ijrmms-isrm-v19-1982-correçãoefeitoformacargapontual-greminger

6
Int. J. Rock Mech. Min. Sci. Geomech. Abstr. Vol. 19, pp. 241 to 246, 1982 0148-9062]82/050241-06103.00/0 Printed in Great Britain. All rights reserved Copy right © 1982 Perg amo n Press Ltd Technical ote Experimental Studies of the Influence of Rock Anisotropy on Size and Shape Effects in Point Load Testing M. GREMINGER* INTRODUCTION In the last decade the point-load strength test, a simple indirect tensile test, has gained considerable inter- national approval. However, in tensile testing import- ant scale effects must be expected, especially if stress gradients are produced, as is the case in indirect tensile tests [2]. The influence of specimen shape on the point- load strength of rock cores was considered by Reich- muth [3], who proposed a rather complex relationship for the determination of a constant tensile strength, whose practical value was questioned by Broch & Franklin [1]. They recommended as a replacement for the tensile strength a point-load strength index: P It = D-~ (MPa) (1) where It = strength index, P = fracture load, D = dis- tance between loading cones. However considerable variations of It, dependent on both size and shape were found by Broch & Franklin. Consequently, the intro- duction of a reference index I~(50) was recommended, which corresponds to the point-load strength index of a diametrally loaded rock core of 50 mm dia. If other core sizes are tested the respective point-load strength indices must be reduced to I~(50). In effect, they propose a size correction factor for the point-load strength index, which is a function of the distance between the loading points only, and can be obtained from empiri- cal correction-curves or a nomogram. The considerably larger shape effect should be avoided by testing speci- mens with specified geometries. The strength anisotropy index, la, the ratio of point- load strengths in the strongest and weakest directions, serves as a quantitative measure for the anisotropy of point-load strength. Any influence of rock anisotropy on the scale effect was not mentioned by Broch & Franklin. Further studies of the scale effect in point-load test- ing have been conducted by Brook [4, 5]. He developed Arbeitsgruppe Felsmechanik, Institut fiir Geologic, Ruhr-Univer- sit,it Bochum, 4630 Bochum, F.R. Germany. a relationship between strain energy and strained volume in point-load testing and found the fracture load, P, and the cross-sectional area, A, of the loaded specimen to be the relevant quantities for determining m ~ 0.75 P = C. A', C = constant ( 2) requires no restriction on specimen geometry and is therefore applicable to arbitrary sizes and shapes. Size effects again are eliminated by reduction to a reference- index, which is now related to a cross-sectional area A*= 500mm 2 (D_ 25 mm). A shape correction is obtained by using the cross-sectional area, A, instead of the distance, D, between the loading points. The size and shape corrected value of the point-load strength is, after Brook [5], P(A) 5000.75 T~00 = ~zv-~ 500 (MPa) (3) Any influence of anisotropy on the scale effect and its correction is, however, not mentioned by Brook. An experimental study has been initiated, therefore, to investigate the directional dependence of size and shape effects of the point-load strength of anisotropic rocks. In addition, the applicability of Broch & Frank- lin's [1] empirical relation between the uniaxial com- pressive strength, a¢, and the point-load strength refer- ence-index, I,(50), has been examined for anisotropic rocks. Their result trc = 24 I~(50) (4) has been confirmed later by Bieniawski [6] and Brook [4,5], but none of these previous investigators took strength anisotropy into consideration. Pells [7] com- pared measured values of compressive strengths of twelve rock types with those predicted by equation (4). He reports significant differences between these values for six rock types, emphasizing that four of them were isotropic. 241

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8/13/2019 IJRMMS-ISRM-v19-1982-CorreçãoEfeitoFormaCargaPontual-Greminger

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I n t . J . R o c k M e c h . M i n . S c i. G e o m e c h . A b s t r . Vol. 19, pp. 241 to 246, 1982 0148-9062]82/050241-06103.00/0

Prin ted in Gre at Bri ta in . Al l r igh t s reserved Copy right © 1982 Perg amo n Press Ltd

T e c h n i c a l o t e

E x p e r i m e n t a l S t u d i e s o f t h e I n f lu e n c e o f

R o c k A n i s o t r o p y o n S i z e a n d S h a p e E f f e c t s

in P o i n t L o a d T e s t in g

M . G R E M I N G E R *

I N T R O D U C T I O N

In t h e l a s t d e c a d e t h e p o i n t - l o a d s t r e n g t h t e s t , a s i m p l e

i n d i r e c t t e n s i l e t e s t , h a s g a i n e d c o n s i d e ra b l e i n t e r -

n a t i o n a l a p p ro v a l . Ho we v e r , i n t e n s i l e t e s t i n g i m p o r t -

an t sca le e f fec t s mus t be expec ted , espec ia l ly i f s t ress

g ra d i e n t s a r e p ro d u c e d , a s i s t h e c a s e i n i n d i r e c t t e n s i l e

