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Research at CSIRO on numerical modelling for mining geomechanics
Computers and Geotechnics 5 (1988) 81-103
RESEARCH
AT
CSIRO
ON NUMERICAL
MODELLING
FOR MINING
GEOMECHANICS
M.A. Coulthard CSIRO Division of Geomechanlcs, P.O. Box 54, Mount Waverley, Victoria 3149, Australia and G. Beer CSIRO Division of Geomechanics, Private Bag 3, Indooroopilly, Queensland 4068, Australia
ABSTRACT The Division of Geomechanlcs CSIRO, has an extensive research programme involving the development and verification of computer programs for modelling in mining geomechanlcs. The scope of the Division's work is outlined, the various numerical techniques being developed are described and some applications of the programs are illustrated. Ongoing efforts to make the programs more accessible to mine design engineers, and plans for future research, are discussed. INTRODUCTION
CSIRO Research
and
will
generally. interact about
Commonwealth
Organlsatlon
government, which
the
Each
- receives
charged
benefit
with
30%
is
of the
funding
and by commerclallsatlon
The
role
of the
most the
in
thirty
Australia) of
Australia
funding
or
or so Divisions
"client
group"
by undertaking
Division
its
from
of
the within
collaborative
work
in
- in metalliferous clvil
and
offshore
Industrial
the
Australian
performing
CSIRO
research community
is required
and to obtain or contract
research,
is
to conduct
research
and control of the behavlour
activities
take place.
is becoming
that
of rock
At present,
the
of geomechanics
or coal mines, both surface and underground engineering
to
up to
advances.
bulk of the Division's work is associated with the application in mining
and
Australian
in industry
of Geomechanlcs
for prediction
in which engineering
Scientific
responsibility
of its technological
will improve our capacity and soll masses
with
industry
an appropriate
of its
(of
increasingly
- but
important.
81
Computers and Geotechnics 0266-352X/88/S03'50 © 1988 Elsevier Applied Science Publishers Ltd, England. Printed in Great Britain
82 The more fundamental
research at the Division has potential
application
in all
these areas of engineering. Research
activities
at the Division
include fundamental
theoretical
studies of rock fracture and of joint mechanics
development
of computational
and/or
weak
stresses
of
and
the performance
marketing
of
of rock
computer
of excavations
measuring
studies
and
objective
at operating
at
the
of
this
paper
modelling
Division,
philosophy
discussed.
hybrid
Stress
and
is
to
to Australian
programs,
for stability
industry
the
capabilities
which
are
being
to
outline
some
our
methods,
discontinuity,
are
work
of
covered
in the
fluid
flow
the direction
is outlined.
in porous
their
the
of
the
developed
or
applications
to
post-processors
are
and
programs
summarised
in
first,
computational finite
difference,
following
section,
element,
then
media
and then
modelling
distinct
are described.
fractured
of future research
The different
in
including
finite
analysis and rock reinforcement
for modelling
hardware
of
through
describe
techniques
underlying
analysis
displacement
Finally,
means
produced
at specific mine sites.
general
element,
mass
by
also
The types of problem that are being tackled are outlined the
induced
rock
and
techniques
to transfer
and
of
mechanisms
industry,
programs
in jointed
pre-mining
field
reinforcement
with
the Division endeavours
computational
enhanced
for
large-scale
and
it has developed.
The
problems
and
collaboration
instruments,
CSIRO research, technology
its
for analysis
instruments
deformations;
Through
various
and
and
behaviour mines.
media
techniques
experimental
in the laboratory;
is
boundary
element
techniques
and used
Various programs
are
described
next.
in computational
modelling
at CSIRO
and their associated
graphical
pre-
types
computer
an
Appendix,
and
and software on which each is operational
the
of
and
are indicated.
GEOMECHANICS PROBLEMS FACED BY THE AUSTRALIAN MINING INDUSTRY
There
are
encountered
in
computational
many mining,
sections,
efficiency,
restricted
access
and
modelling
subsequent
need
different
to
a
most
of
which
techniques.
of
geomechanics
we
are
As
will
computer
in scope.
library
diversity of problems
for
types
seeking be
programs
A design engineer
different
that must be faced.
programs
problem
to
develop
discussed
are,
for
in
that
are
effective detail
simplicity
in and
in industry will therefore to be
able
to
tackle
the
83 Research
at
the Division
of Geomechanics
reflects
our
commitment
to
study problems which are of the greatest current or potential concern to the mining industry in Australia.
These include:
Under~round Metal Mininff: stope design,
including stability of walls and pillars and effects of
major structural features and/or highly jointed rock; rock support and reinforcement; use of mine fill; blast vibration mlnimisation.
Surface Metal Mining: slope design, including structural geology and rock block stability; rock support and reinforcement; blast vibration minimlsation.
Underground Coal Mining; design of longwall and other mining layouts; stability of pillars, including post-yleld weakening; face support requirements in the vicinity of caving roof strata; effects of induced subsidence on surface improvements such as dams; gas outbursts; storage of gas in disused mines.
Surface Coal Mining; stability of high walls and spoil piles; surface subsidence due to withdrawal of ground water.
PHILOSOPHY F O R N U M E R I C A L MODELLING
The
computational
potentially,
very
methods
powerful
which
tools
for
are
described
improving
our
in
this
paper
understanding
are,
of
the
mechanics of the complex systems with which we must deal in geomeehanics, and for assisting the practising mining engineer to design safe and economical excavations.
There are five broad stages along the route from theoretical
conception of a computational technique to its application by design engineers in industry:
i.
Mathematical
analysis
of
a
conceptual
includes the relevant physical principles.
model
of
the
system,
which
84 2.
Coding and testing of techniques
for numerical
solution
of the resulting
equations.
3.
Verification against
of
simple
the
computer
program
test
problems
which
with other computational
4.
5.
Validation
of
the
model
by
with laboratory
Development
of
analysed
solutions
or
semi-analytically
or
detailed
comparison
of
the
results
of
and field measurements.
a user-friendly
interactive
are
analytical
methods.
calculations
including
against
interface
graphics
to
the main
for preparation
program,
usually
of input data and display
of results.
The process some
iteration
measurements
of development
around these
require
refinement
details of the physics
This
paper
concentrates
of
the
of
constitutive
theoretical
their computer coding,
on the
to which
best suited and illustrating
program will usually
as discrepancies
that must be included,
the types of design problem
Details
of a particular
stages,
models,
later
stages
the use of different
of the process,
computer
underlying
stress analysis,
and the
outlining are
at CSIRO.
programs,
and of
cited below.
or adapted to handle the
into three general
stability
of
techniques
programs
specific
can be obtained from the references
listed above may be grouped
discussed next:
reassessment
computational
The computer programs which have been developed problems
involve
calculations
and so on.
the various
formulation
between
analysis,
categories,
which are
and fluid flow.
STRESS ANALYSIS
Numerical induced
methods
displacements
and soil masses.
distinct
discretization
are
stresses
now
widely
resulting
used from
for
of more
effective
and more
efficient
predicting
excavations
the
in rock
in this field
numerical
techniques
such problems.
Differential (FE),
analysis total
One of the major tasks facing research workers
is the development for analysing
of
and
methods
element
of
(DE)
stress and
analysis,
finite
of the entire problem domain
such
difference
as
the
(FD)
finite
element
methods,
require
into a mesh of elements.
The true
85 boundary
conditions
at
infinity
must
be
approximated
by
imposition
of
(somewhat arbitrary) displacements and/or stresses around the periphery of the mesh.
The strength of these methods
constitutive tensile
behaviour
yielding
shear zones,
of
within
geologic
is their ability to model
materials.
a continuum,
and
can be represented by FEs;
displacements other hand,
For
instance,
the behaviour
slip,
the complex shear
of major
and/or
faults
in blocky systems can be modelled with the DE method. integral techniques
or
separation and large relative
such as the boundary element
On the
(BE) method can
accurately treat the infinite or semi-inflnite geometries which usually apply in
geomechanics,
and
only
require
discretization
of
the
boundaries
excavations or of material zones - within the problem domain. is
most
efficient
for
linearly
elastic
behaviour.
of
The BE method
The
displacement
discontinuity (DD) method is a special case of BE methods, and is designed for analysis of tabular excavations such as in underground coal mining.
Hybrid
programs
have
been
developed
recently
to
complementary advantages of these different methods.
capitalise
Usually,
on
the
a differential
method of analysis is used to model nonlinear behaviour which is loealised in the near field, such as in the immediate vicinity of an excavation.
Boundary
elements may be coupled to the periphery of the FE or DE region to represent the essentially
elastic
continuum
far-field rock behaviour
and the boundary
conditions at infinity.
Each developed programs
of at
these the
will
different
Division
be
numerical
techniques
of Geomechanics,
available
which
can
be
so used
is
that to
a
being
studied
library
analyse
of
and
computer
efficiently
the
stresses in any type of geomechanieal system.
Finite Element Method
The
FE
method
is
the
most
widely
analysis of stresses in complex systems. subject
has
been
based
upon
programs
used
computer-based
technique
for
Much of the Division's work on the originally
developed
in
the
United
States, which have since been modified and adapted for our use.
A two-dlmenslonal,
plane
the U.S. Bureau of Mines.
strain program NTJTEP2
[i] was developed
for
It includes a rock material model which allows for
yielding in shear, via a Drucker-Prager yield criterion and an associated flow rule,
or
modelling
in
tension.
major
rock
A
Goodman-type
faults.
joint
Modifications
element made
is also
available
at CSIRO have
for
included a
86 simple
post-yield
weakening
model and generalisation stresses
[2].
behaviour
of
This a
enhancement
of
the
elasto-plastic
bulk
material
of the joint model and of the imposition of initial
program
faulted
mine
has
been
pillar
used
[3]
to
and
the
model,
for
stability
instance,
of
the
exposures
of
cemented mine fill. The finite element program ADINA can treat
two-
or
material models and with CSIRO
analyses
static
and of
[4] is a general-purpose
systems,
with
or geometric nonlinearities,
in studies
of mining
three-dimensional
or
dynamic
loadings.
in studies
geometric
"birth"
It has
of acoustic methods
been
of assessing
of ground vibrations
attenuation
of
a wide
package which
range
of nonlinear
and "death"
of elements,
used most rock mass
extensively
conditions
induced by blasting.
acoustic
pulses
[5]
have
at
ahead
Dynamic
enabled
more
accurate estimation of material attenuation of pulses radiated from a surfacemounted acoustic
source.
