I

‘ I I

Proceedings of the International Symposium on Fundamentals of Rock Joints/ Bjorkliden / 15-20 September 1985

.

I

, - i I !

Edited by OVE STEPHANSSON Luled University of Technology, Sweden

S

-PUBLISHERS

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, make any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

DISCLAIMER

Portions of this document may be illegible in electronic image products. images are produced from the best available original document.

,

ORGANIZATION

The symposium was organized within the Swedish National Group of ISRM by the Swedish Rock Engineering Research Foundation - BeFo and the Division of Rock Mechanics at the Lulea Uni- versity of Technology.

Organizing Committee c;f the Symposium on Fundamentals of Rock Joints. 0 Stephansson, (chairman), Division of Rock Mechanics, Lulea University of Technology, Swe- den N Barton. Norwegian Geotechnical Institute, Oslo, Norway

I

H Einstein. MIT.-Cambridge. USA T Franzen. Swedish Rock Engineering Research Foundation, Stockholm, Sweden C Gerrard. CSIRO. Highett,Australia R E Goodman. University of California, Berkeley, USA G Pande. University of Wales. Swansea, United Kingdom

Centek Printed b!: TECE TRYCK Lule i . Sweden Centek Publishers 1985

ISBN 91-86998-03-X

Sponsored by: Swedish Natural Science Research Council

PUBLISHERS Postadress: S-951 87 Lule2 Telefon: +46-920-910 00 Telex: 80207 Centek S

-

Em-=-----

t ' &<'

., . .. -.

Proceedings of the lnternabonal Symposium on Fundamentals of Rock Joints/ Bjorkhden / 15-20 September 1985

Fractal geometry of two-dimensional fracture networks at Yucca Montain, southwestern Nevada

ABSTRACT

2 F r a c t u r e t r a c e s exposed on t h r e e 214- t o 260-m pavements i n t h e same Miocene ash-f low t u f f a t Yucca Mountain, southwestern Nevada, have been mapped a t a s c a l e o f 1:50. The maps are two-dimensional s e c t i o n s th rough t h e t h r e e - dimensional network o f strata-bound f r a c t u r e s . A l l f r a c t u r e s w i t h t r a c e l e n g t h s g r e a t e r than 0.20 rn were mapped. The d i s t r i b u t i o n o f f r a c t u r e - t r a c e l e n g t h s i s log-normal. The f r a c t u r e s do n o t e x h i b i t w e l l - d e f i n e d s e t s based on o r i e n t a t i o n .

p rove u s e f u l f o r model ing f r a c t u r e f l o w and mechanical responses o f f r a c t u r e d rock , an a n a l y s i s o f each o f t h e t h r e e maps was done t o t e s t whether such networks a r e f r a c t a l . These networks proved t o be f r a c t a l and t h e f r a c t a l dimensions (D) a r e t i g h t l y c l u s t e r e d (1.12, 1.14, 1.16) f o r t h r e e l a t e r a l l y separated pavements, even though v i s u a l l y t h e f r a c t u r e networks appear q u i t e d i f f e r e n t . The f r a c t a l a n a l y s i s a l s o i n d i c a t e s t h a t t h e network p a t t e r n s a r e s c a l e independent over two orders o f magnitude f o r t r a c e l e n g t h s r a n g i n g from 0.20 t o 25 m.

Since f r a c t a l c h a r a c t e r i z a t i o n o f such complex f r a c t u r e - t r a c e networks may

1. INTRODUCTION

F r a c t u r e s fo rm three-dimensional in te rconnected networks i n n e a r l y a l l rocks a t o r near t h e E a r t h ' s sur face. Open-fracture networks a r e t h e pr imary avenues o f r a p i d t r a n s p o r t f o r l i q u i d and gaseous f l u i d s th rough rock masses. I n c o n t r a s t t o f r a c t u r e f low, m a t r i x f l o w g e n e r a l l y i s s i g n i f i c a n t o n l y f o r s low t r a n s p o r t r a t e s . F o r r a p i d t r a n s - p o r t , f r a c t u r e f low g e n e r a l l y dominates m a t r i x f l o w i n n a t u r a l g e o l o g i c systems o f m i n e r a l i z i n g f l u i d s , petroleum, n a t u r a l gas, and ground water. F rac- t u r e f l o w can exceed m a t r i x f l o w p a r t i c u l a r l y when t h e g e o l o g i c system i s d i s t u r b e d by an induced pressure d i f f e r e n t i a l , such as t h e pumping of pe t ro leum o r ground water , t h e pro- d u c t i o n o f n a t u r a l gas, o r t h e ponding o f water beh ind dams. Measured

