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R eques t s o k s am pl es

Speci m ens

Speci m ens

P roperty requested

since tested

tested

pe r

1.12.1952

rock sam ple

U niaxial com pressive strength

72

2277

6597

2,89

U niaxial tensile strength 12 249 316

1,27

T riaxial strength 13 261t 96 4 3,69

M odulus of e lasticityt 54

60 7

3072

5,06

P oisson s ratio:j: 53 565

2882

5,10

I

T O T A L first three

I

properties)

97

2787

7877

2,83

T A B LE II

S U M M A R Y O F T H E C S IR R O C K T E ST IN G S E R V IC E S . T O T H E M IN IN G IN D U S T R Y D U R IN G P A ST

20 Y E A R S

N O TE S : .Excluding research tests

tlncludes different stress ratio conditions

:j:D eterm ined on the sam e specim ens as for strength properties

Plate I-Sim ple equipm ent for the point-load strength test. Its loading capacity

is 125 kN and it costs RI5 t o m a nu fa ct ur e.

JOURN L OF THE SOUTH FRI N INSTITUTE OF MINING ND MET LLURGY

also concluded that it m ight be

realistic to use laboratory-deter-

m ined fracture criteria for the pre-

diction of failure in the underground

situation.

In view of these argum ents, one

should exam ine w hat rock-m aterial

properties are needed for practical

e ng in ee rin g d es ig n.

U S E O F R O C K P R O P ER T IE S

IN D E S IG N

W hat rock properties are required

by the design engineer? H ow are

they obtained1 M ust the results be

accurate1 T o answ er these questions,

a study w as m ade of the requests for

rock testing subm itted to the R ock

M echanics D ivision of the C S IR

over a period of tw enty years. A

clear m odus oper ndi in the past

and the current needs for the

property testing of rock m aterial

have em erged. T able II provides

som e inform ation com piled during

th is r es ea rc h.

T his survey has show n that the

m ining engineer requires m ainly tw o

rock-m aterial properties, nam ely, the

u ni xi l ompressive streng th and the

tr i x i l s tr en gth of rock. T o obtain

this inform ation, the design en-

gineer is prepared to supply betw een

2 to 3 rock specim ens for the tests

see T able II). H e is interested in

the accuracy of results to w ithin 10

to 20 per cent, has a lim ited budget

at his disposal for rock m echanics

tests, and is in a hurry. H e does not

w ant to w orry about all the other

factors appearing in T able 1. H e

em phasizes that this approach is

dictated by his practical experience,

and, in any case, this is only for

prelim inary design since he designs

as he goes along w ith m ining.

T he se fin ding s c onfirm th at p ra ctic-

al experience is still recognized

today as the m ost reliable basis for

the design of the m ajority of rock

structures. T his agrees w ith a recent

opinion3 that the function of the

rock m echanics engineer is not to

com pute accurately but to judge

soundly. In this respect, good practic-

al experience and the correct feel

of the problem are essential.

T he view should therefore be

supported that, w hile theoretical

m ethods are necessary to provide

further understanding of the sub-

ject, a practical assistance m eaning-

M R H 1974

3 3

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Uniax ial co mpressiv e stren gth

Point.load strength index

Rock Material Standard deviation Standard deviation

No. of

Mean Core

No. of

Mean

specimens MPa

MPa

%

size

specimens

MPa MPa

I

%

NX 20

2,83 0,25

8,8

Sandstone 20 64,5 4,85 7,5 BX 40 3,09 0,32 10,4

EX 30

3,36 0,28

8,3

NX 20

8,10 1,00

12,3

Quartzite

20

188,4

9,66 5,1

BX 20

9,70

1,29

13,3

EX 20

11,96

1,38

11,5

Norite (w eak )