t e s t s [ 2 ] . T h e i n f l u e n c e o f s p e c i m e n s h a p e o n t h e p o i n t -

l o a d s t r e n g t h o f r o c k c o r e s w a s c o n s i d e r e d b y R e i c h-

m u t h [ 3 ] , w h o p r o p o s e d a r a t h e r c o m p l e x r e l a ti o n s h i p

fo r t h e d e t e rm i n a t i o n o f a c o n s t a n t t e n s i le s t r e n g t h ,

w h o s e p r a c ti c a l v a l u e w a s q u e s t i o n e d b y B r o c h &

F r a n k l i n [ 1 ] . T h e y r e c o m m e n d e d a s a r e p l a c e m e n t f o r

t h e t e n s i l e s t r e n g t h a p o i n t - l o a d s t r e n g t h i n d e x :

P

I t = D-~ (M Pa ) (1 )

wh e re I t = s t r e n g t h i n d e x , P = f r a c t u re l o a d , D = d i s -

t a n c e b e t w e e n l o a d i n g c o n e s . H o w e v e r c o n s i d e r a b l e

v a r i a t io n s o f I t, d e p e n d e n t o n b o t h s i ze a n d s h a p e w e r e

f o u n d b y B r o c h & F r a n k l i n . C o n s e q u e n t l y , th e i n t ro -

d u c t i o n o f a r e f e r e n c e in d e x I~ (50 ) wa s r e c o m m e n d e d ,

w h i c h c o r r e s p o n d s t o t h e p o i n t - l o a d s t r e ng t h i n d e x o f a

d i a m e t r a l ly l o a d e d r o c k c o r e o f 5 0 m m d ia . I f o t h e r

c o re s i z e s a r e t e s t e d t h e r e s p e c t i v e p o i n t - l o a d s t r e n g t h

i n d i c e s m u s t b e r e d u c e d t o I~(50 ). I n e f f e ct , t h e y p ro p o s e

a si z e c o r r e c t i o n f a c t o r fo r t h e p o i n t - l o a d s t r e n g t h

i n d e x , wh i c h i s a fu n c t i o n o f th e d i s t a n c e b e t w e e n t h el o a d i n g p o i n t s o n ly , a n d c a n b e o b t a i n e d f r o m e m p i ri -

c a l c o r r e c t i o n - c u rv e s o r a n o m o g r a m . T h e c o n s i d e r a b l y

l a rg e r s h a p e e f fe c t s h o u l d b e a v o i d e d b y t e s t i n g s p e c i-

m e n s w i t h s p e c i f i e d g e o m e t r i e s .

T h e s t r e n g t h a n i s o t ro p y i n d e x , l a , t h e r a t i o o f p o i n t -

l o a d s t r e n g t h s i n t h e s t ro n g e s t a n d we a k e s t d i r e c t i o n s ,

s e rv e s a s a q u a n t i t a t i v e m e a s u re fo r t h e a n i s o t ro p y o f

p o i n t - l o a d s t r e n g t h . An y i n f lu e n c e o f ro c k a n i s o t r o p y

o n t h e s c a le e ff e c t wa s n o t m e n t i o n e d b y B ro c h &

F ra n k l i n .

F u r t h e r s t u d i e s o f t h e s c a l e e f f ec t i n p o i n t - l o a d t e s t-

i ng h a v e b e e n c o n d u c t e d b y B r o o k [ 4, 5 ]. H e d e v e l o p e d

A r b e i t s g r u p p e F e l s m e c h a n i k , I n s t i t u t fi ir G e o l o g i c , R u h r - U n i v e r -

s it ,i t B o c h u m , 4 6 3 0 B o c h u m , F . R . G e r m a n y .

a r e l a t i o n s h i p b e t we e n s t r a i n e n e rg y a n d s t r a i n e d

v o l u m e i n p o i n t - l o a d t e s t i n g a n d fo u n d t h e f r a c t u re

l o a d , P , a n d t h e c ro s s - s e c t i o n a l a r e a , A , o f t h e l o a d e d

s p e c i m e n t o b e t h e r e l e v a n t q u a n t i t i e s fo r d e t e rm i n i n gt h e p o i n t - l o a d s t r e n g t h . H i s r e l a t i o n s h i p

m ~ 0 .75

P = C . A ' , C = c o n s t a n t (2)

r e q u i r e s n o r e s t r i c t i o n o n s p e c i m e n g e o m e t ry a n d i s

t h e re fo re a p p l i c a b l e t o a rb i t r a ry s i z e s a n d s h a p e s . S i z e

e f f e c ts a g a i n a r e e l i m i n a t e d b y r e d u c t i o n t o a r e f e r e n c e -

i n d e x , wh i c h i s n o w r e l a t e d t o a c ro s s - s e c t i o n a l a r e a

