-

-

I~

I--

-

- c-- ~ I

-Undrained strength 10

t:)

+.

o100

-f' -

i-

'tcolculoted

90(.

80i.;

1

--1-

-1,-

f:;:~

.-~~

I 95/.

03 - 3016 persq.ln. 97'S%

o pore PI'! r,rSU/1 0'1. ts1J fit 0

-- -

TaooO

{.odd

nme to failure - minutes 40

, I L II

t s~'iesult;r I---

V r-If I ~

'(1'-

t::--

r lel/lateo'

- --

,..!!no'IYJI1eo'stren/th 10

8,,0%

_I_ I 90%

I ;do~;nlte

Ii

P;- 3016 pe S'l.in.

9~%J

97-5%

(Tyrissfi iTfiatlon

%

1,000

TQOOO

77me to failure - minutes Fig, 125, The variation in strength with time to failure in drained compression tests; normally consolidated samples of remoulded clay (a) Weald clay (b) London clay (c) Kaolinite

RAT E

177

OF l'E T I C

p~essure i.S set up. A.s this dissipates in the drain d test, the strength decreas's

fairly rapidly with time to failure, until the urve relating strength with time flattens off to a slope corresponding to the viscous component of the strength. 30

Weald CluJ. (~,Jiwldei1)

()m/ro~'ned sWgth ............ r-

03 test · 10 Ib ptJr SII-In. 03 max o 'operSI( in.

·,2

IS 10 I

t:)

o

100

/I)()(}

10.000

TIme to fOIJure - minutes Fig. 126. The variation in strength with time to failure in drained compression test ; over-consolidated samples of rt!mould l'd clay

For the over-consolidated sample the coeffi cient of consolidation is much higher than for the normally consolidated clay, and in conseq uence the time necessary to achieve full dissipation is much shorter.

(2) Undrained tests (i) Effect 011 the value of apparent cohesioll cu' The van atlon in undrained strength with rate of leading has received considerable attention [Taylor, 1943; Casagrande et al. , 1948, 1949, 1950 ; asagrande. 1951]. The results have usuaJly been presented so as to show the variation in compression strength with rate of axial strain. The results for Boston Blue lay arc shown in Fig. 127. In 50 . 40

.~

,....

-

--

-

..,

IS-

... 30

'" ..... ~

Baston BIlle Cloy,

.. 20 ~ I:)'

I

'il

,

~fO

-

10 3

ill -

fOZ

,I

l11

-

fOl

AXIal strain /. per minute (after Toylor

ffH.3)

Fig. 127 . The variation in strength with rate of axial strain for undrained tests

on Boston Blue clay order to compare the results more readily with the drained test results they have been replotted on the basis of time to failure in Fig. 12 and t~e results for a series of undrained tests on remoulded Weald Clay have been mcluded. It can be seen that the slopes of the lines are very similar and, as in the case of I2-M.S.P.

THE TRIAXIAL T ES T: APPI!NDIX 6()

4

J JLOY-(CJOLlLdi) ?J

£:/os,

50

V

.

Weold Cloy (remoulded) /

10

o

1,000

TOO

10

Time to failure - minutes Fig. 128. The variation in strength with time to failure for undrained tests on Weald clay and Boston Blue clay the drained tests, the decrease in strength for a tenfold increase in time to failure is approximately 5%. (ii) Comparisol1 of the values of c' and cp' measured in undrained and drained tests. If drained and undrained t_s:sts with pore-pressure measurement are to be compared, the measured strengths should be corrected to the same time to failure. The pore pressure introduces an additional variable into the undrained test results and the correction is applied most conveniently to the drained test results . As the duration of the undrained test is usually less than the time required for the drained test the straight portion of the graph relating strength to the logarithm of time to fai lure should be produced as shown in Fig. 129.

so 1- -

- -./'

20 t)'

}~U1UL..,L ....

I- -

- 1-

~ f-

I-'

dromed test results-

mtnlmum time to I'ollure In droined test

time to failure In undromed test

I

t:r 10

o

TO

1.000

n me to rotlure -minutes

To.ooo

Fig. 129. The correction of the drained strength of a clay to the time to failure used in undrained tests

RA TE

OF TEST!

G

179

The correction necessary for the drained test results may then b found. If complete data on the variation in measured strength with time to failure for a particular clay is not available, the approximate correction of a 5% inc rea In strength for a tenfold decrease in time to failure may be used.

High rates of loading Where very high rates of loading are used the viscous effects become more important [Casagrande, 1951]. Tests of this type require special apparatus and technique and will not be con idered here.