The work on ground vibrations
is outlined
later in
this paper.
More
recently,
a
two-dimensional
finite
element
program,
been developed with the aim of modelling yield zones in weak rock, coal.
Strain
novel
softening
constitutive
theories yield
of plasticity
zone
of the yielded
equation
which
(M.E.
growth predicted
falls
Duncan by
the
geologic within
Fama, strain
materials the
in preparation). model
has
especially
is modelled via a
framework
softening
FESOFT,
of deformation The
substantial
is illustrated
in
Figure i [6]. RESIDUAL STRENGTH <
.......
PEAK STRE~TH
ELASTIC
3O
20
n~
1~
,o
;
;METRES
o
\
o
,o
~o
METRES
FIGURE i. Comparison of elastic and nonlinear solutions in a 25 m coal pillar between simulated longwall panels. The stress distributions from mid-pillar to rib are shown on the left, and stresses in the panel flank are on the right, o v and a h are the vertical and horizontal stresses respectively [6].
87 Boundary Element Method
The program BITEMJ systems
containing
structural discussed method
([7],
regions
discontinuities
[8]) can model two-dimensional
with
in the introduction
is much
simpler
different
represented
than
by
to this for
elastic
properties,
Goodman-type
section,
excavations
joint
and
the FE method.
This,
with
elements.
data preparation
in
As
for the BE
and other
relative
advantages and disadvantages of BE and FE analyses of a faulted rock pillar, are discussed further in [3]. being
A range of verification studies with BITEMJ is
reported by Crotty and Brady
([9]
and Figure 2),
and the program has
been applied to back analysis of movement on a fault which caused a seismic event at the Mt. BITEMJ
is
Australia, has
Charlotte Mine,
installed
on
mini
Western Australia
computers
at
a
(M.F.
number
of
Lee,
unpublished).
mine
sites
around
and is being used by geotechnical consultants for mine design.
also been modified
to take advantage
of the vector processing
It
power of
CSIRO's Cyber 205 supercomputer.
A
three-dimensional
program,
CAVERN
[i0,
ii],
is
presently
being
modified extensively at the Division, with the ultimate objective of producing a program
equivalent
in capabilities
to BITEMJ.
The
original
program was
developed at M.I.T., as a hybrid BE-FE code, with finite elements to represent structural
features
such as tunnel linings.
Restriction of the code to BE-
only analysis of underground excavations, and reformulation of the calculation of stresses and displacements
at interior points,
have greatly increased its
accuracy and computational efficiency (J.M. Sisson, in preparation;
Figure 3).
It is now being applied in analyses of multiple stoping configurations.
Displacement Discontinuity Method
The DD method is ideally suited to modelling planar excavations, are
encountered
mining. of
in the mining
Program MINLAY
planar
excavations
anisotropic
elastic
of
tabular
orebodies
from
in
a
rock
properties.
measurements
analyses of
pillar
such as
in underground
coal
[12] can perform three-dimensional DD stress analyses mass The
composed
program
behaviour of material in the excavation plane, Results
or
with
MINLAY
stresses
have and
can
of
parallel
also
layers
represent
with
nonlinear
such as pillars or caved rock.
been surface
compared
satisfactorily
subsidence
longwall coal mining [13]; some are illustrated in Figure 4.
associated
with with
88 2.0~ '
stress
1.0 ~--
T
scare
_ _ _ _
0-0-
~
- I . 0 ~-
I
-2-0~
[ 0.0
I 1-0
-J 2-0
Xl/a FIGURE 2. Results of BITEMJ analysis of a tunnel intersected by a strength plane of weakness - tangential stresses in the tunnel face [9].
0.6 0.0 ~
spherical cavity in a uniaxial stress field
~
=
~
_..
._
.: ....... :
.....
m.
-0+6 -1.2.
~
low-
.,i---'--'-4
"
-1.8 -2.41.0
1.5
2.0
2.5
distance from centre of cavity (r/a)
I T
analytical CAVERN loaded axis CAVERN equatorial plane 1
FIGURE 3. V e r i f i c a t i o n isoparametric elements field.
•
CAVERNequatorial plane 2 I
IIllI
analysis using m o d i f i e d v e r s i o n of CAVERN - six 9-node over surface of spherical cavity in uniaxial stress
89
B
LI I
o
~12
AVERAGE STRESSMETER RESULTS
NUMEREALMODEL: - - - m - - LAYEREDANISOTROPIE (SEALED) 13 ,, ,~ {UNSEALED) @ ISOTROPIE(SEALED) O ,, {UNSCALED)
7 6
11
m / I
#/ U ~ I0
-~5
i [
i/ °
,/"1,,<
/ ~3-
.
o
2
o
°n ......
10
l
i IN
9o8 ~m
i
7<
I
6'-
_J
/
1°
1-A
i
I
I
30
20
10
AI
3.6
0
METRES FIGURE 4. Measured stresses calculated with program MINLAY
MSPOSTA -
¢OntOWP
dO6 TITLE : M S ~ t A ~ R
plot
ahead [13].
Of
of
cl08uP6
F'==~=RE'~SON ~
5
a
longwall
face
(OZ)
5
/
/1~---J
/--J
with
those
~.m.~,,~
P " ~ L A R PROBLEM- 3014 SEAM SEP. Window
I I
compared
I
L I
Mining
3 Step N u m b e c :
Number:
l
LEGEND -
-
M%nlng G e o m l t r y
0 0.005 0.01 O.Ot3 0.02 0.025
0.03 0.035 0.04 0.045
FIGURE 5. Analysis of rib pillar at Renison Bell tin mine with program BESOL/MS221. Contours of excavation closure in the vicinity of the monitored pillar area. Elements are 4 m square and the pillar is approximately 12 m by 160 m in plan.
90 The
program
BESOL/MS221
[ 1 4 ] can
which may be
folded or faulted,
earth.
host
The
material.
Walton,
mass
excavations
is
treated
as
a
in multiple
at the surface
uniform
elastic
seams of the
anisotropic
This program has recently been applied in a study of mining in two
orebody horizons
being
rock
model
and which may outcrop
at Renison
to be published) compared
with
Bell
tin mine
in Tasmania
(K.E.
McNabb
and R.J.
with calculated pillar stresses and rock deformations
field
measurements.
Some
results
from
that
study
are
shown in Figure 5.
Finite Difference Method
Program FLAC
[15]
is a two-dimensional
explicit
finite
which can model both material and geometric nonlinearities. at
the
Division
underground models
coal
at
present
mining.
to reproduce
to
analyse
In particular,
surface the
the observed variation
difference
subsidence
ability
of
code
It is being used induced
different
by
material
of subsidence with panel width
being studied (M.A. Coulthard & A.J. Dutton,
is
to be published).
Hybrid Boundary Element - Finite Element Method
A combination the
analysis
regional finite
of
complex
nonlinear elements
virtually
of BE and FE meshes mining
material
which
infinite,
excavations.
behaviour,
are
coupled
elastic
is used by program BEFE
to
rock mass.
together with
allows
support
elements
combination
for
consideration
and ground
boundary This
gives the user the best of both worlds, BE analysis,
BEFE
jointing
[16,17]
of
by using
representing of the
the
two methods
i.e. the reduced data requirements of
the viability
of the FE method
in dealing with a
Cyber 205 supercomputer
and is accessible
nonlinear rock mass.
Program BEFE runs on CSIRO's
through the Australia-wide CSIRONET network. mine planning
feasibility studies,
BEFE is currently being used for
for mine design and for "trouble shooting"
exercises to pinpoint problem areas in difficult mining situations.
An example of a coupled BEFE analysis mesh
has
mass
near
boundary which
is
been the
cut
open
to reveal
excavation
elements assumed
and
surrounding to
be
the the
elastic.
the
is shown in Figure 6(a) where the
finite
geometry FE mesh Note
elements of
the
represent that
"artificial" boundary conditions have to be used,
in
representing
excavation the
this
infinite type
of
the
itself.
rock The
rock mass, analysis
in contrast to an analysis
no
91
/--BOUNDARY ELEMENTS /REPRESENTING iNFINITE
.,,jji j)fJiiiiiiijiJ iiiHifiiiii!ilJ iiiiiii!i
PLANES OF WEAKNESS
FINITEELEMENTS REPRESENTING THE "NEAR-F/ELD"ROCK SCALE: I
I
4.0rn
FIGURE 6(a). Cut out mesh for the analysis of a mine coupled finite element - boundary element program BEFE.
excavation
using
the
X IOE-3m
I ×
Y
l
0.4
-
0.8
0.3
-
0.4
~
o.~-o.~
~
o_o.~
0
3
metres m
Z
"
FIGURE 6(b). Results of analysis on a horizontal cross-section contours show the amount of dilation (m) on joint planes.
(A-A).
Filled
92 which uses finite elements only.
In this analysis the FE region was described
by a multi-laminate material model, with one set of planes results
from the analysis
are shown
in Figure 6(b),
of weakness.
which depicts
Some
the amount
of dilation on the planes of weakness in the rock mass on a horizontal section A-A.
Further examples are reported in [18] and [19].
Hybrid Distinct Element - Boundary Element Method
The distinct
element programs which
of highly jointed, developed by Dr. yield
a
more
discontinuous Peter
Cundall
efficient
are being used for stress
analysis
rock masses are derived from codes originally and co-workers.
hybrid
technique,
Coupling
was
carried
to a BE region,
out
by
Brady
et
to al.
[20,21].
Program HYDEBE
is based upon a rigid block DE code
elastic BE formulation
[22].
