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M O D E L L I N G T H E S T R E S S- S T R A IN B E H A V I O U R O F S A TU R A T E DR O C K S U N D E R G O I N G T R IA X I AL D E F O R M A T I O N U S IN G C O M P L E X

E L E C T R IC A L C O N D U C T I V I T Y M E A S U R E M E N T S

R W . J. G L O V E R 1 J . B . G O M E Z 2 , R G . M E R E D I T H 2 , S . A. B O O N 2,E R . S A M M O N D S 2 a n d S . A . F. M U R R E L L 2Ilnstitute of Fluid Sciences, Tohoku University, Sendai 980-77, Japan; 2Rock and Ice Ph ysicsLaboratory, Research School fo r Geological and G eophysical Sciences, U niversity College London,Gow er Street, London, W C1E 6BT, U.K

Ab stra c t . Meas uremen t of complex e lec tr ica l conduct ivi ty as a funct ion of f requency is an extremelysensi t ive probe for changes in pore and crack volume, c rack connect ivi ty, and crack surface topogra-phy. Such m easurements have b een made as a funct ion of pore f luid chemis try, hydros ta t ic conf iningpressure, as well as u niaxi al and triaxial deformation. This paper w ill; (1) describe the effects of triax-ia l deformation on the com plex e lec tr ica l condu ct ivi ty of sa tura ted porous rocks , (2) use the e lec tr ica lda ta to m odel the m echanica l s t ress-s tra in behaviour , and, (3) compare the mo del led behavio ur withthe s t ress-s t rain behavio ur measured dur ing the deformation. Exper imenta l cond uct ivi ty da ta t rackshow the rock undergo es compact ion with progress ive loss of c rack volum e, fol lowed by di la ta tiondue to new crack formation, growth of existing cracks, crack interlinkage, and finally failure, asaxial strain is increased. We have used the complex electrical data to produce a direction-sensitive(anisotropic) c rack d amage parameter , and used i t to ca lcula te the effec t ive Yo ung's mo dulus b yemploying the models of Walsh and Bruner . Comparison of the synthe t ic s t ress-s t ra in curves soproduced, w ith the ex per imenta l ly der ived s t ress-st ra in curves shows go od agreement , par t icular lyfor undra ined tes ts . This m odel l ing is an impro vemen t on s imilar curves produced us ing isotropiccrack damage parameters der ived f rom acoust ic emiss ion data . The impro vemen t is l ike ly to be dueto the direc t ional sens it ivi ty of the e lec tr ica l conduct ivi ty measuremen t , and i ts abi l i ty to discr iminatebetween the formation of isola ted cracks , and those cracks tha t contr ibute to the inter-connected crackspace i .e . those cracks upon which transport properties of the rock such as electrical conductivity,and m echanica l propert ies d epend m ost c r i t ical ly dur ing t r iaxial deformation.Key wo rds: Comp lex e lec tr ica l conduct ivi ty, Stress-s t ra in model l ing, Cracked sol ids , Tr iaxia l defor-ma t ion

1. IntroductionI t is the ch allenge of transport property ge oscientis ts to und erstand the effect of rockstructure upon the transport of f luids, electrical current, and heat, throug h crustalrocks. T hese are im por tant goals because the unders tanding of the composi t ion,evolution, and dynamic processes occurring in the Earth 's crust depend largelyupon a g ood unders tanding of these basic t ranspor t processes . Indeed, they arecentral to ma ny o f the practical prob lems with en vironm ental, comm ercial , social,and e con om ic implica tions that we face today. For example, transport properties ofsaturated rocks are imp ortant in the efficient extraction of hydrocarbons, optimiza-tion of heat extraction from geoth ermal resources, safe design of repositories forSurv eys in Geophysics 17: 307 -330 , 1996.

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308 p . w . J . G L O V E R E T A L.r a d i o a c t i v e a n d c h e m i c a l l y t o x i c w a s t e s , a n d p r o v is i o n o f w a t e r f r o m u n d e r g r o u n dw a te r r e s e r v o i rs .