A * = 5 0 0 m m 2 ( D _ 2 5 m m ) . A s h a pe c o r r ec t io n is

o b t a i n e d b y u s i n g t h e c ro s s - s e c t i o n a l a r e a , A , i n s t e a d o f

t h e d i s t a n c e , D , b e t we e n t h e l o a d i n g p o i n t s . T h e s i z ea n d s h a p e c o r r e c t e d v a l u e o f t h e p o i n t - l o a d s t r e n g t h i s ,

a f t e r B r o o k [ 5 ] ,

P (A) 5 0 0 0 .7 5

T~00 = ~zv -~ 500 (M Pa) (3)

An y i n f l u e n c e o f a n i s o t ro p y o n t h e s c a l e e f f ec t a n d i ts

c o r r e c t i o n i s , h o we v e r , n o t m e n t i o n e d b y B ro o k .

An e x p e r i m e n t a l s t u d y h a s b e e n i n i t i a t e d , t h e r e fo re ,

t o i n v e s t i g a t e t h e d i r e c t i o n a l d e p e n d e n c e o f s i z e a n d

s h a p e e f f e ct s o f t h e p o i n t - l o a d s t r e n g t h o f a n i s o t ro p i c

ro c k s . I n a d d i t io n , t h e a p p l i c a b i l i t y o f B ro c h & F ra n k -

l i n 's [ 1 ] e m p i r i c a l r e l a t i o n b e t we e n t h e u n i a x i a l c o m -

p re s s i v e s tr e n g t h , a ¢ , a n d t h e p o i n t - l o a d s t r e n g t h r e f er -

e n c e - i n d e x , I , ( 5 0 ) , h a s b e e n e x a m i n e d fo r a n i s o t ro p i c

ro c k s . T h e i r r e s u l t

trc = 24 I~(50) (4)

h a s b e e n c o n f ir m e d l a t e r b y B ie n i aw s k i [ 6 ] a n d B r o o k

[4 ,5 ] , b u t n o n e o f th e s e p r e v i o u s i n v e s t i g a t o r s t o o k

s t r e n g t h a n i s o t ro p y i n t o c o n s i d e ra t i o n . P e l l s [ 7 ] c o m -

p a r e d m e a s u r e d v a l u e s o f c o m p r e s s i v e s tr e n g t h s o f

t we l v e ro c k t y p e s w i t h t h o s e p re d i c t e d b y e q u a t i o n (4 ) .

H e r e p o r t s s i g n i fi c a n t d i ff e r e n c e s b e t w e e n t h e s e v a l u e s

fo r s ix ro c k t y p e s , e m p h a s i z i n g t h a t f o u r o f t h e m we re

i s o t ro p i c .

241

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2 4 2 T e c h n i c a l N o t e

A cr i t i ca l inves t iga t ion o f the va l id i ty o f un iax ia l

c o m p re s s i v e s t r e n g th p re d i c t i o n b y p o i n t - l o a d i n d e x

wi t h r e s p e c t t o a n i s o t ro p i c ro c k s a p p e a r s t h e re fo re

necessary .

T E S T R E S U L T S

C o r r e c t i o n o f s i z e a n d s h a p e e f f e c t s i n p o i n t - l o a d t e s t i n g

N u m e r o u s p o i n t - l o a d t e s t s h a v e b e e n p e r f o r m e d o n

fo u r ro c k t y p e s w i th v a r i o u s d e g re e s o f s t r e n g t h a n i -

so t rop y ( Io = 1 .05 to l a = 5 .7 ) in o rde r to eva lua te

these e ffect s. Tw o ex t re m e d i rec t ions , i . e . para l le l and

n o rm a l t o t h e p l a n e o f we a k n e s s we re c o n s i d e re d .

B e c a u s e o f t h e w i d e r a n g e o f s t r e n g t h a n i s o t ro p i e s

c o v e re d b y t h e ro c k s c h o s e n , t h e r e s u l t s s h o u l d b e

a p p l i c a b l e t o o t h e r a n i s o t ro p i c ro c k s i n s p i t e o f t h e

l i m i t e d n u m b e r o f ro c k t y p e s i n v e s t i g a te d i n t h i s s t u d y .

T h e fo l l o wi n g ro c k m a t e r i a l s h a v e b e e n t e s t e d : am e d i u m - g r a i n ed , w e a k l y b e d d e d C a r b o n i f e r o u s R u h r -

S a n d s t o n e w i t h a q u a r t z c o n t e n t o f 70 , 2 09 /0 f e l d s p a r

m i n e ra l s, 8 m i c a a n d a d d i t i o n a l m i n e ra l s a n d 2 p o r -

o s i t y ; a De v o n i a n s l a te f ro m N u t t l a r (R h e n i s h m a s s i v e )

wi th a co n ten t o f phy l lo s i l ica tes o f 80 , 10 ca lc i t e ,

a n d 1 0 q u a r t z p l u s f e l d s p a r ; a n A l p i n e O l i g o c e n i c

g n e i s s f ro m S o n d r i o (S wi t z e r l a n d ) c a l l e d C h i a n d o n e -

Gn eiss wi th 45 o f quar tz , 35 fe ldspar minera l s , 18 /o

m i c a , a n d 2 a d d i t i o n a l m i n e ral s , a n d a M e s o z o i c

a u g e n g n e i s s f ro m Gra u b i i n d e n (S wi t z e r la n d ) w i t h 1 5

a u g e n o f m i c ro c l in e a n d q u a r t z a n d 85 /0 g ro u n d m a s s

cons i s t ing o f 55 quar tz , 25 mica , 15 fe ldspar min -era l s , and 5 add i t ion a l minera l s .