APPENDIX 5

Correction for Air Trapped between the Sample and the Rubber Membrane This ('orrection is based on the assumption that the difference between the pressure in the air and water in the pore space may be negl cted a small compared with the other stress changes. The relationship between pore pressure and volume change under undrained conditions can then bc deduced from Boyle's law and Henry's law of solubility. Let Vo denote initial volume of sample, - V" denote initial volume of voids in sample, So denote initial degree of saturation of sample, 'V denote initial volume of air trapped between sample and rubber membrane, Po denote initial pressure (absolute) in the pore space H denote Henry's coefficient of solubility (approximately 0'02 volumes of and air per unit volume of water at 20 ° C). The initial volume of free air is thus (l-So)V,,+v and of dissolved air SoV"H. Hence the total volume of air at Po absolute (47)

At a new pressure p (absolute), this becomes

(48)

V,,(l-So+SoH+vfV,,)Polp

The volume of dissolved air at this new pressure is again SoV"H, and hence the free air volume is

(49) The cbange in volume of the pore fluid, neglecting the compressibility of the water itself, is due to the change in volume of the free air. Hence L\V = V,,[(l-So+SoH+vfV,,)Polp-SoH-( 1-SO)-VfVlI] i.e. (SO) L\VfV" = (Po/p-l)(l-So+ oH+ v / V ,,) If "0 denotes the initial porosity, V" = noVo, and equation (SO) can be rearranged in the form;

v=

~o~~~-110(1-So+SoH)] Vo

.

(51)

180

THE TRIAXIAL TEST: APPENDIX

5

The values of no, So and Vo are determined from the initial dimensions of the sample, its weight and the specific gravity of the soil particles. The value of D. V is measured by the quantity of fluid entering the cell, and P is given by the porepressure apparatus. The initial pressure Po is taken as atmospheric pressure. Owing to the approximations involved in the basic assumptions· the calculated value of v is influenced by the magnitude of the pore-pressure change, but the error is not serious. This may be checked by direct measurement in two particular cases: (a) If the pore pressure is raised sufficiently to cause full saturation, the volume change in the sample is no(l-So)Vo. The amount by which the reading on the volume indicator exceeds this is the volume of entrapped air, if other possible sources of error are neglected. (b) In the K 0- test, the percentage volume change is given directly by the axial strain. The difference in the two measured values should again equal the initial volume of trapped air. Test results indicate that the trapped air in the case of a 4-in. diameter sample of compacted soil may amount to about 1 o ~ of the volume of the sample. Compressibility results must therefore be expressed in terms of the corrected volume change (D. V -v)/V o' In the early stages of the test, where the value of D. V is less than the calculated value of v, incomplete bedding of the membrane is occurring and the true volume changes cannot be calculated. It will be obvious that the entrapped air also effects the value of B or E measured in the test. 1 he difference can readily be calculated by the method outlined above. Trapped air results in an over-estimate of B which is usually neglected for practical purposes. • There are three basic assumptions: (1) that the pressure of the air in the voids of the sample does not differ significantly from the pressure in the pore water, (2) that the pore water pressure is correctly measured by the test equipment and (3) that the initial pressure in the air in the voids is atmospheric, i.e., is at the same initial pressure as the trapped air. It is clear from recent work by Hilf (1956) and from tests at Imperial College that a significant error may arise in the overall result of a calculation based on these assumptions . This is most marked in soils having a relatively high clay fraction, compacted at, or on the dry side of, the optimum water content. On the other hand, in soils having a low clay fraction and compacted at higher water contents, the error is no greater than that associated with the probable accuracy of the calculated values of "0 and So. Further work j required to evaluate ~hc individual errors in the three assumptions.