T r a d i t i o n a l ly m o s t e f f o rt h a s b e e n g i v e n t o u n d e r s t a n d i n g t h e e f f e c t o f f l u idf lo w t h r o u g h r o c k s . H o w e v e r , e l e c t ri c a l m e t h o d s a r e o f g r o w i n g i m p o r t a n c e a s aw a y o f i n v e s t i g a t in g t h e i n t e r a c t i o n a n d m i g r a t i o n o f f l ui d s t h r o u g h c r u s ta l r o c k s .M e a s u r e m e n t s o f c o m p l e x e l e c t r ic a l c o n d u c t i v i t y a s a f u n c t i o n o f f r e q u e n c y r ep -r e s e n t a n e x t r e m e l y s e n s it i v e p r o b e f o r t h e c h a n g e i n p o r e a n d c r a c k v o l u m e , c r a c kc o n n e c t i v i ty , a n d c r a c k s u r f a c e t o p o g r a p h y . It i s a v e r y u s e f u l m e t h o d f o r o b t a i n i n gi n f o r m a t i o n a b o u t t h e s t r u c tu r e o f th e r o c k u n d e r a w i d e r a n g e o f e n v i r o n m e n t a lc o n d i t i o n s .

O n e o f t h e p r o b l e m s i n t h e u n d e r s t a n d i n g o f t h e f l o w o f e l e c tr i c a l c u rr e n t st h r o u g h s a t u ra t e d ro c k s i s t h e l a r g e n u m b e r o f ro c k p r o p e r t ie s t h a t h a v e t h e p o t e n -t ia l t o a f f e c t t h e m e a s u r e d e l e c t r ic a l c o n d u c t i v it y . W e k n o w t h e c o n d u c t i v i t y isa f f e c t e d b y c r a c k m i c r o - s t ru c t u r e p a r a m e t e r i z e d b y ( i) t ot a l c r a c k v o l u m e a n d s i zed is t r ibu t ion , ( i i ) c r ack aspec t r a t io d i s t r ibu t ion , ( i i i ) c r ack o r ien ta t ion d i s t r ibu t ion ,a n d ( iv ) c r a c k c o n n e c t i v i t y . I t c a n a l s o b e a f f e c t e d b y c r a c k s u r f a c e c h a r a c t e r i s ti c s ,s u c h a s ( v ) s u r f a c e fr a c t a l d im e n s io n , ( v i) c r a c k s u r f a c e a re a , a n d ( v ii ) s u r f a c e a r e ac o n n e c t i v it y . I n t h e l o w t e m p e r a t u r e l i m i t ( 0 - 2 5 0 ~ t h e e l e c t ri c a l p r o p e r ti e s o fe l e c t r o ly t e s a tu r a t e d r o c k s a r e d o m in a t e d b y t h e c h a r a c t e r i s t i c s o f th e p o r e f lu id;( v i ii ) i o n i c c o n c e n t r a t i o n , ( ix ) i o n i c c o m p o s i t i o n , a n d ( x ) pH . A t h ig h e r t e m p e r a -t u r es t h e c o m p o s i t i o n , p ro p e r ti e s , a n d r e l a ti v e a b u n d a n c e s o f m i n e r a l p h a s e s o f t h er o c k m a t r i x b e c o m e i m p o r t a n t a s s o l i d s ta t e c o n d u c t i o n b e g in s t o b e s i gn i fi c a nt .O th e r r e s e a r c h e r s m a y i n c lu d e o th e r p a r a m e te r s i n t h i s l is t , e i t h e r i n g e n e r a l , o rf o r s p e c if ic r o c k s a m p l e s . W h a t i s m o r e , e a c h o f th e s e p a r a m e t e r s w i ll h a v e d i f -f e r e n t c o n t r i b u t io n s t o t h e o v e r a l l e l e c tr i c a l p r o p e r t ie s o f t h e r o c k d e p e n d i n g u p o nt h e r o c k m a t r i x , s a t u r a t i n g f l u i d , a n d e n v i r o n m e n t a l c o n d i t i o n s o f t e m p e r a t u r e ,c o n f in in g p r e s s u r e , d e v i a to r i c p r e s s u r e , a n d p o r e - f l u id p r e s s u r e , a n d a r e f u r t h e rc o m p l i c a t e d b y t h e n a t u ra l a n i s o t r o p y o f m o s t r o c k s a m p l e s . T h e e f f e c t o f e a c h o ft h e s e p a r a m e t e r s w i l l c h a n g e d u r i n g r o c k d e f o r m a t i o n , a s c r a c k s c l o se , f o r m , a n dp r o p a g a t e .

