With Variable Slope Angles

319 Pages·2012·48.71 MB·English

Computer-Aided Optimal Open Pit Design
With Variable Slope Angles
by
Reza Khalokakaie
B. Sc., M. Sc.
Submitted in accordance with the requirements for the degree of
Doctor Philosophy
of
Department Mining Mineral Engineering
of and
The University Leeds
of
1999
September
I
The is his
candidate confirms that the work submitted own and that appropriate credit
has been has been
to the
given where reference made work of others
In The
name ofAllah,
Most Gracious,
Most Merciful
To Zahra, daughter Negin,
my wife my
family
my parents and all my
for. their throughout
encouragement and support
.
have helped finishthis
these to
all years which me
research
1
Acknowledgements
First Allah
thanks to the the to
of all, grateful who gave me ability and patience complete
this
research.
I like deep
to thanks to
would express my gratitude and sincere my supervisors,
Professor P. A. Dowd Dr. R. J. Fowell, for their invaluable help,
and advice, support and
Without have been
throughout this them this
encouragement work. research would never
finished. The data for by Professor P. A. Dowd is highly
the
case studies provided also
appreciated.
I Dr. C. Xu for his in Dr., J.
to thank the
wish advice programming software and
Martin for his help.
Thanks are due to Miss C. McConnell, the secretary of the Department of Mining
Mineral Engineering, for her kind help during few
the
and past years.
Special due friends have
thanks to
are also my colleagues and who contributed
directly indirectly
to this
or study.
My thanks to Zahra, daughter Negin,
appreciation and sincere my wife my my
family for during
their these
parents and all my patience, support and encouragement all
years.
Finally I like to thank the Ministry Culture Higher Education of the
would of and
Islamic Republic IRAN for this the University
of research work and ý of
-sponsoring
Shahroud for funding
me.
11
Abstract,
The has increased large low deposits
to the
use of open pit mining extract and grade with
with
in demand for in
growth raw materials, with the advances mining technology and
and
depletion high Development
the
of grade readily accessible orebodies. and extraction
by is decades
this that
of minerals method a complex operation may extend over several
large investments. Before it is
the to
and require very starting operation, necessary
design final in determine
the the to
size and shape of pit order minable reserves and
be It is locate dump,
to to the
amount of waste removed. also needed waste processing
develop The limit depends
to
plant, access roads and a production program. ultimate pit
most
factors. One the important factors is the the
upon many of pit slopes which affect
be When dealing
stripping ratio and amounts of waste to removed. with complex
may
deposits in the in different the due to
which pit slopes vary parts of orebody slope
stability
requirements, it is to take into in the
necessary account variable pit slopes
designing limit.
the
of pit
pit
Determination the limit 'in is the ' important
of open pit mining one of most
design factors be during life
times the the the
which may considered many of mine as
design in future information is during
the the
parameters change or more obtained
of
Therefore use is in design
the to the
operation. a computer essential order pit as
As the
rapidly as possible. a result, a number of algorithms such as various versions of
flow
the Lerchs-Grossmann
moving cone method, algorithm, network or maximal
techniques, Korobov dynamic techniques
algorithm, programming and parameterization
have been developed determine limit
to the optimum ultimate pit since the advent and
The these is to determine the
wide spread use of computers. main objective of algorithms
limit in designed
optimum pit order to maximise the overall mining profit within the pit
limit
to the
subject mining constraints.
111
Abstract
Of these, the Lerchs-Grossmann is known for being the
algorithm well only
limit. However,
the true the
method which always yields optimum pit algorithm which
based fixed by block
theory that the
utilises graph was on slope angles are governed
dimensions it introduced. In the fact that have been
when was spite of many attempts
incorporate
to them
made variable slope angles, none of provide an adequate solution
by This
there
where are, variable slopes controlled complex structures and geology.
is deal It is
to
algorithm reconsidered and modified with variable slope angles. assumed
divided into domain
that the the
orebody and surrounding waste are regions or sectors
is by four
the the
within which rock characteristics are same and each region specified
including North, South, East West face
principal slope angles and slope angles.
Consequently deposit follow
through the to the
slope angles can vary rock characteristics
independent block dimensions. In
the two
and are of addition, methods were also
developed four from information
to the to
estimate principal slope angles geotechnical
as input in design
the
use parameters optimal pit, algorithm.
A general PC developed to determine the limit
software was also optimum pit
for The is Windows
with variable slope angles an open pit mine. software a application
be implemented 32-bit Windows 95, Windows
that'can
under operating systems such as.
