1999-Cuccovillo, T , Coop, M R (1999)

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On the mechanics of structured sands
T. CUCCOVILLO� and M. R. COOP{
To date the effect of structure on the behaviour
of natural sands has focused almost exclusively
on the component of bonding, and the effect of
fabric has been largely overlooked. The paper
describes a detailed investigation of the beha-
viour of two natural sands by means of triaxial
testing over a wide range of pressures. One
material had bonding as the principal element
of its structure and the other fabric. Following
on from a paper of Cuccovillo and Coop which
examined the in¯uence of the two structural
elements on the small-strain stiffness, the cur-
rent paper develops a new framework for the
yielding and large-strain behaviour. It is sug-
gested that structure should be considered as an
element of the nature of a sand in addition to
properties such as mineralogy, particle shape
and grading. The resulting framework is then
capable of encompassing the patterns of beha-
viour seen for both bonding- and fabric-domi-
nated sands. While bonding results in a cohesive
mode of shearing, it is demonstrated that when
fabric dominates, the shearing behaviour re-
mains predominantly frictional, although the
rates of dilation and peak strengths may be very
much higher than for the reconstituted soil at
the same stress±volume state. It is shown that it
is not necessarily the position of the state of the
soil relative to the critical-state line that distin-
guishes strain-hardening and strain-softening be-
haviour, but the proximity to the boundary
determined in isotropic compression.
KEYWORDS: fabric/structure of soils; laboratory
tests; sands; soft rocks.
Jusqu'ici, l'effet de structure sur le comporte-
ment des sables naturels s'est axe presque ex-
clusivement sur le composant de liaison; l'effet
de la texture a eÂte le plus souvent oublieÂ. Cet
expose deÂcrit une eÂtude deÂtailleÂe du comporte-
ment de deux sables naturels au moyen d'essais
triaxiaux dans une vaste fourchette de pressions.
Pour l'un des mateÂriaux, le composant de liaison
eÂtait l'eÂleÂment principal de sa structure et pour
l'autre, c'eÂtait sa texture. Faisant suite aÁ une
eÂtude de Cuccovillo et Coop qui avaient examineÂ
l'in¯uence des deux eÂleÂments structuraux sur la
rigidite de petite deÂformation, cet expose deÂvel-
oppe un nouveau cadre de travail pour l'eÂlasti-
cite et le comportement de grande deÂformation.
Nous suggeÂrons que la structure devrait eÃtre
consideÂreÂe comme un eÂleÂment de la nature d'un
sable en plus des proprieÂteÂs comme la mineÂralo-
gie, la forme et la taille des particules. Le cadre
de travail qui en reÂsulte est alors capable de
tenir compte des modeÁles de comportement con-
stateÂs pour les sables domineÂs par le composant
de liaison et les sables domineÂs par la texture.
Alors que la liaison donne un mode coheÂsif de
cisaillement, nous deÂmontrons que lorsque la
texture domine, le comportement au cisaillement
demeure en preÂdominance frictionnel bien que
les taux de dilatation et les reÂsistances de pointe
puissent eÃtre beaucoup plus eÂleveÂs que dans le
cas de sols reconstitueÂs et rameneÂs au meÃme
eÂtat de tension-volume. Nous montrons que ce
n'est pas neÂcessairement la position de l'eÂtat du
sol par rapport aÁ la ligne d'eÂtat critique qui
distingue le comportement de durcissement aÁ
l'effort et de ramollissement aÁ l'effort mais la
proximite de la frontieÁre deÂtermineÂe en com-
pression isotrope.
INTRODUCTION
The behaviour of sands in laboratory or ®eld tests
has traditionally been related to their relative den-
sity (Dr), but more recent work has highlighted the
de®ciencies of this approach. Experimental studies
in the triaxial apparatus (e.g. Coop & Lee, 1993;
Lade & Yamamuro, 1996) have shown that, pro-
vided suf®ciently high pressures are reached, it is
possible to identify a normal compression line
(NCL) which lies parallel to the critical state line
(CSL). It was then shown that strain-softening and
strain-hardening modes of behaviour were de®ned
not by Dr but by the combination of the speci®c
volume (v), mean effective stress ( p9) and deviato-
Cuccovillo, T. & Coop, M. R. (1999). GeÂotechnique 49, No. 6, 741±760
741
Manuscript received 30 July 1998; revised manuscript
accepted 30 June 1999.
Discussion on this paper closes 30 June 2000; for further
details see p. ii.� South Bank University, London; formerly City Uni-
versity, London.
{ City University, London.
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ric stress (q9) that de®nes the location of the state
of the soil relative to the NCL or CSL. This was
in accordance with a critical state framework and,
when associated with an analysis of the volumetric
changes in stress±dilatancy terms, could be used to
describe accurately the peak states observed. The
locations of the CSL and NCL were found to be
different for different sands (Coop & Cuccovillo,
1998) and were shown to be related to the amount
of particle breakage that the soil underwent during
loading and hence to the nature of the soil parti-
cles. This nature was considered to be the grading,
together with the mineralogy of the particles and
their shapes. One of the principal drawbacks of
this work was that it was almost all carried out on
reconstituted sands. Studies of the behaviour of
natural sands have, in contrast, been relatively rare,
particularly as a result of the dif®culty of retrieving
undisturbed samples.
Structure in sands has often been simply identi-
®ed with the bonding which arises from inter-
particle cementing, since interparticle forces are
negligible, and it is on this component of structure
that most recent research has been focused (e.g.