T h i s , t h e re f o r e , is t h e c o n u n d r u m t h a t e l e c tr i c a l m e a s u r e m e n t s o n r o c k s o f fe r :t h e i n t e r p r e ta t i o n o f t h e c o n d u c t i v i t y i n t e r m s o f p h y s i c a l p a r a m e t e r s i s c o m p l e x ,b u t t h i s i s a l s o a m e a s u r e o f i t s g r e a t p o t e n t i a l a s a p r o b e f o r e l u c id a t i n g a w id er a n g e o f r o c k p a r a m e t e r s.

I t is i m p o r t a n t t h a t w e r e s tr i c t o u r s t u d y t o s i m p l i f y t h e p r o b l e m . A c c o r d i n g l y ,t h e r e s t o f t hi s p a p e r w i l l d e a l w i t h l o w t e m p e r a t u r e s , w h e r e a ll c o n d u c t i o n o c c u r se i t h e r t h r o u g h t h e p o r e f l u i d o r a l o n g t h e s u r f a c e o f c r a c k s a n d p o r e s . W e w i l la l so c o n c e n t r a t e u p o n c l e a n s a n d s t o n e s o f h i g h p e r m e a b i l i ty . T h i s a l l o w s u s t oi g n o r e t h e c o m p l i c a t i n g e f f e c t o f c l a y m i n e r a l s , a n d e n s u r e t h a t w e c a n f u l l ys a t u r a t e o u r s p e c i m e n s r e l i a b l y . A l t h o u g h m e a s u r e m e n t s o f c o m p l e x e l e c t r i c a lc o n d u c t i v i t y w e r e a l so m a d e a s a f u n c t i o n o f f r e q u e n c y ( 2 0 H z t o 1 M H z ) d u r i n ge a c h d e f o r m a t i o n te s t, o n l y t h e v a r i a t io n a t 1 k H z w i l l b e d i s c u ss e d . U n f o r t u n a t e l yth e r e i s n o s p a c e t o i n c lu d e a d i s c u s s io n a b o u t h o w th e e l e c t r i c a l d i s p e r s io n s

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MODELLING THE STRESS-STRAIN BEHAVIOUR OF SATURATED ROCKS 3 09a s a f u n c t i o n o f f r e q u e n c y , r e s u l t i n g f r o m s u r f a c e c o n d u c t i o n , d e v e l o p d u r i n gd e f o r m a t io n . T h e r e s u l t o f t h e s e r e s t r ic t i o n s a ll o w s u s t o s t u d y c h a n g e s i n t h e p o r ea n d c r a c k m i c r o - st r u c t u re .

W e h a v e m a d e c o m p l e x e l e c t ri c a l p r o p e r t y m e a s u r e m e n t s d u r i n g t ri a xi a l d e f o r -m a t io n . E l e c t r i c a l p r o p e r t i e s a t lo w f r e q u e n c i e s (1 k H z ) , a n d l o w t e m p e r a tu r e s a rec o n t r o l l e d b y c o n d u c t i o n th r o u g h t h e p o r e f l u id , a n d t h e d i s t ri b u t io n o f t h e p o r e a n dc r a c k s p a c e . C o n s e q u e n t l y , t h e s e e l e c t r i c a l p r o p e r t ie s a r e a f u n c t i o n o f t h e p o r e a n dc r a c k m ic r o - s t r u c tu r e a n d t h e p o r e - f l u id c h a r a c t e r i s t ic s . E x p e r im e n ta l d a t a o b t a in e dd u r i n g t r i ax i a l d e f o r m a t i o n t r a c k s h o w t h e r o c k u n d e r g o e s i n it ia l c o m p a c t i o n a n dl o ss o f c r a c k v o l u m e , f o l l o w e d b y d i l a ti o n , d u e t o n e w c r a c k f o r m a t i o n a n d g r o w t ho f e x i s t i n g c r a c k s , a n d e v e n tu a l l y c r a c k i n t e r l i n k a g e , f r a c tu r e l o c a l i z a t i o n a n d r o c kf a i l u r e ( G lo v e r e t a l . , 1 99 4 a) . T h e i n - p h a s e c o m p o n e n t o f c o n d u c t i v i t y a t l o w f r e -q u e n c i e s m o n i t o r s h o w c r a c k v o l u m e c h a n g e s p e r p e n d i c u l a r a n d a l o n g t h e a x i s o fd e f o r m a t i o n , w h i l e t h e r e l a t iv e a m o u n t s o f i n - p h a s e a n d o u t - o f - p h a s e c u r r e n t f lo wis a m e a s u r e o f t h e to r t u o s i ty o f t h e p o r e a n d c r a c k s y s t e m .

