Engineering Rock Mechanics

142 Rock masses

deformation of the intact rock; the other due to the deformability of the
discontinuities.
The contribution made by the intact rock to the deformation, 61, is oL/E
(i.e. strain multiplied by length). The contribution made by a single
discontinuity to the deformation, &, is o/ED (remembering that ED relates
stress to displacement directly). Assuming a discontinuity frequency of A,
there will be AL discontinuities in the rock mass and the total contribution
made by these to the deformation will be L& which is equal to oAL/ED.
Hence, the total displacement, &, is

with the overall strain being gven by

Finally, the overall modulus, EMASS, is given by

A suite of curves illustrating this relation is given in Fig. 8.2 for varying

discontinuity frequencies and stiffnesses. It is simple to extend this formula

for multiple intact rock strata with differing properties, discontinuity

frequencies and discontinuity stiffnesses, and hence model stratified rock

with discontinuities parallel to the bedding planes.

s

EMASSt EMASS' 'intact

.........................

EFlELD may be 0.1 &tact

• Frequency, A
  Figure 8.2 Variation of in situ rock deformability as a function of the discontinuities
  (idealized case for a single set of discontinuities).