Clough et al., 1981). Cemented sands have been
seen to have patterns of behaviour that resemble
those observed for structured clays and which are
related to the elements of the soil structure created
by the geological processes experienced by the soil
since its deposition. State alone has therefore been
considered insuf®cient to account for those patterns
of behaviour which do not conform to the critical
state framework. To distinguish features of beha-
viour arising from structure from those related to
changes in state, an approach that has been widely
adopted has been to compare the response of the
natural soil to that of the corresponding reconsti-
tuted soil (e.g. Leroueil & Vaughan, 1990). Triaxial
test data for shearing of structured soils have often
been normalized with respect to the NCL and/or
the CSL of the reconstituted soil. Although this
approach has been very useful in highlighting
qualitatively many features deriving from structure,
it has failed to provide a uni®ed framework that
could identify and fully describe mechanical
features such as yielding, strength and a state
boundary surface for structured soils. Further de-
velopment of a consistent framework for natural
sands has been prevented by the dif®culty in
identifying a variable which could quantify struc-
ture, as p9, q9 and v do for state, and it is this
aspect of the mechanics of structured sands that is
a central theme of this paper.
For some cemented sands, in particular the
carbonates, the usual comparisons with the beha-
viour of reconstituted soils were not initially possi-
ble, ®rstly because it was dif®cult to reconstitute
the cemented soil without breaking its delicate
shell particles and secondly because the interpreta-
tion of the data was often complicated by large
variations in the properties of the intact samples.
This led some researchers to test arti®cially ce-
mented sands, making comparisons not with the
reconstituted soil but with soils made up of the
same constituents in which bonding had not been
allowed to develop (e.g. Huang & Airey, 1993;
Coop & Atkinson, 1993). Using this method,
Cuccovillo & Coop (1993) examined the in¯uence
of the strength of the cement bonds by varying the
amount of cement addedto an arti®cially cemented
carbonate sand. Fig. 1 shows a schematic represen-
tation of the isotropic compression behaviour they
observed. The effect of the cement was to make
the initial stress±strain behaviour stiffer and elas-
tic, so that the gradual yield seen for the loose
sand, which was attributed to the onset of particle
breakage, was not seen for the cemented sand. The
key difference in the behaviour of the strongly and
weakly cemented soils was that the former reached
states outside the intrinsic NCL de®ned by the
uncemented soil, while the weakly bonded soil
yielded before reaching the NCL. During shearing,
three modes of behaviour could be identi®ed, as
illustrated in Fig. 2, depending on the initial state
of the sample relative to the yield curve of the
cement bonds. At con®ning pressures which were
low relative to the strength of the bonds, the
behaviour was elastic up to a well-de®ned yield,
followed by strain-softening towards a critical state.
At intermediate pressures, yield occurred before
reaching the critical state, so no peak strength was
seen and the failure was essentially frictional. The
only effect of the bonding at these intermediate
pressures was therefore a stiffening of the initial
stress±strain behaviour. At the highest pressures,
the behaviour was ductile from the start as the
Intrinsic isotropic
normal compression line
sw
v
ln p ′
w
s
Uncemented
Cemented
Weak
Strong
Fig. 1. Schematic comparison of the isotropic com-
pression of weakly and strongly cemented carbonate
sand
742 CUCCOVILLO AND COOP
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bonding had been broken during compression, and
the stress±strain behaviour tended towards that of
the uncemented soil. The effect of an increase in
the cement content was to expand the yield curve
of the cement bonds.
The type of framework shown in Figs 1 and 2
has been developed considering only the compo-
nent of soil structure arising from bonding. The
in¯uence of fabric has, however, been largely over-
looked, either because of a lack of data for intact
sands with their intact fabric preserved or because
of the belief that, unlike clays, this in¯uence was
not important for sands, even if Barton (1993)
identi®ed that for many coarse-grained soft rocks
the transition from a loose sand to a sandstone
involved not only the creation of bonding but also
changes to the fabric. This paper will discuss the
in¯uence of both aspects of structure on the mech-
anics of sands, comparing and contrasting the
behaviour of two sands, a calcarenite which has
bonding as the dominant structural feature and a
silica sandstone for which fabric is more impor-
tant. Cuccovillo & Coop (1997b) examined the
small-strain behaviour of the two materials, and
the current paper now extends that work to exam-
ine the behaviour at larger strains. In this investi-
gation some of the data for the calcarenite are
those from Coop & Atkinson (1993), which have
been reinterpreted in the light of the new methods
of analysis.
Yield surface
of cement
Critical-state line
1 2 3
Yield point
Critical state
1
2
3
q ′/p ′
M
q ′
p ′
εa
Fig. 2. Schematic diagram showing modes of shearing
behaviour for cemented carbonate sands (after Coop
& Atkinson, 1993)
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ON THE MECHANICS OF STRUCTURED SANDS 743
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SOIL DESCRIPTIONS
Table 1 gives a summary of the principal
characteristics of the two structured sands. The
silica sandstone was from the Lower Greensand
series and was recovered as a block sample from
about 5 m depth in a quarry near Maidstone, Kent.
The soil is characterized by strong particles bonded
by a weak cement. It was deposited during the
Cretaceous in a shallow marine environment
(Casey, 1961) and in its geological history it has
been subjected to deep burial followed by the
erosion of the overlying strata, so that it has been
overconsolidated, with a past maximum vertical
effective stress estimated to be around 9 MPa. An
iron oxide cement was then deposited around the
quartz grains at a late stage in the geological
history from groundwater ¯owing through the sand
(Warren, 1995). A scanning electron micrograph
(SEM) of a polished section is shown in Fig. 3.
The cement is the white material which appears to
weld the particles together. There is only a small
amount of cement present, and so the low speci®c
volume v of 1´45 is clearly related to the particle
packing, or fabric, and not to the in®lling of the
void spaces with cement. Apart from the relatively
small amount of cement, Dapples (1972) has iden-
ti®ed that the weakness of this type of bonding
results from the poor adhesion of the iron oxide to
the quartz.
