Classic Open Pit MiningClassic Open Pit Mining

Issues and CharacteristicsIssues and Characteristics©2007 – minor modifications 2009 and 2010 Dr. B. C. Paul©2007 – minor modifications 2009 and 2010 Dr. B. C. Paul

The concepts indicated in these slides are considered common knowledge to The concepts indicated in these slides are considered common knowledge to those familiar with the field. Many of these ideas have been published in a those familiar with the field. Many of these ideas have been published in a

variety of different texts and papers over time – no one of which was variety of different texts and papers over time – no one of which was specifically used as an outline for this work.specifically used as an outline for this work.

Classic Open Pits Characterized by Oval Classic Open Pits Characterized by Oval Shape, Benches, spiraling roadsShape, Benches, spiraling roads

These pits expand withoutMoving and generally Target a vein or steeplyDipping stock on ore

The Slope EffectThe Slope EffectWhat happens if weChange the slopeAngle?

What just happened to the overburden volume?

What just happened to our stripping ratio?

Conclusion – Pit Slope Makes a Big Difference in Open Pits

Implications for Slope EffectImplications for Slope Effect

In long area strip mines where things broke In long area strip mines where things broke down to 2 dimensions slope did not impact down to 2 dimensions slope did not impact stripping ratiostripping ratio

Here in this static 3D pit geometry the Here in this static 3D pit geometry the impact is hugeimpact is huge

Obviously having a steeper slope improves Obviously having a steeper slope improves economicseconomics

Limiting SlopesLimiting Slopes

One limit is geologic – having the pit slide in on One limit is geologic – having the pit slide in on you is bad for investment (and possibly your you is bad for investment (and possibly your health if you are at the bottom)health if you are at the bottom)

One exercise commonly taught in rock mechanics One exercise commonly taught in rock mechanics courses is plotting fractures on stereo netcourses is plotting fractures on stereo net– Illustrates how many fractures are opened up by Illustrates how many fractures are opened up by

benchesbenches

Daylighted fractureOffers an opportunityTo slide off.

Non-Daylighted fracture offers littleRisk

Probability of FailureProbability of Failure

Not all daylighted fractures will slipNot all daylighted fractures will slip Not every non-daylighted fracture will holdNot every non-daylighted fracture will hold More major extensive daylighted fractures More major extensive daylighted fractures

more likely a major failure ismore likely a major failure is– One New Mexico mine lost entire pit as slide One New Mexico mine lost entire pit as slide

slipped in over several monthsslipped in over several months

Significance of FailureSignificance of Failure

Some small failures will take a few hours to Some small failures will take a few hours to clean up – can risk these to save moneyclean up – can risk these to save money

Larger regional failures are fatal, probably Larger regional failures are fatal, probably cannot endure much riskcannot endure much risk

Can tolerate daylightedFractures on benches Daylighted fractures on over-all

Pit slope are another matter

A Lesson in Open Pit TerminologyA Lesson in Open Pit Terminology

Toe

Crest

Bench

Berm

Over-all Pit Slope

Note that the toe toCrest slope is muchSteeper than the over-all

Localized single bench failures from a steep toe to crest slope are much moreTolerable than an over-all pit slope failure over the entire side of a pit.

Pit SlopesPit Slopes

Quarries in strong rock can sustain about 80 Quarries in strong rock can sustain about 80 to 85 degree toe to crest slopesto 85 degree toe to crest slopes

Geology determines limits but about 58 to Geology determines limits but about 58 to 72 degrees is a common range for toe to 72 degrees is a common range for toe to crest in open pit metal.crest in open pit metal.

Over-all slopes often more conservativeOver-all slopes often more conservative– Frequently less than 45 degreesFrequently less than 45 degrees

Cannanea Mexico is nearly 60Cannanea Mexico is nearly 60

The Equipment ConsiderationsThe Equipment Considerations

Why benches?Why benches?– Benches stop rolling rocks (a rock rolling down Benches stop rolling rocks (a rock rolling down

600 ft and hitting you in the head will split your 600 ft and hitting you in the head will split your scull – even if there are no brains)scull – even if there are no brains) Benches act as rock catchers – they need to be wide Benches act as rock catchers – they need to be wide

enough for this – with the aid of a berm (around 10-enough for this – with the aid of a berm (around 10-15 feet)15 feet)

– Benches match equipment digging heightBenches match equipment digging heightWoops!