20

253,0 2,25 0,9

NX 20

11,00

1,22

11,1

~~~NX

20

13,13

0,89

6,8

Nor ite (s tr on g)

20

313,4

5,21 1,7

BX 20

13,69

1,54

11,2

EX 20

15,78

0,78

4,9

l

:z

.. f

M

-I

10

.E

~-

01

C

v

..

~ 0

G

5

~C

'0

L

TABLE III

COMPARATIVE ACCURACY OF UNIAxIAL COMPRESSIVE AND POINT-LOAD TESTING

ful to the design engineer should be

encouraged, even if it involves the

sacrifice of accuracy for sim plicity

and speed of application.

It is believed that, in the de-

term ination of rock properties, such

practical assistance should involve

the fo llo win g a pp ro ac h:

(i) the recommendation of a quick

and cheap means for determ in-

ing the uniaxial compressive

strength of rock materials; and

(ii) the provision of a sim ple m ethod

for estimating the triaxial

strength of rock m aterials.

20

The above two requirements will

now be considered in turn.

DETERMINATION OF THE

UNIAXIAL COM PRESSIVE

STRENGTH

T he uniaxial com pressive strength

of rock materials is relatively easy

to determ ine, and standardized test

procedures are available4. This, how -

ever, involves laboratory tests that

necessitate careful specim en prepa-

ration and rather expensive testing

apparatus. Attention should there-

fore be drawn to the study by Broch

p

0 Broeh and Franklin11972)

x

0' Andrca et al .0965)

+

T his stud y

15.

1

- E

5 -

02

0 50

le

0

x

and F ranklin

5

of the use of index

tests. Their detailed research showed

that the point-load strength index,

determined on unprepared rock cores

i n th f i l

u sing por tabl e equ ipmen t,

can provide the uniaxial com pressive

strength of rock materials with an

accuracy well comparable with that

derived from laboratory tests.

In view of the promising results

obtained by previous researchers, it

was decided to investigate this

m atte r furth er.

The apparatus used for the present

study is shown in Plate I. It will

x

0

x

x

x

N~~tr~

x

0

x

10 0

5

150 200 250

U niaxial eom prcssivc strength de. M Pa

35 000

314 MARCH 1974

Fig. I~Relationship between index I s a nd s tre ng th Uc for NX core (54 mm dia.)

JOURNAL OF THE SOUTH AFRICAN INSTITUTE OF M INING AND METALLURGY

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50

4. 0

SO

20

NX

f

10

.

.

7

I

5

J

2

;O

~O

30

20

11..

~

EX

-f

-f

VI

)( 10

: I

9

Z

8

- 7

6

;

~

8/11/2019 v074n08p312

5/9

1

06 00

~0,6

rJ c

~rJc

OC

3

SILTSTONE

an d

MUDSTONE

2

TABLE IV

CLASSIFICATION OF ROCK MATERIALS FOR STRENGTH

Description

P oin t-lo ad stren gth

index, MPa

U nia xia l c ompre ss iv e

strength, MPa

Very high strength

H igh strength ..........

Medium s trength. . . . . . . . .

L ow stren gth ...........

Very low strength . . . . .

> 200

100-200

50-100

25-50

< 25

> 8

4-8

2- 4

1- 2

< 1

ing the uniaxial com pressive strength

of rock for practical engineering

purposes. Table IV lists the corres-

ponding strength ranges for the

strength classification of rock ma-

terials8.

ESTIMATION OF THE

TRIAXIAL STRENGTH

While determ ination of the uni-

axial compressive strength of rock is

a simple matter, this is not true

for the collection of the triaxial

strength data, which involves lab-

oratory tests requiring tim e-consum -

ing specimen preparation and

sophisticated testing equipment.

Yet, as Table 11 demonstrates, the

triaxial strength data are in demand

and there are no simple index tests

for this purpose.

It is believed, however, that a

case exists for the

estimation

of the

triaxial strength of rock from failure

criteria.

A criterion of failure is an alge-

braic expression of the mechanical

condition under which a material

fails by fracturing or deforming

beyond some specified lim it. This

specification can be in terms of load,

deformation, stress, strain, or other

parameters.

.

The search for failure criteria for

rock has been conducted for a

considerable number of years and,

although much progress has been

made9-1I, the practical design en-

