1970_Time dependent behaviour of jointd rock.pdf

7/28/2019 1970_Time dependent behaviour of jointd rock.pdf

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R a & M e c h a n i es 2 , i 2 3 - - 1 3 7 ( 1 9 70 )@ b y S p r i n g e r - V e r l a g 1 9 7 0

T i m e - D e p e n d e n t B e h a v i o u r o f F r a c tu r e d R o c kB y

Z . T . B i e n i a w s k iW i t h l 0 F i g u r es

( R e e e i v e d o n M a r c h 9 , 1 9 7 0 )

S u m m a r y - - Z u s a m m e n f a s s u n g - - R s u m T i m e - D e p e n d e n t B e h a v i o u r o f F r a c t u r e d R o ck . K n o w l e d g e o f t h e t i m e - d e p e n d e n tb e h a v i o u r o f f r a e t u r e d r o ck i s p a r t i e u l a r l y i m p o r t a n t i n d e s i g n i n g ro c k s t ru e t u r e s f o r lo n g -t e r m s t a b i l i ty . T h i s p a p e r i s a n a t t e m p t t o d e t e r m i n e t h e t im e - d e p e n d e n t b e h a v i o u r o ff r a e t u r e d r o ck a s it m i g h t p r e v a i l u n d e r i n - s i t u e o n d i t i o n s . T h e f o l l o w i n g e as c s a r e e o n -s i d e r e d :

(i) G r a d u a l l y i n c r e a s i n g e o m p r e s s i o n a t d i f f e r e n t b u t e o n s t a n t r a t e s o f d e f o r m a t i o n ;(ii) G r a d u M l y i n c r e a s i n g e o m p r e s s i o n a t e h a n g i n g r a t e s o f d e f o r m a t i o n ;

( ii i) C e n s t a n t l o a d a p p l i e a t i o n f o r v a r i o u s t i m e d u r a t i o n s .I t is s h e w n t h a t f r a e t u r e d r o c k do e s h a v e a l o n g - t e r m s t r e n g t h a n d w h i l e i t s re s i s t a n e e

a n d d e f o r m a t i o n a r e i n i t i a l l y a f f e e t e d b y t i m e , s t a b i l i t y i s r e a c h e d a t a e e r t a i n s t a g e . I ti s t h u s p o s s i b l e t o d e t e r m i n e l o n g - t e r m s t a b i ] i t y e u r v e s f o r f r a e t u r e d r o c k . T h i s m a y y i e l dd e s i g n d a t a f o r s t a b l e r o c k s t r u e t u r e s s u b j e e t e d t o l o w r a te s o .f l o a d i n g .D a s z e i t a b h n g i g e V e r h a l t e n v o n g e b r o e h e n e m G e s t e i n . F r d e n E n t w u r f v o n F e l s -k o n s t r u k t i o n e n , d i e b e r l a n g e Z e i t r ~ u m e s t a b i l s e i n s o l l e n , i s t e s b e s o n d e r s w i c h t i g , d a sz e i t a b h n g i g e V e r h a l t e n v o n g e b r o c h e n e m G e s t e i n z u k e n n e n . I n d e r v o r l i e g e n d e n A r b e i tw i r d v e r s u ch t , d a s z e i t a b h n g i g e V e r h a l t e n v o n g e b r o & e n e m G e s t e i n z u e r m i t t el n , w i e e s

u n t e r u n t e r t g i g e n B e d i n g u n g e n i n E r s c h e i n u n g t r e t e n k n n t e .F o l g e n d e F l l e w e r d e n b e h a n d e l t :(i ) A l l m h l i c h s t e ig e n d e D r u c k b e l a s t u n g b e i v e r s c h i e d e n e n , j ed o c h k o n s t a n t e n V e r -

f o r m u n g s g e s c h w i n d i g k e i t e n ;( i i ) A l l m h l i c h s t e i g e n d e D r u c k b e l a s t u n g b e i v e r n d e r l i c h e n V e r f o r m u n g s g e s c h w i n -d i g k e i t e n ;

(i i i) K o n s t a n t e L a s t a u f b r i n g u n g w h r e n d v e r sc h i ed e n la n g e r Z e i t r u m e .E s w i r d n a & g e w i e s e n , d a g e b r o c h e n e s G e s t e i n e i n e L a n g z e i t f e s t i g k e i t b e s i t z t u n d d a S t a b i l i t t zu e in e m g ew i s s e n Z e i t p u n k t e r r e i c h t w i r d , o b w o h l W i d e r s t a n d u n d V e r f o r m u n g

a n f n g l i c h d u r ch d i e Z e i t b e e i n f l u t w e r d e n . E s i s t d a h e r m g l ic h , L a n g z e i t s t a b i l i t t s k u r v e nf r g e b ro e h e n e s G e s t ei n z u b e s t i m m e n . D i e s k a n n z u r E . r a rb e i t u n g v o n E n t w u r f s d a t e n f i irs t a b i le F e l s k o n s t r n k t i o n e n f h r e n , d i e g e r i n g e n B e l a s t u n g s g e s c h w i n d i g k e i te n a u s g e s e t z t s in d .L e c o m p o r t e m e n t d e l a r ac h e f r a e tu r e e n fo n e t i o n d u t e m p s . L a e o n n a i s s a n e e d u e o m -

p o r t e m e n t d e l a r a c h e f r a e t u r e e e n f o n e t i o n d u t e m p s o s t p a r t i e u l i e r e m e n t u t i l e a u e a l e u ld e l a s t a b i l i t p r o l o n g e d e s s t r u e t u r e s r o c h e u s e s . A u s s i a - t - o n c h e r c h d t e r m i n e r l e e o m -p o r t e m e n t p r o b a b l e , e n f o n c t i o n d u t e m p s , d ' u n e r a c h e f r a e t u r e e n r g im e n a t u r e l. O n ae n v i s a g l e s v e n t u a l i t s s u i v a n t e s :

(i ) u n e e o m p r e s s i o n e r o i s s a n t e a v e e d i f f r e n t e s v i t e s s e s d e d f o r m a t i o n e o n s t a n t e s ;( ii) u n e e o m p r e s s i o n e r o i s s a n t e a v e c d e s v i t e s s e s d e d f o r m a t i o n v a r i a b l e s ;

( ii i) u n e e ha .r ge d e g r a n d e u r e o n s t a n t e d e d u r e v a r i a b l e .Rock Mechan ics, Vol. 2/3 9


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124 Z . T . B i e n i a w s k i :On a d6m ont r6 que l a roehe f r ae tu re p o s s ~de en e f f e t une s t a b i l i t de longue du re .B i e n q u ' a u d b u t s a r s i s t a n c e e t s a d 6 f o l ~ a t i o n s o i e n t a f f e c t e s p a r l e t e m p s - - s a s t a b i l i t e s t a t t e i n t e u n e c e r t a i n e p o q u e . I1 e s t a i n s i p o s s i b l e d e d t e r m i n e r d e s c o u r b e s d e s t a b i l i t d e l o n g u e d u r e d e s r o c h e s f r a c t u r e s . C e c i p o u r r a i t f o u r n i r d e s d o n n e s p o u r l e c a l c u l d es t a b i l i t d e s t r u c t u r e s r o c h e u s e s s o u m i s e s d e s t a n x d e c h a r g e m e n t m o d r s .

l n t r o d u c t i o nK n o w l e d g e o f th e b e h a v i o u r o f f r a e t u r e d r o c k i s o f e o n s i d e r ' a b l e p r a e t i e a l

i n t e r e s t . F o r i n s t a n e e , a t g r 'e a t d e p t h s , f r a e t u r i n g o f r o ck a r o u n d e x e a v a~ i o n s i su s u a l l y u n a v o i d a b l e . I n o t h e r e a se s , f r a e m r e d r oc k m a y e r e n b e d e s i r a b l e ; f r a c m r e dr o c k i s le s s p r o n e t o s u d d .e n a n d v i o l e n t f a i l u r e t h a n s t r o n g , s o l i d ro c k a n d h e n e et h e f o .r m e r i s l e ss l i k e l y t o l e a d t o r o c k b u r s t s . F u r t h e r , i f i n t h e e a s e o f r o o m -a n d - p i l l a r s t o p i n g w i t h p a n e l s , y i e l d i n g o f i n d i v i d u a l p i l l a r s i n a p a n e l i s i n t r o -d u e e d b u t t h e s t a b i l i t y o f t h e p a n e l a s a w h o.le i s n o t e n d a n g e r e d , g r e a t e r e x tr ae ~ ;i ono f o r e w i ll b e a e h i ev e d . T h u s , p r o v i d e d t h e b e h a v i o u r o f f r a e t u r e d r o c k e a n b eu n d e r s t o o d a n d e o n t ro . ll e d , i t s p r e s e n e e e o u l d r e d u e e h a z a r d s a n d e r e n r e s u l t i ns i g n i f i e a n t e e o n o m i e a d v a n t a g e s .

