Engineering Rock Mechanics

Collated worldwide in situ stress data 61

500

,^ I. k = -+ 0.5

i2 ... I! O .*

0

/'

.

I

7. ; Australia
   1; v United States
   VI' A Canada
   I o Scandinavia
   I I Southern Afnca
   I Other regions
   I

k= Average horizontal stress

Vertical stress uv

Figure 4.15 Collated worldwide in situ stress data: mean horizontal
component (after Hoek and Brown, 1980).

stress

best approach, because the complete stress tensor was not available in all
cases. They suggested two formulae as envelopes for all the data in their
compilation, viz.

100

• 
  
  
  
  • 0.3 < k < E+ 0.5.
  
  
  
  

Note that the shaded vertical column in Fig. 4.15 gives the range of k-ratios

from 0.33 to 1.00 that was predicted from simple elasticity theory and that,

with increasing depth, the k-ratios given by the envelope formulae

above tend towards 0.3 < k < 0.5. Thus, for significant depths, one

could argue that the elasticity model provides some indication of the

k-value.

It is manifestly clear from the data, however, that it is the rule rather than

the exception that the horizontal stress component (defined as the mean

of the two horizontal components) is larger than the vertical stress

component. For example, at depths likely to be encountered in civil

engineering, say 0-500 m, in 92% of the studied cases (100% of the cases

outside Canada), the magnitude of the mean horizontal stress exceeds that

of the vertical stress component. Also, at typical mining depths (say,

anywhere between 0 and 1000 m), the same trend applies. Of course, we