THE MEASUREMENT AND ANALYSIS OF
EARTH MOTION RESULTING FROM
UNDERGROUND ROCK FAILURE
by
Noel C. Jo u g h in
A T h e s is p re s e n te d t o th e F a c u lty of
E n g in e e rin g o f th e U n i v e r s i t y o f the
W itw a t e r s r a r u , Jo han n esb u rg
For the Degree of D octor of Philosophy
A u g ust, 1966
TKE MEASUREMENT AND ANALYSIS OF EARTH MOTION
RESULTING FROM UNDERGROUND ROCK FAILURE
S UMMARY
Thu s e is m ic method w^s used to i n v e s t i g a t e t h e e f f e c t s
o f underground rock f a i l u r e .
This method i s p a r t i c u l a r l y
a t t r a c t i v e s i n c e , i n p r i n c i p l e , i t i s p o s s i b l e to l o c a t e th e
fo c u s o f a v i o l e n t rock f a i l u r e , to d e te rm in e t h e q u a n t i t y
o f energy r a d i a t e d by th e f a i l u r e , and t o d e te rm in e the
mechanism o f th e f a i l u r e .
The c o n s i d e r a t i o n s i n t h e d e sig n
o f a s e is m ic network a r e g iv e n and th e method o f i n t e r p r e t i n g
th e d a t a i s a l s o d e s c r i b e d .
The s e is m ic netw ork was i n s t a l l e d a t th e Harmony Gold
Mine i n th e Orange F ree S t a t e , and c o n s i s t e d o f n in e
seism o m eters lin k e d by means o f c a b le t o a 1 6 -c h a n n e l t a p e reco rd er.
The netw ork o p e r a te d c o n tin u o u s ly , and th e t a p e -
r e c o r d i n g s were p ro c e s s e d on a r e p la y machine a t th e
Bernaxu P r i c e I n s t i t u t e o f G eophysical R esearch .
The. a c c u ra c y w ith which s e is m ic e v e n ts c o uld be lo c a t e d
was - 100 f e e t w ith 90 p e r c e n t c o n fid e n c e .
During th e f i r s t
y e a r o f r e c o r d in g , 3100 s e is m ic e v e n ts were l o c a t e d ra n g in g
i n m agnitude from 1C5 f t . - l b s .
to 10
f t . - l b s . of ra d ia ted
e n e rg y .
I t was found t h a t t h e r e were two d i s t i n c t groups of
s e is m ic e v e n ts .
95 p e r c e n t of th e e v e n t s o c c u rre d a t an
e l e v a t i o n between th e r e e f p la n e and a weak band o f rock
300 f e e t above th e p la n e , i n which c a s e 85 p e r c e n t were
above a d v an c in g f a c e s and 10 p e rc e n t above w o rk ed -ou t a r e a s .
The re m a in in g 5 p e r c e n t o c c u rre d in a co n fin e d group n e a r
/ a d o le rite . . . .
a d o l e r i t e s i l l a t an e l e v a t i o n of ab o u t 2400 f e e t above
the r e e f p l a n e .
The s e is m ic o b s e r v a tio n s were compared w ith
some e a r l i e r s t r a i n m e a s u re c e rts i n th e V e n t i l a t i o n S h a f t .
This com parison showed t h a t th e e l e v a t i o n of th e s e is m ic
e v e n ts c o in c id e d w ith the e l e v a t i o n of re g io n s where measured
e x t e n s i o n a l s t r a i n s i n the ro c k exceeded th e o r i g i n a l
com pressive s t r a i n i n the r o c k .
I t was concluded t h a t rock
f a i l u r e was l i m i t e d to a zone e x te n d in g to a h e ig h t o f
a p p ro x im a te ly 300 f e e t above t h e e x c a v a tio n and t h a t th e
zone extended l a t e r a l l y a s th e f a c e s advanced, e x c e p t t h a t
rock f a i l u r e a l s o o c c u rre d i n a c o n fin e d r e g io n a t th e
d o le rite s i l l .
A l a r g e p r o p o r t i o n of th e s e is m ic e v e n ts and damage due
to r o c k f a i l u r e o c c u rre d n e a r th o s e f a c e s which were most
h ig h ly s t r e s s e d .
Energy must be r e l e a s e d when th e s i z e o f
th e mine e x c a v a tio n i n c r e a s e s .
The energy r e l e a s e p e r u n i t
a r e a was compared w ith damage d ue t o rock f a i l u r e ,
s e i s m i c i t y and th e s to p e la b o u r re q u ir e m e n ts .
A ll t h e s e
f a c t o r s showed a marked i n c r e a s e as th e energy r e l e a s e r a t e
in creased .
I t was concluded t h a t th e r a t e o f en erg y r e l e a s e
i s a s i g n i f i c a n t p a ra m e te r i n p r e d i c t i n g th e m agnitude o f
problem s a r i s i n g from ro c k f a i l u r e and t h a t th e s e problems
a rc e a s i l y manageable when th e r a t e o f energy r e l e a s e i s
Q
p
l e s s th a n 10 f t . - l b s . p e r fathom .
There was no d i f f e r e n c e in th e b e h a v io u r o f s e is m ic
e v e n ts o f d i f f e r e n t s i z e , ex cept t h a t a l l the e v e n ts o f
m agnitude 107 f t . - l b s . and 108 f t . - l b s . o c cu rred a t dy kes.
A lthough b l a s t i n g t r i g g e r e d a l a r g e number o f e v e n ts , more
than 50 p e r c e n t o c c u rre d w ell o u t s i d e b l a s t i n g t i m e , and
th e r a t e a t which s e is m ic e v e n ts o c c u rre d f l u c t u a t e d q u ite
w id e ly , even when th e r a t e o f m ining was n e a r l y c o n s t a n t .
/f
(ill)
The t o t a l amount of energy r a d i a t e d by t h e s e is m ic
e v e n ts was f o u r o r d e r s o f m agnitude l e s s than tho c a l c u l a t e d
amount o f e n e rg y r e l e a s e d by m ining.
Only a sm all f r a c t i o n oV th e damage was accompanied by
s e is m ic a c t i v i t y , which im p lie s t h a t t h e damage was due to
f a l l s o f ro c k which had been f r a c t u r e d b e fo re th e r o c k f a l l s
occurred.
The o n ly manner in which t h i s ty p e of damage can
be reduced i s t o re d u c e t h e e x te n t o f t h e f r a c t u r i n g , by
re d u c in g th e energy r e l e a s e r a t e , o r by improving th e typ e
o f s u p p o rt i n t h e s l o p e s .
C u rre n t t h e o r i e s ahow t h a t some rock ty p e s can f a i l
v i o l e n t l y o r n o n - v i o l e n t l y , depending on th e manner i n which
t h e ro c k i s lo a d e d .
I t i s shown t h a t t h e s e t h e o r i e s may
e x p l a i n th e s t a b l e developm ent of th e f r a c t u r e zone;
however, the l a r g e q u a n t i t i e s o f energy t h a t a r e d i s s i p a t e d
s t a b l y can o n ly be d i s s i p a t e d by f r i c t i o n i n th e f r a c t u r e
zone;
a r e l a t i v e l y sm all f r a c t u r e zone i s r e q u ir e d to
d i s s i p a t e t h i s e n e rg y .
S tu d i e s o f t h e mechanism of t h e seism ic e v e n ts showed
t h a t the mechanism was some form o f v o lu m e tric c o l l a p s e .
The mechanism of some of th e s e is m ic e v e r t s c o u ld , t h e r e f o r e ,
be a sudden grow th i n the f r a c t u r e z o n e , t h e c o l l a p s e o f
f r a c t u r e d ro c k n e a r th e f a c e o r I n w orked-out a r e a s , o r the
sudden f a i l u r e of a volume o f ro c k s l i g h t l y removed from
th e e x c a v a t i o n .
The mechanism of th e s e ism ic e v e n ts n e a r
th e d o l e r i t e s i l l was n o t c l e a r l y r e s o l v e d ;
i t c o u ld ,
however, have te e n a s h e a r movement.
/
ATPINDIX 1 .
THE MEASUREMENT AND ANALYSIS OF
EARTH MOTION RESULTING FROM
UNDERGROUND ROCK FAILURE
by
N oel C. J o u g h in
A T h e a ia p r e s e n t e d t o th e F a c u l t y o f
E n g i n e e r i n g o f t h e U n i v e r s i t y o f th e
Wi t w s t e r a r a n d , J o h a n n e s b u rg
F o r th e D egree o f D o c to r o f P h ilo s o p h y
A u g u st, 1966
DBCLnRATION BT C^POIAAIS
I , ho# 1 Cain J o u g h ln , hereby d e c la r e th a t t h l e
T h eela la my own work and th a t th e m a te r ia l h e r e in
hae n ot been su b m itted by we fo r a n o th e r d eg ree a t
any o th e r U n iv e r s it y .
(i)
THE MEASUREMENT AND ANALYSIS OF EARTH MOTION
RESULTING FROM UNDERGROUND ROCK FAILURE
S UMMARY
The s e i s m i c method vms used t o i n v e s t i g a t e t h e e f f e c t s
o f u n d e rg ro u n d ro c k f a i l u r e .
a ttr a c tiv e sin ce ,
T h is method i s p a r t i c u l a r l y
i n p r i n c i p l e , i t i s p o s s i b l e to l o c a t e t h e
fo c u s o f a v i o l e n t rock f a i l u r e , t o d e te r m in e t h e q u a n t i t y
o f en erg y r a d i a t e d by t h e f a i l u r e , and t o d e te r m in e th e
mechanism o f t h e f a i l u r e .
The c o n s i d e r a t i o n s i n t h e design,
o f a s e i s m i c n e tw o rk a r e g i v e n and th e method o f i n t e r p r e t i n g
th e d a ta i s a lso d e sc rib e d .
The s e i s m i c n e tw o rk was i n s t a l l e d a t t h e Harmony Gold
Mine i n t h e Orange F re e S t a t e , and c o n s i s t e d o f n i n e
s e is m o m e te rs l i n k e d by means o f c a b l e t o a 1 6 - c h a n n e l t a p e reco rd er.
The n e tw o rk o p e r a t e d c o n t i n u o u s l y , and t h e t a p e -
r e c o r d i n g s w ere p r o c e s s e d on a r e p l a y m achine a t t h e
B ern ard P r i c e I n s t i t u t e o f G e o p h y sic a l R e s e a r c h .
The a c c u r a c y w i t h w hich s e i s m i c e v e n t s c o u ld be l o c a t e d
was - 100 f e e t w i t h 90 p e r c e n t c o n f i d e n c e .
D urin g th e f i r e t
y e a r o f r e c o r d i n g , 3100 s e i s m i c e v e n t s w ere l o c a t e d r a n g in g
i n m a g n itu d e from 10
f t . —l b s .
to 10
f t . —lb s . o f r a d i a t e d
energy.
I t was fourri t h a t t h e r e were two d i s t i n c t g ro u t
seism ic e v e n ts .
of
95 p e r c e n t of t h e e v e n t s o c c u r r e d a t an
e l e v a t i o n bf ween t n
r e e f p la n e and a weak band o f ro c k
300 f e e t above t h e p l a n e , i n w hich c a s e 85 p e r c e n t were
above a d v a n c in g f a c e s and 10 p r o a n t above w o rk e d -o u t a r e a s .
The r e m a in in g 5 p e r c e n t o c c u r r e d i n a c o n f in e d g ro u p n e a r
/ a d o le rite . . . .
(1 1 )
a d o l e r i t e s i l l a t a n e l e v a t i o n of a b o u t 2400 f e e t above
th e r e e f p la n e .
The s e i s m i c o b s e r v a t i o n s were compared w i t h
some e a r l i e r s t r a i n m easurem ents i n t h e V e n t i l a t i o n S h a f t .
T h is c o m p a riso n showed t h a t th e e l e v a t i o n o f t h e s e i s m i c
e v e n t s c o in c i d e d w i t h th e e l e v a t i o n o f r e g i o n s where m easured
e x t e n s i o n a l s t r a i n s i n the r o c k exceeded th e o r i g i n a l
c o m p r e s s iv e s t r a i n i n th e r o c k .
I t was c o n c lu d e d t h a t rock
f a i l u r e was l i m i t e d to a zon e e x t e n d i n g to a h e i g h t o f
a p p r o x i m a t e l y 300 f e e t above t h e e x c a v a t i o n and t h a t t h e
zone e x te n d e d l a t e r a l l y a s t h e f a c e s a d v a n c e d , e x c e p t t h a t
r o c k f a i l u r e a l s o o c c u r r e d i n a c o n f in e d r e g i o n a t th e
d o le rite s i l l .
A l a r g e p r o p o r t i o n o f t h e s e i s m i c e v e n ts and damage due
t o r o c k f a i l u r e o c c u r r e d n e a r th o s e f a c e s w h ic h w ere most
h ig h ly s tr e s s e d .
Energy m ust be r e l e a s e d when t h e s i z e o f
t h e mine e x c a v a t i o n i n c r e a s e s .
The en erg y r e l e a s e p e r u n i t
a r e a was compared w i t h damage d u e t o ro c k f a i l u r e ,
s e i s m i c i t y and th e s t o p e l a b o u r r e q u i r e m e n t s .
A ll th e se
f a c t o r s showed a marked i n c r e a s e a s t h e en erg y r e l e a s e r a t e
in c re a s e d .
I t was c o n c lu d e d t h a t t h e r a t e o f e n e rg y r e l e a s e
i s a s i g n i f i c a n t p a r a m e te r i n p r e d i c t i n g t h e m a g n itu d e o f
p ro b le m s a r i s i n g from r o c k f a i l u r e and t h a t t h e s e pro blem s
a r e e a s i l y m a n ag e a b le when t h e r a t e o f e n e rg y r e l e a s e i s
o
2
l e s s th a n 10 f t . - l b s . p e r fath om .
T h e re was no d i f f e r e n c e i n th e b e h a v io u r o f s e i s m i c
e v e n t s o f d i f f e r e n t s i z e , e x c e p t t h a t a l l th e e v e n t s o f
m a g n itu d e 1 0 7 f t . - l b s . and 10P f t . - l b s . o c c u r r e d a t d y k e s .
A lth o u g h b l a s t i n g t r ? - g e r e d
a l a r g e number o f e v e n t s , more
t h a n 50 p e r c e n t o c c u r r e d w e ll o u t s i d e b l a s t i n g t i m e ,
nd
t h e r a t e a t which s e is m ic e v e n t s o c c u r r e d f l u c t u a t e d q u i t e
w i d e l y , even when t h e r a t e o f m in ing was n e a r l y c o n s t a n t .
/ The . . . .
(Hi)
The t o t a l amount ol e n e rg y r a d i a t e d by t h e s e is m ic
e v e n t s was f o u r o r d e r s o f ruagnltude l e s s th a n th e c a l c u l a t e d
amount o f e n e r g y r e l e a s e d by minxng.
Only a s m a ll f r a c t i o n o f t h e damage was accom panied by
s e i s m i c a c t i v i t y , w hich im p l i e s t h a t th o damage was d u e t o
f a l l s o f r o c k w hich had been f r a c t u r e d b e f o r e t h e r o c k f a l l s
occurred.
The o n ly manner i n w hich t h i s ty p e o f damage can
be re d u c e d i s t o re d u c e t h e e x t e n t o f t h e f r a c t u r i n g , by
r e d u c i n g t h e e n e rg y r e l e a s e r a t e , o r by im p ro v in g th e ty p e
of support in th e s to p e s .
C u r r e n t t h e o r i e s show t h a t <*cme ro c k t y p e s can f a i l
v io le n tly or n c n -v io le n tly ,
t h e ro c k i s l o a d e d .
u pen d in g on th e manner i n w hich
I t i s shown t h a t t h e s e t h e o r i e s may
e x p l a i n th e s t a b l e d e v e lo p m e n t o f t h e f r a c t u r e z o n e ;
how ever, th e l a r g e q u a n t i t i e s o f e n erg y t h a t a r e d i s s i p a t e d
s t a b l y can o n ly be d i s s i p a t e d by f r i c t i o n i n t h e f r a c t u r e
zone;
a r e l a t i v e l y s m a ll f r a c t u r e zo n e i s r e q u i r e d t o
d i s s i p a t e t h i s energy.
S t u d i e s o f t h e mechanism o f t h e s e is m ic e v e n t s showed
t h a t the mechanism was some form o f v o l u m e t r i c c o l l a p s e .
The mechanism o f seme o f t h e s e i s m i c e v e n ts c o u l d , t h e r e f o r e ,
be a sudden g ro w th i n th e f r a c t u r e z o n e , t h e c o l l a p s e o f
f r a c t u r e d r o c k n e a r t h e f a c e o r i n w c rk e d - o u t a r e a s , o r th e
su d d e n f a i l u r e o f a volume o f r o c k s l i g h t l y removed from
th e e x c a v a tio n .
The mechanism o f t h e s e is m ic e v e n t s n e a r
t h e d o l e r i t e s i l l was n o t c l e a r l y r e s o l v e d ;
i t co u ld ,
h ow ever, have been a s h e a r movement.
/ APPLNDIX 1 .
CONTENTS
INTRODUCTION
CONSIDERATIONS IN TH7 DESIGN OF THE
SEISMIC NETWORK
S e ism o m e ter l a y o u t
R e c o rd e r d e s i g n
DATA PROCESSING
The l o c a t i o n o f s e i s m i c e v e n ts
Energy d e t e r m i n a t i o n
Mechanism s t u d i e s
F i r s t m otion a n a l y s i s
S p e c tra l a n a ly sis
GEOLOGICAL ENVIRONMENT
DISCUSSION AND RESULTS
M ag n itud e o f s e i s m i c e v e n ts
P la n l o c a t i o n o f e v e n ts
E le v a tio n af se ism ic ev en ts
S t r a i n m easurem ents
The r a t e o f e n e r g y r e l e a s e
Tem poral b e h a v i o u r o f s e i s m i c e v e n t s
Trem ors and damage
Mechanism o f s e i s m i c e v e n ts
S t a b l e e n e rg y d i s s i p a t i o n
U n stab le r e l e a s e of energy
V isu a l o b s e rv a tio n s
F i r s t m o tio n th e o r y
F i r s t m o tio n r e s u l t s
S p e c tra l a n a ly sis r e s u lts
SUMMARY OF CONCLUSIONS
APPENDICES
ACKNOWLEDGEMENTS
REFERENCES
FIGJUBC
F lg .l
Delay tim e h y p e r b o la s
2
P la n p o s i t i o n o f s e is m o m e te rs
3
E l e v a t i o n of s e is m o m e te rs
4
S e is i.ic reco rd
5
O v erall freq u en cy resp o n se
6
L o c a to r
7
G e o l o g i c a l s e c t i o n from
s u rfa c e to e x ca v a tio n
8
G eo lo g ical s e c tio n n e a r
e x c a v a tio n
D i s t r i b u t i o n o f I'h aki S h a le
10
T o ta l energy o f d i f f e r e n t
s i z e d e v e n ts
11
F la n p o s i t i o n o f s e i s m i c e v e n t s
12
F la n p o s i t i o n o f s e i s m i c e v e n ts
13
P la n p o s i t i o n o f
1h
P la n p o s i t i o n o f s e i s m i c e v e n t s
13
P la n p o s i t i o n o i s e is m ic e v e n ts
16
V e r tic a l d i s t r i b u t i o n o f seism ic
even t s
17
P l a n o f e v e n t s a t t h e Harmony S i l l
18
V e r t i c a l s e c tio n th ro u g h th e
V e n tila tio n S haft
19
Change i n s t r a i n i n t h e
V e n t i l a t i o n S h a f t w i t h tim e
20
C om parison betw een s t r a i n and
s e is m ic m easurem ents
21
P la n o f th e f o u r r e g i o n s s e l e c t e d
f o r th e e n erg y r e l e a s e r a t e
anal.ye i s
22
P la n o f t h e s e i ’mlc e v e n t s t h a t
occu rred In th e fo u r re g io n s
s e le c te d f o r th e energy r e l e a s e
ra te a n aly sis
' smic e v e n t s
Page
23
P la n o f t h f c e n t r e s o f damage t h a t
o c c u r r e d i n th e f o u r r e g i o n s
s e l e c t e d f o r t h e e n e rg y r e l e a s e
r a te a n a ly sis
62
Graph of damage v s . --nergy r e l e a s e
ra te
63
Graph o f la b o u r r e q u i r e m e n t s v s .
en ergy r e l e a s e r a t e
63
Graph o f s e i s r i c i t y v s . en erg y
re le a se r a te
63
Graph o f t o t ;1 s e i s m i c en erg y v s.
e n e rg y r e l e a s e r a t e
63
D i u r n a l d i s t r i b u t i o n o f s e is m ic
e v e n t s a t H arm onj, a t V i r g i r i a
and a t th e Harmony 3 i l l
67
D iu rn al d i s t r i b u t i o n o f d i f f e r e n t
s i z e d e v e n ts
68
D a ily d i s t r i b u t i o n o f s t o p i n g h o le s
and com p ressed a i r
70
D a ily d i s t r i b u t i o n o f e v e n t s a t
Harmony, a t V i r g i n i a md a t t h e
Harmony S i l l
71
The v a r i a t i o n w i t h tim e o f th e
m in in g a c t i v i t y and s e i s m i c
a c tiv ity
73
The v a r i a t i n w i t h tim e o f t h e
a c t i v i t y of d i f f e r e n t siz e d e v en ts
74
34
The d i u r n a l d i s t r i b u t i o n o f damage
78
35
G r i f f i t h ' s Loci
91
36
C r i t i c a l v a lu e ; o f nc
94
37
P la n o f t h e i l ^ e v r i h a u la g e ,
2 S haft
24
25
26
27
28
29
30
31
30
F i r s t m o tio n r e l a t i o n p a t t e r n s
f o r die"! . a t i .ms i n p ,<y,
yy
e , e.„_ , u.
102
zz
107
39
F i r s t m o tio n r a d i a t i o n p a t t e r n s
f o r d i s l o c a t i o n s i n Ux
108
40
F i r s t m o tio n r a d i a t i o n p a t t e r n s
fo r d is lo c a tio n s in U
109
/ ....
( v ii)
page
Fig* 41
F 'i r e t m o tio n r a d i a t i o n p a t t e r n s
f o r d o u b le d i s l o c a t i o n s i n
XX
42
43
44
45
’ ey y ’ e zz
C e n t r a l p r o j e c t i o n o f th e f i r s t
m o tio n s o f an e v e n t w ith a l l
f i r s t ro t.io rj ra re fa c tio n
115
C e n t r a l p r o j e c t ! ' n ?f t h e f i r s t
m o tio n s o f an e v e n t w ith some
f i r s t m o tio n s :OL ^ r e s s i c r
116
C e n t r a l p r o j e c t i o n o f the f i r s t
m o tio n s o f an e v e n t
f o r w hich
t h e r a . n a t i o n p a t t e r n 3oes n o t
f i t any s t a n d a r d p a t t e r n
118
a ) A m i s s i l f r a m o f two s e i s m i c e v e n ts
b) Two .• n o t i o n s o f t h e P waves o f two
e v e n ts
46
112
122
S p e c t r a a t d i f f e r e n t seis m o m e te rs f o r
an e v en t o f m a g n itu d e 104 f t . - l b s .
n e a r th e e x ca v a tio n
124
S p e c t r a o f d i f f e r e n t s e is m o m e te rs f o r
an e v e n t of m a g n itu d e 10° f t . - l b s .
n e a r th e e x ca v a tio n
125
S p e c t r a o f d i f f e r e n t se is m o m e te rs f o r
an e v e n t a t t h e H < ony S i l l
126
The chang e i n a p p a r e n t v e l o c i t y i n
m u l t i l a y e r e d m edia.
132
G raphs o f t h e a p p a r e n t v e l o c i t y v s .
t h e e l e v a t i o n ab ov e r e e f f o r some
seismome>' r s
134
14A
T e c e n tr a l p ro je c tio n
138
15A
The t r a n r i e n t s p e c t r o g r a p h
142
16A
S p e c t r a l a n a l y s e s o f some s ta n d a r d
waveform s
143
Tue -frequency r e s p o n s e o f t h e He 11S e a rs r c d o l HS1 s e is m o m e te r
145
18A
C i r c u i t d ia g ra m o f t h e r e c o r d and
re p la y a m p lifie rs
146
19A
C i r c u i t d ia g ra m o f t h e d e v ic e
p e r f o r m in g t h e o p e r a t i o n r t (/2 d t
'o
C i r c u i t d ia g ra m o f t h e d i g i t a l c lo c k
47
48
1A
t o 3A
4A
t o 13A
17A
20A
L
147
148
the measurement and analysis of
EARTH MOTION RESULTING FROM
UNDERGROUND ROCK FAILURE
INTRODUCTION
R o c k b u r s ts have been a p a r t o f South A f r i c a n g o ld m inin g
lo r
..ore th a n a h a l f - c e n t u r y .
With th e p a s s a g e o f tim e ,
m in in g m ethods have been e v o lv e d which have a l l e v i a t e d th e
s e v e rity of ro c k b u rsts.
However, a s mines become d e e p e r ,
t h i s problem t h r e a t e n s to become v e r y s e r i o u s .
I t h a s become
o b v io u s t h a t e m p i r i c a l m ethods w i l l n o t p r o v id e a s a t i s f a c t o r y
s o l u t i o n ana i n t e n s i v e r e s e a r c h h a s been la u n c h e d a t a b e t t e r
u n d e r s t a n d i n g o f th e r o c k b u r s t mechanism.
In e a r l y 1 )6 3 , when t h i s s tu d y was commenced, t h e
t h e o r i e s t h a t had b e en p ro p o s e d and t h e more r e l e v a n t
o b s e r v a t i o n s which had be en p u b l i s h e d a r e a s f o l l o w s .
The
c o n c e p t o f a f r a c t u r e dome was p o p u l a r amongst most m ining
e n g in ee rs.
^ re
was no u n i f o r m i t y i n t h i s t h e o r y ;
one form
was t h a t t h e ro c k i n th e dome i s h e a v i l y f r a c t u r e d and i s
h e l d up by V o u s s o ir a r c h e s , and a n o t h e r was t h a t th e dome
i s a r e g i o n i n which s t r a t a s e p a r a t i o n o c c u r s , so t h a t th e
h a n g in g w a ll d e v e lo p s i n t o a number o f beams ( B ic c a rd JeP D e) ^
T h e r e was b e en c o n s i d e r a b l e d i s c u s s i o n
f r a c t u r e zone;
th e e x t e n t o f t h i s
some b e l i e v e d t h a t i t e x te n d s r i g h t th ro u g h
t o s u r f a c e and o t h e r s t h a t i t e x te n d s o n ly a few t e n s o f f e e t
i n t o th e h a n g i n g w a l l .
D cn k h au c/' ) a t t e m p t e d t o p r e d i c t t h e
s h a p e o f t h e f r a c t u r e dome by u s in g th e th e o r y o f e l a s t i c i t y
and a maximum t e n s i l e and s h e a r s t r e s s a s a f a i l u r e c r i t e r i o n .
He c o n c lu d e d t h a t th e h e i g h t o f t h e f r a c t u r e dome would be o f
t h e same m a g n itu d e a s th e s p a n o f t h e e x c a v a t i o n .
B arcza
and von W i l l i c h ^ ^ r e p o r t e d some s t r a t a movement m easurem ents
made a t Harmony Gold Mine which showed th e e x t e n t t o which
/ movements . . . .
—2 —
movements o c c u r r e d i n th e h a n g i n g w a l l .
These m easurem ents
were c o n s i d e r e d by Denkhaus, H i l l and Roux<4 ) t o d e m o n s tr a te
"an a l n o s t c l a s s i c a l d evelopm ent o f t h e f r a c t u r e dome".
Wi&gi l l ( ^ i n t r o d u c e d th e c o n c e p t o f " m a c r o p l n s tic flo w "
i n t o t h e f r a c t u r e dome t h e o r y .
In t h i s c o n c e p t th e ro c k
b e h a v e s a c c o r d i n g t o some o f t h e s o i l m echan ics law s a n d , i n
a d d i t i o n , e x h i b i t s tim e d e p en d e n t p r o p e r t i e s .
R o c k b u r s ts
w ere c l a s s i f i e d b r o a d ly i n t o two c a t e g o r i e s , nam ely, i n t r a d o s a l and e x t r a d o s a l , i . e . , b u r s t s o r i g i n a t i n g i n s i d e and
o u t s i d e t h e f r a c t u r e zone r e s p e c t i v e l y .
P re to riu s^
has
g i v e n a good d e s c r i p t i o n o f some f a c t o r s i n f l u e n c i n g th e
d i f f e r e n t ty p e s of ro c k b u rs t.
U l t r a s o n i c t e c h n i q u e s were
u s e d by P u ts c h and S z e n d re V ' 1 to d e te r m in e t h e e x t e n t o f
t h e f r a c t u r e zone s u r r o u n d i n g s to p e f a c e s .
They were a b l e
t o d e t e c t f r a c t u r e p l a n e s a t a d i s t a n c e o f 10 f e e t i n t o th e
r o c k , and showed t h a t t h e f r a c t u r e i n t e n s i t y d e c r e a s e d w ith
d i s t a n c e i n t o th e r o c k .
I n an i n v e s t i g a t i o n i n t o V i t w a t e r s r a n d E a r t h T rem ors,
Gone, Selifiman and 3 t e p h e n (8 ) found t h a t t h e s e tr e m o r s had
t h e i r o r i g i n s c l o s e to mine w o rk in g s .
A more i n t e n s i v e
u n d e rg ro u n d s e i s m i c i n v e s t i g a t i o n by Cook^ ^ r e v e a l e d t h a t
th e m a j o r i t y o f s e i s m i c e v e n t s o c c u r w i t h i n 100 f e e t o f th e
w ork in g f a c e and t h a t t h e r e were many more s e i s m i c e v e n t s
t h a n m a n i f e s t a t i o n s o f damage.
Between 1963 and 1966, a
che.nge i n th o u g h t became e v i d e n t , th e em phasis was t a k e n
o f f th e f r a c t u r e dome and t u r n e d to a s m a ll f r a c t u r e zone
a ro u n d th e e x c a v a t i o n w ith th e r e m a in d e r o f t h e ro c k b e in g
co n tin u o u s and n e a rly e l a s t i c .
Hoek(1C) h as d e m o n s t r a t e d
t h a t ro c k b e h a v e s e l a s t i c a l l y up t o f r a c t u r e and t h a t th e
m o d if ie d G r i f f i t h th e o r y i s an a d e q u a te f a i l u r e c r i t e r i o n
u n d e r s t a t i c lo a d c o n d i t i o n s .
&yder and O f f i c e r 1
O r t l e p p and N l c o l l ^1 1 ^ and
^ have shown t h a t th e movements i n t h e
ro c k a ro u n d a n e x c a v a t i o n a r e s a t i s f a c t o r i l y p r e d i c t e d by
/ e la stic ity
....
-
3
-
e l a s t i c i t y t h e o r y a p p l i e d to a c o n tin u o u s rock m ass.
The
d e v elo p m en t o f e l e c t r i c a l a n a lo g u e s baaed on e l a s t i c i t y
th e o r y h ave g i v e n a d d i t i o n a l im p e tu s t o th e p r e s e n t
p o p u la rity of th is th e o ry .
<*'00^
F u r th e r m o re , p u b l i c a t i o n s by
have le d t o a b e t t e r u n d e r s t a n d i n g o f th e
b a s i c m e ch a n ic s o f ro c k f a i l u r e and r o c k b u r s t s .
The s e i s m i c te c h n i q u e p ro m is e s t o be t h e most f r u i t f u l
o b s e r v a t i o n a l method o f a t t a c k on th e r o c k b u r s t problem ,
s i n c e i t a l l o w s m easu rem en ts o f ro c k movements d e ep w i t h i n
t h e ro c k mass to be made.
fe a tu re s;
I t h a s t h r e e v e ry a t t r a c t i v e
i t e n a b l e s t h e f o c u s o f a v i o l e n t e v e n t to be
l o c a t e d , i t e n a b l e s a q u a n t i t a t i v e d e t e r m i n a t i o n o f th e
k i n e t i c e n e r g y r a d i a t e d by t h e e v e n t to be made and i t i s
t h e o r e t i c a l l y p o s s i b l e t o d e te r m in e th e movements t h a t t a k e
p l a c e a t th e f o c u s .
F o llo w in g on th e s u c c e s s f u l s e is m ic
e x p e r im e n t a t B e t Rand P r o p r i e t a r y M ines, L im ite d (E. R. P. M. )
i t was d e c i d e d t o s e t up a second one a t a d i f f e r e n t m ine.
•he Harmony Gold Mine was s e l e c t e d b e c a u s e i t was prone t o
r o c k b u r s t s and e a r t h tr e m o r s and th e g e o l o g i c a l e n v iro n m e n t
d i f f e r e d from t h a t a t E .R .P.M .
There was a l s o t h e f e a r t h a t
Harmony m ight e n c o u n t e r a s e v e r e r o c k b u r s t problem be ca u se
p r e l i m i n a r y s t r e n g t h t e s t s showed t h a t t h e q u a r t z i t e t h e r e
was s t r o n g e r th e n a t E .R .P.M .
I t wag th o u g h t t h a t ro c k
f a i l u r e s a t Harmony m ig h t, t h e r e f o r e , be more v i o l e n t th a n
t h o s e a t E .R .P .M .
The E .R .P .M . s e is m ic netw ork was d e s ig n e d t o l o c a t e
e v e n t s o c c u r r i n g n e a r one l o n g w a l l s t o p e .
Harmony i s a
c o m p a r a t i v e l y new mine and t h e w o rk e d -o u t a r e a i s much
s m a lle r.
