Engineering Rock Mechanics

56 In situ stress

x

a

a

• 8
  e

(4

x

a

a

c

5

e

Inhomogeneous

medium

Homogeneous

medium

I

I

RE" Size

0

IIIIIIIIIIIII

Size

Figure 4.12 Variability in measured values with respect to sample volume,

illustrating the REV. (a) General concept. (b) Example data scatter.

past and present effects on the stress state, has led to a plethora of terms

describing different types of stress. In order that clarity is preserved

here, this chapter concludes with a glossary of terms associated with in situ

stress.

4.6 Predictions of natural in situ stress states

based on elasticity theory

We have mentioned that the in situ stress field is conveniently expressed

via the orientations and magnitudes of the principal stresses. As a first

approximation, therefore, let us assume that the three principal stresses of

a natural in situ stress field are acting vertically (one component) and

horizontally (two components). Following this assumption concerning

orientations, it becomes possible to predict the magnitudes of these

principal stresses through the use of elasticity theory.

4.6.7 The vertical stress component

We might expect that the vertical stress component increases in magnitude