Questions and answers: rock mechanics interactions and rock engineering systems^235,Letter indicates the mechanism listed inLetters indicate interaction between twoLetter indicates the principal factor414.1Letters indicate interaction between
principal factorsLetter indicates the principal factortwoNote that the principal factors, Fractures, Rock Stress and Water Flow,
could have different positions on the leading diagonal of the interaction
matrix and the specific interactions would then be located in different
off-diagonal positions. However, this would not alter the information
contained in the interaction matrix.
414.3 Under what conditions is a matrix symmetrical? Why will
almost all rock mechanics interaction matrices be asymmetrical?
A14.3 A matrix is symmetrical if the complementary off-diagonal terms
are equal. For example, the matrix in A14.2 would be symmetrical if
Interaction FS were equal to Interaztion SF, and
Interaction FW were equal to Interaction WF, and
Interaction SW were equal to Interaction WS.
Most rock mechanics interaction matrices will not be symmetrical
because the influence of a principal factor X on a principal factor Y will
not generally be the same as the complementary influence of principal
factor Y on principal factor X. This is evidenced by the complementary
interactions described in A14.1 and illustrated in the matrix in A14.2,
which are clearly not the same.
414.4 In order to consider also the interaction of rock engineering
activities with the rock mechanics factors, extend the^3 x^3 inter-
action matrix of 414.2 to a^4 x^4 interaction matrix by adding the
extra leading diagonal term CONSTRUCTION. Write a one-phrase
explanation of the content of each of the six extra off-diagonal in-
teraction boxes introduced by adding the leading diagonal term,
CONSTRUCTION.
A74.4 The required 4 x 4 interaction matrix is shown below. The 'one-
phrase explanation' in the boxes in the fourth column and fourth row
are examples of potential interactions that might be involved; other
examples are possible.
Note that the boxes in the fourth column represent influences that
the rock mechanics factors have on construction, either in terms of
the engineering design or the events that occur on site during rock