Classic Open Pits Characterized by Oval Shape, Benches, spiraling roads These pits expand without Moving and generally Target a vein or steeply Dipping stock on ore
The Slope Effect What happens if we Change the slope Angle? 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 Effect In long area strip mines where things broke down to 2 dimensions slope did not impact stripping ratio Here in this static 3D pit geometry the impact is huge Obviously having a steeper slope improves economics
Limiting Slopes One 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 net –Illustrates how many fractures are opened up by benches Daylighted fracture Offers an opportunity To slide off. Non-Daylighted fracture offers little Risk
Probability of Failure Not all daylighted fractures will slip Not every non-daylighted fracture will hold More major extensive daylighted fractures more likely a major failure is –One New Mexico mine lost entire pit as slide slipped in over several months
Significance of Failure Some small failures will take a few hours to clean up – can risk these to save money Larger regional failures are fatal, probably cannot endure much risk Can tolerate daylighted Fractures on benches Daylighted fractures on over-all Pit slope are another matter
A Lesson in Open Pit Terminology Toe Crest Bench Berm Over-all Pit Slope Note that the toe to Crest slope is much Steeper than the over-all Localized single bench failures from a steep toe to crest slope are much more Tolerable than an over-all pit slope failure over the entire side of a pit.
Pit Slopes Quarries in strong rock can sustain about 80 to 85 degree toe to crest slopes Geology 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 conservative –Frequently less than 45 degrees Cannanea Mexico is nearly 60
The 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 height Woops! Bigger shovels allow bigger bench Height – but require bigger trucks
Why Benches Continued Flat area on benches provides room for equipment to move –Bigger trucks have bigger turning radius Truck Shovel Plan view of bench work area
Grade Control and Limits on Bench Heights Usually have to dig whole bench toe to crest –Cannot select ore Some Mining Depends on selecting only best ore for processing –Can loose selectivity as bench height increases
Economics and Advantages of Bench Height Maintaining bench area involves a cost –Less bench area = less cost –Higher benches are cheaper (usually) In drilling for blasting it takes time to set up for every hole drilled –Higher benches allow larger more accurate holes –Allow greater spacing – uses drill time more effectively
Example The 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?
Determining a Bench Height Grade Control Wise the limit is 40 feet Rock Mechanic Wise the limit is 60 feet Loading Machine Limitation Height is 47 feet The most limiting factor is grade control –We need to keep bench height at 40 feet
Determining a Bench Width To stop rocks from rolling need at least 10 feet At least 20 ft 75 ft Turning Radius About 40 feet for 37 foot length Shovel 5 5 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 Geometry 40 ft 67º 125 ft 40 ft X Tan(67)= 40/X so X= 40/tan(67) = 17 ft After the over-all Slope indicated by This dotted line
Calculating Along = 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 being Mined) ?
Final Pit Slope 17 ft + 10 ft = 27 ft 40 ft ? Finding a final pit slope (not considering a road and Based only on 10 ft catch Benches) Arctan(40/27) = ? = 56º
Pit Slope Limits Geological Over-All Pit Slope Limit = 47º Geometry based final pit slope = 56º Geometry based working slope = 15.73º During the working phase geometry will dictate the pit slope at 15.73º At the end of pit life as slopes are steepened to final geology limits slopes to 47º
Example Continued Finding the economic limit of the pit –The Much Dough Deposit can sustain stripping ratios of 5:1 before reaching break-even –How deep can the pit go? We will use a little computer program in Xcel
I’ll Enter Some Geometry Info My Bench Height My slope We will Assume Other data Such as Our ore And waste Density and The diameter Of the ore body Are case specific
Checking the Output Stripping Ratio for going down 1 bench when already have 1 Is 0.39 to 1 which is well below the 5 to 1 limit.
Over-All Look at Spreadsheet Input Area Incremental Stripping ratio area Average Stripping Ratio Geometry Calculations
Advancing the Pit Downward Increase number Of existing benches To 2 Incremental Stripping ratio for 3 rd bench is 0.69 to 1
Continuing Our Activity Bench #12 is the Last economic bench With a S.R. of 4.83:1 (continuing to #13 Will get a 5.44:1 ratio) Note that we can Reach a limiting depth Of 480 ft.
The Depth Effect Note that as a pit goes deeper the stripping ratio increases until it reaches an economic limit Rule 1 – as slope decreases S.R. increases Rule 2 – as depth increases S.R. increases
Damages from our Degree Slope Had I been able to mine At the Geologic Limit Of 47º instead of the Equipment limit at 15.73º I would have reached 1800 feet depth (roughly 4 times more Ore would be Economic)
Practical Steepening Considerations The slope limiting factor was the need to have working room for the equipment But 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 nuts –Most 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 ahead Trick #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.
Suppose We Only have Full Working Room on Every 4 th bench ? 160 ft Total = 283 Atan(160/283) = 29.48º This type of planning normally gets Working slopes in the 30 to 35 Degree range.
Working Pits Pits usually go in at working slope –Often initial pit is mined top down to open the deposit Mine then picks a direction and distance to push- back –Push back is worked at the working slope –Slope is steepened as limit of the push back is reached Mine then picks the next push-back direction –They have to open a number of working benches –As these benches are opened the slope declines to the working slope Cycle Repeats until the final pit slope is reached.
How Big is My Push-Back Distance To push back the mine must open a certain number of shovel positions –Usually more than the actual number of shovels Suppose I open 7 benches for 3 shovels –Suppose I need at least 25 meters of width for working bench –Suppose my regular bench width is 10 meters –Every active bench needs an extra 15 meters –7 of them need 105 meters so my minimum pushback size would be 105 meters.
How Do I Arrange My Benches in a Push Back In the Example I could have 7 different work spaces –That would mean 7 benches each with road access Suppose 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.
How 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 trouble –See 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 characteristics –Mother nature likes to put stuff all over creation and not build anything to a standard –One of the ways to get even ore feed is to blend ore from different parts of the mine Working faces that are far apart give me more blending options than if all my shovels are working together.
The Distance Factor As pits go deeper the roads to the surface get longer –Trucks drive further so that ore and waste from the bottom of the pit is more expensive to move than that at the top Sometimes the impact of distance can limit the pit depth before the stripping ratio does
Checking Our Case Study Our economic limit appears to be 1800 ft Generally 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 point 19,000 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 (it would have made 4 closer to the top)
Impact of Distance Greater haul cost reduces the earnings on a ton of ore Greater haul costs increase the cost of OB removal If haulage is about 35% of direct mine cost –O.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
The Haulage Distance Effect If increased Haul costs limit us To about 4:1 S.R. then the pit Will reach about 1560 ft – not 1800 ft (haulage economics Controlled the depth Of the pit)
Industry 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 convey –Result – 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
Radical Ideas Putting inclined hoists on the pit surface or just in the wall and hauling the ore straight up the side with a skip –Was done at least once in New Mexico –Has been the object of many studies over time
Now Its Your Turn You 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.