W e h a v e r e l a t e d t h e c h a n g e i n n e w c r a c k v o l u m e to m i c r o - c r a c k d a m a g e , a n dh e n c e t o t h e c o n s t i t u t i v e s tr e s s - s tr a in b e h a v io u r d e s c r i b in g t h e d e f o r m a t io n h i s t o r yo f t h e ro c k s a m p le . T o d o t h i s w e h a v e d e r iv e d a d i r e c t i o n - s e n s i t i v e ( a n i s o t ro p -ic ) d a m a g e p a r a m e t e r i n t er m s o f m e a n n e w c r a c k v o l u m e c h a n g e , d e r iv e d f ro me le c t r i c a l da t a . W e th e n u s e t h e b ri t t le d a m a g e m o d e l s o f W a l s h ( 1 96 5 a ; 1 9 6 5b )a n d B r u n e r ( 19 7 6 ) t o d e r i v e s t r es s -s t ra i n c u r v e s f r o m t h e e v o l u t i o n o f t h e d a m a g ep a r a m e t e r. T h e s e s t re s s -s t ra i n c u r v e s c a n b e c o m p a r e d w i t h t h o se m e a s u r e d d u r i n gt h e d e f o r m a t i o n o f ro c k s a m p l e . T h i s a p p r o a c h i s t h e s a m e a s t h a t u s e d b y S a m -m o n d s e t a l . ( 1 99 4 ), b u t t h e y u s e d a n i s o t ro p i c d a m a g e p a r a m e t e r d e r i v e d f r o m A Edata .

2 . E x p e r i m e n t a l P r o c e d u r e s2.1 . SAMPLEMATERIALD a r l e y D a l e s a n d s to n e w a s u s e d f o r al l t r ia x i a l e x p e r im e n t s . T h i s is a w e l l i n d u r a t e df e l d s p a th i c s a n d s t o n e w i t h a p o r o s i t y in t h e r a n g e 1 6 - 2 8 % a n d a h i g h p e r m e a b i l -i ty . M e a s u r e m e n t s w e r e p e r f o r m e d o n r i g h t c y l i n d e r s w i t h d i a m e t e r s o f 4 0 r a m ,a n d l e n g t h a p p r o x i m a t e l y 1 10 r a m . A x i a l e n d s u r f a c e s w e r e g r o u n d f la t a n d p a r -a l le l . E a c h s a m p le w a s s a tu r a t e d w i th i n i ti a l l y p u r e d e io n i z e d w a t e r t h a t h a d b e e nd e g a s s e d b y v a c u u m f o r 2 4 h o u r s p r i o r t o u se b y u s i n g a v a c u u m t e c h n i q u e .2.2. TRIAXIAL DEFORMATION

S a m p l e s w e r e s l e e v e d w i t h h e a t s h r in k a b l e p o l y o l e f in a n d p l a c e d i n t h e p re s s u r ev e s s e l / lo a d f r a m e a s s e m b l y . A c o n f i n i n g p r e s s u r e o f e it h e r 25 o r 5 0 M P a w a sa p p l i e d i n s t ag e s , w h i l e m o n i t o r i n g c h a n g e s i n t h e c o m p l e x e l e c t ri c a l c o n d u c t i v -i t y f r o m 2 0 H z t o 1 M H z . T r i a x i a l d e f o r m a t io n w a s s t a r t e d at a c o n s t a n t st r a in

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3 1 0 P.W.J. GLOVER ET AL.r a t e (1 .6 1 0 - 6 s - 1 ) u n t i l f a i l u r e o c c u r r e d , d u r i n g w h i c h t h e c o m p l e x e l e c t r i c a lc o n d u c t i v i t y w a s m o n i t o r e d .

