Engineering Rock Mechanics

64 In situ stress

high shear stresses can be present and result from tectonic activity. In Fig.
4.17, we illustrate the subduction zone off the coast of Chile, the genesis of
the Andes and hence the likely high horizontal normal stresses we would
expect from such activity. In fact, both the largest surface and largest
underground mines in the World are in Chile-and they both show strong
signs of stress-related phenomena in terms of rock slope instability and
rockbursts, respectively.

4.8.3 Rock anisotropy

In Section 4.6.2 we derived the expression v/(l - v) as the ratio between the

horizontal and vertical stresses and noted that for v varying between^0

and 0.5 the corresponding k-ratio varied from 0 to 1. We will be discussing

anisotropy in much greater detail in Chapter 5, on strain, and in Chapter

10 on inhomogeneity and anisotropy. It is worth mentioning here, though,

that there are three types of isotropy commonly considered in

rock mechanics, namely: complete isotropy, transverse isotropy and

orthotrop y.

Our earlier calculation was for a rock with complete isotropy (having the

same properties in all directions). It is possible to calculate the k-value for

a material which is transversely isotropic (having different properties in the

vertical direction to the horizontal directions), and for the orthotropic case

(having different properties in three perpendicular directions). The

explanation, both mathematical and intuitive, for these types of isotropy

and the associated elastic material constants is given in Chapter 5. The

important point is that the k-values for each case are as shown in

Fig. 4.18 by the terms in parentheses.

As indicated by the sketches in the figure, transverse isotropy might well

represent relatively unfractured sedimentary rocks, whereas, orthotropy

Isotropic Transversely Orthotropic

isotropic

X (horizontal)

vxz+v v

6, = Qy = ( 1 ") -v OZ ox = cy = ( 1 vxz -v ) oz ox = ( I -Vxy yz vyx xy ) oz

v = VXY = vx, = vyz v XY =v YX =v

Figure 4.18 Relation between vertical and elastically induced horizontal stresses for

the different types of isotropy.