2Classic Open Pits Characterized by Oval Shape, Benches, spiraling roads These pits expand withoutMoving and generallyTarget a vein or steeplyDipping stock on ore
3The 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
4Implications for Slope Effect In long area strip mines where things broke down to 2 dimensions slope did not impact stripping ratioHere in this static 3D pit geometry the impact is hugeObviously having a steeper slope improves economics
5Limiting SlopesOne limit is geologic – having the pit slide in on you is bad for investment (and possibly your health if you are at the bottom)One exercise commonly taught in rock mechanics courses is plotting fractures on stereo netIllustrates how many fractures are opened up by benchesDaylighted fractureOffers an opportunityTo slide off.Non-Daylighted fracture offers littleRisk
6Probability of Failure Not all daylighted fractures will slipNot every non-daylighted fracture will holdMore major extensive daylighted fractures more likely a major failure isOne New Mexico mine lost entire pit as slide slipped in over several months
7Significance of Failure Some small failures will take a few hours to clean up – can risk these to save moneyLarger regional failures are fatal, probably cannot endure much riskCan tolerate daylightedFractures on benchesDaylighted fractures on over-allPit slope are another matter
8A Lesson in Open Pit Terminology BermNote that the toe toCrest slope is muchSteeper than the over-allCrestBenchToeOver-all Pit SlopeLocalized 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.
9Pit SlopesQuarries in strong rock can sustain about 80 to 85 degree toe to crest slopesGeology determines limits but about 58 to 72 degrees is a common range for toe to crest in open pit metal.Over-all slopes often more conservativeFrequently less than 45 degreesCannanea Mexico is nearly 60
10The Equipment Considerations Why benches?Benches stop rolling rocks (a rock rolling down 600 ft and hitting you in the head will split your scull – even if there are no brains)Benches act as rock catchers – they need to be wide enough for this – with the aid of a berm (around feet)Benches match equipment digging heightWoops!Bigger shovels allow bigger benchHeight – but require bigger trucks
11Why Benches ContinuedFlat area on benches provides room for equipment to moveBigger trucks have bigger turning radiusTruckShovelPlan view of bench work area
12Grade Control and Limits on Bench Heights Usually have to dig whole bench toe to crestCannot select oreSome Mining Depends on selecting only best ore for processingCan loose selectivity as bench height increases
13Economics and Advantages of Bench Height Maintaining bench area involves a costLess bench area = less costHigher benches are cheaper (usually)In drilling for blasting it takes time to set up for every hole drilledHigher benches allow larger more accurate holesAllow greater spacing – uses drill time more effectively
14ExampleThe Much Dough Deposit is a large vertical cylinder of ore. It is to be mined by open pit. The company will use Kittenpillar 997s for digging. The hydraulic shovel has a digging height of 47 feet and will be teamed with Kittenpillar 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. Your rock mechanics calculations indicate you could sustain an over-all slope of about 47 degrees with toe to crest slopes on benches of about 67 degrees for benches up to 60 feet in height. Your grade control team indicates they can maintain good selectivity with benches as high as 40 feet.Q- What is a realistic bench height and over-all slope for this pit?
15Determining a Bench Height Grade Control Wise the limit is 40 feetRock Mechanic Wise the limit is 60 feetLoading Machine Limitation Height is 47 feetThe most limiting factor is grade controlWe need to keep bench height at 40 feet
16Determining a Bench Width To stop rocks from rolling need at least 10 feetAt least 20 ft75 ft Turning RadiusShovelAbout 40 feet for 37 foot length5 ft wall clearance + 75 ft turn radius + 37 feet length + 5 foot from edge = 122(say about 125 foot bench width for working.)5
17Looking at Geometry 125 ft After the over-all Slope indicated by This dotted line40 ft40 ft67ºXTan(67)= 40/X so X= 40/tan(67) = 17 ft
18Calculating AlongA slope that allows working room is called a working slope(mines maintain working slopes when an area is still beingMined)40 ft?= 142 ftTan (?) = 40/142 so ? = arctan(40/142) = 15.73º
19Final Pit Slope Finding a final pit slope (not considering a road and Based only on 10 ft catchBenches)Arctan(40/27) = ? = 56º40 ft?17 ft + 10 ft = 27 ft
20Pit Slope Limits Geological Over-All Pit Slope Limit = 47º Geometry based final pit slope = 56ºGeometry based working slope = 15.73ºDuring the working phase geometry will dictate the pit slope at 15.73ºAt the end of pit life as slopes are steepened to final geology limits slopes to 47º
21Example Continued Finding the economic limit of the pit The Much Dough Deposit can sustain stripping ratios of 5:1 before reaching break-evenHow deep can the pit go?We will use a little computer program in Xcel
22I’ll Enter Some Geometry Info My slopeWe willAssumeOther dataSuch asOur oreAnd wasteDensity andThe diameterOf the ore bodyAre case specificMy Bench Height
23Checking the OutputStripping Ratio for going down 1 bench when already have 1Is 0.39 to 1 which is well below the 5 to 1 limit.
