Computer Aided Mine Design
(Part I – Ultimate Pits)
Mnge 315
©Dr. B. C. Paul spring 2003
Computer Aided Mine Design
• Many surface mines (especially
metal/industrial mineral) are designed
with computer packages
– Mintec Example
– Packages are comprehensive from exploration
to operation
• Many more limited packages that do parts
of design
– Autocad and some of add-ons
Our Scope
• We are not going to learn a package
– (They change anyway and companies have
specific preferences)
• We will look at what the basic steps are
and an overview of how they work
– Will be explained at a conceptual
understanding level
– Will not attempt to teach how to do or
program the calculations
How Does Computer Aided Design
Work
• First - geology of the mineralization is worked
out
– Exploration data working with geologists
– Really same step as traditional methods
• Second – The data is converted into a 3D block
model of the mineralization
– A crude model is 100 X 100 X 100 blocks (ie.
100,000) – detailed over 1,000,000
– Mineral character and other properties of each block
are assigned to the block (computers process as
array)
How are Block Models Built
• Sampling programs obtain specimens of
the mineralization and rock
– Often done with core drilling
• Geologic and preliminary exploration
normally identifies the structure and basic
mineral zones likely present
– Computer package is used to help determine
where to sample to obtain the most useful
information with the least expense
The Building of Block Models
• Samples are analyzed for the key
parameters that will determine the value
of the mineralization
– Put into a sample Data Base
• Computer then interpolates the sample
data to a grid of blocks using Kriging
What is Kriging
• Basic idea is that a sample from near by is
likely to be more similar than one that is
distant
– Kriging compares samples for their similarity
to each other at different distances
– The similarity as a function of distance is
plotted graphically as a “Semi-Variogram”
– A curve is fitted to the similarity as a function
of distance graph Variance
Distance
More Kriging
• The blocks of the block model are then “Kriged”
•
using the mathematical function fitted to the
“Semi-Variogram” (also called the Variogram by
people who don’t know better)
Block Values are assigned a weighted average of
the values of the samples around them
– Advance calculus techniques are used to give the
most weight to the samples most likely to be similar
as determined by the mathematical function fitted to
the “Semi-Variogram”
• (There is a “Geostatistics” Class available as one
of your electives that will get down to detail)
At the End of the Day
• You have a series of blocks
– Often separate rock formations are made
separate sets of blocks
• The blocks are each assigned geologic
parameters that define the value of the
“ore”
– For metal mines this will most likely be ore
grade (percentage of the rock that is the
mineral of interest)
Metal/Industrial Minerals Dilemma
• Coal and Quarry people had similar value in all pay
material
– Minable/ Non-Minable or get first is largely based on cheapest
material to get
• Usually means avoid things that screw you up
• Metal/ Industrial Minerals
– Mineral of interest is usually only part of the rock to be mined
– Disseminated deposits have no clear boundaries
• Grade of mineralization just decreases and fades out
• Result – Metals and Industrial Minerals usually need
multiple parameters in their block models to explain
what a block of ground really is
– Still quite doable with a computer today
Using the Block Model
• You have a Geologic Block Model
– Collections of blocks each assigned one or more geologic
parameters that define its economic value
• Computer Aided Packages today relay this information to
mining machinery
– Blocks are just cubes with imaginary boundaries
– Shovels get location of the “blocks” with satellite or radio relays
– Sensors on the digging motion help position the buckets to line
up and take controlled material from block model
– Keep track of what material is in each truck
– Data sent to the processing plant to help adjust the process to
exactly what has been taken
– Blocks are continuously updated and refined using data from drill
holes made for blasting
Adapting Block Models for Mine
Planning
• Geologic parameters of each block provide
information on potential value of block
– Also have an X, Y, Z coordinate location on the block
• Take the mining and processing costs
most likely for the type of mine you are
thinking about
– Estimate the $ value of each block
• Obviously done by giving functions to the computer
• Result is called an Economic Block Model
Economic Block Models
• Economic Block Model assigns each block
only one number
– The dollar value (or cost) of mining that block
$
The Cut-Off Grade Issue
• Value of the mineral in the block is determined
•
by the market
Cost of mining and processing a block is
determined by what is done with it
– It would cost more to grind a block to power and put
it through a flotation mill than to dump it.