gineer is still left without a failure

criterion that can meet his needs.

This is best illustrated by the fact

that two-hundred years after Cou-

lomb presented his well-known cri-

terion (1773), it was stated12: 'In

short, a large amount of research has

yet to be done on rock failure

criteria, possibly even more than

has been published to date'. While

this statement is obviously rather

pessim istic judging from the amount

of material already published on the

subject, Jaeger and COOkI3 justly

believe that failure criteria based on

6

M AR CH 1974

the actual mechanism of fracture,

which are more sophisticated than

the theories of Coulomb, Mohr, and

Griffith, have yet to be developed,

since som e em pirical relations fit the

experim ental results better.

The author believes that, to meet

the imm ediate needs of the practical

rock engineer at the present stage of

development of rock mechanics,

attention should be directed to

em pirical criteria for estimating the

triaxial strength of rock. Such

criteria can be selected by fitting

a

0'1

O 'e

NORITE

3

2

(~)007: 1

00

cr I

O'c

3

2

( )

0075

03

+1

Oc

00

~

Oc

suitable equation into experim ental

data, and they need not have

a

theoretical basis. They serve to

meet the practical requirements of

adequate prediction, simplicity of

use, and speed of application.

EMPIRICAL CRITERIA FOR

TRIAX IA L STREN GTH

The requirement for an empirical

triaxial strength criterion is that,

from the knowledge of the uniaxial

compressive strength of a given rock

material, values of the major princi-

pal stress, crI>should be predicted,

using a2=a3 as an input value (the

influence of the intermediate princi-

pal stress a2 can be neglected for

practical purposes). The aim is to

predict a M ohr streng th en velope fo r

a rock material from which one can

also obtain its cohesion and friction

data.

0 1

de

2

QUARTZ IT E

3

.

.

rJ3

)

0075

-

+1

rJe

0.75

(~~)

+ 1

. S ltS T ON '

X

MUOSIONE

06

00

~

rJc

0.6

,',2

Fig. 3-Stresses at failure in triaxial compression for five rock materials

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The present study of the literature

published on the subjectll. a 8

re -

vealed that the empirical criteria

proposed by M urrell14 and by Hoek16

are particularly suitable for esti-

mating the triaxial strength of rock.

T hese criteria are not contradictory,

and the choice of one instead of the

other depends solely on practical

convenIence.

In 1965, Murrell14 proposed the

f ollow ing equat io n:

A

a1=Faa +ac,

. . . . . .

where

al

is the major principal

stress, aa is the m inor principal stress,

ac is the uniaxial compressive

strength, and A an d F a re con stant s.

In normalized form , equation (2)

can be rewritten as follows:

A

~=k

[

~

]

+1,

ac ac

CRITERION I

where k is a co nstan t.

Normalized form means the ex-

pression of the stresses as dim ension-

less ratios ofthe uniaxial com pressive

strength of the material. This has the

advantage that, since effects such as

the specimen size, environmental

conditions, and testing techniques

are presumably sim ilar in both

numerator and denominator, they

are elim inated upon norm alization.

Furtherm ore, the direct comparison

of a number of tests on the same

p lo t is p ossible.

In Fig. 3, the triaxial strength

results are plotted as al/ac versus

aalac

for five rock types, the two

parameters of equation (3) are de-

term ined from the experimental

data, and Criterion I is fitted for

each rock type.

A particularly useful form for an

empirical criterion was proposed by

H oe k1 6 as fo llo ws:

0

Tm-To=B

[

am

]

,

ac ac

where

Tm

is the maximum shear

stress and am the mean normal

stress given as:

a1-aa

Tm=~

=

a1

+a a

(5 )

m

2

..

and B, 0, and TO are constants. For

practical purposes16,

To=at

(uni-

a xia l ten sile stre ngth).

-

~f

(2 )

..

:g

...

a:

:;;

NORM 'AL S TR E SS

f)

---

Fig. 4-M ohr s graphical