This program was extended at CSIRO to include a
model for fully bonded passive rock reinforcement
The
more
deformations difference to
zones,
represent
handle
powerful
within
program
a
the
behaviour
at
or dynamic
the joints between the blocks. roof collapse and surface
method
Dutton,
pillar
recovery
of
[ 2 4 ] can
element
by
model
elastic
discretising
different
between
blocks.
loading of a blocky
interfaces
system,
it
and
plastic
into
finite
The
program
can
and fluid flow in
It is currently being used at CSIRO to analyse
subsidence
and A.J.
of
effects
UDEC
distinct
[23].
as well as employing a variety of joint constitutive models
quasi-static
Coulthard
and an anisotropie
induced by underground coal mining
to be published; with
a
mining
Figure 7);
suspended
sequences
reinforced
on
stope
(M.A.
the undercut-and-fill concrete
stability;
mat;
the
and
the
reinforcement of a coal mine roof by point-anchored bolts.
STABILITY ANALYSIS
3-D Rock Block Stability
A
new
method
three-dimenslonal, by
intersecting
program BLOCKS dimensional blocks;
was
joints ([25],
block
developed
at
CSIRO
for
assessing
the
stability
rigid rock blocks with an arbitrary number of faces, near
[26]).
structure
an
excavation.
This
method
is
of
formed
incorporated
in
The program can reconstruct the hidden threearound
a complex
excavation;
eliminate
selected
and analyse the stability against sliding of individual surface
93
I
I_ L L I L L I I J J
L
I
I
I
]
I
1
I
I
]
I
I
I
[
FIGURE 7. Preliminary analysis distinct e l e m e n t p r o g r a m UDEC. blocks, hidden
display package,
J
I
l
I
]
I
L
I
I
I
]
[27]
has
of complex
Warburton's
recently action
roof caving,
formulation
this
also
theory
with
views, with graphical
if desired.
work
simulate
paper
of block
as calculated
Detailed perspective
extended
The
I
the help of an auxiliary
to better
blocks.
]
I
]
J
I
[
I
I
~
I
L
I
L
l
I
of coal mine
can be obtained with
of keystone-llke
support
between
[
I
and internal sections can be displayed
Warburton
bolt
I
J
using a limiting equilibrium method. line removal,
concept
1
by
developing
one of the modes clarifies
the
a
new
of rock
relationship
and an alternative
developed
by Goodman and Shl [28].
SARAT (Structural And Reinforcement
A set of programs structural block
geology
stability
as
Analysis Toolkit)
is being developed
in
the
vicinity
a
function
of
of
to assist engineers
a proposed
excavation
design support
and reinforcement
to stabilise
wedges.
package
a
The
orientations
includes
and to plot stereonet
curves for various reinforcement processor program
for
support
the
BLOCKS;
polyhedral
program
wedges,
displacements
and
using and
forces.
for
the
joint
orientation
block
static
process
nonlinear
SARAT
and
field
location,
data
on
the rock and rock
joint
a data base of load-displacement embedment
definition analysis
of
to
stability
2-D
triangular
calculate
is a menu-driven
lengths;
and
load-displacement
interactions,
examine
two- and three-dimensional
to
types and different
three-dimenslonal
and programs
systems,
contours;
to analyse
excavation,
a pre-
analysis and
3-D
characteristics
of
wedge
package
with
and
support
spreadsheet
94 type
of
input,
microcomputers
which
is
designed
for
use
on
(S.M. Matthews and A.G. Thompson,
IBM
PC
or
compatible
to be published).
FLUID FLOW IN FRACTURED AND POROUS MEDIA
There are various problems that involve the simultaneous water in coal. dangerous address
phenomenon these
of
outbursts
problems
the
in
finite
active
the flow of gas and water
in coal
[29]).
This
(Implicit
code
model outbursts version
uses
and accounts [30],
an
IMPES
for
the unusual
code
coal
GASFLOW
was
(an early version Pressure,
ability
To
written
to
is reported
in
Explicit
of coal
mines.
Saturation)
to adsorb
gas.
To
the output from GASFLOW was used as input to a modified
of the FE stress
had a capacity
underground
difference
simulate
formulation
flow of gas and
These include the storage of gas in disused coal mines and the
analysis
to treat body
program NTJTEP2.
forces
of arbitrary
This version magnitude
of NTJTEP2
and direction
in
each element.
Regional subsidence due to ground water withdrawal at surface brown coal mines
has
nonlinear
been
simulated
consolidation
using [31].
a one-dimensional The
associated
also been applied to explain the observed heave occurring
near
the
impoundment
regional
subsidence.
Future
difference program,
model
COMPAC,
in the midst have
movements
been
of has
of the land surface which
of surface water ground
finite
computer
is
of the ongoing predicted
as
a
function of time and different postulated water pressure scenarios.
OTHER COMPUTATIONAL MODELLING WORK
Ground Vibrations Due to Blasting
Limitation
of
blast
vibrations
to
meet
statutory
increasingly important issue in mining practice.
requirements
is
an
Measured vibration levels at
a site are influenced by the weight and type of explosive used in each delay, the delay
time sequence,
random scatter
the wave passes through the rock mass, free
surfaces,
Dynamic due
and
resonances
that
may be
FE analyses were used recently
to a single
blasthole
firing,
from seismic attenuation models
in delay
and
initiations,
energy
loss as
interaction of the blast wavefront with induced
by
the blast
vibrations.
[32] to study free surface vibrations the results
combined with
information
in a Monte Carlo simulation of ground surface
vibrations from a large-scale blast.
95 Reinforcement
of Rock Joints
Program of
grouted
various with
SHEAR is a static relaxation
or
point
combinations
FE
or
reinforced
DE
anchored
with
of axial and/or shear forces.
codes
for
discontinuity
laboratory pull-out
code for modelling
reinforcement
the in
modelling rock.
of
a
rock
of
rock
preliminary
and shear tests on fully cement-grouted
are shown in Figure 8 (S.K. Choi,
subjected
to
The program can be coupled
reinforced
Examples
the interaction
Joints
mass
or
any
modelling
of
7-wire superstrand
to be published).
TRANSFER OF TECHNOLOGY TO INDUSTRY
Any user of complex
computer
programs
faced with the problem of interpretation results
that may be produced.
display
deformations
can greatly use
assist
they
preparation contours,
stress
have and
checking,
Development
so.
Many
programs.
A further
Benchmark
enable
it
which
plotting
which
of
can
areas of yield,
in industry
design,
interfaces
and post-processing
figures
computational
is
are to
imperative
simplify
displaced
data
meshes,
in
this
paper
programs
has been
given a
work over the last five years have
aspect of the task of facilitating in
industry
on mini-computers,
analyses
programs
been
prepared
with
these
of
simple
on a range
has
been
personal
finite of mini
the application
conversion computers
element,
of
of CSIRO's
codes
to
run
and graphics workstations.
boundary
and personal
the
element
computers
were
and
distinct
reported
in
These have recently been extended to include Sun workstations.
Finally, have
the
mine
is
terminal or hard copy device.
of such pre-
programs
interactively
[34].
then
programs,
or highlight
If engineers
in routine
above
They are listed in the Appendix and in [33].
computer
element
and
in the Division's of
users.
user-friendly
etc. on a graphics
strong emphasis or
analysis
available
described
quantity of numerical
post-processing
within a mesh,
even experienced
computational
that
Graphical
and stresses
such as those
of the enormous
been
CSIRO's
several stress analysis programs
modified
Cyber 205
that machine.
to
take
advantage
supercomputer,
of
the
and are being
(BITEMJ, vast
BEFE, ADINA and UDEC)
computational
released
for bureau
power
of
usage
on
96
100
~
60
..,,,j
~
40
2O 0
,
I
0
D
10
I
20
.90
I
~
40
50
AXIAL OISPLACEPIENT(mm)
22O 180 lz~O ~
100
so 2O I
0
I
I
10 ZO 30
I
I
40
50
I
60
I
70
,I
80
SHEAR DISPLA EENENT(rom) FIGURE 8. Comparison of computational modelling of fully grout reinforcement with laboratory experiments. Laboratory results calculations: X
97 TRENDS IN FUTURE RESEARCH AT CSIRO
In the next few years, Geomechanics available
computational
interfaces engineer,
much of the research
will be concentrated
on
modelling
graphics
who
programs.
workstations
usually
has
efforts
on the application
little
will
In
be
particular,
developed
computer
to be used much more widely,
of
user-frlendly
which
training,
reliably and obtain quick answers which are displayed will enable the models
of the Division
to mine design of already
to
allow
operate
in graphical
a mining
the
models
form.
This
with great benefits
to the
mining industry through improved mine design.
Several will
be
Industries input
substantial
sponsored
by
Research
Another, conditions",
as
of Australia.
MINLAY,
design
aspects
requirements
for longwall
two mine
be
developed
for
generation
Mineral graphical
of two- and
coal mine layout design for Australian
of
BEFE
analysis
roadway
Energy Research Development
This project will coordinate
FESOFT,
and
Geomechanlcs
least
will
In one, which
(Australian
boundary element and finite element meshes.
Council
for
in 1988.
AMIRA
and the automatic
will be supported by the National
such
workstation
through
software
geometries
on "Rational underground
Demonstration programs
will be commencing
companies
Association),
of mine excavation
three-dlmenslonal
projects
mining
of
and
UDEC
layouts
performance,
for
on
a
for underground
pillar
faces will be addressed.
sites will be used to validate
use
stability,
stand-alone coal and
mines. support
Detailed monitoring
the package
and
and enhance
of at
for application
in
Australian mines.
In results
addition
to
of previous
development
the
above
research,
of computational
work
to
assist
transfer
to
industry
of
the
there
is still more work to be done on further
models.
Some of the tasks which will be tackled
in the next year or two are:
*
a more
efficient
modelling
of joints
and
faults
in
three
dimensions,
with the boundary element method; *
dynamic modelling of blasting effects;
*
assessment
of methods
for modelling
changes
in rock mass
permeability
due to coal mining under and near surface water storage reservoirs; *
integration
of more realistic modelling of the effects of ground support
into stress analysis programs.
98 CONCLUSIONS
CSIRO
has
a
substantial,
active
modelling for mining geomechanics. developed
and
enhanced
to
research
programme
in
numerical
Various computational techniques are being
provide
the
means
for
efficient
and
effective
solution of many different problems that must be faced by the mining industry. User-friendly
interfaces
to
programs,
menu-driven
and
using
graphics,
are
being designed to facilitate the application of the programs by mine planning engineers.
