Rock Mass In-Situ Stress - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 216

1978, Illies & Greiner 1979, Illies et al. 1981, Scheidegger & Ai 1986). The presence
of tectonic stresses may also be inferred from seismic processes (Raleigh et al. 1972,
Haimson 1973, Ahorner 1975, Zoback 1992, Xie et al. 2010).
Interrelations between structural elements of a rock mass and the in-situ stresses are
comprehensively discussed in Fecker & Reik (1997), for example. However, the interpre-
tation of the rock mass's structures with regard to the in-situ stress state can easily lead
to misjudgments because the present stress state may differ considerably from the stress
state existing at the time of origin of these structures.

Analytical solutions for simple conditions corresponding to uplift and faulting
are given in Jaeger & Cook (1979). An analytical method to determine stresses
due to gravity and tectonic stress in an anisotropic rock with irregular topography
is presented in Pan et al. (1995).
Generally, as already mentioned, the results of stress measurements should be inter-
preted with the aid of numerical analyses. If the measurement results match the stress
fi eld computed under the assumption of stresses due to gravity alone (Fig. 9.5) the as-
sumption made may be regarded as appropriate. If this is not the case, then additional
stresses must be introduced into the analysis in such a way that the computed results are
in agreement with those obtained from measurements.
In the case of a symmetric series of ridges and valleys with infi nite length in y direction
(Fig. 9.5) an additional horizontal tectonic stress

Δσ x can be simulated by a constant

horizontal displacement δ x applied by means of spring elements, as described in Section

10.5.1 (Fig. 10.17) on the plane of symmetry at the middle of the valley. In case of an
isotropic, elastic rock mass this displacement

δ x is

(9.7)

if

is assumed. L x is the dimension of the computation section in the x direction (L x = 250
m in Fig. 9.5).
Figure 9.7 shows the distribution of the principal normal stresses in a symmetric series
of ridges and valleys with infi nite length due to gravity and an additional horizontal
tectonic stress of Δσ x = 7.5 MPa simulated by a horizontal displacement of δ x = - 90 cm

according to (9.7) applied at the middle of the valley.