Clay Minerals (1998) 33, 651-660
The effects of salt solutions on the
properties of bentonite-sand mixtures
P. G . S T U D D S ,
D . I. S T E W A R T *
AND T . W . C O U S E N S
Department of Civil Engineering, University of Leeds, Leeds, LS2 9JT, UK
(Received 15 June 1997; revised 13 October 1997)
A B S T R A C T : The swelling behaviour and hydraulic conductivity of Na-bentonite powder and
bentonite-sand mixtures (10 and 20% of bentonite by dry weight) have been measured with distilled
water and various salt solutions (0.01, 0.1 and 1 mol/l concentrations), It was found that in dilute
solutions, the bentonite in mixtures subjected to small confining stresses swells sufficiently to
separate the sand particles and reach a clay void ratio similar to that achieved by bentonite alone. At
high stresses, or in strong solutions, the bentonite in a mixture has insufficient swelling capacity to
force the sand particles apart and swelling is limited by the sand pore volume. The hydraulic
conductivity of a mixture depends on the bentonite void ratio, and the porosity and tortuosity of the
sand matrix. A design model is proposed to predict the engineering properties of a mixture over a
range of confining stresses from the properties of its constituents and the permeant.
Barriers with a low hydraulic conductivity are used
as part of waste containment systems to prevent
groundwater contamination by leachate from the
waste. Where suitable low hydraulic conductivity
soils are not locally available, such a material can
be produced by adding Na-montmorillonite (Nabentonite) to a coarse native soil. Such 'bentonite
improved soils' are used as a component of landfill
liner systems (Cowland & Leung, 1991), and also
to form containment barriers by in situ mixing (Day
& Ryan, 1995) and in slurry wall techniques (Evans
et al., 1995).
Two advantages of using bentonite-sand mixtures
instead of natural clays as barriers are that they
undergo less shrinkage on drying (Dixon et aL,
1985) and are less susceptible to frost damage
(Kraus et aL, 1997). On drying, the reduction in the
bentonite-void ratio brings the sand particles into
contact p r o v i d i n g m e c h a n i c a l stability and
preventing further macroscopic shrinkage. Upon
freezing, ice growth is uniformly distributed
throughout the mixture so that there is no change
in the macrostructure. However, once thawed and
* Corresponding author
saturated, the bentonite remains able to swell to fill
any voids, resulting in very low hydraulic
conductivity.
When bentonite-sand mixtures are used for
landfill liners and environmental containment
barriers, they must meet two performance criteria;
they must limit hydraulic flow, and they must have
suitable mechanical properties to ensure their
structural integrity during construction and operation. As the leachate in a landfill (or the groundwater at a contaminated site) can vary spatially and
temporally, liners and barriers must be designed to
be mechanically stable in, and resist the passage of,
a variety of pore fluids.
This paper presents data on the swelling
behaviour and hydraulic conductivity of Nabentonite and bentonite-sand mixtures with various
solutions. A model is proposed that can be used to
predict the swelling and hydraulic conductivity of a
bentonite-sand mixture in salt solutions representative of leachates, from the properties of the
bentonite in the solution, and the sand compressibility, porosity and tortuosity. This model can also
be used to estimate the component of the applied
stress supported by the sand particles, and therefore
the mechanical behaviour of a mixture.
~;3 1998 The Mineralogical Society
652
P . G . Studds et al.
BACKGROUND
Mollins et al. (1996) proposed that bentonite-sand
mixtures can exist in two characteristic states. At
low confining stress, the clay in the mixture is able
to swell against the surcharge and separate the sand
particles to reach the same void ratio, for a given
surcharge, as bentonite alone. At high confining
stress the clay-void ratio, upon filling the sand
pores, is greater than the clay-void ratio in
equilibrium with the surcharge stress, and the
sand particles remain in contact. Mollins et al.
(1996) proposed that when the sand particles are
not in contact, the effective confining stress must be
supported by osmotic pressure between clay
particles, and that the confining stress required to
bring the sand particles into contact depends on the
bentonite content of the mixture.
When there is a continuous sand matrix, Graham
et al. (1986) suggested that the externally applied
effective stress is supported partially by interparticle forces between sand grains and partially
by osmotic pressure between clay particles.
