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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.)
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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
;
~
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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
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(
).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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Boart Hard Metal Products S.A.
Limited.
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