f rac tu re-ne twork p e r m e a b i l i t i e s i n some areas a r e 6-7 o r d e r s o f magnitude g r e a t e r than rock m a t r i x p e r m e a b i l i t i e s (e.g. , Montezar and W i 1 son, 1985).

E f f o r t s t o q u a n t i t a t i v e l y model and t o understand f l o w p r o p e r t i e s o f f r a c t u r e networks a r e p r e s e n t l y under way (e.g., Long and Witherspoon, 1985). The use o f f r a c t u r e - f l o w models t o a p p l i e d problems i s c o n t i n g e n t upon t h e s i z e , shape, o r i e n t a t i o n , c o n n e c t i v i t y , aper tu re , s u r f a c e roughness, and s p a t i a l d i s t r i b u t i o n o f f r a c t u r e s .

f r a c t u r e - t r a c e networks on two-dimen- s i o n a l s e c t i o n s t h r o u g h t h e t h r e e - dimensional f r a c t u r e network. We then c h a r a c t e r i z e t h e two-dimensional f r a c t u r e - t r a c e maps u s i n g f r a c t a l geometry.

I n t h i s paper, we present maps o f

2. FRACTURE MAPS

As p a r t o f an e f f o r t t o charac- t e r i z e the f r a c t u r e network a t Yucca Mountain i n southwestern Nevada (F ig . 1). we have prepared 1:50 s c a l e maps o f f r a c t u r e t races exposed on t h r e e pave- ments from 214 t o 260 m i n area i n Miocene ash-f low t u f f s . The pavements a re subhori zon ta l p lana r sur faces t h a t we c lea red o f t a l u s , s o i l , and vegeta- t i o n t o p rov ide complete exposure o f t he ash-f low t u f f bedrock. ments a re i n the same ash- f low subun i t , t h e upper l i t h o p h y s a l subun i t o f t h e T i va Canyon Member o f t h e Pa in tb rush T u f f (Sco t t and o thers , 1983). The pavements a re designated by numbers 100, 200, and 300. Pavement 100 i s l oca ted 500 meters south o f pavements 200 and 300, which a r e 15 meters a p a r t , eas t and west.

All f r a c t u r e s w i t h t r a c e l eng ths grea ter than 0.20 m were mapped. The maps f o r pavements 100, 200, and 300 are shown on F igures 2 , 3, and 4, respec t i ve ly .

2

The pave-

_ _ _ - I I

.,\,,>, I

...,-

3. THE FRACTURES

The p a t t e r n s o f f r a c t u r e s on F igu res 2, 3, and 4 are composites o f c o o l i n g f r a c t u r e s w i t h t u b u l a r s t r u c - t u r e s (Bar ton and o thers , 1984) formed s h o r t l y a f t e r emplacement of t h e ash- f l o w t u f f and l a t e r f r a c t u r e s formed i n response t o t e c t o n i c s t resses t h a t p ro- duced t h e Basin and Range p rov ince and p o s s i b l y t h e Las Vegas-Walker Lane shear zone (Barton, 1984). The v e r t i - c a l e x t e n t o f t h e f r a c t u r e s i s l i m i t e d by t h e l i t h o l o g y because t h e f r a c t u r e s a r e s t ra ta -bound w i t h i n t h e upper l i t h o p h y s a l subuni t .

3.1 F r a c t u r e o r i e n t a t i o n s

The po les t o f r a c t u r e sur faces and bedding f o r a l l t h r e e pavements a r e p l o t t e d toge the r i n s te reograph ic p ro - j e c t i o n on F i g u r e 5. The f r a c t u r e s

N

F i g u r e 5. Combined po les t o f r a c t u r e sur faces f o r a l l t h r e e pavements. b i s p o l e t o bedding. Lower-hemi sphere equal-area p r o j e c t i o n (580 po les ) .

