Triaxial Testing of Granular Soil (Colliat-Dangus, 1988)

8/11/2019 Triaxial Testing of Granular Soil (Colliat-Dangus, 1988)

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Authorized Reprint 1988 from Special Technical Publicat ion 977 1988

Copyright American Society for Testing and Materials, 1916 Race Street, Phila delphi a, PA 19103

Jean Louis Colliat-Dangus, Jacques Desrues, ami Pierre Foray

Triaxial Testing of Granular Soil Under

Elevated Cell Pressure

REFERENCE: Colliat-Dangus,J. L., Desrues, J., and Foray, P., Triaxial Testing of Granular

Soi1 Under Elevated Cell Pressure, Advanced Triaxial Testing

of

Soi1 and Rock, ASTM STP

977, Robert T. Donaghe, Ronald C. Chaney, and Marshall L. Silver, Eds., American Society

for Testing and Materials, Philadelphia, 1988, pp. 290-310.

ABSTRACX

A study

of

triaxial testingunder elevatedce11 ressurespresented.The nfluence

of test conditions, namely

end

lubrication and slenderness atio, on such tests s discussed.

Results of a tomodensitometric nvestigation of interna1homogeneity are given. The main

resultsof the high pressure tudy are presented, ncluding ime

effects on isotropic compression.

KEY WORDS:

triax ial test, high pressure, ubricatedends, slendernessatio, calcareous and,

density, x-ray, tomodensitometer, time effect

Some classicgeotechnical engineering field problems, including high embankment dams,

piles, and deep tunneling, involve mean pressures significantly higher than those found in

common practice. A new interest in th is subject stems from specific offshore geotechnical

problems, especially ones in which long piles and/or marine calcareous sand deposits are

concerned.

The purpose of this study, undertaken as part of a research program on offshore piling,

was to characterize and compare the behavior of two sands, a marine calcareous one and

a siliceous one, under high confining stresses. Within this work, a preliminary study was

conducted to evaluate the influence of the experimental conditions of the specimen end

restraint and slenderness ratio on the result of drained compression triaxial tests performed

under both low and elevated confining pressures.

Two main types of specimens are considered: (1) the conventional specimen (rough ends,

length-to-diameter ratio [LID] = 2) and (2) the specimen using lubricated ends and a

slenderness ratio reduced to 1. Two kinds of granular materials of different mineralogic

composition are used: a siliceous sand and a marine calcareous Sand. Besides current triaxial

experiments on these specimens, original tests were performed using an x-ray scanner ap-

paratus to investigate the interna1 homogeneity of the specimens.

The behavior of granular materials under elevated ce11pressures is discussed for both

stages of the triaxial test: isotropic compression and triax ial shear. Special attention is paid

to the effects of time on this behavior.

In this paper, the words

low pressure

and high pressure Will be used; a numerical definition

of the threshold between these two domains cannot

be

given because the sensitivity of

* Project engineer, GE OD IA Offshore G eotechnical

Consultants,

16, rue M dric, Paris, France.

2 Charg de recherche Centre National de la Rech erche Scientif ique (CN RS ) and ma itre de confr-

ences, GEO NUM team, respect ively, Inst i tut de Mcanique de Grenoble, BP 68. 38402 St. Mart in

dHres, France.

290


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COLLIAT-DANGUS ET AL. ON TRIAXIA L TESTIiG OF GRANULAR SOILS

291

granular materials to mean stress is signif icantly dependent (as Wil l be shown) on the min-

eralogy of the sand particles, among other factors. For si liceous materials, the ce11 ressures

used in common practice of triaxial testing (lower than 1 MPa) cari be considered as defining

a low-pressure range, while higher pressure Wil l be considered as the high-pressure range.

Effe cts of End Lubrication and Slendem ess Ratio on Drained Com pression Triaxial

Tes ts: Low- and Higb-Pressure Range

Previous Works

End Restruint in Triuxial Test&--The basic requirements for reliable triax ial testing are

controlled specimen preparation to ensuring reproducible initia l state, complete saturation

of the specimen, well-centered axial load, negligible friction on the loading ram, well-

controlled ce11and pore pressures, and accurate measurements of axial load, axial defor-

mation, and volumetric change. These requirements are easily fulfilled as far as research

tests in the low-pressure range are concerned. However, lesssatisfactory test conditions cari

be encountered when dealing with industria l tests or with high-pressure apparatus.