BIBLIOGRAPHY A DRESEN, A ., DI BLACI O, E. and KJAER Ll, B. 1957. onvegiall Geouclmiral Institute's Triaxial Equipm('llt, Norwegian Gcotechnical Institut . BAKER , B. 1881. " The actual lateral pressurc of carthwo rk ", Mill. Proc. IlISt . Cit'. Engrs, 65 :140- 186. BI HOP, A. W . 1948. "Som c factors invoh 'cd in the design of a larg earth dam in the Thames Vallc)''', Proc. 211d Inl . Calif. Soil Mech., 2 :13- 18. BISHOP , A. W. 1950 (a). " Summarizt!d proceedings of a conference on stress analys is ", B ritish JO!lrll. A ppl. Phys., 1 : 241 -25 1. - - 1950 (b). ' f Discussion on m eas uremt!nt of shea r strength of soils", Geotechnique, 2 : 113- 11 6. - - 1952. "The stability of earth dams", Ph.D . Thesis, niversi ty of London . - - 1954 (a). ,. The u e of pore-press ure coeffici 'nts in practict!", Geotechlliqul', 4 : 148- 152. - - 1954 (b) . Correspondence, Gtfot('chllique, 4 :43 5. - - 1955. "The usc of the slip circle in th e stability analysis of slopes", Gtfotechnique, 5: 7-17. - - 1957 (a). "Embankment Dams: Prin ciples of Design and tab ili ty Anlllysis", Contribution to H y dro-Electric Eligilleen'ng Practice , cdited by J. uthri e Brown. London : Blackie & Son . Pp . 349-406. - - 1957 (b). .. Some factors controlling the po re press ures set up durin!{ the construction of earth dams ", Proc. 4th lilt . Conf. Suil Mec"., 2 : 294-300. - - and ELDIN, GAMAL. 1950. .. Undrained triaxial tests on saturatt!d sands and their significanct! b the general th eory of shear strength ", Gtfu leclmiqut' , 2 : 13- 32. - - and - - 1953 . " Tht! dft!ct of-stress history on the rdation between cp and porosity in sand ", Proc. 3rd lilt . Ccmj. Soil Mech., 1 : 100- 105. - - and H ENKEL, D . J. 1953 (a). "Port! press ure chan ges durin g shear in two undisturbed clays", Proc . 3rd 1111. ('O llf. Soil Mech ., 1 :94- 99. - - and- - . 1953 (b). .. A consta t-pressure control for the tri axial-compression test ", Gtfotechniquf!, 3 : 339- 344 . BJERRUM, L. 1954 (a). "Geotechni cal prope rties of Norwegian marine clays", G eotechnique, 4: 49- 69. - - 1954 (b) . Theoretical and Experimental II1t'l!s ligatiom all thl! S hear S trmgth of Soils, Norw gian G eotechni cal lnstitute, Pub!. No .5 . - - and EIDE, O. 1956. "Stability of struttt!d excavations in clay", Gt!oteclmiqlle, 6 :32-47. - - and KJAERNSLl, B. 1957. "Analysis of the stability of some Norwegian natural clay slopes ", Gt!oteclmiqul!, 7 : 1- 16. - - and ROSENQVIST, 1. Th. 1956. .. orne experiments with artificiall y sedi men ted clays", Gt!otechniqul!, 6 :124-137. BRITISH STANDARDS INSTITUTION. 1948. "Methods of test for soil classification and compaction ", B .S. 1377. BUJSSON, M . 1948. " Tassements evalues d'apres les essais 0 dometriquescomparaison des hypoth ses-appareil triaxial ", Travaux, No. 164 :319-321. CAFFYN, J. E . 1944. " A study of constant stress rheometers ", JOIl71l . Sci. i7lstmm., 21: 213- 216 . CASAGRANDE, A . 1936. "Characteristics of cohesionless soils affecting the stability of slopes and earth fills" , JOUTn . Boston Soc. Civ. Engrs, 23 : 13- 32. - - CORSO, J. M., and WILSON, . D. 1950 ... Report to Waterway Experiment Station on the 1949- 1950 program of investigations of long-tim e loading on the strength of clays and shales of constant water content", Harvard U niversity. tllt

