7_Chapter 7 Discontinuities in Rock- Description and Presentation for Stability Analysis

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PART 2

Rock SlopesOn 7 April 2000 at 11.00 a.m., Adrian Adams photographed a rock fall atCharmouth, Dorset, England. The tower or column of Belemnite Marl of LowerJurassic age had become detached from the main cliff face for many years,before it suddenly came thundering down. A sequence of photographs showingthe event is given below.

Copyright Charmouth Heritage Coast Centre.



CHAPTER SEVEN

Discontinuities in rock: description and

presentation for stability analysis

Description of rock discontinuitiesIn soils, slope failures range from being circular in relatively homogeneousmaterials to being non-circular or planar in layered soils. In rock, however,most slope failures are controlled by ever-present discontinuities such as joints, faults and fractures. These discontinuities are planes of weaknessacross which there is little or no tensile strength. Slope failures will befeasible or not and will propagate depending on the extent, pattern andtypes of discontinuity present in the rock mass. The assessment of rockslopes for their susceptibility to failure must, therefore, incorporate adescription system (see below) and a means for presenting orientationdata in a form that can be used directly in stability analysis (this will beseen later to be the hemispherical projection).

BS 5930: 1999, Code of practice for site investigations , includes the

following types of discontinuity.. Joint : a discontinuity in the body of rock along which there has been

no visible displacement.. Fault : a fracture or fracture zone along which there has been recogniz-

able displacement.. Bedding fracture : a fracture along the bedding (bedding is a surface

parallel to the plane of deposition).. Cleavage fracture : a fracture along a cleavage (cleavage is a set of par-

allel planes of weakness often associated with mineral realignment).. Induced fracture : a discontinuity of non-geological origin, e.g. brought

about by coring, blasting, ripping, etc. They are often characterized byrough fresh (i.e. no discoloration or surface mineral coatings) surfaces.

. Incipient fracture : a discontinuity which retains some tensile strength,which may not be fully developed or which may be partially cemented.Many incipient fractures are along bedding or cleavage.

Of these, joints and bedding fractures are the most common and in mostcases these form a distinct pattern of parallel or sub-parallel sets. The orien-tation of these sets can in combination with the excavated or natural face ofthe rock, bring about one or more failure mechanisms that involve free-fall,

195



sliding or rotation of rock blocks. In the special case of randomly orientateddiscontinuities failure is likely to occur on a circular plane in a similarmanner to soils. Clearly the description of the discontinuities in rock iscritical to the identi®cation of potential failure mechanisms in fracturedrock masses. The important characteristics of discontinuities which mustbe recorded can be placed under the headings of the following checklist:

. orientation

. spacing (one dimension)

. block size and shape (spacing in three dimensions)

. persistence

. roughness

. wall strength

. wall coating

.aperture and in®lling. seepage

. discontinuity sets.

Most of these characteristics are illustrated in Fig. 7.1. Table 7.1 sum-marises the nature and signi®cance and these characteristics.

Filling

Aperture

Discontinuity set

Discontinuity set

Roughness

Block size

P e r s i s t e n c e

Dip and

dip directionSpacing

Seepage

Fig. 7.1 Observations and measurements required for the description of discontinuities

SHORT COURSE IN SOIL AND ROCK SLOPE ENGINEERING

196



T a b l e 7 . 1 D e s c r i p t i o n o f d i s c o n t i n u i t i e s

P r o p e r t y

M e a s u r e m e n t


m e t h o d

L i m i t a t i o n s

U s e s

O r i e n t a t i o n

( F i g s . 7 . 1 a n d 7 . 2 )

T h e c o n v e n t i o n d i p d i r e c t i o n / d i p s h o u l d b e

u s e d , e . g . 0 2 6 / 8 6 ( N o t e i n o r d e r t o a v o i d

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

d i r e c t i o n s h o u l d a l w a y s b e r e p o r t e d a s 3

d i g i t s , e . g . 0 0 6 a n d t h e d i p a s 2 d i g i t s , e . g . 0 9 )

G e o l o g i c a l c o m p a s s

( F i g . 7 . 3 a , b ) o r a

c o m p a s s ( F i g . 7 . 3 c )

a n d a c l i n o m e t e r

( F i g . 7 . 3 d )

O r i e n t a t i o n o f d i s c o n t i n u i t i e s

c a n n o t b e d e t e r m i n e d

a c c u r a t e l y f r o m c o r e s a m p l e s

u n l e s s t h e c o r e h a s b e e n

o r i e n t a t e d ( B a r r , 1 9 7 7 ) o r t h e

f r a c t u r e s h a v e b e e n

c o r r e l a t e d w i t h t h o s e i n t h e

b o r e h o l e u s i n g a d e v i c e s u c h

a s a b o r e h o l e i m p r e s s i o n

p a c k e r ( H i n d s , 1 9 7 4 ; B a r r a n d

H o c k i n g , 1 9 7 6 )

O r i e n t a t i o n i s o n e o f t h e

c r i t i c a l p a r a m e t e r s t h a t

d e t e r m i n e s f a i l u r e

m e c h a n i s m a n d i s u s e d

i n k i n e m a t i c f e a s i b i l i t y

a n a l y s i s

D i s c o n t i n u i t y s e t s

( F i g . 7 . 1 )

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

a v e r a g e o r i e n t a t i o n o f e a c h s e t d e t e r m i n e d

H e m i s p h e r i c a l

p r o j e c t i o n

P e r m i t s i d e n t i ® c a t i o n

o f l i k e l y f a i l u r e

m e c h a n i s m s

S p a c i n g ( o n e

d i m

e n s i o n ) ( F i g . 7 . 1 )

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

s e t ; t h e c o n v e n t i o n i s t o m e a s u r e s p a c i n g

p e r p e n d i c u l a r t o t h e d i s c o n t i n u i t i e s . I n c o r e s

w i t h s t e e p l y d i p p i n g d i s c o n t i n u i t i e s , i t m a y

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

t h e c o r e a x i s ; i f s o ,

t h i s s h o u l d b e s t a t e d . F o r

s c a n l i n e s u r v e y s s p a c i n g i s g e n e r a l l y

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

S u r v e y o r ' s

m e a s u r i n g t a p e ( 3 0

o r 1 0 0 m ) ( F i g . 7 . 3 e )

T h e u s e o f v e r t i c a l b o r e h o l e s

w i l l i n t r o d u c e d i r e c t i o n a l b i a s

i n t o d i s c o n t i n u i t y s p a c i n g

m e a s u r e m e n t s . I t i s

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

b o r e h o l e s b e u s e d t o r e d u c e

t h e b i a s

. S c a n l i n e s s h o u l d b e

i n t h r e e n e a r o r t h o g o n a l

d i r e c t i o n s t o r e d u c e b i a s

S p a c i n g i s u s e d t o

d e d u c e d e g r e e o f

s t r u c t u r a l a n i s o t r o p y

a n d b l o c k s i z e a n d s h a p e

B l o c k s i z e a n d s h a p e

( s p a c i n g i n t h r e e

d i m

e n s i o n s )

T h e s p a c i n g o f d i s c o n t i n u i t i e s i n t h r e e

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

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

b o u n d e d b y d i s c o n t i n u i t i e s ( s e e T a b l e 7 . 2 ) .

R o c k b l o c k s m a y b e a p p r o x i m a t e l y e q u i -

d i m e n s i o n a l , t a b u l a r

o r c o l u m n a r i n s h a p e

T h e t h r e e - d i m e n s i o n a l c h a r a c t e r i s t i c s o f

d i s c o n t i n u i t i e s c a n n o t b e m e a s u r e d

e f f e c t i v e l y f r o m a b o r e h o l e / c o r e

S u r v e y o r ' s

m e a s u r i n g t a p e

( 3 0 o r 1 0 0 m )

( F i g . 7 . 3 e )

S e e a b o v e

U s e d a s a i d i n

d e t e r m i n i n g t h e l i k e l y

f a i l u r e m e c h a n i s m , e .

g .

w h e t h e r t o p p l i n g i s m o r e

l i k e l y t h a n s l i d i n g

CHAPTER 7 DISCONTINUITIES IN ROCK

197



T a b l e 7 . 1 C o n t i n u e d

P r o p e r t y



m e t h o d


U s e s

B l o c k s i z e a n d s h a p e

( s p a c i n g i n t h r e e

d i m

e n s i o n s )

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

f r o m o n e - d i m

e n s i o n a l s p a c i n g

m e a s u r e m e n t s

P e r s i s t e n c e ( F i g . 7 . 1 ) D e s c r i p t i v e t e r m i n o l o g y c a n b e a p p l i e d t o

s e t s ; a c t u a l m e a s u r e m e n t s o f t r a c e l e n g t h s

a r e p r e f e r r e d f o r i n d i v i d u a l d i s c o n t i n u i t i e s

A t a p e i s e s s e n t i a l w h e r e a c t u a l

m e a s u r e m e n t s a r e r e q u i r e d

S u r v e y o r ' s


( 1 0 o r 3 0 m )

( F i g . 7 . 3 e )

V e r y l i m i t e d i n f o r m a t i o n i s

a v a i l a b l e f r o m c o r e s

M e a s u r e m e n t s a r e s c a l e

d e p e n d e n t a n d t h e s i z e o f t h e

e x p o s u r e s h o u l d b e r e c o r d e d .