Beyond these basic requirements, additional specifications to improve the homogeneity

of the test have been proposed by several workers. End restraint was recognized, a long

time ago, to be responsible for strong heterogeneous responses, such as barreling and

localization of deformation along failure planes. Bishop and Henkel discussed this point in

their c lassic book [Z]; it was also underlined by Sowers in the introductory paper of the

ASTM symposium on laboratory testing of soils in 1963 [2]. Roscoe and co-workers con-

ducted a series of tr iaxia l compression and extension tests, with measurements of axial and

radial strains, revealing severe nonuniformities throughout the specimen [3]. Kirkpatrick

and Belshaw showed experimentally the existence of rigid cones inside the specimen due

to end restraint [4].

Because the triaxial test is an elemental test, performed to obtain mechanical properties,

the specimen should be perfectly homogeneous. From a more technical point of view, the

area correction that is necessary to take into account the radial variation of the specimen

during the test in order to calculate the actual axia l stress (and estimate the membrane

action on the actual lateral pressure) cari be obtained from axial and volumetric strains only

as long as the specimen shape remains cylindrical. In other cases, additional assumptions

must be made: cylinder of average area [5] or more realistic generant shapes, such as

parabolic or sinusoidal ones.

Lubricated End Platens and Slenderness Ratio-Antifriction devices were designed and

tested in order to suppress end-restraint effects. The most popular device is lubricated end

platens, using one or several rubber disks, coated with silicone grease in contact with the

polished steel platens. Such devices were developed by Bishop and Green [5], Rowe and

Barden [6], Biarez [7], and others.

If the antifriction device works, the slenderness ratio (length to diameter) should have

no effect on the test results; actually, the value of this ratio varies over a wide range from

one author to another. Most authors recommend use of rather short specimens, with enlarged

lubricated ends [6,8-241 essentially because this arrangement allows one to suppress the

rigid cones, and then to improve the homogeneity of the test up to large axial strains. A

theoretical study by Vardoulakis indicated that, regarding the bifurcation from the homo-

geneous deformation mode (cyl indrical shape) to an axisymmetric diffuse heterogeneous

mode, the bifurcation stress generally increases by decreasing the slenderness ratio; hence,

shorter specimens would tend to shear more homogeneously up to large strains [15].


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ADVANCED TRIAXIAL TESTING OF SOIL AND ROCK

A typ ical result of the improved boundary conditions in triaxial tests on dense cohesionless

materials is to smooth out the pronounced peak observed commonly in classic ests. Most

published results of lubricated-end tests on dense sand show a soft maximum in the curved

stress ratio (aI/o,) versus axial strain, followed by a slight softening. Some authors consider

that this softening is due to remaining imperfections and present results from improved tests

without any decrease in stress ratio 191.

Strength

Parameters-Regarding the influence of the modified test conditions on the

strength parameters, various opinions are expressed in the literature. Bishop and Green,

concluding a very detailed experimental study in 1965 on that question, estimated that, as

long as the slenderness ratio is 2, conventional and frictionless ends give the same friction

angle at peak stress; shorter specimens give higher angles, unless Perfect end lubrication is

provided [5]. The value corresponding to

LID

= 2 is estimated to be the truc friction

angle. Many authors disagree with these conclusions and conclude from their own experi-

ments that the friction angle with conventional ends is always slightly higher [6,11,16,17].

Drescher and Vardoulakis, in a theoretical analysis based on a static method of slices ,

corroborate these findings [18].

Bedding Error-Although there is general agreement on the use of lubricated platens and

a slenderness ratio reduced to 1 (essentially because of the improved homogeneity of the

test), another specific problem concems experimentalists -the so-called bedding errer. Bed-

ding errer is related to the measurement of the axial strain at the very beginning of the test;

it is due to the deformation of the antifriction device which is generally much more com-

pressible than the specimen. Several recent works are devoted to this problem [9,16,19].

For drained compression tests, using specimens with a slenderness ratio of 2, the bedding

error cari lead to ini tial moduli 60% lower if frictionless conditions are used [5,6,11,14].

However, the end-restraint effect cari, in turn, induce an overestimation in the modulus

[27]. Goldscheider attempted to determine a correction to be applied to the axial strain by

evaluating the difference between conventional and lubricated tests [19]; the scatter of the

results is significant. Other authors use a local measurement of the axial strain in the central

part of the specimen for calculating the initial modulus [9].

Current works devoted to bedding errer by the authors research team Will not be discussed

here. (This topic is reviewed in Ref 20; related information cari also be found in Ref 21.)

Experiments

Description of the Problem-The experiments reported in the first part of this paper were

perfonned as a preliminary study, with the intention of determining what test conditions

should be used in an experimental program on calcareous sand tested in drained triaxial

compression under elevated ce11pressures. TO the authors knowledge, the only work on

soi ls for pressure ranges up to 10 MPa was published by Roy and Lo in 1971 [14]. The

conclusions of that work were favorable to the use of improved test conditions for the same

reasons as apply to the low-pressure range: improving the specimen shape (cylindrica l) at

the end of the test and preventing the premature development of predominant failure surface.