Provided that the bentonite in the mixture has
swollen to completely fill the pores in the sand
matrix, the clay-void ratio of the bentonite in a
mixture (ec, the volume of voids/volume of dry
clay) can be calculated from the sand porosity of
the matrix (n~, the volume of voids and dry clay/
volume of sand), in such a situation, the fraction of
the effective stress supported by the bentonite
within a mixture (and therefore the fraction of the
effective stress supported by the sand matrix) can
be calculated from vertical effective stress/void
ratio data for bentonite alone.
Mollins et al. (1996) extended a model developed
by Porter et aL (1960) for diffusion through soil, to
the problem of hydraulic flow through a bentonitesand mixture. By arguing that flow through a
mixture is through bentonite filled pores in the sand
matrix, they developed the relationship:
kmix = ns Ts kclay
(I)
where kclay is the hydraulic conductivity of bentonite
at the same void ratio as the bentonite occupying the
pore space within the sand matrix of the mixture, and
n~ and % are the porosity and tortuosity of the sand
matrix (where the tortuosity is defined as the square
of the ratio of the macroscopic path length to the
microscopic path length).
Several empirical relationships have been
proposed for calculating the tortuosity of a soil
from its porosity (see Boudreau, 1996). Amongst
the more widely known of these relationships is that
proposed by Archie (1942). Using the definition of
tortuosity stated above, Archie's equation can be
written as:
% -- -
(n--l)
(2)
ns
where the exponent 'n' depends on the soil type,
and varies from 15 for coarse sand, to 10 for
swelling clays (after Lerman, 1979).
Most published work on the swelling and
hydraulic conductivity of bentonite-sand mixtures
has used water as the pore fluid (e.g. Dixon et al.,
1985; Graham et al., 1986; Mollins et al., 1996).
However, it has been shown that both the swelling
and the hydraulic conductivity of a clay are highly
dependent on the pore fluid (Slade et al., 1991; Di
Maio, 1996). To date, no model has been proposed
for describing the behaviour of bentonite-sand
mixtures with other pore fluids.
MATERIALS
The materials used in this study were SPV 200
grade Wyoming bentonite supplied by Volclay, and
Knapton Quarry sand. The SPV bentonite originates
from Lovell, Wyoming and is a well-ordered Namontmorillonite with minor quartz and cristobalite
impurities (M. Batchelder, pers. comm.). Knapton
Quarry sand is a slightly silty fine angular quartz
sand. Other properties of SPV bentonite and
Knapton Quarry sand are given in Table 1.
The test solutions were distilled water and Na, K,
Cs, Mg, Ca and AI chloride solutions at 0.01, 0.1
and 1 mol/l concentration. The salt solutions were
prepared from analytical grade reagents and
distilled water.
EXPERIMENTAL
WORK
S w e l l i n g tests
The swelling behaviour of Wyoming bentonite
with different pore solutions was investigated over
a range of vertical effective stresses. Samples of
bentonite powder were placed in an oedometer ring,
spread uniformly, subjected to a vertical stress, and
either distilled water, or one of the chloride salt
solutions, was allowed access to the sample from a
reservoir. The sample height was monitored until
swelling ceased, at which point the final void ratio
was calculated from the initial void ratio and
Bentonite-sand mixtures
653
TABLE 1. Properties of Wyoming bentonite and Knapton Quarry sand.
Wyoming bentonite
Specific surface I = 780 m2/g
Average particle size 2 _ 2 ]am
Specific gravity 3 = 2.751
Moisture content 3 _ 13.34~
(as supplied)
pH 4 = 7.30
Liquid limit 3 = 354%
Plastic limit 3 _ 27%
Cation exchange capacity 5 = 95 mEq/100 g
Knapton Quarry sand
Effective s i z e ( D l o ) 3 = 0.07 mm
Percentage fines 3 = 7%
Specific gravity 3 = 2.67
Moisture content 3 ~4.50/0
(as supplied)
Maximum void ratio 6 = 0.86
Minimum void ratio 6 = 0.40
x Measured by the Blaine technique described in B.S. 12 (British Standards Institute, 1958).
2 Measured by laser particle size analyser.
3 Determined in accordance with B.S. 1377 (British Standards Institute, 1990).
4 Determined on a suspension of 20 g of bentonite in 400 ml of distilled water.
5 Measured by distillation with neutral ammonium acetate and titration with acid, Klute (1986).
6 Determined by methods described in Head (1980).
change in sample volume. Bentonite-sand mixtures
(10 and 20% bentonite by dry weight) were
prepared and tested in a similar manner to the
bentonite specimens.