– Decided on whether the extra expense of ore
treatment is recouped from the material
• Need to Determine a “Cut-Off-Grade”
– Only material above a certain grade is processed as
ore
More Cut-Off Grade Issues
• May be more than one type of processing
–
–
–
–
Cu ore can be ground and put through floatation
Cu ore can be leached in vats or piles
Cu ore can be dumped
May have more than one Cut-Off Grade
• Polymetallic deposits contain more than one
mineral of interest
– Lead Zinc and Silver often together
– Cut-Off may be based on sales value of several
minerals
Cut-Off Grades and Block Models
• In translating Geologic Block Model to
Economic you have to determine COV
before you can assign costs
• Common COV is the “Break Even Cut-Off
Grade”
– Take cost of processing rock
• Calculate the minimum mineral content that will
pay the cost
• That is your break-even cut-off grade
What the ##@@!!*
• “Break-Even Stripping Ratio” determines the
maximum OB that can be moved
– Cost to recover ore depends on OB
• How can you calculate a COV then?
• When Converting a Geologic to Economic Block
Model determine each block value individually
– Ie. Break-Even COV is based only on direct mining
and processing cost
• What would you do with the block if it were right on the
surface
• Other Routines will deal with the OB issue
The Surface Issue
• Classroom drawing have level surfaces
– Real life does not
• How do you deal with the shape of the
surface?
• Air Blocks
– Blocks located above the mine surface provide
no profit and have no cost to move
– Blocks are assigned zero value and called “Air
Blocks”
The Next Step
• We have an Economic Block Model
– Millions of blocks with assigned dollar values
• The OB has negative values
• The Air Blocks have zero values
• Computer Routines Will Examine the
Model to determine what the largest
profitable group of blocks is that can be
mined
– That group of blocks will define the “Ultimate
Pit” – how large the surface mine will become
How Do You Do That?
• Simplest Method to explain called
“Floating Cone Miner”
• Computer begins examining the top blocks
one at a time
– Looking for a block with a positive value
– If it finds a positive block it will move the
block to its “mined” blocks record
• Replace the block with an air block
– It just cybermined a block of ore
Floating Cones Continue
• Often top level of blocks are nothing but air or
overburden
– Usually finds nothing
• Computer then examines next row down
– Looks for a block with positive value
• If it finds a block it will look at the blocks above
– Blocks above are usually air or OB
• (because if it were ore it probably already got cybermined)
– Blocks above are added with the ore block
• If the added total is positive the computer puts all the
ore blocks in the ore mined column and all the OB blocks
in the OB column and replaced them with “air blocks in
the block model
• They were just cybermined
Whats Above Me?
How About This?
Can you really
Mine straight up
And down?
This one – of course
-$5.40
-$5.40
-$5.40
-$5.40
$0
$0
$0
-$5.50
-$5.50
-$5.50
$45
-$5.50
-$5.50
-$5.50
Computer is programmed with a “Cone Angle” – Tells it how to
Look at the blocks above and determine if they need to be mined
As you see this cone floating around on the model in search of minable ore begin
To understand why it is called a floating cone miner.
Adding Things Up
-$5.40
-$5.40
-$5.40
-$5.40
$0
$0
$0
-$5.50
-$5.50
-$5.50
$45
-$5.50
-$5.50
-$5.50
$45
-$5.40
-$5.40
=$34.20
$34.20 > 0
Action
-$5.40
-$5.40
$0
$0
$0
$0
$0
-$5.50
-$5.50
-$5.50
$0
-$5.50
-$5.50
-$5.50
Now we are ready to move on to the next block
Cone Angles
• Routines differ in how pit slope angles are handled
• Some use a single input put angle
– Go up with a cone
– Any block that gets hit or nicked is included in the calculation of
block group value
• Some routines keep a maximum slope in each block
– Ie they did not completely convert the geologic block model to
an economic block model
– They may allow partially mining a block
• These cone angles come out of your rock mechanics
work on slope stability
What Happened to Working Slope?
