CHAPTER 5
Pit limits
5.1 INTRODUCTION
The time has now come to combine the economics introduced in Chapter 2 with the mineral
inventory developed in Chapter 3 under the geometric constraints discussed in Chapter 4 to
define the mineable portion of the overall inventory. The process involves the development
andsuperposition of ageometric surface called apit onto themineral inventory. Themineable
material becomes that lying within the pit boundaries. A vertical section taken through such
a pit is shown in Figure 5.1. The size and shape of the pit depends upon economic factors
and design/production constraints. With an increase in price the pit would expand in size
assuming all other factors remained constant. The inverse is obviously also true. The pit
existing at the end of mining is called the ‘final’ or the ‘ultimate’ pit. In between the birth
and the death of an open-pit mine, there are a series of ‘intermediate’ pits. This chapter will
present a series of procedures based upon:
(1) hand methods,
(2) computer methods, and
(3) computer assisted hand methods
Mineral
Inventory
Mineable Material
Pit Limit
Figure 5.1. Superposition of a pit onto a mineral inventory.
409
for developing pit limits. Within the pit are found materials of differing value. Economic
criteria are applied to assign destinations for these materials based on their value (i.e. mill,
waste dump, leach dump, stock pile, etc.). These criteria will be discussed. Once the pit
limits have been determined and rules established for classifying the in-pit materials, then
the ore reserves (tonnage and grade) can be calculated. In Chapter 6, the steps required to
go from the ore reserve to production rate, mine life, etc. will be presented.
5.2 HAND METHODS
5.2.1 The basic concept
Figure 5.2 showsan idealized cross-section through an orebody which outcrops at the surface
and dips to the left at 45
◦
. There are distinct physical boundaries separating the ore from
the over- and under-lying waste. The known ore extends to considerable depth down dip
and this will be recovered later by underground techniques. It is desired to know how large
the open-pit will be. The final pit in this greatly simplified case will appear as in Figure 5.3.
The slope angle of the left wall is 45
◦
. As can be seen a wedge of waste (area A) has been
removed to uncover the ore (area B). The location of the final pit wall is determined by
examining a series of slices such as shown in Figure 5.4.
For this example the width of the slice has been selected as 1.4 units (u) and the thickness
of the section (into the page) as 1 unit. Beginning with strip 1 the volumes of waste (V
w
)
and ore (V
o
) are calculated. The volumes are:
Strip 1:
V
w1
= 7.5u
3
V
o1
= 5.0u
3
The instantaneous stripping ratio (ISR) is defined as
ISR
1
(instantaneous) =
V
w1
V
o1
(5.1)
45°
Ore
Waste
5 Units
Figure 5.2. Cross-section through an idealized orebody.
Open pit mine planning and design: Fundamentals410
Hence
ISR
1
= 1.50
Assuming that the net value from selling one unit volume of ore (that money remaining after
all expenses have been paid) is $1.90 and the cost for mining and disposing of the waste is
$1/unit volume, the net value for strip 1 is
NV
1
= 5.0 × $1.90 −7.5 × $1 = $2.00
Outline of Final Pit Surface
Ore (B)
45°
Waste (A)
Waste
45°
Figure 5.3. Diagrammatic representation of the final pit outline on this section.
Surface
(1)
(3)
(4)
Waste
Waste
V
o1
V
w1
(2)
Ore
Figure 5.4. Slices used to determine final pit limits.
Pit limits 411
If the process is now repeated for strips 2, 3 and 4, the results are as given below:
Strip 2:
V
w2
= 8.4u
3
V
o2
= 5.0u
3
ISR
2
= 1.68
NV
2
= 5.0 ×$1.90 − 8.4 ×$1 = $1.10
Strip 3:
V
w3
= 9.45u
3
V
o3
= 5.0u
3
ISR
3
= 1.89
NV
3
= 5.0 ×$1.90 − 9.45 ×$1 = $0.05
∼
=
$0
Strip 4:
V
w4
= 10.5u
3
V
o4
= 5.0u
3
ISR
4
= 2 .10
NV
4
= 5.0 ×$1.90 − 10.5 ×$1 =−$1.00
As can be seen, the net value changes from (+)to(−) as the pit is expanded. For strip
3, the net value is just about zero. This pit position is termed ‘breakeven’ since the costs
involved in mining the strip just equal the revenues. It is the location of the final pit wall.
The breakeven stripping ratio which is strictly applied at the wall is
SR
3
= 1.9
Since the net value of 1 unit of ore is $1.90 and the cost for 1 unit of waste is $1, one can
mine 1.9 units of waste to recover 1 unit of ore (Fig. 5.5).
Surface
L
o
Ore
Waste
V
w
⫽ 50u
3
(9.5u)
L
w
Strip 3
(5u)
V
o
⫽ 62u
3
Figure 5.5. Final pit outline showing ore-waste distribution.
Open pit mine planning and design: Fundamentals412
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