1. Computer Aided Mine Design (Part I – Ultimate Pits) Mnge 315 ©Dr. B. C. Paul spring 2003

2. Computer Aided Mine Design Many surface mines (especially metal/industrial mineral) are designed with computer packages 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 Many more limited packages that do parts of design –Autocad and some of add-ons

3. Our Scope We are not going to learn a package 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 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

4. How Does Computer Aided Design Work First - geology of the mineralization is worked out 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 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)

5. How are Block Models Built Sampling programs obtain specimens of the mineralization and rock 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 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

6. The Building of Block Models Samples are analyzed for the key parameters that will determine the value of the mineralization 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 Computer then interpolates the sample data to a grid of blocks using Kriging

7. What is Kriging Basic idea is that a sample from near by is likely to be more similar than one that is distant 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 Distance Variance

8. 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) 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 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) (There is a “Geostatistics” Class available as one of your electives that will get down to detail)

9. At the End of the Day You have a series of blocks 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” 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)

10. Metal/Industrial Minerals Dilemma Coal and Quarry people had similar value in all pay material 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 Usually means avoid things that screw you up Metal/ Industrial Minerals 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 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 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

11. Using the Block Model You have a Geologic 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 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

12. Adapting Block Models for Mine Planning Geologic parameters of each block provide information on potential value of block 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 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 Obviously done by giving functions to the computer Result is called an Economic Block Model Result is called an Economic Block Model

13. Economic Block Models Economic Block Model assigns each block only one number Economic Block Model assigns each block only one number –The dollar value (or cost) of mining that block $

14. The Cut-Off Grade Issue Value of the mineral in the block is determined by the market 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 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” Need to Determine a “Cut-Off-Grade” –Only material above a certain grade is processed as ore

15. More Cut-Off Grade Issues May be more than one type of processing 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 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

16. Cut-Off Grades and Block Models In translating Geologic Block Model to Economic you have to determine COV before you can assign costs 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” Common COV is the “Break Even Cut-Off Grade” –Take cost of processing rock Calculate the minimum mineral content that will pay the cost Calculate the minimum mineral content that will pay the cost That is your break-even cut-off grade That is your break-even cut-off grade

17. What the ##@@!!* “Break-Even Stripping Ratio” determines the maximum OB that can be moved “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? How can you calculate a COV then? When Converting a Geologic to Economic Block Model determine each block value individually 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 What would you do with the block if it were right on the surface Other Routines will deal with the OB issue Other Routines will deal with the OB issue

18. The Surface Issue Classroom drawing have level surfaces Classroom drawing have level surfaces –Real life does not How do you deal with the shape of the surface? How do you deal with the shape of the surface? Air Blocks 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”

19. The Next Step We have an Economic Block Model We have an Economic Block Model –Millions of blocks with assigned dollar values The OB has negative values The OB has negative values The Air Blocks have zero 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 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

20. How Do You Do That? Simplest Method to explain called “Floating Cone Miner” Simplest Method to explain called “Floating Cone Miner” Computer begins examining the top blocks one at a time 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 Replace the block with an air block –It just cybermined a block of ore

21. Floating Cones Continue Often top level of blocks are nothing but air or overburden Often top level of blocks are nothing but air or overburden –Usually finds nothing Computer then examines next row down 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 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) (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 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 They were just cybermined

22. Whats Above Me? -$5.40 $0 -$5.50 $45 -$5.50 $0 -$5.50 This one – of course How About This? Can you really Mine straight up And down? 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.

23. Adding Things Up -$5.40 $0 -$5.50 $45 -$5.50 $0 -$5.50 $45 -$5.40 =$34.20 $34.20 > 0

24. Action -$5.40 $0 -$5.50 $0-$5.50 $0 -$5.50 Now we are ready to move on to the next block

25. Cone Angles Routines differ in how pit slope angles are handled Routines differ in how pit slope angles are handled Some use a single input put angle 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 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 These cone angles come out of your rock mechanics work on slope stability

26. What Happened to Working Slope? You may remember that need a certain amount of bench room for equipment to work 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 We are working on “Ultimate Pit” after every slope and ton of ore than can be mined has been mined

27. Routine Continues Computer moves down to the 3 rd level looking for positive value blocks Computer moves down to the 3 rd 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 Cybermines the whole thing if value is positive Moves on looking more if the cone comes up negative Moves on looking more if the cone comes up negative Computer keeps dropping one level after another till it is done Computer keeps dropping one level after another till it is done –“Ultimate Pit” is the set of Air Blocks in the model

28. Woops Factors -$5 $10-$5 $70-$5 $25 -$5 - -$15 + $10 = -$5

29. Working on Woops -$5 $10-$5 $70-$5 $25 -$5 -$40 + $70 = $30

30. Cybermining -$5 $0 -$5 $10$0 -$0-$5 $0-$5 $25 -$5 $0 Now the Cone Is Profitable 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.

31. Harder to Fix -$5 $25 -$5 $0 T This Pit is Not Profitable

32. Weaknesses of Floating Cones -$5 $25 -$5 $0 This Pit is Profitable Unfortunately Floating Cones will never see this Since they look at only one block at a time and Sometimes profitability requires looking at groups

33. Solutions Floating Cone Miners are in a class called Heuristic Routines 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 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) Requires fairly powerful computer (which we easily have today)

34. Choices and Limitations Learch Grossman includes some fairly restrictive assumption about uniform slopes 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 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 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 Bottle-Line - In the end you will have an ultimate pit that is somewhat close to the true optimum

35. Things Not Included Ultimate Pit generated by computer is generally a smooth walled thing 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 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