The new s e i s m i c netw o rk was, t h e r e f o r e , a b l e to
c o v e r th e e n t i r e mine so t h a t t h e o v e r a l l rock movement
p a t t e r n c o u ld bo d i s c e r n e d w i t h o u t l o s i n g to o much l o c a t i o n
accu racy .
I n a d d i t i o n , t in netw ork was a r r a n g e d t o o p e r a t e
c o n tin u o u sly .
/ CONSIDERATIONS . . . .
c o n sid e r a t io n s i n the desig n of the s e i s m i c network.
The moot v e r s a t i l e method o f r e c o r d i n g , s t o r i n g end
m a n i p u l a t i n g d a t e i s by means o f t a p e - r e c o r d e r s .
For
s e i s m i c n e tw o r k s , th e t a p e - r e c o r d e r s must be m u l t i ­
c h a n n e l l e d to accommodate a l l t h e s e is m o m e te rs and tim e
sig n als.
The tim e s i g n a l s t a k e th e form o f a sequ en ce o f
cod ed p u l s e s which g i v e t h e tim e o f day a t any i n s t a n t .
F o r l o c a t i o n p u r p o s e s , th e most c o n v e n ie n t ty p e o f r e c o r d
i s a v i s u a l o n e , c o n s e q u e n t l y th e t a p e - r e c o r d e r s must d r i v e
a p h o to g rap h ic o s c illo g r a p h .
I t was d e s i r a b l e t o do a l l
a a t a p r o c e s s i n g a t t h e B ern ard P r i c e I n s t i t u t e i n J o h a n n e s b u rg ,
t h e r e f o r e i t was n e c e s s a r y t o o n e r a t e a r e c o r d deck a t th e
Harmony Mine and a r e - p l a y deck i n J o h a n n e s b u rg .
S e ism o m e ter L a y o u t:
When a f a i l u r e o r e x p l o s i o n o c c u r s in r o c k , waves t r a v e l
o u t r a d i a l l y from t h e d i s t u r b a n c e .
In s o l i d , homogeneous
r o c k t h e r e a r e two modes o f wave p r o p a g a t i o n , nam ely,
c o m p r e s s i o n a l and s h e a r .
The c o m p r e s s i o n a l , o r P, wave
t r a v e l s f a s t e r t h a n t h e s h e a r , o r 3 wavu.
I f a t a p o in t
"em o te from t h e s o u r c e , th e d i f f e r e n c e i n tim e s o f a r r i v a l
to P and 3 waves can be m e a s u re d , th e n t h e d i s t a n c e
a t h e s o u r c e to t h e m e a s u rin g p o i n t can be c a l c u l a t e d .
i or
t h i s to be done th e v e l o c i t i e s o f th e P and S waves
must be known.
In p r a c t i c e i t i s n o t e asy t o d e te r m in e when
th e 3 wave a r r i v e s b e c a u s e i t i s u s u a l l y o b s c u re d by t h e coda
o f t h e P wave, e s p e c i a l l y when t h e P-3 i n t e r v a l i s s h o r t .
A l t e r n a t i v e l y , i f t h e r e a r e two m e a s u rin g p o i n t s end th e
d i r e c t i o n o f t h e s o u r c e i s known, th e d i s t a n c e o f th e s o u r c e
can be c a l c u l a t e d u s i n g th e d i f f e r e n c e i n tim e s o f a r r i v a l o f
th e P waves a t th e two m e a s u rin g p o i n t s .
C o n s id e r two
me- e a r i n g p o i n t s 3^ "nd S2 s e p a r a t e d by a d i s t a n c e 2d , th e
l o c u s o f a s o u r c e p o i n t which p ro d u c e s a c o n s t a n t d i f f e r e n c e
xn th e tim e s o f a r r i v a l ( d e l a y t i m e ) a t ^
and So, i s n
h y p e rb o la .
/ F ig u r e 1 ............
f ig u r e
1
F i g u r e 1 snowo a f a m i l y o f h y p e r b o la s f o r d i f f e r e n t d e la y
tim e s.
The c u r v e s a r e f o r e q u a l in c re m e n ts i n d e la y t i m e ,
w here th e d e l a y tim e i s i n
d im e n s io n le s s form
D elay Time = 2—1 = ?
2d
a = P wave v e l o c i t y
t = d e l a y tim e i n sec o n d s
The s p a a i n g betw een t h e h y p e r b o la s i s a m easure of th e
a c c u r a c y w ith which a s o u r c e p o in t can be l o c a t e d .
Imagine
a s o u r c e p o i n t which c a n l i e anywhere a lo n g a r a d i a l l i n e
from 0 and making a n a n g le
lin e 9 = 0 ,
b etw een
and
0 w ith th e l i n e S-jSp. Along th e
th e h y p e r b o l a s a r e norm al t o
t h e r a d i a l l i n e and a r e c l o s e l y s p a c e d , th e r e s o l u t i o n i s
b e st h ere:
o u t s i d e S1 and S2 th e l i n e i s c o i n c i d e n t w ith
t h e h y p e r b o la f o r T = 1 , and t h e r e s o l u t i o n i s z e r o .
r a d ia l lin e
The
i s c o i n c i d e n t w ith t h e h y p e r b o la T = 0 when
0 = 90° and t h e r e s o l u t i o n i s a g a in z e r o .
I n g e n e r a l , th e
r e s o l u t i o n i s b e s t a t s m a l l a n g le s and c l o s e t o th e o r i g i n ;
th e h y p e r b o l a s a l l become a s y m p t o tic
to r a d i a l l i n e s so
t h a t a t l a r g e d i s t a n c e s th e r e s o l u t i o n te n d s t o z e r o .
From
F i g u r e 1, i t c a n be s v e n t h a t t h r e e m e a s u rin g p o i n t s a r e
r e q u i r e d t o o b t a i n a u n iq u e l o c a t i o n i n a tw o - d im e n s io n a l
s p a c e , and t h a t f o r good r e s o l u t i o n , t h e t h r e e m e a s u rin g
p o i n t s s h o u ld l i e a t t h e c o r n e r s o f an e q u i l a t e r a l t r i a n g l e
w hich e n c l o s e s th e s o u r c e .
S i m i l a r l y i n t h r e e d i m e n s io n s ,
f o u r m e a s u r in g p o i n t s a r e r e q u i r e d to p r o v id e a unique
s o l u t i o n , and t h e optimum c o n f i g u r a t i o n o f t h e f o u r p o i n t s
i s a t th e c o r n e r s o f a t e t r a h e d r o n w hich e n c l o s e s th e s o u r c e .
A d d i t i o n a l m e a s u rin g p o i n t s s u r r o u n d in g t h e s o u r c e w i l l
g r e a t l y im prove th e a c c u r a c y o f th e l o c a t i o n .
A c o -p la n a r
a r r a y o f m e a s u rin g p o i n t s w i l l hove a v e r y p o o r r e s o l u t i o n
and a m b ig u ity I n a d i r e c t i o n norm al t o th e p l a n e .
In s e l e c t i n g th e s i t e s f o r s e is m o m e te rs on th e mine,
th e o b j e c t was t o e n c l o s e a s much o f t h e mine w o rk in g s os
p o s s i b l e , w i t h t e t r a h e d r a l a r r a y s o f s e i s m o m e t e r s ................
PLAN OF HARMONY ON A GRID OF 5000 FEET,
SHOWING THE POSITIONS OF SEISMOMETERS
1 TO 9 AND THE BOUNDARY OF THE VIRGINIA
PORTION.
caet Dcm » rstum
A VERTICAL SECTION THROUGH HARMONY SHOWING THE POSITIONS OF
SEISMOMETERS 1 TO 9, THE SURFACE AND THE REEF PLANE.
- 9 F ig u r e 2 and F ig u r e 3 show t h e p la n p o s i t i o n and e l e v a t i o n
o f t h e s e l e c t e d s e ism o m e te r s i t e s .
Seism om eters 1 , 2 , 3 ,
4 , 5 and 6 were o i l s i t u a t e d i n h a u la g e s below t h e r e e f p l a n e ,
7 and 8 were i n i n t e r m e d i a t e p u m p - s ta tio n s h a lf - w a y up s h a f t s ,
anc 9 was on s iu rfn c e .
S eism o m eters 1 , 2, 3 , 7; 3, 4 , 6, 8 ;
and 2 , 3 , 5, 9 form t h r e e o v e r l a p p i n g t e t r a h e d r a l a r r a y s .
A ll t h e
s e is m o m e te rs were r i g i d l y f i x e d i n th e ends o f
d i a m o n d - d r i l l h o l e s 100 f e e t lo n g , to r e d u c e n o i s e from
a c t i v i t y i n t h e h a u la g e s and t o m inim ize wave s c a t t e r i n g
e f f e c t s from th e h a u l a g e s .
Thu s u r f a c e s e is m o m e te r was f i x e d
i n s a n d s t o n e 100 f e e t below s u r f a c e .
A ll th e s e ism o m e te rs
were v e r t i c a l e x c e p t 1 , 4 and 5, which d e t e c t o n ly h o r i z o n t a l
m o tio n .
T h is a r r a y a l s o c o v e re d a p o r t i o n o f t h e n e ig h b o u r ­
i n g V i r g i n i a M ine.
A l l th e s e is m o m e te rs were l i n k e d to th e
t a p e - r e c o r d e r by means o f tw in c o n d u c to r s c r e e n e d c a b l e .
A ll t h e c a b le was c a r r i e d i n s t a n d a r d e l e c t r i c a l c o n d u it f o r
p r o t e c t i o n a g a i n s t t h e f t and m e c h a n ic a l damage.
The c o n d u i t
p r o v id e d e x t r a s c r e e n i n g which was an a d v a n ta g e s i n c e a l l
th e c a b l e s were i n c l o s e p r o x im ity w ith h ig h v o l t a g e power
c a b le s.
The t a p e - r e c o r d e r was s i t u a t e d u n d e rg ro u n d a t t h e
17 l e v e l s t a t i o n , 3 s h a f t , so t h a t i t would n o t be n e c e s s a r y
t o b r i n g a l a r g e number o f c a b l e s up th e s h a f t to s u r f a c e .
I t was n e c e s s a r y to u s e e x i s t i n g t e l e p h o n e w ire i n th e
s h a f t s t o l i n k th y s u r f a c e s e is m o m e te r and t h e s e is m o m e te rs
i n th e pump s t a t i o n s
to t h e t ^ p ^ - r e c o r d e r .
T h is r e s u l t e d i n
a l a r g e amount o f c r o s s - t a l l ; from te le p h o n e b e l l b r i n g i n g ,
and a s m a l l amount o f c r o s s - t a l k betw een s e is m o m e te rs 8 and
9 which u sed t h e same te l e p h o n e c a b l e .
The c r o s s - t a l k from
the b e l l s was o f no c o n se q u e n c e s i n c e i t r a r e l y o c c u r r e d a t
t h e same time a s a s e i s m i c e v e n t .
A l t o g e t h e r 1 0 0 ,0 0 0 f e e t
o f c a b l e was u sed t o j o i n t h e s e is m o m e te rs t o t h e r e c o r d e r .
The s e is m o m e te rs were H a l l —S e a r s , Model HS—1 w i.h a
n a t u r a l frequency of 4 .5 c / s .
They have a s e n s i t i v i t y o f
/ 0 .5 v o lts . . . .
—
10
—
0 . 5 v o l t s p e r in c h p e r second w ith a 1000 ohm l o a d .
The
fr e q u e n c y r e s p o n s e o f t h e s e is m o m e te rs i s shown in
A ppendix 4 .
R e c o r d e r D e s ig n :
The s e n s i t i v i t y r e q u ir e m e n ts o f th e r e c o r d i n g s y ste m
a re tw o -fo ld .
a ) The f i r s t m o tio n s o f th e s e i s m i c e v e n t s must be s h a r p
and c l e a r f o r good a c c u r a c y and f o r f i r s t m o tio n s t u d i e s .
T h is i m p l i e s t h a t t h e r e c o r d e r must have a good h ig h
f r e q u e n c y r e s p o n s e and h ig h s e n s i t i v i t y .
b) For e n e rg y d e t e r m i n a t i o n and mechanism s t u d i e s by means
o f s p e c t r a l a n a l y s i s , the w i d e s t p o s s i b l e bandw idth arai
low d i s t o r t i o n a r e r e q u i r e d .
The most s e r i o u s form o f
d i s to r tio n is s a tu r a tio n d i s t o r t i o n , th e re fo re th is
r e q u ir e m e n t i m p l i e s a low s e n s i t i v i t y .
A n oth er form o f
d i s t o r t i o n w hich som etim es o c c u r s i n s e is m ic a m p l i f i e r !
when th e s i g n a l l e v e l becomes h i g h , i s b l o c k i n g .
The s e is m ic expe? ^jnent a i E .R .P .X . r e v e a l e d t h a t
;he
m a g n itu d e s of th e s e i s m i c e v e n t s t h a t c o u ld be s a t i s f a c t o r i l y
x
q
l o c a t e d ra n g e d from 10 f t . - l b s . t o 10 f t . - l b s . , and t n a t
most e n e rg y was c a r r i e d i n t h e 20 c / s to ICO c / s f r e q u e n c y
ra n g e .
i s 10^.
The ra n g e i n th u e n e rg y o f th e e v e n t s t o be e x p e c te d
S in c e th e e n e rg y i s p r o p o r t i o r a l t o t h e s q u a r e o f
t h e p a r t i c l e v e l o c i t y and s i n c e s e is m o m e te rs a r e s e n s i t i v e
t o p a r t i c l e v e l o c i t y , t h e ra n g e i n o u t p u t from th e
s e i s . o m e te r w i l l be 10^ o r 60 d b .
I t was a l s o found t h a t
t h e f i r s t m o tion o f a 10^ f t . - l b . e v e n t a t a d i s t a n c e o f a
few th o u s a n d f e e t from t h e s e is m o m e te r c a u s e d an o u t p u t o f
10 nV from t h e s e is m o m e te r .
The lo w e r l i m i t t o th e ban d w idth
was s e t by t h e s e is m o m e te r which had a c u t - o f f j u s t below
4 .5
c /s.
The u p p e r l i m i t was s e t by a t t e n u a t i o n o f s e i s m i c
waves i n r o c k ;
o v e r a d i s t a n c e o f 4000 f e e t , t h e
/ a tte n u a tio n . . . .
a t t e n u a t i o n o f a 1000 c / s wave i s 20 ao more th a n t h a t o f
a low f r e q u e n c y wave, t h e r e was c l e a r l y no p o i n t i n
a t t e m p t i n g t o r e c o r d waves of n i g h e r f r e q u e n c y .
f i n a l l y , t h e r e c o r d e r was s i t u a t e d u nd erg ro u n d and i t
was c o n v e n ie n t t o g i v e i t a t t e n t i o n o nly once a day and
t h e r e f o r e t h e ta p e had to play f o r 24 h o u r s .
The r e - p l a y
m achine had to ru n a t a h i g h e r speed th a n t h e r e c o r d machine
so t h a t t h e t a p e s c o u ld be p la y e d back i n a norm al w orking
day.
A r e - p l a y sp ee d f o u r tim e s h i g h e r th a n th e r e c o r d sp eed
was s e l e c t e d ;
t h i s had th e a d v a n ta g e t h a t t h e o u t p u t from
t h e r e - p l a y h e a d s was f o u r tim e s h i g h e r ;
h ow ever, ♦ne s i g n a l
f r e q u e n c y was a l s o f o u r tim e s high r , and t h i s posed
d i f f i c u l t i e s in tr a n s c r ib in g to a v is u a l re c o rd .
The l o n g e s t
1 . 5 m il ta p e a v a i l a b l e was 5000 f t . lo n g , so t h e ; th e r e c o r d
sp ee d had t o be 0 .6 i n s . p e r s e c .
The s p e c i f i c a t i o n s o f t h e r e c o r d i n g s y s te m w e r e :
a ) Record s p e e d 0 . 6 i n s / s e c .
b) R e - p la y sp eed 2 .4 i n s / s e c .
c ) At l e a s t 10 c h a n n e ls
d ) Dynamic ra n g e o f 60 db .
e ) S e n s i t i v e to 10 uV s i g n a l i n p u t .
f ) F req u e n c y r e s p o n s e from 4 t o 1000 c / s .
g ) B lo c k in g must r o t o c c u r i n t h e a m p l i f i e r s .
h ) Compromise betw een h ig h s e n s i t i v i t y and
c u t-o ff d is to rtio n .
No s t a n d a r d t a p e - r e c o r d e r s were a v a i l a b l e w ith th e s e
s p e c i f i c a t i o n s and t h e c ; s t o f m o d ify in g s t a n d a r d m achines
was found to be p r o h i b i t i v e .
be d e s ig n e d and b u i l t .
C o n s e q u e n tly m achines h d to
The b a s i c f e a t u r e s o f t h i s d e s i g n
were k e p t s i m i l a r to t h o s e o f t h e r e c o r d e r a t T,.R . P . M . , so
t h a t t - p e s r e c o r d e d a t E.R .P.M . c o u ld be p r o c e s s e d on th e
new equipm ent i f n e c e s s a r y .
The to p e t r a n s p o r t s y ste m was
i d e n t i c t 1 w ith th e E .R .P.M . s y s te m , e x c e p t f o r a change i n
- 12 t h e ta p e t e n s i o n i n g a r r a n g e m e n t.
The r e c o r d - r e p l a y h e ad s
were a l s o i d e n t i c a l w ith th e E.R .P.M . r e c o r d e r ;
th e y were
E . N . I . 1 6 - t r c c k h e ad s f o r a one in c h t a p e . The r e c o r d r e p l a y c h a r a c t e r i s t i c o f t h e u e h ead s was 20 db down a t 4 c / s
and 1000 c / s r e c o r d f r e q u e n c y , when th e ta p e speed was 0 .6
i n / s e c . on r e c o r d and 2 .4 i n / s e c . on r e p l a y .
d e s i r e d ban d w id th was 4 c / s t o 1000 c / s , i t
S in c e t h e
was n e t p o s s i b l e
t o make u s a o f m o d u la tio n te c h n i q u e s b e ca u se an even l a r g e r
bandw idth would have been n e c e s s a r y .
In g e n e r a l , s o p h i s t i c a t e d te c h n i q u e s o r e r e q u i r e d t o
o b t a i n a s i g n a l t o n o i s e r a t i o o f 4 0 d b . a t low t a p e s p e e d s ,
t h e r e f o r e a dynamic ra n g e o f 60 db c o u ld be- a t t a i n e d by u s in g
two c h a n n e l s , one w ith a g a j n 30 a^ l o s s t h a n th e o t h e r , and
e a c h h a v in g a s i g n a l t o n o i s e r a t i o o f a t l e a s t 30 d b .
The
E .R .P .K . r e c o r d e r u s e d B.C. B ia s in g which r e s u l t e d i n a
s i g n a l to n o i s e r a t i o o f 30 d b .
A.C. b i a s i n g c o u ld have
p r o v id e d an im provem ent i n t h e s i g n a l to n o i s e r a t i o and a
s l i g h t improvement i n th e l i n e a r i t y a t th e e x p en se of more
com plex e l e c t r o n i c c i r c u i t i n g and a p o o r e r h ig h f r e q u e n c y
response.
v.C. B i a s i n g i s more c r i t i c a l t o a d j u s t m e n t s w h ile
D.C. b i a s i n g i s more prone to low f r e q u e n c y n o i s e c a u s e d by
d u s t p a r t i c l e s on t h e U pe.
D.C. b i a s i n g was s e l e c t e d f o r
th e Harmony r e c o r d e r s i n c e i t p ro v id e d th e a d e q u a te s i g n a l
t o n o i s e r a t i o o f 30 ub and a t o t a l h arm onic d i s t o r t i o n o f
l e s s th a n 5 p e r c e n t .
There w ere 16 t r a c k s a v a i l a b l e , n in e were a l l o c a t e d to
h i g h s e n s i t i v i t y c h a n n e ls f o r each s e is m o m e te r, s i x t o low
s e n s i t i v i t y c h a n n e ls f o r s e l e c t e d s e is m o m e te r s , and one to
tim e s i g n a l s .
B lo c k in g of «he a m p l i f i e r s wrs c irc u m v e n te d by n o t u s in g
c a p a c ito rs
p s
c o u p l i n g e l'- r .o n ts b etw een th e a m p l i f i e r s t a g e s .
S in c e a good low f r e q u e n c y r e s p o n s e wee r e q u i r e d , th e
a m p l i f i e r s t a g e s w ere d :.r e c t c o u p le d .
The i n p u t and o u tp u t
/ sig n a l . . . .
- 13 s i g n a l l e v e l s on t h e r e c o r d and r u p ln y s i d e s w ere i d e n t i c a l ,
so t h . : t t h e r e c o r d rnd r e p l a y a m p l i f i e r s were mode i d e n t i c a l ,
e x c e p t f o r e q u a l i z a t i o n i n th e - e p l a y a m p l i f i e r s .
The f i r s t
two s t a g e s w ere d i f f e r e n t i a l a m p l i f i e r s which have good
l i n e a r i t y and good s t a b i l i t y .
The f i n a l s t a g e s were a common
e m i t t e r s t a g e cnu a d r i v e r s t a g e f o r d r i v i n g t h e 3 ohm h e a d s ,
i n t h e c a s e o f th e r e c o r d e r , and 15 ohm g a lv a n o m e te r s , i n th e
case o f th e re p la y deck.
A c i r c u i t diagram i s shown i n
A ppendix 4 .
On i n s t a l l i n g t h e r e c o r d e r i n t h e m ine, two d i f f i c u l t i e s
arose.
The f i r s t d i f f i c u l t y , which was a n t i c i p a t e d , was t h a t
50 c / s p ic k u p from The mine power s u p p ly n e c e s s i t a t e d th e
f i r s t s t a g e o f th e a m p l i f i e r b e in g p la c e d a t t h e s e is m o m e te r.
The seco nd d i f f i c u l t y was th e a p p e a r a n c e o f a s lo w ly v a r y i n g
D.C. v o l t a g e on th e c a b l e from th e s e is m o m e te rs t o the
reco rd ers.
The s o u r c e o f t h i s v o l t a g e was n e v e r i d e n t i f i e d ;
h o w e v e r, i t a p p e a r e d t o be ruJ --ted to u n d e rg ro u n d e l e c t r i c
lo c o m o tiv e s.
T his v o l t a g e u p s e t th< o p e r a t i o n o f the d i r e c t
c o u p le d a m p l i f i e r s t a g e s ,
and c o u p l i n g t r a n s f o r m e r s had t o
be i n t r o d u c e d a t each end o f th e c a b l e .
The o s c i l l o g r a p h u se d was a H a l l - S u a r s 2 4 -c h a n n e l
g a lv a n o m e te r t y p e , t h e n a t u r a l f r e q u e n c y o f th e g a lv a n o m e te rs
was 500 c / a .
g r a p h i c p'tpe1”.
The r e c o r d was p roduced on 1 0 -in c h wide p h o to ­
The maximum p a p e r sp ee d was 15 i n s / s e c .
I t was n e c e s s a r y t o know t h e time a t which s e i s m i c e v e n t s
o c c u r so t h a t th e y c o u ld be c o r r e l a t e d w i t h m in in g a c t i v i t y ,
r o c k b u r s „s and e a r t h t r e m o r s .
fo r t h i s purpose.
a
d i g i t a l c lo c k was d e s ig n e d
The c lo c k produced a s eq u e n c e of t e n
b i n a r y coded p u l s e s r e p e a t e d t h r e e tim e s a s e c o n d .
The
f i r s t p u l s e was a m ark er p u ls e and was s l i g h t l y b ig g e r t h a n
th e o t h e r s , th e r e m a in in g n in e p u l s e s d i v i d e d t h e day i n t o
q
2 p a r t s , i . e . , a p p r o x im a te ly 2 . 8 m i n u t e s . The c lo c k
t h e r e f o r e gave t h e tim e t o t h e n e a r e s t 1 .4 m in u te s .
/ FIGURE 4 ............
v<>Vv>
4“
yf
■<
M |M*
V<^Vye
W
W
y^V )
^ v \^ ,V
-w S e « « W W »
4h 4 u
FIGURE 4
RECORD OF TWO SEISMIC EVENTS SEPARATED BY H7 SECONDS. TRACES MARKED V
ARB PARTICLE VELOCITY, AND TRACES MARKED F ARE ENERGY FLUX. THE PULSE.
TRACE REPRESENTS THE TIME IN CODE.
W*W4-^W
- 15I n f i g u r e 4 , t h e second t r u c e from t h e bottom i e t h e tim e
t r a c e and t h e co d e i n d i c a t e s t h a t t h e tim e i a 1 1 .0 3 a.m .
The s p a c i n g betw een th e p u l s e s woe 25 m i l l i s e c o n d s , so t h a t
t h e c l o c k a l s o s e r v e d a s a f r e q u e n c y r e f e r e n c e i n o r d e r to
c h e c k t h a t t h e s p e e d o f t h e r e c o r d d e c k , t h e r e p l a y deck and
t h e o s c i l l o g r a p h re m a in e d c o n s t a n t .
The tim e code a l s o s e r v e d
a s a p o s i t i o n r e f e r e n c e a lo n g th e l e n g t h o f t h e t o p e ;
for
ex am ple, i f i t was d e s i r e d t o re -e x a m in e a s e i s m i c e v e n t f o r
f u r t h e r p r o c e s s i n g , i t was on e a s y m a t t e r t o f i n d t h e e v e n t
by l o o k i n g f o r t h e tim e a t which i t o c c u r r e d .
The h e a d a on th e r e c o r d d e ck were a l i g n e d r e l a t i v e to
t h e h e a d s on t h e r e p l a y dock su c h t h a t when a p u ls e was
s i m u l t a n e o u s l y a p p l i o d t o a l l c h a n n e ls on t h e r e c o r d d e c k ,
t h e s t a g g e r betw een s i g n a l s on a tim e b a se was l e s s th a n one
m i l l i s e c o n d on t h e p h o to g r a p h ic r e c o r d .
Bach c h a n n e l o f th e
e n t i r e r e c o r d i n g s y s te m was c a l i b r a t e d f o r a m p litu d e and
f r e q u e n c y r e s p o n s e and s e n s e o f f i r s t m o tio n .
S ta n d a rd s i g n a l s
from a low im pedance s i g n a l g e n e r a t o r were a p p l i e d i n p a r a l l e l
w ith e ach s e is m o m e te r i n t h e m ine, so t h a t t h e e n t i r e system
was c a l i b r a t e d .
To c a l i b r a t e f o r s e n s e o f f i r s t m o tio n ,
p o s i t i v e p u l s e s were a p p l i e d t o t h e p o s i t i v e t e r m i n a l s o f
t h e s e is m o m e te rs and the d i r e c t i o n o f m o tion o f t h e
o s c i l l o g r a p h t r a c e was o b s e r v e d .
F ig u r e 5 shows t h e o v e r a l l
f r e q u e n c y r e s p o n s e o f t h e s y s te m , i n c l u d i n g t h e fre q u e n c y
r e s p o n s e o f t h e s e is m o m e te r s .
th a n in te n d e d ;
The bandw idth was n a r r o ^ r
how ever, i t was a d e q u a te f o r e n e r g y
d e te r m in . t i o n s and s p e c t r a l a n a l y s i s , s i n c e most o f th e
e n e r g y i s c a i r i e d i n th e 20 t o 100 c / s r a n g e ,
/ FIGURE 5.
db
gain
Relative
0
3
6
9
12
100
Frequency
FI3URB «5
c/s
THH FREQUENCY RESPONSE OF THE ENTIRE RECORDIN'! SYSTEM,
INCLUDING THE FREQUENCY RESPONSE OF THE SEISMOMETER.
KXX)
- 17 An e l a b o r a t e t r i g g e r system was b u i l t i n t o t h e r e p l a y
s y s te m .
The p u rp o se o f t h e t r i g g e r was t o s e t th e o s c i l l o ­
g ra p h i n m o tio n whenever an e v e n t o c c u r r e d , so t h a t th e ev en t
c o u ld be r e c o r d e d a u t o m a t i c a l l y .
I t was i n te n d e d t h a t th e
t r i g g e r s h o u ld s e l e c t o n ly e v e n ts t h a t c o u ld be l o c a t e d ,
t h e r e f o r e a t r i g g e r was produced o n ly when t h e r e was a s i g n a l
p r e s e n t on f o u r o r more c h a n n e ls and on c o n d i t i o n t h a t t h e s e
s i g n a l s o c c u r r e d w i t h i n 1 /8 second o f e ach o t h e r .
( 1 /8 second
was t h e r e p l a y t r a v e l tim e o f a P wave betw een t h e most w id ely
spaced seism o m e te rs).
The t r i g g e r o p e r a t e d s a t i s f a c t o r i l y i n
s e l e c t i n g s e i s m i c e v e n ts r e c o r d e d on th e m a g n e tic t a p e ;
h ow ev er, i t was r e j e c t e d b e ca u se numerous f a l s e t r i g g e r s
r e s u l t e d a t b l s t i n g tim e i n th e .nine and from t r a n s i e n t s
p r o b a b ly c a u s e d by th e s t o p p i n g and s t a r t i n g o f e l e c t r i c
lo c o m o tiv e s u n d e r g r o u n d .
su p e rio r;
M o n ito rin g by e a r was found t o be
s e i s m i c e v e n t s were r e a d i l y d i s t i n g u i s h a b l e from
o t h e r s i g n a l s and w ith a l i t t l e
e x p e r i e n c e i t was p o s s i b l e
t o e s t i m a t e t h e m a gn itu de o f th e e v e n t .
I t was a ls o found th a t p l a y i n g t h e ta p e bock i n 6 h o u rs
or 4 tim es reco rd in g spued, r e su lte d i n a b u i l d - u p o f
unplayed ta p e s .
The rep la y speed was changed t o 8 tim e s the
record in g speed fo r m onitoring purposes, and when a s e is m ic
e v e n t occurred, the speed was sw itched b ack to 4 tim e s f o r
making the photographic record.
/ DATA PROCESSING............
— 18 —
data p r o c essin g
Th.s l o c a t i o n , o f
E vents
The method o f l o c a t i n g s o is m ic e v e n ts h a s been d e s c r i b e d
by Cook( 9 ) .
The method makes u se o f a d e v ic e known a s th e
" l o c a t o r " , F ig u r e 6 .
The l o c a t o r i s an a n a lo g u e com puter
and i s a s p a t i a l s c a l e model o f t h e s e is m o m e te rs i n th e m ine.
The t i p s o f t h e v e r t i c a l r o d s r e p r e s e n t t o s c a l e th e p o s i t i o n s
o f t h e s e is m o m e te r s .
S t r i n g s p a ss up e a c h r o d and ru n ov»r
p u l l e y s so t h a t t h e y heng down i n f r o n t o f a s c a l e on th e
w a ll.
The s c a l e i s c a l i b r a t e d i n f e e t and each d i v i s i o n
r e p r e a e r c s 200 f e e t .
A s t r i n g can be p u l l e d ou t from each
s e is m o m e te r p o s i t i o n and t h e l e n g t h t h a t i s p u l l e d o u t can
be m easured by t h e m o tio n o f an i n d i c a t o r a t t a c h e d t o th e
s t r i n g , a s i t moves o v e r t h e s c a l e on th e w a l l .
/
FIGURE 6 .............
- 20 To c a r r y o u t a l o c a t i o n f o r a s e is m ic e v e n t , the
d i f f e r e n c e s i n tim e s o f a r r i v a l ( d e l a y tim e s ) o f P waves a t
e a c h s e is m o m e te r e r e d e te r m in e d from t h e p h o to g r a p h ic r e c o r d .
These d e la y tim e s a r e c o n v e r te d i n t o d i f f e r e n c e s i n d i s t a n c e s
o f t h e s e i s m i c e v e n t from th e s e is m o m e te r s , by m u l t i p l y i n g
th e d e l a y tim e s by th e P wave v o i o c i t y .
The i n d i c a t o r s a r e
t h e n a d j u s t e d t o c o rre s p o n d t o th e d i f f e r e n c e s i n d i s t a n c e s
f o r each s e is m o m e te r .
The
:us o f th e e v e n t can t h e n be
lounri by j o i n i n g a l l th e s t r i n g s t o g e t h e r end m a n i p u l a t i n g
t h e common p o i n t su ch t h a t a l l th e i n d i c a t o r s form n
h o riz o n ta l s tr a ig h t lin e .
The p o s i t i o n o f t h e coamon o o i n t
r e p r e s e n t s t h e p o s i t i o n o f th e f o c u s and th e p o s i t i o n whore
a l l t h e i n d i c a t o r s l i n e up r e p r e s e n t s th e tim e o f o r i g i n o f
t h e s e i s m i c e v e n t to a s u i t a b l e s c a l e .
The l o c a t i o n so
o b t a i n e d i s c e l l e d th e f i r s t l o c a t i o n .
In p r a c t i c e t h e v e l o c i
v f t h e P waves v a r i e s a lo n g
d i f f e r e n t p a t h s on a c c o u n t o f th e n o n - u n i f o r m i t y o f t h e
g e o l o g i c a l s t r a t a and on a c c o u n t o f t h e f r a c t u r e d r o c k c l o s e
to t h e e x c a v a t i o n .
I d e a l l y thu v e l o c i t y o f p r o p a g a tio n s h o u ld
be d e te r m in e d f o r each p a th to a s e is m o m e te r, i . e . , f o r each
se s m i c a l l y
c t i v e a r e a i n t h e m in e .
The P wave v e l o c i t y was
d e te r m in e d f o r t h r e e r e g i o n s i n t h e mine c o r r e s p o n d i n g t o each
o f t h e t h r e e t e t r a h e d r a l s e is m o m e te r a r r a y s .
