Engineering Rock Mechanics

242 Rock mechanics interadions and rock engineering systems

This type of study for a rock mechanics problem with many interacting

parameters helps to clarify the circumstances, can give direct guidance

for establishing a tailor-made rock mass classification, and will indicate

the possibilities of applying a coupled mathematical model to represent

the system (which for this example are remote because of the difficulty of

representing all the interactions by explicit mathematical formulae). The

analysis presented here was used to establish the parameter weighting

factors in a rock mass classification scheme for assessing the relative

instability of 20 natural slopes (Mazzoccola and Hudson, 1996).

Note that the approach considers the system structure, rather than the

system operation, and therefore represents a simple first-level audit, as

indicated in the top part of Fig. 14.1.

414.10 One of the most important aspects of the systems approach

is establishing when positive feedback in the system can occur,

because positive feedback loops can cause instabilities.

(a) Explain the meaning of the terms 'negative feedback' and

'positive feedback', and give examples of each in engineering rock

mechanics.

(b) Also explain how engineering actions can mitigate or eliminate

positive feedback (equivalent to altering the mechanisms in the

off-diagonal boxes of the interaction matrix).

A 14. 10 (a) Consider the interaction
matrix mechanism path shown to the
right (from A14.6, but this could be
any interaction matrix). A disturb-
ance or perturbation at the Start posi-
tion travels through the loop of mech-
anisms and arrives back at the Start
position.
Negative feedback: the effects of the
intervening mechanisms reduce the
perturbation.
Positive feedback: the effects of the
intervening mechanisms increase the
perturbation.
In engineering rock mechanics, most mechanisms reduce such per-
turbations, and mechanism loops are generally associated with negative
feedback. Generally, disturbances attenuate and die out. However, mech-
anism loops with positive feedback can occur. Because the disturbance is
then enhanced through the operation of the feedback loop, instabilities
can occur.

Examples of cases which can have either negative or positive feedbacks

Consider the three cases illustrated below: a rock block on a slope

begins to slide, energy is released during rock failure around an ex-

cavation, and water is flowing through a rock fracture. There could be

negative or positive feedback in each of these cases.