Bigger shovels allow bigger benchHeight – but require bigger trucks

Why Benches ContinuedWhy Benches Continued

Flat area on benches provides room for Flat area on benches provides room for equipment to moveequipment to move– Bigger trucks have bigger turning radiusBigger trucks have bigger turning radius

Truck

Shovel

Plan view of bench work area

Grade Control and Limits on Bench Grade Control and Limits on Bench HeightsHeights

Usually have to dig whole bench toe to crestUsually have to dig whole bench toe to crest– Cannot select oreCannot select ore

Some Mining Depends on selecting only Some Mining Depends on selecting only best ore for processingbest ore for processing– Can loose selectivity as bench height increasesCan loose selectivity as bench height increases

Economics and Advantages of Economics and Advantages of Bench HeightBench Height

Maintaining bench area involves a costMaintaining bench area involves a cost– Less bench area = less costLess bench area = less cost– Higher benches are cheaper (usually)Higher benches are cheaper (usually)

In drilling for blasting it takes time to set up In drilling for blasting it takes time to set up for every hole drilledfor every hole drilled– Higher benches allow larger more accurate Higher benches allow larger more accurate

holesholes– Allow greater spacing – uses drill time more Allow greater spacing – uses drill time more

effectivelyeffectively

ExampleExample

The Much Dough Deposit is a large vertical cylinder of ore. The Much Dough Deposit is a large vertical cylinder of ore. It is to be mined by open pit. The company will use It is to be mined by open pit. The company will use Kittenpillar 997s for digging. The hydraulic shovel has a Kittenpillar 997s for digging. The hydraulic shovel has a digging height of 47 feet and will be teamed with Kittenpillar digging height of 47 feet and will be teamed with Kittenpillar 440 trucks with a full turn radius of 75 feet with each truck 440 trucks with a full turn radius of 75 feet with each truck being 37 feet in over-all length and about 16 feet in width. being 37 feet in over-all length and about 16 feet in width. Your rock mechanics calculations indicate you could Your rock mechanics calculations indicate you could sustain an over-all slope of about 47 degrees with toe to sustain an over-all slope of about 47 degrees with toe to crest slopes on benches of about 67 degrees for benches crest slopes on benches of about 67 degrees for benches up to 60 feet in height. Your grade control team indicates up to 60 feet in height. Your grade control team indicates they can maintain good selectivity with benches as high as they can maintain good selectivity with benches as high as 40 feet.40 feet.

Q- What is a realistic bench height and over-all slope for Q- What is a realistic bench height and over-all slope for this pit?this pit?

Determining a Bench HeightDetermining a Bench Height

Grade Control Wise the limit is 40 feetGrade Control Wise the limit is 40 feet Rock Mechanic Wise the limit is 60 feetRock Mechanic Wise the limit is 60 feet Loading Machine Limitation Height is 47 feetLoading Machine Limitation Height is 47 feet

The most limiting factor is grade controlThe most limiting factor is grade control– We need to keep bench height at 40 feetWe need to keep bench height at 40 feet

Determining a Bench WidthDetermining a Bench Width

To stop rocks from rolling need at least 10 To stop rocks from rolling need at least 10 feetfeet

At least 20 ft

75 ft Turning Radius

About 40 feet for 37 foot length

Shovel

55 ft wall clearance + 75 ft turn radius + 37 feet length + 5 foot from edge = 122(say about 125 foot bench width for working.)

Looking at GeometryLooking at Geometry

40 ft

67º

125 ft

40 ft

X

Tan(67)= 40/X so X= 40/tan(67) = 17 ft

After the over-allSlope indicated byThis dotted line

Calculating AlongCalculating Along

17+125 = 142 ft

40 ft

Tan (?) = 40/142 so ? = arctan(40/142) = 15.73º

A slope that allows working room is called a working slope(mines maintain working slopes when an area is still beingMined)

?

Final Pit SlopeFinal Pit Slope

17 ft + 10 ft = 27 ft

40 ft

?

