Stress-Strain Behavior of Jointed Rock - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 80

oped by Berry et al. (1974). This approach is based on studies carried out by Walsh
(1965a, 1965b, 1965c) and Walsh & Brace (1966) on the effect of cracks on the elastic
properties of intact rocks. Accordingly, the rock mass can be described by a special case
of transverse isotropy with only three independent equivalent elastic constants. Equa-
tions for the equivalent elastic constants of a rock mass that is separated by two sets of
non-persistent, open discontinuities, which are perpendicular to each other, are given
by Hu & Huang (1993).
The elastic properties of rock masses with discontinuity systems, which are not perpen-
dicular to each other and/or contain non-persistent discontinuities, can be formulated
with the aid of a “crack tensor”, also referred to as a “fabric tensor” or “fracture tensor”,
introduced by Oda (1982).
However, all these analytic approaches to estimating the elastic properties of jointed
rock are not suitable for application because the deformability of discontinuities can
hardly be estimated. It is therefore recommended to evaluate the deformability of joint-
ed rock on the basis of site investigation, fi eld testing, back analysis and experience, as
described in Section 18.1.
In most cases the elastic rock mass deformability can be related to structural models as
shown in Fig. 2.33. Accordingly, in jointed rock, in addition to elastic and transversely
isotropic behavior, orthotropic elastic behavior may also be relevant. A regularly jointed
rock mass with one to three persistent, mutually perpendicular discontinuity sets can be
described by an equivalent orthotropic continuum. This type of anisotropy is charac-
terized by the following compliance matrix:

(3.86)

The nine independent elastic constants E 1 , E 2 , E 3 , G 1 , G 2 , G 3 , ν 1 , ν 2 and ν 3 , as well

as the three dependent Poisson's ratios ν 6 of an orthotropic rock mass, are

defi ned in Fig. 3.25 by means of normal and shear stresses and strains.

ν 4 , ν 5 , and

A layered rock mass with discontinuities fi lled with soil or an alternating sequence of
different rock types allow a reasonable estimate of the mean thicknesses of the individ-
ual rock layers and/or discontinuity fi llings so that a reliable estimation of the elastic
constants may be possible.