Hydraulic conductivity tests
Two methods were used to investigate the
h y d r a u l i c c o n d u c t i v i t y o f the b e n t o n i t e and
bentonite-sand mixtures to the various permeants.
The first method calculated the hydraulic conductivities of the swelling test specimens from their
consolidation response upon application of a load
increment. The second method was direct measurement using a Rowe cell constant head test.
R o w e cell s p e c i m e n s w e r e p r e p a r e d b y
spreading a uniform thickness of material across
the base of the cell, applying a surcharge stress,
vacuum de-airing, and then allowing access to the
appropriate test solution. A back pressure was
applied to the drainage lines to improve specimen
saturation. Next, a hydraulic gradient (of ~50) was
applied across the specimen in a direction parallel
to the surcharge stress, and the amount of inflow
and outflow were recorded. Typically, inflow
b e c a m e equal to o u t - f l o w a b o u t 24 h after
application of the hydraulic gradient, by which
time <20% of the specimen's pore fluid had been
replaced. The flow rate at 20% replacement was
used to calculate the initial hydraulic conductivity
of the specimens.
With the more concentrated solutions, the flow
rate did not vary after 20% of the pore fluid had
been replaced. However, when the pore fluid was
either distilled water or a 0.01 mol/l solution the
flow-rate decreased with time (as salts from the
clay were eluted) reaching a roughly steady state
when the pore fluid had been replaced twice (taking
~40 days). As the pore fluid is not replaced during
consolidation, the hydraulic conductivity calculated
from the consolidation data is broadly comparable
with the initial hydraulic conductivity in the direct
tests. Also from a practical point of view, the higher
and more quickly m e a s u r e d initial hydraulic
conductivity would generally be that measured for
engineering purposes, and therefore these data are
presented in this paper.
RESULTS
AND
DISCUSSION
Swelling: bentonite in distilled water and salt
solutions
Figure 1 shows swelling data for bentonite tested
with distilled water, plotted on axes of void ratio
against the logarithm of the vertical effective stress.
At vertical effective stresses below ~200 kPa the
void ratio of the clay is very sensitive to the vertical
effective stress, decreasing approximately linearly
with the logarithm of the stress. A straight line has
been fitted to this data by simple regression
analysis. Above 200 kPa the void ratio of the clay
654
P.G. Studds et al.
14=
14-
12
1210-
10
.o
x
0,0 lmol,'l
o
O.lrnol/l
9
lrnol/I
x
x
x
9 ,o
|
._o 8
8
9~
.~0
0
4-
4-
2-
2I
o
........
I
to
........
I
too
........
x
*
0
I
vertical effective stress (kPa)
1000
10
100
vertical effective stress (kPa)
1000
Fla. 1. Swelling of bentonite powder with distilled
water.
FIG. 2. Swelling of bentonite powder with different
strength chloride salt solutions.
is less sensitive to changes in vertical effective
stress, but still appears to decrease linearly with the
logarithm of the stress, and a straight line has also
been fitted to these data.
Swelling data for Wyoming bentonite tested with
the 0.01, 0.1 and 1.0 mol/1 chloride salt solutions
are shown in Fig. 2. For clarity, data for different
chloride salts are not differentiated, as the different
salts gave broadly similar trends (full details are
given by Studds et al., 1996). At low vertical
effective stresses the highest void ratios were
reached with the lowest strength solutions, and for
each concentration the void ratio of the clay
decreases approximately linearly with increasing
vertical effective stress (some of the scatter,
especially in the 0.01 mol/l solution data, results
from differences in the cation). All the data
converge at about 200 kPa, when the void ratio
was -1.5.
mately l0 and 90 kPa for the mixtures containing
10% and 20% of bentonite, respectively). Above
these 'threshold stresses' the decrease in the clayvoid ratio is less sensitive to increases in vertical
effective stress. Mollins et al. (1996) suggested that
this change in behaviour results from the sand
particles being brought into contact and supporting
a component of the vertical effective stress.