T h e m e c h a n i c a l p ro p e r t i e s o f t h e s e ro c k s a r e l i s t e d in

T a b l e 1 fo r t h e t wo p r i n c i p a l d i r e c t io n s . T h e t e s t r e s u l ts

(F i g s 1 -4 ) f ro m d i a m e t r i c a l l y l o a d e d c o re s w i t h d i a m -

e t e r s o f 3 0, 4 4 , a n d 6 2 m m a n d o f c o n s t a n t s h a p e s h o w

t h a t p o i n t - l o a d s t r e n g t h i n d i c e s fo r t h e s m a l l d i a m e t e r

c o re s c a n b e u p t o t wo t i m e s l a rg e r t h a n t h o s e fo r t h e

l a rg e r d i a m e t e r c o re s. T h i s c l e a r l y d e m o n s t r a t e s t h e

ex is tence o f a size e ffec t . Th e a dd i t ion a l shap e e f fec t

wa s e v a l u a t e d i n a x i a l p o i n t - l o a d t e s t s o n s p e c i m e n s o f

d i f fe r e n t w i d t h t o h e i g h t r a t io s . F o r c o n s t a n t D b u t

d i f fe ren t L I D r a t i o s t h e p o i n t - l o a d s t r e n g t h i n d e xs h o w s a v a r i a t io n , wh i c h c a n e x c e e d a r a t i o o f 5 t o 1

(see F igs 1 -4) . All wid th to he igh t ra t io s have b een

e q u a l t o o r g r e a t e r th a n 1 , a s r e c o m m e n d e d b y P e n g

[8 ] . T h e d e v i a t i o n (95 i n t erv a l ) o f i n t h e a v e ra g e

t we l v e p o i n t - l o a d t e s t s p e r c o n f i g u ra t i o n u s u a l ly

a m o u n t s to _ 1 0 -2 5 , w i t h t h e u n d e r s t a n d a b l e e x c e p -

t i o n o f Nu t t l a r -S l a t e l o a d e d p a ra l l e l t o t h e p l a n e s o f

we a k n e s s .

T h i s l a rg e v a r i a b i l i t y o f l s D ) cou ld g rea t ly l imi t i t suse as a s t reng th index va lue , un less re fe renc e is made

t o a s t a n d a rd s iz e a n d r e s p e c t i v e c o r r e c t i o n f a c t o r s fo r

s ize and shap e e f fec t s a re ava i lab le . S ca le e f fec t s cer -

t a i n ly c o u l d b e a v o i d e d b y u s i n g s p e c i m e n s o f r e fe r -

e n c e -d i m e n s i o n s o n l y . A l t h o u g h d e s i r a b le , t h is h o w e v e r

wo u l d b e r a t h e r i m p ra c t i c a l s i n c e it wo u l d e l i m i n a t e t h e

g re a t a d v a n t a g e o f t h e p o i n t - l o a d t e s t t h a t n o s a m p l e

p re p a ra t i o n i s r e q u i r e d . T h e a p p l i c a t i o n o f s u it a b l e

s c a l e c o r r e c t i o n p ro c e d u re s i s t h e r e fo re i n d i s p e n s a b l e .

B e c a u s e o f th e q u a l i t a t i v e s i m i la r i ty o f t h e c u rv e s o f

F igs 1 -4 ( fu ll cu rves ) i t is to be exp ec ted tha t sca le

e f f e ct s a r e i n d e p e n d e n t o f ro c k t y p e a n d l o a d i n g d i r e c -t ion .

In o rd e r t o e s t a b l i s h s u i t a b l e c o r r e c t i o n f a c t o r s b y

wa y o f a n a ly t i c a l f u n c t i o n s fo r t h e s i z e a n d s h a p e

d e p e n d e n c e a n d i n p a rt i c u l a r t o d e t e c t a n y d e p e n d e n c e

o n t h e d e g re e o f a n i s o t ro p y , l i n e ar , e x p o n e n t i a l , a n d

p a ra b o l i c fu n c t i o n s we re d e t e rm i n e d f ro m t h e e x p e r i -

m e n t a l d a t a b y r e g re s s io n a n a l y s is . T h e b e s t f i t w i t h t h e

e x p e r i m e n t a l d a t a c o u l d b e o b t a i n e d b y a p a r a b o l ic

fu n c t i o n , a s fo rm e l y a s c e r t a i n e d b y e . g. Gu i d i c i n i et al.