A i d s t h e i n t e r p r e t a t i o n o f

t h e r e l a t i v e i m p o r t a n c e

o f d i s c o n t i n u i t i e s , e . g . a

s i n g l e h i g h l y p e r s i s t e n t

d i s c o n t i n u i t y i s l i k e l y t o

b e m o r e i m p o r t a n t t h a n

a s e t o f l o w p e r s i s t e n c e

d i s c o n t i n u i t i e s

T e r m i n a t i o n

T h e n a t u r e o f t h e d i s c o n t i n u i t y t e r m i n a t i o n

s h o u l d b e r e c o r d e d i n t h e c o n t e x t o f t h e s i z e

o f t h e e x p o s u r e . A d i s c o n t i n u i t y m a y s t a r t

a n d e n d w i t h i n t h e e x p o s u r e

V i s u a l r e c o g n i t i o n

M e a s u r e m e n t s a r e s c a l e

d e p e n d e n t a n d t h e s i z e o f t h e

e x p o s u r e s h o u l d b e r e c o r d e d

A i d s t h e i n t e r p r e t a t i o n o f

t h e r e l a t i v e i m p o r t a n c e

o f d i s c o n t i n u i t i e s

R o u g h n e s s ( F i g . 7 . 1 ) D e s c r i p t i o n s o f r o u g h n e s s s h o u l d b e m a d e a t

t h r e e s c a l e s w h e r e p o s s i b l e ( I S R M

, 1 9 7 8 )

L a r g e s c a l e ( t e n s o f m e t r e s ) r e p o r t e d a s

m e a s u r e d w a v e l e n g t h a n d a m p l i t u d e

I n t e r m e d i a t e s c a l e ( s e v e r a l m e t r e s ) i s

d i v i d e d i n t o s t e p p e d , u n d u l a t i n g o r p l a n a r .

W a v e l e n g t h a n d a m p l i t u d e m a y a l s o b e u s e d

S m a l l s c a l e ( s e v e r a l c e n t i m e t r e s ) i s d i v i d e d

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

s u p e r i m p o s e d o n t h e i n t e r m e d i a t e s c a l e .

W a v e l e n g t h a n d a m p l i t u d e m a y a l s o b e u s e d

S m a l l - s c a l e r o u g h n e s s m a y b e m e a s u r e d

u s i n g a p r o ® l i n g t o o l o r c o n v e r t e d t o a J o i n t

R o u g h n e s s C

o e f ® c i e n t ( B a r t o n , 1 9 7 1 ) u s i n g

p u b l i s h e d r o u g h n e s s p r o ® l e s o r a ® e l d t i l t

t e s t ( B a r t o n , 1 9 7 6 ; B a r t o n e t a l . , 1 9 8 5 )

S u r v e y o r ' s


( 3 0 m ) , s t r a i g h t

e d g e , s c a l e r u l e ,

p r o ® l i n g t o o l

( F i g . 7 . 3 f ) , p r o ® l e

c h a r t s ( I S R M

, 1 9 7 8 ) ,

g e o l o g i c a l c o m p a s s

o r i n c l i n o m e t e r

( e . g . D r D o l l a r ' s

i n d i c a t o r Ð

F i g . 7 . 3 d )

I t m a y n o t b e p o s s i b l e t o

m e a s u r e

r o u g h n e s s a t t h e

l a r g e a n d i n t e r m e d i a t e s c a l e s

d u e t o t h e s i z e o f t h e

e x p o s u r e . O n l y s m a l l - s c a l e

r o u g h n e s s c a n b e m e a s u r e d

u s i n g c o r e s a m p l e s

R o u g h n e s s i s i m p o r t a n t

i n t h e d e t e r m i n a t i o n o f

t h e s h e a r s t r e n g t h o f

d i s c o n t i n u i t i e s .

I n t e r m e d i a t e a n d l a r g e -

s c a l e r o u g h n e s s w i l l

h a v e t h e g r e a t e s t

i n ¯ u e n c e

o n s l o p e

s t a b i l i t y


198



I f t h e r o u g h n e s s h a s a p r e f e r r e d o r i e n t a t i o n

( e . g . s t e p p e d , s t r i a t e d ) t h e

o r i e n t a t i o n s h o u l d

b e r e c o r d e d

A t a p e , s c a l e r u l e a n d p r o ® l i n g t o o l a r e

r e q u i r e d f o r t h e s e m e a s u r e m e n t s

A n i n d i v i d u a l j o i n t m a y b e d e s c r i b e d a s

w a v y ( w a v e l e n g t h 1 2 m , a m

p l i t u d e 1 m ) ,

s t e p p e d ( w a v e l e n g t h 2 m , a m

p l i t u d e 0 . 2 m )

o r s m o o t h

A t a p e , s c a l e r u l e a n d p r o ® l i n g t o o l a r e

r e q u i r e d f o r t h e s e m e a s u r e m e n t s

W a l l s t r e n g t h

T h e u n c o n ® n e d c o m p r e s s i v e s t r e n g t h o f t h e

d i s c o n t i n u i t y w a l l s i s d e t e r m i n e d f r o m i n d e x

t e s t s s u c h a s

t h e S c h m i d t h a m m e r ( B a r t o n

a n d C h o u b y

, 1 9 7 7 )

S c h m i d t h a m m e r

I n d e x t e s t s s u c h a s t h e

S c h m i d t c a n b e u n r e l i a b l e f o r

t h e a c c u r a t e d e t e r m i n a t i o n o f

s t r e n g t h

P r o v i d e s i n d i c a t i o n o f

d e g r e e o f a s p e r i t y

b r e a k a g e

t h a t w i l l o c c u r

d u r i n g s h e a r i n g a c r o s s

t h e d i s c o n t i n u i t y

W a l l c o a t i n g

A n y m i n e r a l c o a t i n g d i s c o n t i n u i t y w a l l s

s h o u l d b e d e s c r i b e d . P a r t i c u l a r a t t e n t i o n

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

a s c h l o r i t e . W

h e r e v e r p o s s i b l e t h e e x t e n t o f

t h e c o a t i n g s h o u l d b e r e c o r d e d a n d t h e s e t o r

s e t s w i t h w h i c h i t i s a s s o c i a t e d


E s t i m a t i n g t h e e x t e n t o f

m i n e r a l c o a t i n g s c a n b e

d i f ® c u l t p a r t i c u l a r l y i f

e x p o s u r e s a r e l i m i t e d

T h e p r e s e n c e o f l o w -

f r i c t i o n m i n e r a l c o a t i n g

w i l l s i g n i ® c a n t l y r e d u c e

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

( i . e . t h e f r i c t i o n a n g l e f o r

s m o o t h d i s c o n t i n u i t i e s ) .

T h e p r e s e n c e o f s u c h

c o a t i n g w

i l l m e a n t h a t

t h e s h e a r s t r e n g t h o f t h e

d i s c o n t i n u i t i e s a f f e c t e d

m u s t b e m

e a s u r e d r a t h e r

t h a n e s t i m a t e d

W a l l w e a t h e r i n g a n d

a l t e r a t i o n

A f a c t u a l d e s c r i p t i o n o f t h e w e a t h e r i n g /

a l t e r a t i o n o f d i s c o n t i n u i t y w a l l s s h o u l d b e

m a d e ( A p p r o a c h 1 ; B S 5 9 3 0 : 1 9 9 9 ) . T h e

m a n i f e s t a t i o n o f w e a t h e r i n g / a l t e r a t i o n o f

d i s c o n t i n u i t i e s i s m o s t l i k e l y t o b e b y

i n c r e a s i n g a p e r t u r e s ( t h r o u g h d i s s o l u t i o n )

a n d / o r d i s c o l o r a t i o n a n d s t r e n g t h r e d u c t i o n

( t h r o u g h c h e m i c a l d e c o m p o s i t i o n ) . A p e r t u r e

a n d w a l l s t r e n g t h a r e d e s c r i b e d s e p a r a t e l y

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

w e a t h e r i n g / a l t e r a t i o n t h a t m u s t b e


T h e w e a t h e r e d /

a l t e r a t i o n

s t a g e o f t h e

d i s c o n t i n u i t y w a l l s w i l l

a f f e c t t h e

s h e a r s t r e n g t h

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

t h e d i s c o n t i n u i t i e s


199



T a b l e 7 . 1 C o n t i n u e d

P r o p e r t y



m e t h o d


U s e s

W a l l w e a t h e r i n g a n d

a l t e r a t i o n

d e s c r i b e d h e r e i s d i s c o l o r a t i o n . T h e e x t e n t

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

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

A p e r t u r e a n d

i n ® l l i n g ( F i g . 7 . 1 )

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

s h o u l d b e r e p o r t e d . F u l l d e s c r i p t i o n o f r o c k ,

s o i l o r m i n e r a l i n ® l l s h o u l d b e p r o v i d e d . T h e

o b s e r v e r s h o u l d c o m m e n t o n w h e t h e r t h e

r e p o r t e d a p e r t u r e s a r e p r e s e n t i n t h e i n t a c t

r o c k m a s s , o r a c o n s e q u e n c e o f

g e o m o r p h o l o g i c a l / w e a t h e r i n g a g e n c i e s , o r

w h e t h e r d u e

t o e n g i n e e r i n g a c t i v i t i e s o r

c r e a t i o n o f t h e e x p o s u r e . T h e t h i c k n e s s a n d

t y p e o f i n ® l l s h o u l d b e r e p o r t e d u s i n g

s t a n d a r d t e r m s , e . g . 1 m m s u r f a c e ® l m o f

c a l c i t e , 1 0 m m c e m e n t e d b r e c c i a , s t i f f b r o w n

s a n d y c l a y

S c a l e r u l e ,

f e e l e r g a u g e s

A p e r t u r e i s d i f ® c u l t /

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

c o r e s a m p l e s . A p e r t u r e m a y

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

i t s e l f u s i n g a d e v i c e s u c h a s a

b o r e h o l e i m p r e s s i o n p a c k e r

( B a r r a n d H o c k i n g , 1 9 7 6 )