24Over-All Look at Spreadsheet Geometry CalculationsInput AreaIncrementalStripping ratioareaAverage StrippingRatio
25Advancing the Pit Downward Increase numberOf existing benchesTo 2IncrementalStripping ratio for3rd bench is0.69 to 1
26Continuing Our Activity 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.
27The Depth EffectNote that as a pit goes deeper the stripping ratio increases until it reaches an economic limitRule 1 – as slope decreases S.R. increasesRule 2 – as depth increases S.R. increases
28Damages from our 15.73 Degree Slope 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)
29Practical Steepening Considerations The slope limiting factor was the need to have working room for the equipmentBut do I need to be able to work on every bench at the same time?There are usually practical limits to the number of loaders and trucks you can run without going nutsMost mines will have about 2 to 5 loaders.Usually they will have some extra work places to move the loaders to so they can prepare aheadTrick #2 – Does the pit have to expand in all directions at the same time.Can use “Push Backs” – have a full working slope only in certain directions at any one time.
30Suppose We Only have Full Working Room on Every 4th bench Atan(160/283) = 29.48ºThis type of planning normally getsWorking slopes in the 30 to 35Degree range.160 ft?Total = 283
31Working Pits Pits usually go in at working slope Often initial pit is mined top down to open the depositMine then picks a direction and distance to push-backPush back is worked at the working slopeSlope is steepened as limit of the push back is reachedMine then picks the next push-back directionThey have to open a number of working benchesAs these benches are opened the slope declines to the working slopeCycle Repeats until the final pit slope is reached.
32How Big is My Push-Back Distance To push back the mine must open a certain number of shovel positionsUsually more than the actual number of shovelsSuppose I open 7 benches for 3 shovelsSuppose I need at least 25 meters of width for working benchSuppose my regular bench width is 10 metersEvery active bench needs an extra 15 meters7 of them need 105 meters so my minimum pushback size would be 105 meters.
33How Do I Arrange My Benches in a Push Back In the Example I could have 7 different work spacesThat would mean 7 benches each with road accessSuppose I build one very wide bench with room for 4 shovels (about 100 meters) and another with room for 3 shovels (about 75 meters).Now I only need 2 sets of roads.
34How Do I Choose? Cheaper is better? For most metals and industrial minerals (things most likely to be mined by a classic open pit), processing of ore is usually more expensive than mining the ore.Processing Plants that have troubleSee increases in operating costs (that can easily offset any savings in mining)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)Both of the above.Processing Plants like steady grades of ore with similar characteristicsMother nature likes to put stuff all over creation and not build anything to a standardOne of the ways to get even ore feed is to blend ore from different parts of the mineWorking faces that are far apart give me more blending options than if all my shovels are working together.
35The Distance FactorAs pits go deeper the roads to the surface get longerTrucks drive further so that ore and waste from the bottom of the pit is more expensive to move than that at the topSometimes the impact of distance can limit the pit depth before the stripping ratio does
36Checking Our Case Study Our economic limit appears to be 1800 ftGenerally haul roads must be at least 10 ft long for every foot of rise (more than that rips up transmissions – and violates laws in some cases)Suggests at the bottom of the pit the road may be 18,000 ft long – lets allow 1000 ft to dump point19,000 ft – traveled two ways is 38,000 ft or 7.2 miles round tripAt that distance the truck may only make 2 trips an hour (it would have made 4 closer to the top)
37Impact of DistanceGreater haul cost reduces the earnings on a ton of oreGreater haul costs increase the cost of OB removalIf haulage is about 35% of direct mine costO.B. removal near the bottom would be about 135% of normal (when haul costs doubled)5/1.35 = limit may be about 3.73: 1 at the bottom
38The Haulage Distance Effect If increasedHaul costs limit usTo about 4:1S.R. then the pitWill reach about1560 ft – not 1800 ft(haulage economicsControlled the depthOf the pit)
39Industry Responses to the Limit In-pit crushing and conveying – have the trucks carry the ore to a point in the pit a constant distance away – then crush and conveyResult – you keep the flexibility of haul trucks for mining but the increased haul distances in more mined out upper areas of the pit are handled by conveyors which have a lower unit cost for moving material
40Radical IdeasPutting inclined hoists on the pit surface or just in the wall and hauling the ore straight up the side with a skipWas done at least once in New MexicoHas been the object of many studies over time
41Now Its Your TurnYou will need to figure a working and final pit slope.You will need to determine how deep a pit can actually become before it is economically infeasible to go further.Homework #4 is now assigned.