Planning Surface MinesPlanning Surface MinesMnge 315Mnge 315

©Dr. B. C. Paul 2003©Dr. B. C. Paul 2003

Steps in PlanningSteps in Planning

• Determine what it is that you might mineDetermine what it is that you might mine– Explore for and define the limits of your Explore for and define the limits of your

depositdeposit•Geology Classes and working with Geologists will Geology Classes and working with Geologists will

help you to do thishelp you to do this

– Build a model of your mineralizationBuild a model of your mineralization•We will look at working with two of the most We will look at working with two of the most

common types of mineralization modelscommon types of mineralization models– We’ll dodge how we got them (Geostatistics Course that We’ll dodge how we got them (Geostatistics Course that

could be one of your electives)could be one of your electives)

Steps in PlanningSteps in Planning

• In fact you have to make some general In fact you have to make some general guesses about how you might mine it – guesses about how you might mine it – including surface or undergroundincluding surface or underground

• Since God and this course both chose surface Since God and this course both chose surface mining we’ll assume for now it is a surface mining we’ll assume for now it is a surface methodmethod

• Determine how much of your material is Determine how much of your material is ultimately minable by surface methodsultimately minable by surface methods– Called finding the ultimate pitCalled finding the ultimate pit

• You will get to do some of this in this class - Yippi!!!You will get to do some of this in this class - Yippi!!!

Steps in PlanningSteps in Planning

• With minable reserve definedWith minable reserve defined– Determine your mine size and lifeDetermine your mine size and life

• Involves economics beyond this classInvolves economics beyond this class– An advance surface mining topic (possible elective)An advance surface mining topic (possible elective)

– Select a mining sequence and schedule to Select a mining sequence and schedule to develop out to your pit limitsdevelop out to your pit limits•Our class examples will be with surface methods Our class examples will be with surface methods

that have fixed advance directionthat have fixed advance direction•For some open pits this is an Operations For some open pits this is an Operations

Research Exercise (possibly in an OR elective)Research Exercise (possibly in an OR elective)– Tell you about it but not train you to do itTell you about it but not train you to do it

Steps in PlanningSteps in Planning

• Select an Equipment Fleet Capable of Meeting Select an Equipment Fleet Capable of Meeting the Development Planthe Development Plan– We will do at least the Truck-Shovel parts of that in We will do at least the Truck-Shovel parts of that in

this classthis class

• Design mine plants and support infrastructure Design mine plants and support infrastructure to meet mines needsto meet mines needs– Dr. Mohanty’s mineral processing plantsDr. Mohanty’s mineral processing plants– Possibly some stuff from Material HandlingPossibly some stuff from Material Handling– (if this were U.G. might need ventilation but that is (if this were U.G. might need ventilation but that is

the evil competition so we don’t talk about that here)the evil competition so we don’t talk about that here)

Lets Try an Example of Finding Lets Try an Example of Finding the Ultimate Pitthe Ultimate Pit

Angle 45 degrees Thickness 20 ft

Angle 10 Degrees

Where Did This Thing Come From?From the projector.

Actually a series of cross sections of the deposit isOne of the mineralization models that explorationTeam may generate

My ObjectiveMy ObjectiveDefine how far down the dip the mine can advanceBefore the SR becomes uneconomic

My TechniqueMy TechniqueLook at each increment of advance for its stripping ratioUntil the ratio becomes uneconomic.