Two 20 l b .
e x p l o s i v e c h a r g e s w ere f i r e d i n each s h a f t p i l l a r and a 100 l b .
c h a r g e was f i r e d i n a s to p e c e n t r a l l y s i t u a t e d i n th e m ine.
A s e is m o m e te r was p la c e d c l o s e to th e c h a r g e and c o n n e c te d
t o th e t a p e - r e c o r d e r so t h a t t h e tim e o f o r i g i n c o u ld be
d e term in e d .
The T a b le below shews t h e v e l o c i t i e s o b t a i n e d .
/ T a b le . . .
S e ism o m e ter
3 S haft B la st
a ft/se c .
2 S h aft B last
a ft/se c .
1
Stope B la s t
a ft/se c .
1 8 .7 0 0
2
3
1 8,9 0 0
1 8 .7 0 0
1 9 .0 0 0
1 8 ,4 0 0
1 9 .0 0 0
1 8 ,3 0 0
1 7 ,4 0 0
4
5
1 9 ,0 0 0
1 8 ,8 0 0
7
1 9 ,8 0 0
8
1 9 ,2 5 0
1 9 ,7 0 0
9
1 8 ,0 0 0
The low v a lu e o b t a i n e d f o r s e is m o m e te r 5 i n th e c a s e
o f t h e s t o p e b l a s t a r o s e b e c a u s e t h i s s e is m o m e te r was c l o s e
to t h e b l a s t and th e P wave t h e r e f o r e t r a v e r s e d a h ig h
p ro p o rtio n of fra c tu re d rock.
t o be r a t h e r s m a l l ;
The 20 l b . c h a rg e was found
i n th e c a s e o f +he 2 s h a f t b l a s t t h e
t i r s t m o tio n a t s e is m o m e te rs 3 and 5 was n o t p e r f e c t l y c l e a r
Seismometers
and t h e s e me s u re m e u ts a r e s u b j e c t t o some d o u b t.
1 t o 6 d e t e r m i le t n e p la n p o s i t i o n o f an e v e n t c l o s e to t h e
r e e f p la n e .
R em arkably c o n s i s t e n t r e s u l t s were o b ta in e d on
t h e l o c a t o r when a v a lu e o f 1 9 ,0 0 0 f t / s e c . was u sed f o r a l l
t h e s e s e is m o m e te r s , and t h i s v a lu e was c o n s e q u e n t l y a d o p te d
« a th e p wave v e l o c i t y i n th e v i c i n i t y o f th e r e e f .
S e is m o m e te rs 7 , 8 and 9 d e te r m in e th e e l e v a t i o n o f s e i s m i c
e v e n t s c l o s e to t h e r e e f p l r n e .
The
v e lo c i ty to th e se
s e is m o m e te r s d i f f e r e d by a f e w p e r c e n t from 1 9 , 0 0 0 f t / s e c . ,
so t h a t t h e f i r s t l o c a t i o n i s s l i g h t l y i n e r r o r .
l o c a t i o n can be o b ta in e d a s f o l l o w s :
A second
S in c e th e a p p ro x im a te
tim e o f o r i g i n o f t h e s e i s m i c e v e n t h a s been d e te r m in e d from
t h e f i r s t l o c a t i o n , th e t r a v e l time t o each s e is m o m e te r i s
known.
Thu d i f f e r e n c e s i n d i s t a n c e t o each s e is m o m e te r can
be o b t a i n e d more a c c u r a t e l y by m u l t i p l y i n g e a c h t r a v e l tim e
by t h e c o r r e s p o n d i n g c a l i b r a t e d v e l o c i t y .
These c o r r e c t e d
d i f f e r e n c e s i n d i s t a n c e a r e th e n a p p l i e d to t h e l o c a t o r t o
y i e l d t h e sec o n d l o c a t i o n and a b e t t e r a p p r o x im a tio n t o th e
tim e o f o r i g i n , so t h a t o t h i r d l o c a t i o n con be o b t a i n e d .
I n P r a c t i c e t h e r e i s no a d v a n ta g e i n o b t a i n i n g a t h i r d
l o c a t i o n s i n c e t h e v e l o c i t i e s o r e n o t s u f f i c i e n t l y w e l l known
and b e c a u s e t h e r e i s f r e q u e n t l y d i f f i c u l t y i n d e te r m in in g t h e
tim e o f i r n v
1 o f th e P wave a t each s e is m o m e te r .
approx­
i m a t e l y 30 p e r c e n t o f t h e f i r s t m o tio n s s t a r t i n on in d e c is iv e
raannur, w ith t h e r e s u l t t h a t i n 10 p e r c e n t o f t h e c a s e s very
little
improvement i s a t t a i n e d when making a secon d l o c a t i o n .
The l o c a t i o n o b t a i n e d i s i n e f f e c t a l e a s t s q u a r e s s o l u t i o n
to t h e fo c u s o f t h e e v e n t .
This comes ab o u t i n th e fo llo w in g
B ecause th e s y ste m i s l i n e a r , t h e l e a s t s q u a r e s s o lu tio n
way.
t o th e tim e o f o r i g i n i s th e a r i t h m e t i c a v e r a g e o f th e
p o s i t i o n s o f th e i n d i c a t o r s on th e l o c a t o r and s i n c e i t i s
/ e r y e a s y t o e s t i m a t e when t h e i n d i c a t o r s form th e b e s t
h o r iz o n ta l s t r a i g h t l i n e , th e s o lu tio n i s e f f e c t i v e l y a l e a s t
sq u ares one.
A f t e r t h e sec o n d l o c a t i o n th e c o - o r d i n a t e s o f
t h e fo c u s were found t o be a c c u r a t e to w i t h i n - 100 f e e t w.th
9 0 co n fid en ce.
For t h e m a j o r i t y o f t h e s e i s m i c e v e n t s , o n ly
t h e wi r s t l o c a t i o n was o b t a i n e d .
The se is m o m e te rs were
d i s t r i b u t e d o v e r a r e g i o n 1 1 ,0 0 0 f t . w ide, so t h a t t h i s
a c c u r a c y c o r r e s p o n d s to an o v e r a l l m e a s u rin g a c c u r a c y o f - Ijt.
S in c e th e s e is m o m e te r d i s t r i b u t i o n and t h e v e l o c i t y
d i s t r i b u t i o n i s a s y m m e tr ic a l w ith r e s p e c t to th e r e e f p l a n e ,
a n e r r o r i n th e v e l o c i t y c a l i b r a t i o n would r e s u l t i n b ia s e d
lo c a tio n s,
a
method h a s been d e v i s e d which e n a b l e s th e
v e r t i c a l p o s i t i o n ( e l e v a t i o n ) o f a s e is m ic e v e n t to be
d e te r m in e d in d e p en d e n tly o f th e v e l o c i t y c a l i b r a t i o n .
The
method i s d e s c r i b e d i n Appendix 1 , and some exam ples a r e
shown;
t h e r e i s good a g re em e n t betw een t h i s method and th e
e l e v a t i o n s d e te r m in e d by th e v e l o c i t y c a l i b r a t i o n s .
/ E n erg y
....
F o r t he s p h a r i c a l r a d i a t i o n o f sel inic
t o t a l e n u rg y r a d i a t e d i s ,
B * ro 4’
fC T ’
v ‘
It
n ergy, the
.........
(1)
. h e r e V = in a ta n t& n e o u a p c r t i c l e v e l o c i t y a t c d i s t a n c e
r from t h e fo c u s
C = a or 0
& — P wave v e l o c i t y
9 = S wave v e l o c i t y
P = d e n s i t y o f medium
A l l t h e te rm s on t h e r i g h t - h a n d s i d e o f (1) a r e known,
fhe
d e n s i t y o f q u a r t z i t e i s 167 l b s / f t 5, and r i s obtained from
th e l o c a t o r .
The a v e r a g e P wave v e l o c i t y is 19,000 f t , / s e c .
and th e b wave v e l o c i t y can be c a l c u l a t e d from
* 0 .6 4 1 a
(2 )
where v - P o i s s o n 's R a t i o
= 0 .1 5 f o r q u a r t z i t e .
A s e is m o m e te r o n ly g i v e s t h e component o f t h e p a r t i c l e
v e l o c i t y a lo n g t h e a x i s of th e seismome e r , so t h a t t h e
a n g le o f i n c i d e n c e o f t h e waves a t tho s e is m o m e te r h a s t o be
e te r m in e d from t h e l o c a t o r .
t h e 3 wave i s n o t known;
The a n g le o f p o l a r i z a t i o n o f
how ever, the en erg y i s d e te r m in e d
from v e r t i c a l and h o r i z o n t a l s e is m o m e te r s , so t h r t th e mean
v a lu e i s n o t s e r i o u s l y i n e r r o r .
An e l e c t r o n i c d e v ic e was d e s ig n e d t o p e rfo rm t h e
o p e ra tio n
V* d t where t = 1 /2 s e c .
shown i n Appendix 4 .
A c i r c u i t diagram i s
The d io d e s o p e r a t e n o n - l i n e a r l y and
b c c k - t o - b o c k so t h a t a l l odd h a rm o n ic s c a n c e l ,
t h e o u tp u t
i s th e n p r o p o r t i o n a l to t h e s q u a r e o f t h e s i g n a l .
The
s q u a r i n g i s v e ry good o v e r th e ra n g e o f sigs a l s a p p l i e d t o
— 24 —
th .
o u tp u t o f th e d e v ic e c o rre s p o n d s to the e n v e lo p e o f th e
en ergy f l u x .
E i g h t d e v i c e s were c o n s t r u c t e d and c o n n e c te d
o u t p u t s Oi th e r e p l a y deck c o r r e s p o n d in g to seism o m eter;
1 to 8 .
The s u r f a c e se is m o m e te r was n o t u sed f o r en erg y
d e t e r m i n a t i o n s s i n c e t h e a m p litu d e of v i b r a t i o n n e a r a f r e e
s u r f a c e i s g r e a t e r t h a n i n th e s o l i d ro c k f a r from a f r e e
su rfacs.
The o u t p u t s o f t h e e i g h t s q u a r i n g d e v i c e s wore
a p p l i e d to t h e re m a in in g 8 c h a n n e ls o f t h e 24-channel
o scillo g ra p h .
The whole sy ste m was c a l i b r a t e d by ap plyin g
s i g n - I s o f known a m p litu d e
t t h e s e is m o m e te r t e r m i n a l s and
m e a s u rin g t h e o u t p u t s o f e ach s q u a r i n g d e v ic e on the photo­
g ra p h ic re c o rd ,
J i g u r e 4 shows two e v e n t s o f m agnitude 1 0 4 f t . - l b s . and
x 1 0 4 f t . - l b s . t h a t o c c u r re d w i t h i n 21/2 s e c o n d s o f one
a n o th e r.
The t r a c e s marked F a r e th o s e o f t h e e n e r g y f l u x
and t h o s e marked V o r e t h e p a r t i c l e v e l o c i t y ;
th o s e i n
p a i r s a r e t h e low s e n s i t i v i t y and t h e h ig h s e n s i t i v i t y
c h a n n e l s o f £ s e is m o m e te r .
Most o f t h e e n e rg y i s c a r r i e d
i n t h e S wave.
The e n e rg y was c a r e f u l l y d e te r m in e d f o r a b o u t 50 s e is m ic
e v e n t s c o v e r in g th e f u l l m a gn itu de r a n g e .
These e v e n t s were
th e n r e g a r d e d a s s t a n d a r d s and o i l o t h e r e v e n t s were compared
w ith t h e s e t o e s t i m a t e t h e m a g n itu d e , which was t h e n e s t i m a t e d
t o th e n e a r e s t o r d e r o f m a g n itu d e .
became op; : r v n t ;
A s im p le r u l e o f thumb
t h e m agnitude was t e n tim e s g r e a t e r i f th e
d u r a t i o n o f t h e wave t r a i n was a b o ut tw ic e os lo n g .
I t was
fou nd t h a t th e e n e rg y d e te r m in e d by th e d i f f e r e n t s e is m o m e te rs
d i f f e r e d by o s much a s o f a c t o r o f 5 f o r most e v e n t s .
T his
v a r i a t i o n was a n t i c i p a t e d s i n c e i t was n o t expocced t h a t th e
r a d i a t i o n would bo s p h e r i c a l .
The mean o f t h e e i g h t v a l u e s ,
h o w ev er, gave a good q u a n t i t a t i v e e s t i n t ce o f th e e n erg y
re le a se d s e is m ic o lly .
/ M echanism. . . .
Mechanise s t u d i e s , .
T here o r e two com plem entary te c h n i q u e s which have been
u se d w ith some s u c c e s s i n s tu d y in g e a r th q u a k e mechanisms,
n am ely , F i r s t M otion A n a ly s is and S p e c t r a l A n a l y s i s .
F i r s t M otion^an o i y g i s .
This te c h n i q u e i s based on th e
t a c t t h a t t h e s e n s e o f m otio n a t a d i s t a n t p o i n t i s r e l a t e d
t o t h e m o tio n a t t h e f o c u s o f a s e i s m i c s o u r c e .
T h e o re tic a lly
i t i s p o s s i b l e to d e te r m in e th e c o m p lete i n i t i a l m o tion and
t h e r e f o r e t h e mechanism a t th e f o c u s , by d e t e r m i n i n g th e f i r s t
m o tio n a t a l a r g e number o f p o i n t s around t h e f o c u s .
The
t h e o r y of f i r s t m o tio n h a s been g iv e n a u t h o r i t a t i v e l y by
iih9P o f C and ( f i l b e r t i n
m ech an ism s.
which th e y d e a l w ith a l l p o s s i b l e
The main c o n c l u s i o n s o f t h i s th e o r y a r e g iv e n
t h e s e c t i o n im m e d ia te ly p r e c e d in g th e s e c t i o n on f i r s t
m o tio n r e s u l t s .
.h e method o f f i r s t m o tio n s i s t o d e te r m in e w h e th e r t h e
f i r s t m o tio n a t each s e is m o m e te r i s e i t h e r c o m p re ss io n o r
r a r e f a c t i o n and t h e n t o f i t t h e f i r s t m o tio n s o f a l a r g e
number o f s e is m o m e te rs t o one o f t h e f i r s t m o tio n p a t t e r n s
p ro d u c e d by d i f f e r e n t m echanism s.
Only P wave f i r s t m o tio n s
c o u ld be examined i n t h i s s t u d y , s i n c e th e S wave f i r s t m o tio n
was o b s c u r e d by th e coda o f t h e P wave.
A c e n t r a l p r o j e c t i o n i s use'* t o r e p r e s e n t th e t h r e e d i m e n s i o n a l d i s t r i b u t i o n o f s e is m o m e te rs on p a p ^ r ,
p r o j e c t i o n i s o b ta in e d a s f o l l o w s :
T his
t h e p la n e o f t h e p a p e r
( p r o j e c t i o n p la n e ) i s h o r i z o n t a l and a t u n i t d i s t a n c e above
t h e fo c u s o f t h e s e is m ic e v e n t .
The normal l i n e from th e
f o c u s to t h e p la n e i n t e r s e c t s th e p la n e a t 0 .
A s tra ig h t lin e
from t h e fo c u s t o th e s e is m o m e te r i s drawn t o i n t e r s e c t th e
p la n e i n P, t h i s l i n e makes an a n g le 0 w ith t h e normal f r i j
t h e fo c u s t o t h e p l a n e .
P i s th e p r o j e c t i o n o f th e
s e is m o m e te r and 0 i s th e p r o j e c t i o n o f t h e fo c u s on th e p l a n e .
The d i s t a n c e OP i s g iv e n by
OP = t a n 0
The p r o j e c t i o n i s b e s t s u i t e d t o an a r r a y o f seis m o m e te rs
i n one h a l f - s p a c e o n l y .
In t h e s eism o m e te r l a y o u t a t Harmony,
,0r‘lL oCiamorati'te rs l i e i n th e h a l f - s p a c e above t h e f o c i o f th e
seism ic e v e n ts .
I n th e c a s e o f t h e s e is m o m e te rs i n the: lo w e r
h a l f - s p a c e , 0 i s s l i g h t l y g r e a t e r th a n 9 0 °, i . e . , 0 ^ 90° + 6
where 6 I s s m a l l .
These seis m o m e te rs have been p l o t t e d i n th e
c e n t r a l p r o j e c t i o n a s though 0 = 90° - 6
and t h e p r o j e c t e d
p o i n t h a s b e e n marked - v e t o i n d i c a t e t h a t t t e
s e is m o m e te r
l i e s i n th e lo w e r h a l f - s p a c e .
The main r e a s o n f o r c h o o s in g t h i s p r o j e c t i o n i s t h a t a
p la n e p a s s i n g th ro u g h t h e fo c u s p r o j e c t s a s a s tr a ig h t l i n e .
The d i r e c t i o n o f th v l i n e c o r r e s p o n d s t o th e s t r i k e d i r e c t i o n
o f t h e p l a n e , and t h e d i s t a n c e o f t h e l i n e from 0 g i v e s th e
a n g le of d i p o f th e p l a n e . In th e r a d i a t i o n p a t t e r n f o r s h e a r
movements, r e g i o n s o f c o m p re ss io n and r a r e f a c t i o n a r e d i v i d e d
by two p la n e s w hich p a s s th ro u g h th e fo c u s and i n t e r s e c t a t
r ig h t a n g le s.
I f 0^ and 0^, a r e th e a n g le s o f d i p o f th e tu o
p l a n e s , th e n th e a n g l'
9 betw een th e two s t r a i g h t l i n e s which
form t h e p r o j e c t i o n s o f t h e two p l a n e s i s g iv e n by
Cos 9 = t a n 0^ t a n 0 2
(3 )
T h is r e l a t i o n s h i p i s d e r i v e d i n Appendix 2 .
Now Cos 0 < 1 ,
t h e r e f o r e a t l e a s t one o f t a n 0 1 and t a n 0 ? i s l e s s th a n o n e.
T h is i m p l i e s t h a t a t l e a s t one p r o j e c t i o n l i n e must p a s s 0 a t
a d ista n c e l e s s
th a n u n i t d i s t a n c e .
T h is c o n d i t i o n i s o f
im p o r ta n c e i n e s t a b l i s h i n g o r r e j e c t i n g t h e s h e a r mechanism
a s a mechanism f o r s e i s m i c e v e n ts i n m in e s .
The s h e a r
mechanism h a s been found t o be th e most common ty p e o f
e a r t h q u a k e mechanism .
/
S p ectral
...........
- 27 -
SUB.c t r a l a n U y m m .
T his te c h n i q u e , d a used to determine
th e e x t e n t o f r u p t u r e end l a I n I t s I n f a n c y ;
i t h a s only
been u se d s u c c e s s f u l l y m a f „ . c a s e s f o r e a r th q u a k e s
fSSSzEsnahem and J C k s o s ) I n t h e s e c a s e s th e a n a l y s i s . a s
done by means o f s u r f a c e , a v e s .
The th e o r y f o r body . a y e s
h a s been exam ined by H l r a s c . a and S t a u d e r ' " ) f o r some id e a l
g e o m e t r i c a l c o n f i g u r a t i o n s and no p r a c t i c a l s o l u t i o n s have
beun r e p o r t e d .
Thia method i s bosed on t h e f a c t t h a t a s e is m ic s o u rc e
o c c u p ie s , f i n i t e s p a c e and th e chang es a t th e s o u r c e ta k e
p l a c e i n f i n i t e tim e .
Hirasnwa and S t u u d e r ■17) have shown
t h a t " t h e f i n i t e n e s s o f th e s o u r c e a f f e c t s o n ly th e F o u r i e r
s p e c t r a o f P and S w aves, and h a s no e f f e c t e i t h e r on th e
d i s t r i b u t i o n o f c o m p r e s s i o n - r a r e f a c t i o n o f th e P wave, o r on
th e p o l a r i z a t i o n a n g le o f th e 3 wave".
In o t h e r w ords, th e
s o u r c e f i n i t e n e s s a f f e c t s t h e w ave-shape o f t h e P and 3 w aves,
whiuo th e t i r s t m o tio n p a t t e r n i s d e te rm in e d by t h e ty p e o f
mechanism ( e . g . , s h e a r o r t e n s i l e r u p t u r e ) .
In t h e c a s e o f
a u n i l a t e r a l l y p r o p a g a t i n g r e c t a n g u l a r r u p t u r e s u r f a c e , th e
e f f e c t o f t h e s o u r c e f i n i t e n o s s on th e s p e c t r a o f t h e P and
3 waves i s e x p r e s s e d by
e x p . -illj(X f Y)
3i n cX
u>X
S in a>Y
uuY
where w = a n g u l a r f r e q u e n c y o f th e F o u r i e r component
X and Y r e p r e s e n t t h e g eo m etry of th e s o u r c e i n
r e l a t i o n t o t h e s e is m o m e te r i n term s o f th e v e l o c i t y
o f p r o p a g a t i o n o f t h e r u p t u r e and th e v e l o c i t i e s o f
t h e P and 3 waves.
The main f e a t u r e i s t h a t t h e r e a r e p a r t i c u l a r f r e q u e n c i e s
w = T
’ * = Y
Gt *h ich th e s p e c t r a have z e r o a m p litu d e
and a p h a se change by n r a d i a n s , where m and n a r e i n t e g e r s .
/ The method . . . .
- 28 Tho method o f e p e o t r o l a n o l y a l , t h e r e f o r e re d u c e s t o
d e t e n t i n i n g th e F o u r i e r t r s n s f o r o o f th e P end s eoves end
e x e n i n i n g t h e spuoti-uo f o r minima i n o m p lltu d e end c h an g e s
°f ” ^
Ph08e - M c h w m
X and V m
O f b l e X and y t o be o a l c u l n t e d .
t u r n g iv e th e d im e n s io n s o f t h e r e c t a n g u l a r r u p t u r e
and i t s v e l o c i t y of p r o p a g a t i o n i n r e l a t i o n t o th e s e is m o m e te r.
V h ve to bo , e t e r n i s e d a t a number o f s e is m o m e te rs i n
o r d e r t o d e te r m in e t h e a b s o l u t e d lm e n s tn s o f t h e source.
ad d itio n ,
In
t h e f a u l t p la n e h a s to be d e te rm in e d by means o f
f i r s t m o tio n s .
A t r a n s i e n t s p e c t r o g r a p h w ith th e t r a d e name " r t s s i l y z e r "
Wes used t o d e te r m in e th e a m p l i t u d e component o f th e F o u r i e r
tr a n s f o r m o f t h e w aves;
t h e s p e c t r o g r a p h d o es n o t g iv e t h e
P h a se component o f th e F o u r i e r t r a n s f o r m .
two modes o f o p e r a t i o n ,
T h is d e v ic e h a s
( a ) i t p ro d u c e s a t h r e e - d i m e n s i o n a l
g ra p h o r " w is s i l g r a m " i n which tim e l a th e a b s c i s s a , fr e q u e n c y
t h e o r d i n a t e and th e i n t e n s i t y o f t h e g rap h r e p r e s e n t s
a m p litu d e ,
(b ) i t p ro d u c e s a " s e c t i o n ” o r g ra p h o f a m p litu d e
v e r s u s f r e q u e n c y a t any p a r t i c u l a r i n s t a n t i n t i m e .
The
" M i s s i l y z e r " and some s p e c t r a o f s t a n d a r d waves a r e shown
i n A ppendix 3 .
Only P waves con be a n a ly z e d i n t ’ i s s tu d y
s i n c e t h e cod a o f th e P waves i n t e r f e r e w ith t h e S waves.
' he grfe 1 v i r t u e o f t h i s method i s t h a t t h e minima, o r
z e r o s , i n a m p litu d e o c c u r r e p e a t e d l y and i n th e c a s e o f an
i d e a l s o u r c e , a t r e g u l a r i n t e r v a l s o f fr e q u e n c y A a , so t h a t
a number o f v a l u e s Aw c a n be o b t a i n e d .
Note t h a t i n th e
c a s e o f the i d e a l r e c t a n g u l a r r u p t u r e t h e r e a r e two f a m i l i e s
oi minima y i e l d i n g A ix and Awy, which have to be d i s t i n g u i s h e d .
A
f u r t h e r g r e a t v i r t u e o f t h i s method i s t h a t t h e p o s i t i o n s o f
t h e z e r o s o r minima i n th e a m p litu d e s p e c tru m o f a P wave a r e
u n a f f e c t e d by t h e medium th r o u g h which th e P wave h a s p a s s e d
o r by th e r e c o r d i n g e q u ip m e n t, p ro v id e d t h a t harm onic
d i s t o r t i o n does not o ccu r.
L in arr a tte n u a tio n , d isp e rsio n
/ end . . . .
and s c a t t e r i n g o f t h e wove, can o n ly change r e l a t i v e
a m p l i t u d e s and p h a se s o f t h e s p e c t r a l com ponents, anu can
have n , e f f e c t on components t h a t a r e m is s in g from t h e s p e c tru m .
^ r i o u s d i f f i c u l t i e s a r i s e i n t h i s method w ith d e v i a t i o n s
from th e i d e a l r e c t a n g u l a r u n i l a t e r a l m p t u r
c o n o t.n t v e lo c ity .
I f th e v e l o c i t y o f p ro ;
p r o p a g a tin g a t
c tio n v a rie s
s l i g h t l y , t h e F o u r i e r sp e c tru m becomes c o n tin u o u s w ith
i n d i s t i n c t minima i n th e p l a c e s o f th e z e r o s ,
i f an a b r u p t
change o c c u r s i n t h e v e l o c i t y , th e s p e c tru m i s c o m p le te ly
a lte re d .
I f th e ru p tu re has f i n i t e th ic k n e s s , e . g . , a
p r o p a g a t i n g f a i l u r e o f a volume o f r o c k , a t h i r d f a m ily o f
minima i s i n t r o d u c e d i n t o t h e s p e c tr u m .
H irrsa w a and
£ i 2 u d e r (1Z/ have shown t h a t when t h e i d e a l r u p t u r e p r o p a g a te s
b i l a t e r a l l y , z e r o s no l o n g e r a p p o a r i n th e s p e c tru m e x c e p t i n
th e c a s e o f p e r f e c t l y s y m m e tric a l p r o p a g a t i o n .
C o n se q u e n tly
s p e c t r a l a n a l y s i s can be o f v a lu e o n ly when the geom etry o f
th e seism ic so u rc e is v ery sim p le .
/ GEVLCGIChL ENVIRUm.,.NT
- 30 -
GEOLOGICAL
environment
s e i s r . i c netw ork c o v e r s thu e n t i r e Harmony Gold Mine
and P o r t i o n o f t h e n e ig h b o u r in g V i r g i n i a Gold Mine.
At
t h e s e w in e s , t h e W itw a te rs rc n d system r o c k s , Upper D i v i s i o n ,
a s h a llo w b a s i n d i p p i n g a t a p p ro x im a te ly 7° to th e W est,
ih c B ^ s a l R ee f i s mined and i s a p p r o x im a te ly 5000 f e e t below
surface.
F i g u r e s 7 and 8 show, r o s p e c t l v e l y y a g e n e r a l i z e d
v e r t i c a l s e c t i o n from s u r f a c e t o r e e f , and a s e c t i o n g i v i n g
g r e a t e r d e t a i l i n th e v i c i n i t y o f th e r e e f .
T here a r e t h r e e
f e a t u r e s t o which f r e q u e n t r e f e r e n c e i s n u d e ;
th :y a re the
Harmony S i l l , t h e Upper S hale M arker and th e Khaki S h a le .
The H rmony S i l l i s i n t r u s i v e d o l e r i t e i n t e r s p e r s e d w ith
q u a rtz v e in s.
to bo weak.
I t s c o n t a c t s w ith th e q u n r t z i t e a r t l i a b l e
The Upper Shale M arker i r a band o* wetk r o c k .
The Khaki S h a le v a r i e s w id e ly th r o u g h o u t th e m ine.
F ig u r e 9 shows th e d i s t r i b u t i o n i n p l a n , t h e a r e a w ith
th e c o a r s e h a t c h i n g r e p r e s e n t s t h e Khaki S h a le .
The s h a l e
i s so m etim es t h r e e f e e t t h i c k and v a r i e s i n i t s s e p a r a t i o n
from th e B asa l r e e f .
iVhere i t has been e ro d e d away, a
d e f i n i t e b e d d in g p la n e e x i s t s .
The s t o p i n g w id th i s d i c t a t e d
by t h e c o n d i t i o n s i n t h r h a n g in g w a ll.
When the Khaki S h a le
i s t h r e e o r more f e e t from t h e r e e f , i t i s p o s s i b l e to
m a i n t a i n th e n to p in g w id th a t a b o u t 42 i n c h e s ;
however, when
t h e s h a l e i s c l o s e r , t h e h a n g in g w a ll i s more d i f f i c u l t t o
c o n t r o l so t h a t t h e s t o p i n g w id th becomes a p p r o x im a te ly
60 i n c h e s .
/ FIGURES 7 and 0
FIGURE 7
\ g en er a lised oeclogical s e c t io n on
HARMONY PROM STIRPACE TO THE REEF
PLANE.
FIGURE 8
1-ART OF A iENERALISED GEOLOGICAL
SECTION SHOWING DETAILS NEAR THE
REEF PLANE.
FIGURE 9
PLAN SHOWING THE DISTRIBUTION OF THE
KHAKI SHALE AND THE INTERSECTION OF THE
SILL IN VIRGINIA WITH THE REEF.
THE KHAKI SHALE IS REPRESENTED BY THE
COARSE HATCHING.
11= ° f t e r ' 0CC"
ln
. t o p e s , i n v h i c h caa(tj a u
t h e ro o k up t o th e to p c o n t a c t o f th e Khaki S hale f a l l s down.
The e x p o se d ro c k above t h e Khaki Shale a l e a y s a p p e a r s sound
and h a s . i d o l , sp ac e d f r a c t u r e p l a n e s ,
n o c k b u r s ts o c c u r
i n f r e q u e n t l y and u s u a l l y r e s u l t i n damage . r i c h t a k e s a fee
day s t o c l e a r .
The ro ck i n t h e f o o t . a l l i s q u a r t z i t e f o r a g r e a t d e p th .
In th e V i r g i n i a a r e a , f i g u r e 9, t h e r e i s a s h o l l o , d i p p i n g
s i l l which in - s r s e c t s th e r e e f .
This s i l l a p p e a r s t o be a
to n g u e from a l a r g e r and d e e p e r s i l l ,
i s not w e ll known.
th e p o s i t i o n o f which
The o n ly f o o t w a l l damage t h a t I s e v e r
observed occu rs a t t h i s s i l l .
When ruining t a k e s plc.ee i n s t o p e s w ith a aiJb'
un,
t h e h a n g i n g . a l l i s r e l a t i v e l y easy t o o o n t r , 1 and r o c k f a l l s
a re in fre q u e n t.
On th e o t h e r h a n d , i n r e m n s - a , i.a n g in g w aU
c o n t r o l i s d i f f i c u l t and r o c k f a l l s and rockt,
-,s o c c u r
f r e q u e n tly in s p i t e of in cru cso d s u p p o rt.
/ DISCUSSION nND RESULTS.
uitilUtiSlON AND RESULTG
M agnitude o f ^ y i e mi c
o t i s n i c netw ork commenced c o n tin u o u s r e c o r d i n g on
t h a nth A u g u st. 1964.
In th s f i r s t y ear of re c o rd in g ,
3100 s e i s a l c e v e n t s . e r e l o c a t e d .
These ra n g e d I n n a g n ltu d ,
from 10
More t h a n h a l f o f th e
f t . - l b s . t o 108 f t . - l b s .
e v e n t s o f m ag nitud e 103 f t . - l b e . co uld be l o c a t e d , « h l l e a
h ig h p r o p o r t i o n o f m ag nitud e 104 f t . - l b e . .n d - 1 1 o f
g n it
i 10
1t . - r b e . and g r e a t e r were l o c a t e d .
t h i s y e a r , o n ly on t h r e e d a y s . e r e no r e c o r d s o b t a i n e d , and
on t h e s e d a y s no tre m o rs o r
th o u g h t, th e r e f o r e , th a t
an
damage . e r e r e p o r t e d .
I t Is
e v e n t s o f l o ' f t . - l b s . and
more have been r e c o r d e d and l o c a t e d .
The Table b e lo v sho es
t n e number o f e v e n t s o f d l f . e r e n t s i z e s l o c a t e d d u r i n g th e
f i r s t y ear o i re c o rd in g .
M agnitude f t . - l b s .
Number o f L v e n ts
105
104
105
l 06
107
108
1768
897
29?
119
11
2
F i g u r e 10 shows t h e t o t a l e n e rg y r a d i a t e d by d i f f e r e n t
s i z e d e v e n t s d u r i n g th e y e a r .
The t o t a l f o r e v e n ts o f
m ag n itu d e 1 0 ^ f t . - l b s . i s somewhat h i g h e r t h a n shown i n
F i g u r e 10 , s i n c e o n ly ab o u t h a l f o f t h e s e e v e n ts were
lo c a te d .
/ FIGURE 10
D uring
Magnitude
FIGURE l u
of
events
f t - lbs
THE DISTRIBUTION OF THE TOTAL ENERGY
RADIATED BY SEISMIC EVENTS OF DIFFERENT
SIZES OVER A PERIOD OF ONE YEAR.
- u m a lj.O n
QT
Se,amlC ”TOntS ™ r e l y o c c u r re d i n . c r i n g e a u rrc u n d e d
by e x t e n s i v e a o i i d r e e f , b u t o c c u r re d moat f r e q u e n t l y above
a c t i v e f a c e s i n rem nant a r e a s .