Reconstituted samples of both the silica sand-
stone and the calcarenite were created by gently
breaking the cement bonds while avoiding damage
to the particles. For the silica sandstone Cuccovillo
& Coop (1997b) found it to be impossible to
recreate the intact speci®c volume by compaction of
the reconstituted soil. The only way that this could
be achieved was to overconsolidate the sample by
isotropic compression in the triaxial apparatus, but
the maximum stress of 70 MPa required to do this
was far in excess of that ever experienced by the
natural soil. The reason for the high density of the
silica sandstone in situ was identi®ed from an
examination of the thin section shown in Fig. 4,
which shows a well-developed interlocking fabric.
Dusseault & Morgenstern (1979) and Maxwell
(1964) have attributed the development of this type
of `locked' fabric in geologically old silica sands
(pre-Quaternary) to pressure solution at the particle
contacts, where the contact stresses are very much
higher than the overburden stress. This then allows
the particles to rearrange relative to one another,
creating large grain contact areas and achieving
particle packings which cannot be recreated when
the soil is reconstituted, as the original interparticle
contacts have been lost. This well-de®ned fabric
was therefore created while the soil was buried
Fig. 3. Scanning electron micrograph of the silica
sandstone (after Cuccovillo & Coop, 1997b)
Fig. 4. Thin section of the silica sandstone (width of
photo equivalent to 0´7 mm; plain white light and
stained void spaces)
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deeply and long before the cement was deposited.
The deposition of the iron oxide after the geological
overconsolidation and the development of the fabric
is then the reason why the bonds are still intact, as
the strains experienced by the soil subsequent to
these events were small. Although there is a natural
variation in thedegree of bonding of the Lower
Greensand, all the samples used in the current study
were taken from the same block and so had a
uniform speci®c volume and degree of bonding.
The calcarenite samples were retrieved by triple-
tube rotary coring and come from the site of the
North Rankin offshore platform in Western Austra-
lia. By comparison with the silica sandstone this
calcarenite may be characterized as having weak
particles and a strong interparticle cement. The soil
is a biogenic carbonate sand comprising shells
deposited in a warm coastal sea environment during
the Pleistocene. Thin sections of two of the samples
are shown in Fig. 5. The particles are angular,
resulting in an open fabric. Under the cross-polar-
ized light used to take the photographs, the void
spaces are black and the white fringe that surrounds
each particle is the cementing, which is calcium
carbonate deposited soon after the time of deposi-
tion of the particles. The type of shells and the
amount of cement deposited are both sensitive to
the precise depositional environment (Fookes, 1988;
Apthorpe et al., 1988), and since the rates of
deposition are slow, there are large and apparently
random variations in the nature of the soils over
small intervals of depth.
Most of the calcarenite samples were from
depths between 127 and 142 m. The variations
within this range of depths of both the particle
natures and the amount of cement deposited are
evident in Fig. 5 and result in a wide range of
speci®c volumes for the samples tested (1´68 to
2´03). Despite these differences, the soils, when
reconstituted, were found to have remarkably simi-
lar properties. Cuccovillo & Coop (1993) found
that a single state boundary surface could be
de®ned for all of the reconstituted samples tested.
Another important feature that can be seen qualita-
tively in Fig. 5 is the relationship between speci®c
volume and degree of cementing. The more heavily
cemented sample is much denser, partly as a result
of the in®lling of the void spaces with the cement.
The geological loading history of the soils has
been one of ®rst loading only, and since the in situ
stresses are well below those at yield, the cement
has preserved the depositional fabric.
Fig. 5. Thin sections of the calcarenites (width of photos equivalent to 1´4 mm; cross-polarized light): (a) loose and
weakly bonded; (b) dense and strongly bonded
ON THE MECHANICS OF STRUCTURED SANDS 745
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LABORATORY EQUIPMENT AND PROCEDURES
Triaxial tests were carried out in a variety of
apparatuses covering a range of stresses from
50 kPa to 70 MPa. Each of the apparatuses was
computer controlled and data-logged and is de-
scribed in detail by Cuccovillo & Coop (1999).
Most tests were instrumented with a new system
for the local measurement of the axial strain of the
sample based on miniature linear variable differen-
tial transformers (Cuccovillo & Coop, 1997a).
Combined with new sample preparation methods
and modi®cations to the setting-up procedure in
the apparatus to ensure the coaxiality of the axial
loading system with the sample (Cuccovillo &
Coop, 1997b), it was possible to resolve the stiff-
ness of the materials tested down to strains of
0´0001%. Although the data examined in this paper
are for larger strain levels, it was found that these
improvements were also necessary for a correct
de®nition of the yield point during shearing.
ISOTROPIC COMPRESSION
When isotropically compressed, the intact calcar-
enite reached states which were impossible for the
reconstituted soil (Fig. 6(a)) and from this point of
view the bonding may be characterized as strong
within the scheme shown in Fig. 1. A clear rela-
tionship existed between the speci®c volumes and
mean effective stresses at yielding, which resulted
in the identi®cation of an isotropic yield locus.
This was found to be substantially coincident with
the postyield compression curves and thus de®ned
the boundary for the possible states attainable in
isotropic compression. The offset between the iso-
tropic boundaries of the intact and reconstituted
soils reduced as the speci®c volume decreased,
until the two boundaries became coincident. The
isotropic boundary of the intact soil has therefore
been modelled as bilinear, as indicated. One group
of four samples, from a narrow depth range
(133´7±135´5 m), was found, however, to have
yield points which lay signi®cantly below those of
all the other samples (Fig. 6(b)) and closer to the
intrinsic NCL de®ned by the reconstituted samples.
This is characteristic of a weaker bonding, which
is likely to have resulted from a depositional
environment that was signi®cantly different from
those in which the other calcarenites were created.
As none of these weaker samples was loaded far
beyond yield, the postyield compression line which
is shown, and will be used in later analyses, has
been assumed to converge with the intrinsic NCL
at the same point as for the stronger-bonded soils.
