66 In situ stress
+++++*~x*~x~c++++~uxx~%%~++++
++++++*%xxxrr+++~~xxxx%k+++t+
+++++++?l%xxxr+++sxwxxk%++++++
+++++++%2xxxr+++*xn*xkk++++++
+++++t++2x*xr+++**x%kk+t+++++
++t+t+t+~Z*x---*.x*~k~+t~~+~+
t+tt+ttt~zfrc----\~~~~t+tt+++
++++tttt)z~*-----\x~tttt+++++
++++++t++/f*----- -z\ft+++++++
+++++~~~+/c--------it~~~~++++
+ + + + + ++++ ++++ + + + + +
+++++~%~+~.-------C/t~~~+++++
+++++++++\x------- ~/+++++++++
+++tS+ttt~x------**~~tt+t++++
++++++tf~~*-g--c~r*z~~t++++++
+t+tttttk%*x.*-six*zj++tt++++
t+++t+~tk*xx*++~*r*%2++++++++
+++t++~4~xx~~+++~xxxs+++tt++t
++++++~~~nxnc+++r~xxx~~+++~+t
+++++~%**n*~+++++~xxx~~++++++
++++k~~~nxn~++++carxx~%~++~t+
Figure 4.19 Example of the effect of a discontinuity on the near-field stress state,
for an applied hydrostatic two-dimensional stress with the discontinuity having a
modulus of 10% of the host rock (from Hyett, 1990). The crosses represent the
magnitudes and directions of the principal stresses. Note how the stress field close
to the discontinuity is quite different from the far-field stress.be several metres long and only causing a perturbation in the region where
the stress determination happens to be made. One can easily imagine the
bias and the spread of results that would be obtained by measuring the
stresses in boreholes through the rock around the fracture in the diagram.
We feel that the large spread of stress state data is mainly due to the
combined effects of a hierarchy of such fracture systems, which we know
exists in all rocks. It follows that a wide spread in measured values is not
necessarily due to bad experimental techniques: on the contrary, the spread
itself can indicate a great deal about the in situ stress state.
The discontinuity illustrated in Fig. 4.19 has an effective modulus of 10%
of the host rock. It is interesting to consider the effect on the stress field
when the discontinuity modulus varies from zero to infinity. This is
illustrated in Fig. 4.20, in which the principal stresses are altered in the
vicinity of the discontinuity. In Case 1, we consider an open discontinuity,
similar to the unsupported excavation surface described in Section 3.9. In
this case, the major principal stress is diverted parallel to the discontinuity
and the minor principal stress takes on a value of zero perpendicular to the
discontinuity. In Case 1, the diagram could represent an open discontinuity
or an open stope in an underground mine.
In Case 2, in Fig. 4.20, the discontinuity is filled with a material having
the same modulus as the surrounding rock. Under these circumstances,
and assuming no slip, the discontinuity would be mechanically
transparent, with the magnitudes and orientations of the principal