heavy metals effects

1. ORIGINAL PAPER
Geotechnical Characteristics of Copper Mine Tailings:
A Case Study
Abolfazl Shamsai Æ Ali Pak Æ
S. Mohyeddin Bateni Æ
S. Amir Hossein Ayatollahi
Received: 23 June 2005 / Accepted: 22 June 2007 / Published online: 18 July 2007
Ó Springer Science+Business Media B.V. 2007
Abstract Waste management issue in mining
industry has become increasingly important. In this
regard, construction of tailings dams plays a major
role. Most of the tailings dams require some kinds of
remedial actions during their operational lifetime,
among which heightening is the most common. In the
first stage of the remedial provisions for Sarcheshmeh
Copper Complex tailings dam in Iran, it has been
decided to use hydrocyclone method to provide
suitable construction material due to the high cost
associated with using borrow materials for heighten-
ing of the dam. To undertake this project a series of
laboratory experiments was performed to determine
the copper ‘original tailings’ and ‘cycloned materials’
geotechnical characteristics to evaluate the applica-
bility of the cycloned materials for construction
purposes. Different laboratory experiments were
conducted to determine the grain-size distribution,
Atterberg limits, specific gravity, maximum density,
shear strength parameters, consolidation coefficient,
and hydraulic conductivity. The results were com-
pared with those of similar mines to check whether
they follow the trends observed in other copper
tailing materials elsewhere. Variation of the cohesion
and internal friction angle versus different compac-
tion ratios were studied in order to determine realistic
shear strength parameters for tailing dam stability
analysis. In this study, using oedometer test, a mild
linear relation between void ratio and the consolida-
tion coefficient has been found for tailings materials.
By considering the effects of void ratio and weight of
passing sieve #200 materials, a new relationship is
proposed that can be used for estimating the copper
slimes hydraulic conductivity in seepage analysis of
tailings dams.
Keywords Copper tailings Á Geotechnical
characteristics Á Hydrocyclone Á Sar-chesh-meh
copper mine
1 Introduction
A common environmental issue associated with the
mineral industries is the disposal of a huge mass of
tailing materials regularly produced from their
A. Shamsai
Department of Civil Engineering, Sharif University of
Technology, Tehran, Iran
e-mail: shamsai@sharif.edu
A. Pak (&)
Department of Civil Engineering, Sharif University of
Technology, Azadi Avenue, Tehran 11365-9313, Iran
e-mail: pak@sharif.edu
S. M. Bateni
Department of Civil and Environmental Engineering,
Massachusetts Institute of Technology, Cambridge, MA,
USA
e-mail: smbateni@mit.edu
S. A. H. Ayatollahi
Science and Research Unit, Azad University, Tehran, Iran
123
Geotech Geol Eng (2007) 25:591–602
DOI 10.1007/s10706-007-9132-9

2. processing operations. Historically, mining industries
do not have a good reputation because of releasing
their waste materials to the surrounding environment.
Tailings dams as a practical solution have played an
important role in protecting valuable soil and water
resources from contaminated slurries. Tailings dams
are considered the largest man-made structures in the
world. They are generally comprised of three types of
materials: (1) factory sediments (2) mine tailings (3)
deposited materials. Normally, considerable bodies of
water may be stored behind tailings dams, so dam
failure can cause disastrous damages to lives, prop-
erties, and the surrounding environment. Hence
design, construction, and operation of these dams
call for a high level of care in engineering practice.
Vick (1983) has provided a comprehensive reference
to tailings dam literature in various fields. He has
described the differences between tailings embank-
ments and classical water retention-dams from a
geotechnical standpoint. Soil instability problems
associated with tailings dams building on sensitive
clays were studied by Capozio et al. (1982). Klohn
(1981) has presented an overview of the geotechnical
studies required for design of tailings dams. Mittal
and Morgenstern (1975) presented the design param-
eters for copper mines tailings dams. They demon-
strated that average hydraulic conductivity for sand
tailings is best predicted by the well-known Hazen’s
formula. A full research was performed on copper
mine sands and slimes properties by Volpe (1975).