I n ® l l t h i c k n e s s a n d t y p e

c a n n o t b e d e t e r m i n e d

e f f e c t i v e l y f r o m c o r e s a m p l e s

s i n c e i t i s l i k e l y t o h a v e b e e n

w a s h e d o u t / c o n t a m i n a t e d b y

t h e d r i l l ¯ u s h ¯ u i d

W h e r e t h e t h i c k n e s s o f

i n ® l l i s e q u a l o r g r e a t e r

t h a n t h e r o u g h n e s s

a m p l i t u d e ( s m a l l /

i n t e r m e d i a t e s c a l e ) t h e

s t r e n g t h o f t h e i n ® l l w i l l

h a v e a d o m i n a n t e f f e c t

o n t h e s h e a r s t r e n g t h o f

t h e d i s c o n t i n u i t y

T h e p r e s e n c e o f i n ® l l

a n d s m a l l a p e r t u r e s w i l l

r e d u c e t h e p e r m e a b i l i t y

o f t h e d i s c o n t i n u i t i e s

S e e p a g e ( F i g . 7 . 1 )

E v i d e n c e o f s e e p a g e a s s o c i a t e d w i t h e a c h

d i s c o n t i n u i t y s e t s h o u l d b e r e c o r d e d . W h e r e

r u n n i n g w a t e r i s o b s e r v e d i s s u i n g f r o m a

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

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

k n o w n v o l u m e a n d w a t c h w i t h a s e c o n d

h a n d

V i s u a l r e c o g n i t i o n ,

v e s s e l o f k n o w n

v o l u m e a n d s t o p

w a t c h

S e e p a g e

c o n d i t i o n s

a s s o c i a t e d w i t h i n d i v i d u a l

d i s c o n t i n u i t i e s c a n n o t b e

d e t e r m i n e d f r o m c o r e

s a m p l e s o r t h e b o r e h o l e

S e e p a g e o b s e r v a t i o n s

w i l l g i v e a n i n d i c a t i o n o f

d r a i n a g e c h a r a c t e r i s t i c s

o f p a r t i c u l a r

d i s c o n t i n u i t y s e t s a n d

h e n c e t h e p o t e n t i a l f o r

t h e b u i l d - u p o f j o i n t

w a t e r p r e s s u r e a n d t h e

c o n s e q u e n c e s t h i s h a s

o n s l o p e s t a b i l i t y


200



Orientation

The orientation of discontinuities in a rock mass is of paramount import-ance to design in rock slope engineering. The majority of discontinuitysurfaces are irregular, resulting in a signi®cant amount of scatter ofmeasurements being made over a small area. To reduce this scatter it isrecommended that a 200 mm diameter aluminium measuring plate beplaced on the discontinuity surface before any measurement is made. Inmany cases, there may not be enough of the discontinuity surface exposedto allow the use of such a plate. If the exposure cannot be enlarged then asmaller plate must be used. A suitable combined compass and clinometer

(geological compass) to which measuring plates can be attached is shownin Hoek and Bray (1981). The most common types of geological compass isthe Silva compass (type 15T) and the Clar type compass (see Fig. 7.3a,b).These devices combine a compass and an inclinometer. This allows themeasurement of both dip and dip direction using the same instrument.Discontinuity orientations may also be measured using a digital compassand a Dr Dollar's clinometer (Fig. 7.3c,d).

Many compasses have the capacity to correct for differences betweenmagnetic north and true north. It is recommended that this adjustmentis always set to zero; corrections can be made later during processing orplotting (Priest, 1993). It should also be noted that compass needles

Dipdirection

N

α = Dip direction measuredclockwise from north

β = Dip

αβ

Discontinuity

Dip vector

Fig. 7.2 De®nition of dip and direction


201



balanced for magnetic inclination in the northern hemisphere will beseverely out of balance in the southern hemisphere. Furthermore, elec-tronic (digital) compasses set up for use in the northern hemisphereshould not be used in the southern hemisphere.

Through careful use of the conventional geological compass and prac-tice it is possible achieve a resolution of less than 30 seconds in dip anddip direction on readily accessible discontinuities (Priest, 1993). However,Ewan and West (1981) conclude that different operators measuring the

Fig. 7.3 Tools used for the description of discontinuities: (a) Silva type 15T geological type compass; (b) Clar type compass (manufactured by Carl Zeiss Jena Ltd)


202



orientation of the same feature have a maximum error of Æ10 8 for dipdirection and Æ58 for dip angle.

Discontinuity setsA discontinuity set represents a series of near parallel discontinuities(refer to Fig. 7.1). The appearance of the rock mass together with itsmechanical behaviour will be strongly in¯uenced by the number of setsof discontinuities that intersect one another. The number of sets tends tocontrol the degree of overbreak in excavations and structural anisotropyof the rock mass. The more discontinuity sets there are, the more isotropic

Fig. 7.3 (c) Digital compass; (d) Dr Dollar's clinometer


203



the rock mass becomes. This may be modi®ed, however, by the spacingassociated with one or more of the discontinuity sets. The number of

sets also affects the degree to which the rock mass can deform without fail-ure of intact rock.A number of sets may be identi®ed by direct observation of the exposure.

The total number of sets present in the rock mass, however, is normallydetermined from a statistical analysis of the discontinuity orientationdata which makes use of hemispherical projection methods (Matherson,1983; Priest, 1985, 1993) which are described later.

SpacingDiscontinuity spacing is a fundamental measure of the degree of fractur-ing of a rock mass and hence it forms one of the principal parameters in the

Fig. 7.3 (e) Surveyor's measuring tape; (f) pro®ling tool, length 140 mm


204



engineering classi®cation of rock masses. In particular, for tunnelling thisproperty has been used in the classi®cation for support requirements(Barton et al. , 1974; Bieniawski, 1976) and for foundation settlementpredictions on rock (Ward et al. , 1968). The spacing of adjacent dis-continuities largely controls the size of individual blocks of intact rock.In exceptional cases, a close spacing may change the mode of failureof the rock mass from translational to circular. In such cases wherethe joints are extremely closely spaced the rock mass will tend tobehave like a granular soil and joint orientation is likely to be of littleconsequence.

Discontinuity spacing may be considered as the distance between onediscontinuity and another. More speci®cally ISRM (1978) de®nes dis-continuity spacing as the perpendicular distance between adjacentdiscontinuities. It is easier when collecting spacing data in the ®eld toadopt the former more general de®nition. For example, a randomsample of discontinuity spacing values may be obtained from a linearscanline survey (described later). Such a survey provides a list of thedistances along the scanline to the points where it is intersected by thediscontinuities which have been sampled. Subtraction of consecutiveintersection distances provides the discontinuity spacing data. Perpen-dicular discontinuity spacing data may be determined during dataprocessing in the of®ce. It is more meaningful if such measurements aremade for discontinuities of the same type (e.g. the same discontinuity set).

Priest (1993) de®nes three different types of discontinuity spacings.. Total spacing : the spacing between a pair of immediately adjacent

discontinuities, measured along a line of general, but speci®ed,location and orientation.

. Set spacing : the spacing between a pair of immediately adjacentdiscontinuities from a particular discontinuity set, measured along aline of any speci®ed location and orientation.

. Normal set spacing : the set spacing when measured along a line that isparallel to the mean normal to the set.

The mean and range of spacings between discontinuities for each setshould be measured and recorded. Ideally these measurements shouldbe made along three mutually perpendicular axes in order to allow forsampling bias. Where discontinuity sets are readily identi®able in the®eld the normal set spacing of each set may be recorded in terms of themaximum, minimum and modal (most frequent) or mean spacing. Acomprehensive treatment of the statistical analysis of discontinuityspacing and frequency is given by Priest (1993).

Discontinuity spacing data are best presented in the form of histograms.Histograms may be produced for individual sets of discontinuities or for all


205



discontinuities intersecting a scanline. If the discontinuities in a particularset exhibit a regular spacing they will give rise to a normal distributionand a mean spacing may be easily determined. In many cases fracturesare clustered or randomly spaced giving rise to a negative exponentialdistribution (Priest and Hudson, 1976). Examples of joint frequencydistributions measured from scanlines in sandstone and mudstone aregiven in Fig. 7.4. The histograms show a close agreement with thenegative exponential distribution expressed as:

f x eÿ x 7:1

where is the mean discontinuity frequency per metre. By ®tting anegative exponential distribution to the spacing data the mean spacingmay be determined from 1 = .

Priest and Hudson (1976) established the following relationshipbetween Rock Quality Designation (RQD) and the mean discontinuityfrequency per metre ( ):

RQD 100e ÿ0 :1 0:1 1 7:2

where RQD is a parameter normally derived from drillcore (Deere, 1964)and is commonly used in the classi®cation of rock masses.

Block size and shapeBlock size and shape are important indicators of rock mass behaviourin slope stability. Rock masses containing tabular or columnar-shaped

15

10

5

00 5

F r e q u e n c y : %

10 15 20 25 30 35 40 45 50 55 60 65 70 75

Discontinuity spacing: cm

f (x ) = λ e –λ x

486 entriesMean spacing 0·112 m

Fig. 7.4 Histogram of discontinuity spacing (after Yenn, 1992)


206



blocks may be more prone to toppling rather than sliding. A small blocksize may result in ravelling or circular failure brought about by the rockmass behaving like a granular soil.