When an i s l a n d o r p e n i n s u l a
a b u tm e n t r e a c h e d a w id th o f 500 f e e t , t h e r e . e r e d e f i n i t e
o i g n s o f an i n c r e a s e i n s e i s m i c a c t i v i t y , and th e s e i s m i c i t y
r a p i d l y a s th e ab u tm en t became n a r r o w e r .
7’h e se
e f f e c t s can be s e e n i n F i g u r e s 11 t o 1 5 , each o f which shows
t h e e v e n t s o c c u r r i n g i n a s ix -w e e k p e r i o d .
The f i g u r e s ,
drawn on a g r i d o f 2000 f e e t , a r e a r r a n g e d s e q u e n t i a l l y , and
show two f a c e p o s i t i o n s , r e p r e s e n t i n g th e b e g in n in g and end
o f a th r e e - m o n th p e r i o d .
The s e is m ic e v e n ts p l o t t e d i n e ach
f i g u r e o c c u r r e d e i t h e r d u r in g th e f i r s t o r sec. nd h a l f o f
each p e r io d .
Only t h e e v e n t s t h a t o c c u r r e d d u r i n g t h e f i r s t
l i v e months o f t h e y e a r a r e shown, s i n c e t h e p a t t e r n f o r th e
r e m a in in g p e r t o f th e y e a r was v e ry s i m i l a r .
/ SCALEI FIGURES 11-15
SCALE SHOWING MAGNITUDES OF THE SEISMIC
EVENTS PLOTTED IN FIGURES 11 TU 15
O ,^ 8
FIOURE 11
PL/N POSITION OF SEISMIC EVENTS
1 1 th Anous'” TO 5 0 th SEPTEMBER, 1964
^
0
■i
FIGURE
FLAN FOGI .'ION OF SEISMIC EVENTS
1st OCTOBER +o 15th NOVEMBER, 1964
1
FIGURE 13
2
PLAN POSITION OF SEISMIC EVENTS
1 6 th NOVEMBER to 3 1 s t DECEMBER, 1964
3
FIGURE 14
P lan p o s it i o n of s e i s m i c events
l e t JANUARY tc 1 4 th FEBRUARY, 1965
FIGURE IS
FLAN POSITION OF SEISMIC EVENTS
15th FEBRUARY to 31f* MARCH, 196*
- 44 A g r e a t number o f e v e n ts hove o c c u rre d I n th e remnant
1" E3.
i n t h e r e g i o n 7 2 . even though th e ground . a s v e ry
i r r e g u l a r , due to numerous s m a l l f a u l t s , none o f . n i e h had
° t h r ° ‘ 0 t m° r e t h M 10
v e ry f e . e v e n ts o c c u r r e d .
hy com paring f i g u r e s 11 t o 15, t h e change I n s e i s m i c i t y
ns
th e re m n a n t I n D3 i s mined a . a y c a n be s e e n .
T h is
s h o u ld be compared . 1 t h D l, . h e r e th e e v e n ts became more
f r e q u e n t and I n c r e a s e d I n m agn itu de a s m ining p r o g r e s s e d .
The e v e n t s t h a t o c c u r r e d I n D2 and o t h e r . o r k e d - o u t a r e a s
. e r e p r o b a b ly a s s o c i a t e d . I t h r e c o m p r e a s l c n .
s t o n e . a l l s and
o t h e r form s o f . a e t e f i l l i n g . e r e sometimes u s e d , and t h e s e
co u ld be e x p e c te d t o u n d e rg o movement .h e n th e lo a d on them
becemti h i g h .
Dykes p la y e d a m a jo r r o l e i n p ro d u c in g th e l a r g e s t
e v e n ts.
A l l t h e e v e n t s o f m agnitude 107 f t . - l b s . and 108
f t . - l b s - wore l o c a t e d w i t h i n 200 f e e t o f a dyke;
l o c a t e d r i g h t on a dyke
most were
Twenty f i v e p e r c e n t o f t h e e v e n ts
of m a g n itu d e 106 f t . - l b s . were l o c a t e d w i t h i n 200 f e e t o f a
dyke and t e n p e r c e n t o f th e t o t a l w ere, w i t h i n t h e l i m i t s
o f e r r o r , on a d y k e .
A number o f s m a ll dykes have n o t been
c h a r t e d , so t h a t t h i s a s s o c i a t i o n co u ld be even c l o s e r .
The dyke i n B4, f i g u r e 11, was p a r t i a l l y mined c u t i n 1962,
and was s t i l l th e s o u r c e o f some s e is m ic e v e n ts i n 1964.
On comparing Figure 9 with F i g u r e s 11 to 15, t h e r e i s
no obvious d iffe r e n c e in seism ic a c t iv it y between th e
r e g i o n s where the Khaki Shale i s present and where i t i s
a b se n t.
S l g v a t l o n o f S e la m lr E v e n ts
The v e r t i c a l d i s t r i b u t i o n o f a r e p r e s e n t a t i v e sam ple o f
e v e n t s i , shown i n F ig u r e 16.
A l l t h e e v e n t s used f o r d raw in g
t h i s h i s t o g r a m wore l o c a t e d tw i c e , u s i n g t h e c o r r e c t e d
v e lo c itie s.
There o r e two d i s t i n c t s e t s o f e v e n ts ,
one group
betw een 2 ,4 0 0 and 2 ,8 0 0 f e e t above t h e r e e f p la n e ana th e
o t h e r b etw een 0 and 300 f e e t above th e r e e f p l a n e .
T h ere i s
a m a jo r g e o l o g i c a l d i s c o n t i n u l t j a s s o c i a t e d w i t h each o f
th e „
g ro u p s,
The Harmony F i l l l i e s i n t h e u p p e r g ro u p , and
t h e lo w e r g ro u p l i e betw een th e r e e f and t h e Upper S h ale
M ark er.
( F i g u r e s 7 and 8 ) .
The v e r t i c a l d i s t r i b u t i o n o f e v e n t s i n F ig u r e 16 d o es
n o t depend on th e m agn itu de o f t h e s e is m ic e v e n t s .
The s i z e s
o f t h e e v e n t s n e a r t h e Harmony S i l l ranged from lO*5 f t . - l b s .
t o 106 f t . - l b s .
The Harmony S i l l i s n o t p a r a l l e l w ith t h e r e e f ;
i n some
P l a c e s i t i s 2 ,8 0 0 f e e t above th e r e e f and a t t h e V e n t i l a t i o n
S h a f t o n ly 1 ,8 0 0 f e e t , c o n s e q u e n tly th e r e i s a s p r e a d in th e
e l e v a t i o n o f t h e e v e n ts i n th e h is to g r a m .
The e v e n ts a t t h e
S i l l d id n o t o c c u r above t h e e n t i r e m ining e x c a v a t i o n ;
th e y
w e re c o n f in e d to a sm a ll s t r i p - l i k e r e g i o n w hich i s p a r a l l e l
w ith th e I r o n C u r t a i n Dyke.
/ FIGURE 16
2700
2400
feet.
2100
;
1800 :
Height
above
Reef
1500 ;
1200
;
9oo;
600
300
0
0
20
40
60
Number of se ism ic events
L’RE 16
THK VERTICAL DISTRIBUTION 0? THE
seism ic
events relative to the
REEF PLANS.
'
i
Shaft
s :
f
/
FIOURB 1 7
PLAN ON A ORID OF 2000 FEET SHOWTNO THE
POSITIONS OF THE SEISMIC EVENTS THAT
OCCURRED NEAR THE HARMONY SILL OVER THE
PERIOD 11 AUGUST, 1964 TO 11 JANUARY, 1965.
■
— 48 F i g u r e 17 shows t h e p l a n d i s t r i b u t i o n o f t h e s e e v e n t s .
The p o e s i W l i t y t h a t t h e s e e v e n t s m ight l i e on th e i n t e r s e c t i o n c f t h e I r o n C u r t a i n Dyk- and th e Harmony S i l l was
in v e stig a te d .
The p o s i t i o n o f t h e dyke a t t h e e l e v a t i o n o f
t h e s i l l i s n o t known;
how ever, tho dyke d ip s a t 65° a t th e
r e e f p l a n e , and a ssu m in g t h i s d i p to rem ain unchanged, t h e
i n t e r s e c t i o n o f t h e dyke and s i l l would bees * own i n F ig u r e 17.
No c o n c l u s i o n s can be drawn frcm t h i s r e - u l t .
th e
The s t r i p on
ip p e r g ru u p o f e v e n t s l i e c an be e x t r a p o l a t e d t o
p a s s th r o u g h t h e V e n t i l a t i o n S h a f t .
M easurem ents o f v e r t i c a l
movements i n t h e V e n t i l a t i o n S h a f t r e p o r t e d by 0 r t l e p p (20)
showed c o n s i d e r a b l e d i f f e r e n t i a l movement i n th e v i c i n i t y o f
t h e Harmony S i l l .
T h is movement was accom panied by c r a c k s
i n t h e s h a f t l i n i n g and by th e in flo w o f w a te r , and i s
exam ined i n g r e a t e r d e t a i l i n t h e f o ll o w i n g d i s c u s s i o n .
The Upoer S h a le M arker i s a t an a v e ra g e h e i g h t o f
300 f e e t above th e r e e f p la n e and i t t h e r e f o r e a p p e a r s t h a t
t h i s weak band o f ro ck form s a boundary .'or th e lo w e r g ro u p
o f seism ic e v e n ts .
d istrib u tio n ;
There i s a d i s t u r b i n g f e a t u r e ab ou t t h i s
n o t i c e t h a t i f t h i s d i s t r i b u t i o n were s h i f t e d
downwards by 100 f e e t ( th e 90* c o n f id e n c e l i m i t ) , th e peak
i n t h e d i s t r i b u t i o n would c o i n c i d e w ith th e r e e f p la n e .
To
r e s o l v e t h i s d o u b t, th e a l t e r n a t i v e method o f d e te r m in in g
th e e l e v a t i o n d e s c r i b e d i n Appendix 1, was employed to
d e t e r m i n e th e e l e v a t i o n s o f t h e s e is m ic e v e n t s .
;,s can be
s e e n i n A ppendix 1, t h i s method a g r e e s w ith th e e l e v a t i o n s
o b t a i n e d by u s i n g th e v e l o c i t y c a l i b r a t i o n s , end i t must be
a c c e p t e d t h a t t h i s a s y m m e tr ic a l d i s t r i b u t i o n i s r e a l .
It
i s n o t u n r e a s o n a b l e t h a t an a s y m m e tr ic a l d i s t r i b u t i o n s h o u ld
a r i s e , s i n c e t h e g e o l o g i c a l e n v iron m ent i s a s y m m e tr ic a l and
t h e h a n g in g w o ll te n d s t o be w eaker t h a n th e f o o t w a l l .
/ S e is m ic . . . .
bt ia m ic e v a n t s muat W ==au=l a t ,d , 1 t h t h „ v i o l e n t
° t l U r “ ° f r0 C k ' thUa °
° f t h e d i s t r i b u t i o n o f th e
s e i s a i c e v e n t s v o u ld r e v e a l t h e f r a c t u r e z o n e . The o n ly mode
o f l a r g e s c a l e f r a c t u r i n g which may no t be d e t e c t e d
a eisra ic ally is s t r a t a s e p a ra tio n .
S in c e t h e bonding betw een
w e ll d e f i n e d s t r a t a may be weak, s t r a t a s e p a r a t i o n can o c c u r
a t low t e n s i l e s t r e s s l e v e l s , r e s u l t i n g i n a low s e is m ic
y ie ld .
T h e r e f o r e , th e ty p e o f f r a c t u r e dome which i s made
up o f s t r a t a s e p a r a t e d i n t o huge beams may n o t be d e t e c t e d ;
h ow ever, should t h e s e beams f a i l , enormous amounts o f s e i s m i c
e v e rg y would h r r e l e a s e d .
The ty p e j f f r a c t u r e done e n v is a g e d
by D e n k h o u s lt; would r e s u l t i n l a r g e amounts o f s e is m ic en erg y
b e in g r e l e a s e d , s i n c e t h e ro ck i s r e q u i r e d t o f a i l a t h ig h
s h e a r wind t e n s i l e s t r e s s l e v e l s .
ih e d i s t r i b u t i o n o f s e is m ic e v e n ts shown i n f i g u r e 16
i n d i c a t e s t h a t t h e f r a c t u r e zone i s c o n f in e d to a narrow
r e g i o n 300 f e e t h ig h , betw een t h e e x c a v a t i o n and t h e Upper
S h a le M a rk e r.
T h is zone e x te n d s h o r i z o n t a l l y w ith th e f a c e s ,
as th e se advance.
S ill.
F r a c t u r e may, how ever, o c c u r a t the Harmony
A lth o u g h i t i s n o t c e r t a i n t h a t s t r a t a s e p a r a t i o n does
n o t o c c u r betw een th e Upper S h a le Marker and th e Harmony B ' l l ,
i t i s m ost u n l i k e l y t h a t v e r t i c a l f r a c t u r i n g o c c u r s h e r e .
S i n c e t h e s e i s m i c o b s e r v a t i o n s a r e n u t i n agreem ent w ith
th e a c c e p t e d t h e o r i e s on t h e s t a t e
f th e ro c k m ass, t h e o n ly
e v id e n c e t h a t h a s e v e r been used to v e r i f y dome th e o r y i n a
deep mine i a re -e x a m in e d h e r e .
T h is i n f o r m a t i o n was k in d l y
made a v a i l a b l e by Rand M inus, L im ite d , and c o n s i s t s o f
v e r t i c a l s t r a i n m easurem ents made i n th e V e n t i l a t i o n S h a f t
a t Harmony.
I t must be em phasized t h a t t h e s e m easurem ents
wurw o r i g i n a l l y r e p o r t e d by B arcza and von W l l l l c h ^
who
made no a t t e m p t t o i n t e r p r e t them i n term s o f dome t h e o r y ;
h ow ever, i n a s u b s e q u e n t p a p e r by JDonkhnus . H i l l and Roux^
th e y w ere r e g a r d e d a s c o n c l u s i v e e v id e n c e o f th e f r a c t u r e
dome.
/ S tra in . . . .
J'le a B u ru n iH n to
V - n t i l c t i o n S h a f t a t th a harmony Mine I s un iqu e I n
S ou th n f r i c n I n t h a t no p i l l a r was l e f t f o r th e s u p p o r t o f
the S h a ft.
M ining o p e r a t i o n s commenced a t th e f o o t o f th e
s h a f t a n d e x te n d e d a lm o s t s y m m e tric a lly ab o u t I t f o r th e
f i r s t 5 y e a r s o f th e l i f e o f th e n i n e .
I t was a n t i c i p a t e d
t h a t movements i n t h e s h a f t would y i e l d some in f o r m a t io n on
th e b e h av io u r of th e s t r a t a .
To measure t h e s e movements,
40 pegs 3 f e e t l o n g verb i n s t a l l e d i n a v e r t i c a l row a t t h e
a i d e o f t h e s h a f t , and m easurem ents of t h e d l s t a n e s betw een
t h e pegs were ma.de a t r e g u l a r i n t e r v a l s .
F ig u r e 18 i s a
v e r t i c a l s e c t i o n th ro u g h t h e V s n ' f l a t i o n S h a f t showing th e
p o s i t i o n o f th e pegs i n r e l a t i o n to the g e o l o g i c a l s t r u c t u r e .
/ FIGURE 18
- 51 -
4*7
ML
V V V
V v v j
V V V
V V V
V V V
& V V V
V
v
C om pact ne#t omyg#Bi<H«ni
(avo with few omygaaio^Qi
bonds
V I
V
V v
V
V v.
VV V
V V
.1
Harmony *u
k
pebble c e n g te rp r o le s
occ u r o c c e i'l
wo
- • D pebble longiom eroie
wueritm
B eso t reef eeeovol-on
FIGURE 18
VERTICAL SECTION THROUGH THE
VENTILATION SHAFT SHOWING THE
POSITIONS OF THE PEGS IN RELATION
"0 THE GEOLOGICAL STRUCTURE.
A
- 52 -
lln „ d
° 3 n C re te -
with
o 9 -ln c h l . y . r o f u n r e ln f o r o e d
« - " t = l r , d o a lci™ c h lo rid e ,
c o h s o a u e n t l y S e v e re s h r i n k ^ , o c c u r re d end th e c o n c r e t e was
m<,ChmUCSl S t r t " « t h -
V~° 1,01,11
“
" aS f ° Und t h ^
" d e t a i l e d r e c o rd o f th e
" tc k e ^
" . t e r in flo w b e c c e
n c t l c e n b ! . a t a u c c e a e l v e l y h i g h e r l e v e l s a s m ining p r o g r e s s e d .
" o b s e r v a t i o n i s t o bo e x p e c te d b e c a u s e , even i n th e c a s e
o f a c o n t i n u o u s e l a s t i c m odel, e l a s t i c r e l a x a t i o n would
s t r e t c h t h e s h a f t a t p r o g r e s s i v e l y h i g h e r l e v e l s a s th e
e x c a v a t i o n e n l a r g e d , and s o a llo w f i s s u r e s t o open and c a u s e
s h r i n k a g e c r a c k s i n t h e l i n i n g t o become o b v io u s .
I t i s assum ed t h a t t h e v e r t i c a l component o f t h e v i r g i n
s t r e o S a t any p o in t i s e q u a l to th e w eigh t o f t h e super­
in c u m b e n t ro c k a t t h a t p o i n t .
B efo re s t r a t a s e p a r a t i o n o r
h o r i z o n t a l f r a c t u r i n g can o c c u r , th e v e r t i c a l v i r g i n s t r e s s
mUtit U® reci07ed from t h e r o c k and a l a r g e v e r t i c a l s t r a i n
must o c c u r by e l a s t i c r e l a x a t i o n .
The modulus f o r r e la x a tio n
i n the v e r t i c a l d i r e c t i o n i s a p p ro x im a te ly e q u a l to the Young's
m o du lus.
S in c e th e t e n s i l e s t r e n g t h i n t h e v e r t i c a l d ir e c tio n
i s assumed t o be z e r o th e c r i t e r i o n f o r s t r a t a s e p a r a t i o n o r
h o riz o n ta l fra c tu rin g is
V e rtic a l S tra in >
t i c - 1 V irg in ot r o s s
Y oung's Modulus
O r t l e p p and N i c o l l 1 ] 1 '
made m easurem ents o f th e move­
m ents i n t h e q u a r t z i t e below t h e e x c a v a t i o n a t th e Harmony
Mine.
They found t h a t t h e i r m easurem ents a g r e e d r e a s o n a b l y
w e ll w ith t h e movements p r e d i c t e d by e l a s t i c
th e o r y , when a
v a lu e o f a p p r o x i m a t e l y 10 x 10A p . s . i . was used f o r th e
Y oung's M odulus.
T h is v a lu e w i l l be a d o p ted f o r th e Young's
Modulus i n th e h a n g in g w a il .
A t o p i c a l v a lu e f o r t h e d e n s i t y
o f q u a r t z J t e i s 170 l b s / f t . 3 .
/ FIGUR3 19
THb VARIATION OF STRAIN WITH TIME, AT
DIFFERENT LEVELS IN THE VENTILATION
SHAFT. THE WOKEN LINES REPRESENT THE
ELASTIC STRAIN DUE TO RELAXATION.
* 7
“ 8 'JU S t r a l " 0 t T C rl° “ °
i n th e
l" ti
C gElnSt
^
th o m t i o r o a t r a l n due t0
e l c i s t i e r e U , a t l o „ t a 3hown l e t h e d o t U d ^
^
o p e r a t i o n s =oM e „ c e d I n 3,.pt e n b e r,
' ' C’e U la r l n t e r V a l a u n S U W -
nnd m s n n u rs m n te s u r e
1959.
No meanursfjonta
k 0 r6 Bndi’ Cg“ l n U , l t i l 1962 - - * - h i c h s t a g e a n u n b tr o f pegs
h a ' s u f f e r e d d n m g e . 0r t ^ < 2 0 ) ahowed
by 1 % )
r o c o n p r e s s i o n had o c c u r re d a n d th e s h a f t had a lm o s t r e g a in e d
i t s ^ rig in c l le n g th .
Pege 36 t 0 24 =
The T e r t l c = l s t r a i n between th ese pegs
. c s so g r e a t t h a t bed s e p a r a t i o n and f r a c t u r e must have
occurred in t h i s re g io n .
Most o f th e s e is m ic e v e n t s a l s o
occurred h e re .
Pegs 24 t o 2 3 :
The m x im u n s t r a i n was 40 p e r c e n t h i g h e r
th a n th e m a i i n u , r e l a x a t i o n s t r a i n .
A l a r g e c r a c k was observed
i n t h e s h a f t l i n i n g between t h e s e pegs a t a p o i n t c o rre s p o n d in g
t o t h e c o n t a c t b etw een th e K im berley S c r i e s and t h e E ls burg
S c rie s,
t h i s i n d i c a t e s t h a t s t r a t a s e p a r a t i o n p ro b a b ly
occurred a t t h i s c o n ta c t.
Pegs 23 t o 22 .
The s t r a i n was a t a l l tim e s l e s s th a n the
r e l a x a t i o n s t r a i n , t h e r e f o r e no s t r a t a s e p a r a t i o n o c c u r re d here
Pegs 22 t o 21.
th a n t:.
The maximum s t r a i n was 30 p e r c e n t more
re la x a tio n s tra in .
A l a r g e q u a n t i t y o f w a te r was
o b s e r v e d to flow i n t o the s h a f t n e a r peg 21;
how ever, th e
s h a f t l i n i n g was i n good c o n d i t i o n and had o nly a few s m a ll
crocks.
S tra ta sep a ra tio n
P«gs 21 t o 2 0 .
a t one p o i n t o n ly r n
le ss .
iey have o c c u r re d betw een t h e s e peg s.
The s t r a i n exceeded th e r e l a x a t i o n s t r a i n
r t h e most p o r t i t was c o n s i d e r a b l y
Thu s h a f t l i n i n g was i n e x c e l l e n t c o n d i t i o n and no
w a te r was o b s e rv e d t o flow i n t o th e s h a f t .
The ro c k was
p r o b a b ly u n f r a c t u r e d i n t h i s r e g i o n .
Pegs 20 t o 19 .
The s t i o i n was 15 p e r c e n t h i g h e r th a n
t h a t f o r r e l a x a t i o n and c l a r g e q u a n t i t y o f w ater was o e se rv e d
to n o w i n t o the s h o r t ,
rh e g e o l o g i c a l r e c o r i o f th e s h a f t
showed no Obvious d i s c o n t i n u i t y h e r e ,
however, c b o re h o le
d r i l l e d o n ly 300 f e e t away from th e s h a f t shows,. . v ery narrow
in tru siv e s i l l a t th is le v e l.
The s t r a t a may have s e p a r a t e d
o t t h i s d i s c o n t i n u i t y , b u t t h e s e p a r a t i o n would have been
l e a s t h a n 1 /4 i n c h .
r e g s 19 t o 1 7 .
The s t r a i n h e re was l e s s th a n t h a t f o r
r e l a x a t i o n and t h e s h a f t l i n i n g was o b serv ed t o be i n goo.
c o n d i t i o n , t h e r e f o r e no bed s e p a r a t i o n o c c u r re d h , r e .
Pegs 17 t o 16.
The maxi,,urn s t r a i n was f o u r tim e s t h a t
due t o e l a s t i c r e l a x a t i o n .
There was a v ery l a r g e cruel, i n
th e s h a f t a t a p o i n t c o r r e s p o n d in g t o t h e up p e r c o n t a c t o f
t h e Harmony S i l l .
a t th is S il l.
The s m a l l g ro up o f s e is m ic e v e n t s o c c u rre d
O t r a - a s e p a r a t i o n must have o c c u r re d h e r e .
Pegs 16 t o S .
The s t r a i n was a t a l l t l r e o l e s s th a n
the r e l a x a t i o n s t r a i n , which i n d i c a t e s t h a t t'-.is ro ck was
p r o b a b ly s o l i d .
lo g s 8 to s u rfa c u .
s t r a i n wan s m a l l ;
E r r l i e r than S eptem ber, 1956, t h e
a f t e r Sep tem ber, 1958, a l t e r n a t i n g r e g io n s
o f h ig h c o m p re s s io n and t e n s i o n were o b s e r v e d .
Such a
s i t u a t i o n i s p h y s i c a l l y most im pro b ab le and t h i s a p p a r e n t l y
anom alous b e h a v io u r was p r o b a b ly due to damage to some p e g s.
I t i s assum ed t h a t no s t r a t a s e p a r a t i o n o c c u r s above peg 16.
The r e s u l t s o f th e s e i s m i c and s t r a i n measurem ents e r e
sum m arized i n F ig u r e 20.
Both s e t s of o b s e r v a t i o n s show t h a t
t h e h i g h l y f r a c t u r e d r e g i o n e x te n d s o n ly to a h e i g h t o f ab o u t
300 f e e t ab ov e th e e x c a v a t i o n , and t h a t f r a c t u r e o r
s e p a r a t i o n o c c u r s a t th e Harmony S i l l .
/ FIGURE 20
-
56
mmm
V
J*
V
V
V
V
L
11
V
V 1/
11
V
11
-2501)
V
-JQK
V
v
v JSSO
V
V
1A_ V V
15_ V/ V
V V
IS­
Strata separation
Possible strata
separation
.*• V
IS.. •. . •
ia _ s •
Strata se p a ra t on
Heavily tractu rid
l l ’RR 2V
Pew seismic
events
J5QQ
•
IL
IL
•
. • . --fOQC
• •. .
22-
. •
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Possible str ,ta
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2000
4
-5 0 9 '
Numerous
seismic events
A CCNFAH1.1CN RELATIVE T( THE i BO LOGICAL
PTRPC7!TR3 Or’ THE CONCLUSIONS FROM ""IE
STRAIN MriAS’T I'M ;N TS AND THE S E I S M I C
OPSERNATIONS.
- 57 The e t r a n .
-u ra m e n te show t h a t th e r a c k b e t . e e n
th e K im b erley a e r i e , a i d th e Harmony S i l l may have s e p a r a t e d
in to th re e s la b s .
T h is c o n c lu s io n 1 . based on th e modulus o f
c o u ld be a r g u e d t h a t no s t r a t a s e p a r a t i o n o c c u r r e d .
In a n ,
e v e n t , i f s t r a t a s e p a r a t i o n has o c c u r r e d , t h e s e s l a b s a r e
p r o b a b ly u n b ro k e n s i n c e no s e is m ic a c t i v i t y was o b serv ed i n
t h i s re g io n .
S t r a t a s e p a r a t i o n a t t h e Harmony S i l l o c c u r re d a t a
s u rp ris in g ly e arly sta g e .
The s t r a i n exceeded th e r e l a x a t i o n
s t r a i n i n M a y , 19b7 when t h e span o f th e e x c a v a tio n was only
1500 f e e t .
On th e b a s i s o f a c o n tin u o u s e l a s t i c medium th e
s t r e s s ch an ge in d u c e d by th e e x c a v a tio n a t t h i s d i s t a n c e
s h o u ld be much s m a l l e r t h a n th e normal v i r g i n s t r e s s , so
t h a t s t r a t a s e j a r a t i o n would n o t be e x p e c te d .
f a ir ly la rg e
A lso , th e
.iergy r e l e a s e s d e t e c t e d s e i s m i c a l l y a t t h i s
s i l l a re d i f f i c u l t to e x p la in .
T h e re fo re i t a p p e a r s t h a t th e
f r a c t u r e mechanism a t th e s i l l i s no t sim p ly one o f s t r a t a
s e p a ra tio n .
I t can be c o n c lu d e d t h e r e f o r e t h a t both th e s e is m ic
o b s e r v a t i o n s and t h e s t r a i n measurem ents i n d i c a t e d t h a t most
o f t h e f r a c t u r i n g was l i m i t e d
to a zone expending to a h e i g h t
o: a p p r o x i m a t e l y 300 f e e t above the e x c a v a t i o n .
The h e i g h t
o f t h i s zone was n o t r e l a t e d t o th e h o r i z o n t a l e x t e n t o f th e
s u r r o u n d i n g e x c a v a t i o n , and i t extend ed latere.* l y a s t h e
faces advanced.
The ro c k mass did n o t e x h i b i t g r o s s
i n e l a s t i c b e h a v i o u r e x c e p t i n a r e s t r i c t e d r e g i o n a t th e
Harmony S i l l where u n e x p la in e d movements o c c u r r e d .
/ The K a te . . . .
- 58 The R ate o f
,
The d e t a u c d mechanism o f ro c k b u n a ta and o t h e r forma of
damage due to rook f a i l u r e i s s t i l l unknoan.
s t r i a e of th e
e n e rg y c h a n g e s which n e c e s s a r i l y o c c u r when an e x c a v a tio n i a
Bade UndergroUnd
t 0 - > - v i d e th e b e a t u n d e rs ta n d i r * o f
th e Phenomena l e a d i n g t o rock f a i l u r e and damage ( C o o k < W , .
I t i s common knowledge t h a t th e damage and r o c k b u r a t h a za rd
i n c r e a s e s w ith d e p t h and i s g l a t e s t a t rem nants and i n
r e g i o n s mined i n an i r r e g u l a r manner.
The o b s e r v a t i o n s above
have q u a l i t a t i v e l y shown t h a t e e i s m i c l t y l a a l s o r e l a t e d t o
th e c o n f ig u r a tio n o f th e e x ca v a tio n .
The r a t e a t which e n e rg y
i s r e l e a s e d a s an e x c a v a t i o n i s e n la r g e d p r o v id e s an o b j e c t i v e
p a r a m e te r t o d e s c r i b e m ining geom etry i n term s which a r e
s i g n i f i c a n t t o ro c k f a i l u r e .
I n th e f o ll o w i n g d i s c u s s i o n , i t
i s shown e m p i r i c a l l y t h a t th e r a t e of energy r e l e a s e p e r u n i t
a r e a i n c r e a s e i n th e s i z e o f an e x c » / a t i o n i s c l o s e l y r e l a t e d
to s e i s m i c i t y and i n c i d e n c e o f damage i n th e m ines.
ih e r a t e o f en erg y r e l e a s e was d e te rm in e d by means o f an
e l e c t r i c a l r e s i s t a n c e a n a lo g u e d e s c r i b e d by Cook and SchumanAf 9 ^
Tne v a l u e o f t h e e n e rg y r e l e a s e r a t e o b ta in e d from th e a n a lo g u e
r e f e r s t o e l a s t i c ro c k b e h a v io u r ;
any d e v i a t i o n from e l a s t i c
b e h a v io u r would r e s u l t i n a h i g h e r en erg y r e l e a s e r a t e .
In
th e p r e c e d i n g s e c t i o n i t was shown t h a t th e rock mass does
n o t e x h i b i t g r o s s i n e l a s t i c b e h a v io u r .
The most r e a l i s t i c method o f a s s e s s i n g damage i s to
d e te r m in e th e in c o n v e n ie n c e i t c a u s e s .
The mine keep s a
r e c o r d o f t h e d a i l y a c t i v i t i e s i n each s t o p e .
I t is th e re fo re
p o s s i b l e t o d e te r m in e th e days s p e n t i n c l e a r i n g w orking p l a c e s
a f t e r r o c k b u r s t s anu r o c k f a l l s .
The number o f days d e l a y
a r i s i n g from t h i s c a u s e per u n i t a r e a mined i s , t h e r e f o r e ,
used t o a s s e s s th e damage, o r in c o n v e n ie n c e , to th e mine
cau sed by ro c k f a i l u r e s .
I t i s a l s o p o s s i b l e to d e te rm in e
/ th e . . . .
- 59-
. nujnbtr c f U b o,m r s e ,p l„ yea ln 6acb vorklng p U c
,c
th a i " d 4 1 tl0 n a l
O ' - i n t a l n l ^ B0t , 8 t a , t c r y
. t i n . c o n t r o l c a n be a n i m a t e d from th e a d d i t i o n a l number
o f a a n - c h i f t a p e r u n i t a r e a mined.
Four p o r t i o n * o f t h e mine were choser. f o r makin* a
c o m p a r is o n .
The,
a ll dose t ^ ^ r
„
g e o lo g ic a l
-n c e s were c . a miniir.wm, and the averag e a to p in g w id th
was 42 in c h e s i n a l l r e g i o n s .
The f o u r r e g ie ns a:.*e shown, i n
r e l a t i o n t o t h e whole mine m F i g u r e 21.
T»c f a c e p o s i t i o n s
a r e £ howsi i n th e F i g u r e , r e p r e s e n t i n g a y e a r ' s m in in g .
R egion
1 c o n t a i n s a re m n a n t i n which a g r e a t d e a l o f damage and
s e i s m i c a c t i v i t y o c c u r r e d and f o r which t h e a v e r a g e en erg y
r e l e a s e r a t e was h i g h .
Thlr, rem nant wai not r e g a r d ;d by t h e
mine management a s e x c e p t i o n a l l y d i f f i c u l t ;
however, th e m ining
c o n d i t i o n s were f a r more d i f f i c u l t th a n i n th e o t h e r W i - e
re g io n s.
Region 2 con tain s i lo n g w a ll f a c e w ith a l a r g a s p a n ,
but n o t l a r g e enough f o r c o m plete c l o s u r e to have o c c u r re d a t
th e c e n tr e .
M ining co n d itio n s were good and t h e a v e r a g e e n e rg y
r e l e a s e r a t e was m o d e r a te .
R egions 3 and 4 c o n t a i n lo n g w a ll
f a c e s w i t h a s h o r t s p a n , c o n s e q u e n tly th e a v erag e en erg y
r e l e a s e r a t e was lo w .
The mining c o n d i t i o n s were e x c e l l e n t .
F i g u r e 22 shows a p l a n view o f t h e s e is m ic e v e n ts t h a t
o c c u r r e d i n t h e f o u r r e g i o n s d u r in g th e y e a r ' s m in in g .