representation of stress

al

=

ma jo r princ ipal s tr es s

a2

=

m in or p rin cip al stre ss

axx=

norm al stress at failure

TX Z =

shear stress at failu re

C

=

cohesion

4 . =

angle of friction

f3

=

angle of shear failure

(3 )

The Tm an d am quantities are

given physical interpretation (see

Fig. 4) as the maximum shear stress

acting in the specimen at failure

and the normal stress acting on the

plane of the maximum shear stress.

They are the radius of a Mohr stress

circle at failure and the distance

from the origin to its centre. A

failure criterion expressed in this

3, 0

2, 0

u

10

..

I 1,0

hE

0,7

.,

..;.C.

..

4)

0,5

,.

+

0,

0, 3

0, 3

0.

0, 5

0, 7

way defines the locus of points at the

top of Mohr failure circles and is

referred to as the maximum shear

s tre ss lo cu s.

The suitability of equation (4) for

rock materials is best evident from

Fig. 5, where the results of triaxial

tests on three rock types are plotted

on l ogari thmic sca le s. For the sake of

clarity, other rock types are not

shown in Fig. 5. It should be noted

that this figure permits a direct

evaluation of the constants Band 0

because B is given by the value of

Tm-To) aC

when

amlac=l,

and the

value of 0 is given by the slope of

the straight line through the ex-

perim ental points. For the com plete

evaluation of these constants, the

value of

TO

must also be known and,

as this is equal to at , the ratio of

atlac must be specified in equation

(4). H owever, for practical purposes

in rock mechanics, the uniaxial

te ns ile s tre ng th , at , is usually one-

tenth* of the uniaxial compressiv~

*This aspect w as investigated during the

present study, and it was found that the

accuracy of prediction of empirical

criteria is lowered by only about 1 per

r cent when compared with the actual

l

v alu es o f at an d a c.

.

..

.

. +

.,A

..

~

.~+

0

Norite

.

Quartzite

+ 5 andstone

1,0

2,0

3,0

41 J

5,0

C1m/ac

Fig. 5-Experimental data for maximum shear and mean normal stresses at

failure for three rock types

OURNAL OF THE SOUTH AFRICAN INSTITUTE OF MINING AND METALLURGY

MARCH

1974

7

8/11/2019 v074n08p312

7/9

(

).9

t'm

~).9

--

0,80

:~

+ 0,1

--

0,78

::

+0,1

(le

de

o

2 3

o

2

3

O'm

O 'm

de de

2

2

'Cm

SANDSTONE

'(m

S IL TSTON E

-

de

and

de

MUDSTONE

. SILTSTO NE

x N UD ST ON E

0,9

0.9

Cm

~dm)

Tm

0,70

(:~)

+Oj1

=O,75 d;

+0,1

de=

2

3

0

2

3

dm dm

de

de

Fig. 6-Relations between the maximum shear and mean normal

stresses at

fa ilu re fo r fiv e ro ck ma te ria ls

strength, ac and equation (4) can

be rew ritten as follow s:

C

~=B

[

am

]

+0,1

ac ac

CRITERION II

One reason for the choice of the

m axim um shear stress Tm and the

mean normal stress am in place of

shear and normal stresses

Txz

an d

axx (see Fig. 4) is that the con-

struction of

Tm

an d

am

c ir cl es and

the fitting of a Mohr envelope is,

as will be seen later, a simple and

reliable graphical operation. This is

not the case when fitting an envelope

by eye to a set of experimentally

determ ined Mohr circles. Such an

envelope often does not include the

scatter of experimental values be-

cause it is usually fitted to the circles

of m axim um diam eter.

In Fig. 6 the triaxial results are

plotted as Tm/ac versus am/ac fo r

five rock types, and the two para-

m eters of equation (5) are determ ined

from the experimental data and

2

Lm

de

NORITE'

318 MARCH

1974

(5 )

Criterion II is fitted for each rock

type.

The parameters for Criteria I and

II-equations (3) and (5)-were de-

term ined from 412 test specimens

in volvin g 5 qu artz ite s (91 sp ec im en s),

5 sandstones (109 specimens), I

norite (35 specim ens), 4 m udstones

(86 s~ecimens), and 4 silts tones (91

specimens). The results are given in

Table V, which also includes the

average prediction errors for each

rock type. These prediction errors

were calculated as the difference

between observed aI and predicted