Finding a final pit slope(not considering a road andBased only on 10 ft catchBenches)

Arctan(40/27) = ? = 56º

Pit Slope LimitsPit Slope Limits

Geological Over-All Pit Slope Limit = 47Geological Over-All Pit Slope Limit = 47ºº Geometry based final pit slope = 56ºGeometry based final pit slope = 56º Geometry based working slope = 15.73ºGeometry based working slope = 15.73º

During the working phase geometry will During the working phase geometry will dictate the pit slope at 15.73ºdictate the pit slope at 15.73º

At the end of pit life as slopes are steepened At the end of pit life as slopes are steepened to final geology limits slopes to 47ºto final geology limits slopes to 47º

Example ContinuedExample Continued

Finding the economic limit of the pitFinding the economic limit of the pit– The Much Dough Deposit can sustain stripping The Much Dough Deposit can sustain stripping

ratios of 5:1 before reaching break-evenratios of 5:1 before reaching break-even– How deep can the pit go?How deep can the pit go?

We will use a little computer program in XcelWe will use a little computer program in Xcel

I’ll Enter Some Geometry InfoI’ll Enter Some Geometry Info

Cone Pit

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Input ControlDiameter Ore 2100 ftPit Slope 15.73 degreesPit Slope in radians 0.27454Density of ore 4700 lbs/yd^3Density of Overburden 4100 lbs/yd^3 Incremental Stripping Ratio for Pit One Going to Pit TwoNumber of Existing Benches 1 Total Volume Pit 2 13289007 yd3Present Depth 40 ft Total Volume Pit 1 5856595 yd3Increase in Depth 40 ft Incremental Volume 7432412 yd3New Depth 80 Ore Volume Cylinder 2 10262536 yd3Diameter Origional Pit 2384.038 Ore Volume Cylinder 1 5131268 yd3

Diameter Ore

Pit Slope

Ore

Waste

Portion of Cone not Mined

Present Depth

Increase in Depth

My Bench Height

My slopeWe willAssumeOther dataSuch asOur oreAnd wasteDensity andThe diameterOf the ore bodyAre case specific

Checking the OutputChecking the Outputlbs/yd^3lbs/yd^3 Incremental Stripping Ratio for Pit One Going to Pit Two

Total Volume Pit 2 13289007 yd3ft Total Volume Pit 1 5856595 yd3ft Incremental Volume 7432412 yd3

Ore Volume Cylinder 2 10262536 yd3Ore Volume Cylinder 1 5131268 yd3Incremental Ore Vol. 5131268 yd3Incremental Waste Vol 2301144 yd3Incremental Vol. SR 0.448455265Weight of Increm Ore 12058480 tonsWeight of Increm Waste 4717346 tonsWeight Based SR 0.391205656

Stripping Ratio for going down 1 bench when already have 1Is 0.39 to 1 which is well below the 5 to 1 limit.

Over-All Look at SpreadsheetOver-All Look at Spreadsheet

Input Area

IncrementalStripping ratioarea

Average StrippingRatio

Geometry Calculations

Advancing the Pit DownwardAdvancing the Pit DownwardCone Pit

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Input ControlDiameter Ore 2100 ftPit Slope 15.73 degreesPit Slope in radians 0.27454Density of ore 4700 lbs/yd^3Density of Overburden 4100 lbs/yd^3 Incremental Stripping Ratio for Pit One Going to Pit TwoNumber of Existing Benches 2 Total Volume Pit 2 22484982 yd3Present Depth 80 ft Total Volume Pit 1 13289007 yd3Increase in Depth 40 ft Incremental Volume 9195975 yd3New Depth 120 Ore Volume Cylinder 2 15393804 yd3Diameter Origional Pit 2668.076 Ore Volume Cylinder 1 10262536 yd3Height of total cone (origional) 375.735 Incremental Ore Vol. 5131268 yd3Diameter Incremental Pit 2952.114 Incremental Waste Vol 4064707 yd3Height of total cone (incremental) 415.735 Incremental Vol. SR 0.792144713

Weight of Increm Ore 12058480 tonsWeight of Increm Waste 8332649 tonsWeight Based SR 0.691019856