O n e o .f t h e m o s t u s e f u l a p p r o a e h e s t o s t u d i e s o f f r a e t u r e d r o c k i s t h e d e t e r -m i n a t i o n o f t h e s o e a l l e d " e o m p l e t e l o a d - d e f o . r m a t i o n e u r v e s " (B i e n i a w s k i e t a l ,1 9 6 9 ; J a e g e r a n d C o o k , 1 9 6 9 , p . 1 6 7 ). D i a g r a m m a t i e a l l y , t h i s i s i l l u s t r a t e d i nF i g . 1 : U p t o th e s t r e n g t h f a i l u r e , m a r k e d A , th e r o c k r e m a i n s p r a e t i e a l l y i n t a e t .T h e r o c k b e h a v i o u r b e y o n d p o i n t A i s g o v e r n e d b y t h e s t if f n e s s o f t h e l o a d i n g

PBj A \O4 S ~cF i g . 1 . S p e e i m e n r e s i s t a n e e - d e f o r m a t i o n d i & g r a m a n d t e s t i n g m a c h i n e l o a d - d e f o r m a t i o nd i a g r a m s f o r s o f t (AB) a n d s t i f f (AD) m a c h i n e s

X = l o a d P o r r e s i s t a n e e R ; Y = d e f o r m a t i o nW i d e r s t a n d s - V e r f o r m u n g s - D i a g r a m m v o n P r f k r p e r u n d L a s t - V e r f o r m u n g s - D i a g r a m m vo nP r f m a s c h i n e n f r , w e i c h e " (AB) u n d , s t e i f e " (AD) M a s c h i n e n

X = L a s t P o d e r W i d e r s t a n d R ; Y = V e r f o r m u n gG r a p h i q u e r s i s t a n e e - d f o r m a t i o n d ' u n e h a n t i l lo n e t g r a p h i q u e s c h a r g e -d p l a .e e m e n t p o u rdes mach ines d ' e . s s a i mo l le (AB) e t r a i d e (AD)

X = & a r g e P o u r si s ta . n ee R ; Y = d p l a e e m e n tm a e h i n e , r e p r e s e n t e d b y l i n e s AB a n d AD, r e s p e e t i v e l y , f o r a s o f t a n d a s t i f tm a e h in e . B e y o n d s t r e n g t h f a i l u r e , i n e r e a s e in s p e e i m e n d e f o r m a t i o n , As, r e s u l t si n d e e r e a s e d r e s i s t a n e e , R e . In t h e e a s e o f t h e s o f t ( c o n v e n t i o n a l ) l o a d i n g m a e h i n e( a b o u t 5 0 M N / m s t i f fn e s s ) , t h e a p p l i e d l o a d P B w o u l d b e higher t h a n t h e s p e e i-m e n r e s i s t a n e e Rc. T h e s p e e i m e n t h u s f a i l s v i o l e n t l y a t p o i n t A - - a b e h a v i o u ro f t e n o b s e r v e d i n r o ck . I n a s t i f f l o a d i n g m a e h i n e ( m o r e t h a n 5 0 0 M N / m s t i ff n e s s ) ,t h e a p p l i e d l o a d PD w o u l d b e lower t h a n t h e s p e c i m e n r e . si s ta n e e Re. T h i s s i t u a t i o n


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Time-Dependent Beh aviou r of Prac tured Rock 125is "s table" and wi th increasing spec imen deformat ion , the resis tance of the spee i -men gradual ly decreases a long l ine ACE in Fig. 1.S inee the ro& ma te r i a l i s i n a f racmred s t a t e a f t e r s t r eng th fa i lu re , hav ingpassed i t s maximum load bear ing capac i t .y , a va luable mea .ns of obta in ing anins igh t in to the behav iou r o f f r ae tu red rock i s p rov ided by s tudy ing the eom-p le te " load -de fo rma t ion" o r r a the r " re s i s t anee -de fo rn la t ion" eu rves ob ta ined inst i f t tes t ing maehines.The eoncept of eomple te Ioad-deformat ion eurves or ig ina ted in s tudies onconcre te in compress ion conduc ted by R s e h (1960) in Ge rmany . He a l soobta ined the f i rs t comple te load-deformat ion curves in tension , aga in for eoncre te(R s eh , 1963). The des i rab i l i ty of ob ta in ing in fo rma t ion on the behav iou r o frock a f t e r s t r eng th fa i lu re was f i r s t po in ted ou t by Cook (1965) , fo l lowed up byF a i r h u r s t a n d C o o k ( 19 6 5) . T h e f i r s t c o m p le t e l o a d - d ef o r m a t i o n c uI a~ es f o rr oc k w e re o b ta i ne d b y B i e n i a w s k i ( 19 66 ) a n d b y C o o k a n d H o j e m ( 19 66 ).Since then rauch a t tent ion has been devoted in rock mechanies to th is subjec t andb es id e s e xt en si ve l a b o r a to r y t es ts ( B i e n i a w s k i , 1 96 7 ; W a w e r s i k , 1 9 68 ;B i e n i a w s k i , 1 96 9) t he f i r s t u n d e r g r o u n d t e s t s h a v e n o w a ls o b e en u n d e r t a k e n( B i e n i a w s k i , 1 9 7 0 ) .I t now only remains to establ ish the fae tors whieh inf luence the behaviouro f f racmred rock .

F a c t o r s o f I n f l u e n c e o n t h e B e h a v i o u r o f F r a c t u r e d R o c kThe behav iour o f f r ae tu red rock i s cha rae te r i zed by the re s i s t ance -de fo rma t ioncurve a f te r s t rength fa i lure , in the region where the curve has a nega t ive s lope .As d iseuss ed abov e (see Fig. 1), the s pecim en will fai l vio lent ly if the negativeslope of the rock resis tance-deformat ion cui~:e i s s teeper than the (nega t ive) s lopercpresent ing the s t i f fness of the loading machine . Knowledge of the fae tors whichdetermine the so lpe of the resis tance-deformat ion eurve a f te r s t rength fa i lure i stherefor e of par t icu la r imp ortanc e i f v io lent fa i lure of f rac tur ed rock is to be avoided.Resu l ts o f r eeen t s tud ie s have shown (B ie n ia w s k i , 1969) tha t inc rea s ingconfin ing pressure tends to f la t ten the nega t ive s lope of the rock. Thus, a f rae-tured rock see imen is more s table in t r iax ia l compression than in uniaxia l com-pression . In addi t ion , i t was found then tha t a change in spec imen shape , forexample , a h igher width to he ight ra t io , a lso resul ts in a f la t ten ing of the nega t iveslope . A ree tangular (oblong) spee imen is more s table than a eubiea l spec imenhaving the same cross-sec t ion .I t w a s al so r ee e n tl y s h o w n ( B i e n i a w s k i , 1 9 7 0) t h a t ro ck m a t e r i al s h a v in ga h igher uniaxia l compressive s t rength e r a h igher modulus of e last ic i ty , or both ,have s teeper nega t ive s lopes than mater ia ls wi th lower s t rength or modulus va lues .Consequen t ly "hard" high-st rength rock wi l l be more prone to v io lent fa i lure than' sof t" , low-st ren gth rock.The fac tor whi& has not as ye t been invest iga ted is the inf luenee of t imeon the behaviour of f rac tured rock. This fae tor i s of par t icula r in te rest as i t i sassoc ia ted wi th the !ong-te rm stabi l i ty of f rac tured rock. I t i s the purpose ofth is paper to contr ibute to the knowledge of th is aspee t .Whi le no in fo rma t ion on t ime-dependen t behav iou r o f f r ac tu red rock eou ldbe found on the l i te ra ture , some da ta of in te rest to the present s tudy have beenrepor t ed fo r eonc re te by R s e h (1960) . In F ig. 2 , a f t e r R s ch , s t r e ss - s t ra inre la t ionships a re g iven for concre te subjee ted to var ious constant s t ra in ra tes . I twi l l be noted f rom th is f igure tha t , wi th increasing ra te of s t ra in ing , the uniaxia lcompressive s t rength as wel l as the modulus of e last ic i ty ( in the unfraemred s ta re )increase . I t i s in te rest ing to reea l l tha t ident ica l behaviour i s a lso typica l of rock( S e r d e n g e c t i a nd B o o z e r , ] 96 1) .