F i g u r e 23 shows t h e same plan view w i t h damage c e n t r e s
o c c u r r i n g o v e r t h e same y e a r ;
th e d i a m e t e r s o f t h e c i r c l e s
r e p r e s e n t t h e e x t e n t o f t h e damage measured i n d a y s d e l a y .
Only damage and s e i s m i c e v e n ts t h a t o c c u rre d i n t h e f o u r
r e g i o n s a r e shown.
A verage v a l u e s f o r a l l th e v a r i a b l e s i n each o f t h e
f o u r r e g i o n s were d e t e r m i n e d .
/ FIGURE 21
y
%
FIGURE 21
PLAN SHOWING THE FOUR REGIONS SELECTED
FOR COMPARING THE RATE OF ENERGY RELEASE
WITH DAMAGE, LABOUR REQUIREMENTS AND
SEISMICITY.
_
i LAN ON \ '-HID Or' 1000 PKrlT PHOWIN 1
THE ICO IT IONS Or THE ONION IC fi'/ENTo
THAT OCCURRED IN THE E'NR RBOION?
? ELECTED FOR COMPARISON WITH THE
RATE OF ENERGY h LEAPS.
3 0W S
O tlW
Pi.am -V A ;HI : OF 10C0 FBET CHOWiN?
7H-: '!FOT.l:BS OF nAMA'IS ■’’HAT o c c u r r e d
I*; IB FOUR RE ir o n s .1ELECTED FOR
COXP'-RICON WITH THE '.A"'R OF EMBROY
FA
I
I
1
1
I
I*
I
I
t—
W*—
• ■VH
.«MP»
—
I-------------1------------ 1 -
Xx
'
I
1
;
«/ t
r
i
4- i
i
i
i.a
,<
!
ewe, ww w • V*.«» *• w—1
-h
FIGURES
P i» .j4
DAMAGE MEASURED IN DAYS DELAY PER 1000 FATHOMS^
r LOTTED AGAINST '"HE E.’fERGY RELEASE RATE.
'
Fi*r 26
2”
RATE.
-HE NUMBER OF SEISMIC BVT TS OF DIFFERENT SIZES
PER 1000 FATHOMS/ PLOTTED AGAINST THE ENERGY
RELEASE RATE.
THE TOTAL SEISMIC ENERGY 1 10' 7ED AGAINST .HE
KNRRGY HELEASE RATE.
— 64 —
F i g u r e s 24 t o 27 show damoge, l a b o u r , a e lo m io l.jr and
13111 S e lS " iC e n e r 8>" r e s p e c t i v e l y , p l o t t e d a g a i n s t the
energy r e l e a s e r o t e .
The i n c id e n c e o f damage l a alm ost
l i n e a r l y d e p e n d e n t on th e e n e rg y r e l e a s e r a t e ;
i t is a lso
d e p e n d e n t on o t h e r f a c t o r s , su ch a s g e o l o g i c a l c o n d i t i o n s
and t h e ty p e o f s u p p o r t used i n t h e a to p e a.
Thus, i n a
p a r t i c u l a r mine where s t a n d a r d s u p p o r t methods a r e p r a c t i s e d ,
l i e e n e r g y r e l e a s e r a t e w i l l s e r v e a s a r e l i a b l e p a ra m e te r
f o r p r e d i c t i n g damage.
At Harmony i t can be s a i d t h a t vhen
th e e n e rg y r e l e a s e r a t e i s l e s s th an 108 f t . - l b s . p e r s q u a r e
fa th o m , m in in g c o n d i t i o n s w i l l be good.
The s i m p l e s t m ining
g e o m e try would c o n s i s t of two lo n g w a ll f a c e s a d v a n c in g away
from e a c h o t h e r i n t o v i r g i n g r o u n d ;
e v e n t u a l l y th e s to p e
s p a n becomes so l a r g e t h a t c l o s u r e t a k e s p la c e a t th e c e n t r e
o f t h e s t o p e and t h e en ergy r e l e a s e r a t e r e a c h e s a maximum
v a lu e .
The maximum energy r e l e a s e r a t e i s 0 .9 5 x 106 f t . - l b s . /
2
fathom^ f o r a 42 in c h s t o p i n g w id th a t a d e p th o f 5000 f e e t ,
w hich f a l l s w i t h i n th e c r i t e r i o n f o r good m ining c o n d i t i o n s .
The l a b o u r r e q u i r e d to mine th e remnanc i n r e g i o n 1 i s
tw ic e t h a t r e q u i r e d to mine an e q u i v a l e n t a r e a i n t h e
r e g i o n s , which means t h a t th e c o s t o f m ining i s a p p ro x • e l y d o u b le .
F u rth erm o re t h e h a za rd p e r u n i t a r e a mined i s
a n o r d e r o f m ag nitu de h i g h e r , s i n c e tw ic e a s many men a r e
e x p o se d t o f i v e tim e s a s much damage.
More i s o l a t e d re m n a n ts
i n t h e m in e , i n which t h e en erg y r e l e a s e r a t e was s t i l l
h i g h e r , have r e s u l t e d i n f a r w orse m in in g c o n d i t i o n s , and i t
i s d o u b t f u l w h e th e r i t was w o rth w h ile m in in g th o s e re m n a n ts .
7
T h e re were only two s e i s m i c e v e n ts o f m agnitude 10
f t . - l b s . , and b o th o c c u r r e d i n r e g i o n 1 .
The t o t a l s e is m ic
e n e r g y r a d i a t e d by th e l a r g e s t e v e n t s e x ce e d s t h e t o t a l
s e i s m i c e n e rg y r a d i a t e d by a l l t h e s m a l l e r e v e n ts f o r any
re g io n .
F ig u r e 10
s
' iOw s
t h i s phenomenon f o r th e whole m ine;
i n a r e m n a n t , how ever, i t was f a r more pronounced th a n t h i s .
/ C o n se q u e n tly . . . .
C c n e e q u o n tly F i g u r e 27 . a s
^ m o s t c o m p le te ly c o n t r o l l e d
by th e l a r g e s t s e i s m i c e v e n ts i n each r e g i o n .
Under rem nant
c o n d i t i o n s , t h e t o t a l s e is m ic energy was l e s s t h a n 10~4 o f
th e e n e r g y r e l e a s e d .
This im p lie s t h a t t h e v a s t m a j o r i t y
o f th e e n e rg y r e l e a s e d i s d i s s i p a t e d i n a s t a b l e manner and
t h a t t h e mcchaniem o f u n s t a b l e o r v i o l e n t en erg y r e l e a s e Aa
obscured.
From F i g u r e 26 i t i s i n t e r e s t i n g t o n o te t h a t th e r a t i o
o f the s m a l l e v e n t s to th e l a r g e e v e n ts d e c r e a s e d when th e
en e rg y r e l e a s e r a t e was h ig h o r when e x tre m e ly l a r g e e v e n ts
'c c u r r e d .
This b e h a v io u r i s c o n t r a r y to t h a t o f e a r th q u a k e s
w here Ih e r a t i o o f s m a l l e a r th q u a k e s t o l a r g e e a r th q u a k e s i s
ap p ro x im a te ly a c o n sta n t f o r d i f f e r e n t re g io n s .
/ Temporal B e h a v io u r. . . .
T .a ja o ra l B e h a v io u r o f S e ism lr
The Harmony and V i r g i n i a Mines u s e a c e n t r a l i z e d b l a s t i n g
s y s te m , w i t h t h e r e s u l t t h a t a l l c h a r g e s i n t h e s t o r e s i n eaoh
m ine a r e f i r e d i n a m a t t e r o f 10 t o 30 m in u te s .
At V i r g i n i a
t h e b l a f i t i n e tim e i s u s u a l l y 3 .0 0 p.m . to 3 .3 0 p . m . , and a t
Harmony i t
i s u s u a l l y 4 .3 0 p.m. t o 5 .3 0 p.m.
b l a s t i n g i s a p p r o x im a te ly one hour e a r l i e r .
On S a tu rd a y s
F ig u r e 28 shows
t h e d i u r n a l d i s t r i b u t i o n o f (a) a l l th e s e is m ic e v e n ts n e a r
t h e r e e f p la n e a t Harmony, ( b) a l l th e s e is m ic e v e n ts a t
V i r g i n i a and (c ) a l l t h e s e is m ic e v e n ts a t th e Harmony S i l l
t h a t o c c u r r e d d u r i n g th e f i r s t y e a r o f r e c o r d i n g .
Tne e v e n ts
a t t h e Harmony S i l l o c c u r re d random ly, but th e e v e n ts a t th e
r e e f p la n e w ere s t r o n g l y i n f l u e n c e d by b l a s t i n g .
The peak
i n t h e V i r g i n i a d i s t r i b u t i o n was e a r l i e r and n a rro w e r th a n
t h e peak i n th e Harmony d i s t r i b u t i o n , c o rre s p o n d in g t o e a r l i e r
and a n a r r o w e r s p r e a d i n b l a s t i n g t im e s .
At V i r g i n i a , 50 p e r c e n t o f a l l t h e e v e n ts o c c u rre d
b e tw e e n 2 . 0 0 p.m. and 5 .0 0 p . m . , and a t Harmony l e s s th a n
40 p e r c e n t o f a l l
7 . 0 0 p .m . ;
t h e e v e n t s o c c u rre d betw een 3 .0 0 p.m. and
t h i s i m p l i e s t h c t t h e m a jo r ity o f s e is m ic e v e n ts
w ere n o t t r i g g e r e d by b l s t i n g .
I t was th o u g h t t h a t e v e n ts
o f a p a r t i c u l a r s i z e might be more s e n s i t i v e to b l a s t i n g
th a n o t h e r s and t h e d i u r n a l d i s t r i b u t i o n f o r each m agnitude
was d e t e r m i n e d , F ig u r e 29*
Only t h e
is tr lb u tto n s for
Harmony a r e shown, s i n c e t h o s e f o r V i r g i n i a were s i m i l a r .
T h e re i s no o b v io u s d i f f e r e n c e betw een t h e s e d i s t r i b u t i o n s
and a g a i n 40 p e r c e n t t o 50 p e r c e n t o f t h e e v e n t s o c c u r re d
betw een 2 . 0 0 p.m . and 5 .0 0 p .m ., i n t h e c a s e o f V i r g i n i a ,
and 3 .0 0 p .m . and 7 .0 0 p.m . I n th e e n s e o f Harmony.
The
l a r g e amount o f s e i s m i c a c t i v i t y t h a t o c c u rre d w i t h o u t
e x t e r n a l s t i m u l u s t e s t i f i e s to th e tim e d e p e n d e n t b e h a v io u r
o f ro c k f r a c t u r i n g .
/ FIGURE 27
Hdrmony
events near reel
n
>06
:
100
/■
/
.
l i t
$ 1 7
• « to n w
events
h iim
acsmc
Virginia
o
.00
H arm ony
FIGURE ?A
^
e v e n ts n e ar sill
THE DIURNAL DISTRIBUTION OF ALL THE
SGISMIC EVENTS THAT OCCURRED DURING
ONE ’BAH NEAR THE REEF AT HARMONY,
NEAR THE REEF AT V IR G IN IA , AND NEAR
THE HA MONY S I L L .
— 68 —
♦ W ft-lH
*W’1 I
'
1
)
1
I •
i i »
n il)
» i T T"
uo
1*
110
no
•o
i
to
•0
so
40
M
1C
111
10
0
FIGURE 29
r lG U K 6
1 I
, 4 $ I ? • • 10 0 II 1 I l k S O T O O I O r
THE DIURNAL DISTRIBUTION I:' S', ISM I ,
^
0F DIFpBRENT giZKD THAT
OCCURRED DURING ONE YEAR NEAR THE
REEF IN HARMONY.
— 69 —
I t 13 a l s o i n t e r e s t i n g t o s e e h e th e s e i s m i c i t y v a r i ,
Lea
t h r o u g h o u t t h e week, .and i t i s more i n f o m a t i v e i f t h i s
can
be compared w ith t h e a c t i v i t y i n t h e mine. The b e s t method
o f e s t i m a t i n g t h e m ining a c t i v i t y i s by means of th e number
o f h o l e s d r i l l e d and b l a s t e d i n t h e s t o p e s .
I t has been
s u r g e s t e i t h a t s i n c e th e m iners re c o rd t h e number o f h o le s
d rille d
th e m s e l v e s , th e y might r e p o r t d i s h o n e s t l y on Mondays
and o a t u r d a y s .
The Harmony Mine management i s c o n f id e n t t h a t
th e r e p o r t i n g i s h o n e s t ;
fa c to r,
however, as a check on t h e human
t h e t o t a l number o f s t o p i n g h o le s d r i l l e d was compared
w i t h t h e t o t a l amount o f compressed a i r used d u r i n g t h e
w orking s h i f t .
P i u re 30 shows t h ° d a i l y d i s t r i b u t i o n o f
t h e t o t a l number of s t o p i n g h o le s d r i l l e d and o f t h e t o t a l
amount o f co m pressed
t i r used between 7 .0 0 a.m. and 3 .0 0 p.m .
The c om pressed a i r i s a l s o used f o r p u rp o se s o t h e r th a n ro c k
d rillin g ;
h o w e v er, s i n c e t h e r e a r e no s e r i o u s d i s e r p a n c ie s
betw een t h e two d i s t r i b u t i o n s , i t can be con clud ed t h a t t h e
re p o rte d h o le s
' r i l l e d r e f l e c t s th e tru e s i t u a t i o n .
The
s l i g h t l y s m a l l e r amount o f compressed a i r used on S a tu rd a y s
shown i n P i u r e 30 i s n o t n e c e s s a r i l y i n d i c a t i v e
f le ss
d r i l l i n g , s i n c e d r i l l i n ' can s t a r t b e f o r e 7 .0 0 a.m . on
S a tu rd a y s.
F i g u r e 31 shows th e d a i l y d i s t r i b u t i o n o f (a)
a l l t h e s e i s m i c e v e n t s ne.’r t h e r e e f a t Harmony, (b) a l.
t h e s e i s m i c e v e n t s a t V i r g i n i a and (c ) a l l th e s e i s m i c e v e n ts
a t the
Inrmony S i l l .
B re a k in g t h e s e d i s t r i b u t i o n s down i n t o
d i s t r i b u t i o n s f o r d i f f e r e n t s iz e d e v e n ts y i e l d s p a t t e r n s
s i m i l a r t o t h o s e i n F ig u r e 31.
The e v e n ts m a r th e r e e f
have a d i s t i n c t minimum on Sundays and a weak marl mum in
t h e m id d le o f t h e w eek.
The l a r g e number of e v e n ts on
Sundays a g a i n i n d i c a t e * tim e dependent b e h a v io u r i n rock
fra c tu rin g .
/ FIGURE 29 . . . .
—
:70
—
rn Q5
3 M
o 4
"5 CO 05
as rn 3
a, ad P
o co
o o
O 6, W
ft*
O
p
25
25
25 &
01 X ^ u u o j» d
uu d f
poo
w o i u»»Mi«q sy u n jio p i .<»jdujo 3
e-
co
SP
8 ^ 5
32 =
I I .
in
8 8 ,r
cn
3 p 13
>*
p
i - V
H A•>h
M
-< m ro
QP A
A
. \ \ v, A< ^Vx
e-» A
T
U)
.01 X vjunuuo
J*d
p » n (JP S»1°H
o
'JS
-4
&H
u
F5'
V ..
J,
Vi
jo e A
o
jo
*
3 'U J f t s
A vop
)0 } O i
k
32 s h o w , t h e v a r i a t i o n , 1 t h t i m e o i t h e t o t a l
fig u r e ,
num ber o f
slo p in g
o f ev en ts
near th e
t o t a l num ber o f
A fir e
h o le s d r ille d
er.oh w e e k ,
r e e f a t H arm ony m
broke
out
of
a m arked
o tn er
th e
tim e s,
w id e ly
co n sta n t.
ot
th e
th e
In th e
The e v e n t s a t
correspond
reef.
w ith
th e
F ig u r e
ev en ts;
th e
sep arated
reef
u su a lly
fr e q u e n tly
p la n e
E ven ts
m a g n itu d e
in
th e ir
10*
th ree sm a ll
a c tiv ity
seconds
und.
to
fo llo w e d
ev en ts.
This, t y p e
ev en ts
it
m ech a n ism
th e
e v e n t a in
size d
in
a n d no c o n n e c t i o n
even ts a t
swarm s w i t h
a few
hours.
th e
th e
an d
10
ft.-lb s .
th e r e e f
is
near
to
are
o f lo w s e i s m i c
E ven ts
b e h a v io u r h in t s
S ill
even ts
m arked t e n d e n c y
by a p e r i o d
of
th e
T he e v e n t s
a r e s o m e tim e s a cco m p a n ied
th e
th e
near
th e d if f e r e n t
im m e d ia te n e ig h b o u r h o o d .
ft.-lb s .
r o u g h ly
-a c tiv ity
S eism ic
o f m a g n itu d e 1 0
and
of
in d e p e n d e n t
be no i n t e r d e p e n d e n c e b e tw e e n
occur
m ech a n ism c f
of
se ism ic
s h o w a v e r y much l e s s
preceded
a c tiv ity
b<
at
has flu c tu a te d
a c tiv ity
sea so n a l v a r ia tio n s
c o u ld
by a few
sw a r m in g .
to
reef;
H arm ony 5 1 1 1 a r e q u i t e
in
caused
h a s r e m a in ed a p p r e c i a b l y
peaks
show s th e
tid e s
H arm o n y S i l l
th e
over a la r g e
n e -r th e
a c tiv ity
the: p e a k s i n
th ere app ears
w ith e a r th
a c tiv ity
se ism ic
1964
i n m in in g a c t i v i t y ,
a lth o u g h
There w ere no o b v io u s
th e
th e
se ism ic
m in in g a c t i v i t y
m in in g r a t e ,
a sta n d still
The r e d u c t i o n
how ever,
w h ile
In ea ch w eek .
I n t h e m in e o n t h e 2 9 t h O c t o b e r ,
m in e .
d ecrease
t o t a l num ber
ea ch w eek , end t h e
e v e n ts n ea r th e H n m o n , h i l l
and b r o u g h t m in in g o p e r a t i c - . t „
p o r tio n
th e
diff#
of
by
two o r
th a t
th e
o n t from t h e
p la n e .
/ FIGURE ) 2
Holes drilled
All events neor re
All events ot sill
70
60
X 10
50
week
40
f 20
Holes
drilled
per
JO
IO
m
—
3
THE HARMONY SILL.
Holes d n u ed
Events 10 > 1J
70
Events 10
Events Ilf + 10 * 1^
60
X 10
SO
Holes
drilled
per
wee*
40
30
20
lO
Of
»
«
SIZE? PER WEEK.
«
S ^ 2 T » V K : luk
The H arm ony
« ln a k e e pa a r e d o , , of t r e m o r s .
a n o t e o f t h e tim e whenever th e y f e l t a tre m o r.
T he
This
r e c o r d o b v i o u s l y c a n n o t he c o m p le te, and tre m o rs
o r i g i n a t i n g I n n e ig h b o u r in g mines could a l s o have been
recorded.
By com paring t h e tim e a t w hich a tre m o r o c c u r re ,
w i t h t h e t i m e s o f t h e s e is m ic e v e n t s , i t was p o s s i b l e to
I d e n t i f y t h e s o u r c e o f t h e tre m o r and i t s m a g n itu d e .
Of
t h e r e p o r t e d t r e m o r s , 80 p e r c e n t co rre sp o n d e d w ith s e is m ic
e v e n t s , t h e r e m a in d e r p ro b a b ly o r i g i n a t e d In n e ig h b o u rin g
m in e s .
T a b le I shows th e p e rc e n ta g e o f d i f f e r e n t s i z e d
e v e n t s n o t i c e d as tr e m o r s .
The :-.ine a l s o keeps a r e c o r d o f "R o ck b u rst R e p o r t s " .
The damage t h a t was r e p o r te d was p r i m a r i l y i n th e n a t u r e
ol r e c k f a l l s w hich a f f e c t e d an a r e a ranging from 300
s q u a r e f e e t t o 8000 s q u a re f e e t i n e x t e n t .
was n o t r e p o r t e d .
Minor damage
In some c a s e s , rock f e l l s were
accom panied by damage t o t h e f a c e , and i n 20 p e r c e n t o f
t h e c a s e s no r o c k f a l l was r e p o r t e d , b u t the damage was
d e s c r i b e d a s " f a c e bumped".
92 p e r c e n t o f th e r e p o r t e d
i n c i d e n t s o c c u r r e d in d e c l a r e d rem nant a r e a s , w h ile t h e
r e m a in i ig i n c i d e n t s o c c u rre d on c o m r a b u tm e n ts.
S e is m ic e v e n ts can be a s s o c i a t e d w ith damage by
c om paring th e p la n p o s i t i o n o f th e e v e n ts w i t h th e known
p o s i t i o n o f th e damage.
In a number o f c a s e s t h e tim e
a t w h ich th e damn go o c c u rre d was a l s o known.
S in e
th e
tim e a t w hich th e s e i s m i c e v e n ts o c c u rre d i s known, t h e
tim e a t w hich th e damage o c c u rre d can be d e te rm in e d i n
t h o s e c a s e s f o r which t h e time was n o t known.
/ TABLE I
-
76 -
M ag n itud e f t . - l b s .
W
10
T o t a l Number o f
E v e n ts
Harmony + V i r g i n i a
c ,c
£ A s s o c i a t e d w ith
Trem 0r8
1n4
10
, S
lo 5
106
107
10e
152
62
6
2
100
°
4 '6
21
42
50
I 8 -8
1 8 -=
15.4
75
lo o
-
564
313
118
51
4
_
’ A s s o c i a t e d w ith
E a ™ n ? T & : g in ia
T o t a l Number o f
E v e n t s : Harmony
% A s s o c i a t e d w ith
R e p o r te d Damage:
Harmony
0
1*3
5 .1
22
0
The d a t a i n t h i s Table i s f o r th e p e rio d 1 1 th August
1964 to 1 1 th J a n u a r y , 1965, e x c e p t f o r t h e minor
damage which c o v e r s a 12 day p e r io d o n ly .
'ABLE I I
C o rre la tio n
T o tal
Icod
D o u b tfu l
Number o f
In c id e n ts
660
264
35
Number o f
In c id e n ts
as * o f T o tal
100*
40*
5*
Very D o u b tfu l
40
6%
Non
321
40.
^
/ O fficial . . . .
O f f i c i a l " B o c k f c u r a t r e p o r t s " s u b r d t t e d between t h e
i l t h AiV'ust, 1964 and 11th J a n u a r y , 1965 were c o m p a r e d w i t h
se ism ic
1 1 th
e v e n ts.
Jan u ary ).
(Very few r e p o r t s w ere s u b m itte d a f t e r
81 p e r c e n t of th e r e p o r te d i n c i d e n t s o f
damage c o u ld be p o s i t i v e l y i d e n t i f i e d w ith s e is m ic e v e n t s ,
t h e r e m a in in g i n c i d e n t s w ere a l l s m a l l .
A more i n t e n s i v e experim ent was c on d ucted to d e te r m in e
t h e r e l a t i o n s h i p betw een s e is m ic e v e n ts and minor damage.
The s e i s m i c e v e n t s were l o c a t e d w i t h i n 36 hours o f t h e i r
o ccu rren ce.
Th
c o - o r d i n a t e s o f th . f o c i o f th e e v e n ts
w ere im m e d ia te ly r e l a y e d to the m ine, whereupon an o b s e r v e r
would he s e n t t o th e n e a r e s t p o i n t t o th e fo c u s of each
e v e n t t o s e t w h e th e r t h e r e had been any damage.
This
e x p e r im e n t was c a r r i e d ou t f o r 12 days d u r in g w hich tim e
100 e v e n t s w e re l o c a t e d and nr o f f i c i a l "R o ck b u rst r e p o r t s "
w ere s u b m i t t e d .
The n a t u r e of th e damage observed was
s m a l l r o c k f a l l s , broken s t i c k s and s c a l i n g .
Table I shows
th e p e r c e n ta g e o f d i f f e r e n t s iz e d e v e n ts c a u s in g damage;
m in o r damage, i . e . , damage t h a t i s n o t r e p o r t e d , and th e
o f f i c i a l l y " R e p o rte d damage" a r e shown s e p a r a t e l y .
/ FIGURE 34
om
(•)
'M l
%
to
1* Oct
IMS
s
S
Mi
j j t k. i . . i .
■^.LUU.
OKI
* m
Ik)
FIGURE 34
a)
THE DIURNAL D IS TR IB U TIO N OF O FFIC IA LLY
REPORTED DAMAGE.
b)
THE DIURNAL D IS TR IB U TIO N OF S EISM IC EVENTS
THAT COINCIDED WITH DAMAGE WHICH PREVENTED
NORMAL M INING OPERATIONS IN THE STORES.
: r -::
‘
- 79 F ig u r e 34a shows t h e d i u r n a l d i s t r i b u t i o n o f o f f i c i a l l y
r e p o r t e d damage from U t h A ugust, 1964 t o 11th J a n u a r y , 1965.
T his d i s t r i b u t i o n shows a s u r p r i s i n g amount o f damage d u r in g
t h e w o rk in g s h i f t , namely betw een 7 a .m . and 2 p.m.
The
Mine Management f e e l s f , t t h i s d i s t r i b u t i o n a r i s e s from
b i a s e d r e p o r t i n g , s i n c e on p s y c h o lo g i c a l g ro u n d s, a r o c k f a l l
o c c u r r i n g d u r i n g th e w orking s h i f t i s more l i k e l y t o be
r e p o r t e d t h a n one o c c u r r i n g i n o f f - s h l f t p e r i o d s .
In a d d itio n
th e " r o c k b u r e t r e p o r t i n g " i s n o t c o m p le te, c o n s e q u e n tly an
a l t e r n a t i v e method f o r a s s e s s i n g damage was a d o p te d .
The
d a i l y a c t i v i t i e s i n e ach s to p e a r e r e c o r d e d , and i t i s th u s
p o s s i b l e t o d e te r m in e th e days on which th e normal mining
o p e r a t i o n s were o b s t r u c t e d by r o c k f a l l s o r r o c k b u r s t s .
The
number o f d a y s on which normal m ining o p e r a t i o n s were p r e v e n te d
i n a s t o p e i s a measure o f th e s e v e r i t y o f th e damage.
At Harmony t h e m in ing c y c l e ta k e s th e fo llo w in g form:
on one day a s to p e f a c e i s d r i l l e d and b l a s t e d , and on th e
n e x t day i t i s c le a n e d by means o f s c r a p e r s .
No n ig h t s h i f t
work was c a r r i e d on i n th e s to p e s under c o n s i d e r a t i o n .
A c co rd in g t o t h i s method of a s s e s s i n g damage, only ro c k ­
b u r s t s o r r o c k f a l l s which p re v e n te d d r i l l i n g and b l a s t i n g
and s c r a p i n g a r e c o n s id e r e d damaging.
I n o r d e r t o i d e n t i f y a s e is m ic e v e n t w ith an i n c i d e n t
o f dam age, two c o n d i t i o n s have t o be f u l f i l l e d ;
t o be c o i n c i d e n t i n time and i n s p a c e .
th e y have
The e x a c t time a t
which damage o c c u r re d i s n o t known, s i n c e th e r e c o r d s only
g iv e th e d ays on which a s to p e was i n a c t i v e .
If a ro c k fa ll
o c c u r r e d a f t e r t h e w orking s h i f t had l e f t t h e s to p e a t a b o u t
2 .0 0 p . m . , i t would o n ly be n o t i c e d on th e n e x t d ay , which
would t h e n be r e c o r d e d a s th e f i r s t i n a c t i v e day.
However,
i f t h e r o c k f a l l o c c u r re d d u r in g t h e working s h i f t ,
t h e t day
on w hich th e r o c k f a l l o c c u r re d would be r e c o r d e d a s th e
ft r e t in a c tiv e day.
Thus, to form a time c o r r e l a t i o n , the
/ s e is m ic .........
— 80 —
s e i s m i c e v e n t musu have o c c u rre d between 2 .0 0 p.m. on th e
day b e f o r e t h e f i r s t I n a c t i v e day end 2.0G p.m. on the f i r s t
in a c tiv e day.
When Monday was th e f i r s t I n a c t i v e day, th e
s e i s m i c e v e n t must have o c c u rre d between 2 .0 0 p.m. on
S a tu r d a y and 2 .0 0 p.m. on Monday.
There a re a few s i t u a t i o n s
w hich do n o t f i t t h i s tim e c o in c id e n c e c o n d i t i o n ; f o r example
i f a r o c k f a l l o c c u r r e d in. an
‘-'once t r a c k c u t t i n g ( a . t . c . )
d u r i n g t h e w o rk in g s h i f t , i t would no t p re v e n t d r i l l i n g and
b l a s t i n g on t h e one s to p e fa c e a d j o i n i n g i t , b u t i t would
p r e v e n t c l e a n i n g i n th e o t h e r s t o p e .
Thus i t was p o s s i b l e
f o r one r o c k f a l l to c au se i n a c t i v i t y on d i f f e r e n t days i n
"d jo in in g s to p e s .
A lro a r o c k f a l l could bo fo llo w e d by a
sec o n d r o c k f a l l and a s e is m ic e v en t a day o r more l a t e r , and
th e s e i s m i c e v e n t would th u s not be i d e n t i f i e d w ith any
damage.
The a c c u r a c y o f l o c a t i o n of t h e s e is m ic e v e n ts in
a p p r o x i m a t e l y 100 f e e t .
The a c c u ra c y w ith which th e co­
o r d i n a t e s o f t h e c e n t r e o f th e damage can be d e te rm in e d i s
a l s o a b o u t 100 f e e t , s i n c e a s to p e f a c e can have a le n g th
o f 1 0 f e e t and a r o c k i a l l a t one end i n an a . t . c . , s a y ,
c o uld c a u s e a s to p p a g e .
I t i s f e a s i b l e t h a t th e f o c a l
mechanism o f a s e is m ic e v e n t co uld e x te n d o ver a d i s t a n c e
o f 100 f e e t , and i t i s a l s o f e a s i b l e t h a t a v i o l e n t ev en t
c o u ld c a u s e a r o c k f a l l a t a d i s t a n c e o f 200 o r 300 f e e t away.
Hence i t h a s been c o n s id e re d r e a s o n a b le t o choose th e
c o n d i t i o n t h a t th e s e is m ic e v en t sh o u ld be l e s s th a n 500
f e e t away from t h e c e n t r e o f damage.
I t was d e c id e d to make c o r r e l a t i o n s on t h r e e b a se s i n
o r d e r t h a t e x c e p t i o n a l c a s e s and m is u n d e r s ta n d in g s i n th e
r e p o r t i n g of th e f i r s t i n a c t i v e day may be in c lu d e d :
/
1)
G ood
....
t ) sood c o r r e l a t i o n .
The oeiem lc ev en t o u s t o c c u r b e tw e e n
2 .0 0 p.m . on th e any b e fo re and 2 .0 0 p.m. on th e f i r s t
i n a c t i v e day end must be l e s s th a n 500 f e e t from th e
c e n t r e o f damage.
i i ) D o u b tf u l c o r r e l a t i o n .
be twee.
The s e is m ic e v e n t must occur
2 .0 0 p.m. two days b e fo re and 2 .0 0 p.m. one day
b e f o r e t h e f i r s t i n a c t i v e d ay, and must bo l e s s th a n
500 f e e t from t h e c e n t r e o f damage.
H i ) Very D o u b tfu l c o r r e l a t i o n .
The s e is m ic e v en t must l i e
w i t h i n 700 f e e t o f t h e damage and must o c cu r between
2 .0 0 p.m . t h r e e days b e f a r e th e f i r s t i n a c t i v e day and
2 .0 0 p.m . one day a f t e r th e f i r s t i n a c t i v e d a y .
i v ) No c o r r e l a t i o n .
No s e is m ic ev en t can bo found which
f u l f i l s any o f th e c o n d i t i o n s i n c a t e g o r i e s ( i ) ,
(ii)
or ( i l l ) .
When more th a n one s e is m ic e v e n t f u l f i l l e d th e s e
c o n d i t i o n s , t h e l a r g e r e v e n t was s e l e c t e d u n l e s s th e s m a l l e r
e v e n t was much c l o s e r t o th e c e n t r e o f damage.
The Harmony Mine Management mode t h e i r r e c o r d s from th e
1 1 th A u g u s t, 1964 t o 18th O c to b er, 1965 a v a i l a b l e f o r
ex am in atio n .
I n th e r e c o r d s a d i s t i n c t i o n was made between
damage due t o r o c k f a l l s and damage due t o r o c k b u r s t s .
f a b l e I I shows t h e number o f i n c i d e n t s o f damage f a l l i n g
i n t o th e d i f f e r e n t c o r r e l a t i o n c a t e g o r i e s , f o r which a
s e i s m i c e v e n t c a n be f o u n d .
Only 11 p e r c e n t o f t h e
i n c i d e n t s l i e i n th e d o u b t f u l c a t e g o r i e s and s i n c e o n ly a
s m a l l f r a c t i o n o f tn v s e i n c i d e n t s can be e x p e c te d t o be
d i r e c t l y r e l a t e d to s e is m ic e v e n t s , they were grouped w ith
the
1no c o r r e l a t i o n * c a te g o r y i n th e fo llo w in g a n a l y s i s .
Thus i t can be c o n clu d e d t h a t a t l e a s t h a l f th e damage as
n o t accom panied by s e is m ic a c t i v i t y of s u f f i c i e n t i n t e n s i t y
t o be l o c a t e d by th e s e is m ic r e c o r d i n g n e tw o rk .
