Engineering Rock Mechanics

124 Rock masses: deformability, strength and failure

0246 8 10 12 14 16 18 20

3L (fracture frequency), rn-I

48.2 For the unfractured and fractured stratified rock mass geo-

metries described in 48.1, develop expressions for the composite

shear modulus of a rock mass, G,, using a shear stress t and the

parameters ti, Gi, Ai, and Gdi.

A8.2 Unfractured strata

We are investigating the case of simple shear. If we consider the dis-

placement of the rock under the action of a shear stress, we can consider

y and 6 as in the sketch below.

\=

L

7

Using these definitions, for small 6, the engineering shear strain of

each unit can be written as y = t/G x 6/t, and so the shear deformation

of a single unit of intact rock is 6, = t,(t/G,), with the total shear

deformation being given by 6T = E, 6, = E, t,(t/G,). Providing 6~ is

sufficiently small to allow small angle approximations, then the total

shear strain is

6T El: I

E=-=-,

L Cti

1

and as a result the rock mass shear modulus is given by

I t t