Rock Mass In-Situ Stress - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 212

In the frequently occurring case of horizontal bedding or schistosity ( β = 0) Equations

(9.4) and (9.5) reduce to

(9.6)

This ratio of horizontal and vertical stress as a function of n = E 1 /E 2 , ν 1 and ν 2 is eval-

uated in Fig. 9.3.

Figure 9.3 Ratio of horizontal and vertical in-situ stresses due to gravity in a transversely isotropic,
elastic rock mass with horizontal ground surface and horizontal isotropic plane as a function of the
elastic constants, Cartesian coordinates, see Fig. 9.2 (Wittke 1990)

For a vertical bedding or schistosity ( β = 90°) Equations (9.4) and (9.5) take on the

following form:

(9.4a)

(9.5a)

If the shear strength along an inclined discontinuity set is small, such as the bedding or
schistosity illustrated in Fig. 9.2, the shear strength may be exceeded under the stresses
due to gravity. In such cases irreversible shear displacements arise and the in-situ stress
state may be computed analytically, accounting for the plastic limit state of the rock
mass or numerically using the FEM.
If the rock mass cannot carry any shear stress, as in the case of rock salt (Chapter 5),
the in-situ stress state is hydrostatic: σ x = σ y = σ z .