[9 ] o r S u n d a e [1 0 ] .

T h e v a r i a t i o n o f I s D ) wi t h s a m p l e s i z e (d i a m e t r a l

and ax ia l t es t s ) i s bes t descr ibed by

I s D ) o c D - a w ith 0.466 ~ a ~< 0.577 (5)

w i t h n o i n d i c a t i o n o f a n y d e p e n d e n c e o f t h e e x p o n e n t a

o n a n i s o t ro p y . A v e ry i m p o r t a n t c o n c l u s i o n i s t h e re -

fo re , t h a t t h e s i ze c o r r e c t i o n f a c t o r i s i n d e p e n d e n t o f t h e

d e g re e o f a n i s o t ro p y a n d o f t h e l o a d i n g d i r e c t i o n . I t c a n

b e wr i t t e n i n t h e fo rm

C o = w it h D * = 5 0 m m (6)

w i t h a r e f e re n c e - d im e n s i o n o f 5 0 m m r e c o m m e n d e d b yIS R M [1 1 ] . S e t ti n g b y a p p ro x i m a t i o n a = 0 .5 r e su l t s i n

TABLE 1. M ECHANICAL ROCK PROPERTIES IN THE TWO PRINCIPAL DIRECTIONS

L o a d i n g

T y p e o f r o c k d i r e c t i o n a c ( M P a ) E ( M P a ) v 2 ( k m / s e c ) p ( k N / m 3 )

A u ge n gne i s s I I S c h i s t os i ty 150 48 , 800 4 . 14 26 .5_LS chis tos i ty 178 34,500 2.68 26.5

R u h r - S a n d s t o n e I I B e d d in g 1 53 3 9 , 0 0 0 4 .1 8 2 5 .5Be dd i ng 177 34 , 600 3 . 57 25 .5

Ch i a n do ne - G ne i s s I I S c h i s t os it y 104 38 , 900 3 .51 26 .6_LS chis tos i ty 164 37,800 2.81 26.6

N u t t l a r - S l a t e I I S c h i s t os it y 104 60 , 600 5 . 66 27 .7

t rc : u n i a x i a l c o m p r e s s i v e s t r e n g t h .

E : t a n g e n t Y o u n g ' s m o d u l u s .

v L l o n g i t u d i n a l w a v e v e l o c i t y .

p : d e n s i t y .

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T ech n i ca l N o t e 2 4 3

o

Q.

3 0

2 0

B e f o r e c o r r e c t i o n

+ L / D = 4• L / D = : 5

• L / D = 2

• L / D = 1 5

• L / D = I

A f t e r c o r r e c t i o n+

o L ' 3 0 m m• n L ' 4 4 m m

& L - 6 2 m mo

OL=E

m .. .,....,

I 0

%

. • x %

\ m .

I I I I I I

0 2 0 4 0 6 0 0 2 0 4 0 6 0

D , m m D , m m

a ) b )

F i g . I . P o i n t - l o a d s t r e n g t h o f a u g e n g n e i s s l o a d e d a ) p a r a l l e l a n d b ) n o r m a l t o s c h i s to s i t y ,

oO -

3 0

2 0

I0

3 0

o ~ • . 2 0

I0

aN.

4 2

I I I I I I0 2 0 4 0 6 0 0 2 0 4 0 6 0

D , m m D , m m

( a ) ( b )

F i g. 2. P o i n t - l o a d s t r e n g t h o f R u h r - S a n d s t o n e l o a d e d a ) p a r a l le l a n d b ) n o r m a l t o t h e b e d d i n g p l a n es .

R.M.M.S 19/5--C

2O

oa.

IO

30 ~ - 3 0

2 0

of i t .~E

• ' ; - m - I 0

e

i I I I I0 2 0 4 0 6 0 0 2 0 4 0 6 0

D , m m D , m m

a ) b )

F i g . 3 . P o i n t - l o a d s t r e n g t h o f C h i a n d o n e - G n e i s s l o a d e d a ) p a r a l l e l a n d b ) n o r m a l t o s c h is t o s i ty .

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T e c h n i c a l N o t e

TABLE2. POINT-LOADSTRENGTH NDICES s(50) OF THE ROCKS NVESTIGATED

l s ( 5 0 ) ll ( M P a ) L ( 5 0 ) ~ MPa)Type of rock I 2 3 I 2 3

Augen gneiss 6.4 6.6 6.1 6.9 6.9 6.8 1.05Ruhr -Sa nds tone 7.9 7.9 7.8 8.9 8.5 8.9 i.15

Chi andone-Gneiss 3.6 3.8 3.6 10.6 10.0 10.6 2.80Nutt lar -Slate l.l 1.4 1.5 8.5 8.2 8.4 5.70

I. Determined from test results by interpolation between 44 and 62 mm.2. Determined by size correction of diametral test results.