The results of swelling tests on bentonite-sand
mixtures using 0.01 mol/1 salt solutions as the pore
fluid are shown in Fig. 4, together with the best-fit
straight line for bentonite swelling in these
solutions. The response of a 20% bentonite-sand
mixture in 0.01 mol/1 salt solutions is similar to that
observed for the same mixture in distilled water. At
low vertical effective stresses the response of the
mixture was similar to that of bentonite alone,
deviating from that response at vertical effective
stresses >~70 kPa. However, the clay-void ratio of
Swelling: bentonite-sand mixtures in distilled
water and salt solutions
14-
Figure 3 shows the swelling data for bentonitesand mixtures tested with distilled water, plotted on
axes of clay-void ratio against the logarithm of the
vertical effective stress. The best-fit straight line for
bentonite alone is shown as the solid line. The
dashed and dotted lines in Fig. 3 (and in Figs. 4
to 6) are discussed in the section on the engineering
model. At low vertical effective stresses, the
behaviour of the bentonite-sand mixtures is similar
to that of the bentonite alone. However, as the
vertical effective stress increases, there is a
deviation from bentonite behaviour at a stress
which depends on the bentonite content (approxi-
13-"
12-
9
lO%mixtures
9
20%mixtures
11-10-
97.
6.
5.
4.
3.
2o
1
IOO
1ooo
vertical effective stress (kPa)
FIG. 3. Swelling of bentonite-sand mixtures with
distilled water.
Bentonite-sand mixtures
11:L
10
~
"
10% mixtures
9
2oO,o m , x t . . . .
655
14t3..
t2"11 ~
9
9
10% mixtures
20% mixtures
I0-
"A~
o
32
7
~
s'
42
3'
2"
t
31
0
1
. . . . . . . .
i
.
.
10
.
.
. . . .
"-"..........
.
100
.
i
1000
vertical effective stress (kPa)
0
........
I
10
........
I
100
........
I
1000
vertical effective stress (kPa)
FIo. 4. Swelling of bentonite-sand mixtures with
various 0.01 mol/l salt solutions.
Fio. 5. Swelling of bentonite-sand mixtures with
various 0.1 mol/1 salt solutions.
a 10% bentonite-sand mixture is consistently greater
than that of bentonite in a 0.01 mol/l salt solution
over the range of vertical effective stress investigated, although the two data sets converge at low
effective stress.
Figures 5 and 6 show the results of the swelling
tests on bentonite-sand mixtures using 0.1 and 1.0
mol/1 salt solutions as the pore fluid, respectively.
The appropriate best-fit straight lines for bentonite
swelling are also shown. In the 0.1 mol/1 solutions
(Fig. 5) the clay-void ratio of a 10% bentonite-sand
mixture is consistently greater than that of a 20%
bentonite-sand mixture, which, in turn, is consistently greater than that of bentonite alone. This
suggests that in both mixtures a proportion of the
vertical effective stress is supported by the sand
matrix over the entire stress range investigated,
because the stress required to confine the bentonite
at the calculated clay-void ratios is less than the
applied stress. Indeed, at low stresses the clay-void
ratio in the 10% mixture is very close to that
measured in a free swell test (ec = 9.9), indicating
that the bentonite is being subjected to very little
stress.
In the 1.0 mol/l solutions, the void ratio reached
by Wyoming bentonite in a free swelling test is
~4.0. All the tests for the 10% bentonite-sand
mixtures resulted in estimated clay-void ratios >4.0,
suggesting that the bentonite does not fill the pores
of the sand when tested with these solutions, so a
clay-void ratio cannot be found. In a 20% mixture,
the clay has sufficient swelling capacity to
completely fill the sand pores when the vertical
effective stress is >10 kPa. Only these data are
shown in Fig. 6,
Hydraulic conductivity." bentonite
._o
1413:
12:
I1109-
9
20% mixtures
7-
~ s2
4-
32
22
1o
, ,~1
10
........
I
100
........
I
1000
vertical effective stress (kPa)
FIo. 6. Swelling of bentonite-sand mixtures with
various 1 mol/l salt solutions.
