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.
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
Berm
Crest
Bench
Toe
Note that the toe to
Crest slope is much
Steeper than the over-all
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.
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 1015 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
Shovel
About 40 feet for 37 foot length
5 ft wall clearance
+ 75 ft turn radius + 37 feet length + 5 foot from edge = 122
5
(say about 125 foot bench width for working.)
Looking at Geometry
125 ft
40 ft
After the over-all
Slope indicated by
This dotted line
40 ft
67º
X
Tan(67)= 40/X so X= 40/tan(67) = 17 ft
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
?
17+125 = 142 ft
Tan (?) = 40/142 so ? = arctan(40/142) = 15.73º
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
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
Cone Pit
Diameter Ore
Pit Slope
Enter Your Information in the
Present Depth
yellow fields below
Waste
We will
Input Control
Assume
Diameter Ore
Other data Pit Slope
Pit Slope in radians
Such as
Density of ore
Density of Overburden
Our ore
Number of Existing Benches
And waste Present Depth
Increase in Depth
Density andNew Depth
Diameter Origional Pit
The diameter
Of the ore body
Are case specific
My slope
Ore
Increase in Depth
2100
15.73
0.27454
4700
4100
1
40
40
80
2384.038
ft
degrees
lbs/yd^3
lbs/yd^3
ft
ft
Portion of Cone not Mined
Incremental Stripping Ratio for Pit One Going to Pit Two
Total Volume Pit 2
13289007 yd3
Total Volume Pit 1
5856595 yd3
Incremental Volume
7432412 yd3
Ore Volume Cylinder 2
10262536 yd3
Ore Volume Cylinder 1
5131268 yd3
My Bench Height
Checking the Output
lbs/yd^3
lbs/yd^3
ft
ft
Incremental Stripping Ratio for Pit One Going to Pit Two
Total Volume Pit 2
13289007 yd3
Total Volume Pit 1
5856595 yd3
Incremental Volume
7432412 yd3
Ore Volume Cylinder 2
10262536 yd3
Ore Volume Cylinder 1
5131268 yd3
Incremental Ore Vol.
5131268 yd3
Incremental Waste Vol
2301144 yd3
Incremental Vol. SR 0.448455265
Weight of Increm Ore
12058480 tons
Weight of Increm Waste
4717346 tons
Weight Based SR
0.391205656
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
Geometry Calculations
Input Area
Incremental
Stripping ratio
area
Average Stripping
Ratio
Advancing the Pit Downward
Cone Pit
Diameter Ore
Pit Slope
Enter Your Information in the
Increase number
Of existing benches
To 2
Incremental
Stripping ratio for
3rd bench is
0.69 to 1
Present Depth
yellow fields below
Waste
Ore
Increase in Depth
Input Control
Diameter Ore
Pit Slope
Pit Slope in radians
Density of ore
Density of Overburden
Number of Existing Benches
Present Depth
Increase in Depth
New Depth
Diameter Origional Pit
Height of total cone (origional)
Diameter Incremental Pit
Height of total cone (incremental)
2100
15.73
0.27454
4700
4100
2
80
40
120
2668.076
375.735
2952.114
415.735
ft
degrees
lbs/yd^3
lbs/yd^3
ft
ft
Portion of Cone not Mined
Incremental Stripping Ratio for Pit One Going to
Total Volume Pit 2
22484982 yd3
Total Volume Pit 1
13289007 yd3
Incremental Volume
9195975 yd3
Ore Volume Cylinder 2
15393804 yd3
Ore Volume Cylinder 1
10262536 yd3
Incremental Ore Vol.
5131268 yd3
Incremental Waste Vol
4064707 yd3
Incremental Vol. SR 0.792144713
Weight of Increm Ore
12058480 tons
Weight of Increm Waste
8332649 tons
Weight Based SR
0.691019856
Continuing Our Activity
Cone Pit
Diameter Ore
Pit Slope
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.
