Page 213 - Rock Mechanics For Underground Mining

LINKED COMPUTATIONAL SCHEMES

Theformchosenfortheconstitutivefunction f mayrepresentisotropicortransversely
isotropic elasticity, Mohr-Coulomb plasticity, Hoek-Brown yield, strain softening, or
anisotropic plasticity defined by ubiquitous joints.
In the numerical implementation, equations 6.48–6.56 are solved sequentially
through a series of time steps of duration t. Thus the solution procedure is essentially
a time-based integration of the governing equations to yield the displacements and
state of stress at a set of collocation points in the medium. One of the advantages of
the procedure is the relative ease with which equations describing forces generated in
support and reinforcing elements, or drag forces from fluid flow, can be incorporated
in the analysis.
The wide utilisation of FLAC in both rock engineering design and in fundamental
studies of rock deformation confirms its acceptance as a sound analytical tool.

6.9 Linked computational schemes

The preceding discussion has noted the advantages and limitations of the various com-
putational methods. In many cases, the nature of mine excavation design problems
means that the boundary element method can be used for design analyses, particu-
larly if the intention is to carry out a parameter study in assessing various options.
In those cases where non-linear material or discrete, rigid-block displacements are
to be modelled, the scale of a mining problem frequently precludes the effective or
economical use of finite element or distinct element codes. The solution is to develop
linked schemes, where the far-field rock is modelled with boundary elements, and the
more complex constitutive behaviour is modelled with the appropriate differential
method of analysis. A domain of complex behaviour is then embedded in an infi-
nite elastic continuum. The advantages of this approach include, first, elimination of
uncertainties associated with the assumption of an outer boundary for the problem
domain, as required by the differential methods. Second, far-field and elastic material
behaviour is represented in a computationally economical and mechanically appro-
priate way with boundary elements. Finally, zones of complex constitutive behaviour
in a mine structure are frequently small and localised, so that only these zones may
require the versatility conferred by a differential method. The implied reduction in the
size of zones to be modelled with a differential method again favours computational
efficiency. An example of the development of a linked method and its application in
excavation design is given by Lorig and Brady (1982).

Figure 6.12 Resolution of a cou-
pled distinct element–boundary ele-
ment problem into component prob-
lems.

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