Engineering Rock Mechanics

1 22 Discontinuities

r

i

/

d

In Fig. 7.8, a sampling line intersects the traces of one idealized set of
discontinuities: this may be a scanline on a rock surface, for example. Note
that the discontinuity traces are parallel, persistent and linear, but are not
regularly spaced. We assume that the length of the line perpendicular to
the discontinuities has length L and intersects N discontinuities. The
discontinuity frequency along the set normal, A, is equal to NIL. Along the
scanline, inclined at angle 8 to the discontinuity set normal, the
discontinuity frequency is calculated by the same method: for the same
number of intersected discontinuities, N, the length of the line is Llcos 8
and the discontinuity frequency along the scanline, &, is given by

N

L/COStl L

As =- =-case = acose.

N

The discontinuity frequency is always positive and therefore we have

I \

I

I - I 90"

/

270" 1

/ \ I

J e Di&ntinuitie$ (^24004) \ 120"
/
210 .%
Because & is always positive, the discontinuity frequency, having
magnitude and direction, may be considered to be two vectors rather than
one, as illustrated in the right-hand part of Fig. 7.8. Note that the
fundamental set frequency is given by the maximum distance from the
origin to the outer dashed circle, i.e. in the 0" and 180" directions.
Apart from the fact that discontinuity frequency must always be positive,
it can be resolved like a force as illustrated in Fig. 7.8. As the scanline is
rotated from 8 = 0" to 8 = 90", & varies from its maximum value of A to
zero: obviously, & = 0 occurs when the scanline is parallel to the
discontinuities. However, as 8 is increased beyond 90", the discontinuity
frequency increases again, to a maximum of A when Q = 180". The resultant
cusp in the locus at 8 = 90" has an important effect as we progress to
considering more than one discontinuity set.
The case illustrated in Fig. 7.8 is the most anisotropic case possible for
the variation in discontinuity frequency, because the ratio of the greatest
to the least frequency is infinite. Note also that the directions of maximum