Figure 7 is a graph of the logarithm of hydraulic
conductivity vs. the logarithm of void ratio for
bentonite tested with distilled water and the
chloride salt solutions (data from both the direct
and the indirect test methods are presented in
Fig. 7). For each solution strength, the hydraulic
conductivity of the bentonite increases as the void
ratio increases. Also, at a given void ratio, the
hydraulic conductivity of Wyoming bentonite
increases as the ionic strength increases (e.g. at a
void ratio of 3 the hydraulic conductivity was
~2 x 10 -11 m/s in distilled water, but 2 x 10 -9 m/s
in 1 mol/1 salt solutions). For clarity, data from
different chloride salts are not differentiated as the
different salts gave similar trends, and best-fit lines
P.G. Studds et al9
656
9
I mol/I o
9p
1E-9
o o.1 rnol/I
:/,x
.......
eQ 9
9:
~'IE-lO
81E-tt
x <'
.2
x
,~
water
x
decreases with increasing pore-solution concentration. Therefore, at a given voids ratio the effective
porosity of a clay will increase as the solution
concentration increases.
o
Hydraulic conductivity: bentonite-sand
mixtures
-- ~x
E
~1E-12 -
1 mol/I
0.1 m o l / I
x
0,01 mol/I solt~tions
o
.
.
.
.
.
solutions
9
9
.
solutions
distilled water
.
11o
void ratio
FIG. 7. Hydraulic conductivity of bentonite with
distilled water and different strength chloride salt
solutions.
have been calculated for each concentration.
However, the hydraulic conductivity measured
with the 0.01 and the 0.1 mol/l solutions tended
to increase slightly with increasing cation valence.
No valency effect was discernible in the data from
tests with the 1.0 mol/l solutions.
The trend for increasing hydraulic conductivity
with increasing permeant concentration probably
results from the influence of the permeant on
effective porosity (the pore space available for
conductive flow)9 Dixon et al. (1985) suggested that
the effective porosity of a clay is less than the total
pore space per unit volume because some of the
pore space is occupied by surface or bound water
which has a greater viscosity than free water.
Diffuse double layer theory (see for example van
Olphen, 1977) predicts that double layer thickness
Figure 8 shows the hydraulic conductivity of the
bentonite-sand mixtures tested with distilled water.
The best-fit line for bentonite alone is also shown
for comparison. The main trends are: (1) at a given
clay-void ratio the hydraulic conductivity of a
mixture decreases as wt% clay decreases; and (2)
the hydraulic conductivity of each mixture increases
as the clay-void ratio increases. The dotted and
dashed lines fitted to the data shown in Fig. 8 (and
in Figs. 9 and 10) are discussed later9
Figures 9 and 10 show the hydraulic conductivity
of the bentonite-sand mixtures tested with the 0.01
and 0.1 mol/l chloride salt solutions, respectively.
The appropriate best-fit lines for bentonite alone are
also shown. The main trends are similar to those for
bentonite-sand mixtures with distilled water; the
hydraulic conductivity of a mixture decreases as the
wt% clay decreases and the hydraulic conductivity
of a particular mixture increases as the clay-void
ratio increases.
The hydraulic conductivity of bentonite-sand
mixtures was not measured with the 1.0 mol/1 salt
solutions because the majority of the swelling data
collected with these solutions had clay-void ratios
which exceeded those in free swelling, indicating
that there are partially empty pores in the sand
matrix through which preferential flow may occur.
9
20% mixtures
9
20% mixtures
9
10% mixtures
9
10% mixtures
1E.-9
1E-9 -
.'
#/"
~tE-tO.
p. 9149
E
', 1E-10
~ IE-11 -
o~ IE-11
o
o
/
"~ 1E-12 -
.
.
.
///
A
1E-12
.
.
.
.
t
IE-13
.
.
.
.
to
clay*void rati~
FIG. 8. Hydraulic conductivity of bentonite-sand
mixtures with distilled water,
.
.
.
t
lo
clay-void r a t i o
F]o. 9. Hydraulic conductivity of bentonite-sand
mixtures with 0.01 mol/l salt solutions.
Bentonite-sand mixtures
ENGINEERING
MODEL
One-dimensional swelling behaviour
It is proposed that the swelling behaviour of a
bentonite-sand mixture in any pore solution can be
calculated from the swelling response of the
bentonite and the load deformation characteristics
of the sand by assuming that the overall vertical
effective stress applied to a bentonite-sand mixture
is equal to the algebraic sum of the components
supported by the sand matrix and the bentonite gel.