The block size is determined from the discontinuity spacing in onedimension, number of sets and persistence. The number of sets and theorientation of discontinuities will determine the shape of the resultingblocks. Since natural fractures are seldom consistently parallel, however,regular geometric shapes such as cubes, rhombohedrons and tetra-hedrons rarely occur.

BS 5930: 1999 recommends the descriptive terms for block size andshape given in Table 7.2. A more quantitative approach to block sizedescription is given by ISRM (1978).

Other descriptive terms which give an impression of the block size andshape include:

. massive : few fractures or very wide spacing

. irregular : wide variations of block size and shape

.crushed : heavily jointed to give medium gravel size lumps of rock.

Persistence and terminationPersistence refers to the discontinuity trace length as observed in an expo-sure. It is one of the most important factors in discontinuity description, butunfortunately it is one of the most dif®cult to quantify. One of the commonproblems that arises is the measurement of the persistence of major jointswhich are continuous beyond the con®nes of the rock exposure. It isrecommended that the maximum trace length should be measured, andcomment made on the data sheet to indicate whether the total tracelength is visible and whether the discontinuity terminates in solid rock

Table 7.2 Block size and shape (BS 5930: 1999)

First term (size) Maximum dimension

Very large > 2 mLarge 600 mm±2 mMedium 200 mm±600 mmSmall 60 mm±200 mmVery small < 60mm

Second term (shape) Nature of block

Blocky Equi-dimensionalTabular One dimension considerably smaller than the

other twoColumnar One dimension considerably larger than the

other two


207



or against another discontinuity. Clearly, persistence is very much scaledependent and any measurements of persistence should be accompaniedby the dimensions of the exposure from which the measurements weremade. Matherson (1983) considers persistence to be a fundamentalfeature in quantifying the relative importance of discontinuities in arock mass.

Wall roughnessThe wall roughness of a discontinuity is a potentially important compo-nent of its shear strength, particularly in the case of undisplaced andinterlocked features. In terms of shear strength, the importance of wallroughness decreases as aperture, or in®lling thickness or the degree ofdisplacement increases. In cases where adjacent walls are not fully inter-locked or mated the wall roughness will directly in¯uence the degree ofcontact which in turn effect the compressibility of the discontinuity.

In general, the roughness of a discontinuity can be characterized by thefollowing.

. Intermediate and large-scale roughness (Table 7.1). First-order wallasperities which appear as undulations of the plane and would beunlikely to shear off during movement. This will affect the initial direc-tion of shear displacement relative to the mean discontinuity plane.

. Small-scale roughness (Table 7.1). Second-order asperities of the planewhich, because they are suf®ciently small, may be sheared off duringmovement. If the wall strength is suf®ciently high to prevent damagethese second-order asperities will result in dilatant shear behaviour.In general this unevenness affects the shear strength that wouldnormally be measured in a laboratory or medium-scale in situ shear test.

Intermediate and large-scale roughness may be measured by means ofa surveyor's measuring tape or rule placed on the exposed discontinuitysurface in a direction normal to the trend of the waves. The orientationof the measuring tape, together with the mean wavelength and maximum

amplitude should be recorded. In some cases it may be necessary to assessthe roughness in three dimensions in which case a compass and discinclinometer are recommended (Hoek and Bray, 1981). In many cases,however, the measurement of intermediate and large-scale roughness ismade dif®cult or impossible by the extent to which the discontinuitiesare exposed. Small-scale roughness may be assessed by pro®ling thediscontinuity surface. Short pro®les ( < 150 mm) can be measured using apro®ling tool (Fig. 7.3f ) that is obtainable in most home improvementstores. Longer pro®les may be measured using a 2 m rule as describedby ISRM (1978). A number of quantitative techniques for measuringroughness are described in detail by ISRM (1978).


208



As mentioned in Table 7.1 the orientation of roughness features such assteps and undulations in relation to the direction of sliding can have asigni®cant effect on shearing resistance. If the direction of sliding isparallel to the steps or undulations these features will have a negligibleeffect on shearing resistance. If the direction of sliding is perpendicularto the roughness features the shearing resistance is increased signi®-cantly. Clearly, the orientation of such roughness features should berecorded wherever possible.

Wall strengthWall strength refers to the equivalent compression strength of the adja-cent walls of a discontinuity. This may be lower than the intact strengthof the rock owing to weathering or alteration of the walls. The relativelythin `skin' of wall rock that affects shear strength and compressibilitycan be tested by means of simple index tests. Barton and Choubey(1977) explain how the Schmidt hammer index test can be used to esti-mate wall strength d from the following empirical expression

log 10 d %0:88 R 1:01 7:3

where is the unit weight of the rock material (MN/m 3 ), R is the reboundnumber for an L-type Schmidt hammer and d ranges from 20 MPa toapproximately 300MPa. The apparent uniaxial compressive strengthcan be estimated from scratch and geological hammer tests (Table 7.3)

It is recommended that such tests be carried out on freshly broken rocksurfaces such that the estimated wall strength may be directly comparedwith that of the intact rock. It is likely that the intact strength may be meas-ured in the laboratory as part of the investigation and this will provide ameans of calibrating these somewhat crude ®eld measurements.

Aperture, in®lling and wall coatingsAperture is the perpendicular distance separating the adjacent rock wallsof an open discontinuity, in which the intervening space is air or water

®lled. Discontinuities that have been ®lled (for example, with clay) alsocome under this category if the ®lling material has been washed outlocally.

Large apertures may result from shear displacement of discontinuitieshaving a high degree of roughness and waviness, from tensile openingresulting from stress relief, from outwash and dissolution. Steep or verticaldiscontinuities that have opened in tension as a result of valley formationor glacial retreat may have extremely wide apertures measurable in tensof centimetres.

In most sub-surface rock masses, apertures may be closed (i.e.< 0.5 mm). Unless discontinuities are exceptionally smooth and planar it


209



will not be of great signi®cance to shear strength that a `closed' feature is0.1 mm wide or 1.0 mm wide. Such a range of widths however may have agreater signi®cance with respect to the compressibility of the rock mass.

Large apertures may be measured with a tape of suitable length. Themeasurement of small apertures may require a feeler gauge. Details ofmeasurement techniques may be found in ISRM (1978).

In®lling refers to material that separates the adjacent rock walls of a dis-

continuity and that is usually weaker than the parent rock. Typical ®llingmaterials are sand, silt, clay, breccia, gouge and mylonite. Filling mayinclude thin mineral coatings and healed discontinuities. Mineral coatingssuch as chlorite can result in a signi®cant reduction in shearing resistanceof discontinuities (Hencher and Richards, 1989). In general, if the ®lling isweaker and more compressible than the parent rock its presence mayhave a signi®cant effect on the engineering performance of the rockmass. The drainage characteristics of the ®lling material will not onlyaffect the hydraulic conductivity of the rock mass but also the long- andshort-term mechanical behaviour of the discontinuities since the in®llmay behave as a soil.

Table 7.3 Rock material strength

Term Uncon®ned compressivestrength: MPa

Field estimation of hardness

Very strong > 100 Very hard rock, more than one blow ofgeological hammer required to breakspecimen

Strong 50±100 Hard rock, hand-held specimen can bebroken with single blow of geologicalhammer

Moderate strong 12.5±50 Soft rock, 5mm indentations with sharpend of pick

Moderately weak 5.0±12.5 Too hard to cut by hand into a triaxialspecimen

Weak 1.25±5.0 Very soft rock, material crumbles under®rm blows with the sharp end of ageological pick

Very weak rockor hard soil

0.60±1.25 Brittle or tough, may be broken in thehand with dif®culty

Very stiff 0.30±0.60 Ã Soil can be indented by the ®ngernailStiff 0.15±0.30 Ã Soil cannot be moulded in ®ngersFirm 0.08±0.15 Ã Soil can be moulded only by strong

pressure of ®ngersSoft 0.04±0.08 Ã Soil easily moulded with ®ngersVery soft <0.04 Ã Soil exudes between ®ngers when

squeezed in the handÃThe uncon®ned compressive strengths for soils given above are double the undrained shear strengths


210



ISRM (1978) suggests that the principal factors affecting the physicalbehaviour of in®lled discontinuities are as follows:

. mineralogy of ®lling material

. grading or particle size

. over-consolidation ratio (OCR)

. water content and permeability

. previous shear displacement

. wall roughness

. width of in®ll

. fracturing or crushing of wall rock.

If the thickness of the in®ll exceeds the maximum amplitude of theroughness the properties of the in®ll will control the mechanical behaviourof the discontinuity. Clearly the wall roughness and the thickness or widthof in®ll must be recorded in the ®eld. An engineering description of thein®ll material should be made in the ®eld and suitable samples takenfor laboratory tests. The in®ll should be carefully inspected in the ®eldto see whether there is any evidence of previous movement (for example,slickensides) since this is likely to reduce the shearing resistance of thefracture signi®cantly.

SeepageWater seepage through rock masses results mainly from ¯ow through

discontinuities (`secondary permeability') unless the rock material is suf®-ciently permeable that it accounts for a signi®cant proportion of the ¯ow.Generally it should be noted whether a discontinuity is dry, damp or wetor has water ¯owing continuously from it. In the latter case the rate of ¯owshould be estimated. Of course such observations are dependent upon theposition of the water table and the prevailing weather conditions. It isimportant to note whether ¯ow is associated with a particular set ofdiscontinuities.

