Rock Mass In-Situ Stress - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 218

ever, here, depending on the orientation of the isotropic plane, the horizontal dis-
placements δ y which arise due to gravity must be accounted for as well. If

the coordinate system is oriented with respect to the isotropic plane, as illustrated
in Fig. 9.2, horizontal displacements arise under the boundary conditions of in-
hibited lateral strain due to the shear strain

δ x and

γ zx which, in consideration of (3.12),

can be expressed as (Wittke 1990)

(9.10)

with

In (9.10), K 0x and K 0y are functions of the elastic constants and the dip angle β ob-

tained from (9.4) and (9.5), respectively, σ z is a function of z given by (9.1a), and in-

tegration of γ zx with respect to z leads to a parabolic function of z for the horizontal

displacement

δ x due to gravity:

(9.11)

For an arbitrary orientation of the isotropic plane, δ x and δ y due to gravity are func-

tions of the coordinates x, y and z.
When dealing with tectonic stresses, it must be kept in mind that these stresses may
have led to failure in the rock mass and, as a consequence, a considerable portion of
these stresses may have died away. Thus, the evaluation of the in-situ stress state under
the assumption of an elastic stress-strain behavior of the rock mass can lead to serious
misinterpretations. Therefore it needs to be checked in each individual case whether the
determined stress state is admissible when the failure and post-failure behavior of the
rock mass is accounted for.