For the silica sandstone, isotropic yielding oc-
curred inside the permissible space of the reconsti-
tuted soil (Fig. 7) and this material may therefore
be classi®ed as a weakly bonded material. The
isotropic boundary of the silica sandstone, there-
fore, is likely to coincide with the NCL of the
original uncemented soil as it was deposited in the
ground. However, the soil as deposited would have
had a slightly different initial grading from that of
the current reconstituted soil because of the parti-
cle breakage that the soil underwent under the high
overburden pressure which this soil, unlike the
calcarenite, had experienced before it became ce-
mented. As was shown by Coop & Atkinson
(1993), the location of the NCL of a soil is
controlled by the initial grading, not the current,
and a correct comparison between the compression
behaviour of the intact soil and reconstituted sam-
ples should, ideally, account for this small differ-
ence in their initial gradings. In any case, the
convergence of the compression data of the intact
soil towards a slightly different NCL from that
found for the reconstituted soil could not be con-
®rmed because of the limitation on the con®ning
stress in the apparatus.
SHEARING
When sheared, the calcarenite was found to
reach the same critical states as the reconstituted
soil, de®ning a CSL in v±ln p9 space that was
parallel to the NCL of the reconstituted soil (Coop
& Atkinson, 1993). The silica sandstone reached
similar stress ratios at the ultimate states to the
reconstituted soil but localized failure of the intact
soil prevented the identi®cation of critical states in
terms of volume. For the reconstituted soil the
CSL was again parallel to the NCL.
An increase in con®ning pressure transformed
the shear behaviour of both structured sands from
strain-softening to strain-hardening. Typical stress±
strain curves are shown in Figs 8 and 9. Here,
except for one undrained test on the calcarenite,
the data are all from drained tests following con-
stant- p9 stress paths. At the start of each test the
values of axial strain were those from the internal
measurements, whereas at large strains the external
measurements have been used.
The strain-softening mode of behaviour was
characterized for both soils by an initially linear
stress±strain relationship and no change in volume.
Cuccovillo & Coop (1997b) demonstrated that the
linear stress±strain behaviour was also elastic and
interpreted the end of this linear elastic response,
which identi®ed yielding, as being the onset of
bond degradation. Despite this common feature the
two soils achieved their peak strength through dif-
ferent modes of shearing. For the calcarenite the
peak states were practically coincident with yield-
ing and were followed by a rapid loss of strength
and volumetric compression. Conversely, for the
silica sandstone, at all but the very lowest con®n-
ing stresses, which are not considered here, the
peak states were accompanied by dilationand
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plastic strains which developed after the soil had
yielded and the bonds had started to degrade. For
the calcarenite the near coincidence of the peak
states with yielding is a clear indication of the
cohesive nature of the peak strength of this struc-
tured sand and the patterns of behaviour may be
adequately described by Fig. 2. For the silica
sandstone, however, the peak strengths were found
to be frictional, as the stress±dilatancy analysis
presented later will show, and the framework
shown in Fig. 2 cannot therefore describe the
behaviour observed.
For both soils, strain-hardening was accompa-
nied by volumetric compression. In the case of the
silica sandstone this was associated solely with a
behaviour that was non-linear from the start of
shearing, indicating that at these con®ning pres-
sures the bonds had been degraded during isotropic
compression and had no further in¯uence on shear-
ing. For the calcarenite, in contrast, at some inter-
Fig. 6. Isotropic compression of the calcarenite: (a) stronger-bonded
samples (after Cuccovillo & Coop, 1997b); (b) weaker-bonded samples
Intact
Reconstituted
4 5 6 7 8 9 10 11 12
ln p ′: kPa
(a)
1.20
1.40
1.60
1.80
2.00
2.20
v
100 1000 10000 100000
p ′: kPa
Intact IB
NCL
CSL
4 5 6 7 8 9 10 11 12
ln p ′: kPa
(b)
1.20
1.40
1.60
1.80
2.00
2.20
v
100 1000 10000 100000
p ′: kPa
Intact (data from Coop
& Atkinson (1993))
Reconstituted
CSL
NCL
RAN3-RAN4
Intact IB
Stronger bonding
Intact IB
Weaker bonding
ON THE MECHANICS OF STRUCTURED SANDS 747
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mediate stress levels, strain-hardening was also
seen to be associated with an initially linear
response. In this case the strength was therefore
frictional and the bonds only contributed to an
increase in the initial stiffness.
At their critical states the intact samples of
calcarenite and silica sandstone reached similar
stress ratios to those of the corresponding reconsti-
tuted soils as shown in Fig. 10. It is believed that
in both cases the CSL is straight and that any
tendency to curve at the high pressures is more
likely to be due to incomplete testing.
The peak strengths of both materials were found
to increase with increasing p9 (Fig. 11). The varia-
tions of the speci®c volumes at the peak for the
intact samples of both soils were small (within
�0:01) and these differences therefore could only
have had a negligible in¯uence on the peak
strengths observed. For the silica sandstone a
unique envelope can be identi®ed which converges
towards the CSL at higher values of p9. The data
for the calcarenite are insuf®cient to identify peak
failure envelopes, but the much lower strength of
sample RAN6 compared to the other intact samples
of calcarenite seems likely to be not only because
of the lower p9 but also, and perhaps predominantly,
because this was one of the four weaker-bonded
samples.
Figure 11 also shows that the peak states de®ned
by the two intact soils lie well above those de®ned
by the reconstituted soils. However, a correct com-
parison needs to account for the in¯uence of
differences in the speci®c volumes between the
intact and reconstituted soils, and this will be done
later by means of a normalization of the data with
respect to an equivalent pressure.
STRESS DILATANCY OF A NATURAL SILICA
SANDSTONE
As for the reconstituted soil, the peak stress
ratios of the intact silica sandstone were achieved
when the rate of dilation was at its maximum. This
indicates that the peak strength of this structured
sand was purely frictional, in contrast to the cohe-
sive nature of the peak strength of the calcarenite.
