Engineering Rock Mechanics

Effect of discontinuities on the proximate state of stress 67

t

Discontinuity

filling

E, - Young’s modulus

of discontinuity

filling

E - Young’s modulus

Major of surrounding

principal (TI rock

stress

Case 1 : E, = 0

Case 2 : E, = E

Case 3 : E, +-m Discontinuity filling is

Open discontinuity

Discontinuity filling has same

modulus as surrounding rock

effectively rigid

Figure 4.20 Effect of stiffness of discontinuity filling material on the stress state. Two
extreme cases are shown-where the discontinuity filling has a modulus of zero
(Case 1) and infinity (Case 3)-together with an intermediate case where the
discontinuity filling has the same modulus as the surrounding rock (Case 2).

> Tectonic

Regional Continental

Local Near field Far field

stresses being unaffected. At the other end of the spectrum, in Case 3, the
discontinuity is filled by a rigid material. Then, the major principal stress
is drawn in perpendicular to the discontinuity and the minor principal
stress becomes parallel to the discontinuity.
In general, for most engineering circumstances such as discontinuities
or back-filled mine stopes, the stress distribution will be between those
shown for Cases 1 and 2. A circumstance between Cases 2 and 3 could arise
where a discontinuity in a soft rock is filled with a stiffer material, e.g.
quartz veins in soft limestone or a volcanic pipe surrounded by softer rocks.
We have mentioned that the discontinuities being considered could be
on a variety of scales. In fact, we would expect effects such as those
illustrated in Fig. 4.20 to be superimposed as a result of the existence of

IT

Grain Layer Jointed Pluton Heterogeneity

scale scale block scale scale scale

Fractal

equilibrium

volumes

Overcore

applied

Small Domain size

Figure 4.21 Stress state-scale relations.

Large