3. Determined by size and shape correction of axial test results.

245

m e a n v a l u e s o f I~ (5 0) d e t e rm i n e d b y d i f fe r e n t m e t h o d s

are l i s t ed in Tab le 2 .

Comparison between uniaxial compressive strength andpoint load strength o f anisotropic rocks

F r o m e x p e r im e n t a l s t u d ie s B r o c h F r a n k l i n [ 1 ]

a n d o t h e r a u t h o r s ( e . g . B i e n i a w s k i [6 ] ) f o u n d d e s p i t e a

c o n s i d e ra b l e s c a t t e r in g o f t h e d a t a a l i n e a r r e l a t i o n

b e t we e n u n i a x ia l c o m p re s s i v e s t r e n g t h a c a n d t h e p o i n t -

l o a d s t r e n g t h i n d e x :

ac = 24 I~(50) (4)

T h e a c c u ra c y o b t a i n e d fo r a s s e ss i n g a ~ h a s b e e n

a s s u m e d s a t i s f a c t o ry .

D i r e c t i o n - c o n tr o l l e d p r e d i c t io n s o f c o m p r e s s i v e

s t r e n g t h b y m e a n s o f I , (5 0 ) h a v e n o t b e e n c o n s i d e re d s o

far . I n o rd e r t o e x a m i n e t h e v a l i d i t y o f e q u a t i o n (4) for

a n i s o t r o p i c r o c k s , u n c o n f i n e d c o m p r e s s i o n t e s t s h a v e

b e e n p e r f o r m e d o n t h e s a m e t y p e s o f r o c k a n d i n t h e

s a m e l o a d i n g d i r e c t i o n s a s i n t h e p o i n t - l o a d t e s ts . T h e

d i a m e t e r o f t h e c o re s u s e d fo r t h i s p u rp o s e wa s

6 2 m m ; a l l h e ig h t t o d i a m e t e r r a t i o s w e re 2 .5 t o 3 . 0 . A

s iz e e f f e ct i n c o m p re s s i v e t e s t s wa s c o n s i d e re d t o b e

negligible.

A c o m p a r i s o n u s in g t h e S t u d e n t - t -t e s t o f m e a s u r e d

c o m p r e s s i v e s tr e n g th s w i t h t h o s e p r e d ic t e d b y m e a n s o f

e q u a t i o n (4) wa s s u c c e s sfu l o n l y fo r a u g e n g n e i s s

( Io = 1 .05 ) . E r ro r s b e t we e n t h e s e v a l u e s we re fo u n d t o

b e p r o b a b l e f o r t h e s l i g h t l y m o r e a n i s o t r o p i c R u h r -

Sa nds ton e ( la --- 1 .15 ) and s ign i f ican t o r h igh ly s ign if i-

c a n t f o r b o t h h i g h l y a n i s o t r o p i c r o c k s , C h i a n d o n e -

Gn eiss ( I , = 2 .8 ) and Nu t t l a r - S la te ( I , = 5 .7 ) (see

Fig. 5).

T h i s r e s u l t i s n o t s u rp r i s i n g s i n ce t h e d i r e c t i o n a l v a r i -

a t i o n o f t h e u n i a x i a l c o m p re s s i v e s t r e n g t h i s r a t h e r d i f-

f e r e n t f ro m t h a t o f t h e p o i n t - l o a d s t r e n g th . T h e p o i n t -

l o a d s t r e n g t h r e a c h e s i t s m a x i m u m a t a l o a d i n g d i r e c -

t i o n n o r m a l t o t h e p la n e s o f w e a k n e s s a n d i ts m i n i m u m

p a ra l l e l t o t h e p l a n e s o f we a k n e s s , wh e re a s t h e u n i a x ia l

c o m p r e s s i v e s t re n g t h n o r m a l t o t h e p l a n e s o f w e a k n e s s

i s gene ra l ly h igher than tha t para l le l to it . Th e m in i -

m u m o f a c , h o we v e r , i s g e n e ra l l y o b s e rv e d a n d a l s o

p r e d i c t e d b y t h e M o h r - C o u l o m b c r i te r i o n [ 1 2 ] f o r a

l o a d d i r e c t i o n a t a n a n g l e o f 4 5 ° - ~ b /2 t o t h e p l a n e s o f

we a k n e s s .

