Rock Mass In-Situ Stress - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 217

Figure 9.7 Isotropic, elastic rock mass with regular topography, principal normal stresses
due to gravity and an additional horizontal tectonic stress of Δσ x = 7.5 MPa (Wittke 1990)

In the three-dimensional case, horizontal tectonic stresses Δσ y can be simulated

by applying the following horizontal displacements at the lateral vertical boundaries of
the computation section:

Δσ x and

(9.8)

(9.9)

If Δτ xy must

be applied. In this more general case, the contributions of the shear stress to

Δσ x and Δσ y are not principal normal stresses, an additional shear stress

δ x and δ y

have to be taken into account. As a consequence, δ x and δ y are not constant any longer

but are functions of the coordinates x and y.

Equations corresponding to (9.7), (9.8) and (9.9) for a transversely isotropic, elas-
tic rock mass can be derived analogously using the generalized Hooke's law. How-