BIBLIOGRAPHY

CASAGRANDE, A. and SHANNON, W. L. 1948 (a). "Stress-deformation and strength characteristics of soils under dynamic loads", Proc. 2nd Int. Coni. Soil Mech., 5: 29- 34. - - and - - 1948 (b). "Research on stress-deformation and strength characteristics of soils and soft rocks under transient loading", Pub. Harvard Univ. Grad. School Eng. Soil Meeh ., Series No. 31. - - and WILSON, S. D. 1949. "Final report to U .S. Waterways Experiment Station on investigation of effect of long-time loading on the strength of clays and shales at constant water content", Harvard University. - - and - - 1951. "Report to Waterways Experiment Station on triaxial research performed during 1950-1951 ", Harvard University. - - and - - 1951 . "Effect of rate of loading on the strength of clays and shales at constant water content", Geotec}l1Iique , 2 :25 1-264. COLLIN, A. 1846. R echerches exptfrimentales sur les glissements sponta1U!s des terrains argileux, Paris: Carilian-Goeurley et Dahnunt. COOLING, L . F. and GOLDER, H . Q. 1942 ... The analysis of the failure of an earth dam during construction", Journ. 11Ist. Civ. Engrs, 19 : 38-55. DELFT SOIL MECHANICS LABORATORY. 1948. Proc. 2nd Int . Conj. Soil Mecll., 6 : 222- 226. FLEMING, H. D. 1952. "Undrained triaxial compression tests on a decomposed phyllite", Proe . 1st Australia and New Zealand Conf. Soil Mech., 112- 122. GEUZE, E. C. W. A. 1953 ... General report on laboratory investigations including compaction tests, improvement of soil properties ", Proe. 3rd Int. COllI Soi: Mech., 2 :3 13- 318. GIB 'ON, R. E. 1953 . "Experimental determination of the true cohesion and angle of internal friction in clays", Proe. 3rd 11It. on/. Soil Mech., 1 : 126- 130. - - and HENKEL, D . J. 1954. "Influence of duration of tests at constant rate of strain on measured' drained' strength ", Gtfotechnique, 4 : 6- 1 S. HABIB , P . 1953 . "Influence de la variation de la contrainte principale moyenne sur la resistance au cisaillemen( des sQls", Proe. 3rd Int.. Coni. Soil Mech., 1 :131- 136. HAMILTON, L. W. 1939. " The effects of internal hydrostatic pressure on the shearing strength of soils", Proc. Amer. Soc. Test Mater., 39 :1100- 1121. HANSEN, J. B. and GIB ON, R. E. 1949. "Undrained shear strengths of anisotropically consolidated clays", Geoteehniqlle, 1 : 189-204. HARDING, H. J. B. 1949. " ite investigations including boring and other methods of sub-surface exploration", Journ . 111st. iv. Engrs, 32 : 111- 137. HARDING, H . J. B. 1952. "The progress of the science of oil Mechanics in the past decade ", Proe. Inst. Civ. Engrs, 1 (1):658- 680. HENKEL, D. J. 1956. "The effect of overc nsolidation on the behaviour of clays during shear", Geoteehnique, 6 :139-1 50. - - 1957. " Investigations of two long term failures in London Clay slopes at Wood Green and Northolt", Pruc. 4th Int. onf. Soil Mech., 2 : 315- 320. - - and GILBERT, G. D. 1952. "The effect of the rubber membrane on the measured triaxial compression strength of clay samples", Geotechnique, 3: 20- 29. - - and KEMPTON, A. W . 1955. "A landslide at Jackfield, Shropshire, in a heavily over-consolidated clay", Geoteehnique, 5:131 - 137. HILF, J. W. 1948. .. Estimating construction pore-pressures in rolled earth dams ", Proe. 2nd Int. Soil Mech., 3 :234-240. - - 1956. "An investigation of pore-water pre sure in compacted cohesive soils", Bureau of Reclamation, Tech. Mem. , 654. HILL, R. 1950. The Mathematical Theory 0/ Plasticity. Oxford : Clarendon Pre S. HOLTZ, W. G. 1947. "The use of the maximum principal stress ratio as the failure ' criterion in valuating triaxial shear tests on earth materials", Proc. Amer. Soc. Test Mater., 47: 1067- 1076.

