Engineering Rock Mechanics

226 Rock mechanics interactions and rock engineering systems (RES]

+ =

Figure 14.2 A 2 x 2 matrix illustrating the positioning of the primary variables and

their interactions.

~rl~~~~l Discontinuity apertures

In the second matrix of Fig. 14.3, one example of how two rock mechanics
parameters can influence each other is shown. On the one hand, a larger
discontinuity aperture leads to increased water flow on the other,
increased water flow can lead to mineral deposition in the discontinuity,
or erosion of the discontinuity surfaces, resulting in alteration of the
aperture. In this matrix, instead of numbers there are rock mechanics
quantities (albeit as words) as the primary parameters. Here, the influence
of A on B is not the same as the influence of B on A, which means that the
matrix is asymmetric. We will be discussing the significance of, and reasons
for, symmetry and asymmetry of matrices later in this chapter.
In the third matrix of Fig. 14.3, we have reproduced the two-dimensional
stress tensor presented in Chapter 3. This is an example of interaction
between the primary parameters. Given a specific stress state, defined, for
example, in terms of principal stresses, the values of the normal stresses o,,
and ow uniquely define zY and zyr We have already noted in Section 3.6
that zY = z , and so the stress matrix is symmetrical. With the analogous
normal strains and shear strains, we also noted at the end of Section 5.1
Y"

(a) Combination (b) Influence (c) Interaction

2+3=5

0

can increase

or decrease

Water

Figure 14.3 Example combination, influence and interaction matrices.