Rock Mass In-Situ Stress - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 214

The distribution of principal normal stresses calculated on the basis of these assump-
tions is shown in Fig. 9.5. It may be recognized that the maximum principal normal
stress near the ground surface runs approximately parallel to the slope. Only at a con-
siderable distance from the slope or at great depth is this stress oriented vertically. Thus,
the in-situ stress is different at each location with regard to direction and magnitude.
Figure 9.5 Isotropic,
elastic rock mass with
regular topography,
principal normal
stresses due to gravity
(Wittke 1990)
An interesting conclusion which can be drawn from this analysis is that the infl u-
ence of topography on the in-situ stresses decreases with increasing depth. This
means that the principal normal stresses due to gravity from a certain depth are
directed vertically and horizontally and may be calculated by (9.1), (9.2) and (9.3)
or (9.4) and (9.5), respectively, assuming elastic rock mass behavior and an aver-
age height of overburden (Fig. 9.6).
In the case of a rock mass with an arbitrary, irregular topography the evaluation of the
in-situ stress state due to gravity requires the conduction of FEM numerical analyses.
Examples are reported in Kiehl (1991b), Wittke & Soria (1983), Soria & Wittke (1988)
and Wittke (1990), these being referred to also in Sections 16.6 and 16.7.