F i g u r e 1. Locat ion o f Yucca Mountain, southwestern Nevada.

78

f r a c t u r e s on r e composites of h t u b u l a r s t r u c - e rs , 1984) formed ment o f t h e ash- r a c t u r e s formed i n s t resses t h a t pro- ange p rov ince and s-Wal k e r Lane 984). The v e r t i - c t u r e s i s l i m i t e d use t h e f r a c t u r e s i n t h e upper

t i o n s

c t u r e sur faces and ! pavements a re , t e reograph ic p ro-

The f r a c t u r e s

p o l e s t o f r a c t u r e f o r a l l t h r e e . b i s p o l e t o

Lower-hemisphere a p r o j e c t i o n (580

-

N c

E d 4 tu I1

Po al L m

0 0

v

4

c, c W

5 > fa a v- 0 a Po E

N

79

- N

E 0 10 N

I1

5 aJ L rrJ v

0 0 cu c, c aJ E aJ 5 5 P

v- 0

Q. m E

aJ U 5 L U I aJ L =I

+3 U m L LL

m

W L 3 03 .r

U

, , I ,

I

I I I

i I

I

80 I

I-

--- . id-

I I /

/ I I

/ I :

,

. .

0

L Q o E

h

N E d N N

I1

m a, L m

a 0 m

v

Y- O

a fu E W u m i U I al L 3 U V m L LL

d

81

range i n s t r i k e f rom 0 t o 360' and i n d i p from 46 t o 90' w i th s l i g h t l y h i g h e r concen t ra t i ons i n t h e southeast and southwest quadrants; h ighes t concentra- t i o n s i n d i p a re between 80 and 90'. The f r a c t u r e s cannot be grouped i n t o we l l -de f i ned se ts based on o r i e n t a t i o n .

3.2 D i s t r i b u t i o n o f f r a c t u r e - t r a c e 1 engths

The combined d i s t r i b u t i o n o f f r a c t u r e - t r a c e l eng ths f o r a l l t h r e e pavements i s shown on F i g u r e 6. The lower end o f t h e d i s t r i b u t i o n i s t r u n - ca ted because no t r a c e l eng ths l e s s than 0.20 m were mapped. The upper end i s t runca ted because many t r a c e l eng ths

100

a g a

f 5 0

i

7 4

exceed t h e dimensions o f t h e pavements. The d i s t r i b u t i o n i s log-normal, even w i t h t h e t r u n c a t i o n of t r a c e l eng ths l e s s than 0.20 m (Baecher and Lanney, 1978).

3.3 F r a c t u r e networks

The f r a c t u r e networks are q u i t e complex and cannot be broken down i n t o we l l -de f i ned f r a c t u r e se ts , each hav ing a c h a r a c t e r i s t i c o r i e n t a t i o n , spacing d i s t r i b u t i o n , and t r a c e - l e n g t h d i s t r i - bu t i on . F r a c t a l c h a r a c t e r i z a t i o n o f such complex f r a c t u r e networks may prove useful f o r model ing f r a c t u r e f l o w and f o r model ing mechanical responses o f f r a c t u r e d rock.

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Trace Length Irn)

F i g u r e 6. Combined d i s t r i b u t i o n o f f r a c t u r e - t r a c e l eng ths f o r a l l t h r e e pavements (580 f r a c t u r e s ) .

52

4. FRACTALS

F r a c t a l geometry 1982). has been a p p l i l o t h e r s t o q u a n t i t a t i v complex p a t t e r n s in n geometry app l i ed t o t f r a c t u r e n e t m r k s sim t i f i e s t h e s p a t i a l an d i s t r i b u t ions.

