Planning Ore Extraction
Sequences in Open Pit Mines
©2012 Dr. B. C. Paul
Note – These slides contain screen shots from the program MineSight
developed by Mintec. Credit for the program is given to its developers. Also
note that these slides have been based on earlier work by the author and may
have content similar to training classes conducted by Mintec.
Maximizing Returns
• NPV is usually increased by bringing
more early earnings and delaying
expenses
• Sequencing pits for high grade ore with
lower stripping ratios tends to do this
• We Need A Method of Finding the Best
Grade Ore to Mine First
How to Make That Happen
• Method #1 - We try to Fake Out the Learch
Grossman Routine
• Lerch Grossman will Find the Juiciest set of ore
blocks that keeps producing more value
• Obviously this must mean that it either finds the
maximum metal pit or the most lucrative ore
• Because not all ore is equally easy to process it is
possible that a set other than maximum metal will be
selected
• We Need to Get Learch Grossman to Pick the
Best of the Best
To Do This We Perform What I
Call A Price Fake
• We tell the computer we have a dismal
market and then ask it to find the
ultimate pit
• Under unfavorable economics only the
better grade ore will get included in the
“fake ultimate pit”
• Learch Grossman however has picked us
the set of blocks that yields maximum
value per ton which is just what we wanted.
We Will Gradually Raise Our
Fake Price As We Do Multiple
Runs
• Each Run will start with the previous pit in place
• Each Run will have the real final pit surface as a
limiting surface
• The result will be a series of nested pits that go
from the best ore to ore of progressively lower
grade
• We have just tricked Learch Grossman into telling us
how to optimize our NPV by sequencing our mining
Terms in Open Pit Benches
Crest
Toe
Catch Bench
Berm
Toe to
Crest Slope
Over-all
Slope
Final Pits Slopes allow
Benches to be wide enough to
Catch rocks and accommodate
A berm. (This is often less than
Than 10 meters).
Geometry of a Working Bench
Shovel
Length
Truck
Truck Width
Shovel
Berm width
Back-up
Truck
Turning
radius
A bench big enough
To accommodate
Equipment working is
Much wider than one
Only intended to catch
Rolling rocks.
Impact of a Working Bench
Over-all
Slope
The over-all slope of the pit is drastically
Reduced if one must accommodate wide
Working benches.
The Pit Slope Problem
• Our Ultimate Pit Was Calculated at Our Final
Pit Slope
• A final pit slope has benches wide enough to catch
falling rock and allow for a road to get equipment
out.
• A bench 10 to 15 meters wide will usually catch
falling rock
• But that may be just barely enough for a truck to drive
forward if the bed drags the highwall and the tire runs
over the berm
• No room for maneuvering the truck for production.
• A Final Pit Slope cannot account for equipment in
operation.
Price-Faking A Learch-Grossman
is Easy, But at What Slope?
• A Final Pit Slope Can be 50-65o
(Depending on rock mechanics slope stability)
• A working Pit with all working benches
would likely have an over-all slope
under 20°
• How do we reconcile this?
Usual Open Pit Practice
• A less than 20° slope would cause the pit’s stripping
ratio to be very high – making the mining method
economically infeasible for a lot of ore
• Why does every bench have to be a working bench?
• Usually it doesn’t have to be
• Mines have enough working benches to allow ore blending
and to keep shovels enough apart to keep them from
“tripping over each other”
• Many open pits will have only 2 to 4 large shovels
• This suggests only about 3 to 6 working benches
• (One for each shovel and then some extra working places)
• If you can keep ore mixed well for the mill it requires less costly
road work if all the shovels work on one bench
Reconciling Factor 1
• Not all Benches have to be working
width
• This will often allow over-all slopes over
30°
• (Your very first initial pit probably does
not have very many benches so it may
really have a very low slope with almost
every bench being a working bench)
The Direction of Pit Advance
• If our 23rd bench is a working bench does it
have to be working width around the entire
pit?
• No
• A pit is 360° around – 2 to 4 shovels can’t move in
all those directions
• Digging out ore also digs out roadways – you don’t
want to be disrupting your roads everywhere at
the same time
• (Ok – you do if this is a conspiracy to make your short
term mine planning engineers have a nervous breakdown)
The Push-Back Reality
• Mines may focus mining on only one side of
the pit
• Starting at the top the widen benches in this
direction as the mine
• At the end of “Pushing Back” the side of the
pit in that direction they re-steepen the slopes
to keep move the advantages of a low
stripping ratio forward in time and make the
pit more economic.