Nevertheless, the idea that test refinements are unnecessary for high-pressure range sti ll

remains common; in the last 20 years, many high-pressure tests have been performed with

conventional conditions, namely rough platens and LID = 2 [22-271.

Hence, the purpose of the preliminary study was to control the effects of improved test

conditions, especially into the high-pressure range.

Moreover, the recent theoretical and experimental advances related to bifurcation analysis


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COLLIAT-DANGUS ET AL. ON TRIAXIA L TESTING OF GRANULA R SOILS

293

(diffuse heterogeneous mode, localization) gave a new motivation in questioning the ho-

mogeneity of tests, as attested by recent work [15,18,28-311. A number of experimental

techniques have been used to control the homogeneity of tests and detect actual localization;

however, in the classic triaxial test performed on cylindr ical specimens only the external

surface of the specimen cari be directly observed. How cari one be sure that an apparent

homogeneous deformation mode (cylindrical shape) does not actually conceal a heteroge-

neous mode of any kind? Tomodensitometry, a recent technique using an x-ray scanner.

cari provide an insight into the interna1 homogeneity. Orig inal tests performed using this

technique are reported hereafter.

Test Procedure-The test conditions compared were: (1) conventional ends, LID = 2;

(2) lubricated ends, LID = 2; (3) lubricated ends, LID = 1. The material used in this

preliminary study is Hostun (Drme, France) RF Sand, a fine angular siliceous Sand, uni-

formly graded (Fig. l), with Ds = 0.32 mm, uniformity coefficient = 1.70, minimum and

maximum volumetric weights of 13.24 and 15.99 kN/m3, respectively, and grain specific

gravity of 2.7.

Some tests in the preliminary study and half of the tests in the high-pressure study reported

in the second part of this paper were performed on a calcareous Sand, referred to here as

SC. Figure 1 shows the grain s ize distribution of this second material, a well-graded Sand,

with D5,, = 0.17 mm, C. = 2.80, yd ranging from 9.81 to 13.01 kN/m3, and G, = 2.67.

The specimens were air pluviated at a constant drop height, from zero (relative density

about 20%) to 1 m (relative density of 90%). This technique ensures homogeneity and

reproducibility of the initia l density.

The radius of the specimens was 100 mm for the low-pressure tests. The specimens were

axia lly strained at l%/min in drained conditions. The membrane was 0.4 mm thick. Mem-

brane correction was applied. The antifriction device used consisted of polished steel platens

(larger than the specimen) and two rubber disks, 0.4 mm thick, coated with s ilicon grease.

Drainage was ensured by a B-mm central porous stone on each platen (see Fig. 7). Axia l

and volumetric strains were calculated from the global height and volume, as 1

= - Log( Hl

HO) and E, = - Log( VIV,) (positive compression).

gravels sands

silts

clays

:.Y

%Y

,(-)&o 2 * aas? as? 9 E

ASTM


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Hereafter, the loose and dense densities refer to the relative densities given in the

preceding paragraph.

Strength Param eters and General

Features-Figure 2 illustrates the typica l stress ratio

versus strain curves obtained for dense and loose specimens under 90 kPa of lateral pressure

for various test conditions.

In good agreement with previous works, the main features observed are:

1. Conventional test conditions (nonlubricated ends,

LID

= 2) on dense specimens lead

to a pronounced stress peak (Fig. 2a, dashed line); shear banding cari be seen on the

specimen. Simultaneously, the increase of the volumetric strain is abruptly stopped (Fig.

2b, dashed line). Moreover, these conventional tests are very sensitive to imperfections.

For example, the dotted line in Figs. 2a and b gives the results for a second conventional

test, identical to the first one except that it had a slight centering fault of the specimen; the

peak stress s significantly lower, and furthermore the volumetric strain stoos much sooner,

indicating very early localization effects.

l 1

0,oo

qo5

0,lO

0,15 0,20 0,25 0,30 035

a

AXiAL STRAiN > El

>

w-

0,05 1

I----I

0,oo

0,05 0,lO 015

0,20 0,25

0,30

0,35

b

AXiAL STRAiN , El

FIG. 2-Influence of the test cond itions on the stress ratio a nd volum etric strain curves, (a,

hj for dense sand and (c, d) for loose Sand.