BIBLIOGRAPHY

I

3

HVORSLEV, M. J. 1937. " ber die Festigkeitseigenschaften gestorter bindig r Boden" , Ingelliorvidellskabelige Shrifler, A No. 45, openhagen. HVORSLEV, M.]. 1939. "Torsion shear tests and their place in the determination of the shearing resistance of soils", Proc. Amer. Soc . Test Mater., 39:9991022. - - 1949. "Subsurface exploration and the sampling of soils for ivil Engineering purposes ", U.S. Waterways Expt. tn . J URGENSON, L. 1934. "The shearing resistance of soils", JOllm. Boston oc. Cif'. El1grs, 21: 242- 275. KENNEY, T. C. 1956. "An examination of the methods of calculating the stability of slopes", M.Sc. Thesis, University of London. KJELLMAN, W. 1936. t'Reports on an apparatus for consummate in\'estigation of the mechanical properties of soils", Proc. 1st lilt . Couf. Soil Mech., 2 :16- 20. - - 1951. "Testing the shear strength of clay in Sweden", Ctfotl'Clmiqlll!, 2 : 225- 232. KOLBUSZEWSKI, J.] . 1948. "An experimental study of the maximum and minimum porosities of sands", Proc. 2nd Int . Conf. Soil Mecll ., 1 : 158- 165 . LAMBE, T. W. 1951. Soil Testillgfor Eug£l1eers. New York: John Wiley; London: Chapman & Hall . LAUGHTON, A. S. 1955. "The compaction of ocean sediments " , Ph.D . Thesis, U ni versity of Cambridgc. LEWIS,]. G . 1954. " The sloping core principle for earth and rock fill dams", M .Sc. Thesis, University of London . OSTERBERG, J. O. 1948. "Testing equipment and rcsearch activities of th Soil Mechanics Laboratory, North Western University", Proc. 21ld lilt. ollf. Soil Mech., 6 :233-242. PARR,);, R. H. G . 1956. ". trength and deformation of clay", Ph.D. Thesis, University of London. PENMAN, A. D. M. 1953. "Shear characteristics of a saturated silt, measured in triaxial compression", Ctfotechlliqlll', 3: 312- 328. PLANTEMA, G. 1953. "Electrical pore-water pressure cells: some designs and experiences ", Proc. 3rd 1nt . Conf. Soil M ech., 1 :279- 282. Proceedings of the Cotiferenee 011. the Stability of Earth lopes, 1954. tockholm (also Geotechniqlle, 5 : 1- 226). REINIUS, E. 1948. "The stability of the upstream slope of earth dams ", Bulletin No. 12. The wed ish State Committee for Building Research. RENDULIC, L. 1937. tt Ein Grundgesetz der Tonmechanik und sein experimentaler Beweis", Bauingenietlr, 18 :459-467. REYNOLDS, O. 1886. tt Experiments showing dilatancy, a property of granular material, possibly connected with gravitation ", Pror. Roy. Imt. , 11 :354-363. ROAD REsEARCH LABORATORY. 1952. Soil Mechanics for Road Engineers. L<>ndon : H.M.S.O. ROSCOE, K. H. 1953. tt An apparatus for the application of simple shear to soil samples", Proc. 3rd Jnt . COlif. Soil Mech ., 1 : 186-191. SEVALDSON, R. A. 1956. " The slide in Lodalen, October 6th 1954", Geoteclmiqlle, 6:167-182. SHERARD, J. L. 1953. "Influence of soil properties and construction methods on the performance of homogeneous earth dams ", Technical Memoratldum 645, Bureau of Reclamation. HOCKLEY, W. G. 1953 . tf Discussion on laboratory investigations including compaction tests, improvement of soil properties", Proc. 3rd Itlt. Conf. Soil Mech., 3 : 122. SKEMPTO ,A. W. 1948 (a). tf The IjJ = 0 analysis of stability and it theoretical basis ", Proc. 2nd Int. Conf. SoU Mech., 1 :72- 78. - - 1948 (b). "A study of the immediate triaxial tests on cohesive soils", Proc. 2nd bit. Conj. Soil Meell., J : 192-196.

BIBLIOGRAPHY SKEMPTON, A. W . 1948 (c) ... Vane tests in the alluvial plain of the River Forth , near Grangemouth ", Geotechnique, 1 : 111- 124. - - 1954. "The pore-pressure coefficients A and B " , Geotechnique, 4 :143- 147 . - - 1957. Discussion On " The planning and design of the new Hong Kong Airport ", Proc. Inst . iv. Engrs, 7 :305- 307. - - and BISHOP, A . W . 1950. " The m easurement of the shear strength of soils " , Geotechnique, 2 : 90-1 08 . - - and - - 1954. " Soils", Chapter X of Building Materials, their Elasticity and Inelasticity. Amsterdam : North Holland Pub. Co. - - and - - 1955. " The gain in stability due to pore-pressure dissipation in a soft clay foundation ",5th Congress Lar!(e Dams , No. 16. - - and GOLDER, H . Q. t 948. " Practical examples of the 4> = 0 analysis of th e stability of clays ", Proe. 2nd Int . Conj. Soil Mech, 2:63-70 . SPENCER, E. 1954. Correspondence, Gdotechnique, 4 : 89. TAYLOR, D. W. 1939. "The comparison of results of direct shea r and cylindrical compression tests " , Proc. A mer. Soc. T est Mater., 39 : 1058-1 070. - - 1941. Seventh progress report on shear research to U.S. Engineers, M .LT. Publication . - - 1943 . inth progress report on shear research to U . . Engineers, M.LT. Pu blication . - - 1944. Tenth progress report on shear research to U.S . Engineers, M.LT. Publication. 1948 (a). Fundamentals of Soil Mechanics. New York : John Wiley; London: hapman & Hall. 1948 (b) . " Shearing strength determinations by undrained cylindri cal compression tests with pore press ure m eas un:ments", Proe . 2nd 1m. Conf. Soil Mech., 5 :45-49 . - - 1951 . "A triaxial shea r investigation on a partially saturated soil ", Amer. Soc. T est Matpr ., Sp . Tech. Pub ., 106 :180- 187 . T EHZAGHI , K . 1932. "Tragfaehigkeit der F lachgruendungen ", 1st COIl!(. Inl. Ass. Bridge Slmct . Eng., 659- 672. - - 1943 . Theoretical Soil M ecl!nn£cs. New York: John Wiley; London: Chapman & Hall. - - and PECK, R. B. 1948. Soil Mechallics ill Ellgilleering Practice. ew York: John Wiley; London: hapman & Hall. U.S. BUREA OF RECLAMATION. 1951. Earth Manual. WARD , W . H., PENMAN, A. D . M. and GIBSON, R. E. 1955 . "Stability of a bank on a thin peat layer" , GdotecJmique, 5 : 154---163 . WATERWAYS EXPERIMENT STATION, VI CKSB URC. 1947. " Triaxial shear research and pressure distribution studies on soils ", Progress Report. WATERWAYS EXPERIMENT STATION, VICKSB URG. 1950. "Triaxial tests on sandsReid Bedford Bend , Mississippi River ", Report No. 5- 3.