T h e a n s w e r t o t h e q u e s t i o n o f a p o s s i b le c o r r e l a ti o n

b e t w e e n t h e m i n i m u m a n d m a x i m u m v a l u e s o f c o m -

p r e s si v e s t r e ng t h o f a n i s o t r o p i c r o c k s a n d t h e a p p r o -

p r i a t e v a l u e s o f p o i n t - l o a d s t r e n g t h a p p e a r s t o b e t h e re -

fo re a n e g a t i v e o n e . T h e e x p e r i m e n t a l r e s u l t s s h o w a

p a r t i c u la r l y p o o r c o r r e l a t io n f o r th e m a x i m u m c o m -

p re s s i v e s t r e n g t h , s i n c e t h e re s i g n i f i c a n t e r ro r s o f u p t o

6 0 ~ w e r e o b s e r v e d b e t w e e n m e a s u r e d a n d p r e d i c te d

v a l u e s. T h e t e s t r e s u l ts c l e a r l y i n d i c a t e t h a t f o r t h e fo u r

ro c k t y p e s o f t h is s t u d y n e i t h e r d e g re e n o r d i r e c t i o n o f

a n i s o t ro p y a g re e b e t we e n u n i a x i a l a n d p o i n t - l o a d t e s t s .

A l t h o u g h t h e li m i t e d n u m b e r o f ro c k t y p e s i n v e s ti -

g a t e d i n t h i s s t u d y d o e s n o t a l l o w a f i n al c o n c l u s i o n

L o a d e d L o a d e d

p a r a l l e l p e r p e n d i c u l a r

A u g e n g n e i s s v •

I o - R u h r s a n d s t o n e o • t - - • - - I

C h i a n d o n e g n e i s s o •I • I

N u t t l a r s l a t e A -

o •

IE

[ 5 0 ] • 2 4 I s [ 5 0 1o

I I I I

0 5 0 I 1 5 2

o c [ 5 0 ) , M P o

Fig. 5. Relation ship between uniaxial compressive strength a, and point-load stre ngth index I, 50).

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2 4 6 T e c h n i c a l N o t e

r e g a rd i n g t h e u s e o f th e p o i n t - l o a d t e s t f o r p r e d i c ti n g

t h e u n i a x ia l c o m p re s s i v e st r e n g t h , t h e c o n s i d e ra b l e p r e -

d i c t i o n e r ro r s o b s e rv e d fo r a n i s o t ro p i c ro c k s c a n n o t

a n d m u s t n o t b e o v e r l o o k e d . T h e p r e d i c t io n s h o u l d

t h e re fo re b e u s e d o n l y w i t h g r e a t c a u t i o n .

T h e r e s u l t s o f b o t h p a r t s o f th i s s t u d y l e a d t o t h e

c o n c l u s i o n t h a t t h e p o i n t - l o a d s t r e n g t h i n d e x s h o u l d

p re fe r a b l y b e u s e d a s a n i n d e p e n d e n t s t r e n g t h p a r -a m e t e r. U n c o n f i n e d c o m p r e s s i o n t e st s s h o u l d b e a d d e d

wh e n e v e r e s p e c i a l l y r e q u i r e d .

t o s i g n i f i c a n t e r ro r s . T h e p o i n t - l o a d s t r e n g t h i n d e x

s h o u l d t h e r e f o r e b e u s e d a s a n i n d e p e n d e n t p a r a m e t e r

a n d a d d i t i o n a l u n c o n f i n e d c o m p re s s i o n t e s t s s h o u l d b e

p e r f o r m e d w h e n e v e r r e q u i r ed .

A c k n o w l e d g e m e n t s - - T h e a u t h o r w o u l d l i k e t o t h a n k P r o f e s s o r H . K .

K u t t e r f o r i n i ti a t i n g t h i s s t u d y , f o r h i s p e r m a n e n t i n t er e s t , a n dn u m e r o u s d i s cu s s i on s .

Received 17 March 1982.

C O N C L U S I O N S

1 ) S i z e a n d s h a p e e f f e c t s i n p o i n t - l o a d t e s t in g o f a n i -

s o t ro p i c ro c k we re e x p e r i m e n t a l l y s h o wn t o b e i n d e -

p e n d e n t o f t h e d eg r e e o f r o c k a n i s o t r o p y a n d i n d e pe n -

d e n t o f t h e l o a d i n g d i r e c t i o n . S t a n d a rd s i ze a n d s h a p e

c o r r e c t i o n f a c t o r s c o u l d t h e re fo re b e a p p l i e d t o t h e fo u r

r o c k ty p e s t e st e d. T h e o b t a i n e d a c c u r a c y < + 1 M P a )

i s su ff ic ien t fo r an index va lue .2 ) B e c a u s e o f t h e w i d e r a n g e o f t h e d e g re e o f a n i -

s o t ro p y I , = 1 .0 5 t o I , = 5 .7 ) o f t h e p o i n t - l o a d

s t r e n g t h e x a m i n e d i n t h i s s t u d y , t h e r e s u l t s s h o u l d

a p p l y t o a l l o t h e r ro c k s c o n s i d e r i n g e v e n t h e s m a l l

n u m b e r o f in v e s t i g a te d ro c k t y p e s .