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COLLIAT-DANGUS ET AL. ON TRIAXIA L TESTING OF GRANULAR SOILS

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2. Lubricated platens and reduced slenderness ratio give a much smoother curve in both

diagrams (Figs. 2a and b, solid lines). The specimen remains nearly cylindrical, although a

diffuse heterogeneous mode of deformation cari be observed in some cases (conic shape).

Improved homogeneity is attested by the much larger dilatancy strain at the end of the test;

on the other hand, the peak strength and the residual strength are not significantly different

from those obtained in classic ests.

3. Classic slenderness LID = 2 associated with lubricated ends leads to iess eproducible

results than reduced slenderness ratio. This is due to the development of an axisymmetric

mode of diffuse heterogeneous deformation, extended to only a part of the specimen (Upper

or lower part). This produces a strength underestimation (Fig. 2a, mixed line), and a

truncated volumetric strain evolution (Fig. 2b).

For loose specimens, Figs. 2c and d show only slight differences between the tests con-

ducted with lubricated ends and LID = 1 or 2. The results of the conventional test are

somewhat different, showing much less contractancy and a slight softening.

Figure

3a

is a summary of the effects of test conditions on strength (peak stress), in terms

of friction angle versus mean normal stress. Two sets of points cari be distinguished, referring

1

r

oose sand 1 _

i

CT3=90kPa 1

0,oo 0,05

o#lo

AXiAL

os5 0,20 0,25 0,30 0,35

C

STRAIN , El

------ -- non-lubricated

ends - H/I)

= 2

3 -0JO -

-

.-

$- -0,05 -

0

-

cr

0,05

0,oo

d

0,05 OJO 035 0,20 0,25 0,30 0,35

AXiAL STRAIN , El

FIG. 2-Conrinued.


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296 ADVAN CED TRIAXIAL TESTING OF SOIL AND ROCK

l3 N VkllS 1VlXV MV3d


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COLLIAT-DANGUS ET AL. ON TRIAXIA L TESTING OF GRANULAR SOILS

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t

I I I I I I

23

0.

i

si

0

I

8

d

I

3PhP 31W A3NVlVllCl >1V3d

5:

0

0


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ADVANC ED TRIAXIAL TESTING OF SOIL AND ROCK

to dense and loose specimens. In both cases, the most prominent feature is the decrease of

the friction angle with the mean stress; the influence of the test conditions is limited to a

few degrees (maximum 4) on the friction angle, while the error due to reproducibility of

the tests, especially in conventional tests and at very low mean pressure, is of the same

order. However, significant variation of the peak axial strain is shown in Fig. 3b, depending

on the test conditions; rough ends induce earlier peaks, as was illustrated in Figs.

2a

and

c. In the same way, but much more marked in dense specimens, the volumetric strain at

the final stage of the test is sensitive to the test conditions (Fig. 3~). This sensitiv ity is due

to almost unavoidably truncated volumetric strain evolution in the conventional tests (due,

in tum, to the localization). This leads to nonsignificant final volumetric strains, as confirmed

by the large scatter observed for conventional tests on the figure. With regard to the dilatancy

rate at peak (Fig. 3d), despite a moderate scatter, it cari be concluded that there is no

significant influence of the test conditions.

These results cari be summarized as follows: rough ends induce restraint, leading to (1)

slightly increased initia l modulus and peak strength (if no premature localization) and (2)

strong tendency to localize, from which neither reliable final volumetric strain nor peak

strength cari be determined; dilatancy rate under a11conditions is more or less the same

before localization occurs. Reduced slendemess ratio allows improved specimen homo-

geneity with regard to the diffuse modes.

High-Pressure

Range-From a comparison of Figs.

2a

and

b

(dense, dilatant) with Figs.

2c and

d

(loose, contractant), one car i hypothesize that the end lubrication and slendemess

effects have less and less nfluence at higher pressures (inducing lower dilatancy). Actually

this is not true, as was shown by comparative tests performed at a lO-MPa ce11 ressure, on

both siliceous and calcareous sands.

The test procedure is described in the second part of this paper. Quite similar results were

obtained for this comparison on loose and dense, HF or SC sands; only the HF dense case

Will be presented.

The comparison between the improved test (sol id line) and the conventional test (dashed

line) is shown in Fig. 4. In the latter, marked barreling was observed, followed by a mul-

tisurface localization. The stress ratio versus axial strain curve has a maximum followed by

a slight softening. In the improved test, the specimen remained cylindrica l up to 50% axial

strain, without discernable localization. The stress-stra in curve shows a monotonie increase

in this case. This could be stated to be the tme elementary response of the material.

