Engineering Rock Mechanics

A rock mechanics-rock engineering interaction matrix 233

Leading diagonal terms

and interaction terms

have equal importance

at45" ,

at 90"

Interchanging axes

• only off-diagonal terms

at 180" , Sign change in

leading diagonal terms,

no interaction hetween axes

Figure 14.10 Three examples of the transformation matrix for rotation of axes.

first number representing the row and the second number the column in
which the term resides. Second, the matrix is asymmetric. Third, as
illustrated in Fig. 14.12, the basic rock mechanics component is contained
within the uppermost 3 x 3 sub-matrix, with the interaction between rock
mechanics and rock engineering occurring in the fourth row and column.
Note that with the clockwise directionality applied to this matrix, the
effect of the rock mechanics on the rock engineering is contained in the
fourth column, whereas the effect of the rock engineering on the rock
mechanics (or rock properties) is given in the fourth row. These matrix
component sets should therefore be seen as design (or pre-construction)
considerations and engineering (or during and post-construction) effects,
respectively.
The interactive elements in Fig. 14.11 are self evident from the sketches.
Well-known concepts arise and areas can be identified which need
research. Element 32 shows the influence of the presence of water on the
in situ stress, which is embodied in the well-known concept of effective
stress: however, the complementary element, 23, is the influence of in situ
stress on water flow-a subject still in its infancy. Similarly, we can point
to elements 23 and 32. The first of these represents the influence of rock
mass structure on water flow-i.e. the fact that discontinuities dictate
permeability, a subject discussed in Chapter 9. The second of these is the
influence of water flow on the rock mass structure, i.e. the weathering of
discontinuities caused by water flow: almost nothing is known of the
mechanics of this subject.
The reader is encouraged to interpret the diagrams representing each
element within the structure of the total interaction matrix. The technique
can be used for all interactions, so it is helpful not only to understand the
underlying structure of such matrices, but also to be able to create new
matrices oneself. For example, the technique was used to present the