/ TABLE I I I . . . .
TABLE I I I
B elay o f more t h a n
3 days
Delay o f
2 o r 3 days
Delay o f
1 day
107
10°
105
H
O
i M agnitude o f s e i s m i c e v e n t , f t - l b s .
105
R o c k b u re t
2
11
0
4
3
R o ck fall
1
3
1
'0
0
R ockburst
-
6
1
R o ck fall
-
12
2
6 ii
6
3
3
i
1 R o ck fall
-
14
19
42
2
36
21
91
217
715
40?o
9 .6 4
7.39" ' 4 .5 >
S e ism ic e v e n ts c o i n c i d i n g w ith
damage, a s a p e r c e n t a g e o f t o t a l
number o f e v e n t s
4
50*
_
„
29_
253
23
69
5 2
4
49
4
T o t a l number o f e v e n ts
11
76
23
!
| 1542
I
1
26
-
Number o f e v e n t s c o i n c i d i n g
with damage
-
r
j R o c k b u rst
|
; No c o r r e l a t i o n
.
J
|
|
- 83 T a b le I I I shows th e number o f
siz e .
i n c i d e n t s o f damage
The aemDge h a s been s u b d iv id e d I n t o t h r e e groups
r e p r e s e n t i n g the s e v e r i t y o f t h e d a m g o .
There . . r e 660
i n c i d e n t s o f dnnnge o f which 80 p e r c e n t d e la y e d
o p e r a t i o n s f o r one d o , o n ly .
Amongst th e s m a l l e s t I n c i d e n t s .
c n ly 58 p e r c e n t c o i n c i d e d w ith s e is m ic e v e n t s , w hile amongst
th e l a r g e r i n c i d e n t s ab o u t 48 p e r c e n t c o in c id e d w ith s e is m ic
e v en ts.
H o c k b u rs ts hcve been d e f in e d by Cook c t . n i . ^ ^ l ) Qg
"damage t o u n d e rg ro u n d w orkings cau sed by u n c o n t r o l l e d
d i s r u p t i o n o f ro c k a s s o c i a t e d w ith a v i o l e n t r o lu n e e of
en erg y a e d i t i o n a l t o t h a t d e r iv e d from f a l l i n g ro ck f r a g m e n ts " .
Bee - u se a b o u t h a l f o f t h e i n c i d e n t s o f damage * e p o rte d a s
r o c k b u r s t s a r e n o t accompanied by s e is m ic e v e n t s , i t must
be c o n c lu d e d t h a t a t l e a s t h a l f o f them a r e n o t p ro p e r
ro c k b u rsts.
Damage r e p o r t e d as r o c k b u r s t s shows a s l i g h t l y
g r e a t e r te n d e n c y t o be accompanied by s e is m ic e v e n ts th a n
damage r e p o r t e d as r c c k f n l l s , p a r t i c u l a r l y i n th e c a s e o f
severe
age.
been i i
r e c t l y c l a s s i f i e d , some c a s e s do show r o c k b u r s t
charade.
" * tc s.
e v e n ts t h ^ t
Thus ever, though a g r e a t d e a l of damage has
T a b le I I I a l s o shows th e number o f s e 4 jmxc
U n a id e d w ith damage;
t h i s number i s shown a s
a p e r c e n t a g e o f t h e t o t a l number of s e is m ic e v e n ts o f each
s i z e t h e t o c c u r r e d o v e r th e same p e r io d a s t h e damage.
There
a r e fe w e r s e i s m i c e v e n t s th a n i n c i d e n t s of damage s i n c e o f t e n
a s e i s m i c e v e n t can be
one s t o p e .
iu v n tifie d
w ith damage i n more th a n
I n f a c t more s e is m ic e v e n ts must have been
a s s o c i a t e d w i t h damage th a n t h a t g iv e n in T able I I I , s i n c e
t h i s a n a l y s i s c o n s i d e r e d damage n e a r s to p e f a c e s o n ly .
The f a c t t h a t few s e is m ic e v e n ts c ause damage w i t h i n a
s h o r t w h ile o f th o ix o c c u r r e n c e , i m p lie s t h a t th e s e is m ic
e v e h ts must o c c u r a t a r e l a t i v e l y l a r g e d i s t a n c e e i t h e r
/ ahead
cheod o f t h e fa c e o r above th e f a c e .
T his c o n c lu s io n le n d s
cru d -ncc to t a e v e r t i c a l d i s t r i b u t i o n o f s e is m ic e v e n ts i n
F ig u r e 1 6 .
m a g n itu d e 10
The v e r t i c a l d i s t r i b u t i o n o f th e e v e n ts o f
f t . - l b s . which c o in c i d e w ith damage i s shown
i n T a b le IV.
TABLE IV
8b0Ve
*300
+200
Number o f e v e n ts o f
m a g n itu d e 10 f t . - l b s .
+100
0
11
11
6
-100
4
TABLE V
D is ta n c e betw een
e v e n t and damage
—ft.
Number o f i n c i d e n t s
0—100
100—200
200—300
300—400
51
66
59
58
400-500
30
These e v e n t s l i e c l o s e r to t h e r e e f p la n th a n th o s e ^.n th e
g e n e r a l v e r t i c a l d i s t r i b u t i o n o f f i g u r e 16.
Table V shows
th e d i s t r i b u t i o n o f th e d i s t a n c e s betw een th e f o c i of s e i s m i c
e v e n t s a n d t h e c e n t r e s of damage which c o in c i d e w ith them;
s i n c e so many d i s t a n c e s l i t betw een 300 f e e t and 500 f e e t ,
i t means t h a t a number of e v e n t s which c o in c id e d w ith
damage w ere n - a l l y u n r e l a t e d to t h e damage, p a r t i c u l a r l y i n
th e c a s e o f s m a ll s e is m ic e v e n t s .
— 85 —
F i g u r e 34b shows th e d i u r n a l d i s t r i b u t i o n o f th e
s e is m ic e v e n t s which c o in c i d e w ith damage.
This d i s t r i b u t i o n
xs s i m i l a r t o t h a t o f Fxgure 28 and d i f f e r e n t from t h a t o f
F i g u r e 3 4 a , and c o n firm s t h a t th e o f f i c i a l " r o c k b u r s t
r e p o r t s " w ere b ia s e d to-vards f r i g h t e n i n g i n s t a n c e s o f
damage.
The main c o n c l u s i o n from t h i s s e c t i o n i s t h a t most of
th e damage o c c u r s unaccompanied by s e is m ic e v e n ts o r th e
v i o l e n t r e l e a s e o f e n e rg y .
v i o l e n t dammg
This im p lie s t h a t th e non­
i s due to th e c o l l a p s e c f ro c k t h a t has
a l r e a d y been f r a c t u r e d .
The o nly prcv. n t a t i v e measure
a g a i n s t t h i s damage i s t c red uce t h e d e g re e o f f r a c t u r i n g
around t h o e x c a v a t i o n and t h e o n ly re m e d ia l measure i s t o
improve th e s u p p o r t i n th e s t o p c s . At Harmony, n i n e - p o i n t e r
p a ck s a t 8 f t . 8 i n . c e n t r e s c o n s i s t i n g o f 2 f t . 8 i n .
c h o ck s have been u sed i n non . a l a t o p e s .
However, a t
p r e s e n t , t h e y a r t now u s in ; th e same n i n e - p o i n t e r pa ck ,
bu t w i t h c o n c r e t e b r i c k s r e p l a c i n g e very a l t e r n a t e row
o f tim b e r;
t h i s pack forms a more r i g i d s u p p o r t
(P e t e r s e n and Bo t h a '
.
The h a n g in g w a ll c o n d i t i o n s
have im proved n o t i c e a b l y w ith th e new s u p p o r t, and i t i s
a n t i c i p a t e d t h a t th e r e w i l l be fe w er r o c k f a l l s i n th e
fu tu re .
The d e g r e e o f f r a c t u r i n g i s d e p en d e n t on t h e
o n c c n t r n t i o n s ahead o f t h e f a c e , and t h e r e f o r e
s t r e s s cone
u s by c o n t r o l l i ;n g
a l s o on t h e r a t e o f eenergy
n e r g y r e l e a s e , th
thus
th e r a t e oo ff ee nn ee rr gg yy rr ee ll ee aa ss ee ,, th e e x t e n t co f f r a c t u r i n g can
he c o n t r o l l e d .
I t has , 1 eady been shown t h a t damage
l a d i r e c t l y r e l a t e d t o t h r r a t e o f e n erg y r e l e a s e .
/ r.:tch-mlam o f . . . .
M echanism o f S r l a K l c Ev r ^
I t h a s been shown t h a t o n ly a minute f r a c t i o n of t h e
e n e rg y r e l e a s e d a p p e a r s i n a v i o l e n t form., t h e r e f o r e t h e r e
must be a l a r g e s c a l e mechanism fo r d i s s i p a t i n g th e b u lk o f
th e energy s t a b l y .
The v i s c o s i t y of h ard ro c k i s f a r too
h ig h t o d i s s i p a t e any a p p r e c i a b l e amount o f energy i n t h e
tim e s c a l e s common i n m in in g , c o n se q u e n tly t h e o n ly way in
w hich en erg y can be d i s s i p a t e d i s by d e v e lo p in g o r c a u s in g
movement on f r a c t u r e s u r f a c e s .
Most p l a s t i c b e h a v io u r i n
har'd r o c k can be a t t r i b u t e d to the growth o f numerous s m a ll
c r a c k s ( G r i f f i t h c r a c k s ) , w h ile t r u e p l a s t i c b e h a v io u r i s
n e g lig ib le .
I n p ro d u c in g f r a c t u r e s u r f a c e s , energy can be
d i s s i p a t e d i n t h r e e fo rm s, nam ely , k i n e t i c e n e r g y , f r i c t i o n a l
e n e rg y and s u r f a c e en erg y w hich in c l u d e s p l a s t i c d e fo rm a tio n
a t crack t i p s .
At t h i s s t a g e i t i s w o rth w h ile t o review some o f t h e most
r e c e n t work on ro ck f r a c t u r e .
In a com prehensive a n a l y s i s ,
Hoek(1 0 ) h a s shown t h a t th e G r i f f i t h ' s Oracle Theory, m o d ified
f o r c l o s e d c r a c k s u n d e r c o m p re ssio n , s a t i s f a c t o r i l y p r e d i c t s
t h e o n s e t o f c r a c k grow th u n d e r s t a t i c lo a d in g c o n d i t i o n s .
The o n s e t o f c ra c k g ro w th i s e x p re ss e d by
t - U6n - -
(
V2
- V)
(5)
w here t - s h e e r s t r e s s p a r a l l e l t o c r a c k s u r f a c e s
o = s t r e s s norm al t o c ra c k s u r f a c e s
n
u = c o e f f i c i e n t o f f r i c t i o n between crack s u r f a c e s
o. = t e n s i l e s t r e n g t h o f rock
t o = u n i a x i a l c o m p re ss iv e s t r e n g t h o f r o c k ,
c
- 87 E q u a tio n ( 5 ) i s d e p e n d e n t on th e o r i e n t a t i o n o f th e c r a c k s
and t h e c r a c k s most l i k e l y to f a i l have an o r i e n t a t i o n
g iv e n by
t a n 26 = ^ / u
w here 9 = t h e a n g le betw een th e crack s u r f a c e s and th e
maximum p r i n c i p a l s t r e s s .
G r i f f i t h ' s t h e o r y p r e d i c t s t h a t ro c k f a i l s un d er
s t r e s s c o n d i t i o n s i n v e r s e l y p r o p o r t i o n a l to the s q u a r e r o o t
of th e crack le n g th .
B r a c e ( 2 3 ^ has shown t h a t th e t e n s i l e
s t r e n g t h o f s e v e r a l ty p e s o f ro c k i s p r e d i c t e d by th e
G r i f f i t h ' s th e o r y when th e c r a c k l e n g t h i s ta k e n a s th e
maximum g r a i n d ia m e te r ,
an'' i n t h e c a s e o f li m e s t o n e , th e
t e n s i l e s t r e n g t h i s i n v e r s e l y p r o p o r t i o n a l to th e s q u a r e
r o o t o f th e maximum g r a i n d i a m e t e r .
E q u a tio n (5) t h e r e f o r e
can be w r i t t e n i n th e f jr m
c =
11
( t - UOn ) 2
.....
(7)
w here 2c = c r a c k l e n g t h
a = c o n sta n t
B race and nprr.b^lakis
^ and Hoek and Pientaw3k_i
h ave shown t h a t u n d e r c o m p re ss io n , c r a c k s do n o t grow a lo n g
t h e i r own l e n g t h , b u t grow i n a d i r e c t i o n such t h a t th e y
te n d to become p a r a l l e l w ith t h e d i r e c t i o n o f th e maximum
p rin c ip a l . t r e e . .
Cook and F a i r h u r g t ^ 1 have used t h i s
phenomenon t o e x p l a i n th e f a i l u r e mode , . s u i t i n g I n th e
fo rm atio n o f s la b s p a r a l l e l to f r e e s u r f a c e s .
They have
a l s o shown t h a t t h i s s t a b l e o r n o n - v l o l e n t f a i l u r e mode i s
d e p e n d e n t on th e method o f l o a d i n g o f th e r „ o k .
/ In a n a l y s i n g . . . .
I n a n a l y s i n g th e en erg y changes a s s o c i a t e d w i t h th e
e x t e n s i o n o f G r i f f i t h ' s c r a c k s , Cbok(15) h as shown t h a t
t h e r a t e a t w hich energy i s s u p p lie d to th e ro c k by the
l o a d i n g s y ste m d e te r m in e s w h e th e r the ro c k f a i l s v i o l e n t l y
or n o n -v io le n tly .
He a l s o shows t h a t u n d e r c e r t a i n
c o n d i t i o n s , the r o c k can f a i l s p o n ta n e o u s ly .
Since t h i s
work i s h i g h l y p e r t i n e n t to th e r o c k b u r s t problem i t has
been examined i n g r e a t e r d e t a i l , and extended s l i g h t l y .
The s t r a i n e n e rg y s t o r e d around an i n f i n i t e l y lo n g
s l i t - l i k e c ra c k o f w id th 2 c , and i n a p la n e s t r a i n , t e n s i l e
stre ss fie ld ,
p e r 2c l e n g t h o f c ra ck i s given by
Ws l ” 71 ^~I~
^
°2
.....
f 0rowan( 2 7 ) )
w here v = P o i s s o n 's R a tio
G =
Modulus o f r i g i d i t y
o =
t e n s i l e s t r e s s i n a d i r e c t i o n normal
to c r a c k s u r f a c e s .
The e n e r g y stored around a penny-shaped c ra c k o f d ia m e te r
2c i n a t e n s i l e s t r e s s f i e l d is g iv e n by
*
s2
4
3
,2 03
( W
2 8))
G
The energy stored around a s l i t - l i k c c r a c k i n a p la n e
s t r a i n com pressive s t r e s s f ie ld pur 2c l e n g t h of c ra c k
i s g i v e n by
w
„ 1 :i - ^ 1
s3
2
G
o5
( S t a r I;( : ‘, ) )
w here T - e h e ir s t r e s s p a r a lle l w i t , th e c ra c k s u r f a c e s .
- 89 -
The e n e r g y s t o r e d around t h e s l i t - l i k e c ra c k s i s 5n/ 4 tim es
t h e e n e r g y s t o r e d around a penny-shaped c r a c k i n a t e n s i l e
s tre ss fie ld .
T h is r a t i o w i l l be a l n o s t t h e same i n
c o m p re s s iv e s t r e s s f i e l d s , d i f f e r i n g only b y a f r a c t i o n o f
P o i s s o n ' s R a t i o , which i s i t s e l f much l e s s th a n v i t y .
T h e r e f o r e , i t i s assumed t h a t the en erg y s t o r e d tnjurai a
p e n n y -s h a p e d c ra c k i n a co m pressiv e s t r e s s f i e l d i s g iv e n by
W3 =
j
^ "g V)t2
c ".................................
(E)
F o llo w in g an argum ent i d e n t i c a l w ith t h a t giv en by
Cook^1 \
th e e n e rg y s t o r e d when t h e r e i s f r i c t i o n betw een
th e crack
su rfaces is
Ws =
I
^ (T
1 lT
- uon ) ' c'
..........
(9)
w here ^ = c o e f f i c i e n t o f f r i c t i o n ,
0n = s t r e s s norm al to c ra c k s u r f a c e s
and th e e n e rg y d i s s i p a t e d i n f r i c t i o n as th e c ra c k s u r f a c e s
move r e l a t i v e t o e a c h o t h e r a s the r o c k i s lo ad ed from z e ro
is
Wp =
f
^
~ -'y l (T
- uon ) pon c-
..
(10)
I f t h e r e a r e n c r a c k s p e r u n i t volum e, arid i f th e i n t e r ­
a c t i o n o f c r a c k s i s ig n o r e d , th e t o t a l e n e rg y s t o r e d around
c r a c k s and d i s s i p a t e d i n them as th e rock i s lo a d e d , i s
(Wq ♦ W-) n - f
(1 - v l n c 5 ( t - Udn ) r
.........
(11)
G
The e n e rg y s t o r e d i n an e l a s t i c m a t e r i a l without, c ra c k s
u n d er p la n e s t r a i n c o n d itio n s is
i (I ~ ^
WE ‘ 4
_ f>
k
+1
••••• (JaO
fie^
G
l o r e o1 = maximum p r i n c i p a l s t r e s s
k
c I n i rum v r i : .
i f
i
3 ti- -.S£
== maximum p r i n c i p a l s t r e s s
=
^
)
Thus t h e t o t a l en erg y per u n i t volume s u p p lie d to a m a t e r i a l
c o n t a i n i n g G r i f f i t h ' s c ra c k s i s
"
"
U
1
-
1-v
+
1
+
#
■>
no)
(T
_
*0
n
)
1
/2 C i
e 1
+
■ 1/2 o 1
w here
2k
-
a
I
°1
/ 2 o3
e 3
+ ke^)
and e^ a r e the p r i n c i p a l s t r a i n s i n th e m a t e r i a l
c o n ta in in g c ra c k s .
Now
= 1 / - , c1 (1 - k) Sin 29
t
°n = 1 / 2 o 1 (1 + k) - 1/ 2 o 1 (1 - k) Cos 29
and
r - uo
i s a maximum when t a n 29= —
n
Thus t h e e q u a t i o n f o r W can be r e w r i t t e n in t h e form
G1 + k c 3 = °1
f k J - 2k l i r + 1 +
{ (1 - k ) 2 - (1 - k2 )
= & = }]
/ 1 +
( 12)
E q u a tio n
-
(12)
is
o n ly v a lid
yrI i Z < k <
V, + p n ~ i?
sin c e
t
-
for
slip
can
pon > 0,
o
> 0.
of
str a ig h t
as
in
+ v
o n ly
o c c u r on th e c r a c k s u r f a c e s .h e n
and s i n c e
fr ic tio n
can o n ly o ccu r .h e n
F or k c o n s t a n t , E q u a tio n
F ig u r e
lin e s
M ie n 0% i s
(1^') y i e l d s
p lo tte d
a la m ily
n g a in st
'35.
/ FIGURE 35
t
k e ,,
,
2~j
o
(t ♦ l it ) X161
FIGURE 35
GRIFFITH'S LOCI UNDER DIFFERENT
LOADING CONDITIONS
- 92 -
T h, p r e s e n c e o f c r e e k s e f f e c t i v e l y re d u c e s th e r i g i d i t y of
th e m a t e r i a l .
I f t h . v a lu e o f c a t f a l l u r * i s s u b s t i t u t e d i n e q u a tio n
( 1 2 ) , a f a m ily o f c u rv e s r e s u l t which r e p r e s e n t the o n s e t of
c r a c k g r o w th .
c, +kc, = n,
tvi
S u b s t i t u t i n g (?) i n (1 2 ) y i e l d s
f k 2 - 2k
+ 1
u
X—V
+ 2 7 na? (1 - k )
_________ _
3 y ! + u 2 { ( ! - k) ^ ! 4 ^2 - (1 + k) d) ’ o,*
= 0' l i i r i ^
+ v ^
.........
(13)
The c u r v e s d e f i n e d by e q u n tic n U 3 ) and shown i n F ig u re 35
h av e b e en c a l l e d G r i f f i t h ' s : c c i .
Cook(lC’ ) h a s shown t h a t
when th e s l o p e o f th e G r i f f i t h ' s Locus i s n e g a t i v e , a d d i t i o n a l
e n e rg y h a s t o be s u p p l i e d to th e ro c k by th e lo a d in g system
t o c a u s e t h e c r a c k s to p r o p a g a te , and v i o l e n t f a i l u r e only
r e s u l t s i f en erg y i s s u p p lie d n t a r a t e g r e a t e r th an t h a t
(15)
which t h e ro c k c a n a b s o r b . Cook' ' h a s d e f in e d b r i t t l e
f a i l u r e a s f a i l u r e o c c u r r i n g when t h e G r i f f i t h ' s lo c u s i s
p o s i t i v e , s i n c e i t a p p e a rs t i r t in t h i s c o n d i t i o n ro c k can
f o i l s p o n t a n e o u s l y , r e l e a s i n g th e re d u n d a n t s t r a i n energy as
k in e tic
energy.
The G r i f f i t h ' s l o c u s , however, o n ly d e s c r i b e s
t h e o n s e t o f c r a c k growth and n o t changes t h a t ta k e p la c e
(25)
a f t e r c r a c k e x t e n s i o n . Hcek and PieniawBiti
have shown
t h a t c r a c k s do n o t p ro p a g a te a lo ng t h e i r own l e n g t h , but
te n d t o grow i n a d i r e c t i o n a p p ro a c h in g
t h a t o f the maximum
p r i n c i p a l s t r e s s , c o n s e q u e n tly (5) uoes
n o t a p p ly a f t e r
c r o c k s h ave s t a r t e d t o grow.
The r e - o r i e n t a t e d c r a c k s
more s t a b l e so t h a t n o n - b r i t t l c f a i l u r e
the
re
may s t i l l o c c u r
when t h e G r i f f i t h ' s Locus i s p o s i t i v e .
Even i f t h e d e t a i l s o f t h e above a r g u m e n t a r e i n c o r r e c t ,
in p r i n c i p l e a c u rv e such as the G r i f f i t h ' s lo c u s e x i s t s .
F o r th e p u rp o s e s o f t h i s d i s c u s s i o n , i t i s o n ly n e c e s s a ry
/
to note
....
t o n o t* t h a t c e r t a i n m a t e r i a l s c o n ta i n in g numerous c ro c k s
may e x h i b i t b o th s t a b l e and b r i t t l e f a i l u r e , d e p end ing „ „
th e lo a d in g c o n d itio n s .
The b r i t t l e f a i l u r e of rock
r e p r e s e n t s a n i n t e r e s t i n g p o s s i b i l i t y f o r th e mechanism o f
r o c k f c u r s ts .
A volume o f ro c k co uld s p o n ta n e o u s ly become
w eaker by b r i t t l e f a i l u r e , sc t h a t th e s u rro u n
would s u d d e n ly c o n v e rg e on t h e f a i l e d rock
energy,
also,
tn g rock
and produce k i n e t i c
th e s t a b l e f a i l u r e o f ro c k c o uld a c c o u n t f o r
th e enormous amounts o f energy d i s s i p a t e d s t a b l y i n m ining
e x c a v a tio n s.
The G r i f f i t h ' s Locus does not n e c e s s a r i l y d e te rm in e when
b r i t t l e fa ilu r e occurs;
how ever, i t can be used to i n d i c a t e
t h e more i m p o r t a n t l o a d in g c o n d itio n s and rock p r o p e r t i e s
which r e s u l t i n b r i t t l e f a i l u r e .
From (1 3 ) , th e G r i f f i t h ' s
Locus i s v e r t i c a l when
0/
= 5 | ..................................................................
(14)
S u b s t i t u t i n g (14) i n (13) y i e l d s
‘ ' 7 * 0 = (1 - a !
oi y
20
| p
5
......
a?)
and s u b s t i t u t i n g (1 5) i n (12) y i e l d s
_______________3 ( 1 — 2k 1-v + k 8)
E q u a tio n (1 6 ) g i v e s t h e v a l u e o f n c J when th e G r i f f i t h ' s
Locus i s v e r t i c a l .
B rittle
f a i l u r e c a n o n l y o c cu r when n c ’
i s l e s s t h a n t h a t g i v e n by (16)
/ FIGURE 36
FIGURE 36
GRAPHS SHOWING THE CRITICAL VALUES
OF nC5 .
BRITTLE FAILURE CANNOT OCCUR
WHEN nC^ L IE S ABO/E THE < RAPHS.
- 35 F ig u r e 36 ahowe th e c r i t i e & l v a l u e , o f n o ' f o r d i f f e r e n t
c o e f f i c i e n t , o f f r i c t i o n and p r i n c i p a l , t r e „ r a t i o , .
A,
k i n c r e a s e s , n c 3 h a s to be l a r g e r f o r s t a b l e f o i l u r e to
o c c u r , end s i n c e the c r i t i c a l v a lu e o f n c 3 ap pro ach es i n f i n i t y ,
i t i s a lw a y s p o s s i b l e t o f i n d a s t r e s s f i e l d which w i l l r e s u l t
in b r i t t l e
fa ilu re ;
however, th e o e j n i t u d e o f t h i s s t r e s s
f ie ld m s t a lso in c re a se .
M te n d t o bo n o re b r i t t l e .
Rock ty p e s w ith a h ig h e r v a lu e of
For dyke n o t o r i a l p
bout 1 .5
and f o r W itw a te rs ra n d q u c r t z i t e p i s about 1 (fjoek ^1 0 ' >f
which c o u ld a c c o u n t f o r th e tendency o f ro c ic b u rs ts t o o c cu r
n ear dykes.
To form no me id e a o f the maximum v a lu e o f n c 3 t h a t can
bo fou nd 4n r o c k s , c o n s i d e r penny-shaped c ra c k s of d ia m e te r
2c l y i n g a t t h e g r a i n b o u n d a rie s a* ,u b ic g r a i n s o f s i z e 2 c .
Each cube i s i n c o n t a c t w ith s i x c r a c k s , and each c ra c k i s
i n c o n t a c t w ith two c u b e s ;
th u s t h e r e a r e t h r e e c r a c k s p e r
volume o f cube and t h e r e f o r e n c 3 = ^ / 8 .
T h is v a lu e hub been o v e r - e s t im a t e d s i n c e n e ig h b o u rin g
c r a c k s would be to u c h in g each o t h e r and s i n c e a l l c r a c k s
would n o t be a c t i v e .
nc3 = 0 .1 .
0 .1 ;
A more r e a s o n a b le e s ti m a te i s
h u refore
The c r i t i c a l v a lu e g iv e n by (16) i s g r e a t e r th a n
h o w e v er, t h i s v r l u e has a l s o been o v e r - e s t i m a t e d s i n c e
th e G r i f f i t h ’s Locus m e re ly r e p r e s e n t s th e i n i t i a t i o n of
c r a c k g r o w th .
I t t h e r e f o r e seems p o s s i b l e t h a t a ro c k such
a s q u a r t z i t a may e x h i b i t both b r i t t l e and n o n - b r i t t l e f a i l u r e ,
s i n c e th e c r i t i c a l v a lu e o f n c 3 may be f a i r l y c l o s e to 0 .1
when a l l o w a n c e s a r e made f o r ch^nge.i in t h e d i r v c t i j n o f
c r a c k prop ug t i o n .
/ S t . d i e Energy. . . .
g tc .b l -' Sn^rgLV D isaip , +i
I t h a s been i n d i c a t e d t h a t th e energy c o u ld be
d i s s i p a t e d by c a u s in g th e s t a b l e growth o f numerous c ra c k s
and t h i s p o s s i b i l i t y i s now i n v e s t i g a t e d .
Cook
h^a d eterm in ed th e energy s t o r e d around a
B l i t - l i k e c ra c k and th e energy d i s s i p a t e d i n f r i c t i o n a s t h e
c r a c k i s a llo w e d t o e x ten d i n ro c k un d er l o a d .
M odifying
t h i s e q u a t i o n f o r penny-rhr.pod c r a c k s y i e l d s
(w . ♦ «„> ■ - §
( r ,
v )
(I?,
Wljen k ~ f), the c r a c k can o nly extend when Oi r e a c h e s the
u n i a x i a l c o m p re ss iv e s t r e n g t h .
Thus f o r k = 0 and p = 1
(17 ) becomes
(W8 + Wp ) ' = |
^ c 5 0c ‘ ( . 2 0 7 ) 1
(18)
I f k > 0 (Wy + Wp) ' w i l l be l e s s th a n t h a t g iv e n by (1 8 ) .
I n a d d i t i o n , energy has to be p ro v id e d to d e v e lo p th e f r e e
s u r f a c e s o f th u c r a c k and t h i s s u r f a c e e n e rg y i s
W^, = 2n
c2 T
where T = f r e e s u r f a c e e n e r g y / u n i t a r e a
T h e re ! r e
(W3 + WF ) ' = 2800 c t o 280 c
where v = 0 . 1 r>
G = 5 x 10' p . s . i .
T = 6 x 10"* t o 6 c 1 0 " ’ l b . i n / i n 2,
c i s in i n c h e s .
I n W i t w n t e r e r a n d q u a r t z i t e th e mnxiriuja g r a i n s i z e , -n,l
t h e r e f o r e th e e f f e c t i v e c ra c k s i z e , v a r i e s from
to 1 in c h .
/1 0 0 inch
Thus th e f r e e s u r f a c e enor&r i s s i g n i f i c a n t
o n ly i n t h e c a s e o f v e ry s m a ll c r a c k s .
In th e f o ll o w i n g
d i n c u a a l o n on th o en erg y d i s s i p a t e d , I t I s Ig n o re d , s i n c e
i t can r e s u l t i n an e r r o r o f only a sm a ll f a c t o r .
/ In # # * *
- 97 I n an ide<_l longw^lj. 8t o p e , the; QUxiQun amount o f energy
t h a t con be r e l e a s e d f o r each volume v mined i s
WR = °o v
(20)
where a Q = v e r t i c a l v i r g i n s t r e s s .
For e a c h volume v ^ in e d , a volume V o f rock must f o i l
t o d i s s i p a t e thv r e l e a s e d e n e r g y .
Suppose th e rock c o n t a i n s
th e maximum number o f c r a c k s end suppose t h a t th o s e c r a c k s
d o u b le i n s i z e so t h a t th e rock becomes alm o st in c o m p e te n t,
th e maximum amount o f energy t h a t can be d i s s i p a t e d i n t h e
volume V by s t a b l e c ra c k grow th i s
(Wg + WF ) ' nV = ( . 2 0 7 ) 2 x |
n ( 2 c ) ' 0C* V
T h is e n e rg y must e q u a l WR, so t h a t V r e p r e s e n t s th e minimum
volume o f r o c k t h a t c o u ld p o s s i b l y d i s s i p a t e t h e e n e rg y .
3o0 0
I h u " v * 0 .3 4 x 2 (1 - v) oc = n o ’
<21)
F o r t y p i c a l v a l u e s e n c o u n te re d a t H rmony,
oo = 6000 p . s . i .
0 = 5 x 10* p . s . i .
v = 0.15
e r ~ 3 0 ,0 0 0 p . s . i .
n c ’ mnx - ° - 1
th e n V = 1700 v
T h is i s i m p o s s i b l e .
I f th e s t o p in g w idth i s 4 f e e t , th e n
th e f a i l e d zone would have t o ex ten d from 3400 f e e t above
t o 3400 f e e t below t h e e x c a v a t i o n .
T h e r e f o r e t h e b ulk o f
th o e n e rg y r e l e a s e d i s n o t d i s s i p a t e d by the grow th of
numerous G r i f f i t h ' s c r a c k s .
The b a e l e m.,ch=nien o f energy d i s s i p a t i o n must be i n
f r i c t i o n , s ' n e e s t r e s s o o n c e n t r c t l o n s oround c r o c k s , e u r f o c e
e n e r g y , v i s c o u s end p l a s t i c e f f e c t s con o n ly a cco un t f o r o
s m a l l f r a c t i o n o f t h e energy d i s s i p a t e d .
/
Tt
Jl3 • • • •
- 98 I t i a b col
phenomenon t h a t the ro c k s u r r o u n d in g an
e x c a v a t i o n ia b ro k e n i n t o alm o st p a r a l l e l s l a b s which s t r i k e
i n a d i r e c t i o n n e a r l y p a r a l l e l w ith th e f a c e ,
ih e s l a b s a r e
known to move r e l a t i v e t o each o t h e r and must t h e r e f o r e
d i s s i p a t e en erg y i n f r i c t i o n .
The f r a c t u r e p la n e s which
s e p a r a t e t h e s l a b s a re commonly c a l l e d s h e a r p la n e s ;
th e
mechanism o f th e developm ent o f th e s e f r a c t u r e p la n e s i s
n o t known, b u t i t c o u ld be t h e s la b b in g mechanism proposed
by Cook and la i r h u r s t '' h .
I t i s no t su g g e s te d t h a t th e
f r a c t u r e zone around th e w orking fa c e and th e ene^py
d i s s i p a t i o n mechanism i s sim ply one of p a r a l l e l s l a b s moving
r e l a t i v e t o e ach o t h e r , b u t i t i s shown t h a t a t m o d e ra te ly
low s t r e s s l e v e l s and a llo w in g sm all movements, t h e energy
r e l e a s e d c o u ld be d i s s i p a t e d i n a c o m p a ra tiv e ly s m a ll
volume o f f r a c t u r e d r o c k .
C o n s id e r a volume of r o c k , V, which i s broken i n t o
s l o b s o f a v e r a g e t h i c k n e s s t , and which d i s s i p a t e s the
e n e rg y r e l e a s e d by mining a volume, v .