Push-Backs and Pit Slopes
• Because push-backs open wider
benches from the top down and then
steepen over-all slopes at the end of a
push-back
• We may be able to take snap shots of
where the mine will be at the end of each
push-back
• Those pit slopes at the end of a push-back
may have about the final pit slope
A Potential Solution
• If we phase our mine advance in “Push
Backs” we may have about final slopes at the
end of each pushback
• Design your mining phases using a final pit slope
• (There may be cases where push-back
stages in a particular direction are not
practical)
• Your very first pit when you start the mine probably
will need all working benches in all directions
A Side Effect of the Push-Back
Solution
• Relying on Push-Backs allowed us to look at
our pit at final slope at the end of each phase
• But it also meant that the distance we “Pushed
Back” had to be big enough to accommodate our
working slopes during the mining that we don’t
see.
• Thus – to work a Push-Back must advance
the mine a minimum distance in a given
direction.
So How Far Would That Distance
Be?
• Suppose we have 10 meter wide catch benches.
• Next we layout the size of our trucks and shovels and
the amount of room they need to turn and manuver.
• Suppose from this we find a working bench needs to be 100
meters wide
• Then we find out that for ore blending reasons we
should have working benches on 3 levels
• To widen from 10 to 100 meters takes 90 meters extra
• We need this 90 meters extra 3 times
• 3X90 = 270 meters – our push back must be 270 meters
Well – After that Philosophy
Lesson We Are Ready to Get
Back to Price-Faking Our LearchGrossman
• Which Panels of Our MSOPIT program
will we change with “Fake Prices”
Of Course the Economics Panel
We Would Have to Change
Where We Stored Our Result
We Would Probably Change Our
Output Report Titles
Lets Think About What We Are
About Ready to do
• We will pick 3 panels where we will
change numbers
• We will fill out new numbers for say 12
price sets one at a time
• We will run our MSOPIT about 12 times
• Sitting there and watching for results
• Does This Sound Fun!
I Didn’t Think So – Lets Try
Another Way
We Will Get the Computer
To do our repetitive runs
Using something called a
Multi-Run
Start MineSight Compass
Pick the Options Tab
Under Multi-Run pick new
Then click on the open folder
Icon.
A Set Of Procedures to Run
Automatically is Called A Package
Your set of responses
Is called responses
We need to give both
A name
Ok – so much for my
Naming creativity
Next we need to
Identify procedures to
Run
Put your curser in the
Procedures box.
If You’ve Had Way to Much Time on Your
Hands you have the Procedure Name
Memorized.
If not position the multi-run window so
You can also see the compass
Procedures list
Then click on the compass procedure
And it appears in the multi-run
Window.
Now Click On Set-Up
We Will Assume You Already
Have Basic Input Because You
Already Got Your Open Pit
The trick of a multi-run is to enter variable names with incrementable numbers
Preceded by a question mark (note the ? Is different than the $ used in Excel)
When the multi-run operates the variable will be changed according to a list.
I Will of Course Vary Which Pit My
Incremental Pit Surface is Stored in.
I’ll Leave Audit Options Blank When
I Will Automatically Run Multiple
Times
I Will Not Save Fake Price
Results into the Block Model
But I will save each output
Report separately under a
Different number.
An Unusual Exit
After entering needed
Needed information and variable
Characters in the procedure
Panel
Click File
Then click Save and Exit
Multi-Run Setup
You Are Taken Directly to a Panel
Where Your Enter Your Variable
Values
My ?01 and ?03
Are fake copper
Prices
My ?02 is the fake
Molybdenum Price
?04 tells me which
Pit surface to send
The result to
?05 is the name of
The report extension
Enter the Values for My First Run
After smelting and refining charges copper bring 25 cents a pound and electrowon
Copper brings 35 cents. Moly in concentrate is 75 cents a pound. I will load my fake
Small pit into shell 27 and use an F1 for my report extension
Now Click Add value for my next run
After Entering the Values for 12
Runs I Return to Procedures
I Designate 12 runs and Enter My
Comment
In this case I only
Needed one
Procedure, but
Multi-runs can be
Used for sequences
Of different
Procedures.