NT Windows 98. It is taking the
and. capable of advantage of all computer memory and
designing the limit for large low deposits due to
optimum pit complex, and grade solving
limitation. The includes both
the memory software graphical and numerical presentation
input data Two have been
of the, and the results of optimisation. case studies used to
validate developed.
the
software
iv
Table Contents
of
Acknowledgements ii
........................................... ................................... ..........................
Abstract iii
......................................................................................................................
Tabled Contents
....................................................................................................... V
List Figures A
of
.............................................................................................................
List Tables
of xvii
...........................................................................................................
CHAPTER 1: Introduction 1
.....................................................................................
1.1- General background 1
...............................................................................................
1.2- The the 7
objective of research project
......................................................................
1.3- Organisation the thesis 8
of
.......................................................................................
CHAPTER 2: Literature 10
review and survey of previous work
..............................
10
2.1- Introduction
.........................................................................................................
2.2- Optimal design 10
open pit
.......................................................................................:
2.2.1- General introduction 10
..................................................................................
2.2.2- Graph 17
theory
..........:.....................................................................................
2.2.3- Network flow techniques 21
or maximal
.........................................................
2.2.4- Floating 22
or moving cone'method
............................................ ...............
2.2.5- The Korobov '...................................................................... 33
algorithm......:.
2.2.6- Dynamic 37
programming
............................................:..................................
2.2.7- Parameterisation 40
........................................................................................
2.2.8- Other
'... '..........: '.
methods
.....::.
2.3- Slope design in 44
open pit mining
............................................................................
44
2.3.1- Introduction'-,
Contents
2.3.2- Types failure 46
of
........:.................................................................................
2.3.3- Shear 49
strength
............................................................................................
2.3.4- Stereographic 51
projection
............................................................................
2.3.5- Limit 53
equilibrium
........................................................................................
55
2.3.6- Probabilistic
methods
.................................................................................
62
2.3.7- Numerical
methods
...................................................................................:
CHAPTER 3: The Lerch's-Grossmann
algorithm with variable slope
63
angles
...............................................................................................
63
3.1- Introduction
...........................................................................................................
64
3.2- Graph
theory
...:..........:..::..............................................................................:......
73
3.3- The Lerchs-Grossmann "::......
algorithm.......
......................................:..........:.........
74
3.3.1- A two-dimensional
example
................. ...........:.................................:........
83
3.4- Mining
and access constraints
.......::.......................................................................
89
3.5- The Lerchs-Grossmann
algorithm with variable slope angles
.................................
92
3.5.1- Variable
slope angles
...........................................................:......................
97
3.5.1.1- An
example
......................................................................................
101
3.5.2- Multiple
variable slope angles
....... ......................................................
110
3.5.2.1- An
example
....................................................................................
3.5.3- Programming
..............................
117
3.5.3.1- Memory
requirements
....................................................................
required for the angles
3.5.3.1.1- Memory
variable slope
118
algorithm
.....: ...........:............................
...................
for '
3.5.3.1.2- Memory the
required multiple variable slope
119
angles algorithm
...................................:............:....:::.........
3.5.3.2- Computing 119
time
................:........................:....................................
3.6- Revenue block 120
model :.......................................
...................................................
3.6.1- Adding blocks to the 125
additional waste model
............................................
3.6.2- Assigning to the blocks 127
slope angles
.........................................................
3.7- Pit bottom 130
smoothing
.........................................................................................
V1
Contents
3.8- Conclusion
135
..........:................................................................................:.............
CHAPTER 4: Slope design
137
procedure.
..............................................................
4.1- Introduction
137
.......................................................................................................
4.2- General information
138
............................................................................................
4.2.1- Orientation 'plane
138
of a
...............................................................................
4.2.2- Orientation line
139
of a
.................................................................................
4.2.3- Four
139
principal slope angles
.....................................:..................................
4.3- Design
140
procedure
..............................................................................:................
4.3.1- Steepest kinematic
141
safe angle with analysis
...............................................
4.3.1.1- Steepest to failure 141
safe angle with regard plane
............................:.
4.3.1'. 2- Steepest to failure 143
safe angle with regard wedge
............................
4.3.2- Design the limit 144
with equilibrium method.........
...................................:......
4.3.2.1- Identification failure 148
of potential mode
................................:..........
4.3.2.2- Calculation of factor safety 148
of
....................:..:..:.............:....:...:...::
4.3.2.2.1- Factor for failure 149
of safety plane
.................:.........................
4.3.2.2.2-
Factor for failure 152
of safety wedge
.........................................
4.3.2.2.3- Factor for failure...... 157
of safety circular
........:..:.......................
4.3.3- Probabilistic approach.......................................:.....:........:.......:............ 163
4.3.3.1--Random 164
number generators
:...:................................. -.................
....
4.3.3.2- Probability distribution 165
..............................................:...............:....