Last economic incrementDefines the ultimate pit limit

Selecting my IncrementSelecting my Increment

Based on convenience or a guessAbout production over somePeriod of time

I pick a 50 ftIncrement down thedip

Investigating My GeometryInvestigating My Geometry

Ore is a 50 X 20 ftBlock

Rectangle Area = Length * Width

1000 Square ft. (Ok it’s a parallelogram because haven’tYet dealt with pit slope)

If I have 1 ft unit thickness and phosphate ore is 170 lbs/cubic ft

170,000 lbs / 2,000 lbs/ton = 85 Tons

If my phosphate ore makes $27/ton the block is worth $2,295

Ok Where Did That Come Ok Where Did That Come FromFrom• How did I know the section was 1 ft thickHow did I know the section was 1 ft thick• Convenience – If I had worked in cubic yards it would Convenience – If I had worked in cubic yards it would

have been 1 yard thickhave been 1 yard thick• Where did that 170 lbs/cubic foot rock density come fromWhere did that 170 lbs/cubic foot rock density come from• If you’ve sampled the ore you know its density. Can also If you’ve sampled the ore you know its density. Can also

use typical densities from Surface Mining or Cat use typical densities from Surface Mining or Cat HandbooksHandbooks

• Where did the $27/ton value come fromWhere did the $27/ton value come from• If you’ve sampled your ore your probably know how much If you’ve sampled your ore your probably know how much

mineral it contains and what the mineral sells formineral it contains and what the mineral sells for• If you’ve taken Dr. Mohanty’s Mineral Processing you If you’ve taken Dr. Mohanty’s Mineral Processing you

probably know about what it costs to processprobably know about what it costs to process• Have an idea what it costs to run equipment to mine the Have an idea what it costs to run equipment to mine the

ore ore

Now for the OverburdenNow for the Overburden

45ºOverburdenBlock isA Trapezoid

Height

Base 1

Base 2

Area = (Base 1 + Base 2)/2 * Height

The Dreaded Pit Slope The Dreaded Pit Slope Question EntersQuestion Enters

My sketch implies thatFootwall of theMineralization will beThe final slope on thatside

Will the Footwall rock stand at 45º ?This information is obtained from rock strengthAnd fracture patterns plotted on stereo nets.Wait for Dr. Kreoger’s Rock Mechanics

For Our Example We Will Say ThatDr. Kroeger Gave Us an Ok

Next We Worry About the Next We Worry About the HighwallHighwall

Let us suppose that the highwallSlope is limited to 35º

Fun With Trapezoid Fun With Trapezoid GeometryGeometry

45º35º100º

I’m setting this up to get theHeight of my Trapezoid

Continuing with the Continuing with the ExcitementExcitement

35º55º

50 ft10º

90º

Height of Trapezoid

Side Adjacent = Hypotenuse * Cos (ß)

Height of Trapazoid = 50 * cos (10º)

49.24 ft

For My Next Mathemagic For My Next Mathemagic TrickTrick

45º35º

Get the Increase in slope length for each 50 ft of advance down dip

49.24 ft

45º

90º

49.24 ft

Chugging on those Chugging on those IncrementsIncrements

Base 1 = 0Base 2 = 49.24Height = 49.24

Plug and Chug

(49.24 + 0)/2 * 49.24 = 1212.31 ft^2

Assume 1 ft thick and 152 lbs/ft^3 forRock density

31.52 Tons

First Stripping Ratio

31.52/ 85 = 0.371:1

Next IncrementNext Increment

New TrapezoidBase 1 = 49.24Base 2 = 98.48Height = 49.24

Plug and Chug

Area = (49.24 + 98.48)/2 * 49.24

3636.87 ft^2 at one ft thickness and

152 lb/ft^3 276.4 TonsStripping Ratio

3.25:1 = 276.4/ 85

So How Long Do I Keep Doing So How Long Do I Keep Doing This?This?