aI expressed as positive percentage

of the predicted value.

It is clear from Table V that both

criteria yield prediction errors that

are very acceptable for practical

engineering purposes. Thus, the

actual application of these criteria

depends solely on practical con-

vemence.

It is recommended that Criteria I

and II should be used as follows:

-Criterion I is employed when

the individual values of aI are

2

Lm

(T e

required for a given as, as will

be the case when the virgin stress

field in a rock mass is known

and its comparison with the

material strength under tri-

axial conditions is needed. For

this purpose, Criterion II is not

suitable.

-Criterion II is employed when-

ever a full Mohr envelope is

required and values of cohesion

and friction of a rock material

are needed. For this purpose,

Criterion I is not recomm ended

because it is valid only for com-

pression.

An example of how Criteria I

and II can be applied in practice will

now be presented.

PRACTICAL EXAMPLE

Consider a problem of estim ating

the uniaxial and triaxial strengths

of a quartzite, for which point-load

index tests on NX cores (diameter

D=54 mm) gave an average failure

load P=23 1 kPa. In the design of

an underground mining excavation

QUARTZITE

JOURNAL OF THE SOUTH AFRICAN INSTITUTE OF MINING AND METALLURGY

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ROCK TYPE

Norite

A =5,0 Error: 3,6%

Quartzite

A =4,5

Error: 9,2%

Sandstone

A=4 0

Error: 5,8%

Siltstone

A =3,0

Error: 5,6%

---

Mudstone

A =3,0

Error:

6,1%

---

ALL ROCK TYPES

A =3,5 Error: 10,4 %

B=0 8

Error: 1,8%

B

=

0,78

Error: 3,2%

B

=

0,75

Error: 2,3

%

B=0 7

Error: 4,2

%

B=0 7

Error: 6,6%

B

=

0,75

Error: 8,3 %

TABLE V

EMPIRICAL CRITERIA FOR TRIAXIAL STRENGTH OF ROCK MATERIALS

CRITERION I

II

a

[

a

]

0,75

~= A

~

+1

ac ac

T

[

a

]

0, .

~=B ~ +0,1

ac ac

involving this rock material at a

depth of 3000 m below surface and

subjected to the virgin stresses of

70 MPa in the vertical direction and

50 M Pa in each horizontal direction,

the follow ing estim ates are required:

(a) uniaxial com pressive strength,

(b) triaxial strength for the in situ

c on fin in g p re ss ure a3=50 MPa,

an d

(c) M ohr envelope.

Solution

(a) The point-load strength index

Is=P/D2=23100/ 54 x 54)=

7,92 MPa. The uniaxial com-

p re ss iv e s tre ng th ac=24 1s=

24 x 7,92=190 MPa.

(b) Criterion I for quartzite is as

follows:

0,75

~=4,5

[

~

]

+1

ac ac

50

0,75

=4,5

[190]

+1=2,65, and

al=2 65 x ac=2 65 x 190

=503,5 M Pa.

The triaxial strength of this

quartzite is far higher than the

acting vertical in situ stress of

70 M Pa.

(c) Criterion 11 for quartzite is as

follows:

0,9

Tm

=0,78

[

am

]

+O,l.

ac ac

The above relationship is plotted

in Fig. 7 and is marked Criterion 11.

Since this criterion defines the

locus of points at the top of Mohr

failure circles, such circles are draw n

in Fig. 7 and a Mohr envelope is

n ex t fitte d.

Fig. 7 provides the material

cohesion of quartzite as

00=0 2 ac=0 2 x 190=38 MPa,

and the angle of friction for quartzite

as

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5. BROCH, E., and FRANKLIN, J. A .

The point-load strength test.

Int. J.

Rock M ech. M in. Sci. vo . 9, 1972,

p p. 6 69 -6 97 .

6. BIENIAWSKI, Z. T. Mechanism of

brittle fracture of rock.

Int. J. Rock

M ech. M in. Sci. vo . 4, 1967, pp.

395-435.

7. INTERNATIONAL SOCIETY FOR ROCK

MECHANICS. Suggested methods for

determining the point-load strength

index of rock materials.

ISRM

Com mittee on Standardization of Lab

oratory Te8t8

Document No.

],

October, 1972, pp.

8-13.

8. BIENIAW SKI, Z. T. Engineering classi-

fication of jointed rock masses. Tran8.

S. Afr. In8tn Civil Engr8. vo . 15,

1973, pp. 335-344.

9. WIEBOLS, G. A., and COOK, N . G. W .

An energy criterion for the strength

o f ro ck in po lyax ia l co mpression . Int.

J. Rock M ech. M in. Sci. vo . 5, 1968,

p p. 5 29 -5 49 .