Methods for collecting discontinuity dataThe method used in collecting discontinuity data will depend largely onthe degree of access to the rock mass. Surface exposures may be availablebut may not be representative of the rock mass at the depth of interest,owing to weathering agencies (for example, stress relief causing reductionin joint spacing and an increase in aperture). In rock slope design, thenecessary rock mass information may be obtained from surface exposuresif available. Drillhole information may be used to supplement the dataobtained from surface exposures. Where surface exposures are not avail-able, or are considered to be unrepresentative of the rock mass, drillholesalone may be the only source of data. Table 7.4 shows how the quality of


211



T a b l e 7 . 4 Q u a l i t y o f i n f o r m a t i o n

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

S o c i e t y o f L o n d o n W o r k i n g P a r t y R e p o r t o n t h e D e s c r i p t i o n o f R o c k M a s s e s ( 1 9 7 7 ) )

T y p e o f i n f o r m a t i o n

D i r e c t

m e a s u r e m e n t

( s u r f a c e

e x p o s u r e , t r i a l

a d i t o r s h a f t )

S u r f a c e

p h o t o g r a p h y

D r i l l h o l e c o r e

O r i e n t a t e d

d r i l l h o l e c o r e

D r i l l h o l e

c a m e r a

D r i l l h o l e

i m p r e s s i o n

p a c k e r

G e o p h y s i c s

a c o u s t i c

m e t h o d s

L o c a t i o n

G o o d

G o o d

G o o d

G o o d

G o o d

G o o d

M e d i u m

T y p e o f d i s c o n t i n u i t y

G o o d

M e d i u m

G o o d

G o o d

G o o d

P o o r

P o o r

D e s c r i p t i o n o f r o c k m a t e r i a l

G o o d

P o o r

G o o d

G o o d

P o o r

N o n e

N o n e

O r i e n t a t i o n : d i p

G o o d

M e d i u m

M e d i u m / P o o r

G o o d

P o o r

G o o d

P o o r

O r i e n t a t i o n : d i p d i r e c t i o n

G o o d

M e d i u m

P o o r

M e d i u m

M e d i u m

M e d i u m

P o o r

S p a c i n g

G o o d

G o o d

M e d i u m

M e d i u m

M e d i u m

M e d i u m

P o o r


G o o d

G o o d

P o o r

P o o r

P o o r

P o o r

P o o r

W a l l r o u g h n e s s : w a v i n e s s

G o o d


P o o r

P o o r

P o o r

P o o r

P o o r

W a l l r o u g h n e s s : r o u g h n e s s

G o o d


M e d i u m

M e d i u m

P o o r

P o o r

P o o r


G o o d

N o n e

M e d i u m

M e d i u m

N o n e

N o n e

N o n e

A p e r t u r e

G o o d

P o o r

P o o r

P o o r

M e d i u m

M e d i u m


I n ® l l : n a t u r e

G o o d

P o o r

M e d i u m

M e d i u m

P o o r

P o o r

N o n e

I n ® l l : t h i c k n e s s

G o o d

P o o r



M e d i u m

P o o r

P o o r

S e e p a g e

G o o d

M e d i u m

N o n e

N o n e

M e d i u m

N o n e

P o o r

N u m b e r o f s e t s

G o o d

G o o d / M e d i u m

P o o r

M e d i u m

M e d i u m

M e d i u m

N o n e

B l o c k s i z e

G o o d

G o o d / M e d i u m

P o o r

M e d i u m

M e d i u m

M e d i u m

P o o r

K e y t o T a b l e 7

. 4

G o o d : f e a t u r e m e a s u r e d r e l i a b i l i t y

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

P o o r : f e a t u r e d i f ® c u l t t o m e a s u r e , o f t e n m e a s u r e m e n t i s i n f e r r e d

N o n e : i m p o s s i b l e t o i d e n t i f y f e a t u r e


212



discontinuity data is affected by the type of access to the rock mass and thetype of survey method used.

It may be seen from Table 7.4 that access to the rock mass via a drillholesuffers from a number of disadvantages. First, a drillhole permits only asmall volume of the rock mass to be viewed such that the persistence ofdiscontinuities cannot be adequately assessed. Second, the orientationof the core must be known before any fracture orientation measurementscan be made. Also, drillholes are prone to directional biasing of disconti-nuity data unless they are drilled with different orientations. For example,if only vertical drillholes are employed any vertical or near vertical sets ofdiscontinuities may be missed altogether or a false impression may begiven with respect to the frequency of these fractures. The only way toovercome this problem is to drill inclined holes at a number of differentorientations. Terzaghi (1965) and Priest (1993) discuss methods of dealingwith directional biasing.

It is impossible to measure aperture from drillhole cores since it isinevitable that the sticks of core will have moved relative to one anotherduring and after sampling. The only way of measuring aperture in thiscase is by inspection of the drillhole wall. This is achieved using aborehole impression packer or a borehole television camera.

Discontinuity in®ll may be washed out or contaminated by the drilling¯uid such that it becomes dif®cult to assess its thickness or propertiesadequately. Mineral coatings on joint walls may be observed in core

samples. It is impossible, however, to assess the degree of coveragefrom such a small sample.

Surface exposures offer a much larger expanse of rock for examinationand permit direct observation and measurement of discontinuities. Theycan be just as prone to directional biasing as the drillhole if only a singleorientation of exposed face is available. Where surface exposures haverevealed one or more discontinuity sets drillholes and drillhole coresmay be used effectively to check whether these persist at depth.

Discontinuity surveysThe rock mass contains a considerable amount of geometrical informationwhich must be collected and interpreted. Clearly an irregular highly frac-tured rock face presents a somewhat daunting challenge to anyone whowishes to quantify the rock structure or discontinuity network in anunbiased manner. It is important, therefore, to ensure that measurementsystems are based upon objective but ¯exible sampling strategies linkedto rigorous data analysis (Priest, 1993). Typically between 1000 and2000 discontinuities should be sampled to provide an adequate character-ization of a site (Priest and Hudson, 1976). This number is generally madeup from samples between 150 and 350 discontinuities taken at between


213



T a b l e 7 . 5 T e r m i n o l o g y a n d c h e c k l i s t f o r r o c k d i s c o n t i n u i t y d e s c r i p t i o n ( B S 5 9 3 0 : 1 9 9 9 )

S p a c i n g

O r i e n t a t i o n


T y p e o f

t e r m i n a t i o n

R o u g h n e s s


A p e r t u r e

F i l l i n g

S e e p a g e

N o . o f s e t s

E x t r e m e l y w i d e

> 6 m

V e r y w i d e

2 t o 6 m

W i d e

6 0 0 m m t o 2 m

M

e d i u m 2 0 0

t o 6 0 0 m m

C l o s e

6 0 t o 2 0 0 m m

V e r y c l o s e

2 0 t o 6 0 m m

E x t r e m e l y c l o s e

< 2 0 m m

T a k e n u m b e r o f

r e a d i n g s ; s t a t e

m i n .

, a v e r a g e

a n d m a x .

D i p a m o u n t

o n l y i n c o r e s

T a k e N o . o f

r e a d i n g s , o f d i p

d i r e c t i o n / d i p ,

e . g . 0 1 5 / 0 8 8

R e p o r t a s

r a n g e s a n d o n

s t e r e o n e t i f

a p p r o p r i a t e

D i s c o n t i n u o u s

C o n t i n u o u s i n

c o r e s

V e r y h i g h

> 2 0 m m

H i g h

1 0 t o 2 0 m m

M e d i u m

3 t o 1 0 m

L o w

1 t o 3 m

V e r y l o w

< 1 m

C a n n o t

n o r m a l l y b e

d e s c r i b e d

T e r m i n a t i o n

x ( o u t s i d e

e x p o s u r e }

r ( w i t h i n r o c k )

d ( a g a i n s t

d i s c o n t i n u i t y )

R e c o r d a l s o

s i z e o f

e x p o s u r e

S m a l l s c a l e ( c m )

a n d

i n t e r m e d e

s c a l e ( m )

S t e p p e d

R o u g h

S m o o t h

S t r i a t e d

U n d u l a t i n g

R o u g h

S m o o t h

S t r i a t e d

P l a n a r

R o u g h

S m o o t h

S t r i a t e d

L a r g e s c a l e

( d m )

W

a v i n e s s

C u r v a t u r e

S t r a i g h t n e s s

M

e a s u r e

a m p l i t u d e a n d

w a v e l e n g t h

f e a t u r e

S c h m i d t

h a m m e r

P o i n t l o a d t e s t

O t h e r i n d e x

t e s t s

V i s u a l

a s s e s s m e n t

C

a n n o t

n o r m a l l y b e

d e s c r i b e d i n

c o r e s

V e r y o p e n

>

1 0 m m

O p e n

2 . 4 t o 1 0 m m

M o d e r a t e l y o p e n

0 . 5 t o 2 . 5 m m

T i g h t

0 . 1 t o 0 . 5 m m

V e r y t i g h t

<

0 . 1 m m

T a k e n u m b e r o f

r e a d i n g s ; s t a t e

m i n . ,

a v e r a g e

a n d m a x .

C l e a n

S u r f a c e

s t a i n i n g

( c o l o u r )

S o i l i n ® l l i n g

( d e s c r i b e i n

a c c o r d a n c e

w i t h 4 1 )

M i n e r a l

c o a t i n g s

( e . g . c a l c i t e ,

c h l o r i t e ,

g y p s u m , e t c .