ACKNOWLEDGEMENTS
The authors wish to acknowledge the cooperation of their colleagues Dane Blair, Xavier Choi, Mary Duncan Fama, Don Helm, Russell MacKinnon, Ken McNabb, Lincoln
Paterson,
Bruce
Perkins,
Janice
Crotty
Sisson,
Alan
Thompson,
Rob
Walton, Peter Warburton and Leigh Wardle in preparing this paper.
Development of several of the computer programs described above has been supported by Australian mining companies, often through collaborative, projects between
CSIRO
and
the
Australian
Mineral
Industries
Research
Association
Limited (AMIRA).
The CSIRO
by
original Professor
Massachusetts made
version
available
respectively,
Herbert
Institute by both
of
CAVERN
Einstein,
of Technology.
Itasca of
program
Consulting
Minneapolis,
was
kindly
Department Programs
Group
under
Inc.
of
made
available
Civil
to
Engineering,
FLAC
and BESOL/MS221
were
and
Crouch
Inc.
collaborative
Research
research
agreements
with CSIRO.
REFERENCES
i.
Chang, C.-Y. and Nair, K. Development and application of theoretical methods for evaluating stability of openings in rock. Report to U.S. Bureau of Mines on C o n t r a c t No. HO 220038, NTIS Report AD-773 861 (1973).
2.
Coulthard, M.A. Plane strain nonlinear finite element program NTJTEP2 - Modifications and corrections for use in mining geomechanics. CSIRO Division of Applied Geomechanlcs, Technical Report No. 129, (1982).
99 3.
Coulthard, M.A., Crotty, J.M. and FabJanczyk, M.W. Comparison of field measurements and numerical analyses of a major fault in a mine pillar. Proc. 5th Int. Contr. on Rock Mech.. Melbourne (1983), pp. D53-D60.
4.
Bathe, K.-J. ADINA - A finite element program for automatic dynamic incremental nonlinear analysis. Report No. 82448-1, Mechanical Engineering Department, Massachusetts Institute of Technology, (1975, revised 1978).
5.
Blair, D.P. Acoustic pulse transmission in half-spaces and finite-length cylindrical rods. GeoDhvs. 50, (1985) 1676-83.
6.
Duncan Fama, M.E. and Wardle, L.J. Numerical analysis of coal mine chain pillar stability. Proc. 6th Int. Congress on Rock Mech.. Montreal (1987), 859-863.
7.
Crotty, J.M. User's manual for program BITEMJ - Two dimensional stress analysis for piecewise homogeneous solids with structural discontinuities. CSlRO Division of Geomechanics, Geomechanics Computer Program No. 5, revision 3 (1987).
8.
Crotty, J.M. and Wardle, L.J. Boundary integral analysis of piecewise homogeneous media with structural discontinuities. Int. J. Rock Mech, Min, Sci, & Geomech, Abstr, 22, (1985) 419-27.
9.
Crotty, J.M. and Brady, B.H.G. Boundary element analysis of excavations in sparsely jointed rock. Int. J. Numer, Anal, Methods Geomech. (submitted for publication).
I0. Ushijima, R.S. A finite element / boundary element procedure for multiple step static analysis of three-dlmenslonal underground structures. Civil Engineer thesis, Massachusetts Institute of Technology (1983). ii. Ushijima, R.S. and Einstein, H.H. Application of three-dimensional coupled finite element - boundary element method. Proc. ASCE Convention. "Rock masses: modeling of underground openings/ probability of slope failure/ fracture of intact rock", ed. C.H. Dowding, Colorado (1985), pp. 21-37. 12. Wardle, L.J. Boundary element methods for stress analysis of tabular excavations. Ph.D. Thesis, Department of Mining and Metallurgical Engineering, University of Queensland (1987). 13. Wardle, L.J. and McNabb, K.E. Comparison between predicted and measured stresses in an underground coal mine. Proc, 26th U,S, SvmD. on Rock Mech.. Rapid City, South Dakota (1985) pp. 531-538.
100 14. Crouch Research Inc. The BESOL system : Part II. Three dimensional programs user guide, Version 1.15. Minneapolis, Minnesota (1986). 15. Itasca Consulting Group, Inc. FLAC: Fast Lagrangian Analysis of Continua (version 2.00). Minneapolis, Minnesota (1987). 16. Beer, G. Implementation of combined boundary element - finite element analysis with applications in geomechanics. Chapter 7 in "Developments in Boundary Element Methods - 4" (P.K. Banerjee. ed.), Elsevier Appl. Science (1986). 17. Beer, G. BEFE - Coupled boundary element - finite element computer program. Structural Analysis Systems, Niku-Lari ed., Pergamon Press, Paris (1985). 18. Beer, G. and Swoboda, G. Application of advanced boundary element and coupled methods in geomechanics. IUTAM Symposium of Advanced Boundary Element Methods, San Antonio, Texas. Applications in Solid and Fluid Mechanics. Springer Verlag, Berlin (1987). 19. Beer, G. Application of the 3-D boundary element and coupled analysis in geomechanics: Case studies. Keynote lecture, 6th ICONMIG, Innsbruck, 11-15 April (1988). 20. Lorig, L.J., Brady, B.H.G. and Cundall, P.A. Hybrid distinct element - boundary element analysis of jointed media. Int. J. Rock Mech. Min, Sci. & Geomech. Abstr, 23, (1986) 303-12. 21
Lemos, J.V. and Brady, B.H.G. Stress distribution in a jointed and fractured medium. Proc. 24th U.S. SvmD. on Rock Mech., College Station, Texas (1983) pp. 53-9.
22
Lorig, L.J. and Choi, S.K. HYDEBE - User's manual (Hybrid distinct element - boundary element code, CSIRO version 1.0). CSIRO Division of Geomechanics, Geomechanics Computer Program No. 7, (1986).
23
Lorig, L.J. A simple numerical representation of fully bonded passive rock reinforcement for hard rocks. Comput. and G e o ~ c h , i, (1985) 79-97.
24. Itasca Consulting Group, Inc. UDEC : Universal distinct element code (version ICG 1.2). Minneapolis, Minnesota (1987). 25. Warburton, P.M. User's guide to program BLOCKS: Reconstruction of blocky rock geometry and analysis of single block stability. CSIRO Division of Geomechanics, Geomechanics Computer Program No. 6, (1985).
101 26. Warburton, P.M. A computer program for reconstructing blocky rock geometry and analysing single block stability. Comuuters & Geosclences, ll, (1985) 707-12. 27. Warburton, P.M. Implications of keystone action for rock bolt support and block theory. Int. J. Rock Mech. Mln. S c l . & Geomech. Abstr. 24, (1987) 283-290. 28. Goodman, R.E. and Shl, G. Block theory and its application to rock engineering. Prentlce-Hall, Englewood Cliffs, New Jersey (1985). 29. Schlanger, H.P. and Paterson, L. Computation of pressure profiles relevant to outbursting in coal mines. Int. J . Numer. Anal. Methods Geomech. ll, (1987) 171-83. 30. Paterson, L. A model for outbursts in coal. Int. J. Rock Mech. Min. S c l . & Geomech. Abstr. 23, (1986) 327-32. 31. Helm, D.C. Prediction of subsidence due to groundwater withdrawal in the Latrobe Valley, Australia. Proc, 6th Int. Congr. on Rock Mech., Montreal (1987),pp. 125-9. 32. Blair, D.P. The measurement, modelling and control of ground vibrations due to blasting. Proc. 2nd Int. Svmu. Rock Fra~mentatlon and Blasting. Keystone, Colorado (1987). 33. Coulthard, M.A. and Perkins, B.R. (compilers) Computer Program Abstracts - April 1987, 4th edition. CSIRO Division of Geomechanics, Technical Report No. 99, (1987). 34. Coulthard, M.A. and MacKinnon, R.H. Stress analysis for rock mechanics on personal computers - performance oJ several programs. CSIRO Division of Geomechanics, Technical Report No. 143, (1987).
I O2 APPENDIX - Summary of CSIRO computer programs for mining geomechanics (Those marked with a were originally developed elsewhere; most have been substantially modified at CSIRO)
PROGRAM NAME (a)
TECHNIQUE
AREA OF APPLICABILITY
COMPUTER TYPES
Stress analysis
BEFE*
BE-FE
2D, 3D, nonlinear materials, static, excavation sequences
mainframe, vector processor (PC pre and post-processing)
BITEMJ
BE
2D, elastic rock, nonlinear joints
mini, mainframe, vector processor
MINLAY
DD
3D, layered anisotropic rock, yielding pillars
mini, PC
FESOFT
FE
2D, post-yield weakening
mini
UDEC*
DE-BE
2D, fully deformable or yielding blocks, slip & separation on joints, excavation sequences
mini, mainframe
ADINA*
FE
2D, 3D, material & geometric nonlinearities, static or dynamic loads, excavation sequences
mainframe, vector processor
CAVERN*
BE
3D, elastic isotropic rock, coupling to structural finite elements
mini, mainframe, vector processor
NTJTEP2*
FE
2D, nonlinear rock and joints, static, excavation sequences
mini, PC
BLOCKS
3D, generates block structure defined by joints, limiting equilibrium analysis of arbitrary-shaped blocks
mini, PC
SARAT
2D, 3D, analysis of support requirements for rock blocks
PC
ID nonlinear consolidation for vertically heterogeneous material
mini, PC
(b)
(c)
Stability analysis
Fluid Flow
COMPAC*
103 (d)
Pre- and Post-Processing Graphics Software
MESHP
GKS or Plotl0
Interactive generation of 2D finite element meshes
mini, PC
FEVEC
GKS
Graphical display of 2D FE meshes, displacements and stress vectors
mini, PC
CONTOUR
GKS
Line or colour fill contouring of 2D FE results, or other data on triangular or quadrilateral grid
mini, PC
BEPP
GKS, Plotl0 or HP-AGP
Graphical display of 2D BE meshes, displacements and stress vectors (designed for use with BITEMJ)
mini, PC
Most of the programs listed above are available for purchase from the Computel Program Librarian, CSIRO Division of Geomechanlcs, P.O. Box 54, Mount Waverley, Victoria 3149, Australia.