MANUFACT

RE R S OF SPE IAL

COM P O ENT

EQ

U E D I N THE

JPME

T AND

PP RAT

D ESC RIB E D I N TIll. BOOK Bonded Seals

Dowty Seals Ltd A hehurch Tt!wkesbury G los.

Circlips

Anderton Springs Ltd Bingley Yorks .

Dial Gauges

J. E. Baty

& o. Ltd 39, Victori a . treet Lond n , S.W.l

Thomas Mcr er Ltd Eywood Road t. Alban lIerts .

.. Fibreglass Re inforced Polyester Resin

"0" Rings

Ashdowns Ltd Eccleston Works Knowslcy Road St. Helens Lanes. Dowty Seals Ltd Ashchurch Tewkcsbury G los. George Angus & Co. Ltd Oil . cal D i"ision Coast Road Wal lsend-on -Tyne Northumberland

"Perspex" Acrylic Sheet

Imperial Chemical Industries Ltd Welwyn Garden City Herts.

"Perspex" Tubing and Fabricated Units

Richard Daleman Ltd 325-327 Latimer Road, London, W.l0

Pipe Connexions

British Ermeto Hargrave Road Maidenhead Bt!rks.

Polythene Tubes

Teneplas Ltd Upper Basildon Pangboume Berks. 1 8S

orporarion Ltd

186

MANUFA TURERS OF SPECIAL EQUIPMENT

Polyvinyl Chloride Tubes

The Micanite and Insulators Co. Ltd Blackhorse Lane Waltham stow London, E.17 Portland Plastics Bassett House Hythe Kent

Porous Discs (Vitrifie d Bauxilite A 80 KV)

Universal Gri nding Wheel Co. Ltd Stafford Staffs.

Pressure Gauges (Standard Test Gauge s)

Budenberg Gauge Co. Ltd Broadheath Manchester Lanes.

Proving Rings

T he Sheffield Testing Works Ltd Blonk Street Sheffield 1 Yorks.

Rubber M e mbranes for 4-in. dia. Sample s

C lockhouse Engineering Ltd Brookhill Road New Barnet Herts.

Rubbe r Membranes for I t-in. dia . Samples

l G. Franklin

Sleeve-Packe d Plug-Cocks (Type A.B.IO)

Richard Klinger Ltd Klingerit Works Sidcup Kent

Stainless Steel Tubes

Accles & Pollock Adelphi London, W.C.2

Testing Machines

Wykeham Farrance Engineering Ltd 127 Edinburgh Avenue Slough Trading Estate Bucks.

Tria xial Cells

Leonard Farnell & Co. Ltd Hatfield Herts.

& Sons 15, Colveston Crescent London, E .8

Wykeham Farrance Engineering Ltd 127 Edinburgh Avenue Slough Trading Estate Bucks.