• You may remember that need a certain
amount of bench room for equipment to
work
– Usually made slope less steep than a final pit
slope based on geology
• We are working on “Ultimate Pit” after
every slope and ton of ore than can be
mined has been mined
Routine Continues
• Computer moves down to the 3rd level looking
for positive value blocks
– If it finds one it cones up to the surface and adds up
the value
• Cybermines the whole thing if value is positive
• Moves on looking more if the cone comes up negative
• Computer keeps dropping one level after
another till it is done
– “Ultimate Pit” is the set of Air Blocks in the model
Woops Factors
-
-$15 + $10 =
-$5
-$5
-$5
-$5
-$5
-$5
-$5
-$5
-$5
-$5
-$5
-$5
-$5
-$5
$10
-$5
-$5
-$5
-$5
-$5
-$5
$25
$25
-$5
-$5
-$5
$70
-$5
-$5
-$5
-$5
Working on Woops
-$40 + $70 =
$30
-$5
-$5
-$5
-$5
-$5
-$5
-$5
-$5
-$5
-$5
-$5
-$5
-$5
$10
-$5
-$5
-$5
-$5
-$5
-$5
$25
$25
-$5
-$5
-$5
$70
-$5
-$5
-$5
-$5
Cybermining
Now the Cone Is Profitable
-$5
-$5
-$5
$0
$0
$0
$0
$0
-$5
-$5
-$5
-$5
-$5
$10
$0
$0
-$0
-$5
-$5
-$5
$25
$25
-$5
-$5
-$5
$0
-$5
-$5
-$5
-$5
To catch situations like this, most floating cone
Miners will start searching from the top of the
Model every time they cybermine a cone to look
For ore on the edge.
Harder to Fix
This
T Pit is Not Profitable
-$5
-$5
-$5
-$5
$0
$0
$0
$0
$0
$0
-$5
-$5
-$5
-$5
-$5
-$5
-$5
$0
$0
$0
$0
-$5
-$5
-$5
-$5
-$5
$25
$25
-$5
-$5
-$5
$0
-$5
-$5
-$5
-$5
Weaknesses of Floating Cones
This Pit is Profitable
-$5
-$5
-$5
-$5
$0
$0
$0
$0
$0
$0
-$5
-$5
-$5
-$5
-$5
-$5
-$5
$0
$0
$0
$0
-$5
-$5
-$5
-$5
-$5
$25
$25
-$5
-$5
-$5
$0
-$5
-$5
-$5
-$5
Unfortunately Floating Cones will never see this
Since they look at only one block at a time and
Sometimes profitability requires looking at groups
Solutions
• Floating Cone Miners are in a class called
Heuristic Routines
– Based on a guess a plug approach
• Is an analytical solution called method of
convex-hulls
– Don’t ask about the math (you don’t want to know)
– Will cut through a block model and get the largest
block of ground that still keeps increasing profit
– Routine is called “Learch Grossman”
• Requires fairly powerful computer (which we easily have
today)
Choices and Limitations
• Learch Grossman includes some fairly restrictive
assumption about uniform slopes
– Real pit slopes that are stable may vary by direction
and rock type
• Heuristic Routines can handle lot of flexibility,
•
•
but are subject to errors
Whittle Programming has tried to impose of few
Heuristic variations on a true Learch Grossman
Bottle-Line - In the end you will have an
ultimate pit that is somewhat close to the true
optimum
Things Not Included
• Ultimate Pit generated by computer is generally
a smooth walled thing
– Ultimately you will have to deal with benches which
are added in as part of the human guided planning
• Usually not done at this time – ultimate pit is
what is left over when mining is done
– Stands to reason that most road and bench networks
are whats left over – not an end you worked toward