The initial modulus is, again, higher in conventional tests (up to 30%). The volumetric

strain curves do not have systematic differences; as n the low-pressure range, the volumetric

strain mobilization seems to be faster, leading here to slightly higher contractancy, despite

the heterogeneity (barreling, localization). The heterogeneity of the volumetric strains in

high-pressure tests Wi ll be discussed n the next section.

Tomodensitometric Survey of the Interna1 Hom ogeneity-The x-ray scanner, well known

for its medical applications, is beginning to be used in the engineering domain. For dry sand

specimens, a simple correlation cari be established between the local x-ray attenuation and

the local compactness; proper calibration for each specific material is required if quantitative

measurements are desired.

Briefly, an x-ray scanner irradiates the abject to be examined, through a range of angles

of incidence. Only a thin slice of the abject is irradiated. For each incidence, the transmitted

x-ray beam is recorded behind the abject by detectors, giving a profile of the integrated

local attenuation along parallel paths inside the slice. From the combination of these profiles,

one cari compute the local attenuation in elementary volumes (voxels). The attenuation


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COLLIAT-DANGUS ET AL. ON TRIAXIA L TESTING OF GFIANUIAR SOILS

299

0

_-.-

1=q/upm

~-

1

-----em____

bricated e% xm-Hz? j

ted ends - H/D=l

-

J -

1 I

l

0 o#lo

920

0,30 0,LO

0,50

AXiAL STRA iN , El

z

qoo

z

2

0,lO

22

E

Y

3

P 0.m

1 I

FIG . 4-Conven tional and improved tes ts under high ce11 ressure.

is affected by the mass density, depending on compactness and minera1 density. Because

the minera1 density is unaffected, the degree of compactness is the variable goveming the

attenuation. A map of the compactness in a cross-section of the sand specimen (averaged

over the thickness of the slice) cari then be obtained.

Practica lly, some difficulties in the numerical process cari result from complicated geo-

metric shapes or very dense inclusions. This leads to completely distorted pictures. The

cylindrical shape of the authors specimens is the optimum. Another difficulty is due to the

modification of the spectrum of the x-ray beam in the first millimeters of their path inside

the material. The less penetrating part of the radiation is absorbed in this zone, while the

remainder goes through the sample; this skin effect gives an overestimated attenuation

(compactness) near the boundary of the section; it cari be avoided by special devices, or

corrections, but the results presented here were obtained without any special disposition.

Hence, the easily discernable extemal white halo should be neglected when evaluating the

results.

Al1 the figures presented were directly photographed on a cathode ray tube (CRT) display.

They cari be interpreted as classic x-ray photographs. In the picture, the darker a zone is,

the looser the material inside that zone is. When profiles are shown, they concem the

attenuation along the zone indicated by dotted lines on the picture. Differences in lightness

and darkness are to be interpreted in relative terms, because the system was not calibrated.

1. Conventional versus improved test conditions on dense HP sand

A special apparatus, designed to allow the tomodensitometric survey of a specimen during

a triaxial test, consists of a rather rustic, manually operated mechanical press. The confining

pressure is produced by atmospheric pressure on the dry specimen under vacuum. After a


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ADVA NCED TRIAXIAL TESTING OF SOIL AND ROCK

given loading step, the specimen cari be unloaded and, stil l under vacuum, removed from

the apparatus and placed in the scanner. It is then possible to control the homogeneity of

the compactness over the specimen at several stages of the test.

Figures

5a

and b show the density inside the conventionally tested specimen, rough ends

and LID = 2, at 10% axial strain. At this stage, a typical failure surface could be directly

observed outside the specimen. In Fig.

5a

a cross-section is shown at the middle height of

the specimen (Z = 10 cm); the failure surface appears clear ly as a dark straight line on the

picture. Darker means looser, SO his figure confirms the strong dilatancy observed inside

the shear bands under low mean pressure, reported in a number of works about strain

localization [28,30,31]. In Fig. Sb another cross-section is shown, a few centimeters below

the Upper platen (Z = 15 cm). The brighter central zone, surrounded by a gray ring, is the

section of the less deformed central cane, induced by end restraint (little dilatancy). More-

over, the failure surface appears to be distorted; this indicates that, during its development,

the surface could not penetrate the rigid zone, but had to pass around it. TO the authors

knowledge, this observation is original. Although indicating only relative values, the density

profiles deserve comment: the lower density, recorded inside the failure surface, is quite

the same in both sections (1670 units); the mean value outside the surface: in the central

section of Fig. 5a, is about 1730, while the value in the r igid cane, in Fig. 5b, is markedly

denser (1880). (These units are uncalibrated, but in monotonie increase with compactness.)

