120 Rock masses: deformability, strength and failureAFigure 8.3 The presence of a fracture in a stressed rock specimen.normal stiffness k, and a shear stiffness k, (or a normal compliance, s,,
and a shear compliance, 8,).
By studying the way in which the intact rock properties and the frac
ture properties combine to determine the properties of the whole-roc1
mass, an estimate of the importance of the various contributions can bc
established. However, because of the geometrical and mechanical com
plexity of the fractures, it is not possible to generate the exact rock mas
properties from such information. If the deformation modulus I, E,, of i
rock mass has not been measured directly and is required for calculatior
and design purposes, the value can either be estimated by combining thc
intact rock and fracture components to provide a composite modulus, o
the modulus can be estimated empirically.
Although the empirical estimations of rock mass deformation mod
ulus seem over-simplified, they can give reasonable predictions and arc
often the only practical method of estimating the modulus. The relation
E, = (2RMR - 100) where E, has units of GPa and RMR > 50 (wherc
RMR is the Rock Mass Rating, see Chapter 12), can give surprisingl!
accurate results (Bieniawski, 1989 2). Another empirical expression ir
E, = 10(RMR-10)/40 GPa which covers the complete RMR range, i.e. fron
low values to 100.
The effect of a single fracture on rock strength can be studied using thc
single plane of weakness theory. Assume that a fracture is present in i
rock specimen as shown in Fig. 8.3. The strength of the specimen wil
then depend on the orientation of the principal stresses relative to thc
fracture orientation. Assuming that failure is induced when the norma
and shear stress components on the fracture satisfy the Mohr-Couloml
failure criterion, we can develop an expression for the specimen strengtl
as a function of BW, the angle between the major principal stress and thc
normal to the fracture.
The normal stress on the fracture is given by
a, = ; (a1 + a3) + ; (a1 - 03) cos 2Bw
The term ‘deformation modulus’, is used in rock mechanics to indicate the apparen* Bieniawski Z. T. (1989) Engineering Rock Mass CZassifications. Wiley, Chichester, 251pp.elastic modulus of an in situ rock mass.