His studies on tailing’s geotechnical parameters such
as specific gravity, void ratio and dry density showed
that the average tailings hydraulic conductivity
decreases with increasing fines content (percent
passing sieve #200). Not many researches are con-
ducted on the effect of fine particles on tailing
characteristics. Aubertin et al. (1996) have done
laboratory investigations on hydraulic conductivity
of homogenized hard rock tailings and discussed the
effect of void ratio and grain size on the tailings’
coefficient of hydraulic conductivity. Matyas et al.
(1983) expressed compressibility of tailings in terms
of void ratio, vertical effective stress and D50 value.
They evaluated the effect of void ratio on tailings
permeability and shear strength.
In this paper, first the results of the experiments
conducted for determining the grain size distribution,
Atterberg’s limits, specific gravity, dry density, and
shear strength parameters of Sarcheshmeh copper
mine tailing materials are described and the results
are compared with those of other copper mines, in
order to investigate the applicability of the results and
routines recommended in the literature for copper
mine tailings. Then, variation of consolidation coef-
ficient, shear strength, and hydraulic conductivity of
copper tailings have been studied in detail, and their
relations to other parameters have been investigated.
Finally, the importance of the findings in tailings dam
design procedure is emphasized.
2 Sar-chesh-meh Copper Mine
Iran is known to have the rank 16th among the
world’s copper producers (Edelstein 2003). The
country’s largest copper mine is located at Sar-
cheshmeh, Kerman province which belongs to the
National Iranian Copper Industries Company (NIC-
ICO). Sarcheshmeh tailings dam has been built and
utilized since 1984. This dam is, in fact, a conven-
tional earth dam with a catchment area of 180 km2
,
design flood discharge of 800 m3
/s, the average
runoff volume of 10 · 106
m3
/year, the height of
75 m and the crest length of 1100 m. Each day
40000 tons of solid material enters the reservoir.
Based on previous investigations, one ton of this
waste material would fill 0.8 m3
of the reservoir
volume (Askari et al. 1994). By 1994 discharged
sediments had filled nearly 55 · 106
m3
of the
reservoir’s free volume and with this rate, the
reservoir was expected to be filled up in a time
between 5 years and 7 years (Askari et al. 1994). In
order to maintain the Sarcheshmeh copper mine
operating, heightening of dam was the normal choice.
Increasing dam height from 75 m (elevation 2010 m)
to 90 m (elevation 2025 m) can enhance the reservoir
volume to about 120 · 106
m3
. For achieving a
sound design and a reliable construction, the geo-
technical properties of the deposited copper tailings
had to be carefully examined.
3 Sar-chesh-meh Copper Tailings Geotechnical
Characteristics
Geotechnical characteristics of Sarcheshmeh original
mine tailings as well as the properties of hydrocy-
clone underflow coarse grained materials were
592 Geotech Geol Eng (2007) 25:591–602
123

3. determined during a series of laboratory experiments.
These characteristics consisted of grain size distribu-
tion, plasticity index (PI), liquid limit (LL), specific
gravity (Gs), in-place density, pulp density, maximum
dry density (cdmax
), optimum moisture content (wopt),
consolidation coefficient (Cv), hydraulic conductivity
(k), and shear strength parameters, including cohesion
(C) and internal friction angle (U). Results reported
herein, are generally the average values of three tests.
3.1 Grain Size Distribution
3.1.1 Original Tailings Material
In this research, 154 laboratory samples for gradation
test and 30 for hydrometry test of Sarcheshmeh whole
tailings (including slimes) were selected. The tests
were conducted according to D422-63 (ASTM
1991a1). Figure 1 illustrates the grain size distribu-
tion curve of Sarcheshmeh tailing materials com-
pared to those of some other copper mines.
Sarcheshmeh tailings gradation curve fall within the
range of Michigan whole tailings (Girucky 1973) and
Philipines whole tailings (Salazar and Gonzales
1973). In general the whole tailings are relatively
coarse, with about 45% passing the sieve #200 (P200)
on average, depending on grinds milling size of the
extracted minerals.