9*


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126 Z.T. Bi en ia ws ki :The most i mp or ta nt observatio.n to be made from Fig. 2 is that the negative

slope of the st.ress-strain curves after strength failure gradually becomes flatteras the rate of strai nin g deereases. Should a simi lar trend be also observed forrock, this could be of considerable practical signifieance, as will be diseussed Iater.

2520 ~ s e c I YEAR15 ~ I MONTHe e

X z10 1670xi ~ IDAY1 0 0 0 0 x 1 0-

5 ~ 1HOUR10 MINUTESio ~ ~ - ; ~ , ~ 6

YF i g . 2 . S t r e s s - s t r a i n r e l a t i o n s h i p s f o,r e o n c r e t e f o r v a r i o u s e o n s t a n t s t r a i n r a t e s ( a,f ~e rRsch, 1960)X = uniaxial eompressive stress (MN/m2); Y = axial strain (10-~); Z = loading dara.tionneeded to attain 6" 10 .3 str ain with the strain rates indieat.edSpannungs-Dehnungs-Diagramm fr Beton unter verschiedenen konstanten Dehnungs-ges.ehwindigkeiten (nach R s e h, 1960)X = einaehsige Druekspannung (MN/rn2); Y = axiale Dehnung (10-a ); Z = erfo.rderlieheBelastungsdauer zur Erreiehung einer Dehnung vo.n 6 10 3 bei den angegebenen Dehnungs-

geschwindigkeiten; year = Jahr; mont.h = Monat; day = Tag; hour = StundeCourbes eontrainte dfo.rmation d' un bton pour diffrentes vitesses de dformationeonstantes (d'aprs R s e h, 1960)X = eontrain te de compressio,n monoaxiale (MN/m2); Y = dformation axiale (10-~) ;Z = dure de &arge ncessaire [o ut atteindre une dformation de 6 ' 10 -a aux vitessesindiques; yea.r = an; month = mois; day = jour; hcur = heure

An investi gation was therefore in itiat ed the purpose of whieh was to derer-mine the load-deformation behaviour of fraetured rock at various strain rates andat eonstant load for var'ious durations. Thre,e eases were eonsidered, believed tobe applieable to in-situ behaviour of rock struetures:

(i) g raduall y inereasing eompression at different but eonstant str ain rates.(ii) gradually inereasing eompression at ehanging strain rates.

(iii) eonstant load. applieation for various time durations.E x p e r i m e n t a l P r o c e d u r e s

The equipment omd teehniques used in this study have been deseribed indetail eisewhere (B ie ni aw sk i et al, 1969). Briefly, the equip ment eonsisted ofa speeially designed eompressive loading ma~hine with var iable l ong itud inal stift-ness o.f up to li 0O MN/m. The axial load on the spe eimen as weil as its axialdeformation were automatieally plotted on a high sensitivity X-Y reeorder. Nomeasurement,s o.f lateral deformation were mode. All tests were eonducted in uni-axial eompression.

The rock material used was a fine-grained sandstone. The speeimens, afterbeing aecurately prepared, were plaeed for over one month under eonditions ofeons tant temperatur'e (20C) and eonst ant hu mid ity (50 /0). Some 30 speeimens


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Time-Dependent Behaviour of Fractured Rock 127were test ed, the specimens being cyli ndri cal in shape and havin g a di ameter of21.6 mm a nd a height of 10.8 mm, thus yield ing a dia ne te r to heigh~ ratio of 2.This geometry was ehosen sinee mine pillars in South Afriea have generally widthto height ratio of 2 and are square in plan.

f i r a d u a l l y l n c r e a s i n g C o m p r e s s i o n a t C o n s t a n t S t r a in R a t e sThe condition of gradually increasing compression at a constant strain rate

is orten encountered in mining such as, for example, in mine pillars during thesystematic extraction of ore in the panel in which they are sit.uated.

In or der to dctermine the influence of str ain rate on the eomplete load-deform ation curve of ro& sub jected to grad uall y inereasi ng eompressive deforma-tion, a series of tests - simil ar to those eondueted by R se h (1960) for eoncrete- - was undertaken.

The experim ental procedure was as follows. Pre lim ina ry tests ware first eon-dueted to determine the average maximum speeimen deformation at rupture. Thisdeformation was found to be 0.15 mm. Then speeimens were subjeeted to graduatlyincreasing eompressive deformation at c o n s t a n t str ain rates such that 0.15 mmdeformatio n would be attain ed after 7 minutes , 2 hours al d 9 hours respeetively.This eorr esponded to str ain rates of 33 10-6/see, 1.94" 10-6/ see and 0.43 - I0 -6per sec respeetively or to rates of deformation of 2 2 10-3 mm/m in, 1.25 l0 -'~ mmper min a nd 0.28 mm/m in, respectively. In this manner , data for rock eomparableto those obtained for eonerete by R s eh (see Fig. 2) -- were obtained.

The re sult s are giv en in Fig. 3, in which eaeh eurve, for a specifie str ainrate, represents an average of a number of tests.

5 0

3C / ~ / 0 - X { ~ ,

2G

005 0 '10 0 "15Y

Fig. 3. hffluence of rate of strain on the complete load-deformation curves of sandstonein uniaxiM eompressionX = load (kN); Y ~ deformation (min)Einf lu der Dehnungsgeschwindigkeit auf die vollstndigen Last-Verformungskennlin ien vonSandstein bei einaehsigem DruckX = La.st (kN); Y = Verformung (mm)Effet de la vitesse de dformation sur les eourbes effort-dformation eomp]tes pour ungrs en eompression monoaxialeX = &arge (kN); Y = dplaeement (min)


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128 Z.T. Bi en ia ws ki :It will be seen from Fig. 3 that a higher strain rate results in a higher modulus

of elastieity (steeper positive slope before strength failure) and in a higher strengthfailure stress of the speeimens. The mo,st important obsmwation is, however, thatthe lower the strain rate (longer duration of loading), the flatter is the slope o.fthe load-defo,rmation eurve after stren gth failure. This is a very signi fieant fin din gas it indieates that the likelihood of violent failure of fraetured rock, if the strain

I o.o~iI~_- l ~ - I l ; ~,ooo0 8 0X I e o s o/+20 / * 0' 31 0 1 0 1 0 a 1 0 - 6 i 0 ~ ' i O ~ I O s I a

Y

Xz " ~ t l f i ' i' - ~ ' " - ~ ' - ' " - ~" ' ' ~ : I I T X - U Ft t - ~ - q ~ . , oi o 1 0 g l O - e I 0 -7 I 0 s 1 0 ] f ~

Y

~~I ; ; 4 ~ b ~ l ~ ' : i ~ - ~ J ~ ~ ~ ~3 : 1 - - - ] ] I l ] ] I l i s i1 0 " ~ o I t T 9 1 0 - a i 0 - ~ 1 0 r , l f f 5 1 O ~

YFig. 4. Inflnenee of strain rate oll strength f~ilure, strain at strength failure and modulus ofclasticity for sandstone in uniaxial eompressionX 1 = strength failure (MN/m2); X 2 = strain at strength failure (10-3); X 3 = modulusof elastiei ty (GN/m2); Y = strain per seeondEinflu der Dehnungsgesehwindigkeit auf Bruehfestigkeit, Bruehdehnung und Elastizitts-modul von Sandstein bei einaehsigem Dru&X~ -- Bruehfestigkeit (NM/m2); X2 = Bruehdehnung (10 a); X~ = Elastizittsmodul (GN/m'~);Y = Dehnung pro SekundeEffet de la. vitesse de dformation sur la rsistanee la rupture, la dformation la ruptureet le module d'lasfieit pour un grs en eompression monoaxialeX 1 = rsistanee la ruptu re (MN/m2); X2 = dfo.rmation la rupture (10-3 ); X~ = moduled'lastieit (GN/m2); Y = dformation par seeonde

increases -- as found in yielding mine pillars left standing for a long period oftime -- will be less the slower the rate of strain. Fraetured ro& subjeeted to slowstrain rates is, therefore, more stable than that subjeeted to higher ones. Thiscan also now explain why rock subjeet to a sudden and violent energy release,such as in a rockburst, fails une ont rol lab ly -- its st abili ty is dim inish ed due toits steep load- defor mation eharaet,eristies after s trengt h failure, at high rates ofstrain.