RESEARCH
AT
CSIRO
ON NUMERICAL
MODELLING
FOR MINING
GEOMECHANICS
M.A. Coulthard CSIRO Division of Geomechanlcs, P.O. Box 54, Mount Waverley, Victoria 3149, Australia and G. Beer CSIRO Division of Geomechanics, Private Bag 3, Indooroopilly, Queensland 4068, Australia
ABSTRACT The Division of Geomechanlcs CSIRO, has an extensive research programme involving the development and verification of computer programs for modelling in mining geomechanlcs. The scope of the Division's work is outlined, the various numerical techniques being developed are described and some applications of the programs are illustrated. Ongoing efforts to make the programs more accessible to mine design engineers, and plans for future research, are discussed. INTRODUCTION
CSIRO Research
and
will
generally. interact about
Commonwealth
Organlsatlon
government, which
the
Each
- receives
charged
benefit
with
30%
is
of the
funding
and by commerclallsatlon
The
role
of the
most the
in
thirty
Australia) of
Australia
funding
or
or so Divisions
"client
group"
by undertaking
Division
its
from
of
the within
collaborative
work
in
- in metalliferous clvil
and
offshore
Industrial
the
Australian
performing
CSIRO
research community
is required
and to obtain or contract
research,
is
to conduct
research
and control of the behavlour
activities
take place.
is becoming
that
of rock
At present,
the
of geomechanics
or coal mines, both surface and underground engineering
to
up to
advances.
bulk of the Division's work is associated with the application in mining
and
Australian
in industry
of Geomechanlcs
for prediction
in which engineering
Scientific
responsibility
of its technological
will improve our capacity and soll masses
with
industry
an appropriate
of its
(of
increasingly
- but
important.
81
Computers and Geotechnics 0266-352X/88/S03'50 © 1988 Elsevier Applied Science Publishers Ltd, England. Printed in Great Britain
82 The more fundamental
research at the Division has potential
application
in all
these areas of engineering. Research
activities
at the Division
include fundamental
theoretical
studies of rock fracture and of joint mechanics
development
of computational
and/or
weak
stresses
of
and
the performance
marketing
of
of rock
computer
of excavations
measuring
studies
and
objective
at operating
at
the
of
this
paper
modelling
Division,
philosophy
discussed.
hybrid
Stress
and
is
to
to Australian
programs,
for stability
industry
the
capabilities
which
are
being
to
outline
some
our
methods,
discontinuity,
are
work
of
covered
in the
fluid
flow
the direction
is outlined.
in porous
their
the
of
the
developed
or
applications
to
post-processors
are
and
programs
summarised
in
first,
computational finite
difference,
following
section,
element,
then
media
and then
modelling
distinct
are described.
fractured
of future research
The different
in
including
finite
analysis and rock reinforcement
for modelling
hardware
of
through
describe
techniques
underlying
analysis
displacement
Finally,
means
produced
at specific mine sites.
general
element,
mass
by
also
The types of problem that are being tackled are outlined the
induced
rock
and
techniques
to transfer
and
of
mechanisms
industry,
programs
in jointed
pre-mining
field
reinforcement
with
the Division endeavours
computational
enhanced
for
large-scale
and
it has developed.
The
problems
and
collaboration
instruments,
CSIRO research, technology
its
for analysis
instruments
deformations;
Through
various
and
and
behaviour mines.
media
techniques
experimental
in the laboratory;
is
boundary
element
techniques
and used
Various programs
are
described
next.
in computational
modelling
at CSIRO
and their associated
graphical
pre-
types
computer
an
Appendix,
and
and software on which each is operational
the
of
and
are indicated.
GEOMECHANICS PROBLEMS FACED BY THE AUSTRALIAN MINING INDUSTRY
There
are
encountered
in
computational
many mining,
sections,
efficiency,
restricted
access
and
modelling
subsequent
need
different
to
a
most
of
which
techniques.
of
geomechanics
we
are
As
will
computer
in scope.
library
diversity of problems
for
types
seeking be
programs
A design engineer
different
that must be faced.
programs
problem
to
develop
discussed
are,
for
in
that
are
effective detail
simplicity
in and
in industry will therefore to be
able
to
tackle
the
83 Research
at
the Division
of Geomechanics
reflects
our
commitment
to
study problems which are of the greatest current or potential concern to the mining industry in Australia.
These include:
Under~round Metal Mininff: stope design,
including stability of walls and pillars and effects of
major structural features and/or highly jointed rock; rock support and reinforcement; use of mine fill; blast vibration mlnimisation.
Surface Metal Mining: slope design, including structural geology and rock block stability; rock support and reinforcement; blast vibration minimlsation.
Underground Coal Mining; design of longwall and other mining layouts; stability of pillars, including post-yleld weakening; face support requirements in the vicinity of caving roof strata; effects of induced subsidence on surface improvements such as dams; gas outbursts; storage of gas in disused mines.
Surface Coal Mining; stability of high walls and spoil piles; surface subsidence due to withdrawal of ground water.
PHILOSOPHY F O R N U M E R I C A L MODELLING
The
computational
potentially,
very
methods
powerful
which
tools
for
are
described
improving
our
in
this
paper
understanding
are,
of
the
mechanics of the complex systems with which we must deal in geomeehanics, and for assisting the practising mining engineer to design safe and economical excavations.
There are five broad stages along the route from theoretical
conception of a computational technique to its application by design engineers in industry:
i.
Mathematical
analysis
of
a
conceptual
includes the relevant physical principles.
model
of
the
system,
which
84 2.
Coding and testing of techniques
for numerical
solution
of the resulting
equations.
3.
Verification against
of
simple
the
computer
program
test
problems
which
with other computational
4.
5.
Validation
of
the
model
by
with laboratory
Development
of
analysed
solutions
or
semi-analytically
or
detailed
comparison
of
the
results
of
and field measurements.
a user-friendly
interactive
are
analytical
methods.
calculations
including
against
interface
graphics
to
the main
for preparation
program,
usually
of input data and display
of results.
The process some
iteration
measurements
of development
around these
require
refinement
details of the physics
This
paper
concentrates
of
the
of
constitutive
theoretical
their computer coding,
on the
to which
best suited and illustrating
program will usually
as discrepancies
that must be included,
the types of design problem
Details
of a particular
stages,
models,
later
stages
the use of different
of the process,
computer
underlying
stress analysis,
and the
outlining are
at CSIRO.
programs,
and of
cited below.
or adapted to handle the
into three general
stability
of
techniques
programs
specific
can be obtained from the references
listed above may be grouped
discussed next:
reassessment
computational
The computer programs which have been developed problems
involve
calculations
and so on.
the various
formulation
between
analysis,
categories,
which are
and fluid flow.
STRESS ANALYSIS
Numerical induced
methods
displacements
and soil masses.
distinct
discretization
are
stresses
now
widely
resulting
used from
for
of more
effective
and more
efficient
predicting
excavations
the
in rock
in this field
numerical
techniques
such problems.
Differential (FE),
analysis total
One of the major tasks facing research workers
is the development for analysing
of
and
methods
element
of
(DE)
stress and
analysis,
finite
of the entire problem domain
such
difference
as
the
(FD)
finite
element
methods,
require
into a mesh of elements.
The true
85 boundary
conditions
at
infinity
must
be
approximated
by
imposition
of
(somewhat arbitrary) displacements and/or stresses around the periphery of the mesh.
The strength of these methods
constitutive tensile
behaviour
yielding
shear zones,
of
within
geologic
is their ability to model
materials.
a continuum,
and
can be represented by FEs;
displacements other hand,
For
instance,
the behaviour
slip,
the complex shear
of major
and/or
faults
in blocky systems can be modelled with the DE method. integral techniques
or
separation and large relative
such as the boundary element
On the
(BE) method can
accurately treat the infinite or semi-inflnite geometries which usually apply in
geomechanics,
and
only
require
discretization
of
the
boundaries
excavations or of material zones - within the problem domain. is
most
efficient
for
linearly
elastic
behaviour.
of
The BE method
The
displacement
discontinuity (DD) method is a special case of BE methods, and is designed for analysis of tabular excavations such as in underground coal mining.
Hybrid
programs
have
been
developed
recently
to
complementary advantages of these different methods.
capitalise
Usually,
on
the
a differential
method of analysis is used to model nonlinear behaviour which is loealised in the near field, such as in the immediate vicinity of an excavation.
Boundary
elements may be coupled to the periphery of the FE or DE region to represent the essentially
elastic
continuum
far-field rock behaviour
and the boundary
conditions at infinity.
Each developed programs
of at
these the
will
different
Division
be
numerical
techniques
of Geomechanics,
available
which
can
be
so used
is
that to
a
being
studied
library
analyse
of
and
computer
efficiently
the
stresses in any type of geomechanieal system.
Finite Element Method
The
FE
method
is
the
most
widely
analysis of stresses in complex systems. subject
has
been
based
upon
programs
used
computer-based
technique
for
Much of the Division's work on the originally
developed
in
the
United
States, which have since been modified and adapted for our use.
A two-dlmenslonal,
plane
the U.S. Bureau of Mines.
strain program NTJTEP2
[i] was developed
for
It includes a rock material model which allows for
yielding in shear, via a Drucker-Prager yield criterion and an associated flow rule,
or
modelling
in
tension.
major
rock
A
Goodman-type
faults.
joint
Modifications
element made
is also
available
at CSIRO have
for
included a
86 simple
post-yield
weakening
model and generalisation stresses
[2].
behaviour
of
This a
enhancement
of
the
elasto-plastic
bulk
material
of the joint model and of the imposition of initial
program
faulted
mine
has
been
pillar
used
[3]
to
and
the
model,
for
stability
instance,
of
the
exposures
of
cemented mine fill. The finite element program ADINA can treat
two-
or
material models and with CSIRO
analyses
static
and of
[4] is a general-purpose
systems,
with
or geometric nonlinearities,
in studies
of mining
three-dimensional
or
dynamic
loadings.
in studies
geometric
"birth"
It has
of acoustic methods
been
of assessing
of ground vibrations
attenuation
of
a wide
package which
range
of nonlinear
and "death"
of elements,
used most rock mass
extensively
conditions
induced by blasting.
acoustic
pulses
[5]
have
at
ahead
Dynamic
enabled
more
accurate estimation of material attenuation of pulses radiated from a surfacemounted acoustic
source.