Diameter Ore

Pit Slope

Ore

Waste

Portion of Cone not Mined

Present Depth

Increase in Depth

Increase numberOf existing benchesTo 2

IncrementalStripping ratio for3rd bench is0.69 to 1

Continuing Our ActivityContinuing Our ActivityCone Pit

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Input ControlDiameter Ore 2100 ftPit Slope 15.73 degreesPit Slope in radians 0.27454Density of ore 4700 lbs/yd^3Density of Overburden 4100 lbs/yd^3 Incremental Stripping Ratio for Pit One Going to Pit TwoNumber of Existing Benches 11 Total Volume Pit 2 215587062 yd3Present Depth 440 ft Total Volume Pit 1 182070481 yd3Increase in Depth 40 ft Incremental Volume 33516581 yd3New Depth 480 Ore Volume Cylinder 2 61575216 yd3Diameter Origional Pit 5224.419 Ore Volume Cylinder 1 56443948 yd3Height of total cone (origional) 735.735 Incremental Ore Vol. 5131268 yd3Diameter Incremental Pit 5508.457 Incremental Waste Vol 28385313 yd3Height of total cone (incremental) 775.735 Incremental Vol. SR 5.531832019

Weight of Increm Ore 12058480 tonsWeight of Increm Waste 58189891 tonsWeight Based SR 4.825640697

Diameter Ore

Pit Slope

Ore

Waste

Portion of Cone not Mined

Present Depth

Increase in Depth

Bench #12 is theLast economic benchWith a S.R. of 4.83:1(continuing to #13Will get a 5.44:1 ratio)

Note that we canReach a limiting depthOf 480 ft.

The Depth EffectThe Depth Effect

Note that as a pit goes deeper the stripping Note that as a pit goes deeper the stripping ratio increases until it reaches an economic ratio increases until it reaches an economic limitlimit

Rule 1 – as slope decreases S.R. increasesRule 1 – as slope decreases S.R. increases Rule 2 – as depth increases S.R. increasesRule 2 – as depth increases S.R. increases

Damages from our 15.73 Degree Damages from our 15.73 Degree SlopeSlope

Cone Pit

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Input ControlDiameter Ore 2100 ftPit Slope 47 degreesPit Slope in radians 0.820305Density of ore 4700 lbs/yd^3Density of Overburden 4100 lbs/yd^3 Incremental Stripping Ratio for Pit One Going to Pit TwoNumber of Existing Benches 44 Total Volume Pit 2 796729815 yd3Present Depth 1760 ft Total Volume Pit 1 762551388 yd3Increase in Depth 40 ft Incremental Volume 34178427 yd3New Depth 1800 Ore Volume Cylinder 2 230907060 yd3Diameter Origional Pit 5382.453 Ore Volume Cylinder 1 225775792 yd3Height of total cone (origional) 2885.987 Incremental Ore Vol. 5131268 yd3Diameter Incremental Pit 5457.054 Incremental Waste Vol 29047159 yd3Height of total cone (incremental) 2925.987 Incremental Vol. SR 5.66081497

Weight of Increm Ore 12058480 tonsWeight of Increm Waste 59546675 tonsWeight Based SR 4.93815774

Diameter Ore

Pit Slope

Ore

Waste

Portion of Cone not Mined

Present Depth

Increase in Depth

Had I been able to mineAt the Geologic LimitOf 47º instead of theEquipment limit at 15.73ºI would have reached1800 feet depth(roughly 4 times moreOre would beEconomic)

Practical Steepening ConsiderationsPractical Steepening Considerations

The slope limiting factor was the need to have working The slope limiting factor was the need to have working room for the equipmentroom for the equipment

But do I need to be able to work on every bench at the But do I need to be able to work on every bench at the same time?same time?– There are usually practical limits to the number of loaders and There are usually practical limits to the number of loaders and

trucks you can run without going nutstrucks you can run without going nuts– Most mines will have about 2 to 5 loaders.Most mines will have about 2 to 5 loaders.– Usually they will have some extra work places to move the loaders Usually they will have some extra work places to move the loaders

to so they can prepare aheadto so they can prepare ahead Trick #2 – Does the pit have to expand in all directions at Trick #2 – Does the pit have to expand in all directions at

the same time.the same time.– Can use “Push Backs” – have a full working slope only in certain Can use “Push Backs” – have a full working slope only in certain

directions at any one time.directions at any one time.

