Rock Mass In-Situ Stress - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 210

(9.2)

Thus, the ratio of the horizontal and vertical principal normal in-situ stress is:

(9.3)

Figure 9.1 In-situ stress state due to gravity in an isotropic, elastic rock mass with horizontal
ground surface (Wittke 1990)

Corresponding relationships for a transversely isotropic, elastic rock mass can be derived
from the generalized Hooke's law with the boundary conditions given in Fig. 9.2. If the x
and y axes run perpendicular and parallel to the isotropic plane being a bedding or schis-
tosity, as illustrated in Fig. 9.2, σ y are the principal normal stresses. According to

Wittke (1990), the ratios of the horizontal and vertical principal normal in-situ stresses
then can be expressed

σ x and

(9.4)

(9.5)