For the improved tests (lubricated ends, LID = l), a question arises: does a specimen

that remains cylindrical after deformation conceal some strong interna1 heterogeneities? As

FIG. 5- Conve ntiona l test: (top) Z = 10 cm, (bottom) Z = 15 cm.


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COLLIAT-DANGUS ET AL. ON TRIAXIAL TESTING OF GRANULAR SOILS

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Wil l be discussed, some heterogeneities do exist, but these are much smaller and limited

than in the conventional test.

Figure 6a shows a section from just beneath the Upper lubricated platen; this rather

surpris ing picture reveals that a very small rigid cane is generated by the small porous stone

placed for drainage at the tenter of the platen. In Fig. 7, a schematic of the actual arrange-

ment, the cane is bordered by a failure surface, clearly identified by its high void ratio (dark

circle in Fig. 6~2).The density measure is, again, about 1650 units. The half angle of this

cane car i be estimated at 25 from another cross-section, 1 cm beneath, as shown in Fig. 7.

This cane, being only a local perturbation, cannot affect significantly the overall measure-

ments.

Figure 6b shows the central cross-section (2 = 5 cm) of the specimen sheared at 20%

axial strain. No failure surface is revealed inside the specimen, despite the large axial strain.

However, a diffuse heterogeneity is observed, namely a denser small zone in the middle of

the specimen (1800). The remainder is in a more or less homogeneous loose state, only

slightly denser (1700) than the density measured inside the failure surfaces. This supports

the idea of a cri tica l void ratio, which cari be reached immediately after localization inside

the shear bands, or at large strains in the homogeneous specimens. No clear explanation of

the denser central zone is proposed; further experiments are needed to clarify that point.

2. High pressure tests on calcareous sand

The SC specimens, once consolidated and strained under lO-MPa ce11pressure, remain

sufficiently cohesive to be easily handled. It is then possible to put them, once dried, inside

FIG. 6-Improved test: (top) Z = 8 cm, (bottom) Z = 5 cm.


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302


E

loading cap

lubrication

cross section

\ layer

.-.-.---.

-+.- .-.-. -.

lateral

+.--membrane

FIG. 7-Lubricated end, porous stone and x-ray cross-sections.

the scanner. Figure 8 shows a section of such a specimen, along its axis (not a cross-section).

The specimen was sheared to extreme strain (50%). A typical barrel-like shape is observed,

but the most interesting result is the effect of end restraint: the rigid cones remain

significantly looser than the other parts of the specimen. This result is quite reasonable

because the material in these cones undergoes less stress and strain, and therefore less

contractancy; however, it is commonly assumed that high mean pressure erases any restraint

effect. It is shown here that the heterogeneity of strains, and therefore of particle crushing

and alteration, is severely affected by restraint.

These tomodensitometric results confirm in a unique way that the lubricated ends and

reduced slenderness ratio ensure improved (but not Perfect) homogeneous behavior in

triaxial tests, in both the low- and high-pressure ranges.

High-Pressure Triaxial Tests

Test Procedure

Consolidated drained (CD) compression triax ial tests were performed under elevated ce11

pressures (up to 15 MPa) on both materials already used in the preliminary study: the

siliceous HF sand and the calcareous SC Sand.

FIG. 8-Transverse sectio n of a specimen tested under high pressure and under conventional

conditions.


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COLLIAT-DANGUS ET AL. ON TRIAXIAL TESTING OF GRANU LAR SOILS

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902

0.03

qo4

1

o#lo

O,ll

,

w

_ q15


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304

ADVANCE D TRIAXIAL TESTING OF SOIL AN0 ROCK

2,50 ,

i-

l

0

.O

-0-o -

SOkrn

0--

2

,--o--o-

1

/

_ _ _ _ _ - - - - - - - T - - e

lQ 2k@a

- c - - -

/ - -

1~50 AXIAL STRAIN 8 t

1dense calcareous sand SCD1

-------LA

------4-d-_-

3COkFb

--.-

1

FIG. Il-Stress-strain-volume change curves-dense calcareous San d.


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COLLIAT-DANGUS ET AL. ON TRIAXIA L TESTING OF GRANULA R SOILS

305

.A11 tests were performed on saturated specimens. Full saturation of the specimen was

achieved by a precirculation of carbon dioxide gas and application of a back pressure of 300

kPa; this back pressure was kept constant during the test by a self-compensating mercury-

pot system.

Al1 tests were performed under constant confining pressure. Specimens tested at confining

pressure below 5 MPa were enclosed in a high-quality neoprene membrane, 0.5 mm thick;

for higher pressures, two membranes were used. No membrane correction wab applied.

Except in some specific cases, a11 he specimens were sheared at constant strain rate l%/

min, up to large axial strains (50%).

