1. Classic Open Pit Mining
Issues and Characteristics
©2007 – minor modifications 2009 and 2010 Dr. B. C. Paul
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 variety of different texts and papers over time – no one of which was specifically used as an outline for this work.

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. A Lesson in Open Pit Terminology
Berm
Note that the toe to
Crest slope is much
Steeper than the over-all
Crest
Bench
Toe
Over-all Pit Slope
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.

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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?

15. 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

16. Determining a Bench Width
To stop rocks from rolling need at least 10 feet
At least 20 ft
75 ft Turning Radius
Shovel
About 40 feet for 37 foot length
5 ft wall clearance + 75 ft turn radius + 37 feet length + 5 foot from edge = 122
(say about 125 foot bench width for working.) 5

17. Looking at Geometry 125 ft After the over-all Slope indicated by
This dotted line
40 ft
40 ft
67º X
Tan(67)= 40/X so X= 40/tan(67) = 17 ft

18. Calculating Along
A slope that allows working room is called a working slope
(mines maintain working slopes when an area is still being
Mined)
40 ft ?
= 142 ft
Tan (?) = 40/142 so ? = arctan(40/142) = 15.73º

19. Final Pit Slope Finding a final pit slope (not considering a road and
Based only on 10 ft catch
Benches)
Arctan(40/27) = ? = 56º
40 ft ?
17 ft + 10 ft = 27 ft

20. 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

21. 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

22. I’ll Enter Some Geometry Info
My slope
We will
Assume
Other data
Such as
Our ore
And waste
Density and
The diameter
Of the ore body
Are case specific
My Bench Height

23. 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.

24. Over-All Look at Spreadsheet
Geometry Calculations
Input Area
Incremental
Stripping ratio
area
Average Stripping
Ratio

25. Advancing the Pit Downward
Increase number
Of existing benches
To 2
Incremental
Stripping ratio for
3rd bench is
0.69 to 1

26. 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.

27. 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

28. Damages from our 15.73 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)

29. 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.

30. Suppose We Only have Full Working Room on Every 4th bench
Atan(160/283) = 29.48º
This type of planning normally gets
Working slopes in the 30 to 35
Degree range.
160 ft ?
Total = 283

31. 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.

32. 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.

33. 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.

34. 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.

35. 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

36. 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)

37. 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

38. 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)

39. 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

40. 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

41. 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.