• Repetitive task is obviously a Repetitive task is obviously a candidate for spreadsheet workcandidate for spreadsheet work

• How do I know when ultimate pit is How do I know when ultimate pit is reachedreached

• Need a cost for O.B. removal so we can Need a cost for O.B. removal so we can get the break even stripping ratio so get the break even stripping ratio so that when the stripping ratio reaches that when the stripping ratio reaches that limit we can call it our ultimate pitthat limit we can call it our ultimate pit

Overburden Removal CostOverburden Removal Cost

• Let the OB removal cost be $1.2/tonLet the OB removal cost be $1.2/ton– In practice this would be an estimate of In practice this would be an estimate of

the cost based on operations similar to the cost based on operations similar to the one you are consideringthe one you are considering

• Break Even Stripping Ratio isBreak Even Stripping Ratio is– $27/ 1.2 = 22.5 to 1$27/ 1.2 = 22.5 to 1

• To determine the ultimate pit we To determine the ultimate pit we simply keep calculating increments simply keep calculating increments till we reach a 22.5 to 1 ratiotill we reach a 22.5 to 1 ratio

Warning on Average and Warning on Average and Incremental Stripping RatioIncremental Stripping Ratio

• Break-Even Stripping Ratios are intended to Break-Even Stripping Ratios are intended to prevent you from mining material where you prevent you from mining material where you will loose moneywill loose money– When you start loosing money you stopWhen you start loosing money you stop– When the next increment of material looses money you stopWhen the next increment of material looses money you stop

• Average Stripping Ratio for the entire pit will Average Stripping Ratio for the entire pit will still be less than break-evenstill be less than break-even– We do need to make some money and cover our indirect and We do need to make some money and cover our indirect and

other costsother costs– DO NOT keep going until the average stripping ratio equals DO NOT keep going until the average stripping ratio equals

break evenbreak even– If you made money would you keep on going till you lost it all?If you made money would you keep on going till you lost it all?

Your AssignmentYour Assignment

• Use the Conepit Spread Sheet to find the Use the Conepit Spread Sheet to find the ultimate pit limits for the following ore bodyultimate pit limits for the following ore body– The ore body is a vertical cylinder 700 feet in The ore body is a vertical cylinder 700 feet in

diameterdiameter– The Ore weight is 4700 lb/cubic yardThe Ore weight is 4700 lb/cubic yard– The Overburden weight is 4200 lb/cubic yardThe Overburden weight is 4200 lb/cubic yard– The bench height will be 35 feetThe bench height will be 35 feet– The Over-all slope will stand at 42 degreesThe Over-all slope will stand at 42 degrees– The break even stripping ratio is 5:1The break even stripping ratio is 5:1

• Use Conepit to determine how deep the ore Use Conepit to determine how deep the ore body can be mined (ie the ultimate pit)body can be mined (ie the ultimate pit)

The Spread SheetThe Spread Sheet

Input Fields areyellow

Critical OutputFields are Red

The InputsThe Inputs

Present Depth is theDepth the pit has reached(obviously to start withThat will be 0)

The increase in depth isYour bench height

Pit can only go down inInteger numbers of benches(ie 35 ft, 70 ft, 105 ft etc)

Watching the OutputWatching the Output

Critical answers are in theIncremental stripping ratio.

When weight based SRReaches 5:1 the pit isdone

The Planning Function The Planning Function ContinuedContinued

• Ultimate pits can be calculated using a Ultimate pits can be calculated using a variety of methods reviewedvariety of methods reviewed– Assignment used an analytical modelAssignment used an analytical model

• In the slides example, Pit volumes are In the slides example, Pit volumes are calculated by doing average end area calculated by doing average end area methods on each of the cross-sectionsmethods on each of the cross-sections

• The plan view of the pit is prepared by The plan view of the pit is prepared by smoothing between the pit advance from smoothing between the pit advance from each of the cross-sectionseach of the cross-sections

The Geometry Freak-OutThe Geometry Freak-Out

• I had uniform thick seams with a constant I had uniform thick seams with a constant dip, with a land surface with a uniform tiltdip, with a land surface with a uniform tilt– The geometry probably still brings back bad memories The geometry probably still brings back bad memories

from your math classesfrom your math classes

• Real world geometry is often too hard to Real world geometry is often too hard to work out mathematically like in the work out mathematically like in the exampleexample

• Real world – Cross Sections of the Real world – Cross Sections of the potential pit area are prepared from potential pit area are prepared from geologic datageologic data

Digitizers to the RescueDigitizers to the Rescue

You trace around the ore and wasteIncrements with a digitizer (could beAn Autocad Area feature) and theArea will be computed digitally.