)

O t h e r ±

s p e c i f y

R e c o r d w i d t h

a n d c o n t i n u i t y

o f i n ® l l

C a n n o t b e


c o r e s

M o i s t u r e o n

r o c k s u r f a c e s

D r i p p i n g

w

a t e r

W a t e r ¯ o w

m e a s u r e d p e r

t i m e u n i t o n a n

i n d i v i d u a l

d i s c o n t i n u i t y o r

s e t o f

d i s c o n t i n u i t i e s

- - - - - - - - - - - - - - - -

S m a l l ¯ o w

0 . 0 5 t o 0 . 5 l / s

- - - - - - - - - - - - - - - -

M e d i u m ¯ o w

0 . 5 t o 5 . 0 l / s

- - - - - - - - - - - - - - - -

S t r o n g ¯ o w

> 5 l / s

C a n n o t b e


c o r e s

R e c o r d

s p a c i n g a n d

o r i e n t a t i o n o f

s e t s t o e a c h

o t h e r a n d

a l l d e t a i l s

f o r e a c h s e t

214



5 and 15 sample locations chosen to represent the main zones based ongeological structure and lithology. In some cases the extent of the site orthe exposed rock makes such large numbers of measurements impracticalor impossible. In such cases the minimum sample of 200 discontinuitiesshould be taken.

The method of collecting discontinuity data will vary according to thetype of access to the rock mass. The two broad sampling strategies thatcan normally be adopted involve either the logging of drillhole core orthe examination of an exposed rock face.

When using drillholes, a detailed fracture log of the core is requiredtogether with an inspection of the drillhole wall. In the case of exposedrock faces above or below ground the most widely used sampling methodsinclude scanline sampling (ISRM, 1978; Priest and Hudson, 1981; Priest,1993) and window sampling (Pahl, 1981; Priest, 1993).

It is often useful to employ descriptive terms for many of the features ofdiscontinuity, particularly where direct measurements are dif®cult orimpractical due to time constraints. The descriptive terms for most of thekey features recommended by BS 5930: 1999 are shown in Table 7.5.

Fracture logging of drillhole coreA common problem in logging fractures in core samples or in a man-maderock face is identi®cation of arti®cial fractures resulting from the drillingprocess or by the creation of the face (blasting and stress relief). Thesefractures are normally excluded from the log, unless a conscious decisionis made to the contrary which should be clearly stated on the log. A degreeof judgement is therefore required. Arti®cial and natural fractures canoften be distinguished from each other by observing the freshness, bright-ness, staining and erosion of the fracture surface. For example, in thechalk natural fractures often exhibit manganese spots or dendriticpatterns and relatively smooth surfaces, whereas arti®cial fractures areclean and rough.

Every natural fracture which cuts the core should be described in thefollowing manner.

. The position of the fracture in the core sample should be recorded. Apictorial log of the fractures cutting the drillhole may be made fromthis information.

. The angle the fracture makes with the core axis should be noted.Where the orientation of the core is known the dip and dip directionof the fracture should be determined.

. The roughness of the fracture surfaces should be noted.

. If any in®ll is present, its thickness and nature should be described.

. The presence of any mineral coatings should be noted.


215



. Where possible or practical the compressive strength of the fracturesurface should be determined using a Schmidt hammer. A qualitativeassessment of the wall strength may be made by indenting the walland the side of the core using the point of a knife, pick or othersharp implement.

. The average spacing of discontinuity sets identi®ed from the fracturelog may be determined from the recorded positions of the relevantfractures. The general fracture state of the rock mass may be assessedfrom the determination of the total and solid core recovery, the fractureindex and Rock Quality Designation (RQD).

Scanline samplingAlthough many different techniques have been described for sampling

discontinuities in rock exposures (Muller, 1959; Pacher, 1959; Da Silveriaet al. , 1966; Knill, 1971) the line or scanline approach is preferred (Piteau,1970; Broadbent and Rippere, 1970) on the basis that it is indiscriminate(all discontinuities whether large or small should be recorded) andprovides more detail on discontinuity spacing (Priest and Hudson, 1976,1981) and attitude than other methods. There is no universally acceptedstandard for scanline sampling.

In practice, a scanline survey is carried out by ®xing a measuring tape tothe rock face by short lengths of wire attached to masonry nails hammeredinto the rock. The nails should be spaced at approximately 3 m intervalsalong the tape which must be kept as taut and as straight as possible.The face orientation and the scanline orientation should be recordedalong with other information, such as the location, date and the name ofthe surveyor. Where practicable the face and scanline, including a scaleand appropriate label, should be photographed before commencing thesampling process. In cases where the face is irregular it will be necessaryto take photographs from several viewpoints. A simple way to provide ascale is to attach clearly visible markers at say 1 m intervals along thelength of the scanline. Care should be taken to minimize distortion ofthe face on the photographs.

Once the scanline is established the surveyor works systematicallyalong the tape recording the position and condition of every discontinuitythat intersects it. The features that are commonly recorded include thefollowing.

. Intersection distance . This is the distance in metres (rounded tothe nearest cm) along the scanline to the intersection point with thediscontinuity. Where the face is irregular it will be necessary to projectthe plane of fractures not in contact with the tape on to the tape suchthat their position can be accurately recorded. In highly irregular faces


216



this method can lead to signi®cant errors in the determination of jointspacing. Ideally a clean, approximately planar rock face should beselected for scanline sampling.

. Orientation . This is the dip direction and dip of the discontinuities.

. Semi-trace length . This the distance from the intersection point on thescanline to the end of the discontinuity trace. The distance may bemeasured directly, estimated by eye or scaled from a photograph ofthe rock face, when it becomes available. There will be two semi-trace lengths associated with each discontinuity: one above and onebelow for a horizontal scanline; one to the left and one to the rightfor an inclined for vertical scanline.

. Termination . It is helpful to record the nature of termination of eachsemi-trace (see Table 7.5).

. Roughness . A pro®le of small-scale roughness may be made in themanner described earlier or the Joint Roughness Coef®cient (JRC)(Barton, 1973) may be estimated visually. Intermediate and large-scale roughness may be described as in Table 7.5 and amplitudeand wavelength can be measured where necessary.

Other features such as type of discontinuity, nature of in®ll, aperture,water ¯ow, slickensides, are generally reported in a comments columnon the logging sheets. An example of a typical logging sheet is shownin Fig. 7.5.

Further scanlines should be set up on a second rock face, approximatelyat right angles to the ®rst, to minimize the orientation sampling bias. Cor-rections have been devised to compensate for directional bias (Terzaghi,1965; Robertson, 1970) but these will not aid the identi®cation of jointssets which intersect the scanline at low angles ( < 10 8).

The length of the scanline should be at least ®fty times the mean dis-continuity spacing (Priest and Hudson, 1976) in order to estimate the fre-quency of discontinuities to a reasonable degree of precision. Priest (1993)recommends that the scanline should contain between 150 and 350 dis-continuities. Often a compromise must be sought owing to restrictions tosize of face or access to parts of the face.

Window samplingWindow sampling provides an area-based alternative to the linearsampling techniques outlined above which reduces the sampling biasfor discontinuity orientation and size. The measurement techniques areessentially the same as for scanline sampling except that all discontinuitytraces which cross the de®ned area of the rock face are measured.

The sampling window may be de®ned by setting up a rectangle ofmeasuring tapes pinned to the rock face. In order to minimize sampling


217



C o m m e n

t s

A p e r t u r e /

i n f i l l

R o u g

h n e s s


C h a

i n a g e :

m

T y p e

D i p

d i r e c t i o n

D i p

S e

t ( i f

k n o w n

)

D i s c o n

t i n u

i t y

J o b N o .

D a

t e

F a c e o r i e n

t a t i o n

( d i p d i r e c t i o n

/ d i p )

S c a n

l i n e

l e n g

t h ( m )

D e s c r i p

t i o n o

f f a c e

( s i z e ,

r o u g

h / s m o o

t h e

t c . )

L o c a

t i o n O

b s e r v e r

R o c k

t y p e

S h e e

t

o f

P h o

t o N o .

S c a n

l i n e o r i e n

t a t i o n

( d i p d i r e c t i o n

/ d i p )

S t a r t p o

i n t ( d e s c r i p

t i o n

)

F i g . 7 . 5

T y p i c a l s c a n l i n e l o g g i n g s h e e t ( s e e T a b l e 7 . 5 f o r a n e x p l a n a t i o n o f t e r m s u s e d )


218



bias effects it is recommended that the window should be as large as pos-sible, with each side of a length such that it intersects between 30 and 100discontinuities (Priest, 1993). Where possible, two windows of similar sizeshould be set up on mutually perpendicular faces.

In general, area sampling provides a poor framework within which tocollect orientation, frequency and surface geometry data for individualdiscontinuities. The window is likely to contain a large number of rela-tively small discontinuities, making it dif®cult to keep track of whichdiscontinuities have been measured. The process of window sampling isgenerally more laborious than scanline sampling when attempting toapply the same rigorous sampling regime.

Face samplingAt the preliminary stage of an investigation it is often necessary simply

to establish the number of discontinuity sets, the average orientation ofeach set and the relative importance of each set. Matherson (1983) sug-gests that for simple rock slope stability assessments at the preliminarysite investigation phase it is suf®cient to observe persistence, apertureand in®lling in addition to orientation. In such cases it may be expedientto adopt a sampling strategy that is less rigorous than those outlinedabove.

Face sampling involves recording the orientation, persistence, rough-ness, aperture, in®lling and seepage of a representative number of discon-

tinuities in the exposed face. A suitable geological compass should beused for the orientation measurements and the classi®cation recom-mended by BS 5930: 1999 should be used for the other parameters (seeTable 7.5). The size of the sample must be large enough to ensurestatistical reliability. A minimum of 200 measurements per face is recom-mended. Such large sample sizes may preclude the measurement of allthe parameters listed above for each fracture. An evaluation of the impor-tance of each discontinuity, however, should be made. This is normallybased on persistence.