3.1.2 Hydrocycloned Under-flow Materials
Grain size distribution of the cycloned under-flow
particles depends on the feeding material, hydrocy-
clone pressure, initial slurry density and the possi-
bility of adding water to the process. The first
processing stage was performed using a Krebs-D20B
hydrocyclone module and the second using a Krebs-
D26B module. They were carried out with an
exerting pressure of 0.7 atm over 90% of under-flow
materials consisted of particles >74 l. The system
efficiency as the ratio of the final cycloned solids
weight to the initial solids weight, was calculated
about 24%. Grain size distribution curves of pro-
cessed (cycloned) as well as unprocessed (whole)
tailings materials are depicted in Fig. 2. Unified soil
classification system categorizes the processed mate-
rial within SP group.
3.2 Atterberg’s Limits
Generally tailings consist of two parts: finer and
coarser than 0.074 mm (sieve No. 200). The former
part is called ‘tailings slimes’ and the latter ‘sand
tailings’. Sand tailings are usually non-plastic; how-
ever, slimes tailings may exhibit low plasticity. The
plastic properties of Sarcheshmeh tailings slimes
have been determined and compared with those of
Mittal and Morgenstern (1976) and Volpe (1979)
(Table 1). An average LL of 29 and plasticity limit of
6 were derived from 30 laboratory tests conducted
according to the procedure described in D4318-84
(ASTM 1991c). For evaluating the activity (A),
Skempton relation is used:
A ¼ ðPI)=C ð1Þ
in which, PI is plasticity index and C is percent finer
than 0.074 mm.
0
10
20
30
40
50
60
70
80
90
100
0.00010.0010.010.1110100
Grain size - millimeters
ahtreniftnecrePn
Mittal and Morgenstern, 1976
(British Colombia - slimes)
Volpe, 1979
U.S. - average slimesSalazar and
Gonzales, 1973
(Philippines -
whole tailings)
Sarcheshmeh, 2002
(Iran - whole tailings)
Klohn and
Maartman, 1973
(British Colombia
whole tailings)
Girucky, 1973
(Michigan - whole tailings)
Volpe, 1979
(Average whole tailings, 10
U.S. deposits)
Fig. 1 Comparison of
Sarcheshmeh whole tailings
grain size distribution with
those of other copper mine
materials
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123

4. 3.3 In-place Dry Density and Specific Gravity
Specific gravity tests carried out according to D854-
58 (ASTM 1991b) showed that Sarcheshmeh mate-
rials stand at the upper limit of Volpe (1979) results
and appear to have heavier grains. According to this
study, the in-place void ratio ranges from 0.4 to 1.0.
In-place dry density depends primarily on the specific
gravity, type of tailings (sands or slimes), and clay
content. It was tested and measured to be 1.78 ton/m3
(Table 2).
3.4 Maximum Dry Density and Optimum Water
Content
For determining maximum dry density and its
corresponding optimum moisture content, AASHTO
standard method for compaction has been employed
on 25 samples. The tests have yielded a maximum
dry density of 1.8 ton/m3
in optimum water content
(OMC) of 14.18%. These values are in agreement
with those of Aubertin et al. (1996) on hard rock
tailings where they reported a range of 13.0 to 15.2%
for (OMC) corresponding to cdmax
from 1.75 ton/m3
to
1.83 ton/m3
.
3.5 Pulp Density
The common method for determining solid concen-
tration in water is measuring the ‘pulp density’,
which is defined as follows:
Pulp density ¼
Net weight of solid materials
Total weight
Average experimental values show a pulp density
of 0.3 which was consistent with the value stated by
IRCOLD (1998) for tailings pulp density.
3.6 Shear Strength Parameters
In the course of this study four standard laboratory
tests were carried out for determining shear strength
parameters of 150 specimens, namely:
(1) Dry and fast direct shear test
(2) Saturated and slow direct shear test
(3) Consolidated – Undrained triaxial test (CU)
(4) Consolidated – Drained triaxial test (CD)
It should be noted that although unsaturated
conditions may prevail in the body of the tailing
dams, for the sake of comparison between shear
strength parameters of processed and unprocessed
tailings, it was decided to use the standard CU and
CD test in fully saturated conditions.