4.3.4- Factor probability failure 170
of safety or of versus slope angle
.......:....:.........
4.3.5- Determination slope 170
of angles
..................................: ..........
4.3.6- Modification slope angles to four 173
of principal angles
..... ............................
4.4- Data 176
required
............................................................. ..:......................:.::.............
4.5- Example 1 177
...................................:......................................................................
4.6- Example 2'.........................:......... 185
..................... ..............:.........:...................
4.7- Conclusion
194
.
............. ................................................................. .....................................
CHAPTER 5: ' The Software 196
..................................................................................
vii
Contents
196
5.1- Introduction
.:......................................................................................................
5.2- System 196
requirements
..........................................................................................
197
5.3- Structure
the
of software...........:
.................:.......................................................
5.3.1- Program PITWIN32. CPP.......................................................................... 197
197
5.3.1.1--Function
variable_ pit
....................................................................
197
5.3.1.2- Function
multiple_ pit
...:................................................................
198
5.3.2- Program PITWIN32. RC ...............
............................................................
198
5.3.3- Program PITWIN32. RH
..........................................................................
198
5.3.4- Program PITWIN32. DEF
.........................................................................
198
5.3.5- Program PITCLAS S. CPP
..........................................................................
198
5.3.6- Program PITCLASS. H
I
..............................
199
5.3.7- Program PITTOOL. CPP
..........................................................................
199
5.3.8- Program PITSLOPE. CPP
.........................................................................
199
5.3.9- Program PITFUNCT. CPP
....... ..................................... .........................
199
5.3.9.1- Function
variable revenue
:
..... ....... ................................................
199
5.3.9.2- Function ..............
multiple_revenue "................................................
200
5.3.9.3- Function
variable_pitbot
.................................................................
200
5.3.9.4- Function
multiple_pitbot
................................................................
201
5.4- An the'
overview of program
..............................................................................
203
5.4.1- The File Menu
.........................:................................................................
203
5.4.1.1- The New
command
.....:..................................................................
204
5.4.1.2- The Open
command
.............................................................
...........
204
5.4.1: 3- The Edit
command
.........................................................................
205
5.4.1.4- The Close
command
.....................................................
..................
205
5.4.1.5- The Print-command
. ...................................................................
205 205
5.4.1.6- The Print Setup
command
.................
205
5.4.1.7- The Exit
command
............................ ...................................... ........
5.4.2- The Slope Menu.,..
*
............................
5.4.2.1- The Geotechnical Data 206
command
...................................................
5.4.2.2- The Steepest Safe Angle 207
command
................................................
viii
Contents
5.4.2.3- The Kinematic Analysis 207
command
..................................................
5.4.2.4- The Design Slope 207
of command
.......................................................
5.4.2.5- The Result Slope Design Option 207
of
................................................
5.4.2.6- The Principal Slope Angles 208
command
............................................
208
5.4.3- The Run Menu
.........................................................................................
5.4.3.1- The Revenue Block Model 208
option
..................................................
209
5.4.3.2- The Optimum Pit Limit
option
.......................................................
210
5.4.3.3- it Bottom Smoothing
option
........................................................
210
5.4.4- The Graphical Display Menu
....................................................................
210
5.4.4.1- The Block Plot Surface Topography
of command
..........................
211
5.4.4.2- The Block Plot Grade Value
of command
...:......... ...............
211
5.4.4.3- The it Limit Without Smoothing
command
..................................
5.4.4.4- The Fasting Section Without Smoothing 211
command
........................
5.4.4.5- The Northing Section Without Smoothing 212
command
......................
212
5.4.4.6- The Pit Limit With Smoothing
command
.......................................
212
5.4.4.7-The Easting Section With Smoothing
command
.............................
212
5.4.4.8- The Northing Section With Smoothing
command
...........................
212
5.4.5- The Numerical Display Menu
...................................................................
213
5,4.5.1 The it Limit Without Smoothing
command
..................................
213
5.4.5.2- The Result Without Smoothing
command
......................................
214
5.4.5.3- The Pit Limit With Smoothing
command
.......................................
214
5.4.5.4- The Result With Smoothing
command
...........................................
214
5.4.6- The Tools Menu
......................................................................................
5.4.6.1- The Summary Block Model 215
command
of
.......................................
5.4.6.2- The Graphical Display Option 216
command
........................................
5.4.6.3- The Random Access File to Text 217
command
....................................
5.4.6.4- The Blocks Inside the Pit Limit 217
command
......................................
One 218
5.4.6.5- The Multi-Mineral Deposit to
command
.................................
5.4.6.6- The Change Vertical Co-ordinate 218
command.;
....::......:.....................
218
5.4.7- The Help Menu
........................................................................................
ix