In the following analyses of these states, the dila-
tancy d has been de®ned as
d � ÿäå
p
v
äåp
s
(1)
where äåp
v and äåp
s are the plastic components of
the volumetric and shear strains. The dilatancy has
only been calculated for the higher values of the
stress ratio ç(� q9= p9), for which the elastic com-
ponent of both strains is negligible, as are the
bedding errors in äåp
v, which was measured using
an external volume gauge.
In Fig. 12 the peak stress ratio (çp) is plotted
against the maximum dilatancy (dmax). The intact
soil reached a dilatancy of 1´7, which is very much
higher than either the maximum value of 0´3 for
the reconstituted soil or that of 0´75 reported by
Rowe (1969) for reconstituted silica sands with the
densest possible packing. Despite these remarkable
differences, the intact and reconstituted soils fol-
R9
R10
Intact
Reconstituted
NCL
4 5 6 7 8 9 10 11 12
ln p ′: kPa
1.20
v
1.45
1.60
1.75
1.90
100 1000 10000 100000
p ′: kPa
Fig. 7. Isotropic compression of the silica sandstone (after
Cuccovillo & Coop, 1997b)
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lowed the same stress±dilatancy relationship,
which may be described by an equation of the
same form as the ¯ow rule used in Cam Clay
(Roscoe & Scho®eld, 1963), and which was also
chosen by Nova & Wood (1979) for their model
for sands sheared in triaxial compression:
çp � M � ádmax (2)
where M is the value of ç at the critical state and
á is a constant. The ®gure shows, however, that
because of a relatively low value of á for this soil,
¯ow rules such as that of the original Cam Clay or
that proposed by Rowe (1962) cannot be used, as
they signi®cantly overestimate the peak strength.
A large difference between the dilatancies was
still seen when comparisons were made between
the behaviours of the intact and reconstituted soils
at volumetric states which were similar relative to
the CSL. Fig. 13(a) shows values of p9=p9cs at the
peak stress ratio, indicated as ( p9=p9cs)p, plotted
against dmax, where p9cs is an equivalent pressure
taken on the CSL and is de®ned in Fig. 14. For the
same normalized state the dilatancy at peak of the
intact soil is still very much higher than that of
the reconstituted soil. The trend of the data for the
intact soil seems to indicate a linear relationship as
for the reconstituted soil. However, an extrapola-
tion of the line for the intact soil gives an intercept
with a value of ( p9=p9cs)p greater than unity. This
suggests that the CSL of the intact soil in v±ln p9
space is located to the right of that which was
found for the reconstituted soil, although this could
Fig. 8. Typical stress±strain curves for shearing of the calcarenite: (a)
undrained test at p9init � 255 kPa; (b) test at constant p9 of 1400 kPa; (c)
test at constant p9 of 4910 kPa
Yield point
q
∆u
C1
p1′ 5 255 kPa
0 5 10 15 20 25 30
εa: %
(a)
q
: k
P
a
0
500
1000
1500
2000
2500
3000
0
500
1000
1500
2000
2500
3000
∆
u
: k
P
a
Yield pointN3
p ′ 5 1400 kPa
0 5 10 15 20 25 30
εa: %
(b)
q
: k
P
a
0
500
1000
1500
2000
2500
3000
25
0
5
10
15
ε v
: %εv
q
ON THE MECHANICS OF STRUCTURED SANDS 749
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not be con®rmed experimentally, because of strain
localization in some tests and premature ending of
others due to the strain limit of the radial strain
belt. It is possible that the differences in the initial
grading of the intact and reconstituted soils may
have been responsible for the different locations of
their CSLs, as discussed above. Fig. 13(b) shows,
however, that even when the states of the intact
soil are normalized with respect to an offset CSL,
assumed to be parallel to that of the reconstituted
soil, although the intercept is now the same, a
large difference is still seen in the dilatancy of the
intact and reconstituted soils. Even if the high peak
strengths of the natural silica sandstone are fric-
tional, they are therefore only in part a conse-
quence of the high density of the intact soil. Its
interlocked fabric and the presence of some re-
maininginterparticle cementing are therefore be-
lieved to be responsible for the higher strengths of
the intact soil. The values of dilatancy for the
silica sandstone were of a similar order to those
observed in shear box tests by Dusseault & Mor-
genstern (1979) for three natural silica sands which
had several features in common with that tested
here, notably that they were geologically old and
had a quartz composition with a high density and
interlocked fabric.
Qualitative considerations of energy balance
suggest that the dilation of the intact soil after
yielding is inhibited by the interlocked fabric and
by the continued presence of some of the bonding.
Fig. 15 shows that prior to peak the dilatancy
experienced by the intact samples at a given stress
ratio is smaller than that of the reconstituted
samples and that the rate of dilation for the intact
soil decreases as the p9 at which the samples were
sheared reduces. This initial delay is later compen-
sated for by a faster dilation that culminates at
peak. In terms of energy, the total work done by
the stresses at the boundary of the soil element
(ÄW ) is partly dissipated in friction (ÄWfric) and
partly spent in disrupting the structure of the soil
(ÄWstruc), so that
ÄW � ÄWfric � ÄWstruc (3)
For axisymmetry and for a unit volume, equation
(3) can be written as
q9 äåp
s � p9äåp
v � Mp9äåp
s � ÄWstruc (4)
or
q9
p9
� M ÿ äå
p
v
äåp
s
� ÄWstruc
p9äåp
s
(5)
To maintain a balance in equation (5), since M is
a constant, at a given stress ratio, if work is spent
in degrading the bonding and disrupting the soil
fabric the rate of dilation has to decrease. Up to
yielding, the presence of bonding prevents the
intact soil from dilating. After yielding, the gradual
degradation of the bonds and the disruption of the
fabric inhibit the dilation of the soil, which is later
recovered by a more rapid increase of the dilatancy
until a maximum is reached, which both corre-
sponds to and causes the higher peak strength.
