IntroductionExploration and Geology TechniquesOre Reserve EstimationFeasibility Studies and Project Financing

Planning and Design of Surface Mines Definition of Mining Parameters IntroductionMany factors govern the size and shape of an open pit. These must be properly understood and used in the planning of any open pit operation. The importance of each will depend on the particular project, but the following are the key items affecting the pit design: geology, grade and localization of the mineralization, extent of the deposit, topography, property boundaries, production rates, bench height, pit slopes, road grades, mining costs, processing costs, metal recovery, marketing considerations, strip ratios, and cutoff grades. This section will discuss several of these factors. Bench HeightThe bench height is the vertical distance between each horizontal level of the pit. The elements of a bench are illustrated in Fig. 5.1.1. Unless geologic conditions dictate otherwise, all benches should have the same height. The height will depend on the physical characteristics of the deposit; the degree of selectivity required in separating the ore and waste with the loading equipment; the rate of production; the size and type of equipment to meet the production requirements; and the climatic conditions.

Figure 5.1.1 Bench Cross SectionThe bench height should be set as high as possible within the limits of the size and type of equipment selected for the desired production. The bench should not be so high that it will present safety problems of towering banks of blasted or unblasted material or of frost slabs in winter. The bench height in open pit mines will normally range from 15 m (49 ft) in large copper mines to as little as 1 m (3.3 ft) in uranium mines. Pit SlopesThe slope of the pit wall is one of the major elements affecting the size and shape of the pit. The pit slope helps determine the amount of waste that must be moved to mine the ore. The pit slope is usually expressed in degrees from the horizontal plane. A pit wall needs to remain stable as long as mining activity is in that area. The stability of the pit walls should be analyzed as carefully as possible. Rock strength, faults, joints, presence of water, and other geologic information are key factors in the evaluation of the proper slope angle. The slope may be stated as a simple, overall average for the pit (e.g., 45), but a more detailed study may show that the physical characteristics of the deposit cause the pit slope to change with rock type, sector location, elevation, or orientation within the pit. Fig. 5.1.2 illustrates how the pit slopes may vary in the deposit.

Figure 5.1.2 Example of pit slopes varying in a deposit.A proper slope evaluation will give the slopes that allow the pit walls to remain stable. The pit walls should be set as steep as possible to minimize the strip ratio. The pit slope analysis determines the angle to be used between the roads in the pit. The overall pit slope used for design must be flatter to allow for the road system in the ultimate pit. Figures 5.1.3 and 5.1.4 show the need to design the pit with a lesser slope to allow for roads. The pit in Fig. 5.1.3 has been designed with a 45 angle for the pit walls. The pit in Fig. 5.1.4 uses the same pit bottom and the 45 interramp slope between the roads, but, a road has been added. Note the larger pit that results. In the example, almost 50% more tonnage must be moved to mine the same pit bottom.

Figure 5.1.3 Pit designed with a 45 pit slope.

Figure 5.1.4 Pit designed with a 45 interramp slope and a road system.In the early design of a pit a lesser pit slope can be used to allow for the road system. The pit in Fig. 5.1.5 was designed with an overall slope of 38. The overall slope to use will depend on the width, grade, and anticipated placement of the road.

Figure 5.1.5 Pit designed with a 38 overall slope to allow for a 45 interramp slope and a road system.Figure 5.1.6 shows a vertical section of a pit wall from Fig. 5.1.4. The interramp angle is projected from the pit bottom upward to the original ground surface at point B. The overall pit slope angle is the angle from the toe of the bottom bench to the crest of the top bench. Point A shows the intercept of the overall pit slope angle with the original ground surface.

Figure 5.1.6 Figure 5.1.6. Vertical section through a pit wall.Cutoff GradeAs stated by Taylor (1972), a cutoff grade is any grade that for any specified reason is used to separate any two courses of action. The reason used in setting a cutoff grade usually incorporates the economic characteristics of the project. When mining, the operator must make a decision as to whether the next block of material should be mined and processed; mined and stockpiled; mined (to expose ore) and sent to the waste dump; or not mined at all. The grade of the block is used to make this decision. For any block to be deliberately mined, it must pay for the costs of mining, processing, and marketing. The grade of material that can pay for this but for no stripping is the breakeven mining cutoff grade. A second cutoff grade can be used for blocks that are below the mining cutoff grade and would not be mined for their own value. These blocks may be mined as waste by deeper ore blocks. The cost of mining these blocks is paid for by the deeper ore. The final destination of these blocks is then only influenced by costs for the blocks once they have been mined. The blocks can be processed at this point if they can pay for just the processing and marketing costs. Because the revenue for the block does not need to cover the mining cost, the milling cutoff grade is lower than the mining cutoff grade. The cutoff calculation depends on the point of the cutoff decision in the life of the mine. In deciding whether to mine one more block at the end of the mine life, the only costs used would be the cash operating costs and a minimum profit to reflect the opportunity costs of using the money elsewhere. For a decision to mine one more year, the costs would be the cash operating costs, plus the replacement capital needed, plus all general and administrative costs that would be incurred. For a mine in the planning stage, the costs to be used are more complex and must be carefully considered. All direct costs of mining, processing, and marketing should be used. In the mining phase this would include the drilling, blasting, loading, and hauling costs. The processing costs would cover crushing, conveying, grinding, and concentrating costs. Depending on the final form of the product, the marketing costs could include concentrate handling, smelting, refining, and transportation. Additional direct costs for royalties and taxes would also be included. Overhead costs should also be added to the calculation. The general and administrative costs for the mine, mill, and administrative office staff should be included. Until the size of the pit has been determined and the associated overhead costs developed, the costs to be used for the calculation can only be estimated and are therefore subject to later refinement. Depreciation is used in the calculation for the purpose of setting the pit size. As shown in Fig. 5.1.7, the size of the pit will increase if the burden of some costs is removed. The cutoff grade is lower in increment C than in increment B. This is due to the lower costs used in determining the cutoff grade.