The re sults given in Fig. 3 are applie able to rates of stra in d own to 0.43 10 -per seeond (0.15 mm def onn atio n after 9 hours). This is, of course, not eom-parable to in situ eonditions where rauch smaller rates of st.rain are eommon sineethe pillars may be subjeeted to prolonged loading with inereasing strain overmany years.


7/15

T i m e - D e p e n d e n t B e h a v i o u r o f F r a c t u r e d R o ck 1 29I t w o u l d , t h e r e f o r e , b e d e s i r a b l e t o d e t e r m i n e s u ch d a t a f o r r o c k f o r v e r y s lo ws t r a i n r a t e s ( in t h i s e a se 0 . 1 5 m m d e f o r m a t i o n i n o n e y e a r ) , a s w a s a c h i e v ed f o rc o n c r e t e b y R s e h ( se e F i g . 2 ). T h i s w o u l d u n f o r t u n a t e l y b e a v e r y t i m e e o n -s u m i n g p r o c e s s a n d w o u l d a l s o p r e s e n t c o n s i d e r a b l e e x p e r i m e n t a l d i f f i e u l t e s . I n

f a c t , t h e a u t h o r ' s a p p a r a t u s i s n o t e q u i p p e d t o d e m w i t h s u c h s m a l l s t r a n r a t e s .D u e t o t h e i m p o r t a n c e o f t h e m a t t e r , h o w e v e r , e x t r a p o l a t i o n o f t h e r e s u l t sw a s a t t e m p t e d . I t w a s t h o u g h t t h a t i f d e f i n i t e t r e n d s e o u l d b e e s t a b l i s h e d e o n -c e r n i n g t h e i n f l u e n e e o f s t r a i n r a t e o n s t r e n g t h f a i l u r e , m o d u l u s o f e l a s f i e i t y ,s t r a i n a t f a i l u r e a n d t h e n e g a t i v e s l o p e o f t h e l o a d - d e f o r m a t i o n e u r v e a f t e r s t r e n g t hf a i l u r e , t h e n t h e r e l e v a n t d a t a f o r s l o w e r s t r a i n r a t e s e o u l d b e p r e d i e t e d .E x t r a p o l a t i o n o f t h e d a t a o n t h e f i r s t t h r e e v a r i a b l e s , a s o b t a i n e d f r o m F i g . 3 ,i . e . s t r e n g t h f a i l u r e s s t r e s s , s t r e n g t h f a i l u r e s t r a i n a n d m o d u l u s o f e l a s t i e i ty , i ss h o w n i n F i g . 4 ( e x p e r i m e n t a l d a t a - - s o l i d l i n e s, e x t r ~ p o l a t e d d a t a - - b r o k e nl i n e s ) . T h i s f i g u r e s h o w s a d e f i n i t e t r e n d i n t h e s e q u a n t i t i e s , t h u s e n a b l i n g t h e i rd e t e r m i n a t i o n f o r v e r y s m a l l r a t e s o f s t r a / n .T o r e e o g n i s e a t r e n d t h a t w o u l d p e r m i t e x t r a p o l a t i o n o f t h e n e g a t i v e s l o p e a f t e rs t r e n g t h f a ,i lu r e t o v e r y s m a l l s t r a i n r a t e s, t h e r e s u l t s o n s a n d s t o n e a r e e o m p a r e d ,i n F i g . 5 , w i t h t h o s e o b t a i n e d f o r e o n e r et e b y R s e h ( 1 9 6 0 ) , w h o t e s t e d d o w n

2 t1 0 1 0 - u 1 0 - 9 1 ~ s 1 ~ ~o I f f 1 t 0 6

Y

tO s

10'~ .

X

1 3 ' ~ "~ -

F i g . 5 . E f f e e t o f s t r a i n r a t e o n s t r e s s - s t r a i n s l o p e a f t e r s t r e n g t h f a i l u r e f o r s a n d s t o n e a n de o n e r e t e i n u n i a x i a l e o m p r e s s i o nX = s l o p e o f s t r e s s - s t r a i n e u r v e a f t e r s tr e n g t h f a i l u r e ( M N /m 2 ); Y = s t r a i n p e r s e e o n dE in f lu d e r De b~nungsge sc hwind igkei t a u f d ie Ne igun g de r Spa n nun gs -D e hn ung s -K urve na c he r f o l g t e m B r u c h f r S a n d s t e i n u n d B e t o n b e i e i n a c h s i g e m D r u c kX = N e i g u n g d e r S p a n n u n g s - D e h n u n g s - K u r v e n a c h b e r s c h r e i t e n d e r B r u c h f e s t i g k e i t(MN/m2) ; Y = Ve r fo rmu ng p ro Se kun deE f f e t d e l a v i t e s s e d e d f o r m a t i o n s u r l a p e n t e d e l a e o u r b e e f f o r t - d f o r m a t i o n a p r s l ar u p t u r e p o u r u n g r s e t u n b t o n e n e o m p r e s s i o n m o n o a x i a l eX = p e n t e d e l a e o u r b e e f f o r t - d f o r m a t i o n ap r s l a r u p t u r e ( M N / m e ) ; Y = d f o r m a t i o n

p a r s e e o n d et o a s t .r a i n r a t e o f 0 . 1 9 - 1 O - 9 / s e c , i . e . l o a d i n g d u r a t i o n o f o n e y e a r , a s s h o w n i nF i g . 2 . I t w i l l b e s e e n f r o m F i g . 5 t h a t i t i s r e a s o n a b l e t o a s s u m e t h a t t h e d a t af o r s a n d s t o n e ( e x p e r i m e n t a l - - s o l i d l i n e , e x r a p o l a t e d - - b r o k e n l i n e ) w o u l d g i v e


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130 Z.T. Bi en ia ws ki :a similar trend as that for eonerete, particularly in view of the phenomenologicalsimil~rity between eonerete and rock.

Based u pon the data prese nted in Figs. 4 and , an attempt was made to eon-struet the curves depieting the influence of stra in rate on the eomplete stress-stra in for rock. The results are given in Fig. 6. The data are presen ted in terms

125

0.127 X O}sec10 /sec

-9~ 5 ~ 1 0 / s e c

33 300 x lO /sec

e(lrs

lyelrImonth

I d a y

thourI0 m i n

5 10 15 20Y

Fig. 6. St ress-strain rel~tionships for sa~dstone for various cons tant st rain ratesX = uniaxial eompressive stress (MN/me); Y = axial strain (10-s ); Z = durat ion ofloading needed to attain 20" 10 -3 strain with the stra in rates indieatedSpannungs-Dehnungs-Diagramme fiir Sandstein bei verschiedenen konstanten Dehnungs-geschwindigkeitenX = einaehsige Druckspannung (MN/m 2); Y = axiMe Dehnung (10 -s ); Z = erforderlicheBelastungsdauer zur Erreiehung einer Dehnung von 20 ' 10 s bei den angegebenen Deh-nungen; year = Jahr; month = Monat; day = Tag; hour = StundeCourbes eontr~inte-dformation d' un grs pour diverses vitesses de dformation eonsta~ntesX = eontrainte de eompression monoaxiale (MN/m2); Y = dformation axiale (10-~);Z = dure de ehargement ncessaire pour atteindre nne dformation de 2 0-10 -3 auxvitesses de dformation indiques

of stress versus strain to facilitate comparison with Fig. 2 for conerete. In Tab. 1,both stress-st rain and load-deformation data are sum marized for eonvenience.

It will be seen from Fig. 6 that a five-year loading duration at the constantstr ain rate of 0.1 27 ' 10-9/sec, yields a much flatter slope of the eurve afterstrength failure thax4 that for l0 minutes loading durati on at the constant strai nrate of 33 300 10-9/s ec. In faet, fro m Tab. 1, there is a change from 50 9.5 MN/mfor 333 00" 10-9/sec to 42.1 MN/m for 0. 12 7- 10 -9 /s ec -- this is over 12-foldimproveme nt. It is also int erestin g to note from the last eolumn of Tab. 1 thatthere is a gradual increase in the radio of the positive to negative slope with in-ereasing rate of strain. It is believed that these data will be of praetieal signi-fieaaaee for dete rmin ing the long-telzn stab ilit y of struct ures involvi ng fraetu redrock,


9/15

T i m e - D e p e n d e n t B e h a v i o u r o f F r a c t u r e d R o c k 131T a b le 1. l n f I u e n e e o f s t r a i n r a t e o n s t r e n g t h a n d d e f o r m a t i o n e h a r a e t e r i s t i e so f s a n d s t o n e

( e x t r a p o l a t e d f r o m t e s t s w i t h s t r a i n r a t e s d o w n t o 0 .4 3 1 0 - 6 /s e e )