Test Resul ts

The behavior of granular materials was studied for both stagesof the triaxial test: isotropic

compression and triaxial shear. The specimens Wil l be referred to as HFD, HFL, SCD, SCL

tith D and L for dense and loose, respectively, initial compactness.

Time Effects on Granular Materials Under Isotropic

Compression-Previous work has

shown that under elevated confining pressures the compression of sand is not instantaneous

but continues at an ever-decreasing rate over a long period of time, in a way similar to the

phenomenon of secondary compression observed in clays [21,22].

Creep tests, in which the confining pressure was kept constant for 24 h, were performed

to characterize time effects on the compression of granular materials. Typical results, pre-

sented in the class ic semi-log graph (eVversus Log t), are given in Fig. 9. A time effect is

clearly shown, analogous to a viscous phenomenon at a macroscopic scale.

dense s~keous sond HFD/

-l

?AIN , E l

0.60

FIG. 12-Stress-strai*voIume change curves-dense si liceous Sand.


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306


The slope of the secondary compression (that is, the increase in volumetric strain, AE,,

measured between 1 h and 24 h of consolidation), is represented versus the confining pressure

in Fig. 10. Despite a certain extent of scattering in the results obtained, it is shown that this

time effect increases with the confining pressure. For siliceous sand HF, the compression

may be considered instantaneous as long as the pressure is lower than 2 MPa, while, for

calcareous sand SC (composed of fragile particles), time effects occur even at very low

confining pressures.

From these results, a threshold in stress level cari be defined, corresponding to a Sharp

increase in time effect: about 0.8 MPa for the calcareous sand and 6 MPa for the si liceous

one. This threshold car i be called a creep stress,

with reference to the so-called creep

load defined from static pile loading tests.

Grain size analyses, performed at successivestages of the creep tests, showed that time

effects are correlated to grain crushing [32]. Hence, the propagation of the rupture of

particles may be the physical factor responsible for time effects on the compression of

granular materials under elevated stresses. Further research is needed to g ive firm conclu-

sions on that point; nevertheless, it car i be stated that the mineralogy of the particles affects

the value of the creep stress.

Triaxial Shearing Under High Pressures-Figures 11 and 12 give typical stress-strain-

volume change behavior for dense HF and SC sands. The decrease of the friction angle

when increasing the mean stress applied to the specimen is shown in Fig. 13. It is worth

comparing the friction angle measured in the high-pressure range with the so-called char-

- 0,70

-0,60

-0.50

nT

2 -0,40

g -0,30

CY

$

Q

-0,20

.zj -0,lO

2 0,oo

a

OJO

0,20

OS l,O

10

MEAN NORMAL STRESS , (Jm (MFU

FIG. l3-Stress peak friction angl e evolu tion with mea n pressure.


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307

acteris tic angle and the interparticle friction angle. The characteristic angle is defined by

Luong and Touati as the mobilized frict ion angle when the minimum in volume change is

reached in the first stage of low-pressure triaxial tests on dense material [27]. As far as

siliceous Sand is concemed, the actual friction angle does not decrease below these bounds

(32). On the other hand, for calcareous Sand, frict ion angles obtained at high mean pressures

are clearly smaller than the characteristic angle (4, = 39), and than the interparticle friction

angle (4, = 38), the latter determined indirectly on the basis of Rowes stress dilatancy

theory. This means that, for calcareous sands, with high compressibility linked with intra-

particle porosity and brittleness of their grains, the interparticle friction angle, $,, cannot

be considered as a lower limit for the friction angle.

Figures 11 and 12 show that the compressibility of granular materials under triaxial shear

reaches a maximum value and then decreases in the high-pressure range. This behavior is

also shown in Fig. 14 giving the evolution of the rate of volume change at peak stress: at

very high pressures, the rate of volume change at peak becomes zero. This reduction of

Sand compressibility at the peak is related to the transformation of the material that occurred

during the consolidation stage, as pointed out by Billam [33]. If the total volume changes

due to both confining stage and shear stage of the test are considered. a monotonie increase

with increasing pressure is observed (as expected).

P

5

l

0 0

.Y0 O

-,o

. .

.

l,O

10

MEAN NORMAL STRESS < &, (MPa)

FIG. 14-Stress peak dilatancy rate evolution with mean pressure.


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308

ADVA NCED TRIAXIAL TESTING OF SOIL AND ROCKDVANC ED TRIAXIAL TESTING OF SOIL AND ROCK

Odense sand 1dense sand 1

q loose sand \loose sand \

after CD triaxial testfter CD triaxial test

Odense sand 1af ter isotropic compressiondense sand 1af ter isotropic compression

n loose sand \loose sand \

C - % finer than initial dl0- % finer than initial dl0

C

100

2

t

e

1

0)

10

MEANONORMAL STRESS , C&m MPa)

100

FIG. 15-Grain crushing evolution with mea n pressure.