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1
Size (mm)
)%(gnissaP
Final hydrocyclone product
Finer envelope (Unprocessed)
Coarser (Unprocessed)
Fig. 2 Processed and unprocessed grain size distribution curve
Table 1 Atterberg limits of copper tailings slimes
Location Liquid limit % Plasticity index % Activity Source
Western U.S. 40 (Avg.) 13 (Avg.) Not reported Volpe (1979)
British Columbia 0–30 0–11 Not reported Mittal and Morgenstern (1976)
Sarcheshmeh, Iran 26–39 4–12 0.4–1.0 Present study
Table 2 Dry density and specific gravity of copper tailings
Tailings type Gs e cd (ton/m3
) Reference
Sands 2.6–2.8 0.6–0.8 1.59–1.79 Volpe (1979)
Slimes 2.6–2.8 0.9–1.4 2.68–2.07 Volpe (1979)
Sands and
slimes
2.79 0.4–1.0 1.78 Present study
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5. 3.6.1 Unprocessed Material
Variation of cohesion (C) with relative compaction
(Rc) in dry and saturated conditions is illustrated in
Fig. 3. In direct shear tests, the cohesion varies within
the range of 0.1–0.24 kg/cm2
with some irregulari-
ties, apparently due to experimental errors. While in
the triaxial tests, the cohesion shows a strong
increasing trend with the relative compaction.
In Fig. 4, within the whole compaction ratio
domain, the difference between different tests results
for internal friction angle is demonstrated. Lower
values of internal friction angle obtained from direct
shear tests for lower compactions levels, compare to
triaxial consolidated tests, are considerable.
3.6.2 Processed Material
Figure 5 indicates that cohesion of cycloned materi-
als within the entire domain of compaction ratio is
very low and <0.2 kg/m2
. In dry direct shear test, the
cohesion varies from 0.07 kg/m2
to 0.15 kg/m2
,
while in saturated direct shear test the variation is
from 0.02 kg/m2
to 0.07 kg/m2
. Measured values of
cohesion in CU test are greater than the other test
results where the effects of pore pressure in undrained
shearing have caused such differences. Due to the
obtained low values for cohesion, the processed
materials were considered cohesionless.
Figure 6 depicts the processed tailings internal
friction angle versus compaction ratio.
As can be seen the internal friction angle of the
processed material shows a monotonic variation with
increasing relative compaction in all the tests con-
ducted in this study.
3.6.3 Comparison of Shear Strength Parameters
Void ratio is calculated in terms of relative compac-
tion (Rc ¼ cd
cmax
) to make a comparison with previous
results in other copper mines. The formula is as
follows:
e ¼
Gscx
Rccd max
À 1 ð2Þ
0
0.2
0.4
0.6
0.8
1
1.2
1.4
70 75 80 85 90 95 100 105
Relative compaction (Modified AASHTO) %
mc/gk(noisehoC2
)
Dry direct shear Sat.direct shear
CU CD
Fig. 3 Unprocessed tailings cohesion versus compaction ratio
0
5
10
15
20
25
30
35
40
45
70 75 80 85 90 95 100 105
Relative compaction (Modified AASHTO)%
)geD(elgnanoitcirflanretnI
Dry direct shear Sat.direct shear
CU CD
Fig. 4 Unprocessed tailings internal friction angle versus
compaction ratio
0
0.05
0.1
0.15
0.2
0.25
75 80 85 90 95 100 105
Relative compaction (Modified AASHTO %)
mc/gk(noisehoC
2
)
Dry direct shear
Sat. direct shear
CU
CD
Fig. 5 Processed tailings cohesion versus compaction ratio
Geotech Geol Eng (2007) 25:591–602 595
123

6. As shown in Table 3, the undrained strength (CCU)
for whole tailings varies between 0.3 kg/cm2
and
0.97 kg/cm2
. An average value of 0.65 would be
acceptable for design purposes. For slimes, a cohe-
sion value of 0 has been recommended (which is
mostly referred to CD test results) as a confident
design parameter value.
For a better comparison, variation of CU friction
angle versus compaction ratio for unprocessed and
processed materials is shown in Fig. 7.
The compaction ratio of 90% is the value in which
the friction angle difference between processed and
unprocessed materials came about 24%. Therefore in
using cycloned material, in construction of a stable
embankment during heightening of the dam, the
minimum compaction ratio should be 90%.