B o t h d r a i n e d a n d u n d r a i n e d t e s t s w e r e c a r r i e d o u t . I n t h e u n d r a i n e d t e s t s , p o r ef lu i ds w e r e n o t a l l o w e d t o d r ai n f r e e l y d u r i n g d e f o r m a t i o n , a n d t h e p o r e p r e s s u r ew a s n o t m o n i t o r e d , l e a d i n g t o s o m e u n c e r t a i n ty i n th e v a l u e o f p o r e f l u i d p r e s s u r e ,a n d h e n c e s i m p l e e f f e c t i v e p r e s s u r e d u r i n g d e f o r m a t i o n . I n th e d r a i n e d t e s ts , t h ep o r e f l u id w a s a l l o w e d t o d r a i n f r e e l y to a t m o s p h e r i c p r e s s u r e , w h e r e i t w a s c o l -l e c t e d i n a g la s s m e a s u r i n g c y l in d e r. T h e g l a s s m e a s u r i n g c y l i n d e r w a s a r r a n g e d o na n e l e c t ro n i c b a l a n c e i n s u c h a w a y t h a t t h e e x p e l l e d / i m b i b e d f lu i d v o l u m e c o u l db e m e a s u r e d g r a v i m e t r i c a l l y . T h i s v o l u m e t r i c i n f o r m a t i o n w a s u s e d s u b s e q u e n t l yt o c a lc u l a t e t h e v a l u e o f t h e A r c h i e e x p o n e n t , r a , d u r i n g d e f o r m a t i o n .

2.3 . ELECTRICAL CONDUCTIVITY MEASUREMENT

C o m p l e x e l e c t ri c a l c o n d u c t i v i t y m e a s u r e m e n t s h a v e b e e n m a d e u s i n g a t w o e l e c -t r o d e c e l l d e s i g n e d f o r u s e w i t h a 1 5 0 t o n n e l o a d f r a m e a n d 4 0 0 M P a p r e s s u r ev e s s e l w i t h a b a l a n c e d r a m f o r tr ia x ia l d e f o r m a t i o n e x p e r i m e n t s ( F i g u r e 1 ).

T h e e l e c t r o d e s w e r e m a d e f r o m p l a t i n u m - b l a c k e d p l a t i n u m g a u z e ( G l o v e r e ta l . , 1 9 9 4 b ) . I n o u r p r e v i o u s w o r k w e e m p l o y e d f o u r e l e c t r o d e s t o r e d u c e e l e c -t r o d e p o l a r i z a t i o n . W e u s e d t w o e l e c t r o d e s f o r u n i a x i a l a n d t r i a x i a l d e f o r m a t i o ne x p e r i m e n t s b e c a u s e ; ( 1) w e f o u n d t h e u s e o f w e l l b l a c k e d p l a ti n u m e l e c t r o d e si s s u f f i c i e n t t o r e d u c e e l e c t r o d e p o l a r i s a t i o n f o r f r e q u e n c i e s g r e a t e r t h a n 2 0 H z ,( 2) t w o e l e c t r o d e s a r e m u c h e a s i e r t o i n c o rp o r a t e i n t o a c o n d u c t i v i t y c e ll d e s i g n e dt o a p p l y a x i a l s t r e s s e s t o th e r o c k s a m p l e , a n d ( 3 ) w e f o u n d t h e u s e o f f o u r e le c -t r o d e s g a v e l ar g e u n w a n t e d i n d u c t i v e c o u p l i n g b e t w e e n t h e c o n d u c t i v i t y c e l l a n dt h e p r e s s u r e v e s s e l a t h i g h f r e q u e n c i e s m a s k i n g t h e t r u e m e a s u r e m e n t s ig n a l.

T h e e l e c t r o d e s w e r e a t t a c h e d t o e n d p i e c e s o f h a r d e n e d F V 5 4 0 s t a in l e s s s te e lw h i c h a l s o c o n t a i n e d f l u id f l o w c o n n e c t i o n s f o r m a k i n g p o r e - f l u i d p re s s u r e , p o r ef lu i d v o l u m e , a n d p e r m e a b i l i t y m e a s u r e m e n t s . T h i s b l o c k w a s i s o l a te d f ro m t h ep r e s s u r e v e s s e l a n d l o a d f r a m e b y p l a t e s o f c o l d i s o s t a ti c a l ly p r e s s e d p u r e r e c r y s-t a l l i s e d a l u m i n a f r o m D e g u s s a . E l e c t r i c a l l e a d s w e r e a t t a c h e d t o t h e f l u i d f l o w a n de l e c t r o d e b l o c k . A l l f l u i d f l o w l in e s w e r e e l e c t r ic a l l y i s o la t e d f r o m t h e p r e s s u r e v e s -s e l a n d l o a d f r a m e b o t h i n s i d e a n d o u t s i d e th e v e s s e l . T h e s e l in e s w i l l b e a t t a c h e dt o a s p e c i a l l y d e s i g n e d e l e c t r i c a l l y i n s u l a t in g h i g h v o l u m e h i g h p r e s s u r e s e p a r a t o r ,t o a l l o w f l u i d p e r m e a b i l i t y m e a s u r e m e n t s t o b e m a d e u s i n g a d o u b l e a c t i n g p o r ev o l u m o m e t e r .