I Will Next Save My Package and
Responses
This allows me to use the same sequence to do something in the same way each time
Or to come back and selectively edit for changes without having to redo from scratch.
I Click Run and the Multi-Run
Starts
This may take a
While so now I
Can go take a
Break instead
Of tediously
Re-running things
Again and again.
Looking at Our Price Sensitivity
Pits
Observation – Our Price Fake Method did indeed get us stage pits
The Push-Backs Don’t Look Very
Practical
Initial Pit Might Work
(except finish slope is too steep)
360 M
130 M
120 M
Remembering that a practical push-back distance is 90 to 270 meters
Depending on the number of active levels it appears that most slices
Are too thin to be push-backs
And That is One Heck of a Gap
In fact the tendency of price-fake pits to make huge jumps is called “The Gap”.
It is a common problem (and mathematically a feature of Learch-Grossman
Which defines solutions only at certain points)
The Gap
• Large jumps are impractical to schedule as a
push-back
• Learch-Grossman infact solves an altered
problem that only has solutions periodically
defined
• Thus you may raise the price and nothing
happens till the pit jumps.
• Lets try a floating cone and put smaller price
changes in the range where the jump occurs.
Check for Our Price Jump Point
50¢/lb Cu
45¢/lb Cu
65¢/lb Cu
Looks like we jumped between 50 and 65 cents
Well That Wasn’t What I Hoped
For
Initial Pit has 21° Slope
70M
62¢
55¢
65¢
110 M
50¢
58¢
We could mine the 50 cent pit top down, and 58 to 65 cents make a practical one
Active bench push-back
Here is Another Try
45¢
58¢
57¢
65¢
OH GIVE ME A BREAK – that gap is ridiculous
Some Realities About Price Fake
Gaps
45¢
57.3¢
57¢
65¢
We still have our gap. In a long term planning environment we have widely
Spaced drill holes. Our grade estimation variances or the market fluctuations from
A butterfly in Nepal stretching its wings are larger than our gap. The ability to get
Price fakes to completely define our mining sequence is an illusion.
Tools We Have For Getting A
Real Push-Back Plan
• We could always use the price shells and
then try to use our own guesses about
pushback direction to design pushbacks with
the Pit Expansion Tool
• We will ultimately have to do this but we can get
more guidance
• We could run that Floating Cone with
geometric and price constraints to get so
realistic push-back shells before we use the
pit expansion tool.
Enter the Multi-Pit Option
It’s a single radio button on the Design Strategy Panel.
As We Would Guess – We Now
Have to Fill Out an Extra
Geometric Constraints Panel
Practical Constraints
It wants to know about your
Production rate and
Pushback requirements
It wants to know either our
Yearly ore mining or total
Ore mining capacity
(ie – how much material
Can you move in a year)
Note – it is in Ktons –
Units of 1,000 tons
If you are really foggy
About your mining capacity
At this point – relax, this
Only becomes critical if you
Apply a discount rate in the
Here is an important constraint
We can impose a minimum
Tonnage or number of
Blocks in a push back
(this would eliminate some
Of those paper thin 10
Foot push-backs that could
Only be mined by the
Seven Dwarfs from Snow
White)
We can also control
Push-back width (sort of)
What Does Sort of Control PushBack Width Mean?
• The control is not direct
• What you actually control is how many new benches
the pit can go down in a push-back
• Of course this is useful of itself because sometimes a PriceFake only routine will try to open 15 new benches in a year.
Most operators would find that very hard to do.
• The indirect effect is that as one goes down they
usually have to push back at a certain slope – thus a
push down usually also implies a push-over distance.
• Remember this control works best along with
imposing a tonnage that must be mined in a pushback.
You Have a Direct Control on
Which Pit Shells will get
information and how many
phases will be planned.
This identifies the pit
shell Numbers to get
the Information.
You Can Control Pit Expansion
Direction
As a practical matter
Pushing back a pit in all
Directions at once is
Difficult – what would be
Happening to all those
Roads that carry material.
Note that here I can contro
Which parts of the block
Model are considered
In a push-back step.