Based upon the shear strength experiments, vari-
ation of C and U with relative compaction Rc, are
plotted and the equations of the best fitted curves to
the experimental values are shown in Table 4. The C
15
20
25
30
35
40
45
75 80 85 90 95 100 105
Relative compaction (Modified AASHTO %)
)geD(elgnanoitcirflanretnI Dry direct shear
Sat. direct shear
CD
CU
Fig. 6 Processed tailings internal friction angle versus compaction ratio
Table 3 Internal friction angle and cohesion values
Material Initial void ratio (e0) Friction angle (U) Cohesion, CCU (kg/cm2
) Source
Copper tailings, all types – 13–18 0–0.98 Volpe (1979)
Copper beach sands 0.7 19–20 0.34–0.44 Wahler (1974)
Copper slimes 0.6 14 0.64 Wahler (1974)
Copper slimes 0.9–1.3 14–24 0–0.2 Wahler (1974)
Copper whole tailings 0.5–1.1 8 –29 0.30–0.97 Present study
Copper slimes 0.5–1.1 24–37 0.08–0.21 Present study
20
22
24
26
28
30
32
34
36
38
40
60 65 70 75 80 85 90 95 100 105
Relative compaction (Modified AASHTO %)
)geD(elgnanoitcirflanretnI
Processed
Unprocessed
Fig. 7 Variation of CU internal friction angle versus compac-
tion ratio
596 Geotech Geol Eng (2007) 25:591–602
123

7. and U functions are valid for copper whole tailings
and cycloned materials within the range 72% and
102% of Rc variation.
3.7 Consolidation Coefficient
In order to determine the coefficient of consolidation,
and permeability of materials, odometer tests were
conducted (D2435-80, ASTM 1991d). Tailings mate-
rial in initial dry densities of 1.23, 1.32, 1.51 and
1.88 g/cm3
corresponding to relative compactions of
66%, 72%, 82%, and 102%, respectively were
subjected to consolidation test.
The available data suggests that the coefficient of
consolidation (Cv) is generally between 10À3
and
0.1 cm2
/s for beach sand deposits (Volpe 1979). The
values obtained for Sarcheshmeh tailings
(5 · 10À3
cm2
/s) were typical for fine tailings, which
matches with the investigations by Guerra (1973),
Mittal and Morgenstern (1976), Haile and Kerr (1989)
and Santos et al. (1992). For slimes, Cv is generally
about 10À4
–10À2
cm2
/s, in the same range of typical
natural clays. Reported data from the literature for both
sands and slimes tailings are summarized in Table 5.
It should be noted that unlike natural clays,
however, Sarcheshmeh slimes do not reveal a strong
dependency on the value of initial void ratio e0. Data
reported by Mittal and Morgenstern (1976) and others
are compared to those of this research as illustrated in
Fig. 8. Generally, for all materials, Cv shows an
increasing trend with void ratio, like the behavior
usually seen with natural clays at void ratios corre-
sponding to stresses in the range of the preconsolida-
tion pressure. But as shown in Fig. 8, Cv value of
Sarcheshmeh slimes tested for a range of initial void
ratios between 0.3 and 1.1, did not change considerably
from 0.01 cm2
/s. A curve fitting procedure shows that
a linear regression (e0 = 63.814 Cv) is best fitted to
experimental data with a R2
value of 0.905. This
relation can be used as an empirical, yet valid, formula
for estimating Cv for Sarcheshmeh tailings.
Variation of Cv versus total stress is depicted in
Fig. 9, where each curve represents Cv values for a
specific dry density. Apart from the jumps observed
at stress levels lower than 1.0 kg/cm2
, the rest of the
curves show a mild declining trend of Cv with respect
to the total stress increase.
3.8 Hydraulic Conductivity
As mentioned in Sect. 3.7, tailings materials with
initial dry densities of 1.23, 1.32, 1.51 and 1.88 g/cm3
corresponding to relative compaction of 66%, 72%,
82%, and 102% respectively were subjected to
consolidation (oedometer) test. The coefficients of
permeability were estimated using equation
k ¼ Cv Á mv Á cw ð3Þ
The value of mv has been kept constant in calcula-
tion of coefficient of permeability. Same as what is
illustrated in Fig. 9, variation of k with the total stress
for samples with different relative compactions is
depicted in Fig. 10. As shown, k has a decreasing trend
with respect to total stress. But this decreasing trend
becomes milder for total stresses >3.0 kg/cm2
.