10. BRADY, B. T. A mechanical equation

of state for brittle rock.

Int. J. Rock

M ech. M in. Sci. vo . 7, 1970, pp.

385-421.

11. M oGI, K . Fracture and flow of rocks.

TectonophY8ic8 vo . 3, ]972, pp. 541-

568.

12. W AW ERSIK, W . R. D et ai le d a na lY 8i 8

of rock failure in laboratory com

pre8 8ion te8t8 . Ph.D. Thesis, Uni-

versity of M innesota, M inneapolis,

1968.

13. JAEGER, J. C ., and COOK, N. G.

'V .

F un da me nta l8 o f r oc k m ec ha nic 8

Lon-

don, M ethuen, 1969.

14. MURRELL, S. A . F. The effect of

triaxial stress system s on the strength

of rock at atm ospheric tem peratures.

GeophY8. J. Roy. A8tr. Soc. vo . 10,

1 96 5, p p. 2 31 -2 81 .

15. HOBBS, D. W . A study of the be-

haviour of broken rock under triaxial

compression.

Int. J. Rock M ech.

M in. Sci. vo . 3, 1966, pp. 11-43.

16. HOEK, E. Brittle fracture of rock. In:

R oc k m ec ha nic 8 in e ng in ee rin g p ra ctic e

eds. Stagg and Zienkiewicz, London,

John W iley & Sons, 1968, pp. 93-]24.

17. FRANKLIN, J. A . Triaxial strength of

rock mater ia ls . R o ck M e c ha n ic 8 vo . 3,

19 71 , p p. 8 6-9 8.

18. JAEGER, J. C . Friction of rocks and

stability of rock slopes. Geotechnique

vo . 21, 1971, pp. 97.134.

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B ra ck en M in es L im ite d.

B uffe ls fo nte in G .M . C o . L im ite d.

C ap e A sb es to s S ou th A fric a (P ty ) L td .

Com pair SA (Pty) Lim ited.

C on solidate d M urchis on (T vl) G old-

fie ld s D ev elo pm en t C o. L im ite d.

D oornfonte in G .M . C o. Lim ited.

D urban R oodep oort D eep Lim ited.

E as t D rie fo nte in G .M . C o. L im ite d.

E as t R an d P ro p. M in es L im ite d.

F re e S ta te Sa aip la asG .M. Co . L im ited .

F ra se r C h alm e rs S .A . (P ty ) L im ite d.

G ard ne r-D en ve r C o. A fric a (P ty ) L td .

G old fie ld s o f S .A . L im ite d.

The G rootvle i (P ty) M ines Lim ited.

H arm ony G old M ining C o. Lim ited.

H arte be es fo nte in G .M . C o . L im ite d.

H ew itt-R ob in s-D en ve r (P ty ) L im ite d.

H ig hv eld S te el a nd V an ad iu m C orp o-

r at io n L im ited .

H ud em m co (P ty ) L im ite d.

Impa la P la tin u m L im ited .

Ingersoll Rand Co. SA (Pty) Ltd.

Jam es Sydney Company (Pty)

Limited.

K in ro ss M in es L im ite d.

K loof G old M in ing C o. L im ited.

L en nin gs H o ld in gs L im ite d.

L es lie G .M . L im ite d.

L ib an on G .M . C o. L im ite d.

L on rh o S .A . L im ite d.

L ora in e G old M in es L im ite d.

M arie va le C on so lid ate d M in es L im it-

ed .

M atte S melters (P ty) Lim ited .

N orthern Lim e C o. Lim ited.

O 'okie p C oppe r C om pany Lim ited.

P ala bo ra M in in g C o . L im ite d.

P lacer Developm ent S.A. (Pty) Ltd.

P resident S tern G .M . C o. Lim ited.

P retoria P ortland C em ent C o. Lim it-

ed .

P ries ka C op per M ines (P ty) Lim ited.

R an d M in es L im ite d.

R ooiberg M inerals D evelo pm ent C o.

Limited.

R ustenburg P latinum M in es Lim ited

( Unio n Se ct io n ).

R ustenburg P latinum M in es Lim ited

(Rustenburg Section ).

S t. H ele na G old M in es L im ite d.

S ha ft S in ke rs (P ty ) L im ite d.

S .A . L an d E xp lo ra tio n C o. L im ite d.

S tilfo nte in G .M . C o. L im ite d.

The Griqualand Exploration and Fi-

n an ce C o . L im ite d.

The M essina (Transvaal) D evelop-

m en t C o. L im ite d.

T he S te el E ngineerin g C o. Ltd.

T ra ns -N ata l C oa l C orp ora tio n L im it-

ed .

Tvl C ons. Land & E xp lo ra tio n C o.

T su me b C orp . L im ite d.

U nio n C orp ora tio n L im ite d.

V aal R eefs E xploratio n M in ing C o.

Limited.

V en te rs po st G .M . C o. L im ite d.

V ergenoeg M in ing C o. (P ty) Lim ite

Vlakfontein G.M. Co. Lim ited. d.

W elkom G old M ining C o. Lim ited.

W est D riefontein G .M . C o. Lim ited.

W e ste rn D ee p L ev els L im ite d.

W e ste rn H old in gs L im ite d.

W in ke lh aa k M in es L im ite d.

320 MARCH 1974

JOURNAL OF THE SOUTH AFRICAN INSTITUTE OF MINING AND METALLURGY