The work on ground vibrations
is outlined
later in
this paper.
More
recently,
a
two-dimensional
finite
element
program,
been developed with the aim of modelling yield zones in weak rock, coal.
Strain
novel
softening
constitutive
theories yield
of plasticity
zone
of the yielded
equation
which
(M.E.
growth predicted
falls
Duncan by
the
geologic within
Fama, strain
materials the
in preparation). model
has
especially
is modelled via a
framework
softening
FESOFT,
of deformation The
substantial
is illustrated
in
Figure i [6]. RESIDUAL STRENGTH <
.......
PEAK STRE~TH
ELASTIC
3O
20
n~
1~
,o
;
;METRES
o
\
o
,o
~o
METRES
FIGURE i. Comparison of elastic and nonlinear solutions in a 25 m coal pillar between simulated longwall panels. The stress distributions from mid-pillar to rib are shown on the left, and stresses in the panel flank are on the right, o v and a h are the vertical and horizontal stresses respectively [6].
87 Boundary Element Method
The program BITEMJ systems
containing
structural discussed method
([7],
regions
discontinuities
[8]) can model two-dimensional
with
in the introduction
is much
simpler
different
represented
than
by
to this for
elastic
properties,
Goodman-type
section,
excavations
joint
and
the FE method.
This,
with
elements.
data preparation
in
As
for the BE
and other
relative
advantages and disadvantages of BE and FE analyses of a faulted rock pillar, are discussed further in [3]. being
A range of verification studies with BITEMJ is
reported by Crotty and Brady
([9]
and Figure 2),
and the program has
been applied to back analysis of movement on a fault which caused a seismic event at the Mt. BITEMJ
is
Australia, has
Charlotte Mine,
installed
on
mini
Western Australia
computers
at
a
(M.F.
number
of
Lee,
unpublished).
mine
sites
around
and is being used by geotechnical consultants for mine design.
also been modified
to take advantage
of the vector processing
It
power of
CSIRO's Cyber 205 supercomputer.
A
three-dimensional
program,
CAVERN
[i0,
ii],
is
presently
being
modified extensively at the Division, with the ultimate objective of producing a program
equivalent
in capabilities
to BITEMJ.
The
original
program was
developed at M.I.T., as a hybrid BE-FE code, with finite elements to represent structural
features
such as tunnel linings.
Restriction of the code to BE-
only analysis of underground excavations, and reformulation of the calculation of stresses and displacements
at interior points,
have greatly increased its
accuracy and computational efficiency (J.M. Sisson, in preparation;
Figure 3).
It is now being applied in analyses of multiple stoping configurations.
Displacement Discontinuity Method
The DD method is ideally suited to modelling planar excavations, are
encountered
mining. of
in the mining
Program MINLAY
planar
excavations
anisotropic
elastic
of
tabular
orebodies
from
in
a
rock
properties.
measurements
analyses of
pillar
such as
in underground
coal
[12] can perform three-dimensional DD stress analyses mass The
composed
program
behaviour of material in the excavation plane, Results
or
with
MINLAY
stresses
have and
can
of
parallel
also
layers
represent
with
nonlinear
such as pillars or caved rock.
been surface
compared
satisfactorily
subsidence
longwall coal mining [13]; some are illustrated in Figure 4.
associated
with with
88 2.0~ '
stress
1.0 ~--
T
scare
_ _ _ _
0-0-
~
- I . 0 ~-
I
-2-0~
[ 0.0
I 1-0
-J 2-0
Xl/a FIGURE 2. Results of BITEMJ analysis of a tunnel intersected by a strength plane of weakness - tangential stresses in the tunnel face [9].
0.6 0.0 ~
spherical cavity in a uniaxial stress field
~
=
~
_..
._
.: ....... :
.....
m.
-0+6 -1.2.
~
low-
.,i---'--'-4
"
-1.8 -2.41.0
1.5
2.0
2.5
distance from centre of cavity (r/a)
I T
analytical CAVERN loaded axis CAVERN equatorial plane 1
FIGURE 3. V e r i f i c a t i o n isoparametric elements field.
•
CAVERNequatorial plane 2 I
IIllI
analysis using m o d i f i e d v e r s i o n of CAVERN - six 9-node over surface of spherical cavity in uniaxial stress
89
B
LI I
o
~12
AVERAGE STRESSMETER RESULTS
NUMEREALMODEL: - - - m - - LAYEREDANISOTROPIE (SEALED) 13 ,, ,~ {UNSEALED) @ ISOTROPIE(SEALED) O ,, {UNSCALED)
7 6
11
m / I
#/ U ~ I0
-~5
i [
i/ °
,/"1,,<
/ ~3-
.
o
2
o
°n ......
10
l
i IN
9o8 ~m
i
7<
I
6'-
_J
/
1°
1-A
i
I
I
30
20
10
AI
3.6
0
METRES FIGURE 4. Measured stresses calculated with program MINLAY
MSPOSTA -
¢OntOWP
dO6 TITLE : M S ~ t A ~ R
plot
ahead [13].
Of
of
cl08uP6
F'==~=RE'~SON ~
5
a
longwall
face
(OZ)
5
/
/1~---J
/--J
with
those
~.m.~,,~
P " ~ L A R PROBLEM- 3014 SEAM SEP. Window
I I
compared
I
L I
Mining
3 Step N u m b e c :
Number:
l
LEGEND -
-
M%nlng G e o m l t r y
0 0.005 0.01 O.Ot3 0.02 0.025
0.03 0.035 0.04 0.045
FIGURE 5. Analysis of rib pillar at Renison Bell tin mine with program BESOL/MS221. Contours of excavation closure in the vicinity of the monitored pillar area. Elements are 4 m square and the pillar is approximately 12 m by 160 m in plan.
90 The
program
BESOL/MS221
[ 1 4 ] can
which may be
folded or faulted,
earth.
host
The
material.
Walton,
mass
excavations
is
treated
as
a
in multiple
at the surface
uniform
elastic
seams of the
anisotropic
This program has recently been applied in a study of mining in two
orebody horizons
being
rock
model
and which may outcrop
at Renison
to be published) compared
with
Bell
tin mine
in Tasmania
(K.E.
McNabb
and R.J.
with calculated pillar stresses and rock deformations
field
measurements.
Some
results
from
that
study
are
shown in Figure 5.
Finite Difference Method
Program FLAC
[15]
is a two-dimensional
explicit
finite
which can model both material and geometric nonlinearities. at
the
Division
underground models
coal
at
present
mining.
to reproduce
to
analyse
In particular,
surface the
the observed variation
difference
subsidence
ability
of
code
It is being used induced
different
by
material
of subsidence with panel width
being studied (M.A. Coulthard & A.J. Dutton,
is
to be published).
Hybrid Boundary Element - Finite Element Method
A combination the
analysis
regional finite
of
complex
nonlinear elements
virtually
of BE and FE meshes mining
material
which
infinite,
excavations.
behaviour,
are
coupled
elastic
is used by program BEFE
to
rock mass.
together with
allows
support
elements
combination
for
consideration
and ground
boundary This
gives the user the best of both worlds, BE analysis,
BEFE
jointing
[16,17]
of
by using
representing of the
the
two methods
i.e. the reduced data requirements of
the viability
of the FE method
in dealing with a
Cyber 205 supercomputer
and is accessible
nonlinear rock mass.
Program BEFE runs on CSIRO's
through the Australia-wide CSIRONET network. mine planning
feasibility studies,
BEFE is currently being used for
for mine design and for "trouble shooting"
exercises to pinpoint problem areas in difficult mining situations.
An example of a coupled BEFE analysis mesh
has
mass
near
boundary which
is
been the
cut
open
to reveal
excavation
elements assumed
and
surrounding to
be
the the
elastic.
the
is shown in Figure 6(a) where the
finite
geometry FE mesh Note
elements of
the
represent that
"artificial" boundary conditions have to be used,
in
representing
excavation the
this
infinite type
of
the
itself.
rock The
rock mass, analysis
in contrast to an analysis
no
91
/--BOUNDARY ELEMENTS /REPRESENTING iNFINITE
.,,jji j)fJiiiiiiijiJ iiiHifiiiii!ilJ iiiiiii!i
PLANES OF WEAKNESS
FINITEELEMENTS REPRESENTING THE "NEAR-F/ELD"ROCK SCALE: I
I
4.0rn
FIGURE 6(a). Cut out mesh for the analysis of a mine coupled finite element - boundary element program BEFE.
excavation
using
the
X IOE-3m
I ×
Y
l
0.4
-
0.8
0.3
-
0.4
~
o.~-o.~
~
o_o.~
0
3
metres m
Z
"
FIGURE 6(b). Results of analysis on a horizontal cross-section contours show the amount of dilation (m) on joint planes.
(A-A).
Filled
92 which uses finite elements only.
In this analysis the FE region was described
by a multi-laminate material model, with one set of planes results
from the analysis
are shown
in Figure 6(b),
of weakness.
which depicts
Some
the amount
of dilation on the planes of weakness in the rock mass on a horizontal section A-A.
Further examples are reported in [18] and [19].
Hybrid Distinct Element - Boundary Element Method
The distinct
element programs which
of highly jointed, developed by Dr. yield
a
more
discontinuous Peter
Cundall
efficient
are being used for stress
analysis
rock masses are derived from codes originally and co-workers.
hybrid
technique,
Coupling
was
carried
to a BE region,
out
by
Brady
et
to al.
[20,21].
Program HYDEBE
is based upon a rigid block DE code
elastic BE formulation
[22].