C o m p l e x c o n d u c t i v i t y m e a s u r e m e n t s a s a f u n c t i o n o f f r e q u e n c y , f r o m 2 0 H zt o 1 M H z , w e r e m a d e u s i n g a H P 4 2 8 4 A i m p e d a n c e b r i d g e w h i c h w a s c o n t r o ll e db y c o m p u t e r . S o f t w a r e h a s b e e n w r i t t e n t o a l l o w t h e c o m p u t e r t o m a k e l e a d c o r -r e c t i o n s t o t h e d a t a , c o n v e r t t h e p h y s i c a l m e a s u r e m e n t s ( c o m p l e x c o n d u c t a n c e s )i n to s p e c i f ic m e a s u r e m e n t s ( c o m p l e x c o n d u c t i v i t y ) , a n d l o g t h e d at a. T h e s o f t w a r eh a s t h e a b i l i t y t o d i s p l a y e l e c t r i c a l d a t a a s i n - p h a s e a n d o u t - o f - p h a s e c o n d u c t i v i t y ,r e s i s t iv i t y , a n d p e r m i t t i v i ty a s a f u n c t i o n o f f r e q u e n c y , o r a s A r g a n d d i a g r a m s .

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MODELLING THE STRESS-STRAIN BEHAVIOUR OF SATURATED ROCKS 311Acoust ic /EmissionTransducerConnect ionsAluminaInsu la to r ~ _ ._ ,_= .ElectricalConduct ivityConnect ion

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BottomClosure 4 1 8 4 1 8 4 1 8 4ocationRingFigure 1. The two ele ctrode cell desi gned for use with a 150 tonne load frame and 400 MP a pressurevesse l with a balanced ram for triaxial deformation experimen ts.

The initial data were corrected at each frequency to take into account stray resis-tances and inductances associated with the measurement leads and capacitancesassociated with the pressure vessel.

The length of time required for the measurement instruments to make complexconductivity determinations at 50 frequencies from 20 Hz to 1 MHz, combined withthe huge amount of data this would generate, made it necessary to limit the amountof measurements taken. As a compromise we ran experiments which combined highrate measurements o f the electrical properties at 1kHz with occasional measurementof a full frequency scan by writing logging programmes to enable frequency scan

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31 2 P.W.J . GLOVER ET AL.m e a s u r e m e n t s t o b e m a d e a s a n i n t e r r u p t i n th e b a c k g r o u n d r e g u l a r lo g g i n g r o u t in e .T h i s p r o v id e d :

1. a c o m p le t e s e t o f c o m p le x r e si s t iv i t y , c o n d u c t i v i t y , a n d p e r m i t t i v i t y d a t a f o ro n e f r e q u e n c y (1 k H z ) e v e r y 1 5 s e c o n d s t h r o u g h o u t t h e te s t.2 . a c o m p le t e s e t o f c o m p le x r e s i s t iv i t y , c o n d u c t i v i t y , a n d p e r m i t t i v i t y d a t a f o r 5 0

f r e q u e n c i e s fr o m 2 0 H z t o 1 M H z a t te n t o t w e n t y p o i n ts d u r i n g th e te s t. O n l yd a t a s e t 1 w i l l b e d i s c u s s e d i n t h is p a p e r.

T h e f r e q u e n c y u s e d i n th e t e st s s h o w n h e r e w a s 1 k H z , a n d w a s c h o s e n a s t h ef r e q u e n c y a t w h i c h t h e o u t - o f - p h a s e c o m p o n e n t o f t h e e l e c tr i c a l p a r a m e t e r s w a sm i n i m i s e d , i n o r d e r th a t t h e d a t a w o u l d b e a f u n c t i o n o f t h e p o r e a n d c r a c k f lu i d v o l -u m e , w i t h c o n t r i b u t io n s f ro m s u r f a c e c o n d u c t i o n a n d M a x w e l l - W a g n e r d i sp e r s io nm i n i m i z e d .

