2. Computer Aided Mine Design Part II – Pit Sequences ©Dr. B. C. Paul 2000 ©Dr. B. C. Paul summer 2003

3. Next Step is to Determine the Extraction Sequence Principles of Profit 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 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 What you can say and what you can do may not be the same

4. Practical Technique #1 Start at top bench and work out to ultimate pit limit - then drop down to next 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 Most Quarries work this way - run a very steep side over finished benches - only run a few active benches at a time

5. Things Often True for Quarries Problem of surface stripping next to internal waste is minor 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 Most of the rock is production grade –No real advantage to deep ore over shallow No reason to try to get deep fast No reason to try to get deep fast Lowest cost rock is closest to surface Lowest cost rock is closest to surface Minimizing active work areas minimizes costs Minimizing active work areas minimizes costs

6. 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 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

7. Practical ? Technique #2 Start with a central shell and mine out in concentric shells 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 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 In practice work out at working slope to edge and go down only practical # of benches

8. Methods of Developing Open Pit Mining Sequences Eyeball Method 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 May make multiple guesses and then choose best push-back

9. 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 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 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 Just rough block model has 250,000 blocks - hard for humans to follow

10. Price Fake Method Computer ultimate pit algorithms give large pits for good price and small pits for low price Computer ultimate pit algorithms give large 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 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 Give your computer either inflated mining costs or fake low prices Computer will give a little rich pit Computer will give a little rich pit Give it better prices Give it better prices Computer develops a nested series of pits Computer develops a nested series of pits

11. Merits of Price Fake Method Method Produces a Series of Nice Nested pits - good outline of sequence 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 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 Relatively fast execution (unless your using a Learch Grossman on a large block model

12. 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 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 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 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 Need to deal with algorithms not really able to solve multiple slopes

13. More Problems Learch Grossman will only produce pits that have equivalents between real and transformed world 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 All methods do have humans put in most road and bench features

14. The Worst Is Yet to Come Makes a Difference Which Number You Lied about 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 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 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? Can try to change together but what ratio give you the real optimum?

15. A Solution Dr. Wang and Sevim Developed Floating Cone-Like algorithms that find maximum metal pits 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

16. 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 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 Problem with Geologic is Some Things Really are about Economics

17. Economic Realities in a Geologic World Most Deposits are poly-metalic (gold and copper are not of equal value) 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 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 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

18. More Cruel Realities Maximum Metal Pits assume the greatest profit comes from greatest metal 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 Ore is commonly much more expensive to handle and mine than waste

19. The Equal Cost Fallacy Example Two 50,000 ton pits contain 300 oz. of gold (say about $90,000 worth) Example Two 50,000 ton pits contain 300 oz. of gold (say about $90,000 worth) Waste costs $1/ton to handle Waste costs $1/ton to handle Ore costs $15/ton (has to be mined more carefully and then ground) Ore costs $15/ton (has to be mined more carefully and then ground) Pit A has 1 ton ore 49,999 tons waste 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 Pit B has 1,000 tons ore and 49,000 tons waste –Costs $64,000 to process

20. None Entirely Satisfactory Have an Ultimate Pit Have an Ultimate Pit Have a Series of Nested Pits that Push Back to Ultimate Slope Have a Series of Nested Pits that Push Back to Ultimate Slope Need to Reality Temper 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) (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

21. Building In Adjustments Computer pits don’t have benches or road plans Computer pits don’t have benches or road plans –Need to superimpose these in Yes do distort the theoretically perfect optimum sequence Yes do distort the theoretically perfect optimum sequence