For granular materials, grain crushing is the main cause of compressibility under elevated

pressures. Figure 15 gives typical features of both siliceous and calcareous sands. The classic

behavior is recognized here (that is, the main part of grain crushing occurs during the shearing

stage of the triaxial test). The magnitude of crushing is expressed in terms of a crushing

coefficient, C,, defined as 0.1 times the percentage of partic les finer than D,, of the original

Sand. For both sands, grain crushing begins at very low pressure, because of the brittleness

of the calcareous particles and the angularity of the siliceous particles. With higher pressures,

the rate of grain crushing decreases, which is responsible for the decrease in compressibility

already described.

Conclusions

The use of short specimens (ZJD = 1) with lubricated enos ru rlldxial

test is preferable to the use of conventional specimens (nonlubricated ends, LID = 2) for

the determination of stress-strain parameters, because of the improved homogeneity. This

improvement was discussed along these lines, on the basis of global considerations (global

response, specimen shape), and local measurement (x-ray scanner).

Despite the problem of bedding error, these modified experimental conditions were es-

timated to be particularly advantageous, with regard to the following objectives:

0 Uniform distribution of stress nside the specimen, for the study of grain-crushing effect

0 Homogeneous deformation of the specimen, for measurement of significant volume

changes

0 Large axial strains (> 10%)

0 Elevated confining pressures (> 1 MPa)


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309

Clas sic behavior wa s obtained for two type s of granular materials of different mineralogic

com position, tested under elevated confining pressu res: decrease of the friction angle and

high com pressibil i ty related to grain crushing.

In the case of calcareous sand s, characterized by a very high com pressibil i ty, due to the

intraparticle porosity and the brittleness of their grains, the friction angle ma y decrease far

below the interparticle fr iction angle, previously considered as a lower l imit,

Finally, time effe cts (creep) observed during the confining stage of tr iaxial tes ts increase

with the increasing pressure applied to the specim en and seem to be related to the propa-

gation of the rupture of particles.

Acknowledgment

Thanks are due to Pleybert and Mart in, who gave us acces s to and operated the x-ray

scanner of LET I, Centre dtudes Nuclaires de Grenoble, Franc e.

References

[l ] Bishop, A . W . and Henkel, D. J.,

The Measurement of Soi1 Properties in the Triaxial Test,

Edward

Arnold, London, 1957.

[2]

Sowers, G. H. ,

Laboratory Shear Testing of Soi/s, STP

361, Ame rican Society for Testing and

Ma terials, Philadelphia, 1963, pp. 3-21.

[3] Rosc oe, K. H., Schofield, A. N., and Thurairajah, A.,

Laboratory Shear Testing ofsoils, STP

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361, Am erican Societv for Testing and Mate rials, Philadelphia. 1963, pp. 111-128.

I-j

171

PI

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[III

Kirkpatr ick, W . M . and Belshaw, D . J.,

Geotechnique,

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_ .-.- *. -.

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[IZ] Olson, R. E. and Campbel l , L. M. ,

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[13] l7aj;u.V. S., Sadasivan, S. K., and Ventakaraman, M. ,

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[Id] Roy, M. and Lo, K. Y.,

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Vardoulakis,

I., Acta Mechanica,

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Lade, V.,

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I., Geotechnique,

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Results of the International Workshop on Constitutive Relations for Soi & 6-8

Sept. 1982, Gudehus, G. et al . , Eds., Balkema, RotterdamiBoston, 1984, pp. 11-54.

Dendani, H., Flavigny, E., and Fry, J. J., in this volume, pp. 486-500.

Col l iat-Dangus, J. L., Desrues, J. and Flavigny, E..

Revue Franaise de Gotechnique, No. 34,

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[23] Bishop, A. W ., Webb, D. L., and Skinner. A. E . in

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Soi1 Mec hanics and Foundation Engineering, Mon treal, Un iversity of Toronto Press , 1965, pp.

170-174.


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ADVANC ED TRIAXIAL TESTING OF SOIL AND ROCK

[24] Ram amurthy, T., Kanitkar, V. K., and Prakash, K.,

Indian Geotechnical Journal,

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[25] Ram amurthy, T. and Lai, R.

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[27] Luong, M . P. and Toua ti, A., Revue Franaise de Got&hnique, No. 24, 1983, pp. 51-64.

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Triaxial Testing of Granular Soil (Colliat-Dangus, 1988)

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