Suppose We Only have Full Working Suppose We Only have Full Working Room on Every 4Room on Every 4thth bench bench

?

160 ft

17 125 17 30 17 30 17 30 Total = 283

Atan(160/283) = 29.48º

This type of planning normally getsWorking slopes in the 30 to 35Degree range.

Working PitsWorking Pits

Pits usually go in at working slopePits usually go in at working slope– Often initial pit is mined top down to open the depositOften initial pit is mined top down to open the deposit

Mine then picks a direction and distance to push-Mine then picks a direction and distance to push-backback– Push back is worked at the working slopePush back is worked at the working slope– Slope is steepened as limit of the push back is reachedSlope is steepened as limit of the push back is reached

Mine then picks the next push-back directionMine then picks the next push-back direction– They have to open a number of working benchesThey have to open a number of working benches– As these benches are opened the slope declines to the As these benches are opened the slope declines to the

working slopeworking slope Cycle Repeats until the final pit slope is reached.Cycle Repeats until the final pit slope is reached.

How Big is My Push-Back DistanceHow Big is My Push-Back Distance

To push back the mine must open a certain To push back the mine must open a certain number of shovel positionsnumber of shovel positions– Usually more than the actual number of shovelsUsually more than the actual number of shovels

Suppose I open 7 benches for 3 shovelsSuppose I open 7 benches for 3 shovels

– Suppose I need at least 25 meters of width for working Suppose I need at least 25 meters of width for working benchbench

– Suppose my regular bench width is 10 metersSuppose my regular bench width is 10 meters– Every active bench needs an extra 15 metersEvery active bench needs an extra 15 meters– 7 of them need 105 meters so my minimum pushback 7 of them need 105 meters so my minimum pushback

size would be 105 meters.size would be 105 meters.

How Do I Arrange My Benches in a How Do I Arrange My Benches in a Push BackPush Back

In the Example I could have 7 different work In the Example I could have 7 different work spacesspaces– That would mean 7 benches each with road That would mean 7 benches each with road

accessaccess Suppose I build one very wide bench with Suppose I build one very wide bench with

room for 4 shovels (about 100 meters) and room for 4 shovels (about 100 meters) and another with room for 3 shovels (about 75 another with room for 3 shovels (about 75 meters).meters).– Now I only need 2 sets of roads.Now I only need 2 sets of roads.

How Do I Choose?How Do I Choose? Cheaper is better?Cheaper is better? For most metals and industrial minerals (things most likely to be mined For most metals and industrial minerals (things most likely to be mined

by a classic open pit), processing of ore is usually more expensive by a classic open pit), processing of ore is usually more expensive than mining the ore.than mining the ore.

Processing Plants that have troubleProcessing Plants that have trouble– See increases in operating costs (that can easily offset any savings in See increases in operating costs (that can easily offset any savings in

mining)mining)– May loose recovery of the mineral (you already have all your mining cost May loose recovery of the mineral (you already have all your mining cost

into the rock and now you flush it away – ouch there goes your profit)into the rock and now you flush it away – ouch there goes your profit)– Both of the above.Both of the above.

Processing Plants like steady grades of ore with similar characteristicsProcessing Plants like steady grades of ore with similar characteristics– Mother nature likes to put stuff all over creation and not build anything to a Mother nature likes to put stuff all over creation and not build anything to a

standardstandard– One of the ways to get even ore feed is to blend ore from different parts of One of the ways to get even ore feed is to blend ore from different parts of

the minethe mine Working faces that are far apart give me more blending options than if Working faces that are far apart give me more blending options than if

all my shovels are working together.all my shovels are working together.