Let th e a v e ra g e
f r i c t i o n a l f o r c e a c r o s s th e s l a b s u r f a c e s oo pon and the
a v e r a g e r e l a t i v e d is p la c e m e n t between s l a b s bi d .
Thus
th e e n e rg y d i s s i p a t e d i n f r i c t i o n i s
Wf = p 0n d
In th e
‘^
c a s e o f a n i d e a l lo n g w a ll
re le a se d
by m in in g a volume v i s
s t o p e , t h e maximum energy
g iv e n by (2 0 ) , end f o r
s t a b l e e n e rg y d i s s i p a t i o n VR = Vf , thus
v
If u « i
oo
0
sto p ir* L L
t
..........
(23)
= 0 r , t = 2 i i n c h , d * \ in c h , and th e
i s 4 f e e t , t h e n V - ^ h n d t h , f r a c t u r e zone
ne ed o n ly e x t e n d 10 f e e t i n t o the h a n g in g w n ll and 10 f e e t
in to th e fo o tw a ll.
„ l s c o nclu dv d t h a t th « b u lk o f t h . o n - r g , r o l . . . . d
c o u ld be 41. b l p o t c d by f r i c t i o n I n 4 nm cll f m o t u r e to ne
a ro un d th e e x c a v a t i o n .
/ U n s ta b le . . . .
- 99 U n s ta b le R c lc a so n f LntT.^
I t i s n t c e s s a r y t h r t t h e f r a c t u r e zone crounl th e fa c e
must advance c s th e f a c e a d van ces end th e e x te n t o f t h i s
zone must re m a in s u f f i c i e n t l y l a r g e so t h a t the r e l e a s e d
en erg y c_.ii be d i s s i p a t e 1 s t a b l y .
I f f o r any r e a s o n th e
f r a c t u r e zone i s p re v e n te d from ad v an cing n o rm a lly , the
s t r e s s c o n c e n t r a t i o n s i n th e s o l i d rock ctihecd of th e fa c e
become h i g h e r and th e volume o f th e f r a c t u r e d ro c k becomes
s m a l l e r a s th e f a c e a d v a n c e s .
E v e n tu a lly t h i s f r a c t u r e zone
must g row , and s i n c e th e s t r e s s c o n c e n t r a t i o n s i n th e s o l i d
ro c k a r e . h ig h e r , t h e r e i s a g r e a t e r tend ency f o r b r i t t l e
f r a c t u r e to o c c u r , accompanied by th e r e l e a s e o f k i n e t i c
energy.
G e o lo g ic a l i r r e g u l a r i t i e s can a f f e c t t h e advance o f
th e f r a c t u r e z o n e .
For exam ple, f r a c t u r e i n n dyke w i l l
a lm o s t c e r t a i n l y o ccu r a t j t r e s s l e v e l s h i g h e r th a n t h a t
i n th e s u r r o u n d i n g qu; r t z i t e , so t h a t th e developm ent of
t h j f r a c t u r e zone i n t c th e dyke w i l l be r e t a r d e d .
In
a d d i t i o n , dyke m a t e r i a l i s o f t e n more b r i t t l e th a n q u a r t z i t e .
There i s a l s o re a s o n to b e l i e v e t h a t a dyke has a " s t r e s s
s h i e l d i n g " b e h a v io u r ;
th e v i r g i n s t r e s s e s i n th e rock
n e a r a dyke can be d i f f e r e n t from t h a t i n th e ro c k a t th e
-icme d e p t h but f u r from the dyke, ( B a r r o n ).
The s t r e s s
f i e l d i s p r o b a b ly d i f f e r e n t i n th e ro ck on e i t h e r s i d e o f
t h e dyke and d i f f e r e n t from th e s t r e s s in th e dyke i t s e l f .
C l e a r l y t h e dev elo pm en t o f t h e f r a c t u r e zone around an
a d v a n c in g fa c e can be a f f e c t e d t o a f a r g r e a t e r e x t e n t
when th e f a c e i s p a r a l l e l w ith th e dyke th a n when i t i s a t
r i g h t a n g l e s t o i t , i n which c s s th e e x t e n t o f th e f r a c t u r e
zone c an be d i f f e r e n t on e i t h e r s i d e of t h e dyke.
When
t h e f a c e i s p a n 1 1 ,1 w ith th e dyke, t h e r e i s a g r e a t e r
d i s t u r b a n c e i n t h e f r a c t u r e zone * u n th e fa c e , dv n c e s (rom
th e low s t r e s s s i d e o f th e dyk e.
Mining e x p e r ie n c e does
i n f o c t show t h a t more d i f f i c u l t i e s a re e n c o u n te re d on ore
s i d e o f n dyke th a n th e o t h e r .
/ Le£Jot,r ............
L esser g e o lo g ic a l d ie c c n tln u ltlo e
th e
d e v e lo p m e n t
can
o c c u r on c i t h e r
r e d u c tio n
r e str ic t
and
in
in th e
th e
C ook
( 13)
'
a c r u d e ly
based
fa ile d
and
In
has
zone
b r ittle
or a j o i n t
a m e c h a n is m
above
fa sh io n
th e e x te n t
The a r g u m e n t f o r
c o u ld
fa v o u r a b le
c \u se d
by
fie ld s
and a
can
fa ile d
o f th e f a i l e d
th is
but
zone
m e c h a n is m
c o m p r e ssib ility
is
o f th e
zone.
o c c u r n ea r th e
rem oved
b e lie v e d
pi ne,
i n w h ich th e
tw o m o d e l s , t h e u n s t a b l e
fa ilu r e
w id e ly
stress
fa c e a d v a n ces sm o o th ly ,
s h a p e and t h e r e f o r e t h e
d ista n c e
be
d iffe r e n t
zone.
a r o ’ind t h e
p e r io d
m ust n e c e s s a r i l y
th at
o f a fa u lt
proposed
fra ctu red
th e
zone;
^ la o a f f e c t
s e p a r a t i o n b e tw e e n b e d d in g p la n e e
in c r e a se s.
on th e
fra ctu re
sid e
fractu re
fra ctu red
su d d e n ly
o f th e
can
e x c a v a tio n .
can o ccu r in
from th e
a vo lu m e
energy
It is
o f rock
r e le a se
fe a sib le
at
e x c a v a t io n w here th e s t r e s s
fo r such
f a ilu r e to
occur.
It
is
t h a t r o c k b u r s t s and e a r t h tr e m o r s a r e
shear or te n sile f r a c t u r e s .
/ V i s u a l Cbs r v ' t l o n s
so m e
fie ld
a lso
V is u a l Observ^t-iong
AG a p r e l i m i n a r y m e a n s t o d e term in e the mechanism o f
v i o l e n t e v e n t s , s o m e v i s u a l e x a m i n a t i o n s o f h a u la g e s wore
c a rrie d o u t.
T he
of s l a b b i n g o r f r a c t u r i n g around
egree
a h a u l a g e i s an i n d i c a t i o n o f t h e maximum s t r e s s e n c o u n te re d
i n th e l i f e o f t h e h a u l a g e .
Shear
frac tu re s or te n s ile
f r a c t u r e s c c u l d h e r e v e a l e d by ev iden ce o f r e c e n t movement
at
fra ctu re
or
jo in t
p l a n e s and by t h e p r e s e n c e
open
of
crack s.
A ll
b efore
th e
e x te n siv e
h a u la g e s
o th er
e v id e n c e
assum ed
stu p in g
fr a c tu r in g
to
far
A t H arm on y t h e r e
w a ll,
area.
2 S h a ft.
T h is
in te r se c ts
a t Bi
is
th e
at
h a u la g e
is
about
ly
from t h e r e e f
it
" h o le d
above r e e f.
end and t h e
through"
h a u la g e was
a lm o st c o m p le te
e x a m in a tio n
of
h a u la g e was b e in g u sed
c .
th e
th e
la r g e
reef;
it
A and t h e B a s a l R o e f
above r e e f
■r e a t
I t was d e v e lo p e d
s h a f t end,
D It
sir u lta n o o u s-
w ith th e r e s u l t
th a t
o f t h e m in e d -o u t a r e a when t h e
(c o a r s e h a tc h in g )
h a u la g e w as m ade.
h a u la g e was c o n c r e te lin e d
som e d u e t
h o n g in g -
a b o u t m idw ay .above t h e w o r k e d - o u t a r e a .
37 show s t h e e x t e n t
th e
th e
Level h a u l a g e ,
not p a r a l l e l w ith
about 200 f e e t
100 fe e t
could be
over a f a ir ly
37 show s the 1 1
t h e U p p er S h n le M arker a t
0 it
no
su r r o u n d in g r o c k .
o n ly one h a u la g e in
is
th e
severe
There was
o r s h e a r m ovem ent w h ic h
in to
F ig u r e
is
F ig u r e
obscured.
w h ic h f o r t u n a t e l y was d e v e lo p e d
m in ed -o u t
ra te,
around t h e h a u la g e was s o
open cra ck s
exten d
In
a b o v e them .
a h ig h en ergy r e l e a s e
' e a tu r e s were u s u a lly
of
d eveloped
a t Harm ony w e r e
to o k p la c e
b e lo w f a c e s w it h
s la b b in g and
th a t
f o o t w a l l h a u la g e s
w a lls,
g e o lo g ic a l f e a tu r e s .
from
but n ot
The f o o t w a l l
th e s h a f t
a s an a ir w a y ,
and w hen t h e
so
to
of
th e
The
t h a t t h e r e was
m rfflc ien t to o b sc u r e th e
/
pjoiuE 37
•■"BeiF
nnMPLETED.
- 103 Fr^rn «. uo th t. a h r i f t , t h e h a u l a g e w a s i n g o o d
c o n d itio n ;
h a u la g e
how ever,
in
a v ir g in
F rom t n e s h a f t
sla b b in g
w a lls
ste a d ily
t h e r e w as m ore s l a b b i n g th a n i n
stress
fie ld .
to
edge o f th e s h a f t p i l l a r
th e
becam e w o r s e ;
near th e
w e r e l a c e d w i t h c a b l e and a f a i r l y
o f r o c k b o lts
p illa r
had b een u s e d ,
a num ber o f
n ecessary
r o c k b o lts
w h ile
at
stresses
in
tlr
d ir e c tio n
sid e ­
dense p a tte r n
th e
edge o f th e s h a f t
had b e e n
T he c o n c r e t e i n
f o o t w a l l had num erous c r a c k s a c r o s s
reduced
th e
s h a f t th e
had s n a p p e d an d i t
tc i n s t a l l a r c h s u p p o r t .
a
it,
th e
w h ich i n d i c a t e s
o f th e
h a u la g e .
T h is
must b e t r e a t e d w i t h c a u t i o n , s i n c e c a l c i u m
o b se r v a tio n
used i n t h e c o n c r e t e and r e s u l t e d i n s e v e r e
c h l o r i d e was
Between C an d F t h e r e w e r e so m e j o i n t p l a n e s
sh r in k a g e .
f a u l t s o n w hich r a t h e r i n d e f i n i t e s i g n s o f m o v e m e n t
and
w ere
v is ib le .
by 2
mn. t o 5 mm., a n d c o i n c i d e w i t h c r a c k s i n t h e
co n crete.
The
jo in t
p la n e s ap p ear t o
T here w ere no s i g n s
of
h a v e o p e n e d up
s h e a r m ovem ent.
From th e edge o f th e s h a f t p i l l a r t o G, t h e c o n d i t i o n s
in
th e h a u la g e s t e a d i l y improved.
From
C t o D th e h a u la g e
was i n re m a rk a b ly good c o n d i t i o n w ith a l m o s t n o s l a b b i n g
of th e sid ew a lls.
s m a l l d y k es
v isib le .
Tb.
T h e r e were numerous j o i n t p l e n e s ,
nd f a u l t s on which no r e c e n t movement w a s
r ' :< ap
'
"
P '^ r c c tly s o l i d .
From D t o 3 th e s l a b b i n g i n th e h a u la g e g o t
p r o g r e s s i v e l y w orse and was so s e v e r e a t E t h a t t h e
a a c t i o n o f th e h a u la g e was e f f e c t i v e l y h a lv e d .
f e a t u r e s w ere o b scu red by s l a b b i n g ,
Most
however, n e a r E,
, n e r . w„e a v e r t i c a l dyke 3 f e e t wide w hich q u i t e c l e a r l y
had o p e n in g s a lo n g I t s s i d e s .
At t h i s p o i n t th e h s i l n g .
was a b o u t .50 f e e t noove th e e x c a v a t i o n .
f
1t
•
e *•
The o b s e r v a t i o n s
e x iste n c e
and
o f e x te n siv e
f o ” th e
c o n tin u o u s
m ost
e la stic
In g o in g
to
th e r e e f
r e g io n ,
se p a r a tio n
th is
s h e a r m ovem ents o r i
p la n e
No
a sile
ru p tu res,
th ey were c o n s is t e n t w ith a
rock m s s .
fiTom C t o D,
a d ista n c e
o f 100 f e e t norm al
was e f f e c t i v e l y t r a v e r s e d .
On t h e
V e n tila tio n
M arker.
t h e h m g i n g w a l l - l id n o t s h o w t h e
th ere r as d e f in it e ly
se p a r a tio n .
th e
p a rt,
in
no s i g n
In a l l
th is
o f b ed d in g p la n e
o t h e r hand, t h e s t r a i n m e a s u r e m e n t i n
S h aft
showed t h a t e x t e n s i v e b e d d i n g p l a n e
o c c u r re d b e t w e e n th e r e e f and t h e U p p e r S h a l e
s a t i s f a c t o r y e x p l a n a t i o n h a s b een fou n d f o r
d iscrep a n c y .
— 105 F i r s t M otion T h eo ry
The t h e o r y o f F i r s t Motions from s e is m ic s o u rc e s has
b een a u t h o r i t a t i v e l y d e a l t w ith b , Knonoff and O i l b e r t ( ? 2 ) .
They u s e dynamic d i s l o c a t i o n th e o ry to d e r i v e th e e la s to d y n a m ic
r a d i a t i o n from a s e is m ic s o u rc e .
The s e is m ic s o u rc e i s
v i s u a l i z e d a s a g e o m e t r ic a l d i s c o n t i n u i t y a c r o s s which t h e r e
e x i s t s a s u d d e n d i s c o n t i n u i t y i n e i t h e r one component o f th e
s t r a i n t e n s o r o r one component o f th e d is p la c e m e n t v e c t o r .
They show t h a t t h e r e a r e e i g h t in d e p en d e n t models.
I f th e
p la n e z = 0 form s th e g e o m e t r ic a l d i s c o n t i n u i t y , th e n th e
e i g h t in d e p e n d e n t changes which can o c cu r a r e ( i ) th e sudden
a p p lic a tio n of s t r a i n d is c o n tin u itie s in e
, e
X X
, e
J rjr
, e
Z Z
Z X
o r e zy a c r o s s t h e boundary and ( i i ) th e su dd en a p p l i c a t i o n
o f d i s p l a c e m e n t d i s c o n t i n u i t i e s i n ux , uy o r u ^ , a c r o s s t h e
b o u n d a ry .
a d i s c o n t i n u i t y i n th e n i n t h term exy were
If
s u d d e n ly a p p l i e d a c r o s s t h e s u r f a c e , no m otion would be
ra d ia te d .
A s e i s m i c s o u rc e can c o n s i s t of a l i n e a r c o m b in a tio n
o f any o f t h e s e r i g h t d i s l o c a t i o n ty p e s ;
nowever, i n p h y s i c a l
s o u r c e s o n e o f t h e s e d i s l o c a t i o n s w i l l p re d o m in a te .
The m a in c o n c l u s i o n s
p resen ted
r e su lts
tak en a s
th e
d isc o n tin u ity .
to
th e
and have been
fo r
P w aves are g iv e n .
The p l a n e z = 0
o f p r o p a g a tio n
o f th e s t r a in
The s y m b o l A w i l l
be used to
o r d isp la c e m e n t
rep resen t th a t
is s e n s it iv e
th e a m p litu d e o f t h e r a d ia t e d wave w h ich
th e d i r e c t i o n
r a d ia tio n
is
g e o m e tric ,1 d i s c o n t i n u i t y a n d t h e x d i r e c t i o n
th e d ir e c t io n
part o f
b e lo w
in a form m ore s u i t e d t o t h e p r e s e n t a p p l i c a t i o n .
O n ly t h e
as
are g iv e n
of
p r o p a g a tio n o f t h e w a v e , i . e . , A d e s c r i b e s
p a ttern .
The o t h e r s y m b o ls u se d a r e ,
/
(X
• • • •
a = P~wave v e l o c i t y
P - 3-wave v e l o c i t y
X = V e lo c it y o f p ro p a g a tio n o f th e d i s l o c a t i o n
yx ' Yy ^
„ 'ir e d i r e c t i o n c o s i n e s .
A ll th e s t r a i n d i s l o c a t i o n s have a s i m i l a r f i r s t m otion
r a d i a t i o n p a t t e r n which i s u n a f f e c t e d by t h e v e l o c i t y o f
p ro p a g a tio n .
\ z
These a re shown i n F ig u re 33 and a r e
’
\
z ■ 'y
The p a t t e r n s a r e t w o - lo b e d , th e f i r s t m otion in th e one
l o b e r e p r e s e n t s c o m p re ssio n and i n th e o t h e r i t r e p r e s e n t s
ra re fa c tio n .
These d i s l o a tio n s can r e s u l t from th e sudden
y i e l d i n g o r f a i l u r e of th e m a t e r i a l on one s i d e o f the
b o u n d a ry .
The d is p la c e m e n t d i s c o n t i n u i t y , uy , a l s o r e s u l t s
i n a p a t t e r n in d e p e n d e n t o f X and i s shown i n F ig u re 38.
T h is p a t t e r n Au
= yy y 7
i s f o u r - l o b e d , w i t h a l t e r n a t i n g lo b e s of co m pression and
ra re fa c tio n .
T h is ty p e o f d i s l o c a t i o n c o rre s p o n d s to s h e a r
movement i n a d i r e c t i o n a t r i g h t a n g le s t o th e d i r e c t i o n o f
p ro p a g a tio n .
The d is p la c e m e n t d i s c o n t i n u i t i e s i n u , and u , n re
d e p e n d e n t on X and th e r a d i a l on p a t t e r n s a r e shown I t
, l . m r e . 39 and 40 r e s p e c t i v e l y , f o r d i f f e r e n t v a lu e s o f X.
/ FIGURE 38
• 'Z
'
— Iu 7 —
\ Km Ae.,eX
yy
Zi
«K
y
t
\ , - x
\
,
-*
‘ X
i
s
K -XX
FIGURE >>
m
a
m
L
a_ _ _ _ _
z
X
>x
\
\
i
I
z
X-
X •oo
2p
\ - 2XX- ? X
FIGURE 3 9
RAREFACTION.
X
X
boo
X -2>9
X# ^
XbO
,
<
pigurb
»u
- T
- 110 -
V
= 2
+
Au
= i + J i _ r.
'
?p2
a* - p s
z
I n b o th c a s e s t h e p a t t e r n s d e g e n e r a te t o th e two lobed
p a t t e r n when X , 0 .
However, In p r a c t i c e , X has been found
t o be o f t h e o r d e r o f 1 / 2 p f o r most m a t e r i a l s .
Knonoff
and G i l b e r t ' X ) have shown t h a t i f t h e d i s l o c a t i o n e x ten d s
b i l a t e r a l l y o r r a d i a l l y a lo n g th e boundary s u r f a c e , th e f i r s t
m o tio n r a i a t i o n p a t t e r n becomes e q u a l to t h a t f o r X = ®.
Now t h e f i r s t m o tio n r a d i a t i o n p a t t e r n depends only on th e
v e ry l i r s t c h an g e s a t th e d i s c o n t i n u i t y s u r f a c e .
In p r a c t i c e ,
a d i s c o n t i n u i t y w i l l s t a r t a t a p o in t and d e v e lo p a p p ro x im a te ly
r a d i a l l y i n t o a d i s c o n t i n u i t y s u r f a c e , thus i t i s q u i t e l i k e l y
th a t d is lo c a tio n s in u
p a tte rn s fo r X = * .
and u
r e s u l t in t h e i r re sp e c tiv e
A d i s l o c a t i o n in ux c o rre sp o n d s to
s h e a r movement on a f r a c t u r e s u r f a c e p a r a l l e l w ith th e
d i r e c t i o n o f p r o p a g a t i o n , and a d i s l o c a t i o n in uz c o rre sp o n d s
t o th e s u d d e n p r o p a g a tin g e x p an sio n ( o r c o l l a p s e i f m u l t i p l i e d
by - 1 ) o f a l e n t i c u l a r c a v i t y , the e x p an sio n ( o r c o l l a p s e )
t a k i n g p l a c e i n t h e d i r e c t i o n o f th e normal t o th e p la n e of
th e c av ity w a lls .
The d i s l o c a t i o n i n u^ could correspond
t d a t e n s i l e r u p t u r e i n which c a s e n e a r l y a l l f i r s t m e tie r s
would be c o m p r e s s io n , o r i t could correspond to th e c o l l a p s e
o f f r a c t u r e d ro c k i n t h e e x c a v a tio n and in which c a s e n e a r l y
a l l f i r s t m o tio n s would be r a r e f a c t i o n .
The sud den f a i l u r e o f n volume o f rock can be re g a rd ed
a s th e a p p l i c a t i o n o f s t r a i n d i s l o c a t i o n s betw een two
su rfaees.
K nonoff and G i l b e r t ' 521 have g iv e n t h e th e o ry f o r
two d i s l o c a t i o n s
sep a ra ted
by a s m a ll d i s t a n c e , but have
o n ly a p p l i e d i t t o d i s l o c a t i o n s I n u , and e , z s i n c e they
/ c o n sid e re d
....
c o n s i d e r e d th e o t h e r d i s l o c a t i o n s u n l i k e l y i n e a rth q u a k e
m e ch a n ism s.
By a p p ly in g t h e th e o ry to la m in a r o r double
d is lo c a tio n s in e ^ ,
ly y and e ^ , i t i s found t h a t t h e
f i r s t m o tio n s i n a l l d i r e c t i o n s a re r a r e f a c t i o n and th e
p a t t e r n i s shown i n F ig u r e 41.
Vhen th e th e o r y i s a p p lie d t o double d i s l o c a t i o n s in e
xz
cy Z a f o u r lob ed p a t t e r n r e s u l t s as f o r uy i n F ig u re 38.
and
T h u s, i n g e n e r a l , when a volume o f ro c k su d d en ly f a i l s , t h e
f i r s t m o tio n p a t t e r n c o n s i s t s of a summation o f th e p a t t e r n s
f o r a l l ‘ i v e s t r a i n components.
The r e s u l t i n g p a t t e r n is
t h e r e f o r e p r e d o m in a n tly r a r e f a t i o n and i s independent o f the
v e l o c i t y o f p ro p a g a tio n .
T heory shows t h a t fo u r d i s t i n c t i v e f i r s t motion
r a d i a t i o n p a t t e r n s can a r i s e , and th e y a re summarised as
fo llo w s:
i ) F i r s t m otion com pression i n n e a r l y a l l d i r e c t i o n s .
T h is p a t t e r n can r e s u l t from a t e n s i l e r u p t u r e .
11) F i r s t m otion r a r e f a c t i o n i n n e a r ly a l l d i r e c t i o n s .
T h is p a t t e r n can r e s u l t from th e b r i t t l e
f a i l u r e of
a volume o f r o c k , o r th e c o l l a p s e of f r a c t u r e d ro c k
in th e e x ca v a tio n .
Ill)
Two-lobed p a t t e r n r e s u l t i n g from sim ple s t r a i n
d i s l o c a t i o n s o r d i s l o c a t i o n s i n ux and u^ when X
i s v ery sm a ll.
l v ) F o u r - lo b e d p a t t e r n w ith a l t e r n a t i n g lo b e s o f
c o m p re s s io n and r a r e f a c t i o n , a s s o c i a t e d w ith
sh ea rin g e f f e c t s .
/ FIGURE 41
FIGURE 41
FIRST MOTION PATTERN FOR DOUPlfi STRAIN DISLOCATIONS
IN e , e
and <9 . ALL FIRST MOTIONS ARE RAREFACTION
-
113 -
F i r s t M otion Rem,nto
About 30 p ercen t
o f th e
c h a r a c t e r w h ic h c o u ld
fir st
th is
m o tio n s
m o tio n s
hso sn em ergent
n o t be d i s t i n g u i s h e d
th a t w ere
c le a r ly .
O n ly
p e r f e c t l y d i s t i n c t w ere u sed
in
a n a ly sis.
It
is
p a th so
p o ssib le
th a t
se ism o m e te r
w ere
th e
is
o f in c id e n c e
ev en ts
a n g le
In th e
six
r e p la c e d
by h o r i z o n t a l
se ism ic a lly
w ith
ev en ts
of
was
th at
fiv e
p la n e ,
th e
r e g a r d le ss
r e la tiv e
m a jo r ity
th e
fou n d
se ism o m e te r s
fir st
in tro d u ced
se ism ic
se ism ic
th e
fir st
had a l o w s p e e d
th a t
in
co u ld
th e s i x
o f th e s e is m ic
fir st
w ere s e t up
m o tio n s
fr o m
be d is t in g u is h e d .
u sefu l
seism o m eters
e v e n ts n ear th e
reef
m o tio n s w as r a r e f a c t i o n ,
In 1 9 5 2 , fia n e .
o f th e e v en t
S S i l f f i S n an d
th e ir su r fa c e array o f s ix
on a V itw a terera n d
m o tio n s w ere
each
ta p e-reco rd er
such t h a t th e f i r s t
e x c a v a tio n .
to
A second
th e n etw orx a t
seism o m eter s t a t i o n s
o f th e
r a d ia lly
m o t io n s w ou ld be m ore d i s t i n c t .
103 f t . - l b s .
case
n etw ork
The t h r e e
o f th e m in e .
in to
th erefo re,
th e r e e f p la n e w ere
o f t h e m a g n itu d e o r o f th e p o s i t i o n
to
S t e n h o n *8 '
p arts
n etw ork w ith
th e
in
seism o m eters o r ie n t a t e d
a m p lifie r s
The o r i g i n a l
in
be u sed f o r
C o n seq u en tly th e
3 and 6 )
sta tio n
m a g n itu d e
show ed t h a t
(2 ,
p o r ta b le
each
h ig h g a in
o r ig in a l s e is m ic n etw ork ,
m ost a c t i v e
sta g e
on s u r f a c e ;
a curved
m o tio n d a ta
make m o r e s e i s m o m e t e r s u s e f u l .
se ism o m e te r s
In a d d itio n
th an 6 ^ ° t h e f i r s t
r e e f p la n e .
to
se ism o m e te r so
fo llo w
in c id e n c e o f th e waves a t a
s e is m o m e te r s c o u ld
v e r tic a l
a m p lify in g
of
w ere g r e a te r
n ear th e
was m o d ifie d
t h a t a s e i s m i c wave c o u ld
som ew hat u n c e r t a i n , t h u s , w h e n e v e r t h e a n g l e s
rejected .
n o m ore t h a n
th e
fir st
m in e 0 0 p e r c e n t o f t h e
r a r e fa c tio n .
f
Ip
"thi©
• • • •
- 114 -
I n t h e m o d ifie d s e is m ie n e tw o rk , th e f i r s t m otions
c o u ld be d e te rm in e d w i t h c e r t a i n t y on about 9 o r 10
s e is m o m e te rs f o r e a c h e v e n t .
This network was in o p e r a t i o n
f o r a montn and d u r i n g t h i s p e r io d 100 s e is m ic e v e n ts were
a n a l y s e d ; they c o n s i s t e d of some e v e n ts o f magnitude 1C^
4
,
and 10 f t . - l b s . , and a l l t h e e v e n ts g r e a t e r th a n 10 f t
lb s.
F o r 40 p e r c e n t of th e s e is m ic e v e n ts , th e d i s t i n c t
f i r s t m o tio n s w ere a l l r a r e f a c t i o n ;
a c e n tra l p ro je c tio n
o f one o f t h e s e e v e n ts i s shown i n F ig u re 42.
For 26 p e r­
c e n t o f t h e e v e n t s , one seism om eter showed d i s t i n c t
c o m p re s s io n w h ile th e re m a in d e r o f t h e d i s t i n c t m otions
w ere r a r e f a c t i o n .
In 23 p e r c e n t o f the c a s e s , o nly two o r
t h r e e s e is m o m e te rs showed com pressio n and t h e s e seism o m eters
w ere sp ac e d such t h a t th e y la y w i t h i n a cone w ith apex a t
t h e f o c u s , F ig u r e 43.
I n a l l c a s e s , the cone o f com pressive
m o tio n l a y a t an a n g le o f l e s s th a n 30
to th e r e e f p la n e .
The d i s t r i b u t i o n p a t t e r n of f i r s t motions f i t s n e i t h e r
th e f o u r - l o b e d p a t t e r n f o r s h e a r movements, n or th e n e a r ly
a l l c o m p re ss io n p a t t e r n o f a f a s t o r sy m m etrical t e n s i l e
ru p tu re .
S ince th e s e is m ic netw ork c o v e rs m ainly th e upp er
h a lf-sp a c e ,
i t co u ld be argued t h a t th e r a d i a t i o n p a t t e r n
i s i n f a r . tw o -lo b e d w ith th e r a r e f a c t i o n lo b e i n the upper
h a l f - s p a c e and t h e c o m pression lo b e i n t h e lo w er h a l f - s p a c e
where i t would n o t be o b s e rv e d .
The tw o-lo b ed p a t t e r n could
be p ro d u c e d by a sim p le s t r a i n d i s l o c a t i o n , a ve y slow
t e n s i l e r u p t u r e p r o p a g a t i n g v e r t i c a l l y a w a r d s o r a slow
s h e a r movement
p r o p a g a tin g
h o r i z o n t a l l y and u n i l a t e r a l l y .
A s im p le s t r a i n d i s l o c a t i o n I s an u n re a s o n a b le mechanism
s i n c e I t r e q u i r e s t h e e x t e n s i v e f a i l u r e o f th e rock
lo w e r n a l f - s p a c e .
The two r u p tu r e mechanisms a r e a l s o
A
Compression
O
Rarefaction
O'
z
<-
O'
O-
oFIGURE 4 2
A CENTRAL PROJECTION OF THE FIR ST MOTIONS OF A SEISMIC EVENT FOR WHICH ALL
THE OBSERVED FIRST MOTIONS WERE RAREFACTION.
THE + SIGN INDICATES THE
SEISMOMETERS THAT WERE IN THE UPPER HALF SPACE AND THE CIRCLE REPRESENTS
ta n 0 * 1 .
FIGURE 43
A
Com pression
O
Rarefaction
A CENTRAL PROJECTION OF THE FIRST MOTIONS RADIATED BY \ SEISMIC
EVENT FOR WHICH COMPRESSION WAS RADIATED IN A RESTRICTED DIRECTION.
THE BROKEN LINE REPRESENTS THE PROJECTION OF A HYPOTHETICAL COMB
AND THE CIRCLE REPRESENTS t e n 0 * 1 .
u n i l a t e r a l l y , p a r t i c u l a r l y a t t h e a t a r t of th e m p t u r e ,
t h e r e f o r e I t 1 , e x p e c te d t h a t t t e tw o-lobed p a t t e n , f o r a
r u p t u r e physicejL ly cann o t e x i s t .
The mechaniam . h i c h f i t a th e f i r s t motion p a t t e r n h e a t
i s t h e sudden f a i l u r e of a volume o f ro c k (double s t r a i n
d i s l o c a t i o n ) o r th e c o l l a p s e o f f r a c t u r e d rook In th e
e x ca v a tio n .
I t was th o u g h t t h a t f o r th o s e e v e n ts which r a d i a t e d
c o m p re s s io n th e d i r e c t i o n in which th e f i r s t m otions were
c o m p re s s io n m ight show a c o n s i s t e n t r e l a t i o n s h i p t o th e
e x ca v a tio n .
Most of t h e s e is m ic e v e n ts o c cu rred on re m n a n ts ,
so t h a t no s i g n i f i c a n c e could be a tt a c h e d to th e d i r e c t i o n
Ox c o m p r e s s io n ;
however, on any p a r t i c u l a r remnant the
e v e n t s te n d e d t o r a d i a t e com pression i n th e same d i r e c t i o n .
About 15 e v e n ts o c c u r re d on one dyke o f which 7 r a d i a t e d
r a r e f a c t i o n o n l y , th e re m a in d er r a d i a t e d com pression i n a
d i r e c t i o n a t a b o u t 45° t o the s t r i k e d i r e c t i o n o f t h e dy k e .
Seven p e r c e n t of th e s e is m ic e v e n ts d id not f i t any of
t h e s t a n d a r d p a t t e r n s and a p r o j e c t i o n of one o f t h e s e i s
shown i n F ig u r e 4 4 .
The f i r s t m otions cannot be s e p a r a t e d
i n t o f o u r com partm ents c o n ta i n in g com pression and r a r e f a c t i o n
by two s t r a i g h t l i n e s .
Since no s t r a i g h t l i n e s can be found
w hich co u ld form th e p r o j e c t i o n s of two p la n e s a t r i g h t
a n g l e s , t h e mechanism o f t h e s e e v e n ts c an n o t be a s h e a r
movement o r r u p t u r e .
e x h ib it fa u ltin g ,
I t i s noted t h a t e a rth q u a k e s t h a t
c o n s i s t e n t l y r a d i a t e th e f o u r - lo b e d p a t t e r n
o f F i g u r e 39 f o r X « • .
