Engineering Rock Mechanics

236 Rock mechanics interadions and rock engineering systems

Letter indicates the

mechanism listed in

4” Row: Effects of construction

on rock mechanics factors

excavation. The boxes in the fourth row represent the complementary

influences that the construction has on the rock mechanics factors.

414.5 The use of the interaction matrix is helpful for thinking
about any problem involving manifold factors. The principal factors,
located on the leading diagonal, are established first. Then, the
interactions, i.e. the mechanisms linking the principal factors, are
considered in the off-diagonal positions.
For example, when studying natural fractures in the rock mass,
assume that we are interested in the four parameters3 of fracture
orientation, spacing, extent (or persistence) and roughness. Using
these four parameters as the leading diagonal terms of a 4 x 4
interaction matrix, identify the content of the 12 off-diagonal boxes
and hence show that the parameters are likely to be related.

A14.5 Example content for the off-diagonal boxes is shown in the matrix
to the right. Note that the interactions listed are of several forms: direct
cause and effect, commonly observed correlations, and effects caused by
sampling. The existence of the interactions indicates that there will be
relations between the orientations, spacings, extents and roughnesses of
fractures in a given rock mass.

3The correct use of the terms ‘parameter’ and ’variable’ is as follows. The term

’parameter’ refers to the a, b and c in an expression such as ax + by = c, i.e. the

coefficients making the relation specific. The term ‘variable’ refers to the unspecified,

unknown x and y in the equation. However, these terms are used interchangeably in

engineering literature. We have used the term ’parameters’ here for the principal factors

or leading terms of the interaction matrix following historical usage of the word, but the

term ‘variable’ is more appropriate in some cases.