The Distance FactorThe Distance Factor

As pits go deeper the roads to the surface As pits go deeper the roads to the surface get longerget longer– Trucks drive further so that ore and waste from Trucks drive further so that ore and waste from

the bottom of the pit is more expensive to move the bottom of the pit is more expensive to move than that at the topthan that at the top

Sometimes the impact of distance can limit Sometimes the impact of distance can limit the pit depth before the stripping ratio doesthe pit depth before the stripping ratio does

Checking Our Case StudyChecking Our Case Study

Our economic limit appears to be 1800 ftOur economic limit appears to be 1800 ft Generally haul roads must be at least 10 ft long for Generally haul roads must be at least 10 ft long for

every foot of rise (more than that rips up every foot of rise (more than that rips up transmissions – and violates laws in some cases)transmissions – and violates laws in some cases)– Suggests at the bottom of the pit the road may be Suggests at the bottom of the pit the road may be

18,000 ft long – lets allow 1000 ft to dump point18,000 ft long – lets allow 1000 ft to dump point 19,000 ft – traveled two ways is 38,000 ft or 7.2 miles round trip19,000 ft – traveled two ways is 38,000 ft or 7.2 miles round trip

– At that distance the truck may only make 2 trips an hour At that distance the truck may only make 2 trips an hour (it would have made 4 closer to the top)(it would have made 4 closer to the top)

Impact of DistanceImpact of Distance

Greater haul cost reduces the earnings on a Greater haul cost reduces the earnings on a ton of oreton of ore

Greater haul costs increase the cost of OB Greater haul costs increase the cost of OB removalremoval

If haulage is about 35% of direct mine costIf haulage is about 35% of direct mine cost– O.B. removal near the bottom would be about O.B. removal near the bottom would be about

135% of normal (when haul costs doubled)135% of normal (when haul costs doubled)– 5/1.35 = limit may be about 3.73: 1 at the 5/1.35 = limit may be about 3.73: 1 at the

bottombottom

The Haulage Distance EffectThe Haulage Distance EffectCone Pit

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Input ControlDiameter Ore 2100 ftPit Slope 47 degreesPit Slope in radians 0.820305Density of ore 4700 lbs/yd^3Density of Overburden 4100 lbs/yd^3 Incremental Stripping Ratio for Pit One Going to Pit TwoNumber of Existing Benches 38 Total Volume Pit 2 605416535 yd3Present Depth 1520 ft Total Volume Pit 1 576650362 yd3Increase in Depth 40 ft Incremental Volume 28766173 yd3New Depth 1560 Ore Volume Cylinder 2 200119452 yd3Diameter Origional Pit 4934.846 Ore Volume Cylinder 1 194988184 yd3Height of total cone (origional) 2645.987 Incremental Ore Vol. 5131268 yd3Diameter Incremental Pit 5009.447 Incremental Waste Vol 23634905 yd3Height of total cone (incremental) 2685.987 Incremental Vol. SR 4.606055386

Weight of Increm Ore 12058480 tonsWeight of Increm Waste 48451554 tonsWeight Based SR 4.018048315

Diameter Ore

Pit Slope

Ore

Waste

Portion of Cone not Mined

Present Depth

Increase in Depth

If increasedHaul costs limit usTo about 4:1S.R. then the pitWill reach about1560 ft – not 1800 ft

(haulage economicsControlled the depthOf the pit)

Industry Responses to the LimitIndustry Responses to the Limit

In-pit crushing and conveying – have the In-pit crushing and conveying – have the trucks carry the ore to a point in the pit a trucks carry the ore to a point in the pit a constant distance away – then crush and constant distance away – then crush and conveyconvey– Result – you keep the flexibility of haul trucks Result – you keep the flexibility of haul trucks

for mining but the increased haul distances in for mining but the increased haul distances in more mined out upper areas of the pit are more mined out upper areas of the pit are handled by conveyors which have a lower unit handled by conveyors which have a lower unit cost for moving materialcost for moving material

Radical IdeasRadical Ideas

Putting inclined hoists on the pit surface or Putting inclined hoists on the pit surface or just in the wall and hauling the ore straight just in the wall and hauling the ore straight up the side with a skipup the side with a skip– Was done at least once in New MexicoWas done at least once in New Mexico– Has been the object of many studies over timeHas been the object of many studies over time

Now Its Your TurnNow Its Your Turn

You will need to figure a working and final You will need to figure a working and final pit slope.pit slope.

You will need to determine how deep a pit You will need to determine how deep a pit can actually become before it is can actually become before it is economically infeasible to go further.economically infeasible to go further.

Homework #4 is now assigned.Homework #4 is now assigned.