1 0 m i n u t e s1 h o u r1 d a y1 m o n t h1 y e a r5 years

S t r a i nr a t e1 0 ' / s e e

33 300.005 560.00232.007.720.640.13

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10 3 !G N /m 25 . 4 ] 2 9 . 16. l 26 .77.3 22.88.6 19.09.6 15.910.2 13.5

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G N / m15.111.78 .44.22.11.3

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k N m m M N /m42.1 0.058 981.838.9 0.066 900.937.1 0 .079 769.335.4 0.093 641.134.7 0.104 536.533 .6 0 .1 1 1 455 .1

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G r a d u a l l y I n c r e a s i n g C o m p r e s s i o n a t C h a n g i n g S t r a i n R a t e sI n m i n i n g , t h e s t o p i n g o p e r a t i o n s m a y , i n t h e c a s e o f p i l l a r s , e a u s e r e d i s t r i b u -

t i o n o f t h e l o a d o v e r t h e p i l l a r s s u ch t h a t t h e s e m a y b e s u b j e e t e d t o i n e r e a s i n go r d e c r e a s i n g r a t e s o f s t r a i n . I t i s , th e r e f o r e , o f p r a c t i c a l i n t e r e s t t o e x a m i n et h e b e h a v i o u r o f r oc k u n d e r g r a d u a l l y i n e r e a s i n g c o m p r e s s i v e d e f o r m a t i o n a t v a r y -i n g s t r a i n r a t e s .

T o e x p l o r e t h e r e a c t i o n o f f r a c t u r e d t o & t o a s u d d e n e h a n g e i n s t r a i n r a t e ,t w o s e r i e s o f t e s t s w e r e c a r r i e d o u t :

(i) S p e c i m e n s w e r e l o a d e d a t t h e c o n s t a n t s t r a i n r a t e o f 3 3 1 0 - 6 / s e e b e y o n ds t r e n g t h f a i lu r e , u p t o a n a r b i t r a r i l y c h o se n d e f o r m a t i o n o f 0 . 08 m m . T h e n t h es t r a i n r a t e w a s e h an g e d to 0 . 4 3 ' 1 0 - 6 / s e e a n d k e p t e o n s t a n t t h e r e a f t e r . L o a d a n dd e f o r m a t i o n w e r e r e e o r d e d t h r o u g h o u t t h e te s t .

( it ) S p e e i m e n s w e r e l o a d e d a t t h e e o n s t a n t s t r a i n r a t e o f 0 . 4 3 1 0 - 6 /s ee b e y o n ds t r e n g t h f a i l u r e , u p t o a n a r b i t r a r i l y cho,sen d e f o r m a t i o n o f 0 . 1 2 m m . T h e n t h es t r a i n r a t e w a s c h an g e d t o 3 3 " 1 0 - 6 / s e e a n d k e p t c o n s t a n t t h e r e a f t e r . L o a d a n dd e f o r m a t i o n w e re r e e o r d e d t h r o u g h o u t t h e t es t .

T h e e o m p l e t e lo a d - d e f o r m a t i o n e u r v e s d e p i e t i n g t h e r e s u l t s o f t h is s t u d y a r eg i v e n i n F i g . 7 , f r o m w h i c h t h e f o l lo w i n g o b s e r v a t i o n s a r e m a d e :

C o m p a r i n g t h e e as e o f e h a n g i n g t h e s t r a i n r a t e f r om 3 3 ' 1 0 - 6 / s e e t o0 . 4 3 " 1 0 - 6 / s e e ( f u ll e u r v e A ) w i t h t h e e a s e o f k e e p i n g t h e s t r a i n r a t e e o n s t a n ta t 3 3 " 1 0 - 6 / s e e t h r o u g h o u t t h e t e st ( d o t t e d e u r v e A ) , s h o w s t h a t a s u d d e nd e c r e a s e i n t h e s t r a i n r a t e r e s u l t s i n a n i n i t i a l s t e e p e n i n g o f t h e n e g a t i v e s l o p e o ft h e l o a d d e f o r m a t i o n e u r v e , f o l l o w e d b y a f l a t t e n i n g o f t h i s s l o pe . T h e r e a s o n f o rt h e i n i t i a l s t e e p e n i n g i s t h a t f o r a d e e r e a s e i n t h e r a t e o f s t r a i n , t h e r e s is t m a e eo f t h e s p e e i m e n a l s o d e e r e a s e s ( se e F i g . 6 ). S u b s e q u e n t f l a t t e n i n g i n t h e s l o p e i sd u e t o th e f a e t t h a t a s t h e d e e r e a s e d s t r a i n r a t e t a k e s e f fe e t , t h e e o n f i g u r a t i o no f t h e e u r v e i s t y p i c a l f o r t h i s r a t e o f s t r a i n . A s F i g . 7 s h o w s , t h e e u r v a t u r e s o ft h e f u l l a n d d o t t e d e u r v e s f o r 0 . 4 3 " 1 0 - 6 / s e e s t r a i n r a t e a r e th e s a m e .

C o m p a r i n g t h e e a se o f c h a n g i n g th e s t r a i n r a te f r o m 0 . 4 3 - 1 0 - 6 / s e e t o3 3 ' 1 0 - 6 / s e e ( f u l l e u r v e B ) w i t h t h e c a s e o f k e e p i n g t h e s t r a i n r a t e co ns~ aa~ t a t


10/15

132 Z . T . B i e n i a w s k i :0 . 4 3 - 1 0 - 6 / s e c t h r o u g h o u t t h e t e s t ( d o t t e d c u r v e B ) , an i n i t ia l i n e r e a s e i n t h es p e c i m e n r e s i s t a n e e i s a p p a r e n t , f o l lo w e d i m m e d i a t e l y b y a s te e p n e g a t i ve s l op e .T h i s s l o p e is a p p a r e n t l y t h e s a m e a s t h a t o f th e 3 3 " 1 0 - 6 / s e e s t r a i n r a t e e u r v e .Th e c u r v a t u r e s o f t h e f u l l a n d d o t t e d e u r v e s f o r 3 3 l 0 6 /s e e s t r a i n r a t e a r e t h es a me .I t m a y b e c o m m e n t e d f r o m t h e a b o v e o b s e r v a t i o n s t h a t a e ha n g e i n t h e r a t eo f s t r a i n p r o d u e e s a t w o - f o l d e f f e e t o n f r a e t u r e d r e & :

( a ) a n i n i t i a l d e e r e a s e e r i n e r e a s e i n t h e r e s i s t a n e e , e o r r e s p o n d i n g t o a d e -e r e a s e e r i n c r e a s e , r e s p e e t i v e l y , i n t h e s t r a i n r a t e ;

( b ) s u b s e q u e n t f l a t t e n i n g e r s t e e p e n i n g o f t h e n e g a t i v e s l o p e , e o r r e s p o n d i n gt o a d e e r e a s e e r i n c r e a s e , r e s p e e t i v e l y , i n t h e s t r a i n r a t e .

Th e f i r s t e f f e e t i s d u e t o t h e r e l a t i o n s h i p b e t we e n t h e r e s i s t a n e e a n d t h e s t r a i nr a t e ( s ee F i g . 6 - - r e s i s t a n e e d e c r e a s e s w i t h d e e r e a s i n g s t r a i n r a t e ) wh i l e th es e e o n d e f f e c t r e f l e e t s t h e r e l a t i o n s h i p g i v e n i n F i g . 3 , i . e . t h e e u r v a t u r e o f t h ec u r v e i s e h a r a e t e r i s t i e f o r a g i v e n s t r a i n r a t e . I n t h i s e a s e , e o n s i d e r i n g F i g . 7 ,

3{x

2C

lC

50

CURVE A

~;CURVE BI

, - - -%~\ 'x~33 x10-~/

0 i I0.05 0.10 0.15 0-20

YFig. 7. Effect o f ehanging stra,in rate on the beh avio ur of fra eture d rock

X = load (kN); Y = defon nation (mm)Einflu der ver.ndeHi&en Dehnungsgesehwindigkeit auf das Verhalten von gebroehenemGestein

X = Las t (kN); Y = Verform ung (mm)Effet d 'un changement de vitesse de dformation sur le eomportement de la roehe fraemre

X = charge (kN); Y = dplaeemen t (mm)

i f t h e d o t t e d e u r v e A o f 3 3 1 0 - 6 / s e c s t r a i n r a t e i s s h i f t e d t o th e r i g h t a n d s u p e r -i m p o s e d a n d t h e s o l i d c u r v e B o f 33 1 0 - 6 / s e c , t h e n b e , th e u r v e s w i l l e o i n e i d e s i n c et h e c u r v a t u r e s o f th e s e e u r v e s a r e t h e s a me . I n p r a c t i c e b e t h e f f e e t s ( a ) a n d ( b)a b o v e , y i e l d a g r a d u a l t r a n s i t i o n f r o m t h e r e s i s t a n c e c h a n g e t o t h e c u r v a t u r ec h a n g e , d u e t o t h e f a c t t h a t t h e s t r a i n r a t e c a n n o t b e c h a n g e d a b s o l u t e l y s u d d e n l y .S h o u l d t h e r a t e o f s t r a i n b e c h a n g e d r e a l l y s u d d e n l y f r o m h i g h e r t o l o w e r , t h er e s i s t a n c e s h o u l d i m m e d i a t e l y d r o p t o a v M u e c o r r e s p o n d i n g t o t h e l o w e r s t r a i nr a t e a n d t h e n t h e e u r v e s h o u l d i m m e d i a t e l y f o l lo w t h e e u r v a t u r e t y p i c a l o f t h el o w e r r a t e o f s t r a i n .