D u rin g th e p e r i o d t h a t th e m od ified network was i n
o p e r a t i o n , o n ly t h r e e seiem lo e v e n ts were lo c a t e d a t th e
Harmony S i l l •
/ FIGURE 44
A
Compression
O
R arefactio n
o
cr
cf
o*
NOT FIT ANY STANDARD PATTERN. THE CIRCLE REPRESENTS t a n 0 = 1 .
- 119 Those e v e n t s w ere a l l of m agnitude 10^ f t . _ i b s . , and a
number o f t h e f i r s t m o tio n , were i n d i s t i n c t sc t h a t th e
f i r s t m o tio n r a d i a t i o n p a t t e r was not c o n c lu s iv e .
The
d i s t i n c t f i r s t m o tion s of t h e s e e v e n ts , however, were more
f r e q u e n t l y c o m p re ssiv e th a n f o r th e e v e n ts n e a r th e
e x c a v a t i o n , and a l l could have f i t t e d th e fo u r-1 o b ed p a t t e r n
S i m i l a r l y , f o r th e e v e n ts lo c a t e d n e a r th e Harmony S i l l i n
t h e o r i g i n a l n e tw o rk , ab o u t 50 p e r c e n t of th e d i s t i n c t f i r s t
m o tio n s w ere o o m p rc ssiv e , and i n a l l the c a s e s , t h e f i r s t
m o tio n s c o u ld have f i t t e d th e f o u r -lo b e d p a t t e r n .
Thus
th e m echanism o f th e e v e n ts a t th e S i l l may have been a
s h e a r movement.
Cook and Hodgson^ ^
have su g g e s te d t h a t i n a s t e a d i l y
i n c r e a s i n g c o m p re ss iv e s t r e s s f i e l d i n r o c k . a com pressive
p u l s e i s a t t e n u a t e d more r a p i d l y th a n a r a r e f a c t i v e p u l s e .
I f t h e a t t e n u a t i o n i s s u f f i c i e n t l y g r e a t e r i n com pression,
a l l f i r s t m o tio n s would a p p e a r a s r a r e f a c t i o n .
However,
t h e r e w ere a few c a s e s i n w hich two seism om eters were in
l i n e w i t h t h e fo c u s and w ith one seism om eter much c l o s e r
t o t h e f o c u s th a n th e o t h e r .
Both seism om eters alw ays
showed th e same m o tio n , and in the c ase o f
c o m p r e s s ic n ,
t h e m o tio n was a s d i s t i n c t a t t o e f a r seism om eter as a t
t h e n e a r s e is m o m e te r.
T h e re fo re i t I s th o u g h t t h a t t h e
d i f f e r e n c e i n a t t e n u a t i o n betw een com pressive and r a r e ­
f a c t i v e p u l s e s la n o t s u f f i c i e n t t o n u l l i f y the f i r s t
m o tio n p a t t e r n s .
I n c o n c l u s i o n i t can be s a id t h a t t h e mechanism o f
s e i s m i c e v e n t s i s no t a t e n s i l e or s W a r r u p t u r e , but a
v o l u m e t r i c c o l l a p s e o f e i t h e r f r a c h i r e d ro c * o r roc* t h a t
s u d d e n ly f a i l s *
/
s p c c t r a l _ AL-qlyB,U.
•
S p e c t r a l A n al v a 1 b
The t h e o r y o f tU ja g a a s and S ta u d c r ( m
, ^ 0* be
a p p l i e d t o th e s e is ra ic e v e n ts , s i n c e the mechanism i s n o t
a s i m p l e u n i l a t e r a l l y p r o p a g a tin g r u p t u r e .
A more d e t a i l e d
a n a l y s i s f o r a p r o p a g a tin g v o lu m e tric c o l l a p s e was n o t
a t t e m p t e d s i n c e s m a ll d e v i a t i o n s from the i d e a l c a s e
s e r i o u s l y a f f e c t th e sp ec tru m , which f o r th e i d e a l c ase would
be c om p lex.
The sp ectru m c an , however, s t i l l be used to
d e t e r m i n e t h e d u r a t i o n o f an e ven t by making a ssum ptio ns
a b o u t th e v e l o c i t y o f p ro p a g a tio n and the dim ensions o f th e
s o u r c e mechanism.
S in c e a s e is m ic ev en t has f i n i t e d u r a t i o n , i t s time
b e h a v i o u r can be re g a rd e d as th e p ro d u c t of a r e c t a n g u l a r
p u l s e and some o t h e r f u n c t i o n o f tim e , th u s
f(t) = (
w here U ( t)
h (t)
U (t +
| t)
- U (t -
I t)
) x h (t)
= u n i t s t e p f u n c tio n
= a f u n c t i o n of time r e l a t e d
to the v e l o c i t y
o f p r o p a g a tio n and th e dim ensions o f th e
source.
t
= d u r a t i o n o f th e s o u rc e mechanism.
The v e l o c i t y o f p ro p a g a tio n may d i f f e r i n d i f f e r e n t
d i r e c t i o n s , b u t i f i t i s assumed t h a t i t remains c o n s t a n t
i n e a c h d i r e c t i o n , th e n h ( t ) i s in d e p en d e n t of tim e .
A ls o , i f t h e s o u rc e dim en sio ns a r e s m a ll i n r e l a t i o n to
t h e wave l e n g t h o f e l a s t i c waves, i n t e r f e r e n c e o f waves
r a d i a t e d frcm
d
i f f e r e d
p a r t e o f t h e s o u r c e can be ig n o re d
F o r e x am p le, i f th e dim ensions o f th e s o u rc e a r e 100 f e e t ,
P w aves o f f r e q u e n c y l e s s th a n 100 c / s a p p e a r as th o u g h
r a d i a t e d from a lm o s t a p o in t s o u r c e , s i n c e « i s 19,000
ft./s e c .
Thus f o r a H
—
cc and X - c o n s t a n t , a t a
d i s t a n t P o i n t , th e time b ehaviour o f t h e so u rce appears
as
A{ U (t
f(t) -
♦ f r ) _ u ( t _ | T) j
w here A = c o n s t a n t .
The F o u r i e r tr a n s f o r m o f t h i s f u n c tio n i s
F(h>) =
At
V 2n
Gin ^tuu
I
tuu
The minima i n t h i s a m p litu d e spectrum o ccu r a t i n t e r v a l s
of
2 ti A f, t h e r e f o r e
Af
F i g u r e 45a shows a " m issilg ram " o f two s e is m ic e v e n ts
t h a t occurred w ith in
seconds o f e ach o t h e r .
I t can
be s e e n t h a t th e low f r e q u e n c i e s p e r s i s t f o r lo n g e r th a n
th e h ig h freq*: n o t e s ;
the m is s ilg ra m s do not have
s u f f i c i e n t r e s o l u t i o n to y i e l d any f u r t h e r in f o r m a tio n .
F i g u r e 45b shows t y p i c a l s p e c t r a o r " s e c t i o n s " o f th e
P waves o f an ev en t o f m agnitude 10
e v e n t o f m agnitude 10^ f t . - l b s .
f t . - l b s . , and o f an
I t can bv seen t h a t
t h e r e i s v e r y l i t t l e s p e c t r a l c o n te n t above 200 c / s , and
t h a t i n th e c a s e o f t h e 107 f t . - l b s . e v e n t, the minima
a r e so c l o s e l y spaced t h a t th e y a re alm o st i n d i s t i n g u i s h ­
a b l e ( t h e band w id th of th e s p e c tr o g r a p h i s a b o u t 5 c / s ) .
/ FIGURE 45
I 'O N O W A M (J)
KAY m e n u . C O
H H II8 0 C * .K 1
A m ptiiudt
A m f A i t u l«
id* f M b s
(b )
45
B ra s '
In F i g u r e s 46 , 47 %nd 48, s e c t i o n s th ro u g h th e P waves
betw een t h e P and 3 a r r i v a l s ) n ( aoro t y p i c a l 3 e l e „ l c
a r c shown on an expanded freq u en cy s c a l e ,
th e a e 0 tl0 n 8 a r e
f o r d i f f e r e n t s e ism o m e te rs s u rro u n d in g th e f o c u s .
F ig u r e 46
i s f o r a s e i s m i c e ven t o f m agnitude 104 f t . - l b a . t h a t
o c c u r r e d 100 f e e t above t h e r e e f and f o r which a l l observed
f i r s t m o tio n s w ere r a r e f a c t i o n .
F ig u re 47 i s f o r an e v e n t
o f m a g n itu d e 106 f t . - l b a . , 200 f e e t above th e r e e f and f o r
w hich a l l o b s e rv e d f i r s t m otions were r a r e f a c t i o n .
F igu re
48 i s f o r an e v e n t o f m agnitude 5 x 104 f t . - l b s . t h a t
o c c u r r e d n e a r th e Harmony S i l l and f o r which 3 of th e 6
d i s t i n c t f i r s t m otio ns w ere com pression.
The s p e c t r a a r c n o t t h e same a t t h e d i f f e r e n t seism om eters
th u s h ( t ) i s n o t c o n s t a n t and th e s o u rc e mechanism i s n o t
s p h e r i c a l l y s y m m e tr ic a l.
The s p e c t r a a r e only c ru d e ly
s i m i l a r t o t h a t o f a r e c t a n g u l a r p u ls e ;
however, th e y do
show some d i s t i n c t minima and i t i s p o s s i b l e t o make an
e s t i m a t e o f t h e fr e q u e n c y i n t e r v a l between minima.
In
F i g u r e 4 6 , Af i s ab o u t 10 c / s c o rre s p o n d in g to a d u r a t i o n
o f r = 1 / 1 0 s e c . , i n F ig u re 47 Af i s about 3 c / s , t h e r e f o r e
t
» 1/ 3 s e c . , and i n F ig u re 48 Af i s about 6 c / s , t h e r e f o r e
t
= ^ /6 s e c .
These cru d e e s t i m a t e s o f the d u r a t i o n o f th e
s o u r c e mocnanism c o rre s p o n d ro u g h ly w ith th e d u r a t i o n o f the
h ig h a m p l i t u d e p a r t o f the P wave on th e s e is m ic r e c o r d .
S in c e t h e d im e n s io n s o f t h e s o u rc e mechanism a r e n e c e s s a r i l y
l i m i t e d t o d im e n s io n s of th e o r d e r o f 100 f e e t , th e v e l o c i t y
o f p r o p a g a t i o n must be v e ry low.
I n t u i t i v e l y , a low
v e l o c i t y o f p r o p a g a t i o n i s ex pected in a /o lu m e tr i c
c o lla p se .
/ FIGURE 46
FIGURE 46
SECTIONS OR SPECTRA THROUGH THE P WAVES OF A SEISMIC EVENT OF
MAGNITUDE 1 0 * f t . - l b a . THAT OCCURRED NEAR THE REEF PLANE.
THE
NUMBER BELOW EACH SECTION I S THE NUMBER OF THE SEISMOMETER FOR
WHICH THE SECTION WAS MADE.
r
FIGURE 47
SECTIONS OR SPECTRA THROUGH THE P WAVES OF A SEISMIC EVENT CF
MAGNITUDE 10^ f t . - l b s . THAT OCCURRED NEAR THE REEF PLANE. THE
NUMBER BELOW EACH SECTION IS THE NUMBER OF THE SEISMOMETER FOR
WHICH THE SECTION WAS MADE.
n
tMG;-
•
FIGURE 48
y
SECTIONS OR SPECTRA THROUGH THE P WAVES OF A SEISMIC EVENT OF
MAGNITUDE 5 x 104 f t . - l b e . , THAT OCCURRED NEAR THE HARMONY SILL.
THE NUMBER BELOW EACH SECTION IS THE NUMBER OF THE SEISMOMETER
FOR WHICH THE SECTION WAS MADE.
I n c o n c l u s i o n , th e mechanise o f s e is m ic e v e n ts i s n o t
s u f f i c i e n t l y s im p le f o r t h e s p e c t r a l a n a l y s i s te c h n iq u e to
r e v e a l t h e d im en sio n s of th e s o u rc e .
/
SUMMARY OF CONCLUSIONS.
summary of conclusions
The seism ic technique has proved t o be a most rewarding
method o f in v e s tig a tin g v io le n t rock fa ilu r e underground.
Dunne the f i r s t year
rtinging in magnitude
of
recording 3100 seism ic events
103
from
ft.-lb s .
108 f t . - l b s . were
to
lo c a t e d , and th e accuracy with which the events could be
lo ca te d
100
was -
I t w as lo u n d
se ism ic
th e
ev en ts.
90 percent confidence.
f e e t w ith
t h a t t h e r e w e r e tw o d i s t i n c t g r o u p s o f
95 p e r c e n t
o f th e e v e n ts occurred
r e e f p l a n e a n d a w e a k b an d o f r o c k
rt t. f
p la n e , w h ile
S ill
a p p r o x im a te ly 2 4 0 J f e e t
se ism ic
th e
o b se r v a tio n s
th e V e n t ila t io n
show ed
e le v a tio n
w ith
th e
str a in s
e le v a tio n
in
in
th e
to
a zone
above
th e
the
rock.
th e
in
a c o n fin e d
due
w ere
to
rock
in
r e g io n
how ever,
at
p r o p o r tio n
fa ilu r e
to
c o n c lu d e d
as
th e
th a t
p aram eter in
e x te n sio n s!
o r i g i n a l c o m p r e ssiv e s t r a i n
rock
fa ilu r e
was l i m i t e d
o f th e se is m ic
in
th ose
energy r e le a s e
p r e d ic tin g
occurred
of
t h e m in e
per
re le a se d
damage
u n it
which
area
t h e m in e e x c a v a t i o n w as com pared
A ll
th e r a t e
e v e n t s and
th e p arts
The e n e r g y
of
zo n e e x te n d in g l a t e r a l l y
rock fa ilu r e a ls o
rock f a i l u r e ,
la b o u r req u ir e m e n ts.
in c r e a se
c o in c id e d
t h e H arm ony S i l l .
occurred
th e s i z e
w it h dam age du e
str a in
T h is co m p a riso n
o e ism ic e v en ts
an d t h a t t h e
h ig h ly s tr e s s e d .
in c r e a se
The
to a h e ig h t o f a p p r o x im a te ly 300 f e e t
face advanced;
A la r g o
th
was c o n c lu d e d t h a t
th e e x c a v a tio n
as
of
S h a ft.
exceed ed th e
e x te n d in g
Harmony
r e e f p la n e .
o f r e g i o n s w h ere m easured
rock
It
near th e
w e r e com pared w i t h som e e a r l i e r
m easu rem en ts i n
th a t
300 f e e t above th e
r em a in d er o c c u ir e d
above th e
b etw een
of
th e
se ism ic ity
fa cto rs
ra te
energy
and t h e
marked
show ed a
in c r e a se d .
r e le a se
is
stop s
I t was
a sig n ific a n t
m a g n itu d e o f p ro b lem s
/
a r isin g
fr o m
...........
from rock f a ilu r e .and that theae problems are e a s ily
manageable when the r a te of energy r elea se i s l e s s than
10
f t . - l b s . per fathom2 .
There was no d iffe r e n c e in the behaviour 01 seism ic events
o f d iff e r e n t s iz e , except th at a l l the events of magnitude 107
f t . - m s . and 108 f t . - l b s . occurred a t dykes.
Although b la stin g
tr ig g e r e d a la r g e number of ev en ts, more than 50 percent
occurred w e ll o u tsid e b la stin g tim e, and the rate at which
se ism ic even ts occurred flu ctu a ted q u ite w id ely , even when
the ra te o f mining was nearly con stan t.
Only a sm all fr a c tio n o f the damage
was
accompanied by
e ism ic a c t i v i t y , which im p lies th a t the damage was due to
f a l l s o f rock which had been fractured before th e r o c k fa lls
occu rred .
The only manner in which t h is type of damage can
be reduced i s to reduce the exten t of the fractured rock by
reducing th e energy r e le a se r a te , or by improving the t .n e of
support in the s to p e s .
The t o t a l energy radiated by seism ic events of a
p a r tic u la r s iz e exceeded the t o t a l energy radiated by events
o f a sm aller s i z e .
A lso, the to ta l energy radiated by a l l
the se ism ic ev en ts formed a very small fr a c tio n o f the energy
r e le a se d by in c r e a sin g the s iz e of the excavation, th erefore
a mechanism must e x i s t for d is s ip a tin g large q u a n titie s of
energy in a s ta b le manner.
C o o k ^1 ^
a n d F a i r h u r s t a n d Cook^ ^
h a v e inow n t h a t
some rock typ es can f a i l v io le n t ly or n o n -v io ls n tly ,
depending on th e manner in which the rock is loaded.
It
was shown th at th ese th e o r ie s may explain the sta b le
development o f th e fra ctu re zone;
however the large
q u a n tit ie s of energy th at are d issip a te d * ‘.ably can only
be d is s ip a te d by f r ic t i o n in the fra ctu re zone*
a
/ r e la t iv e ly . . . .
r e l a t i v e ly small fra ctu re tone i s required to d is s ip a te
t h is energy.
H r s t motion s tu d ie s of the mechanism of the seism ic
ev e n ts shewed th a t the mechanism was not a t e n s ile or shear
f a i l u r e , but
a
th e r e fo r e
a sudden growth In the fractu re zone, or the
be
volum etric c o lla p se .
The mechanism could
c o lla p s e o f fractured rock near the fa ce or in the workedout a rea s, or the sudden fa ilu r e of a volume of rock
s l i g h t l y removed from the excavation .
The mechanism o f
the seism ic events near the Harmony S i l l was not c le a r ly
reso lv ed but could, however, have been a shear movement.
The s p e c tr a l a n a ly sis did not reveal any u sefu l
inform ation excep t th at the v e lo c it y of propagation of the
volu m etric c o lla p s e was low.
/ SUMMARY
APPENDIX 1
Because the seism om eter, in the . U i t a ,
i . e . ,
N o a . 7
8 , show v e l o c i t i e s higher than those near the r e e l plane,
S h igh er P wave v e lo c it y .
Also there must be a l a er
rock
w ith a very low propagation v e lo c it y near the surface, sin ce
seism om eter 9 shows a low v e lo c it y .
Obviously the apparent
v e lo c it y o f propagation from ar event to a seismometer w ill
th en depend on th e p o s itio n o f the event r e la tiv e to the
seism om eter.
The f o l l o w i n g
e le v a tio n
cf
th e
a lso
by
of
a se ism ic
v e lo c ity
be u se d
th is
is
p resen ted ,
event
to d e te r m in e
be
to
c a lib r a tio n ;
m ethod.
la y e r s
m ethod
th e
th e
w h ich e n a b le s
d e term in ed
v e lo c ity
e le v a tio n
P wave v e l o c i t i e s .
from C to
apparent
v e lo c ity
o f t h e P w ave from 0 t o
th a n
apparent v e lo c ity
tr a v e ls
a c o m p a r a tiv e ly
v e lo c ity
show s
changes;
v a r ia tio n
it
approaches
th e
curve
la y e r s
in
A w ill
from B to
A,
w ill
th at
th e
F ig u re
2A w i l l
an a r b it r a r y
A num ber o f
be th e
in
th e h ig h e r
A.
F ig u re
The g e n e r a l f o r m o f
sam e f o r a n y n u m b er o f
order.
se ism ic
e v e n t s w ere s e le c t e d
a t r andom fr o m
th e
T he f o l l o w i n g p r o c e d u r e w a s c a r r i e d
th e
even t.
event
R e fe r r in g
was o b ta in e d
2A
X (d ista n c e )
as
p o sitio n s
each
The
th e wave
a sy n u L 2t r i c a l
sh a fts.
V,, t h e n
apparent v e lo c it y
a maximum a s X i n c r e a s e s .
in
A, a n d tw o
A w i l l be h i g h e r
o f th e apparent v e lo c ity
be n o t ic e d
event
p a th sh ow n.
because
g r e a te r d ista n c e
can
se ism ic
S a y V, >
have th e
m e d iu m f r o m C t o A t h a n f r o m B t o
th e
c a lib r a tio n
of th e
a wave t r a v e l l i n g
th e
in d e p e n d e n tly
F i g u r e 1A s h o w s a s e i s m o m e t e r a t
h a v in g d i f f e r e n t
th e
r e la tiv e
to
tc
th e
F i g u r e 3A,
on th e
lo c a to r
tw o s e i s m o m e t e r s i n
th e
out fo r
p la n p o s i t i o n
of
by m e a n s o f s e i s m o m e t e r s
/
1 to
...........
seism om eter 7
rv - T T
seismometer 0
h1
The f00U8 TO8 a e llb -
—
n
cf
^
to appear ab(,ve aM
th e r e e f plane, ana , , r eaeh e le v a tio n ,
"
=„ " e r e m easured.
o r ig in ,
d e te r m in e d
v e lo c itie s
The t r a v e l
on t h e
the aietanoee
t i m e fr o m t h e
lo c a to r .
H ence,
v^ a n d 7 g c a n be c a l c u l a t e d
focu s to
th e
the ap p aren t
fo r each e le v a t io n ,
re s e a c h e v e n t th e a p p a ren t v e l o c i t i e s t o se ism o m e te r s 7 , 8
and 9 w e r e o b t a i n e d
se le c te d
F ig u r e s
se ism ic
4A t o
V, v e r s u s
fa r a r e
There a re
a)
rbove r e e f ,
se ism o m e te r s
e le v a tio n
in
t h i s w ay,
1 3 A s h o w so m e o f t h e p l o t s
se ism o m e te r t h a t
th e
e v e n ts w ere a n a ly se d
e le v a tio n
for
is
of
h.
fa cto rs
to
o f apparent v e lo c it y ,
th e n ea r curve i s
th e
focu s
of
from th e f o c u s
e v e n t m ust shew an a p p a r e n t v e l o c i t y
ti.
o f th e
th e
r ig h t
cu rves.
d ip
T h is
a little
p o sitio n
e q u a l,
recurs
still
h ig h e r th a n th e
o f th e
of
e v e n t m ust be
th e n e a r and
a p p lie s even i f
far
th e s t r a t a
se ism o m e te r s;
f o r w h ich
th e
apparent v e l o c i t i e s
how ever,
may s o m e t i m e s
slig h tly
is
o f th e
to
th e
fr e q u e n tly
se ism ic
be n e c e s s a r y
le ft
o f th e
a little
th e
are
a t a s l i g h t l y a sy m m e tr ic a l p o s i t i o n .
e le v a tio n
of
o f th e se ism ic
th e
it
th ere
se ism ic e v e n t.
to
p r a c tic e ,
re a d in g
b)
c o n d itio n
fo ca l
sin c e
e le v a tio n
in te r se c tio n
r e la tiv e
th e
f o r th e
n a m ely ,
The s e is m o m e te r f u r t h e s t
H ence t h e
ani
w h ich p erm it t h e d e t e r m in a t io n
th e e v e n t ,
n earer one.
th e
The c u r v e s m ar k e d n e a r and
7 and 8 ;
nearest
tw o
A ll
f o r a n u m b er o f e l e v a t i o n s .
In
t o c h o o s e an
in te r se c tio n ,
u n c e r ta in ty
in
the
records.
From t h e v e l o c i t y c a l i b r a t i o n f o r s e i s m o m e t e r 8 , a
v e lo c ity
was
fir e d
1 9 ,7 0 0
o f 1 9 ,2 5 0 f t . / s e c .
in
th e
ft./s e c .
w a s o b t a i n e d w hen t h e
r e e f p la n e d i r e c t l y
b e lo w
w hen ttv 1 c h a r g e was i n
th e
it,
charge
and
r e f f p la n e
f and a • • • •
X
'4
X
f
47 4 r
H
if IA
i i Ti m
eT
r I S
K
m
VITH
FIGURES
lu A -1
A
THE VARIATION OF APPARENT VELOCITY
WITH ELEVATION ABOVE THE REEF PLANE
d zew
se ism o B e ttr 7.
S e l . m o . ^ r 9 o n n u n , a c e . Howovor, should
haVe “
aPParent
ft./s e c .
In F ig u r e s
1 9 ,0 0 0
ft,/s e c .
sa tisfy in g
agreem ent
ev en ts
th ese
’ 6 l0 C i^
6 percent l e e r
th an
19,000
4* t o 1 3 i V . 1 .0 r e p r e s e n t s a v e l o c i t y o f
The a rro w s i n d i c a t e
c o n d itio n s.
b etw een th e
occurred
°*=«t
w e ll
two
above
I t can be s e e n
c o n d itio n s
th e
th e m ost l i k e l y
th at
ele v a tio n
th ere i s
and t h a t m o st o f t h e
r e e f p la n e .
good
- 137 ?
a p p e n d ix
In the C entral ^ J . o U o n , planee p .6elllg throueh the
- u s p roject ae s t r a i t U n e e .
Tec planee at r ^ h t a ^ l . e
p asain g t.trough the focue p m ject as t . c In tersectin g s t r a i t
„ neS St an an gle 9 10 e‘ Ch
The angles c , d ip , g , and
02 n f the two Planes are related to 6.
l e t the p ro jectio n plane be the plane 2 . o, with the
lo cu s a t (0 , 0 , - 1 ) . and l e t t „
the d ir e c t)o n
c o sin e s of
Since the two planes are
*t
„ „ and t , . m„ n „
b.
the two plan es, Figure 1 41(a).
a t righ t
angles
+ m, m, + n, n , = 0
The eq u ations o f the two planes are
% + m, y + n , ( z + l ) = o
and
ta x
+ m2 y + n a(z + 1) = 0
The i n t e r s e c t i o n s o f t h e s e two p la n e s w ith the p rojection
p la n e z = 0 a r e
t,
x + m,
y + n,
= 0
t a x + ma y + n a = 0
and
are
show n
C o n sid e r
tw o p o i n t s
in
tw o
E and
14A(fc).
F ig u r e
p o in ts
F on t h e
C and
oth er
D o n one p r o j e c t i o n l i n e and
lin e
m,
E (0,
th en
c d
^
-
=
v
{
—& , 0 )
ID*
-
I Ll
#
,
—
m
F ( - —
and
’
v9
O j
, 0, 0)
J
= 1 - rf - 57 - 0 }
and
CD •
EF = (CD) x (EF) Cob 0
I
IF
_ _ _ _ _
138
FIGURE 14 a
THE CENTRAL PROJECTION
--
-1 3 9 -
C P -E J =
/ v
7
V
v
n ]T
mi 2
T7
V t,®
mT
108 6
n, n 2
V ^ ~ niz
V 1 ~ n 82
Co s 6
o in c e -C^* + m ^ % + n * = i
and
A lso CD
i 3z + m,: +
n,? = 1
*EF = n i n i +
1, -t2
n i n2
a , m2
n i n2
t i t 2m.m2
+ 1 ,1 ,)
e _ n , n.
m.
S in c e t , t 2 +
+ n n2 = 0
thus
- ri, " ,
Cos 0
V 1 ” n ’ 2 V 1 - na2
I n F ig u r e
1 4A (c), c o n s i d e r th e u n i t v e c t o r j g , normal t o
p la n e 1 .
a , = { 1 , , mt , n ,}
n
= Cos a i « s i n 0 1
Cos 0 ,
tan 0 f
v 1 " n i*
S im ila rly
V
~ ‘1?
1 - n 2*
tan 0 ,
Cos 0 = tan 0 , tan 0 2
§
E
5
E
E
~
C e n t r a l P r o j e c t i o n , and o n ly .h e n Coe = = « ,„ 0
a r e t h e p la n e s a t r i g h t a n g l e s .
to e 0
N o tice t h a t th e t . o
p r o j e c t i o n l i n e s must be on o p p o s ite s i d e s o f t h e o r i g i n .
The t r a n s i e n t s p e c tr o g r a p h o r - M i s s i l y z s r - i s an a * U o
S
aUdl° BPe° t r 0 8 r a p h » ^ h produces p e m a n e n t , v i s u a l
complex waveforms.
Two d i f f e r e n t a n a ly s e s of th e
r e c o r d e d d a t a a r e p o s s i b l e w ith t h e " M i s s i l y z e r " .
The f i r s t
a n a l y s i s r e l a t e s freq u e n cy and i n t e n s i t y t o tim e and the
r e c o r d i s c a l l e d a " m ls s il g r a m " .
The second a n a l y s i s r e l a t e s
i n t e n s i t y to fr e q u e n c y a t a p a r t i c u l a r i n s t a n t o f tim e (
o v er
s w id e r dynamic ra n g e th a n th e f i r s t ) and i s r e f e r r e d to
as
a s e c tio n .
The M i s s i l y z e r was u sed in th e 5 to 500 c / s range and
15 to 1500 c / s ra n g e c o rre s p o n d in g to 1.2 5 to 125 c / s and
1 , 75 to 575 c / s s e is m ic s i g n a l fre q u e n c y .
The f a c t o r o f 4
change i n f r e q u e n c y a r o s e becau se t h e r e p l a y deck o f the
s e is m ic n e tw o rk r a n a t a speed 4 tim e s f a s t e r th a n th e
reco rd deck.
F ig u r e 15A shows a g e n e r a l view of th e " M is s ily z e r "
and F i g u r e 16 a shows s e c t i o n s and m is s ilg ra m s f o r a s in e
wave, a s q u a r e wave and a t r i a n g u l a r wave.
The dynamic
r a r v e i n i n t e n s i t y f o r th e m ls s ilg ra m i s 6 d b. w h ile th e
dynamic r a n ,c i n a m p litu d e f o r th e s e c t i o n i s 25 d b . :
b a n d w id th i s 5 c / s .
th e
The a m p litu d e s c a l e i s no t c a l i b r a t e d ,
s o t h a t i t m e re ly r e p r e s e n t s r e l a t i v e a m p litu d e .
Sme
wuve
■ 1
v>
s 50
r
i
2Sf.
Amplitude
LTme
Squori
°r
'/
i
5
-
V0
50
'5
50
rt
100
125
ArpMud«t
T ron^ior
Or ■ —
*«•*
125k
1001-
TSp
5“
■—
i
£
50-
w
175
Ampl't
T-m»
A IM D IX 4
F ig u r e 17 a
The f r e q u e n c y re s p o n s e of th e H a ll-S e a re
model HS1 s eism o m e te r.
F ig u r e 18A
C i r c u i t diagram o f t h e re c o rd and re p la y
a m p lifie rs.
i g u r e 19A
C i r c u i t diag ram o f th e d e v ic e p erfo rm in g
th e o p e r a t i o n (*T v a d t .
o
F i g u r e 20A
C i r c u i t diag ram of th e d i g i t a l c lo c k .
6
A
2
Volts
P#r
inch
per
second
%
100
Frequency
FIGURE 17A
c/s
THE FREQUENCY RESPONSE OF THE HALL-SEAR5 MODEL HS1 SEISMOMETER
-IV
1
r ^ r - 1
8CZ11
BC/II
i
BCZ1I
ion
//on
FIGURE 18A
■;«*
viton
A CIRCUIT DIAGRAM OF THE RECORL AMD REPLAY AMPLIFIERS.
IN THE RECORD AMPLIFIER,
A REPRESENTS THE CABLE FROM THE SEISMOMETER TO THE RECORDER AND AN ATTENUATOR,
AND B REPRESENTS A 3 OHM RECORDING HEAD. IN THE REPLAY AMPLIFIER, A REPRESENTS
AN EQUALIZING NETWORK AND B REPRESENTS A 15 OHM GALVANOMETER.
GALVO
2 sim
680
mm
S6K
2200
FIGURE 19 a
THE CIRCUIT DIAGRAM OF THE DEVICE WHICH PERFORMS THE OPERATION
FI
OURS
?UA
CIRCUIT DIAORAV OF THE DIGITAL CTOCK. THE SERIES OF SWITCHES
13 CONTROLLED BY A 3ERIBS OF CAMS DRIVEN BY AN ELECTRIC CLOCK
MOTOR.
ACKNOVLEDGEI.^T:--;
I n s t i t u t e o f G e o p h y sic s ! R esearch and was spcn scred by
T r a n s v a a l and Orange F re e S t a t e Chamber o f Mines.
ho
Th work
a l s o form s p a r t o f t h e rock mechanics r e s e a r c h conducted by
t h e M ining R esearch L a b o ra to ry o f th e T ran sv a al and Orange
F ree S t a t e Chamber o f Mines.
I vvould l i k e t o th ank th e Management and S t a f f o f th e
Harmony Gold Mining Comoany, Lim ited and th e Research and
/ e n t i l a t i o n D epartm ent o f Rand Mines, Limited fo r t h e i r co­
o p e r a t i o n and a s s i s t a n c e , and f o r p e rm is sio n to u se the d a ta
I
im i n d e b te d to D r. N. .Af. Cook f o r h is h e lp and
g u i d a n c e , and I w ith t o thank Mrs. M. V e a tc o tt, Mrs. A.
M a r t i n s o n , Miss A . P o r t , Mr. G.H.A. K lix and Mr. D. S te p lo
f o r t h e i r a s s i r canoe.
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A rev iew o f
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u n derground
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of th e U n iv e rs ity of th e
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HOEK, B.
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An e l e c t r i c a l
r e s i s t a n c e a n a lo g u e f o r p la n n in g t a b u l a r mine
e x c a v a tio n s.
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R e p o r t N o.7 2 /6 5 , 1 9 6 ;.
~ 152 -
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M ining R ese arch and V e n t i l a t i o n D epartm ent. Report Mo. 1 2 ,
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/
••• •
STARR, A .T.
3 U p i n a c r y s t a l aM n r p tu r e l a a a o l i a
dUe t 0 S h a a r p . 489.
JAEGER, J . G .
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r h U . S t c . , V o l.2 4 , 1928,
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sou rces.
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1 9 6 5 , p p . 2883-2888.
Author Joughin N C
Name of thesis The m easu rem en t and analysis of earth motion resulting from underground rock failure 1966
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