The grouping of data collected from a very large exposure or from anumber of different locations may obscure discontinuity patterns. Ideallythe area studied should be divided into units, domains or structuralregions (Piteau, 1973). Data from each face should be assessed separately.If it can be established that each face shows a similar discontinuity patternit may then be possible to group the data from a number of faces. If differ-ent rock types are present in the survey area the discontinuities observedin each type should be placed in separate groups. Collection of data indomains allows individual or grouped assessment. This is likely to be ofmajor importance where alignment, design or rock type change along aproposed route.


219



Presentation of discontinuity data for stability analysis:the stereonet

Overview Discontinuity data should be presented in a form that allows ease of assim-

ilation and is amenable to rapid assessment. Discontinuities may beshown on maps, scale drawings of exposures or block diagrams whichmay be used to indicate the spatial distribution and interrelationships ofthese features. Such methods, although very useful, do not allow thequantitative assessment of orientation and spacing which are perhapsthe most important aspects of discontinuities within a rock mass. Inmany cases, it is not possible to recognize all the discontinuity sets orassess the dominant orientation of some discontinuity sets in the ®eld.Such factors may only be assessed by statistical analysis of discontinuity

orientation data.Discontinuity orientation data are easier to visualize and analyse ifpresented graphically. The most commonly used method of presentingorientation data is the hemispherical projection. This method allows thedistribution of dip and dip direction to be examined simultaneously andprovides a rapid visual assessment of the data as well as being readilyamenable to statistical analysis. Although this method is used extensivelyby geologists, it is little understood by engineers, since it bears no recog-nizable relationship to more conventional engineering drawing methods.The basis of the method and its classic geological applications aredescribed by Phillips (1971). Rock engineering applications are describedin detail by Goodman (1976), Hoek and Brown (1980), Priest (1980, 1985,1993), Hoek and Bray (1981) and Matherson (1983).

Hemispherical projection methods for display and analysis of discontinuity dataThe hemispherical projection is a graphical method for the presentationand analysis of the orientation of planar and linear features in two dimen-

sions (i.e. on a sheet of paper). All forms of hemispherical projection usean imaginary sphere as a basis for converting three-dimensional data intoa two-dimensional form. The sphere is arranged such that linear featuresor planar features (e.g. discontinuities) found in a rock mass pass throughits centre. The intersection of such lines or planes with the surface of thesphere are projected on to the equatorial plane. The intersection witheither the upper or lower hemisphere is used in the projection process,hence the name hemispherical projection. In most cases where a hori-zontal plane of projection is being used, the intersection with the lowerhemisphere is considered. Such projections are referred to as lowerhemisphere projections.


220



There are two commonly used methods of projection:

. Equal angle projection . This projection accurately preserves the angu-lar relationships between features.

. Equal area projection . This projection preserves the spatial distribu-tion of features.

Equal angle projectionFigure 7.6 shows a vertical section through the imaginary sphere and theconstruction of the equal angle projection. If a line of dip direction anddip intersects the reference sphere in Fig. 7.6 at P H, the projection thispoint is achieved by drawing a straight line from P Hto a point T which ison the surface of the sphere vertically above the centre O. The projectionof P Hoccurs at P where the line P HT passes through the plane of projection.The relationship between the radial distance r ( OP), the radius of thereference sphere R and the dip of the line is given by:

r R tan90 ÿ

27:4

Equal area projectionFigure 7.7 shows a vertical section through the imaginary sphere and theconstruction of the equal area projection. If a line of dip direction and dip

intersects the reference sphere in Fig. 7.7 at P H, the projection this point isachieved by rotating the chord joining P Hto a point B vertically below thecentre of the sphere (O) about point B until it is horizontal. The projectionof P Hoccurs at P HHwhere the arc drawn out by BP Hmeets the horizontal

T

P

P ′

O

r

β

Radius of reference sphere =R

Plane of projection

Imaginary line drawn parallel tothe given line through the centreof the reference sphere

90 – β2

Lower reference hemisphere

Fig. 7.6 Equal angle projection


221



plane of projection. The relationship between the radial distance r H( BPHH),the radius of the reference sphere R and the dip of the line is given by:

r H 2R cos90

27:5

When 08, r H 2R cos 45 8 R 2p . This means that the radius of the

resultant projection is larger than the radius of the reference sphere bya factor of

2p . The point P HHis therefore transferred to point P which is

located at a radial distance r r H= 2p from the centre of the reference

sphere and hence

r R 2p cos 90 2

7:6

The equal area projection method is commonly used in rock engineeringbecause it permits the statistical analysis of discontinuity data.

Plotting lines and planes using hemispherical projectionA line will always be projected as a point. A vertical line will plot as a

single point at the centre of the reference circle and a horizontal linewill plot as two diametrically opposed points on the circumference of

the reference circle.A plane presents a more complex problem. To help understand the projection of a plane (e.g. a discontinuity) it may be thought of as being madeup of a series of lines radiating out (in the plane of the discontinuity) fromthe centre of the reference sphere as shown in Fig. 7.8(a). One of theselines (Ob) will have the same dip and dip direction as the plane and thisline will form a line of symmetry. Each side of this line there will be aseries of lines with dips ranging from the true dip of the plane to 0 8 anddip directions ranging from that of the plane to a direction perpendicularto it. The line of symmetry will plot on the plane of projection closest to thecentre of the reference circle. The other lines will plot progressively

P

B

O

P ′′

P ′r ′

r ′

r

β

Radius of reference sphere = R

Plane of projection

Imaginary line drawn parallel tothe given line through the centreof the reference sphere

90 – β2

Lower reference hemisphere

Fig. 7.7 Equal area projection


222



a

b

O

c

d

Radiating lines inthe plane of thediscontinuity

Reference hemisphere

Direction of dip

Direction of dip

Line of symmetry

Discontinuity

N

S

EW

a

b

c d

Great circlerepresenting the

discontinuity

Line of symmetry

Plane of projection

Pointsrepresentingradiating lines

(a)

(b)

Reference circle

Fig. 7.8 (a) Illustration of a plane/lines cutting the lower part of the

reference sphere. (b) Projection of plane/lines


223



further away until in the extreme the horizontal line (aOd), which is per-pendicular to the dip direction of the plane, will plot on the circumferenceof the reference circle. The locus of the projection of all of these lines willtrace out a great circle on the reference circle (Fig. 7.8(b)).

A vertical plane will plot as a straight line passing through the centreof the reference circle. A horizontal plane will plot directly over thecircumference of the reference circle.

To aid plotting lines and planes and the measurement of angularrelationships between these features (e.g. the orientation of the line ofintersection between two inclined planes) a special type of graph paperhas been produced called a `stereonet'. An equal area stereonet isshown in Fig. 7.9. It is made up of a series of great circles representingplanes dipping due East and due West at dip angles ranging from zeroat the edge of the net to 90 8 at the centre at 2 8 intervals. The projectionof lines and planes are plotted on tracing paper which is overlaid on the

Fig. 7.9 Example of an equal area stereonet


224



stereonet. Since only E and W dipping planes are shown on the stereonetit is necessary to rotate the tracing paper about the centre of the stereonetin order to produce projections of lines and planes at other orientations.

Plotting projections of lines and planes using a stereonetPreparing the stereonet for useTake the stereonet and ®x it (using draughting tape) to a stiff board (A4size). Using a drawing pin make a hole through the centre of the stereonet.Remove the drawing pin and insert it through the back of the board and ®xit in place with some tape. You are now ready to use your stereonet.

Plotting lines and planes using a stereonetAll data are plotted on tracing paper that is placed over the stereonet.

WORKED EXAMPLEProblem 1

Plot the projection of a line dipping at 40 8 towards 120 8.

. Place the tracing paper over the stereonet and pierce it with thepoint of the drawing pin.

. Mark the North Point with a long tick and write `N' above it (Fig.7.10(a)).

. Count 120 8 clockwise from the North Point and place a small tickover the edge of the stereonet (Fig. 7.10(a)).

. Rotate the tracing paper until the tick drawn is over either the EastPoint or the West Point. The East Point is more convenient in thiscase (Fig. 7.10(b)).

. Count 40 8 inwards from the circumference of the stereonet andmark the point with a dot (Fig. 7.10(b)).

. Rotate the tracing paper such the large tick representing the NorthPoint coincides with the North Point of the stereonet (Fig. 7.10(c)).

The dot you have drawn represents the projection of the line.

Problem 2

Using the same piece of tracing paper as for Problem 1, plot the projec-tion of a plane dipping at 50 8 towards 300 8.

. Count 300 8 clockwise from the North Point and place a small tickover the edge of the stereonet (Fig. 7.11(a)).

. Rotate the tracing paper until the tick drawn is over either the EastPoint or the West Point. The West Point is more convenient in thiscase (Fig. 7.11(b)).


225



W

S

NN

E

1 2 0

(a)

W

S

N N

E

(b)

40

Problem 1


226



. Count 50 8 inwards from the circumference of the stereonet andmark the point with a dot (Fig. 7.11(b)).

. Using the gridlines on the net trace out a great circle which passesthrough the dot drawn (Fig. 7.11(b)).

. Rotate the tracing paper such the large tick representing the NorthPoint coincides with the North Point of the stereonet (Fig. 7.11(c)).

The great circle you have traced represents the projection of theplane. Now rotate the tracing paper back to the position it was inProblem 2 when the great circle was drawn. You will note that thepoint you plotted in Problem 1 is on the E±W line. If you measure

the angular distance (by counting squares on the stereonet) along theE±W line between the great circle and the projection of the line inProblem 1 you should ®nd the answer to be 90 8. This indicates thatthe line is perpendicular to the plane.