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Time-D ependen t Beh av iour o f F r ac tu r ed Rock 133A n o t h e r o b s e r v a t i o n w h i e h e a n b e m a d e f r o m F i g. 7 is t h a t a s a r e s u l t o f a

e h a n g e d s t r a i n r a t e f r o m 3 3 1 0 - 6 / s e c t o 0 . 4 3 " 1 0 - 6 / s e e , a t s p e e i m e n d e f o r m a t i o no f 0 . 1 5 m m t h e r e s i s t a n c e o f t h e s p e c i m e n i s i n e r e a s e d f r o m A ~ t o A 2 w h i le , e o n -v e r s e l y , a n i n c r e ~ s e i n t h e s t r a i n r a t e f r o m 0 . 4 3 1 0 - 6 / s e c t o 3 3 1 0 - 6 / s e c y i e l d s ,f o r th e s a m e s p e e i m e n d e f o r m a t i o n o f 0 . 1 5 m m , a d e e r e a s e i n th e r e s i s ta n e e f r o mB s t o B 1. T h i s p h e n o m e n o n i s , o f c o u r s e , d u e t o t h e e f f e c t ( b ) a b o v e . T h i s e u r v a t u r ee f f e e t t h u s y i e l d s t h e d e s i r a b l e e f f e e t o f a d e c r e a s e d r a t e o f s t r a i n , t h a t is , w h e nt h e e u r v a t u r e i n f l u e n e e t a k e s e f f e e t in s u c h a e a s e , n o t o n l y t h e s t a b i l i t y o f f r a e -t u r e d r o c k i s i n e r e a s e d ( f l a t t e r n e g a t i v e s l o p e ) b u t a l s o th e r e s i s t a n c e i s h i g h e r .O n t h e o .t he r h a a d , i n e r e a s i n g t h e s t r a i n r a t e r e s u l t s i n a n e v e n t u a l d e c r e a s e i ns t a b i l i t y ( s t e e p e r n e g a t i v e s l o p e ) a s w e l l as in a d e e r e a s e d r e s i s t a n e e .

T h e a b o v e f i n d i n g s i n d i e a t e t h e u n d e s i r a b l e e f fe e t t h a t a n i n c r e a s e d r a t e o fs tr a. in h a s o n t h e b e h a v i o u r o f f r a e t u r e d r o ck . I n p r a e t i e a l d e s i g n o f r o ck s t r u c t u r e si n v o l v i n g f r a e t u r e d r o ck , c a re s h o u l d b e t a k e n t o e n s u r e t h a t , i f a eh a n g e in s t r a i nr a t e i s t o t a k e p l a c e , i t s h o u l d b e d e c r e a s e d r a t h e r t h a n i n c r e a s e d .

C o n s t a n t L o a d i n g f o r V a r i o u s D u r a t i o n sT h e e o n d i t i o n o f c o n s t a n t l o a d i n g ( l o n g - t e r m l o a d i n g a t c o n s t a n t s t re s s l ev e l)

i s o r t e n f o u n d i n p ra e t i e e , p a r t i e u l a r l y i n m i n i n g w h e n , a f t e r e o m p l e t i o n o f o r ee x t r a e ti o n , r o c k s t r u e t u r e s s u c h as m i n e p i l l a r s a r e l e ft f o r a n i n d e f i n i t e l y l o n gt im e t o s u p p o r t t h e o v e r b u r d e n . I f th e p i l la r s a r e o f a y i e l d i n g t y p e , i . e . i na f ra e t u r e d s t at e , t h e i r b e h a v i o u r u n d e r e o n s t a n t l o a d , o v e r a l o n g p e r i o d o f t im e ,i s o f p a r t i e u l a r i n t e re s t .

I n o r d e r t o d e t e r m i n e t h i s b e h a v i o u r , t e s ts w e r e e o n d u e t e d t o e s t a b l i s h t h el o n g - t e r m s t a b i l i t y o f f r a e t u r e d r o ck . T h e e x p e r i m e n t a I p r o e e d u r e w a s a s fo l lo w s .

R o c k s p e e im e n s w e r e l o a d e d i n th e s t i f t m a e h i n e b e y o n d t h e i r s t r e n g t h f a i lu r e .A t a n a r b i t r a r y l o a d le v e l a f t e r s t r e n g t h f a i lu r e , t h e a p p l i e d l o a d w a s k e p t e o n -s t a n t o v e r s o m e p e r i o d o f t im e . S i n c e , h o w e v e r , t h e r o & w a s i n a f r a e m r e d s t a tea t t h a t s ta g e , i t c o u l d b e e x p e e te d t h a t d u e t o f r a e t u r e p r o p a g a t i o n , t h e r e s i s t a a e eo f t h e s p e e i m e n w o u l d d e c r e a s e a n d i ts d e f o r m a t i o n i n c r e a s e , e v e n i f t h e a p p l i e dl o a d w a s m a i n t a i n e d c o n s t a n t . T h e s p e e im e n r e s i s ta n e e w a s m e a s u r e d b y a l o a de e ll p l a e e d i n s e ri e s w i t h t h e s p e c i m e n w h i l e t h e a p p l i e d l o a d w a s i n d i e a t e d b yt h e s t i f t m a e h i n e p r e s s u r e g a u g e . A u t o m a t i e p l o t t i n g o f t h e s p e e im e n r e s i s ta n c ea n d i ts d e f o r m a t i o n w a s a f f e c te d b y a n X-Y r e c o r d e r . T h e a p p a r a t u s u s e d i s f u l l yd e s e r ib e d e ls e w h e re ( B i e n i a w s k i e t a l, 1 9 6 9 ).

I n F i g . 8 t y p i e a l r e s u l t s o f t h is s t u d y a r e s h o w n . A t p o i n t A i n t h i s f i g u r e,f u r t h e r e x t er n a l I o a d i n g w a s s t o p p e d a n d t h e a p p li e d l o a d w a s m a i n t a i n e d e o n s t a n t.T h e s p e e i m e n e o n t i n u e d t o d e fo r m , h o w e v e r , a s in d i c a t e d b y l in e A B . T h i s d e c r e a s ei n s p e e i m e n r e s i s t a n c e t o o k p l a c e d u r i n g 3 0 m i n u t e s , t h e r a t e o f s t r a i n d e e r e a s eg r a d u a l l y d r o p p i n g a s s h o w n i n t h e in s e r t o f F ig . 8 , u n t i l a t p o i n t B n o f u r t h e re h a n g e i n s p e e i m e n r e s i s t a n c e a n d d e f o r m a t i o n w a s o b s e r v e d . O b s e r v a t i o n w a sc o n t i n u e d f o r o n e h o u r , d u r i n g w h i c h t im e n o e h a n g e o c e u r r e d . T h e a p p l i e d l o a dw a s t h e n i n e r e a s e d a n d t h e s p e c i m e n r e s i s t a n e e a n d d e f o r m a t i o n f o l l o w e d t h e e u r v eBCD, r e s m n i n g i ts n o r m a l e h a r a e t e ri s t ic a t p o i n t C . T h e f a e t t h a t l i n e AB d o e sn o t e o i n d i c e w i t h l i n e A C i s d u e t o t h e s p e c i m e n r e s i s t a n c e d e e r e a s i n g d u e t o t h ed e c r e a s i n g r a t e o f s t r a i n , a s i n d i c a t e d i n t h e i n s e r t i n F i g . 8 .