In addition, as the load-deformation characteristics
of the sand within a mixture cannot be directly
measured, it is further assumed that the relationship
between the change in sand porosity and the
component of vertical effective stress supported
by the sand is independent of the initial sand
porosity. In other words, the clay affects how the
sand particles pack together during sample preparation but does not change the subsequent response of
the sand matrix9 This approach is analogous to the
assumption made within the critical state family of
soil constitutive models that elastic rebound lines
are parallel on a plot of specific volume against the
logarithm of mean effective stress (see Atkinson &
Bransby, 1978).
Swelling data for Wyoming bentonite suitable for
use in the model have already been presented in
Figs. 1 and 2. Figure 11 presents load-deformation
data for Knapton Quarry sand. Figure 11a indicates
that there is a linear relationship between sand
porosity and the logarithm of the vertical effective
stress, and Fig. 1 lb indicates that under a given
vertical effective stress, the sand porosity of a dry
mixture increases linearly with % by dry weight of
657
clay. Using the data in Fig. l i b to determine a
simple arithmetic porosity correction to the loaddeformation data assumes implicitly that in these
tests the effective stress supported by the sand
matrix did not vary with the clay content. As the
clay was dry and did not completely fill the sand
pores, the component of effective stress that it
supported will have been small.
Based on the assumptions above, curves can be
generated that predict the clay-void ratio that would
be achieved by the bentonite within a mixture over
a range of vertical effective stresses by repeated
application of the following procedure: (1) For a
vertical effective stress in the sand matrix, calculate
the sand porosity using the load-deformation
relationship for the sand. (2) For the desired
bentonite content, calculate the clay-void ratio that
would result in complete filling of the sand pores
using the sand porosity from 1. (3) For that clayvoid ratio, estimate the component of vertical
effective stress required to confine the bentonite
gel using swelling data for the bentonite.
(4) Calculate the overall vertical effective stress
supported by the mixture by summing the
components supported by the sand matrix and the
bentonite gel,
Application of this model to the bentonite-sand
mixtures reported in this paper generated the dashed
and dotted lines shown in Figs. 3 to 6 for 10% and
20% bentonite-sand mixtures, respectively. The
model predicts that there is a gradual change in
mixture behaviour with increasing stress from a
0.4
~
0.3
o.I
1E-B -
9
20% mixtures
9
10%mlxtutesmlx~tes
,"
S
,"
//
0.0
1
/=/
tO
~,~
veHieai effective stre=;s (kPa)
(a)
t E~91
.~ 1E-10 -
=..
/
/
i/
9
1000
9
03~
" .~ Note: rneasuted at 30 kPa 6u~harge
8 t~-ii
= /
~E-t2
1E-1~
;
, ,,,~,
,
, , ;
,, ,, ~,,, ,,,
lO
0
(b)
5
I0
I ~;
20
25
% o| dry bentonite in the mixtgre
30
clay-void ralio
FIG, 10, Hydraulic conductivity of bentonite-sand
mixtures with 0,1 reel/1 salt solutions.
F~G, 11, Porosity of Knapton Quarry sand: (a) variation
during one-dimensional compression; and (b) variation
with bentonite content of a dry mixture.
P.G. Studds et al.
658
state where the clay-void ratio is indistinguishable
from that of the bentonite alone to a state where the
clay-void ratio is relatively insensitive to vertical
effective stress, indicating that most of the stress is
supported by the sand matrix. This correlates very
closely with the observed behaviour of bentonitesand mixtures.
Hydraulic conductivity
The hydraulic conductivity of a bentonite-sand
mixture to any salt solution can be calculated from
the hydraulic conductivity of the bentonite to the
same permeant by making two further assumptions:
(1) the flow through a mixture is through bentonitefilled pores in the sand matrix; and (2) the sand
tortuosity is a function of the sand porosity. The
hydraulic conductivity of the mixture can then be
calculated by using the swelling model to estimate
the clay-void ratio and sand porosity of the mixture
under an appropriate surcharge stress, and then
multiplying the hydraulic conductivity of the
bentonite at the appropriate void ratio by a sand
porosity-tortuosity factor (see eqn. 1).
Sand tortuosities for the mixtures have been
calculated from their measured hydraulic conductivity, sand porosity, and the hydraulic conductivity
of the bentonite to the appropriate permeant, and
Fig. 12 presents the variation in sand tortuosity with
sand porosity. Data for the 10% bentonite-sand
mixtures tested with the 0.1mol/t solutions have
been omitted from Fig. 12 for reasons that are
discussed later. The calculated sand tortuosities are
low for a saturated sand (Shackleford & Daniel,
9
20% distilled water
/
9
10% distilled water
9
20% 0.0t mol/I
9 10% O.01mol/I
D 20%0.tmol/I
i ~
9
mIP' u a.