3 ) S p e c i m e n s o f s t a n d a rd s iz e D = L = 5 0 m m )

s h o u l d b e t e s t e d wh e n e v e r p o s s i b l e , e . g . d i a m e t r a l l y

c o m p re s s e d c o re s o f 5 0 m m d i a . T h e e x i s t e n c e o f si z e

a n d s h a p e c o r r e c t i o n f a c t o r s p e rm i t s , h o we v e r , a l s o t h e

t e s ti n g o f sp e c i m e n s o f a rb i t r a ry g e o m e t r i e s , p ro v i d e d

tha t 1 ~ LI ~ 3 . M a x i m u m s p e c i m e n s i z e i s d e t e r -

m i n e d b y t h e l o a d c a p a c i t y o f t h e t e s t i n g m a c h i n e .S p e c i m e n s o f l e ss th a n 3 0 m m d i a s h o u l d n o t b e u s e d ,

s i n c e t h e re t h e l o a d e d a r e a s c a n n o m o re b e c o n s i d e re d

t o b e p o i n t - s h a p e d i n r e l a t i o n t o t h e s p e c i m e n s i z e .

4 ) E s t i m a t i o n o f u n i a x i a l c o m p re s s i v e s t r e n g t h o f

a n i s o t ro p i c ro c k I , > 1 .1 ) b y m e a n s o f Is 5 0 ) c a n l e a d

R E F E R E N E S

1 . B ro c h E . F ra n k l i n J. A . Th e p o i n t - l o a d s t re n g t h t e s t. Int. J.

Rock Mech. Min. Sci. 9, 669-697 (1972).

2 . Pa t e r s o n M . S . Experimental Rock Deformation--The Bri ttl eField, 2 5 4 p p . S p r i n g e r , H e i d e l b e rg (1 97 8 ).

3 . R e i c h m u t h D . R . P o i n t - l o a d t e s t i n g o f b r i t tl e m a t e r i a l s t o d e t e r -

mi n e t e n s i l e s t r e n g t h a n d re l a t i v e b r i t t l e n e ss . Proc. 9th Syrup. on

Rock Mechanics, C o l o ra d o Sc h o o l o f M i n e s , 1 9 67 , p p . 1 3 4 -1 5 9.

A m . I n s t . M i n . M e t a l l . P e t r o l . E n g r s . N e w Y o r k 0 9 6 8 ) .

4 . B r o o k N . A m e t h o d o f o v e r c o m i n g b o t h s h a p e a n d s i ze ef fe ct s in

p o i n t - l o a d t e s t i n g . Proc. Conf. on Rock Engineering, U n i v . o fNe wc a s t l e , p p . 5 3 -7 0 . B r . Ge o t e c h . So c . , Lo n d o n (1 9 7 7 ) .

5 . B ro o k N. S i z e c o r re c t i o n fo r p o i n t - l o a d t e s t i n g , Te c h n i c a l No t e .

Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 1 7 , 2 3 1 -2 3 5

(1980).

6 . B i e n i a wsk i Z . T . Th e p o i n t - l o a d t e s t i n g e o t e c h n i c a l p ra c t i s e .

Engng Geol. 9, 1-11 (1975).

7 . Pe l l s P . J . N . Th e u se o f p o i n t - l o a d t e s t i n p re d i c t i n g t h e c o m-

p r e s s i v e s t r e n g t h o f r o c k m a t e r i a l s , T e c h n i c a l N o t e . Aust. Geo-mech. 2. G5 , N1 , 5 4 -5 6 (1 9 7 5 ) .

8 . Pe n g S . S . S t re s s a n a l y s i s o f c y l i n d r i c a l ro c k d i sc s su b j e c t e d t oa x i a l d o u b l e p o i n t - lo a d . Int. J. Rock Mech. Min. Sci. Geomech.Abstr. 13, 97-101 (1976).

9 . G u i d i c i n i G ., N i e b l e C . M . C o r n i d e s A . T . A n a l y s i s o f p o i n t -l o a d t e s t a s a me t h o d fo r p re l i mi n a ry g e o t e c h n i c a l c l a s s i f i c a ti o n

o f ro c k s . Bull. Int. Assoc. Engng Geol. 7, 37-52 (1973).

1 0 . Su n d a e L . S . E ffe ct o f sp e c i me n v o l u m e o n a p p a re n t t e n s i l es t r e n g t h o f t h r e e ig n e o u s r o c k s . U S B M R I 7 8 46 , W a s h i n g t o n(1974).

1 1. I S R M . S u g g e s t e d M e t h o d s o f d e t e r m i n i n g t h e p o i n t - l o a d s t r e n g t hi n d ex . I S R M C o m m i t t e e o n L a b o r a t o r y T e s t s. D o c u m e n t I , 8 - 1 2

(1973).1 2 . J a e g e r J . C . C o o k N. G. W. Fundamentals of Rock Mechanics

2 r id e d n . C h a p m a n Ha l l , Lo n d o n (1 97 6 ).