This program was extended at CSIRO to include a
model for fully bonded passive rock reinforcement
The
more
deformations difference to
zones,
represent
handle
powerful
within
program
a
the
behaviour
at
or dynamic
the joints between the blocks. roof collapse and surface
method
Dutton,
pillar
recovery
of
[ 2 4 ] can
element
by
model
elastic
discretising
different
between
blocks.
loading of a blocky
interfaces
system,
it
and
plastic
into
finite
The
program
can
and fluid flow in
It is currently being used at CSIRO to analyse
subsidence
and A.J.
of
effects
UDEC
distinct
[23].
as well as employing a variety of joint constitutive models
quasi-static
Coulthard
and an anisotropie
induced by underground coal mining
to be published; with
a
mining
Figure 7);
suspended
sequences
reinforced
on
stope
(M.A.
the undercut-and-fill concrete
stability;
mat;
the
and
the
reinforcement of a coal mine roof by point-anchored bolts.
STABILITY ANALYSIS
3-D Rock Block Stability
A
new
method
three-dimenslonal, by
intersecting
program BLOCKS dimensional blocks;
was
joints ([25],
block
developed
at
CSIRO
for
assessing
the
stability
rigid rock blocks with an arbitrary number of faces, near
[26]).
structure
an
excavation.
This
method
is
of
formed
incorporated
in
The program can reconstruct the hidden threearound
a complex
excavation;
eliminate
selected
and analyse the stability against sliding of individual surface
93
I
I_ L L I L L I I J J
L
I
I
I
]
I
1
I
I
]
I
I
I
[
FIGURE 7. Preliminary analysis distinct e l e m e n t p r o g r a m UDEC. blocks, hidden
display package,
J
I
l
I
]
I
L
I
I
I
]
[27]
has
of complex
Warburton's
recently action
roof caving,
formulation
this
also
theory
with
views, with graphical
if desired.
work
simulate
paper
of block
as calculated
Detailed perspective
extended
The
I
the help of an auxiliary
to better
blocks.
]
I
]
J
I
[
I
I
~
I
L
I
L
l
I
of coal mine
can be obtained with
of keystone-llke
support
between
[
I
and internal sections can be displayed
Warburton
bolt
I
J
using a limiting equilibrium method. line removal,
concept
1
by
developing
one of the modes clarifies
the
a
new
of rock
relationship
and an alternative
developed
by Goodman and Shl [28].
SARAT (Structural And Reinforcement
A set of programs structural block
geology
stability
as
Analysis Toolkit)
is being developed
in
the
vicinity
a
function
of
of
to assist engineers
a proposed
excavation
design support
and reinforcement
to stabilise
wedges.
package
a
The
orientations
includes
and to plot stereonet
curves for various reinforcement processor program
for
support
the
BLOCKS;
polyhedral
program
wedges,
displacements
and
using and
forces.
for
the
joint
orientation
block
static
process
nonlinear
SARAT
and
field
location,
data
on
the rock and rock
joint
a data base of load-displacement embedment
definition analysis
of
to
stability
2-D
triangular
calculate
is a menu-driven
lengths;
and
load-displacement
interactions,
examine
two- and three-dimensional
to
types and different
three-dimenslonal
and programs
systems,
contours;
to analyse
excavation,
a pre-
analysis and
3-D
characteristics
of
wedge
package
with
and
support
spreadsheet
94 type
of
input,
microcomputers
which
is
designed
for
use
on
(S.M. Matthews and A.G. Thompson,
IBM
PC
or
compatible
to be published).
FLUID FLOW IN FRACTURED AND POROUS MEDIA
There are various problems that involve the simultaneous water in coal. dangerous address
phenomenon these
of
outbursts
problems
the
in
finite
active
the flow of gas and water
in coal
[29]).
This
(Implicit
code
model outbursts version
uses
and accounts [30],
an
IMPES
for
the unusual
code
coal
GASFLOW
was
(an early version Pressure,
ability
To
written
to
is reported
in
Explicit
of coal
mines.
Saturation)
to adsorb
gas.
To
the output from GASFLOW was used as input to a modified
of the FE stress
had a capacity
underground
difference
simulate
formulation
flow of gas and
These include the storage of gas in disused coal mines and the
analysis
to treat body
program NTJTEP2.
forces
of arbitrary
This version magnitude
of NTJTEP2
and direction
in
each element.
Regional subsidence due to ground water withdrawal at surface brown coal mines
has
nonlinear
been
simulated
consolidation
using [31].
a one-dimensional The
associated
also been applied to explain the observed heave occurring
near
the
impoundment
regional
subsidence.
Future
difference program,
model
COMPAC,
in the midst have
movements
been
of has
of the land surface which
of surface water ground
finite
computer
is
of the ongoing predicted
as
a
function of time and different postulated water pressure scenarios.
OTHER COMPUTATIONAL MODELLING WORK
Ground Vibrations Due to Blasting
Limitation
of
blast
vibrations
to
meet
statutory
increasingly important issue in mining practice.
requirements
is
an
Measured vibration levels at
a site are influenced by the weight and type of explosive used in each delay, the delay
time sequence,
random scatter
the wave passes through the rock mass, free
surfaces,
Dynamic due
and
resonances
that
may be
FE analyses were used recently
to a single
blasthole
firing,
from seismic attenuation models
in delay
and
initiations,
energy
loss as
interaction of the blast wavefront with induced
by
the blast
vibrations.
[32] to study free surface vibrations the results
combined with
information
in a Monte Carlo simulation of ground surface
vibrations from a large-scale blast.
95 Reinforcement
of Rock Joints
Program of
grouted
various with
SHEAR is a static relaxation
or
point
combinations
FE
or
reinforced
DE
anchored
with
of axial and/or shear forces.
codes
for
discontinuity
laboratory pull-out
code for modelling
reinforcement
the in
modelling rock.
of
a
rock
of
rock
preliminary
and shear tests on fully cement-grouted
are shown in Figure 8 (S.K. Choi,
subjected
to
The program can be coupled
reinforced
Examples
the interaction
Joints
mass
or
any
modelling
of
7-wire superstrand
to be published).
TRANSFER OF TECHNOLOGY TO INDUSTRY
Any user of complex
computer
programs
faced with the problem of interpretation results
that may be produced.
display
deformations
can greatly use
assist
they
preparation contours,
stress
have and
checking,
Development
so.
Many
programs.
A further
Benchmark
enable
it
which
plotting
which
of
can
areas of yield,
in industry
design,
interfaces
and post-processing
figures
computational
is
are to
imperative
simplify
displaced
data
meshes,
in
this
paper
programs
has been
given a
work over the last five years have
aspect of the task of facilitating in
industry
on mini-computers,
analyses
programs
been
prepared
with
these
of
simple
on a range
has
been
personal
finite of mini
the application
conversion computers
element,
of
of CSIRO's
codes
to
run
and graphics workstations.
boundary
and personal
the
element
computers
were
and
distinct
reported
in
These have recently been extended to include Sun workstations.
Finally, have
the
mine
is
terminal or hard copy device.
of such pre-
programs
interactively
[34].
then
programs,
or highlight
If engineers
in routine
above
They are listed in the Appendix and in [33].
computer
element
and
in the Division's of
users.
user-friendly
etc. on a graphics
strong emphasis or
analysis
available
described
quantity of numerical
post-processing
within a mesh,
even experienced
computational
that
Graphical
and stresses
such as those
of the enormous
been
CSIRO's
several stress analysis programs
modified
Cyber 205
that machine.
to
take
advantage
supercomputer,
of
the
and are being
(BITEMJ, vast
BEFE, ADINA and UDEC)
computational
released
for bureau
power
of
usage
on
96
100
~
60
..,,,j
~
40
2O 0
,
I
0
D
10
I
20
.90
I
~
40
50
AXIAL OISPLACEPIENT(mm)
22O 180 lz~O ~
100
so 2O I
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SHEAR DISPLA EENENT(rom) FIGURE 8. Comparison of computational modelling of fully grout reinforcement with laboratory experiments. Laboratory results calculations: X
97 TRENDS IN FUTURE RESEARCH AT CSIRO
In the next few years, Geomechanics available
computational
interfaces engineer,
much of the research
will be concentrated
on
modelling
graphics
who
programs.
workstations
usually
has
efforts
on the application
little
will
In
be
particular,
developed
computer
to be used much more widely,
of
user-frlendly
which
training,
reliably and obtain quick answers which are displayed will enable the models
of the Division
to mine design of already
to
allow
operate
in graphical
a mining
the
models
form.
This
with great benefits
to the
mining industry through improved mine design.
Several will
be
Industries input
substantial
sponsored
by
Research
Another, conditions",
as
of Australia.
MINLAY,
design
aspects
requirements
for longwall
two mine
be
developed
for
generation
Mineral graphical
of two- and
coal mine layout design for Australian
of
BEFE
analysis
roadway
Energy Research Development
This project will coordinate
FESOFT,
and
Geomechanlcs
least
will
In one, which
(Australian
boundary element and finite element meshes.
Council
for
in 1988.
AMIRA
and the automatic
will be supported by the National
such
workstation
through
software
geometries
on "Rational underground
Demonstration programs
will be commencing
companies
Association),
of mine excavation
three-dlmenslonal
projects
mining
of
and
UDEC
layouts
performance,
for
on
a
for underground
pillar
faces will be addressed.
sites will be used to validate
use
stability,
stand-alone coal and
mines. support
Detailed monitoring
the package
and
and enhance
of at
for application
in
Australian mines.
In results
addition
to
of previous
development
the
above
research,
of computational
work
to
assist
transfer
to
industry
of
the
there
is still more work to be done on further
models.
Some of the tasks which will be tackled
in the next year or two are:
*
a more
efficient
modelling
of joints
and
faults
in
three
dimensions,
with the boundary element method; *
dynamic modelling of blasting effects;
*
assessment
of methods
for modelling
changes
in rock mass
permeability
due to coal mining under and near surface water storage reservoirs; *
integration
of more realistic modelling of the effects of ground support
into stress analysis programs.
98 CONCLUSIONS
CSIRO
has
a
substantial,
active
modelling for mining geomechanics. developed
and
enhanced
to
research
programme
in
numerical
Various computational techniques are being
provide
the
means
for
efficient
and
effective
solution of many different problems that must be faced by the mining industry. User-friendly
interfaces
to
programs,
menu-driven
and
using
graphics,
are
being designed to facilitate the application of the programs by mine planning engineers.
