Numerical methods in rock mechanics

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The hybrid FEM/BEM was first proposed in [238],
then followed in [239,240] as a general stress analysis
technique. In rock mechanics, it has been used mainly
for simulating the mechanical behaviour of underground
excavations, as reported in [241–245]. The
coupling algorithms are also presented in detail in [48].
The hybrid DEM/BEM model was implemented
only for the explicit distinct element method, in the
code group of UDEC and 3DEC. The technique
was created in [246–248] for stress/deformation analysis.
In [249–250] a development of hybrid discrete-continuum
models was reported for coupled hydro-mechanical
analysis of fractured rocks, using combinations
of DEM, DFN and BEM approaches. In [251], a
hybrid DEM/FEM model was described, in which
the DEM region consists of rigid blocks and the
FEM region can have non-linear material behaviour.
A hybrid beam-BEM model was reported in [252]
to simulate the support behaviour of underground
openings, using the same principle as the hybrid BEM/
FEM model. In [253], a hybrid BEM-characteristics
method is described for non-linear analysis of rock
caverns.
The hybrid models have many advantages, but special
attention needs to be paid to the continuity or
compatibility conditions at the interfaces between
regions of different models, particularly when different
material assumptions are involved, such as rigid and
deformable block–region interfaces.
2.7. Neural networks
L. Jing, J.A. Hudson / International Journal of Rock Mechanics & Mining Sciences 39 (2002) 409–427
All the numerical modelling methods described so far
are in the category of ‘1:1 mapping’, i.e., the Level 1
methods in Fig. 1. The neural network approach is a
‘non-1:1 mapping’ in the Methods C and D categories of
the Level 2 methods indicated in Fig. 1. The rock mass is
represented indirectly by a system of connected nodes,
but there is not necessarily any physical interpretation of
the geometrical or mechanistic location of the network’s
internal nodes, nor of their input and output values.
Such a ‘non-1:1 mapping’ system has its advantages and
disadvantages.
The advantages of neural networks are that
(1) The geometrical and physical constraints of the
problem, which dominate the governing equations
and constitutive laws when the 1:1 mapping
techniques are used, are not such a problem.
(2) Different kinds of neural networks can be applied
to a problem.
(3) There is the possibility that the ‘perception’ we
enjoy with the human brain may be mimicked in the
neural network, so that the programs can incorporate
judgements based on empirical methods and
experiences.
The disadvantages are that
(1) The procedure may be regarded as simply supercomplicated
curve fitting—because the program has
to be ‘taught’.
(2) The model cannot reliably estimate outside its range
of training parameters.
(3) Critical mechanisms might be omitted in the model
training.
(4) There is a lack of any theoretical basis for
verification and validation of the techniques and
their outcomes.
Neural network models provide descriptive and
predictive capabilities and, for this reason, have been
applied through the range of rock parameter identification
and engineering activities. Recent published works
on the application of neural networks to rock mechanics
and rock engineering includes the following publications.
* Stress–strain curves for intact rock [254].
* Intact rock strength [255,256].
* Fracture aperture [257].
* Shear behaviour of fractures [258].
* Rock fracture analysis [259].
* Rock mass properties [260,261].
* Microfracturing process in rock [262].
* Rock mass classification [263,264].
* Displacements of rock slopes [265].
* Tunnel boring machine performance [266].
* Displacements and failure in tunnels [267,268].
* Tunnel support [269,270].
* Surface settlement due to tunnelling [271].
* Earthquake information analysis [272].
* Rock engineering systems (RES) modelling [273,274].
* Rock engineering [275].
* Overview of the subject [276].
As evidenced by the list of highlighted references
above, the neural network modelling approach has been
widely applied and is considered to have significant
potential—because of its ‘non-1:1 mapping’ character
and because it may be possible in the future for such
networks to include creative ability, perception and
judgement, and be linked to the Internet. However, the
method has not yet provided an alternative to conventional
modelling, and it may be some time before it can
be used in the comprehensive Box 2D mode envisaged in
Fig. 1 and described in [277].
3. Coupled thermo-hydro-mechanical (THM) models
The couplings between the processes of heat transfer
(T), fluid flow (H) and stress/deformation (M) in
fractured rocks have become an increasingly important
subject since the early 1980s [278,279], mainly due to the