INDEX Angle of shearing resistance, 4, 11; see Shear strength parameters Apparent cohesion, 4, 11; see Shear strength parameters Axial strain , measurement of, 37, 38, 78, ]39,146

Drained tests, on saturated cloys, 123 on saturated cloys with " . d(>creosing, 145 on saturated sands, 123 to determine true cohesion and true angle of internal frieti n, 164

Cell pressure: apparatus for controll ing, 44 air reservoir, 44 control cylinder, 50, 57 loaded ram, 45 reducing valve, 44 self-compensati ng mercury control , 45 measurement of, 51 Coefficient of consolidation, 125, 135, ] 62, 175 valu.,s of, 138 Coefficient of earth pressure at rest (Ko), 16,73,140, ]56 vahles of, 143 Compaction of so il samples, 87 ompressibility, 2, 6, 8, 63, J31 , 141 Con solidated -undrain ed tests, J06 definition of, 9 on partly saturated soils, 18, 119 on saturated cohcsionless soils, IS, 106 on saturated coh esive soils, 15, 109 to determine true cohesion and true an gle of internal friction, 164 Con solidation, 2, 9 against a back pressure, 113 anisotropic, 156, 163 reconsolidation in laboratory, 16, 23,106, 109, 125 under Ko conditions, 16, 140, 156 Constant-volume tests, 163 Conversion factors, 190 rrection for strength of rubber membrane and drains, 167 Correction for trapped air, 179 Cross-sectional area of specimen, change due to strain, 28, 103, 113, 145 Cylindrical compression test, 6, 9

Earth dams and fi lls: long-tenn stability, 22 stability during construction, 24 stobi lity when subject to rapid drawdown, 23, 25, 161 Effective stress, principle of, 2 End restraint, influencc of, 28 on strength, 28 on volume change, 29 on pore pressure, 30 Extension tcst, 9, 152

Disturbance, effect of, 12, 16, 83, 87 Drained tests, 18, 122 choice of deformation rate, 124, J75 definition of, 9 effect of rate of testing, 175 failure caused by increasing the pore pressure, 149 on dry materials, J30 on pardy saturated materials, 129

Factor of safety, 22, 23, 27, 160 Failure criterion : in tem1S of effective stress, 4 in terms of total stress, 11 maximum deviator stress, 11, 13 maximum prinl'ipal stress rlltio, 13, 15 Friction on the loading ram, 35, 36, 174 Ko-tests (no lateral strain), 29, 73, 140,157, 180 drained, 143 undrained, 141 Lateral strain indicator, 73 Leaching, effect on ratio e./p, 16 Loading systems, 74 controlled rate of strain, 74, 94, JOO, 107, 112, 122, 141, 147 controll ed stress, 78, 128, 145 for extension tests, 152 Oil supply to loading ram, 42, 100 Over-consolidation ratio, 16,115 Permeability, measurement of, 133, 139, 163 Plane strain, 8, 9, 27 Pore pressure: after rapid drawdown, 4, 23, 25, J61 apparatus for measuring, 52 calibration of, 61 control cylinder, 57 de-airing of, 58 null indicator, 53 changes during shear, 6, 8, 13, 103, 109, 113, 124, 156

.. ~/. "

188

THE TRIAXIAL TEST

Pore pressure, definition of, 2 due to seepage, 4, 22 due to stress change, 4, 5, 11 , 12, 18, 20, 23,30 in a foundation , 2, 4, 23, 24 in earth fill, 4, 12, 24 measurement of,S, 9, 12, 16, 18, 19, 24, 25 , 3D, 52 parameter A, 5, 11 , 113, 11 5 parameter .A, 6, 13, 103 parameter E, 5, 13, 24, 103, 135, 162, 163 , 180 parameter E, 6, 25, 137, 140, 160, 161 ,

tability analysis, 21, 27, 32 in terms of effective strcss, 5, 22 in terms of total stress,S, 11. 23, 26 =0°, II, 23 with partial consolidation , 4, 24 Standard compaction test, 87, 104, 106, 138 Strain at failure: drained tests, 19, 20, 127, 150 undrained tests, 11, 13, 96, 101 St re~s, definition of: dfective, 2 total, 2 Surface tcnsion, 6, 56, 74, 180

Pore-pressure and dissipation tcsts, 24, 131 Principal stresses,S, 8 rotati on of, 8, 27 Proving ring chilracteristics, 78, 147, 158, 171

Test results : consolidated-undrained tcsts with measurement of pore pressureon saturated sand, 110, 111 on saturated cloy. liS, 11 6, 117 , 118 on partly saturated soil, 121 extension test on clay, 15!l draincd tcstson saturated sand, 123, 124 on saturated clay, 128, 129 decreasing, 148, 149 with with increasing pore pressure, 152 extension test on clay , 157 on partly saturated soi l, 130, 131 on dry materials, 133 KG-tests, 142, 143 porc prcssure and d Issipation tests, 136, 137,138 rapid drawdown test, 162 tests to determine true cohesion and true angle of internu l friction, 165, 166 undrained tests with measurement of pore pressure, 15,102,104, lOS , 106 undrained tests without measuremellt of pore pressure, 96, 97, 98 Triaxial cell , 9, 33 for H-in. diameter samp les, 33 for 4-in. diameter samp les, 39 friction on the loading ram, 35, 94, 174 modification for extension tests, 152 Triaxial test : application of, 2, 21 limitations and advantages of, 8, 26