ACKNOWLEDGEMENTS
The authors wish to acknowledge the cooperation of their colleagues Dane Blair, Xavier Choi, Mary Duncan Fama, Don Helm, Russell MacKinnon, Ken McNabb, Lincoln
Paterson,
Bruce
Perkins,
Janice
Crotty
Sisson,
Alan
Thompson,
Rob
Walton, Peter Warburton and Leigh Wardle in preparing this paper.
Development of several of the computer programs described above has been supported by Australian mining companies, often through collaborative, projects between
CSIRO
and
the
Australian
Mineral
Industries
Research
Association
Limited (AMIRA).
The CSIRO
by
original Professor
Massachusetts made
version
available
respectively,
Herbert
Institute by both
of
CAVERN
Einstein,
of Technology.
Itasca of
program
Consulting
Minneapolis,
was
kindly
Department Programs
Group
under
Inc.
of
made
available
Civil
to
Engineering,
FLAC
and BESOL/MS221
were
and
Crouch
Inc.
collaborative
Research
research
agreements
with CSIRO.
REFERENCES
i.
Chang, C.-Y. and Nair, K. Development and application of theoretical methods for evaluating stability of openings in rock. Report to U.S. Bureau of Mines on C o n t r a c t No. HO 220038, NTIS Report AD-773 861 (1973).
2.
Coulthard, M.A. Plane strain nonlinear finite element program NTJTEP2 - Modifications and corrections for use in mining geomechanics. CSIRO Division of Applied Geomechanlcs, Technical Report No. 129, (1982).
99 3.
Coulthard, M.A., Crotty, J.M. and FabJanczyk, M.W. Comparison of field measurements and numerical analyses of a major fault in a mine pillar. Proc. 5th Int. Contr. on Rock Mech.. Melbourne (1983), pp. D53-D60.
4.
Bathe, K.-J. ADINA - A finite element program for automatic dynamic incremental nonlinear analysis. Report No. 82448-1, Mechanical Engineering Department, Massachusetts Institute of Technology, (1975, revised 1978).
5.
Blair, D.P. Acoustic pulse transmission in half-spaces and finite-length cylindrical rods. GeoDhvs. 50, (1985) 1676-83.
6.
Duncan Fama, M.E. and Wardle, L.J. Numerical analysis of coal mine chain pillar stability. Proc. 6th Int. Congress on Rock Mech.. Montreal (1987), 859-863.
7.
Crotty, J.M. User's manual for program BITEMJ - Two dimensional stress analysis for piecewise homogeneous solids with structural discontinuities. CSlRO Division of Geomechanics, Geomechanics Computer Program No. 5, revision 3 (1987).
8.
Crotty, J.M. and Wardle, L.J. Boundary integral analysis of piecewise homogeneous media with structural discontinuities. Int. J. Rock Mech, Min, Sci, & Geomech, Abstr, 22, (1985) 419-27.
9.
Crotty, J.M. and Brady, B.H.G. Boundary element analysis of excavations in sparsely jointed rock. Int. J. Numer, Anal, Methods Geomech. (submitted for publication).
I0. Ushijima, R.S. A finite element / boundary element procedure for multiple step static analysis of three-dlmenslonal underground structures. Civil Engineer thesis, Massachusetts Institute of Technology (1983). ii. Ushijima, R.S. and Einstein, H.H. Application of three-dimensional coupled finite element - boundary element method. Proc. ASCE Convention. "Rock masses: modeling of underground openings/ probability of slope failure/ fracture of intact rock", ed. C.H. Dowding, Colorado (1985), pp. 21-37. 12. Wardle, L.J. Boundary element methods for stress analysis of tabular excavations. Ph.D. Thesis, Department of Mining and Metallurgical Engineering, University of Queensland (1987). 13. Wardle, L.J. and McNabb, K.E. Comparison between predicted and measured stresses in an underground coal mine. Proc, 26th U,S, SvmD. on Rock Mech.. Rapid City, South Dakota (1985) pp. 531-538.
100 14. Crouch Research Inc. The BESOL system : Part II. Three dimensional programs user guide, Version 1.15. Minneapolis, Minnesota (1986). 15. Itasca Consulting Group, Inc. FLAC: Fast Lagrangian Analysis of Continua (version 2.00). Minneapolis, Minnesota (1987). 16. Beer, G. Implementation of combined boundary element - finite element analysis with applications in geomechanics. Chapter 7 in "Developments in Boundary Element Methods - 4" (P.K. Banerjee. ed.), Elsevier Appl. Science (1986). 17. Beer, G. BEFE - Coupled boundary element - finite element computer program. Structural Analysis Systems, Niku-Lari ed., Pergamon Press, Paris (1985). 18. Beer, G. and Swoboda, G. Application of advanced boundary element and coupled methods in geomechanics. IUTAM Symposium of Advanced Boundary Element Methods, San Antonio, Texas. Applications in Solid and Fluid Mechanics. Springer Verlag, Berlin (1987). 19. Beer, G. Application of the 3-D boundary element and coupled analysis in geomechanics: Case studies. Keynote lecture, 6th ICONMIG, Innsbruck, 11-15 April (1988). 20. Lorig, L.J., Brady, B.H.G. and Cundall, P.A. Hybrid distinct element - boundary element analysis of jointed media. Int. J. Rock Mech. Min, Sci. & Geomech. Abstr, 23, (1986) 303-12. 21
Lemos, J.V. and Brady, B.H.G. Stress distribution in a jointed and fractured medium. Proc. 24th U.S. SvmD. on Rock Mech., College Station, Texas (1983) pp. 53-9.
22
Lorig, L.J. and Choi, S.K. HYDEBE - User's manual (Hybrid distinct element - boundary element code, CSIRO version 1.0). CSIRO Division of Geomechanics, Geomechanics Computer Program No. 7, (1986).
23
Lorig, L.J. A simple numerical representation of fully bonded passive rock reinforcement for hard rocks. Comput. and G e o ~ c h , i, (1985) 79-97.
24. Itasca Consulting Group, Inc. UDEC : Universal distinct element code (version ICG 1.2). Minneapolis, Minnesota (1987). 25. Warburton, P.M. User's guide to program BLOCKS: Reconstruction of blocky rock geometry and analysis of single block stability. CSIRO Division of Geomechanics, Geomechanics Computer Program No. 6, (1985).
101 26. Warburton, P.M. A computer program for reconstructing blocky rock geometry and analysing single block stability. Comuuters & Geosclences, ll, (1985) 707-12. 27. Warburton, P.M. Implications of keystone action for rock bolt support and block theory. Int. J. Rock Mech. Mln. S c l . & Geomech. Abstr. 24, (1987) 283-290. 28. Goodman, R.E. and Shl, G. Block theory and its application to rock engineering. Prentlce-Hall, Englewood Cliffs, New Jersey (1985). 29. Schlanger, H.P. and Paterson, L. Computation of pressure profiles relevant to outbursting in coal mines. Int. J . Numer. Anal. Methods Geomech. ll, (1987) 171-83. 30. Paterson, L. A model for outbursts in coal. Int. J. Rock Mech. Min. S c l . & Geomech. Abstr. 23, (1986) 327-32. 31. Helm, D.C. Prediction of subsidence due to groundwater withdrawal in the Latrobe Valley, Australia. Proc, 6th Int. Congr. on Rock Mech., Montreal (1987),pp. 125-9. 32. Blair, D.P. The measurement, modelling and control of ground vibrations due to blasting. Proc. 2nd Int. Svmu. Rock Fra~mentatlon and Blasting. Keystone, Colorado (1987). 33. Coulthard, M.A. and Perkins, B.R. (compilers) Computer Program Abstracts - April 1987, 4th edition. CSIRO Division of Geomechanics, Technical Report No. 99, (1987). 34. Coulthard, M.A. and MacKinnon, R.H. Stress analysis for rock mechanics on personal computers - performance oJ several programs. CSIRO Division of Geomechanics, Technical Report No. 143, (1987).
I O2 APPENDIX - Summary of CSIRO computer programs for mining geomechanics (Those marked with a were originally developed elsewhere; most have been substantially modified at CSIRO)
PROGRAM NAME (a)
TECHNIQUE
AREA OF APPLICABILITY
COMPUTER TYPES
Stress analysis
BEFE*
BE-FE
2D, 3D, nonlinear materials, static, excavation sequences
mainframe, vector processor (PC pre and post-processing)
BITEMJ
BE
2D, elastic rock, nonlinear joints
mini, mainframe, vector processor
MINLAY
DD
3D, layered anisotropic rock, yielding pillars
mini, PC
FESOFT
FE
2D, post-yield weakening
mini
UDEC*
DE-BE
2D, fully deformable or yielding blocks, slip & separation on joints, excavation sequences
mini, mainframe
ADINA*
FE
2D, 3D, material & geometric nonlinearities, static or dynamic loads, excavation sequences
mainframe, vector processor
CAVERN*
BE
3D, elastic isotropic rock, coupling to structural finite elements
mini, mainframe, vector processor
NTJTEP2*
FE
2D, nonlinear rock and joints, static, excavation sequences
mini, PC
BLOCKS
3D, generates block structure defined by joints, limiting equilibrium analysis of arbitrary-shaped blocks
mini, PC
SARAT
2D, 3D, analysis of support requirements for rock blocks
PC
ID nonlinear consolidation for vertically heterogeneous material
mini, PC
(b)
(c)
Stability analysis
Fluid Flow
COMPAC*
103 (d)
Pre- and Post-Processing Graphics Software
MESHP
GKS or Plotl0
Interactive generation of 2D finite element meshes
mini, PC
FEVEC
GKS
Graphical display of 2D FE meshes, displacements and stress vectors
mini, PC
CONTOUR
GKS
Line or colour fill contouring of 2D FE results, or other data on triangular or quadrilateral grid
mini, PC
BEPP
GKS, Plotl0 or HP-AGP
Graphical display of 2D BE meshes, displacements and stress vectors (designed for use with BITEMJ)
mini, PC
Most of the programs listed above are available for purchase from the Computel Program Librarian, CSIRO Division of Geomechanlcs, P.O. Box 54, Mount Waverley, Victoria 3149, Australia.