A FRAMEWORK FOR THE BEHAVIOUR OF
STRUCTURED SANDS
To account for the effect that the presence of
cementing has on the volumetric state Cuccovillo
& Coop (1993) normalized the stress paths for
both the intact and the reconstituted samples of
calcarenite by means of p9cs. Fig. 16(a) shows that
for the samples of intact calcarenite that had not
yielded during isotropic compression, neither a
0 5 10 15 20 25 30
εa: %
(c)
q
: k
P
a
0
2000
4000
6000
8000
10000
25
0
5
10
15
ε v
: %
εv
q
N2
p ′ 5 4910 kPa
Fig. 8. (Cont.)
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Fig. 9. Typical stress±strain curves for constant- p9 shearing of the silica
sandstone: (a) p9 � 900 kPa; (b) p9 � 14 400 kPa; (c) p9 � 60 000 kPa
D1
p ′ 5 900 kPa
0 5 10 15 20 25 30
εa: %
(a)
q
: k
P
a
0 210
ε v
: %
q
500
1000
1500
2000
2500
25
0
5
10
εv
0 5 10 15 20 25 30
εa: %
(b)
q
: k
P
a
0 210
ε v
: %
6000
12000
18000
24000
30000
25
0
5
10
εv
q
A2
p ′ 5 14400 kPa
0 5 10 15 20 25 30
εa: %
(c)
q
: k
P
a
0 210
ε v
: %
15000
30000
45000
60000
75000
25
0
5
10
εv
q
A1
p ′ 5 60000 kPa
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unique yield surface nor a state boundary surface
(SBS) could be identi®ed. In Fig. 16(b) it can be
seen that for the samples that had been compressed
beyond yield, the normalized stress paths contract
progressively towards the SBS of the reconstituted
soil until the isotropic boundary of the intact soil
becomes coincident with the NCL of the reconsti-
tuted soil.
The method of analysis was therefore re-exam-
ined and it was found that by taking an equivalent
Fig. 10. Critical states: (a) calcarenite; (b) silica sandstone
Intact
Reconstituted
CSL
0 10000 20000 30000 40000 50000
p ′: kPa
(a)
0
10000
20000
30000
40000
50000
q
: k
P
a
Intact
Reconstituted
CSL
0 15000 30000 45000 60000 75000
p ′: kPa
(b)
0
15000
30000
45000
60000
75000
q
: k
P
a
?
?
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pressure on the isotropic boundary of the intact
soil ( p9IB; see Fig. 14) it was possible to identify
both yielding and state boundary surfaces. The
approach taken was that of considering the struc-
ture to be an intrinsic property characterizing the
nature of the soil, in the same way that grading,
particle mineralogy and particle shape are for
reconstituted sands. The intact and the reconsti-
tuted calcarenite therefore have different natures,
or, in other words, they are different soils. The
change in nature due to the presence of interparti-
cle bonding in the intact calcarenite is re¯ected by
Fig. 11. Peak states: (a) calcarenite; (b) silica sandstone
N3 (1.74)
C1 (1.75)
RAN6 (1.76)
R1 (1.71)
R2 (1.72)
(1.74)
Ultimate state intact
Ultimate state reconstituted
Peak state intact
Peak state reconstituted
CSL
v at peak
0 1000 2000 3000 4000 5000
p ′: kPa
(a)
0
1000
2000
3000
4000
5000
q
: k
P
a
0 6000 12000 18000 24000 30000
p ′: kPa
(b)
0
6000
12000
18000
24000
30000
q
: k
P
a
Ultimate state intact
Ultimate state reconstituted
Peak state intact
Peak state reconstituted
CSL
Peak envelope intact
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the change in the location of the isotropic bound-
ary. The shearing data for each soil should then be
normalized with respect to the isotropic boundary
for the particular soil. Whereas for the reconsti-
tuted soil, normalizations with respect to either the
NCL or CSL are equivalent because the two lines
are parallel, for the intact soil this is not the case.
The isotropic boundary of the calcarenite in
v±ln p9 space will be referred to in the following
as the intact isotropic boundary (intact IB). This is
represented by two straight lines in Fig. 6: a
steeper initial portion representing the postyield
compression of the intact samples and then, for
values of speci®c volume less than 1´465, a part
Original Cam Clay Rowe
Intact
Reconstituted
ηp 5 0.53dmax 1 1.29
20.5 0 0.5 1 1.5 2 2.5
dmax
0
0.5
1
1.5
2
2.5
η p
Fig. 12. Stress±dilatancy relationship for peak states
of the silica sandstone
Fig. 13. In¯uence of state on dilatancy for the intact
and reconstituted silica sandstone: (a) using the same
CSL location; (b) using an offset CSL for the intact
soil
Intact
Reconstituted
0 0.5 1 1.5 2
dmax
(b)
0
0.5
1
1.5
(p
′/p
′ cs
) p
(p ′/p ′cs)p 5 22.06 dmax 1 1
(p ′/p ′cs)p 5 20.49 dmax 1 1
Intact
Reconstituted
0 0.5 1 1.5 2
dmax
(a)
0
0.5
1
1.5
(p
′/p
′ cs
) p
(p ′/p ′cs)p 5 22.06 dmax 1 1
(p ′/p ′cs)p 5 20.78 dmax 1 1.59
v
CSL
Intrinsic NCL
Compression
of intact
sample
Current
state
pcs′ pe′ pIB′ ln p ′
Fig. 14. De®nition of the normalizing parameters used
in this paper
D3
D5
A2
Intact
Reconstituted
η 5 0.53d 1 1.29
Test
D3
D5
A2
p ′: kPa
3460
5600
14400
20.5 0 0.5 1 1.5 2
d
0
0.5
1
1.5
2
2.5
η
Fig. 15. Comparison between the stress±dilatancy re-
lationships of the intact and reconstituted samples of
the silica sandstone
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which is coincident with the NCL of the reconsti-
tuted soil. As previously discussed, for the four
weaker-bonded calcarenite samples, a lower intact
IB was used than for the other samples (Fig. 6(b)).