A f r a c t a l analys t h r e e f r a c t u r e maps p was done by hand. Gr s i zed square elements t h e maps, and t h e nun elements i n t e r s e c t e d was counted. The re1 t h e g r i d elements I S Log2 o f t he number 0' i n t e r s e c t e d by f r a c t l element size. F o r el f r a c t a l dimension (D va lue of t h e s lope 0 f i t t e d t o t h e p o i n t s t h i s way, t h e f raC ta be determined by t h e

where b i s t h e y - i n t f r a c t a l dimensions (I works l i e between 1 f i dence l e v e l s of 0. par ison , t h e f r a c t a l s t r a i g h t l i n e i s 1; 2; and f o r a volume, 100 has a f r a c t a l d. pavement 200, a frac 1.12; and pavement : dimension o f 1.14.

Because t h e PO by smooth l i n e s ( e i , curved), t h e networ f r a c t a l over t h e SC m o r two orders of these l i n e s are s t r t h e networks can a1 sca le i ndependent o range. F r a c t u r e ne dimensions Close t o a re expected t o hau t i o n a l f l o w a n i s o t r t i c t h a t i s n o t ob\ d i s t r i b u t i o n o f frz

I ' D

i log-normal, even 1 o f t r a c e l eng ths iaecher and Lanney,

i r k s

tworks a r e q u i t e ? broken down i n t o 3 sets, each hav ing zn ta t ion , spac ing

. ace- length d i s t r i - e r a c t e r i z a t i o n o f 2 networks may

i n g f r a c t u r e f l l n i c a l responses

ow

- - - 15 16 1 7 18 19

I

4. FRACTALS

F r a c t a l geometry (Mandelbrot, 1982), has been a p p l i e d by him and o t h e r s t o q u a n t i t a t i v e l y desc r ibe complex p a t t e r n s i n nature. F r a c t a l geometry a p p l i e d t o two-dimensional f r a c t u r e networks s imu l taneous ly quan- t i f i e s t h e s p a t i a l and t race - leng th d i s t r i b u t i o n s .

A f r a c t a l a n a l y s i s f o r each o f t h e t h r e e f r a c t u r e maps p l o t t e d on F i g u r e 7 was ,done by hand. Gr ids o f var ious- s i z e d square elements were placed over t h e maps, and t h e number o f g r i d elements i n t e r s e c t e d by f r a c t u r e t r a c e s was counted. The r e l a t i v e s i z e (K) O f t h e g r i d elements i s p l o t t e d versus t h e Log2 o f t h e number o f g r i d elements (N) i n t e r s e c t e d by f r a c t u r e s f o r each element s ize . F o r each pavement, t h e f r a c t a l dimension ( D ) i s t h e abso lu te va lue o f t h e s lope o f a s t r a i g h t l i n e f i t t e d t o t h e po in ts . t h i s way, t h e f r a c t a l dimension ( 0 ) can be determined by t h e equat ion

When p l o t t e d

where b i s t h e y - i n te rcep t . f r a c t a l dimensions o f a l l t h r e e ne t - works l i e between 1 and 2, w i t h con- f i d e n c e l e v e l s o f 0.99. F o r com- par ison , t h e f r a c t a l dimension o f a s t r a i g h t l i n e i s 1; f o r a plane, i t i s 2; and f o r a volume, i t is 3. Pavement 100 has a f r a c t a l dimension of 1.16; pavement 200, a f r a c t a l dimension of 1.12; and pavement 300, a f r a c t a l dimension o f 1.14.

by smooth l i n e s ( e i t h e r s t r a i g h t o r curved), t h e networks can be s a i d t o be f r a c t a l over t h e s c a l e range 0.20 t o 25 m o r two o rde rs o f magnitude. Because these l i n e s a re s t r a i g h t (no t curved), t h e networks can a l s o be s a i d t o be s c a l e independent over t h e same range. F r a c t u r e networks w i t h f r a c t a l dimensions c lose t o one, such as these, a r e expected t o have s t r o n g l y d i r e c - t i o n a l f l o w an iso t ropy , a c h a r a c t e r i s - t i c t h a t i s n o t obvious from t h e d i s t r i b u t i o n o f f r a c t u r e s t r i k e s .

The

Because t h e p o i n t s can be f i t t e d

83

l a

13

12

- X z m 0 1 1

- (*

-I

10

9

e

. Pavement 100 Pavement 200

~ Pavement 300

;t \

1 I 1 I 1 2 3 4 5 6

K

F i g u r e 7. F r a c t a l p l o t o f f r a c t u r e networks.