Many times you can look at
Economic Shells and Decide Which
Way to Push.
Start
Push back 1
Push back 2
Push back 3
Push back 4
Push back 5
Then down to
The bottom.
Multi-Pit is not the only way to
control expansion direction
The first panel of
MSOPIT allows
Me to consider
Only part of the
Blocks in my
Block model
The thing unique
About Multi-Pit
Is I can control
This while at the
Same time
Imposing ore
Tonnage and push
Back distance
Requirements.
The Last Part of the Multi-Pit
Control Panel
Some of these
Just restate waste
Mining costs and ore
Densities found in
Other parts of the
Run (they can be
Over-ridden here for
Some fine tuning
Tricks)
Sometimes You Want to Impose
that no rock outside the “Ultimate
Pit” will be considered.
You can set the
Ultimate pit as
A surface where
No block outside
Will be considered
As ore to mine.
(just identify the
Shell that contains
Your ultimate pit)
But Wouldn’t I Always Use My
Ultimate Pit as a Limiting Surface?
• Often an ultimate pit is designed using the
mineral prices and operating costs believed
to be most likely
• If you let the multi-pit shells go out of
boundaries later routines can look for
conditions where you might get a little more
• If pits beyond the ultimate are not economically
feasible this will show up that mining the last few
phases may not be economic.
Minimum and Maximum Factors
Control How the Routine
Generates Pits
The values are set
Between 0 and 1
(unless you want
To generate pit
Shells outside your
“Base Case” Ultimate
Pit).
Who ever put in these
Factors needed help
1.5 is more than both
1 and the point 0.4
maximum
How Multi-Pit Avoids “the GAP”
with even tiny price changes
• Lets say the minimum is 0.1
• Multi-Pit looks at each column of blocks
in the block model and designates the
top 10% to be ore – all others are
treated as waste
Ultimate
Pit Line
(no ore
Outside
This
Boundary)
Ore blocks
(actually the top
10% of blocks)
Note that the Program has now
made a clear incremental step in
what is the best rock and what is
less
• The program then attempts to generate a pit
using only the top 10% for ore blocks
• After generating a pit it checks to see if
tonnage and pushback size constraints have
been made
• If yes it declares it found a pit phase advancement
and outputs the result.
If Not?
• The program then takes the top 20% of
blocks as ore (it moves in 10%
increments)
• It trys to generate a pit
• It checks the pits against the constraints
• If it meets the constraints it reports the pit
as the next phase
• If not it tries the top 30% of blocks.
So What Are Maximums More
Than 1?
• 1 is all the oreblocks that were
considered ore in the base “ultimate pit
case”
• 1.1 is the 10% of the blocks beyond that
• These blocks have to have their earnings
boosted by 10% to appear to be ore
• 1.2 is for a 20% boost appearing to be
ore
The Discount Rate Blank
This allows you to
Impose the time
Value of money
On your ore
Sequence planning
If I wanted a 15%
Discount rate I
Would input the
Number 15.
You Can Also Apply Discounting
By Time from another panel
What is Discounting?
• Using Engineering Economics
principles, money received later in time
is work less than money earlier in time
• The discount rate is the percentage of
value lost each year
• MineSight will consider your mining
rates and when certain ore is likely to be
mined and then lower the value of the
block accordingly
Why Would I Do This
• Sometimes when you calculate an ultimate pit
or stage pits you want to tell people very
quickly about what the Net Present Value of
the Pit is
• If you use the direct value of ore you will tell
people how much money will ultimately be
generated
• Discounting lets you approximate NPV before you
have a more complete mine design and cut-off
grade optimization strategy.
I Made A Nasty Remake About
Discounting Earlier
• What’s the Harm
• If you want a quick NPV estimate – nothing
• But if you are going to do a more detailed
design it will distort the results
• As I discount later mined ore I actually will cutback on ore I would strip to get
• Ore 20 years in the future has little NPV impact
today, but 20 years from now $50,000,000
dollars will be $50,000,000, I probably will not
just walk away
Putting Discounting into Blocks
Leads to Double Counting
• After we get our pit stages we will try
different mining rates and cut-off grades
to see what produces the best NPV
• If the blocks have NPV estimates built into
them on general assumptions it will
interfere with NPV accuracy when we
make more detailed assumptions.