9
o~l
#
(4.20-1)
tortuo~,ity= porosity
0.1
o
9
9
9 9 ~9
o.oi
oi
porosity
FJ~. 12. The relationship between the sand tortuoisty
and sand porosity of a bentonite-sand mixture (the
straight-line is Archie's relationship fitted to the data,
and is constrained to pass through the point 1,1).
1991). However, the effective particle size (Dl0) of
Knapton Quarry sand is towards the lower limit of
the sand range, and the sand porosity used in the
calculation was based on the total pore volume (i.e,
no allowance was made for dead-end pores etc.),
Despite a degree of scatter that is inevitable when
low hydraulic conductivities are measured, there is
a clear trend for increasing sand tortuosity with
increasing sand porosity.
To be of utility, an engineering model must be
able to predict the hydraulic conductivity of
different mixtures to a variety of permeants from
a limited number of actual measurements. Some
form of tortuosity relationship must, therefore, be
incorporated into the model. For the purposes of
this paper, Archie's relationship between tortuosity
and porosity (eqn. 2) has been fitted to the data in
Fig. 12 by regression analysis (yielding an exponent
'n' of 4.20). However, as the dependence of sand
tortuosity on sand porosity is uncertain, it is
recommended that any tortuosity relationship used
for design purposes should be validated by
hydraulic conductivity measurements on suitable
mixtures.
The model has been used to generate the dashed
and dotted lines in Figs. 8 to 10 showing the
variation in the calculated hydraulic conductivity of
the 10% and 20% mixtures with clay-void ratio.
The generated lines show two clear trends; the
difference between mixture hydraulic conductivity
and that of the bentonite decreases as the clay-void
ratio increases (for a given mixture, increasing clayvoid ratio corresponds to increasing sand porosity),
and at a given clay-void ratio the hydraulic
conductivity of a mixture decreases with decreasing
clay content (the mixture with the lower clay
content has the lower sand porosity). This
behaviour correlates very closely with the observed
behaviour of the mixtures.
Data for the 10% bentonite-sand mixtures tested
with the 0.1 mol/l solutions (Fig. 10) show a
consistent trend between hydraulic conductivity
and clay-void ratio, demonstrating reproducibility
in the measurements. However, sand tortuosity
values calculated from these data are far lower
than those from the other tests. These calculations
require that the bentonite hydraulic conductivityvoid ratio relationship is extrapolated well beyond
the measurement range to void ratios approaching
the free swelling value of 9.9. The anomaly in
calculated tortuosities is thought to indicate that this
extrapolation is inappropriate, and highlights the
Bentonite-sand mixtures
importance of measuring the bentonite hydraulic
conductivity over a suitable clay-void ratio range
when using this model in practice,
In summary, the model allows the prediction of
the swelling behaviour and hydraulic conductivity
of bentonite-sand mixtures with any aqueous
permeant over the applied stress range of engineering interest from the properties of the bentonite
and the sand, and a limited number of hydraulic
conductivity measurements on suitable mixtures to
calibrate the porosity-tortuosity relationship. It can
also estimate the sand porosity and the effective
stress being supported by the sand, these being the
parameters that govern the long-term strength and
stiffness of bentonite-sand mixtures (Mollins,
1996). The model therefore represents a rational
approach to the design of bentonite-sand mixtures
to meet hydraulic conductivity and mechanical
stability criteria.
CONCLUSIONS
(1) The swelling behaviour of a bentonite-sand
mixture is a function of the pore fluid, the applied
effective stress and the clay content. At low
stresses, the clay swells sufficiently in dilute
solutions to separate the sand particles and reach
a clay-void ratio similar to that achieved by
bentonite alone. At high stresses, or in strong
solutions, the bentonite has insufficient swelling
capacity to force the sand particles apart and
swelling is limited by the sand pore volume. In
this case the bentonite has a higher clay-void ratio
than where it supports the entire applied stress.
(2) The swelling behaviour of a bentonite-sand
mixture in aqueous solutions can be predicted from
the swelling properties of the bentonite in the
appropriate solution, and the load-deformation
properties of the sand.
