Engineering Rock Mechanics

376 Design and analysis of underground excavations

tP

Figure 20.17 Elliptical approximation to the 5% zone of influence from the two-

dimensional stress analysis of a circular excavation (from chapter by J. W. Bray in

Brown, 1987).

Figure 20.18 shows the two main possibilities for the interaction of

stresses between two proximate excavations. The first case shows how

stresses may be amplified between excavations. The second case shows

how stresses may be attenuated, with the production of a so-called 'stress

shadow'. In the first of these cases, the stresses at a point between the

excavations can be higher than the maximum stress induced by any single

excavation, demonstrating an overlap of the zones of influence associated

with the two excavations. This is also the case for the stress shadow, except

then the overlap represents a reduction in the in situ stress.

For two proximate circular excavations with different diameters, the

zones of influence associated with a given level of perturbation will have

different extents for each excavation, and hence different effects on their

neighbours. Consider the case of two circular excavations, one larger than

Stress increases

0 '0

Dominant

t t f t t t held

Stre\\

• \hadow


• c-
  a:----o -
  
  
  • /----
  
  
  
  


• 
  

  Stre\ decrea\e\
  Figure 20.18 Amplification and attentuation of stresses between multiple excavations