ISO

Rapid drawdown, 4, 23, 25, 161 Rates of testing, 9, 19, 30, 175 conso lidated - undrained tests, 107 , 112 drained tests, 9, 124, 175 undrained tests, 32, 177 undrained tests with measurement of pore pressure, 3D, 101 Rubber membranes, 9, 38, 43 correction for Strcngth of, 39, 167 leakage through, 44, 67 Remoulding of clay samples, 87, 97 Sample preparation , 83 compacted samples, 87, 100 dry cohcsion less samples, 92 remoul ded samp les, 87 saturated cohcsionl ess samp les, 90 undisturbed samp les, 83 ensitivity, 83, 87, 97 Shear strength, 2 ratio (u /p for normally consolidated clay, 16, 98 see also, Shear strength parameters S hear strength parameters, effective stress, 4 consolidated- undrained , 16, 18, 20, 113, 119 drained, 18, 123, 130, 131 effect of rate on, 9, 19, 30, 175 effect of softening on partly saturated slimples, 18, 24, 25, 119 true cohesion und true angle of internal friction, 164 undrain ed, 12, 103 Shear strength parameters, total stress, 5 consolidated- undrained, 16, 20, 26, 113 effect of Tate on, 30, 177 undrained, 11, 12,16,23,9 ide drains, 81 , 100, 103, 109,119,127 correction for strength of, 167 S lopes: initial stability, 4, 23 long tenn stability, 4, 22 IItability under drllwdown, 4, 23, 25

(1.

Undrained tests : definition of, 9 effect of rate of testing, 30, 177 extension tests, 152 multi-stage test, 15 on partly saturated cohesive soils, 12 on partly saturated soils with 11 a decreasing, 147 on saturated cohesive soils, 10 witi'! controlled stress ratio, 160 with measurement of pore pressure, 12, 98 with no lateral yield (Ko-test), 140 without measurement of por pressure, 10, 94

DEX

Vane test, 23, 87 Volume change, 2, 5, 29, 63 ap paratus for measuring, 63 based on the direct measu rement of strain , 70 in drained tests, 67 in dry cohesionl css materials, 70 in undrained tests, 63

Volume change, during KII-tests, 137, 141 during shear, 4, 20, J 03, 123, J 28, 130, 147,150, 156 on saturntion , 18. 22 und er all -round pressure, 2, 18, 73, 103, 112.125,129, 132

Primed in Great Britain

A PT /K~7

CONVERSION FACTORS Length:

1 inch 1 foot 1 metre

= 2'540 cm = 12 in. = 30·48 em

= 3·281 ft = 39'37 in.

Area :

1 square inch 1 s9uare foot

= 6'452 sq. cm = 0·09290 sq. metres = 929·0 sq. cm

Volume:

1 cubic inch 1 cubic foot

= 16'39 C.c. = 0·02832 cu. metres

Weight :

1 pound (lb) 1 kilogram (kg) 1 ton

=

Pressure:

lIb/sq. in. 1 kg/sq. cm 1 ton/sq. ft

= 0'4536 kg

2·205 lb = 2240 Ib = 1·120 short tons = 1'016 metric tons

= 0·07031 =

= 1 metric ton /sq. metre = = = 1 atmosphere

Density:

1 lb/eu. ft 1 g/cu. cm

Compressibility : 1 sq. in./lb Permeability :

1 ft/year 1 cm/ econd

Coefficient of Consolidation: 1 in2 ./minute 1 cm 2 /seeond

kg/sq. cm

= 14'22 Ib/sq. in.

15·56 lb/sq. in. 1·094 kg/sq. cm 0·09144 ton /sq. ft 1'422 Ib/sq. in. 14'70 lb/sq. in. 1-\)31 kg/sq. em

= = 0'01602 g/c.c. = 1 metric ton/cu. metre = 62'43 Ib/cu. ft = 14'22 sq. cm/kg = 15'56 sq. ft/ton = 0'9659 X 10- 6 cm/sec = 1·035 X 10° it/year

= 0·1075 cm2 /sec2 = 3·652 X 103 ft /year = 3'044 X 102 ft 2 /month = 9·300 in 2 ./minute = 3'397x 10' ft2 / year = 2'831 X IDs ft2 / month

LIBRARY