(3) The hydraulic conductivity of a bentonitesand mixture to aqueous solutions can be predicted
fi'om the hydraulic conductivity of the bentonite in
the appropriate solution and the porosity and
tortuosity of the sand matrix.
ACKNOWLEDGMENTS
The authors would like to thank M. Batchelder of the
Natural History Museum, London, for the quantitative
XRD analysis.
659
REFERENCES
Archie G.E. (1942) The electrical resistivity log as an
aid in determining some reservoir characteristics.
Petrol. Technol. 1, 55-62.
Atkinson J.H. & Bransby P.L. (1978) The Mechanics o.1
Soils, McGraw-Hill, London.
Boudreau B.P. (1996) The diffusive tortuosity of finegrained unlithified sediments. Geochim. Cosmochim.
Acta, 60, 3139-3142.
British Standards Institute, BS 12 (1958) Portland
Cement (Ordinary and Rapid Hardening),
Appendix A. HMSO Stationery, London.
British Standards Institute, BS 1377 (1990) Methods of
TestJbr SoilsJbr Civil Engineering Purposes. HMSO
Stationery, London.
Cowland J.W. & Leung B.N. (1991) A field trial of a
bentonite landfill liner. Waste Management Res. 9,
277-291.
Day S.R. & Ryan C. (1995) Containment, Stabilisation
and Treatment of Contaminated Soils using in situ
Soil Mixing. Geoenvironment 2000. ASCE
Geotechnical Special Publication No. 46,
1349-1365.
Di Maio C. (1996) Exposure of bentonite to salt
solution: osmotic and mechanical effects.
Geotechnique, 46, 4, 695-707.
Dixon D.A, Gray M.N. & Thomas A.W. (1985) A study
of the compaction properties of potential clay-sand
buffer mixtures for use in nuclear fuel waste
disposal. Eng. Geol. 21,247-255.
Evans J.C., Costa M.J. & Cooley B. (1995) The State-@
Stress in Soil-Bentonite Slurry Trench Cut-off Walls.
Geoenvironment 2000. ASCE Geotechnical Special
Publication No. 46, 1173-1191.
Graham J., Gray M.N., Sun B.C. & Dixon D.A. (1986)
Strength and volume change characteristics of a
sand-bentonite buffer. Proc. 2nd Int. Conf
Radioactive Waste Management, Winnipeg, Man.,
I88-194.
Head K.H.(1980) Manual of Soil Laboratory Testing,
Vol. 1. Pentech Press, London.
Klute A., (1986) Methods of Soil Analysis. Physical and
Mineralogical Methods, Part l, 2nd edition. Am.
Soc. Agronomy, Madison, Wis. USA.
Kraus J.F., Benson C.H., Erickson A.E. & Chamberlain
E.J. (1997) Freeze-thaw cycling and hydraulic
conductivity of bentonitic barriers. ASCE J.
Geotech. Eng., 123, 229-238.
Lerman A. (1979) Geochemical Processes in Water and
Sediment Environments. John Wiley & Sons, New
York.
Mollins L.H. (1996) The design of bentonite-sand
mixtures. PhD thesis, Univ. Leeds, UK.
Mollins L.H., Stewart D.I. & Cousens T.W. (1996)
Predicting the properties of bentonite-sand mixtures.
Clay Miner. 31,243-252.
660
P.G. Studds et al.
Porter L.K., Kemper W. D., Jackson R.D. and Stewart
B,A. (1960) Chloride diffusion in soils as influenced
by moisture content. Proc. Soil Sci. Soc. Am. 24,
460-463.
Shackleford C.D. & Daniel D.E. (1991) Diffusion in
saturated soil. I: Background. A.S.C.E.J. Geotech.
Eng. 117, 467-484.
Slade P.G., Quirk J.P. & Norrish K. (1991) Crystalline
swelling of smectite samples in concentrated NaCI
solutions in relation to layer charge. Clays Clay
Miner. 39, 234-238.
Studds P.G., Stewart D.I. & Cousens T.W. (1996) The
effect of ion valence on the swelling behaviour of
sodium montmorillonite. Proc. 4th lnt. Con]. on Reuse o f Contaminated Land and Landfills, 139-142.
Engineering Technics Press, Edinburgh.
van Olphen H. (1977) An Introduction to Clay Colloid
Chemistry. John Wiley & Sons, London.