Values of an equivalent pressure p9IB were then
calculated for each sample on the appropriate
intact IB. For the reconstituted soil the values of
p9IB were taken on the intrinsic NCL for all
volumes. It should be pointed out that in this type
of normalization the critical states of the intact
soils are identi®ed by a single point only for values
of the speci®c volume smaller than1´465. Critical
states reached at higher speci®c volumes are lo-
cated along the line represented by a value of the
stress ratio ç equal to M and by values of p9= p9IB
smaller than 0´34. This method of analysis was
used by Cuccovillo & Coop (1997b) to examine
the in¯uence of state on the small-strain stiffness
of the calcarenite.
Figure 17 shows the yield surface for the calcar-
Fig. 16. Normalized stress paths for the calcarenite (adapted from
Cuccovillo & Coop, 1993): (a) samples that did not yield in isotropic
compression; (b) samples that yielded in isotropic compression
RAN
Stress path intact
After Coop &
Atkinson (1993)
Yield point
ISBS
RAN5
RAN6
N3
C1
C3
η 5 M
0 3 6 9
p ′/pcs′
(a)
0
3
6
q
/p
cs′
RAN1
RAN4
RAN3
N5
N7
N4
N2
η 5 M
RAN
Stress path intact (weaker bonding)
Stress path intact (stronger bonding)
ISBS
After Coop & Atkinson (1993)
0 1.5 3 4.5 6 7.5
0
1.5
3
4.5
6
p ′/pcs′
(b)
q
/p
cs′
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enite that may be identi®ed using this normaliza-
tion. The yield points in isotropic compression
were located to the left of the isotropic boundary,
resulting in a value of p9=p9IB of less than unity. It
can be seen that, using this approach, the yield
points of the calcarenite now de®ne the same yield
surface irrespective of their degree of bonding. For
the calcarenite, this normalization proved to be of
great importance in accounting for the large varia-
bility of both the speci®c volume and the degree
of bonding of the samples tested and hence for the
in¯uence of both of these factors on the yield
stress.
Figure 18 shows the normalized stress paths of
the intact samples of calcarenite sheared after
isotropic yielding. Superimposed are the stress
paths of the reconstituted samples which de®ne the
intrinsic state boundary surface (ISBS). For the
intact samples sheared from states located on the
portion of the intact IB convergent with the NCL,
the stress paths lie above the ISBS. As the state of
the intact soil prior to shearing approaches the
NCL, the stress path becomes coincident with the
ISBS as shown by sample N5. The normalization
therefore identi®es the space of permissible states
of the intact soil, which could not be achieved by
the p9cs normalization used in Fig. 16. The samples
with weaker bonding reached states which are
above the ISBS but within the space limited by the
stress paths of the more strongly cemented sam-
ples.
In Fig. 19 the stress paths of the calcarenite
samples sheared before isotropic yielding and the
yield surface are superimposed on the ISBS and on
the outer boundary surface de®ned in Fig. 18. In
this representation the values of the state variable
p9=p9IB can now be used to distinguish modes of
shear behaviour of the intact soil. For the calcar-
enite the yield surface, which de®nes the domain
of normalized states in which the shear behaviour
is controlled by bonding, occupies a large portion
of the permissible space. This means that over the
whole pressure range and for the large range of
densities of the calcarenite, the shear behaviour
was mainly cohesive. Frictional behaviour for the
calcarenite, which is behaviour associated with
states beyond the yield surface but still within the
intact SBS, was accompanied by volumetric com-
pression and controlled by a progressive mechan-
ism of bond degradation and particle breakage.
The transition between the cohesive and frictional
modes of behaviour corresponds to a value of
p9=p9IB of 0´42, which is where the yield surface
meets the line of gradient M . For values of p9=p9IB
smaller than 0´42 the calcarenite reached peak
states which were all located on the yield surface,
so that the peak strength was solely cohesive. For
values of p9= p9IB greater than 0´42, the strength
was frictional and coincident with the critical state.
In these cases, however, the interparticle bonding
contributed to an increased stiffness of the soil
prior to yielding (Cuccovillo & Coop, 1997b).
Moving the state of the soil towards the intact IB
does not change the value of stiffness determined
by the bonds but decreases the range of strains
over which bonding enhances stiffness, until for
states on the intact IB the behaviour becomes non-
linear from the start of shearing.
For the silica sandstone, yield and state bound-
ary surfaces were identi®ed by taking an equivalent
pressure on the critical-state line. Because of the
high initial density of the silica sandstone and the
weak bonding its behaviour in isotropic compres-
sion was seen to be similar to that of an uncemen-
C1
D1
η 5 M Yield point (stronger bonding)
Yield point (weaker bonding)
Yield surface
0 0.5 1
0
0.5
p ′/p IB′
q
/p
IB′
Fig. 17. Yield surface for the calcarenite
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ted sand, for which the critical-state line and the
isotropic boundary are parallel. Therefore, for the
silica sandstone the appropriate line of reference
for the normalization can be either the isotropic
boundary or the CSL. In Fig. 20 the states of the
intact soil have been normalized with respect to
values of p9cs taken on a different critical-state line
from that of the reconstituted soil, as was indicated
by the stress±dilatancy data in Fig. 13. The yield
points again identify a clear yield surface, which,
for the silica sandstone, occupies only a small
portion of the permissible space of the intact soil
and is entirely contained within the ISBS. This
demonstrates that the shear behaviour of the silica
sandstone was mainly frictional. States between the
yield and state boundary surfaces were associated
with bond degradation and were accompanied by
dilation on the dry side of the critical state, or
compression on the wet side of the critical state. A
peak strength resulting from cohesion was observed
only at the very lowest pressures. Otherwise the
peak strengths were frictional and substantially
higher than those of the reconstituted soil because
of the greater dilatancy.