Where We Are NowWhere We Are Now

• Note that we used our model of our Note that we used our model of our mineralized ground and worked out to our mineralized ground and worked out to our economic ultimate pit limit.economic ultimate pit limit.– With this done I have a minable tonnageWith this done I have a minable tonnage

• I will use this information to set a crude I will use this information to set a crude idea of how rapidly I will mineidea of how rapidly I will mine– I will use this info to pick a logical increment of I will use this info to pick a logical increment of

pit advance planningpit advance planning

• I will then plan my mine advance I will then plan my mine advance sequence to the ultimate pit limitsequence to the ultimate pit limit

The Advance Sequence The Advance Sequence ProblemProblem• In my example I have an open pit which In my example I have an open pit which

by design must advance down dipby design must advance down dip– I have relatively little freedom in my I have relatively little freedom in my

advanceadvance

• Other open pit scenarios such as the Other open pit scenarios such as the porphyry copper deposit have much porphyry copper deposit have much greater freedom in sequencinggreater freedom in sequencing– We’ll look at some of the more powerful We’ll look at some of the more powerful

tools for that situationtools for that situation

Why is Sequencing Such a Big Why is Sequencing Such a Big Deal?Deal?

• Some may have had engineering Some may have had engineering economics (Engr 361) and know economics (Engr 361) and know about discounted cash flow analysisabout discounted cash flow analysis

• For financial planning you have a For financial planning you have a series of expenses and earnings that series of expenses and earnings that will come in over the life of the minewill come in over the life of the mine– These cash flows can be put on a time These cash flows can be put on a time

lineline

The Discounted Cash Flow The Discounted Cash Flow EngineEngine

• People value money sooner more than People value money sooner more than money latermoney later– If you get it now you can earn interestIf you get it now you can earn interest– Inflation may diminish the buying power of Inflation may diminish the buying power of

future dollarsfuture dollars– The further it is in the future the greater the The further it is in the future the greater the

chance that you might not get itchance that you might not get it

• People develop weighting factors for People develop weighting factors for money depending on how soon they get itmoney depending on how soon they get it

• Add up the weighted dollars for NPVAdd up the weighted dollars for NPV

NPV EffectsNPV Effects

• Big NPVs are goodBig NPVs are good

• Make your cash flow have higher NPV Make your cash flow have higher NPV by putting off expenses (so the by putting off expenses (so the money will have a low weighting money will have a low weighting factor) and move your money factor) and move your money making forward in time (so the good making forward in time (so the good money will have high weighting money will have high weighting factor)factor)

How to Make it HappenHow to Make it Happen

• In case of the open pit that can In case of the open pit that can expand out to limit in any directionexpand out to limit in any direction

• Go after ore with a low stripping ratio Go after ore with a low stripping ratio first – its puts off high stripping ratio first – its puts off high stripping ratio costs till in the futurecosts till in the future

• Go after high grade ore first – it Go after high grade ore first – it moves your biggest profits forward in moves your biggest profits forward in timetime

How Not to SequenceHow Not to Sequence

Pay Dirt

Slice #1Slice #2

Slice #3

Slice #4Slice #5

Slice #6

Slice #7

Slice #8

Why Did That Not Work?Why Did That Not Work?

• We took all our stripping expenses and We took all our stripping expenses and took them up fronttook them up front

• We delayed making any money till as We delayed making any money till as late in the game as possiblelate in the game as possible

• The order we go it does make a The order we go it does make a differencedifference

• We need more powerful models to help We need more powerful models to help us plan our elliptical type open pitsus plan our elliptical type open pits– We’ll review the computer aided models nextWe’ll review the computer aided models next