Illustrated in Fig. 11, the average values of k for
Sarcheshmeh whole tailings have been compared to
that of other copper mines. The range between 10À8
and 10À7
explains the existence of more fine grains in
this mine comparing to data reported by other
sources.
Table 4 Curve fitted functions of cohesion and internal friction angle in terms of relative compaction (Rc%)
Test Unprocessed materials Processed materials
Dry and fast direct shear C = À.2.1 Rc
2
+ 3.8 Rc À 1.5 C = 0
U = 103.8 Rc À 61.6 for Rc > 59% U = 99.8 Rc À 60.7 for Rc > 67%
Saturated and slow direct shear C = 0.15 C = 0
U = 77 Rc À 48.1 for Rc > 62% U = 79.8 Rc À 37.9 for Rc > 47.5%
Consolidated drained (CD) C = 2.2Rc À 1.3 for Rc > 55% C = 0
U = 25.7 Rc + 2.6 U = 63.4 Rc À 22.5 for Rc > 40%
Consolidated undrained (CU) C = 2.7 Rc À 1.7 for Rc > 63% C = 0
U = 39 Rc À 4.7 for Rc > 12% U = 58.8 Rc À 14.7 for Rc > 25%
Geotech Geol Eng (2007) 25:591–602 597
123

8. According to the valuable results obtained during
consolidation tests, it was intended to carry out an
investigation about the k value by comparing the
calculated hydraulic conductivities with the values
estimated from previous studies. In this procedure
some famous formulas such as Hazen (1892), Koze-
ny–Carman modified by Mbonimpa et al. (2002), and
Bates and Wayment (1967) were considered. The
value of k given by the Hazen’s relation (1892) was
initially proposed for uniform loose sand and had been
often used to estimate the hydraulic conductivity of
tailings (Mittal and Morgenstern 1975; Mabes et al.
1977; Volpe 1979; Fell et al. 1993). In the geotech-
nical field this equation is usually written as follows:
k ¼ c2D2
10 ð4Þ
where k is given in cm/s and D10 is in cm, c2 is
considered a material constant. As suggested by
various authors (e.g. Loudon 1952; Vick 1983), a
Table 5 Typical values of coefficient of consolidation (Cv)
Material type Cv (cm2
/s) Source
Copper beach sands 3.7 · 10À1
Volpe (1979)
Copper slimes 1.5 · 10À1
Volpe (1979)
Copper slimes 10À3
–10À1
Mittal and Morgenstern (1976)
Copper whole tailings 5 · 10À3
–2 · 10À2
Present study
Copper slimes 10À2
Present study
0.00
0.01
0.10
1.00
0 0.5 1 1.5
Initial void ratio (e0)
mc(vC
2
)gk/
a b
c d
e f
g h
Fig. 8 (a) Copper slimes: Mittal and Morgenstern 1976. (b)
Copper sands: Mittal and Morgenstern 1976 (c) Copper slimes:
Unpublished. (d) Sarcheshmeh slimes: Present study, (e–h)
Sarcheshmeh whole tailings: Initial dry density = 1.23, 1.32,
1.51, 1.88 g/cm3
0.001
0.01
0.1
0 2 4 6 8 10 12
Stress (kg / cm
2
)
mc(vC
2
)gk/
Dry density = 1.23 (g / cm3)
Dry density = 1.32 (g / cm3)
Dry density = 1.51 (g / cm3)
Dry density = 1.88 (g / cm3)
Fig. 9 Variation of Cv versus total stress for different initial
dry densities
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
0.0 2.0 4.0 6.0 8.0 10.0 12.0
Total stress ( kg / cm
2
)
)s/mc(K
Dry density =1.23 (g/cm3)
Dry density =1.32 (g/cm3)
Dry density =1.51 (g/cm3)
Dry density =1.81 (g/cm3)
Fig. 10 Hydraulic conductivity versus total stress in oedom-
eter test for different initial dry densities
598 Geotech Geol Eng (2007) 25:591–602
123

9. value of 100 is adopted here. It should, however, be
recognized that the c2 value can vary between 60 and
150 approximately, depending upon grain-size
distribution (Kova´cs 1981). Probably the best
known expression for k is the one developed by
Kozeny (1927), based on flow through open tabular
channels. Later, Carman (1937, 1956) introduced the
concept of hydraulic radius to represent the geometric
characteristics of the pore system. The equation
referred to as Kozeny–Carman equation is as follows:
k ¼
c1g
lwqwD2
r
1
S2
e3
ð1 þ eÞ
ð5Þ
In the above equation, c1 is a material parameter,
lw is the water kinematic viscosity in (Pa s), qw is the
water density in (kg/m3
), S is the specific surface, Dr
is the average relative density of solid grains, g is the
gravitational acceleration and e is the void ratio.
