Mechanical properties 137or
u = kS.
This final expression also permits evaluation of the displacements when the
stresses are known through use of the inverse of the matrix k. It should
also be noted that this matrix, containing off-diagonal terms, provides a first
approximation to the the coupling of normal and shear stresses and
displacements, e.g. a term k,, relating to dilation.
For the displacements of in situ discontinuities, the stiffness of the
surrounding rock system will also need to be taken into account. There are
many other practical aspects, such as the fact that the shear stiffness may
be anisotropic in the plane of the discontinuity due to surface features like
striations or lineations. We will discuss in Chapter 8 how the total in situ
rock mass modulus can be predicted from a knowledge of the intact rock
stiffness and the discontinuity stiffnesses.
7.3.2 Strength
Deformability has been considered first following the logic of the complete
stress-strain or stress-displacement curves for intact rock, and now we
consider the strength of discontinuities in shear expressed via the cohesion
and angle of friction. It is normally assumed that the shear strength is a
function of the angle of friction rather than the cohesion. This is a conser-
vative assumption in the sense that discontinuities possess some, albeit low,
cohesion. Basically, we assume that the strength of discontinuities is
predicted by the reduced Mohr-Coulomb criterion, z = 0 tan @: the
basic Mohr-Coulomb criterion was explained in Section 6.5.1. Con-
sideration of any fluid that may be present and the generation of effective
stresses will be discussed in Chapter 9. It is by no means clear that effective
stresses and effective stress parameters can be used for rocks in this
context.
The bi-linear failure criterion illustrated in Fig. 7.22 results from the work
of Patton (1966), who introduced the idea that the irregularity of
discontinuity surfaces could be approximated by an asperity angle i onto
which the basic friction angle @ is superimposed. Thus, at low normal
stresses, shear loading causes the discontinuity surfaces to dilate as shear
displacement occurs, giving an effective friction of (4 + i). As the shear
loading continues, the shear surfaces become damaged as asperities are
sheared and the two surfaces ride on top of one another, giving a transition
zone before the failure locus stabilizes at an angle @. There are many
‘complicating’ factors in this mechanism, such as the roughness of the
surface and the strength of the asperities. This led Barton et QZ. (e.g. 1985)
to propose the empirical relation
z = o,tan[JRC loglo(JCS/o)+@r]
where JRC is the Joint Roughness Coefficient illustrated in Fig. 7.16, JCS is
the Joint Wall Compressive Strength, and @r is the residual friction angle.
The roughness component, i, is composed of a geometrical component and