Stress-Strain Behavior of Jointed Rock - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 77

Examples for the application of computer codes based on fracture mechanics concepts
on rock masses with non-persisting discontinuities can be found, for example, in Gehle
(2002), Kemeny (2003) and Zhang et al. (2006).
Application of discrete models to the stability analyses for rock engineering structures,
in particular in the case of jointed rock with several sets of discontinuities, usually re-
sults in a large computational effort. Moreover, it is impossible to completely determine
the three-dimensional orientation, location and extent of discontinuities in the ground
underneath or around a rock engineering structure. The applicability of discrete models
is therefore limited in practice.
3.4.2 HomogeneousModel
General
The computational effort and the lack of detailed information on discontinuity data asso-
ciated with discrete models gave impetus to the development of models that can describe
the influence of discontinuities with much less effort. In these models referred to as “homo-
geneous models” or “equivalent continuum models” the intact rock and the discontinui-
ties of a rock mass are treated as parts of a continuum: the deformations of the equivalent
continuum include the deformations of the intact rock as well as the deformations resul-
ting from displacements on discontinuities (Wittke 1990). Furthermore, it is assumed in
these models that discontinuities with their average orientations and their characteristic
parameters are located at each point of the rock mass. The application of a homogeneous
model therefore requires the estimation of a so-called “representative elementary volume”
(REV). In the REV, the rock mass can be considered to be statistically homogeneous in
the sense that an increase of this volume does not change the mean stresses and displace-
ments when describing the rock mass as a continuum.
Without the assumption that in each point of the continuum a discontinuity of each
set is present the interaction between individual discontinuities must be taken into ac-
count. Homogeneous models in which deformability and strength of the rock mass are
expressed as a function of orientation, size and intensity of the discontinuities and were
implemented into numerical analysis procedures were formulated, for example, by Cai
& Horii (1993) and Yoshida & Horii (2004). However, such models are sophisticated
and, like discrete models, require a large amount of input data, including informa-
tion on not only the orientation of the discontinuities but also other properties such
as spacing, degree of separation and size. The computational effort and the lack of
detailed information on discontinuity data are the main reasons that these models are
not normally applied to practical rock engineering problems.
The structure of the proposed elastic-viscoplastic stress-strain law of jointed rock can
be described with the aid of the rheological model represented in Fig. 3.23, which is an
extension of the rheological model for intact rock represented in Fig. 3.9 (lower right).
It consists of a spring to describe elastic behavior of the rock mass followed by a series
arrangement of dashpot and sliding elements that are arranged in parallel to each other,
representing the viscoplastic behavior of N discontinuity sets. The spring and each par-
allel arrangement of dashpot and sliding elements correspond to a strain component.