The surface characteristic function was defined by
Chapuis and Montour (1992), Chapuis and Aubertin
(2003) and finally represented as two sets of useful
formulas for granular and plastic soils respectively by
Mbonimpa et al. (2002):
kG ¼ CG
cw
lw
e3þx
ð1 þ eÞ
C1=3
U
D2
10 ð6Þ
kP ¼ CP
cw
lw
e3þx
ð1 þ eÞ
1
q2
s w2v
L
ð7Þ
in which CG = 0.1, CU is the Coefficient of unifor-
mity, CP = 5.6 g2
/m4
, x in Eq. 6 is 2 and v in Eq. 7 is
1.5, qs is solid grain density in (kg/m3
), cw water unit
weight in (KN/m3
), lw water viscosity in (Pa s) and
wL is defined as LL in percent. Here, the results are
controlled by Eq. 6 for low plasticity and low
cohesion materials of Sarcheshmeh tailings (PL = 4–
12).
Another formula is shown in Eq. 8 below, which
was specifically developed for tailings at the U.S.
Bureau of Mines (Bates and Wayment 1967).
k ¼ ½expð x1 þ x2 lnðeD10Þ þ x3 lnðeÞ lnðCUÞ
þ x4ðeCUÞ þ x5ðD10D50ÞŠ
ð8Þ
The following values for the constants have been
proposed: x1 = 11.02, x2 = 2.912, x3 = À0.085, x4 =
0.194, x5 = À56.49. This equation was based upon
over 100 infiltration tests results, for void ratios
between 0.52 and 1.08, D10 values between
0.003 mm and 0.105 mm, D50 values between
0.060 mm and 0.24 mm, and CU values between 2
and 22.
In most of the equations mentioned above, the
value of k depends on two major factors: grain size
and void ratio. Most researchers (e.g. Goldin and
Rasskazov 1992; Sperry and Pierce 1995; Venka-
taraman and Rao 1998) have focused on including
the effect of grain size in their equation with a
specific representative particle size (such as D10,
D50, etc.). In this paper the authors have proposed
that the percentage finer than sieve #200 (P200) be
taken into account as a new parameter to replace the
grain size.