3 . R e s u l t s a n d D i s c u s s i o n

E x p e r i m e n t s w e r e d o n e t o s h o w t h e v a r i a t i o n o f th e c o m p l e x r e si s ti v i ty a t 1 k H z f o rs a m p l e s o f D a r l e y D a l e s a n d s t o n e s a t u r a t e d w i t h i n it ia l ly p u r e w a t e r, t o g e t h e r w i t hth e s t r e s s - st r a in b e h a v io u r . A s a l r e a d y m e n t io n e d , t h e 1 k H z d a t a s e t i s s e n s i t i v e t oc h a n g e s i n th e p o r e a n d c r a c k s t r u c tu r e .

F i g u r e s 2 - 4 s h o w t h e v a r ia t i o n o f th e c o m p l e x r e s is t i v it y at 1 k H z f o r t h re es a m p l e s o f D a r l e y D a l e s a n d s t o n e s a t u r a t e d w i t h i n i t i a l l y p u r e d o u b l e d i s t i l l e dw a t e r a s t h e s a m p l e s w e r e d e f o r m e d a x i a l ly u n t i l f ai l u re t o g e t h e r w i t h t h e s t r e ss -s t ra i n c u r v e f o r e a c h t e s t. F i g u r e 2 s h o w s a n u n d r a i n e d c a s e i n t h e p r e s e n c e o f a2 5 M P a h y d r o s t a t i c c o n f i n i n g p r e s s u re , F i g u r e 3 , a n u n d r a i n e d c a s e w i t h a 5 0 M P ac o n f in in g p re s s u r e , a n d F ig u r e 4 a d r a in e d t e s t w i th a 50 M P a c o n f in in g p r e s s u r e .T h e o u t - o f- p h a s e r e s i st i v it y is m u c h s m a l l e r b e c a u s e t h e f r e q u e n c y a n d s a li n it ie su s e d i n t h e s e t e s ts m i n i m i z e s i t. T h e v a r i a ti o n o f t h e c o m p l e x e l e c t ri c a l b e h a v i o u rh a s a g e n e r i c b e h a v i o u r w h i c h h a s b e e n i l l u s tr a t e d in F i g u r e 5 .

I n t h e t o w a x i a l s t ra in r e g io n ( A , F ig u r e 5 ) t h e p r im a r y p r o c e s s o p e r a t i n g i n t h er o c k i s c o m p a c t i o n o f p o re s a n d c r a c k s . P o r e s a n d c r a c k s t h a t a re m o s t s e n s i t iv eto c lo s u r e a r e t h o s e w i th ( i ) l o w a s p e c t r a t i o s , a n d ( i i ) o r i e n t a t i o n s p e r p e n d i c u l a rt o t h e d i r e c t i o n o f p r i n c ip a l s t r e ss . T h e r e l a t i v e ly lo w l e v e l s o f c o n f in in g p r e s s u r er e s u l t i n t h e d i r e c t i o n o f p r i n c ip a l s t r e s s b e in g a lm o s t a x i a l f o r t h e m a jo r i t y o ft h e d e f o r m a t io n . T h e d o m in a t i n g p r o c e s s , t h e r e f o r e , a t l o w s t ra in s is t h e c lo s u r eo f c r a c k s p e r p e n d i c u l a r t o t h e d i r e c t i o n o f p r i n c ip a l s t r e s s a n d t h e a x i s o f t h es a m p le . C r a c k s w i th t h e i r l o n g a x i s p e r p e n d i c u l a r to t h e s a m p le a x i s a re t h o s et h a t h a v e l e a s t e f f e c t o n t h e s a t u r a te d r o c k e l e c t ri c a l c o n d u c t i v i t y b e c a u s e t h e ya r e p e r p e n d i c u l a r t o t h e c u r r e n t f l o w a n d t h e i r l o s s p r o v id e s l i t t l e c h a n g e i n t h eto r t u o s i t y o f t h e c u r r e n t f l o w p a th s. T h e e f f e c t o f t h i s c l o s u r e i s a s m a l l i n c r e a s e i nth e s a tu r a t e d r o c k e l e c t r i c a l r e s is t i v i ty , a s c r a c k s p e r p e n d i c u l a r to t h e d i r e c t i o n o fc u r r e n t f l o w a r e s u b j e c t e d t o v o lu m e lo s s a n d c lo s u r e . T h e i n c r e a s e i n r e s i s t i v i t y

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