Multi-Pit in MineSights most
Powerful Anti-Gap Tool
There are Other Choices
I Will Use the MultiV Option
The rest of the panels
Are set for ultimate pit.
I click the radio button
For MultiV instead of
Base.
For stage pits I’m also
Considering floating
Cone as good enough
For my approximation.
This Requires Me to Fill Out A
Special Panel to Control the
MultiV
Remember my file 13
Has a number of
Pit surfaces from 0 to
50 available. I have
To say which ones I
Want to fill.
I’m Trying for 21 Steps to Go in
Pits 10 to 30
The bench and block
Range allows us to limit
How much of the block
Model we run calculations
On. (We’re not going to
Do this. You would do it
If your block model
Covered a large area and
The ore was only in one
Area).
The value factors need some explanation.
How MultiV Works
• It calculates the value of each block at full metal
prices
• Then it multiplies the value of each positive block by the
minimum factor
• It then will run a floating cone to pick the pit it will mine
• Next time around it increments the factor one even
step up from the minimum value to the maximum
• It remultiplies the value of each positive block
• It runs a floating cone to pick the next pit surface
• And so on
• Of course a prices really change which blocks are even
positive will change
• This is a different way of trying to pick the most valuable ore.
I Will Let My Values Go From
Almost Nothing to Full Value
Lastly I will order the computer to make sure all my pits are nested
Inside my Lerch Grossman ultimate pit (which I have stored in pit
Surface 2).
Some Multi-V Observations
• Multi-V is really incrementing the value
of blocks
• This is similar to what we did by stepping
through metal prices with a multi-run (Of
course we know “the Gap” nailed us good when we did this)
• Multi-V does not recomputed the value of
blocks every time
• Instead it multiplies an already computed value
by a constant
• It’s kind of a cheap version of a multi-run
The Other Choices
• Multi-Z increments the depth of ore
considered
• Bottoms takes a series of “base strings” that
you entered – projects pits up from them and
then puts the pits in value order
• This can be useful if your orebody produces a
bunch of little pits instead of one big one
• Resources is not a pit design tool at all – it
just reports the ore content a value of an
already developed pit.
At the End of the Process We
Will Have a Series of Practical
Push-Backs
Where Do I Go From Here?
• I have two tools ahead
• MSVALP
• MSVALP lets me consider what mining rate will
give me the best NPV or PVR
• It also lets me consider that I can improve my NPV
and PVR by changing the cut-off grade with time
• MineSight Strategic Planner
• Calculates in detail where you will be pulling ore
from each year of operation
Completing a Long Term Mine
Plan
• By taking your stage pits and using MSVALP
for general optimization
• And then using MSSP to get a detailed plan
• You end up with a detailed year by year plan
of where you will mine and what it will be
worth in the end
• This plan then becomes the basis for day to day
operating decisions when the mine is actually built
Our Decision Now
• When do we use the pit expansion tool
and detail in our roads and benches for
these mining phases we created?
• We could do this before or after we run
MSVALP
• Since benches and roads alter slightly the
exact ore we mine if we do it now we feed
more detail to MSVALP
Decision Time
• On the Other Hand
• MSVALP assumes we will mine each
phase from the top down
• If it finds it needs to prestrip ore to keep the
amount of equipment we need steady it will just
assume it can be done without figuring where
the material will come from
• Since MSVALP is not really specific about
where the material it is mining comes from
– being real specific about roads might not
be important.
Some Educators Observations
• If you are doing a Sr. Design Project you have
a team
• There is a lot of CAD work to put in roads and
benches
• It is hard to have a lot of people working on different
phases at the same time
• This can mean a bunch of team members sitting idle
while the benches are done and then everyone hurrying
to make up for it.
• MSVALP will also be used to consider different mining
rates
• If one of those rate decisions changes your truck size that
could change the road width and ruin a lot of work
someone else has done.
Suggestion
• Break up the team
• Send someone to work on phase bench
and road designs (to be used later in
MSSP)
• Then have other team members use the
rough phases you have now to run the
mining rate and cut-off grade optimizations
of MSVALP
Assignment 1
• Using the File for Which You Did an
Open Pit design a minimum of 7
practical stage pits
• Your first should be a practical top down
initial pit.