A s i g n i f i e a n t f i n d i n g o f t h i s s t u d y w a s t h a t s p e c i m e n r e s i s t a n c e a n d d e f o r m a -t i o n r e m a i n e d e o n s t a n t a t p o i n t B . T h u s , t h e f r a e t u r e d r o c k a t t a i n e d s t a b i t i t y a n db e e a m e f r e e f r o m a n y f r a e t u r e p r o p a g a t i o n a n d t i m e e f f e e t s .

T h e q u e s t i o n n o w a r i s e s a s t o w h e t h e r p o i n t B i s o n e o f a l o c u s o f p o i n t sf o r m i n g a l o n g - t e r m s t a b i l i t y c u r v e f o r f r a e t . u r e d r o c k . I f s u c h a e u r v e d o e s e x i s t ,t h e f u r t h e r q u e s o n i s, w h e t h e r o r n o t i t d e p e n d s u p o n t h e r a t e o f s t r a in .


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134 Z.T. Bi en ia ws ki :In order to answer these questions, further tests were conducted the resultsof whieh are given in Fig. 9 and 10.In Fig. 9 it is shown that a eurve does exist representing a locus of pointsat whieh fractured ro& does not ehange its resistance and deformation with time.

The portion of the curve after strength failure was found from a series of tests,as per Fig. 8, all "po ints B as per Fig. 8" bein g joined. For elarity of present atio nSO

~ I & o ~ o ,~ ~.o ~o

0 0 0 5 0 ' 1 0 0 ' 5 0 ' 2 0

YFig. 8. Dcformation al heha viour of fractured rock und er constant ]oad in uniaxia,]compressionX = load or resistance (kN); Y = deformat ion (mm); Z = changes in rate of st rainbetween points A and B; S = rate of stra in (10-6/sec); T = time (minutes)Verformungsverhalten von gebrochenem Gestein unter konstanter Last bei einachsigem DruckX = Last (L) oder Widerstand (R) (kN); Y = Verformung (mm); L = R = Last =Widerstand; Z = nderung der Dehnungsgeschwindigkeit zwischen den Punkt en A und B;S = Dehnungsgeschwindigkeit (10-8/sek); T = Zeit (Minuten)Comportcment de la roche fracture sous une charge constante en compression monoaxiMeX = charge ou rsis tance; Y = dplacement (mm); Z = changement de la vitesse dedformation entre A et B; S = vitesse de dformation (10-8/sec); T = temps (minutes)only four of these "points B" are shown in Fig. 9. The long term strength of intactrock, ind icat ed in Fig. 9, was obtai ned by subje cting the specimens to long termloading using the techniques and apparatus described elsewhere (Bieniawski,1967, p. 435).The long- term sta bili ty curve (lower curve in Fig. 9) for f ract ured rock wasobtained for specimens subjected to stan dard labora tory rate of loading (0.7 MN/m 2per sec = 100 lbf /inu per sec) corr espo ndin g to a rate of defor mation of 0.02 mmper m in or a st rain rate of 31 10-6/sec.

It is interesting to note from Fig. 9 that the negative slope of the long-terinstability curve is somewhat steeper than that of the original curve: 625 MN/m ascompare d with 510 MN/m. This difference, 22.5 /0, could per haps be at trib ute dto an experimental error. It is thus possible that the long-term stability curvehas the same negative slope as the corresponding eurve for a given rate of defor-


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T i m e - D e p e n d e n t B e h a v i o u r o f F r a c t u r e d R o c k 13 5m a t i o n . O n t h e o t h e r h a n d , t h e r e e o u l d b e a s l i g h t d i f f e r e n e e d u e t o t h e e ff e e t o fg r a d u a l l y d e e r e a s i n g s t r a i n r a t e ( f ro m p o i n t A t o B i n th e i n s e r t i n F i g . 8 ).

I t m a y f u r t h e r b e n o t e d t h a t t h e b r o k e n l i n es i n F i g . 9 a r e p a r a l l e l a n d t h e i rs l o p e o f 1 1 1 0 M N / m i s e lo s e to t h e s t i f f n e s s o f t h e t e s t i n g m a e h i n e u s e d , n a m e l y ,l I 0 0 M N / m . C o n s e q u e n t l y , u n d e r a e o n s t a n t a p p l i e d l o a d , f r a e t u r e d r oc k e o n t i n u e s

5 O

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0 ' 0 4 0 0 8 0 ' } 2 0 ' I Y

F i g . 9. L o n g - t e r m s t a b i l i t y o f f r a c t u r e d r o c k s u b j e e t e d t o a r a t e o f d e f o r m a t i o n o f 0 . 0 2 m mp e r m i n u t eX : l o a d ( k N ) ; Y = d e f o r m a t i o n ( m m ) ; SL = l o n g t e r m s t r e n g t h o f s o li d t o &

L a n g z e i t s t a b i l i t t v o n g e b r o e h e n e m G e s t e in b e i e i n e r V e r f o r m u n g s g e s c h w i n d i g k e i t v o n 0 , 0 2 m mpro . M inu teX ~ L a s t ( k N ) ; Y = V e r f o r m u n g ( m m ) ; SL = L a n g z e i t f e s t i g k e i t v o n f e s te m G e s t e i n

S t a b i l i t l o n g t e r m e d e l a r o eh e f r a e t u r e s o u m i s e u n e v i t e s se d e d p l a c e m e n t d e 0 , 0 2 m mp a r m i n u t eX = & a r g e ( k N ) ; Y : d p l a c e m e n t ( m m ) ; S 1 = r s i s t a n c e d e l o n g u e d u r e d e l a r oe hei n t a e t e

t o d e f o n n a n d d e c r e a s e s i n r e s i s t a n c e a l o n g t h e c h a r a e t e r i s t i c o f t h e t e s t i n g m a c h i n e .T h i s f i n d i n g g i v e s a c o n v e n i e n t m e a n s o f ch e e k in g t h e s t i f f n e s s o f th e l o a d i n gm a e h i n e .

T h e r e s u l t s g i v e n in F i g . 9 t h u s p r o v i d e l o n g - t e r m d a t a o n w h ic h t h e d e s i g no f ro c k s t r u e m r e s e a n b e b a s e d . T h e v a l u e o f th e s e r e s u l t s l ie s i n t h e i r a p p l i e a b i l i t yt o t h e p r e d i e t i o n o f t h e b e h a v i o u r o f r oc k s t r u e t u r e s a f t e r a v e r y l o n g p e r i o d o ft i m e .

T h e d a ta , i n F i g . 9 a p p l y o n l y t o t h e r a t e o f d e f o r m a t i o n o f 0 . 0 2 m m / m i n .D o e s i t a l so a p p l y t o o t h e r r a t e s o f d e f o r m a t i o n , t h a t i s, is i t a p p l i e a b l e to t h et o & t y p e a s s u c h ?

F i g . 1 0 i n d i e a t e s t h a t i t d o e s n o t a p p l y t o o t h e r r a te s o f d e f o r m a t i o n a n dt h a t e a e h r a t e o f d e f o r m a t i o n h a s i t s o w n e h a r a e t e r i s t i e l o n g - t e r m s t a b i l i t y e u rv e .T h i s i s e l e a r f r o m F i g . 1 0 w h e r e t h e l o n g - t e r m s t a b i li t ,y p o i n t s ( b r o k e n l i n e s ) f o rs t r a i n r a t e s o f 3 3 " 1 0 - 6 / s e e a n d 0 . 4 3 " 1 0 - 6 / s e e e a n b e s e en n o t to e o i n e id e .

I t m a y t h u s b e s t t e d t h a t u n d e r e o n s t a n t a p p l i e d l o a d f r a e t u r e d r oc k e v en -t u a l l y r e a e he s s t a b i l i t y b u t i s a f fe e t e d b y t h e p r e v i o u s s t r a i n i n g h i s t o r y . T h e l o n g -


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136 Z . T . B i e n i a w s k i :t e r m b e h a v i o u r o f f r a c t u r e d r o & m a y b e e s t a b l i s h e d f r o m a s y s t e m a t i c d e t e r m i n a -t i o n o f p o s t - f a i l u r e s t r e s s - s t r a i n c u r v e s o f r o c k, a t v a r i o u s s t r a i n r a t e s .

