Engineering Rock Mechanics

Design against stress-controlled instability 377

the other, as in Fig. 20.19. The zone of influence (in this case 5%) associated
with the larger of the two excavations extends beyond the location of the
smaller one, but this larger excavation is outside the zone of influence of
the smaller excavation. Hence, Excavation I does influence the stresses
around Excavation 11, whereas Excavation I1 does not influence the stresses
around Excavation I-at the 5% engineering level.
This concept suggests a means of obtaining a first approximation to the
stress state that exists between the two excavations. The stresses induced
by Excavation I can be calculated at both a point of interest and at the centre
of Excavation 11, and this latter stress state is used to calculate the stresses
induced at the point of interest by Excavation 11. It is essential to understand
that when this procedure is undertaken, the perturbation due to each
excavation must be determined and added to thefield stresses, rather than adding
the two absolute induced stresses. If the latter procedure is used, the field
stresses are effectively duplicated,
Not only are these zones of influence helpful to designers in indicating
zones of high and low stresses, they also indicate the optimal excavation
sequencing of design layouts. For example, considering the two circular
excavations in Fig. 20.19, the question to be answered is, 'Should we create
Excavation I or Excavation I1 first?' The advantage of creating I first is that
the final stress field acting on Excavation I1 will be in place before that
excavation is made, and the process of creating Excavation I1 will not
appreciably affect Excavation I. The advantage of creating Excavation I1 first
is that the excavation is made in an unperturbed stress field, and the tunnel
can be supported in anticipation of the stresses that will be induced
following the creation of Excavation I.
This indicates two design alternatives, so through the use of the concept
of the zone of influence the engineer has a method of considering the
excavation sequencing alternatives. Of the two alternatives presented, the
first is likely to be preferred, as both excavations will be created in stress
fields that will not be subsequently disturbed. Very often, there can be a

/-- \ 5% zone

/ / \ of influence for

/ \I

\

I

I

I

I

\ I

I

I

\ I

\ 1

S% zone \ '\ I

/

/

\

/

I

of influence for

11

Figure 20.19 Mutual interaction between 5% zones of influence for two differently

sized, circular excavations.