Computer Aided Mine Design
Part II – Pit Sequences
©Dr. B. C. Paul 2000
©Dr. B. C. Paul summer 2003
Next Step is to Determine the
Extraction Sequence
• Principles of Profit
– Keep Costs Low and Earnings High
– Defer Costs as Long as Possible
– Get the Maximum Value Ore as Soon as Possible
• Things that cost money
– Stripping (put it off)
– Mining Deep Rock Costs more than mining shallow
– Each active mining area costs additional money to
have
• What you can say and what you can do may not
be the same
Practical Technique #1
• Start at top bench and work out to ultimate
pit limit - then drop down to next
– Can steepen to final slope when drop
because do all push back on level before
going to next
• Most Quarries work this way - run a very
steep side over finished benches - only
run a few active benches at a time
Things Often True for Quarries
• Problem of surface stripping next to internal
waste is minor
– Thus stripping across entire top has little impact
• Most of the rock is production grade
– No real advantage to deep ore over shallow
• No reason to try to get deep fast
• Lowest cost rock is closest to surface
• Minimizing active work areas minimizes costs
Doesn’t Work for Everyone
• Most ore bodies do not outcrop with
best ore at surface and get richer going
down at least for a distance
– Mining all one level first delays access to
profitable ore and maximizes early
stripping costs - the anti-thesis of NPV
maximization
Practical ? Technique #2
• Start with a central shell and mine out in
concentric shells
– Tends to dive on rich ore targets fastest
– Delay heavy stripping activities
• Problem is whole pit is active at same
time and trying to work down at a final
slope
• In practice work out at working slope to
edge and go down only practical # of
benches
Methods of Developing Open Pit
Mining Sequences
• Eyeball Method
– Look for rich low strip target within a practical
number of bench advances
– Move a manually controlled floating cone
miner and place it on the target
– Computer feeds out financial result
– Accept or reject plan
• May make multiple guesses and then
choose best push-back
Merits and De-Merits of Eyeball
Method
• Human control at every step ensures that
sequence will be tempered by practicality
(assuming you had smart humans)
• Human interaction steps limit execution
speed in alternative comparison and thus
number of alternatives
• Just rough block model has 250,000
blocks - hard for humans to follow
Price Fake Method
• Computer ultimate pit algorithms give large
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pits for good price and small pits for low price
Smaller pits are only the most favorable ore but for maximum NPV you want to mine best
stuff first
Give your computer either inflated mining
costs or fake low prices
Computer will give a little rich pit
Give it better prices
Computer develops a nested series of pits
Merits of Price Fake Method
• Method Produces a Series of Nice Nested
pits - good outline of sequence
• Uses the ultimate pit method and software
so don’t need special equipment
• Relatively fast execution (unless your
using a Learch Grossman on a large block
model
Problems of Price Fake
Method
• Nested Pit Structure can make you leave a lot
•
of active areas at considerable cost remember you already committed to costs
when you did the economic model - how does
it know what it does influences costs
Slope Problem
– Ultimate Pit is at a final slope
– Stage Pits must be at working slope
• May have to limit block model to ore falling in the ultimate
pit
• Need to deal with algorithms not really able to solve
multiple slopes
More Problems
• Learch Grossman will only produce pits
that have equivalents between real and
transformed world
– Can have large differences in pit size
– Long blind planning periods are called the Gap
• All methods do have humans put in most
road and bench features
The Worst Is Yet to Come
• Makes a Difference Which Number You
Lied about
• If you jack up your mining costs the
model will avoid high stripping ratios
even at the expense of high grade ore
• If you drop your price the model will
chase high grade ore with little regard to
stripping ratio
• Can try to change together but what
ratio give you the real optimum?
A Solution
• Dr. Wang and Sevim Developed Floating
Cone-Like algorithms that find maximum
metal pits
– Heuristic so can handle multiple slopes
– Could Target Maximum Metal Pits
Why Maximum Metal Cannot Cure
All Problems
• Problem with Economic Block Models is
they build in as yet unproven
characteristics of the mine to the cost
structure
– Maximum Metal attempts to Solve by working
only on geologic block model and delay
economics to other calculations
• Problem with Geologic is Some Things
Really are about Economics
Economic Realities in a Geologic
World
• Most Deposits are poly-metalic (gold and copper are not
of equal value)
– Solution is to try ratio but relative prices change
– Co-product and by-product recovery don’t usually receive equal
attention in real mills and concentrators
• Liberation Size Greatly influences processing costs
– Some high grade deposits are economically infeasible
– Liberation size is often a characteristic of rock type
• Lots of deposits have multiple mineralization phases and rock types
– Would have to build concentrator assumptions in to weight ore
grades and get a quasi-metal grade
More Cruel Realities
• Maximum Metal Pits assume the greatest
profit comes from greatest metal
– Quietly just assumed all rock is equal in
handling cost
• Ore is commonly much more expensive to handle
and mine than waste
The Equal Cost Fallacy
• Example Two 50,000 ton pits contain 300 oz. of
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gold (say about $90,000 worth)
Waste costs $1/ton to handle
Ore costs $15/ton (has to be mined more
carefully and then ground)
Pit A has 1 ton ore 49,999 tons waste
– Costs $50,013 to process
• Pit B has 1,000 tons ore and 49,000 tons waste
– Costs $64,000 to process
None Entirely Satisfactory
• Have an Ultimate Pit
• Have a Series of Nested Pits that Push Back to Ultimate
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Slope
Need to Reality Temper
– Hopefully your target increments had some relationship to likely
mining rates
• (May be nothing more than assuming ultimate Pit was mined out in
about 20 years)
– Watch Out for Increments that dive down more benches than
you can manage
– Watch Out for More Working Areas and Open areas than will be
practical for the approximate scale of operation
Building In Adjustments
• Computer pits don’t have benches or road
plans
– Need to superimpose these in
• Yes do distort the theoretically perfect optimum
sequence