5 0

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F i g . 1 0. I n f ] u e n c e o f s t r a i n r a t e o]1 l o n g - t e r m s t a b i l i t y o f f r a c t u r e d r o c kX = l o a d ( k N ) ; Y = d e f o r m a t i o n ( m m ) ; Z = l o n g - t e r m s t a b i l i t y

E i n f l u d e r D e h n u n g s g e s e h w i n d i g k e i t a u f d i e L a n g z e i t s t a b i l i t t v o n g e b ro ,e he ne m G e s t e inX = L a s t ( k N ) ; Y = V e r f o r m u n g ( m m ) ; Z = L a n g z e i t s t a b i l i t ~

E f f e t d e l a v i t e s s e d e d f o r m a t i o n s u r l a s t a b i l i t d e l o n g u e d u r e d e l a r a c h e f r a e t u r eX ~ & a r g e ( k N ) ; Y = d p l a c e m e n t ( m m ) ; Z = s t a b i l i t d e l o n g u e d u r e

Conc lu s i on s(1 ) U n d e r g r a d u a l l y i n c r e a s i n g c o m p re s :s iv e d e f o r m a t i o n a t c o n s t a n t s t r a i n

r a t e s , d e c r e a s e s i n s t r a i n r a t e r e s u l t i n a f l a t t e n i n g o f t h e s l o p e o f I o a d - d e f o r m a -t i o n c u r v e o f f r a c t u r e d r o c k a f t e r s t r e n g t h f a i l u r e , t h ~ t i s , i n a n i n c r e a s e d s t a b i l i t ya f t e r s t r e n g t h f a i l u r e .

(2 ) C o n v e r s e l y , i n c r e a s i n g s t r a. in r a t e r e s u l t s i n d e c r e a s e d s t a b i l i t y o f f r a c -t u r e d r oc k m a n i f e s t e d b y a s t e e p e n i n g o f t h e n e g a t iv e s l o p e o f t h e l o a d - d e f o r m a t i o nc u r v e a f t e r s t r e n g t h f a i l u r e .

(3 ) A l t h o u g h r e s i s ta n c e a n d d e f o r m a t i o n o f f r a c t u r e d r o ck a r e t im e - d e p e n d e n t ,a f t e r t h e a p p l i c a t i o n o f a c o n s t a n t l o a d f o r a r e l a t i v e l y s h o r t p e r i o d o f t i m e , s t a b i -l i t y i s a c h ie v e d a n d n o f u r t h e r r e d u c t i o n i n t h e r e s i s t ~ n c e o r i n c r e a s e i n d e f o r m a -t io n , i s a p p a r e n t . F r o m t h i s p h e n o m e n o n i t i s p o s s i b l e to c o n s t r u c t a r e s u l t a n tc u r v e o f l o n g - t e r m s t a b i l i t y o f f r a c t u r e d r oc k .

( 4) T h e l o n g - t e r m s t a b i l i t y c u r v e f o r f r a c t u r e d r o c k i s d e p e n d e n t o n th ep r e v i o u s l o a d i n g h i s t o r y o f th e r o ck , i . e . t h e r a t e o f d e f o r m a t i o n p r e v i o u s l ya p p l i e d .

Acknow l e d g emen t sT h e ~ u t h o r i s g r a t e f u l to M e s s r s . U . W . V o g l e r a n d S . J . C o e t z e r f o r t h e i r

a s s i s ta n c e in t h e e x p e r i m e n t a l te s ts a n d t o D r . H . G . D e n k h a u s f o r h i s co n -s t r u c t i v e c r i t i c i s m o f t h e m a n u s c r i p t .


15/15

T i m e - D e p e n d e n t B e h a v i o u r o f F r a e t u r e d I [o c k i 3 7

B i e n i a w s k i , Z .i n d . R e s . S . A f r . , M E G

B i e n i a w s k i , Z .S e i . 4 , 4 0 7 - - 4 3 0 , 1 9 6 7 .B i e n i a w s k i , Z .r oc k . I n t . J . R oc k M e e h .B i e n i a w s k i , Z .

R e f e r e n c e sT . : M e e h a n i s m o f r o c k f r a c t u r e i n c o m p r e s s i o n . R e p . C o u n c . s c i e n t .4 5 9 , 1 9 6 6 .

T . : M e c h a n i s m o f b r i t t l e f r a c t u r e o f r o c k . I n t . J . R o c k M e c h . M i n .

T . , I I . G . D e n k h a u s, a n d U . W . V o g l e r : F a i l u r e o f f ra e t u r e dM i n . S e i . 6 , 3 2 3 - - 3 4 1 , 1 9 6 9 .T . : D e f o r m a t i o n a l b e h a v i o u r o f f r a e t u r e d r o ck u n d e r m u l t i a x i a le o m p r e s s i o n . P r o e . I n t . C o n f . S t ru e t u r e , S o l i d M e e h an i e s a n d E n g i n e e r i n g D e s i g n , J o h n

W i l e y & S o n , L o n d o n , 5 5 / 1 - - 5 5 / 1 0 , 1 9 6 9 .B i e n i a w s k i , Z . T . : L o a d - d e f o r m a t i o n b e h a v i o u r o f e o a l a f t e r f ~ i l u r e . P r o e . 2 n dC o n g r e s s I n t . S o e. R o c k M e eh ., B e l g r a d e , 1 , 4 6 7 - - 4 7 3 , 1 9 7 0 .C o o k , N . G . W . : F a i l u r e o f r o c k . I n t . J . R o c k M e e h . M i n . S e i . 2 , 2 8 9 - - 4 0 3 , 1 9 6 5 .C o o k , N . G. W . , a n d J. P. M . H o j e m : A r i g i d 5 0 - t o n c o m p r e s s io n a n d t e n s io nt e s t i n g m a e h i n e . S . A f r . M e & . E n g r . 16, 8 9 - - 9 2 , 1 9 6 6 .F a i r h u r s t , C ., a n d N . G. W . C o o k : T h e p h e n o m e n o n o f r o & s p l i t t i n g p a r a l l e l toa s u r f a e e u n d e r e o m p r e s s i v e s tr e s s. C h a m b e r o f M i n e s o f S o u t h A f r i e a R e s e ar e h R e p o r tN o . 6 5 / 6 5 , 1 9 6 5 . A l s o i n : P r o e . 1 s t C o n g r e s s I n t . S o e . R o ,c k M e & . , L i s b o n , 1 , 6 8 7 - - 6 9 1 , I 9 6 6 .J a e g e r , J . C ., a n d N . G . W . C o o k : F u n d a m e n t a l s o f r oc k m e e h an i es , M e t h u e n &C o ., L o n d o n 1 9 6 9 .R s e h , H . : R e s e a re h e s to w a r d s a g e n e r al f l e x u r a l t h e o r y f o r s t r u e t u r a l e o n e re t e .

A m e r i e a n C o n e r e t e I n s t i t u t e P r o e e e d i n g s 5 7 , 1 - - 2 8 , 1 9 6 0 .R s e h , H . : V e r f o r m u n g s e i g e n s e h a f t e n v o n B e t o n u n t e r z e n t ri s c h e n Z u g s p a n n u n g e n .V o r u n t e r s u e h u n g e n , M n c h e n , B e r i c h t N r . 4 4 , 1 9 6 3 .S e r d e n g e e t l , S ., a n d G . D . B o o z e r : T h e e f f ee t s o f s t r a i n r a t e a n d t e m p e r a t u r eo n t h e b e h a v i o u r o f ro c k s u b j e e te d t o tr i a x i a l e o m p r e s s i o n . P r o e . F o u r t h S y m p o s i u m o n

R o c k M e e h a n ie s , S o e i e ty o f M i n i n g E n g i n e e r s , N e w Y o r k , 8 3 - - 9 7 , 1 9 6 1 .W a w e r s i k , W . : D e t a i l e d s t u d i e s o f r o c k f r a e t u r e i n e o m p r e s s i o n . T h e s i s , U n i v e r s i t yo f M i n n e s o t a , M i n n e a p o l i s 1 9 6 8 .

Key Words: e f f e e t, s t r a i n r a te , i n e r e a s i n g Io a d , e o n s t a n t l o a d , f r a e t u r e d r o c k , s a n d s t o n e ,c o n e r et e , u n i a x i a l e o m p r e s s i o n , s t i f t t e s t i n g m a e h i n e, t i m e d e p e n d e n e y , l o n g - t e r m s t a b i l i t y ,e o m p l e t e r e s i s t a n e e - d e f o r m a t i o n e u r v e , e o m p l e t e s t r e s s - s t r a i n e u r v e , e x p e r i m e n t M d a t a .

A d d r e s s o f t h e a u t h o r : D r . Z . T . B i e n i a w s k i , H e a d , R o ck M e e h an i es D i v i si o n ,C o u n e i l f o r S e i e n t i f i e a n d I n d u s t r i a l R es ea .r ch , P . O . B o x 3 9 5 , P r e t o r i a , S o u t h A f r i e a .

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