The percentage finer than sieve #200 (P200) distin-
guishes the characteristics of soil, whether it is
cohesive or non-cohesive. This parameter can replace
other soil parameters such as grading and plasticity in
the formulas. Therefore, nine samples of Sarcheshmeh
whole tailings were chosen in which by adding or
subtracting the value of passing sieve No. 200,
desirable specimen for consolidation test were pre-
pared. After carrying out 9 tests for P200 = 55, 60, 65,
70, 75, 80, 85, 90, and 95% (Fig. 12), values of k for
different void ratios were determined indirectly
through consolidation odometer test results. The
relation between k value and the void ratio can be
stated as follows:
1.0E-09
1.0E-08
1.0E-07
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
0 0.3 0.6 0.9 1.2 1.5
Void ratio (e)
)s/mc(ytivitcudnocciluardyhegarevA
Copper slimes (Mittal & Morgenstern, 1976)
Cycloned copper sands (Mittal & Morgenstern, 1976)
Copper-zinc slimes
Copper sands, P200 = 35 % (Volpe, 1979)
Sarcheshmeh (2005)
Fig. 11 Variation of hydraulic conductivity coefficient with
void ratio
Geotech Geol Eng (2007) 25:591–602 599
123

10. k ¼ 0:09 Â 10À0:08P200
e2:8
e þ 1
ð9Þ
The above relation has been obtained by curve-
fitting to the experimental results (with R2
value of
0.984) which represents a simplified Kozeny–Carman
type equation. Despite the simplicity of this equation,
it has a limitation on P200 to be over 50%. However,
it gives k values for a wide range of void ratios
between 0.3 and 1.1. The results of the proposed
formula have been checked by comparing to the
results of other relations for Sarcheshmeh whole
tailings. The parameters used in the analysis were
selected according to the following set of data:
D10 = 0.00164 mm, CU = 30, P200 = 75%,
D50 = 0.03 mm. As it is realized from Fig. 13, Hazen
(Eq. 4), as a basic equation in this field, does not
depend on the void ratio. Hence, it yields an average
value for all tailings. The k value in the formula
presented by the authors varies from 3.72 · 10À9
cm/
s to 8.65 · 10À8
cm/s as lower and upper bounds of
Hazen formula, while Hazen equation gives a con-
stant value of 2.69 · 10À8
cm/s for different material
size grading. The Eq. 6, in which a modified version
of Kozeny–Carman equation has been presented,
shows the closest correlation with the proposed
formula and the measured data. This relevance
appears the best for k values 1.2 · 10À6
. For void
ratios 0.6 the difference between two formulas
increases but they still demonstrate a good level of
consistency.
For the sake of comparison, it can easily be shown
that all the above equations are particular forms of the
following general expression:
k ¼ f
ex1
ð1 þ eÞx2
ð10Þ
1.E-10
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
0 0.2 0.4 0.6 0.8 1 1.2
Void ratio (e)
)s/mc(K
P200=50 P200=55 P200=60
P200=65 P200=70 P200=75
P200=80 P200=85 P200=90
Fig. 12 Experimental test data on hydraulic conductivity of
tailings specimen with P200 varying from 50% to 90%
1.E-10
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
0 0.2 0.4 0.6 0.8 1 1.2
Void ratio (e)
)s/mc(k
Hazen (1892)
Kozeny-Carman Modified Aubertin (1927)
Bates and Wayment (1967)
Measured (This study)
Calculated (This study)
Fig. 13 Validation of the proposed formula for coefficient of
permeability
Table 6 Typical values for x1 and x2 power parameters of k-e
equations
x1 x2 References
2 0 Terzaghi (1943)
3 0 Chardaballas (in Kova´cs 1981)
2 1 Goldstein (1938); de Wiest (1969)
3 1 Carman (1956)
4.55 0 De Campos et al. (1994)
3.8 1 Stone et al. (1994)
4.79 0 Aubertin et al. (1993)
5.16 1 Aubertin et al. (1996)
5 1
2.8 1 Present study
600 Geotech Geol Eng (2007) 25:591–602
123

11. The typical values of parameters x1 and x2 are
presented in Table 6.
4 Conclusions
A series of geotechnical experiments has been
conducted on the whole tails and cycloned materials
of Sarcheshmeh copper mine in order to investigate
the suitability of these materials for construction of
phase two of the Sarcheshmeh tailings dam. The
geomechanical characteristics of these materials are
compared to those of some similar copper mines
elsewhere. Based on the obtained results the follow-
ing conclusions can be drawn:
1. The average values of geotechnical parameters of
Sarcheshmeh copper mine fall within the param-
eters obtained from other copper mines. This
indicates that the relationships proposed for
copper mine tailings can be used for heightening
of Sarcheshmeh tailings dam.
2. A linear relation between the void ratio and
consolidation coefficient has been observed in
Sarcheshmeh slimes. However, slope of the line
is very flat (almost nil) as opposed to the similar
relations observed in other copper mines.
3. A new relation for estimating hydraulic conduc-
tivity is proposed which looks attractive for its
simplicity and also for its new physical repre-
sentation. This equation could advantageously
replace some of the empirical formulae that have
been used in the past and can be applied for quick
estimation of k value for seepage analysis in the
preliminary design phase of copper mine tailings
dams.
Acknowledgments The authors gratefully acknowledge
National Iranian Copper Industries Company (NICICO) for
providing useful data.
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