10.1007 s10706 007-9132-9

12
ORIGINAL PAPER Geotechnical Characteristics of Copper Mine Tailings: A Case Study Abolfazl Shamsai Ali Pak S. Mohyeddin Bateni 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 Geotechnical characteristics Hydrocyclone 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: [email protected] A. Pak (&) Department of Civil Engineering, Sharif University of Technology, Azadi Avenue, Tehran 11365-9313, Iran e-mail: [email protected] S. M. Bateni Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA e-mail: [email protected] 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

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Page 1: 10.1007 s10706 007-9132-9

ORIGINAL PAPER

Geotechnical Characteristics of Copper Mine Tailings:A Case Study

Abolfazl Shamsai Æ Ali Pak ÆS. Mohyeddin Bateni ÆS. Amir Hossein Ayatollahi

Received: 23 June 2005 / Accepted: 22 June 2007 / Published online: 18 July 2007

� 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 � Geotechnical

characteristics � Hydrocyclone � 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: [email protected]

A. Pak (&)

Department of Civil Engineering, Sharif University of

Technology, Azadi Avenue, Tehran 11365-9313, Iran

e-mail: [email protected]

S. M. Bateni

Department of Civil and Environmental Engineering,

Massachusetts Institute of Technology, Cambridge, MA,

USA

e-mail: [email protected]

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

Page 2: 10.1007 s10706 007-9132-9

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

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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

ahtreniftn ecreP

n

Mittal and Morgenstern, 1976 (British Colombia - slimes)

Volpe, 1979 U.S. - average slimes Salazar 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

Geotech Geol Eng (2007) 25:591–602 593

123

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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 cdmaxfrom 1.75 ton/m3to

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 1Size (mm)

)%(

gniss

aP

Final hydrocyclone productFiner 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

594 Geotech Geol Eng (2007) 25:591–602

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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

� 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(noiseho

C2 )

Dry direct shear Sat.direct shearCU 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(e lgna

noit cirflanretnI

Dry direct shear Sat.direct shearCU 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(noiseho

C2 )

Dry direct shearSat. direct shearCUCD

Fig. 5 Processed tailings cohesion versus compaction ratio

Geotech Geol Eng (2007) 25:591–602 595

123

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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 shearSat. direct shearCDCU

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(

elgnanoitci rflanr etnI

ProcessedUnprocessed

Fig. 7 Variation of CU internal friction angle versus compac-

tion ratio

596 Geotech Geol Eng (2007) 25:591–602

123

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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 10�3 and

0.1 cm2/s for beach sand deposits (Volpe 1979). The

values obtained for Sarcheshmeh tailings

(5 · 10�3 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 10�4–10�2 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 � mv � 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 10�8

and 10�7 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 = �.2.1 Rc2 + 3.8 Rc � 1.5 C = 0

U = 103.8 Rc � 61.6 for Rc > 59% U = 99.8 Rc � 60.7 for Rc > 67%

Saturated and slow direct shear C = 0.15 C = 0

U = 77 Rc � 48.1 for Rc > 62% U = 79.8 Rc � 37.9 for Rc > 47.5%

Consolidated drained (CD) C = 2.2Rc � 1.3 for Rc > 55% C = 0

U = 25.7 Rc + 2.6 U = 63.4 Rc � 22.5 for Rc > 40%

Consolidated undrained (CU) C = 2.7 Rc � 1.7 for Rc > 63% C = 0

U = 39 Rc � 4.7 for Rc > 12% U = 58.8 Rc � 14.7 for Rc > 25%

Geotech Geol Eng (2007) 25:591–602 597

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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 c2D210 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 · 10�1 Volpe (1979)

Copper slimes 1.5 · 10�1 Volpe (1979)

Copper slimes 10�3–10�1 Mittal and Morgenstern (1976)

Copper whole tailings 5 · 10�3–2 · 10�2 Present study

Copper slimes 10�2 Present study

0.00

0.01

0.10

1.00

0 0.5 1 1.5

Initial void ratio (e0)

mc(v

C2

)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 / cm2)

mc(v

C2

)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 / cm2)

)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

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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 (Kovacs 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

lwqwD2r

1

S2

e3

ð1þ 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 CGcw

lw

e3þx

ð1þ eÞC1=3U

D210 ð6Þ

kP ¼ CPcw

lw

e3þx

ð1þ eÞ1

q2s 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 lnðCUÞþ x4ðeCUÞ þ x5ðD10D50Þ�

ð8Þ

The following values for the constants have been

proposed: x1 = 11.02, x2 = 2.912, x3 = �0.085, x4 =

0.194, x5 = �56.49. 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(

ytivitcudnocciluardyh

egar evA

Copper slimes (Mittal & Morgenstern, 1976)Cycloned copper sands (Mittal & Morgenstern, 1976)Copper-zinc slimesCopper sands, P200 = 35 % (Volpe, 1979)Sarcheshmeh (2005)

Fig. 11 Variation of hydraulic conductivity coefficient with

void ratio

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k ¼ 0:09� 10�0:08P200e2:8

eþ 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 · 10�9 cm/

s to 8.65 · 10�8 cm/s as lower and upper bounds of

Hazen formula, while Hazen equation gives a con-

stant value of 2.69 · 10�8 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 · 10�6. 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 fex1

ð1þ 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(

KP200=50 P200=55 P200=60P200=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 1.2Void 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-eequations

x1 x2 References

2 0 Terzaghi (1943)

3 0 Chardaballas (in Kovacs 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

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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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