5. CONCLUSIONS

Complex two-dimensional f r a c t u r e - t r a c e networks can be descr ibed quan- t i t a t i v e l y u s i n g f r a c t a l geometry. The f r a c t a l dimensions ( 0 ) a re t i g h t l y c l u s t e r e d (1.12-1.16) f o r t h r e e l a t e r a l l y separated pavements i n t h e same s t r a t i g r a p h i c subun i t , even though t h e f r a c t u r e networks v i s u a l l y appear q u i t e d i f f e r e n t . magnitude, t h e networks are sca le independent, even when t h e t race - leng th d i s t r i b u t i o n s a re t runca ted .

Over two orders o f

We are p r e s e n t l y i n v e s t i g a t i n g whether the f r a c t a l d imension of f r a c t u r e networks v a r i e s w i t h l i t h o l o g y f o r t he strata-bound f r a c t u r e s a t Yucca Mountain.

ACKNOWLEDGMENTS

We thank B. B. Mandelbrot f o r meet ing w i t h the sen io r au tho r a t an e a r l y stage o f t h i s study. We thank Thomas Howard, K u r t S t e r n l o f , and K i 'ohnson f o r h e l p i n g us w i t h i n i t i a l rapping of t h e pavements. T h i s s tudy has been performed i n coopera t i on w i t h the U.S. Department o f Energy, Nevada % c l e a r Waste Storage I n v e s t i g a t i o n s ( In te ragency Agreement DE-AIO8- 78ET44802).

.

REFERENCES

Baecher, G. B., and N. A. Lanney 1978. Trace l e n g t h b iases i n j o i n t surveys. Proceedings, 19 th U.S. Symposium on Rock Mechanics. 1:56- 65.

Barton, C. C. 1984. T e c t o n i c s i g n i f i - cance o f f r a c t u r e s i n welded t u f f , Yucca Mountain, southwest Nevada. Geological Soc ie ty of America Abs t rac ts With Programs 16( 6 ) :438.

Barton, C. C., T. M. Howard, and E r i c Larsen 1984. Tubu la r s t r u c t u r e s on the faces o f c o o l i n g j o i n t s : a new v o l c a n i c fea ture . EOS (Transac- t i o n s o f t h e American Geophysical Union) 65(45):1148.

Long, J. C. S., and P. A. Witherspoon 1985. The r e l a t i o n s h i p o f degree of i n t e r c o n n e c t i o n t o p e r m e a b i l i t y i n f r a c t u r e networks. Journa l o f Geophysical Research 90(B7):3087- 3098.

Mandelbrot, B. 6. 1982. The f r a c t a l geometry o f nature. W. H. Freeman and Co., San Franc isco . 460.

Montezar, Parv iz , and W. E. Wi lson 1985. Conceptual h y d r o l o g i c model o f f l o w i n t h e unsatura ted zone, Yucca Mountain, Nevada. U.S. Geological Survey Water Resources I n v e s t i g a t i o n Report 84-4345.

Scot t , R. 6.. R. W. Spengler, Sharon Oieh l , A. R. Lappin, and M. P. Chornack 1983. Geo log ic cha rac te r o f t u f f s i n t h e unsatura ted zone a t Yucca Mountain, sou thern Nevada: J. W. Mercer, P. S. C. Rao, and I. W. Marine, e d i t o r s , Role o f t h e

I unsatura ted zone i n r a d i o a c t i v e and hazardous waste d i sposa l . Ann Arbor Science, Ann Arbor. 289-335.

Proceedings of the 11

Hackle plur - BYRON R. KULl

Wright State Unim STUART L. DEA Utriversity of Toleo

Hackle plumes j o i n t developm occurring plum faces and s tep Hackle traces, fracture advan j o i n t propagat ture front l i n with regular g a t ins tantaneo r e f l e c t variat w e l l as crack- j o i n t inceptfa

FIGURE 1. Ger hackle plumes.

1. INTRODUCTI

Surface st ponents) most shown in Figui component det: decreasing gr: pagation path t i o n a t a disc are governed 1 s t r e s s e s and 1

I n the felloe