Engineering Rock Mechanics

232 Rock mechanics interactions and rock engineering systems

Interaction XY: the influence of rock stress
on water flow, which is mainly by changing
the apertures of water-bearing fractures.
Interaction 132: the influence of water flow
on rock stress, which is mainly through the
water pressure reducing the normal rock
stress components in the vicinity of water-
bearing fractures.

This 2 x 2 interaction matrix can be ex-
tended to any size matrix by adding further
leading diagonal factors or variables and
considering all the interactions. Because Interaction XY is not the same
as Interaction YX, it is important to consider the cause and the effect in
each case. For Interaction XY, principal factor X is influencing principal
factor Y, whereas for Interaction YX, principal factor Y is influencing
principal factor X. The way in which the rock stress affects the water
flow is not the same as the way water flow affects rock stress. Thus, there
will be pairs of complementary interactions, and a clockwise influencing
convention has been used in the matrix presentation. A composite
mechanism involving more than two principal factors is a series of paths
through an interaction matrix with the appropriate numbers of principal
factors included on the leading diagonal. Tracing these paths is a useful
means of understanding the composite mechanisms, and we give an
example in Q14.6.
Given that the interaction matrix (or some other presentational device)
enables a systematic tabulation of the principal factors and their inter-
actions, a technical audit of the content of an analysis and the analysis
procedures can then be conducted to ensure that the analysis is adequate.
Fig. 14.1 shows a three-level technical audit.

First-level audit

The first step is to ensure that the principal factors required to capture

the essence of the problem are included in the modelling procedures.

These are the leading diagonal terms of the interaction matrix. Then, the

mechanisms linking the principal values are identified as the off-diag-

onal components. This provides the structure of the system. For example,

if the principal factors are the physical variables involved, xl, x2,... , xn,

then the interactions between pairs of variables can be established, as

indicated in the top part of the diagram (Fig. 14.1).

Second-level audit

The second step is to consider how the system components are linked,

either via the interaction matrix or as shown in the middle part of the

diagram (Fig. 14.1).

Using an appropriate model, the system operation is modelled in this

step so that an estimate can be made of the values of those parameters

relating to the design criteria, e.g. the stress should not exceed 100 MPa,

the displacement should not exceed 10 mm, the excavation overbreak

should be less than, say, 5%, and so on.