Enter Your Information in the
Present Depth
yellow fields below
Waste
Ore
Increase in Depth
Input Control
Diameter Ore
Pit Slope
Pit Slope in radians
Density of ore
Density of Overburden
Number of Existing Benches
Present Depth
Increase in Depth
New Depth
Diameter Origional Pit
Height of total cone (origional)
Diameter Incremental Pit
Height of total cone (incremental)
2100
15.73
0.27454
4700
4100
11
440
40
480
5224.419
735.735
5508.457
775.735
ft
degrees
lbs/yd^3
lbs/yd^3
ft
ft
Portion of Cone not Mined
Incremental Stripping Ratio for Pit One Going to P
Total Volume Pit 2
215587062 yd3
Total Volume Pit 1
182070481 yd3
Incremental Volume
33516581 yd3
Ore Volume Cylinder 2
61575216 yd3
Ore Volume Cylinder 1
56443948 yd3
Incremental Ore Vol.
5131268 yd3
Incremental Waste Vol
28385313 yd3
Incremental Vol. SR 5.531832019
Weight of Increm Ore
12058480 tons
Weight of Increm Waste 58189891 tons
Weight Based SR
4.825640697
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 15.73 Degree
Slope
Cone Pit
Diameter Ore
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)
Pit Slope
Enter Your Information in the
Present Depth
yellow fields below
Waste
Ore
Increase in Depth
Input Control
Diameter Ore
Pit Slope
Pit Slope in radians
Density of ore
Density of Overburden
Number of Existing Benches
Present Depth
Increase in Depth
New Depth
Diameter Origional Pit
Height of total cone (origional)
Diameter Incremental Pit
Height of total cone (incremental)
2100
47
0.820305
4700
4100
44
1760
40
1800
5382.453
2885.987
5457.054
2925.987
ft
degrees
lbs/yd^3
lbs/yd^3
ft
ft
Portion of Cone not Mined
Incremental Stripping Ratio for Pit One Going to P
Total Volume Pit 2
796729815 yd3
Total Volume Pit 1
762551388 yd3
Incremental Volume
34178427 yd3
Ore Volume Cylinder 2 230907060 yd3
Ore Volume Cylinder 1 225775792 yd3
Incremental Ore Vol.
5131268 yd3
Incremental Waste Vol
29047159 yd3
Incremental Vol. SR
5.66081497
Weight of Increm Ore
12058480 tons
Weight of Increm Waste 59546675 tons
Weight Based SR
4.93815774
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 4th bench
Atan(160/283) = 29.48º
This type of planning normally gets
Working slopes in the 30 to 35
Degree range.
?
160 ft
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 pushback
– 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
Cone Pit
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)
Diameter Ore
Pit Slope
Enter Your Information in the
Present Depth
yellow fields below
Waste
Ore
Increase in Depth
Input Control
Diameter Ore
Pit Slope
Pit Slope in radians
Density of ore
Density of Overburden
Number of Existing Benches
Present Depth
Increase in Depth
New Depth
Diameter Origional Pit
Height of total cone (origional)
Diameter Incremental Pit
Height of total cone (incremental)
2100
47
0.820305
4700
4100
38
1520
40
1560
4934.846
2645.987
5009.447
2685.987
ft
degrees
lbs/yd^3
lbs/yd^3
ft
ft
Portion of Cone not Mined
Incremental Stripping Ratio for Pit One Going to Pit Two
Total Volume Pit 2
605416535 yd3
Total Volume Pit 1
576650362 yd3
Incremental Volume
28766173 yd3
Ore Volume Cylinder 2 200119452 yd3
Ore Volume Cylinder 1 194988184 yd3
Incremental Ore Vol.
5131268 yd3
Incremental Waste Vol
23634905 yd3
Incremental Vol. SR 4.606055386
Weight of Increm Ore
12058480 tons
Weight of Increm Waste 48451554 tons
Weight Based SR
4.018048315
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.