Fig. 18. Normalized stress paths for reconstituted and intact samples of
the calcarenite sheared after isotropic yielding: (a) stronger-bonded
samples; (b) weaker-bonded samples
η 5 M
0 0.5 1
0
0.5
p ′/p IB′
(a)
q
/p
IB′ N5
1.52
1.54
1.521.66 1.66
Intact (stronger bonding)
reconstituted
v at the start of
shearing
η 5 M
0 0.5 1
0
0.5
p ′/p IB′
(b)
q
/p
IB′
1.52
1.54
1.521.66
1.66
Intact (weaker bonding)
Intact (stronger bonding)
v at the start of
shearing
ISBS
1.73
1.73
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CONCLUSIONS
The shear behaviour of natural sands has been
shown to be controlled by mechanisms which differ
from those for reconstituted sands and which result
from their structure. These mechanisms can be
easily understood once it is recognized that the
nature of a sand is de®ned not only by the type of
the material constituents but also by the processes
experienced in the ground during its geological
history. These processes are re¯ected in the soil
structure, which, it is suggested here, should be
considered as an additional element of the soil
nature. It is then possible to interpret the shear
behaviour of two substantially different structured
sands in the light of the differences in their nature,
which leads to the development of a general frame-
η 5 M
0 0.5 1
0
0.5
p ′/p IB′
q
/p
IB′
Stress path
Yield surface
Outer intact SBS
ISBS
Fig. 19. Normalized stress paths for calcarenite samples sheared prior to
isotropic yielding
0 0.5
0
0.5
Yield surface
Stress path reconstituted
Stress path intact
Yield point intact
ISBS
Hvorslev surfaces
Roscoe surface
Yield surface
0 1 2 3 4 5
0
1
2
3
4
5
η 5 M
p ′/pcs′
q
/p
cs′
Fig. 20. Normalized shear behaviour of the silica sandstone
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work in which the various features of the behaviour
of the two soils are explained in terms of the
stress±volume state of the soil.
As shown by the calcarenite and the silica
sandstone, the isotropic boundary of a structured
sand is controlled by its nature and therefore,
among other things, by its structure. Different
modes of shear behaviour have been shown to be
controlled by the location of the state relative to
the isotropic boundary of the soil. It is only when
the isotropic boundary happens to be parallel to
the critical-state line that reference to either one of
them is equivalent. An isotropic boundary parallel
to the critical-state line was seen for the silica
sandstone, where fabric was the most important
structural feature and for which bonding was weak.
For the calcarenite, in which the structure arose
principally from a strong bonding, the isotropic
boundary was not parallel to the critical-state line,
and references to states on the `dry' or `wet' side
of the critical state become meaningless for distin-
guishing different modes of shear behaviour.
Sands in which structure arises predominantly
from bonding would have shear behaviour which is
largely cohesive and would follow the patterns of
behaviour set out in Fig. 2. As is shown by the
calcarenite, the peak strength would be solely
cohesive and the soil would show brittle failure.
Frictional behaviour would only be seen at con®n-
ing pressures that are suf®ciently high and/or at
densities that are suf®ciently low to cause the
disruption of the bonds owing to yielding. The
frictional behaviour would then be dominated by
compression and particle crushing and the strength
would be achieved through strain-hardening to an
ultimate state. The principal problems for engineer-
ing design in such materials might arise from pro-
gressive failure mechanisms because of the strain-
softening behaviour or from the large volumetric
compression that might occur, which might give
rise to large settlements or reduce the boundary
stresses acting on an engineering structure such as
a pile.
Sands in which the structure arises predomi-
nantly from an interlocking fabric and in which the
bonding is weak would have a shear behaviour that
is largely frictional. This behaviour cannot be
described adequately either by a conventional soil
mechanics framework based on the behaviour of
reconstituted materials or by the patterns of beha-
viour shown in Fig. 2. Fig. 21 identi®es schemati-
cally the main features of behaviour for a fabric-
dominated sand. As shown by the silica sandstone,
the shear mechanisms would be dominated by
dilation, which would be the cause of the peak
strengths. The stress±strain behaviour would be
non-linear for much of the range of con®ning
stresses (case 2b) and, if seen, linearity would be
con®ned to the initial part of shearing (case 2a).
Compression and particle crushing would be lim-
ited to only the very highest stresses (case 3), and
if the sand has a small degree of bonding, cohesive
peaks would only be seen at the lowest con®ning
stresses (case 1). Because of the dilation these
sands would give particularly high bearing capaci-
ties, and design methods for this type of soil could
follow those normally applied to dense sands,
although a determination of the peak strength from
reconstituted samples would greatly underestimate
the strength of the soil in the ground because of
the much greater dilation of the natural material.
To develop a general framework which is valid
for both frictional and cohesive behaviour, it is
proposed that the strain-softening and strain-hard-
ening modes of shear behaviour should be distin-
guished on the basis of the location of the state of
the soil relative to its isotropic boundary rather
than to its critical-state or intrinsic normal com-
pression line.
ACKNOWLEDGEMENTS
The research was funded by the EPSRC, to
whom the authors are grateful. Support was also
given by the Nuf®eld Foundation through a grant
to the ®rst author. The calcarenite samples were
kindly provided by BP International.
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εa
q
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¢
p ¢
q ′
1 2a 2b 3
Yield surface
of cement
Peak
envelope
Critical-state line
Fig. 21. Schematic diagram showing modes of shearing
behaviour for the silica sandstone
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760 CUCCOVILLO AND COOP
	INTRODUCTION
	SOIL DESCRIPTIONS
	LABORATORY EQUIPMENT AND PROCEDURES
	ISOTROPIC COMPRESSION
	SHEARING
	STRESS DILATANCY OF A NATURAL SILICA SANDSTONE
	A FRAMEWORK FOR THE BEHAVIOUR OF STRUCTURED SANDS
	CONCLUSIONS
	ACKNOWLEDGEMENTS
	REFERENCES