It is convenient particularly for the purposes of statistical analysis torepresent a plane by a line which is perpendicular to the plane. Thisline is called a pole. If a plane has dip and dip direction of andrespectively then its pole will have dip and dip direction 90 ÿ and180 respectively. To plot the pole to the plane in the above problemwe must ®rst calculate the dip and dip direction of the pole. The dip and

W

S

NN

E

(c)

Problem 1

Fig. 7.10 Solution to Problem 1


227



W

S

NN

E

(a)

3 0 0

Problem 2

W

S

N

N

E

(b)

50

Problem 2

90˚


228



dip direction of the pole is in this case 90 ÿ50 40 8 and 180 300480 8, 480

ÿ360 120 8, respectively. The procedure for plotting poles

is shown below.

Procedure for plotting polesThe important thing to remember when plotting poles is that the projec-tion of the pole will always be on the opposite side of the stereonet tothe projection of the plane.

Problem 3

Plot the pole representing a plane that is dipping at 70 8 towards 240 8

Calculate the dip and dip direction of the pole:Dip of pole 90 ÿ70 20 8:

Dip direction of pole 180 240 420 8 which is equivalent to a wholecircle bearing of 420 ÿ360 60 8.

Thus the pole to the plane is dipping at 20 8 towards 060 8 (i.e. 060/20).The pole can then be plotted on the stereonet using the technique

described in problem 1.A more convenient way of plotting the projection of a pole to a plane

which avoids calculating the dip and dip direction of the pole is illu-

strated below.

W

S

NN

E

(c)

Problem 2



229



W

S

NN

E

(a)

2 4 0

Problem 3

W

S

N

E

(b)

Problem 3

70

N


230



Place the tracing paper over the stereonet and pierce it with the pointof the drawing pin.

. Mark the North Point with a long tick and write `N' above it.

. Count 240 8 clockwise from the North Point and mark the point witha small tick (Fig. 7.12(a)).

. Rotate the tracing paper such that the small tick is over the WestPoint. You could use the East Point but the West Point is closer(Fig. 7.12(b)).

. Now remember that you are plotting a pole. The plane will plot onthe left side of the stereonet, so the pole will plot on the right side.Since the pole to a vertical plane will plot on the circumference anda pole to a horizontal plane will plot at the centre you will need tocount 70 8 from the CENTRE towards the East Point and mark thepoint with a dot (Fig. 7.12(b)).

. Rotate the tracing paper such the large tick representing theNorth Point coincides with the North Point of the stereonet (Fig.7.12(c)).

Some examples for you to practice on are given in problem 4.

W

S

NN

E

(c)

Problem 3



231



Problem 4

Plot the great circles representing the following planes and the poles tothe planes:

Plane Orientation

A 324/36B 103/30C 210/75D 247/87E 065/05

The answers to Problem 4 are given in Fig. 7.13.



232



Analysis of discontinuity orientation dataIn order to identify the predominant sets in a rock mass and their averageorientations it is necessary to plot the poles for the discontinuity orienta-tion data and carry out a statistical analysis. This analysis makes use ofsimple graphical techniques and permits the identi®cation of discontinu-ity clusters (i.e. sets) from a contoured diagram such as that shown in Fig.7.14. There are a number of different techniques that can be carried out byhand. This can be a time consuming process, however, and is usually doneusing a computer software application.

A simple method for carrying out this process manually is to create arectangular grid on a piece of paper such that the x and y grid increment

N

W E

S

1 – 2% of total population

2 – 3%

3 – 4%

4 – 6%

>3%

Fig. 7.14 Lower hemispherical projection showing concentrations atdiscontinuities (i.e. discontinuity sets)


233



is one tenth of the diameter of the stereonet used to plot the poles as shownin Fig. 7.15(a). A counting device (see Fig. 7.15(b)) can be constructedfrom a piece of clear plastic ®lm. The circles have a diameter which isone tenth of the diameter of the stereronet.

Counting is done by centring the tracing paper with the poles plotted onit over the grid and covering this with a clean piece of tracing paper. Thecounting device is moved such that one of the circles is positioned over the

intersection of two grid lines and the number of poles within the circle isrecorded on the top of tracing paper over the grid line intersection. Forsteeply dipping discontinuities (i.e. poles situated close to the circum-ference of the stereonet) a different procedure is used. In this case thecounting device is centred over the grid and moved to a grid point onthe circumference as shown in Fig. 7.16. The total number of poles inboth half circles is recorded at both grid points, as shown in Fig. 7.16.

A more convenient method of carrying out this analysis is to use agraphical counting method. A wide variety of such methods have beendevised (Kalsbech, 1965; Dimitrijevic and Petrovic, 1965; Stauffer, 1966;Denness, 1970, 1971). Of these, that devised by Dmitrijevic and Petrovic

N

0 ·1 D

D

D

D = Diameter of steronet

Centre

0 ·1 D

0 · 1

D

Fig. 7.15 Simple single cell system for counting poles


234



is the easiest to use. This counting net is constructed from a number ofcircles on a hemisphere each occupying 1% of the surface area. Whenthese are projected on to the equal area net they become ellipsoidal to a

degree consistent with their position on the hemisphere (see Fig. 7.17).

A B

Count at A = 4Count at B = 2Total = 6

0 ·1 D

Fig. 7.16 Procedure for counting poles close to the circumference of thestereonet

N

1716

12

3

4

5

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16171

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Fig. 7.17 Dimitrijevic counting net, after Dimitrijevic and Petrovic (1965)


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A density distribution is obtained by counting the number of plottedpoints lying within each circle or ellipse as shown in Fig. 7.18. An evenand overlapping distribution of ellipses allows the entire area of the netto be covered. No rotation is required during counting. The best resultsare obtained by plotting the poles on to tracing paper and overlayingthis on to the counting net.

One of the disadvantages of using these counting nets to contour poledensity is that the geometry of the net bears no relationship to the distri-bution of poles. When a cluster of poles falls across a boundary betweentwo counting cells, a correct assessment of the pole concentration can

(a)

(b)

8

10

10

9 97 7

8

8

Count = 4 Count = 3

Fig. 7.18 Counting procedure using the Dimitrijevic counting net


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only be obtained by allowing the counting device to `¯oat' from its originalposition and to centre it over the highest concentrations. This is achievedby rotating the counting net about its centre. The counting device shownin Fig. 7.15 has a distinct advantage here since it represents a singlecounting cell (when working away from the circumference of thestereonet) which can be moved to any position. The concept of using arectangular grid as described above is to allow a coarse analysis of thedata while ensuring that a systematic approach is maintained. Once thishas been done ®ner detail may be obtained by using the single countingcell in a `¯oating mode'. This can be time consuming and when checkingcontours of poles derived from a computer programme the Dmitrijevic netwill be adequate. Contouring can be carried out visually interpolatingbetween counts where necessary.

WORKED EXAMPLEProblem 5

In this worked example the discontinuity data given in Appendix 3 havebeen plotted as poles using a stereonet and this is shown in Fig. 7.19(a).

Preparation. Pierce the centre of the counting net with a drawing pin.. Take the tracing paper with the poles plotted on it and align the

drawing pin hole over the drawing pin in the counting net. Nowrotate the tracing paper until the north point lines up with thenorth point on the counting net.

. Secure the tracing paper to avoid subsequent movement.

. Take a clean sheet of tracing paper and place this over the ®rstsheet and secure the tracing paper to avoid subsequent movement.You can now remove the drawing pin.

. Trace the net circumference on the overlay, mark and identify theNorth reference position.

Counting. For each whole circle/ellipse, count the number of points lying

within or on the outline. Mark this value on the overlay at thecentre of each ellipse/circle (see Fig. 7.18(a)).

. For each part-ellipse at the edge of the net, count the number ofpoints lying within or on the outline. Combine this count with thatfrom the part-ellipse on the opposite side of the net (numbers 1 to17 assist this process) (see Fig. 7.18(b)). Mark the total value atthe centre of both part-ellipses.


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. Check that diagonally opposite part-ellipses have the same value.

The results of the counting procedure are shown in Fig. 7.20. Theresults of the analysis are best presented as a contoured diagram in

which the pole count in each ellipse is expressed as a percentage ofthe whole population of poles. In Fig. 7.21 the results of the analysiscarried out in the above worked example have been contoured.

It can be seen from Fig. 7.21 that a number of clusters of poles can beidenti®ed. These have been labelled A, B, C and D in rank orderaccording to the density of poles. The maximum density of polesassociated with each cluster is also shown in Fig. 7.21. The clustersrepresent sets of discontinuities. The relative importance of each setcannot be determined from the density of poles alone. The key attributefor importance, particularly where slope stability is concerned, is

N 1020

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160170190

200210

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340350

S

Fig. 7.19 Raw data for Problem 5


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persistence. If, for example, set D has a very high persistence whereasset A had a very low persistence then in terms of importance set D willrank higher than set A even though more poles were found associatedwith set A. In some cases a single discontinuity with very high persis-tence can rank as the most important feature.

2

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N

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Fig. 7.20 Results of counting procedure showing density of poles per 1 Âarea of net


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N

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2 4

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2 4

6B

C

D

A

6 ·6

6 ·6

5 ·6

12 ·9

B6 ·6

S

No. of poles = 213

Contours = % of total number of poles

Fig. 7.21 Contoured plot of pole concentrations based on the data presented inFig. 7.19


7_Chapter 7 Discontinuities in Rock- Description and Presentation for Stability Analysis

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Transcript of 7_Chapter 7 Discontinuities in Rock- Description and Presentation for Stability Analysis