Figure 5.1.7 Relative pit sizes using different levels of costs.The material in increment C can only be economically mined after the plant has been depreciated. A plant built to handle the material in increment C would not be justified because the revenue would not cover the cost of the plant. If the plant was fully depreciated by the time increment C was mined, the ore would be worth processing. A minimum profit can also be used to calculate the cutoff grade. It will further decrease the size of the pit as shown by increment A in Fig. 5.1.7. The purpose of adding a minimum profit is twofold: (1) it confirms that a block is ore only if it can be mined and processed at a profit; and (2) it sets an economic limit below which a company would find an alternate investment more attractive. The amount of minimum profit to be used is a difficult decision. A true profit calculation would include the role of depreciation, depletion, and taxes. At the design stage, these are not known. An approximation can be made by increasing the costs. Other costs and changes in revenue can be included if they are known. These would include recoveries that vary with the ore grade, mining costs that vary with the distance or elevation of haulage, and the time lag between stripping the waste from a block of ore and the mining of the ore. These values should only be added if they are well known and the added degree of sophistication is warranted. Table 5.1.1 is the calculation of the mining cutoff grade for a copper project with the following parameters: 30kt/d (33,000 st pd) of ore mined for 20 years

$300,000,000capital cost (including replacement capital)

$1.00mining cost per tonne of ore

$0.95mining cost per tonne of waste

$3.00processing cost per tonne of ore

$1.00general and administrative (G&A) cost per tonne of ore

$0.75freight, smelter, and refining (FSR) cost per kilogram of copper

85%overall copper recovery

Table 5.11The results are shown graphically in Fig. 5.1.8. Note that the cutoff grade will increase as the costs increase. The difference between the mining cutoff grade and the milling cutoff grade is shown in Fig. 5.1.9.

Figure 5.1.8 Cutoff grades for different costs and metal prices.

Figure 5.1.9 Relationship of mining and milling cutoff grades.Strip RatioThe strip ratio is the ratio of the number of tonnes of waste that must be moved for one tonne of ore to be mined. The results of a pit design will determine the tonnes of waste and ore that the pit contains. The ratio of waste and ore for the design will give the average strip ratio for that pit. This differs from the breakeven strip ratio used to design the pit. The breakeven strip ratio refers only to the last increment mined along the pit wall. The strip ratio is calculated for the point at which break even occurs and the necessary stripping is paid for by the net value of the ore removed.

The calculation for the breakeven strip ratio (BESR) is: BESR = (A - B)/C where:A = revenue per tonne of oreB = production cost per tonne of ore (including all costs to the point of sale, excluding stripping)C = stripping cost per tonne of waste In certain studies a minimum profit requirement is included in the formula. BESR = [A - (B + D)]/C where:D = minimum profit per tonne of ore. Table 5.1.2 contains the information for calculating the strip ratio for the example used in calculating the cutoff grade previously. The results are shown graphically in Fig. 5.1.10.

Figure 5.1.10 Strip ratios for different ore grades and metal prices.

Table 5.12 Calculation of Breakeven Strip RatiosHead Grade (%Cu) KgCu recovered pertonne ore 1.0 8.50 0.9 7.65 0.8 6.80 0.7 5.95 0.6 5.10 0.5 4.25

tonne Ore kg Cu tonne Ore kg Cu tonne Ore kg Cu tonne Ore kg Cu tonne Ore kg Cu tonne Ore kg Cu

COSTS:

Mining* $1.00

Milling 3.00

G&A 1.00

$5.00 $0.59 $5.00 $0.65 $5.00 $0.74 $5.00 $0.84 $5.00 $0.98 $5.00 $1.18

FSR 6.38 0.75 5.74 0.75 5.10 0.75 4.46 0.75 3.83 0.75 3.19 0.75

$11.38 $1.34 $10.74 $1.40 $10.10 $1.49 $9.46 $1.59 $8.83 $1.73 $8.19 $1.93

Depreciation 1.40 0.16 1.40 0.19 1.40 0.20 1.40 0.24 1.40 0.28 1.40 0.33

Total Cost $12.78 $1.50 $12.14 $1.59 $11.50 $1.69 $10.86 $1.83 $10.23 $2.01 $9.59 $2.26

BREAKEVEN STRIPPING RATIO:

@ $1.75/kg Cu

Value $14.88 $13.39 $11.90 $10.41 $8.93 $7.44

Net 2.10 1.25 .40 (0.45) (1.30) (2.15)

Ratio 2.2:1 1.3:1 0.4:1

@ $2.00/kg Cu

Value $17.00 $15.30 $13.60 $11.90 $10.20 $8.50

Net 4.22 3.16 2.10 1.04 (0.03) (1.09)

Ratio 4.4:1 3.3:1 2.2:1 1.1:1

@ $2.25/kg Cu

Value $19.13 $17.21 $15.30 $13.39 $11.48 $9.56

Net 6.35 5.07 3.80 2.53 1.25 (0.03)

Ratio 6.7:1 5.3:1 4.0:1 2.7:1 1.3:1

@ $2.50/kg Cu

Value $21.25 $19.13 $17.00 $14.88 $12.75 $10.63

Net 8.47 6.99 5.50 4.02 2.52 1.04

Ratio 8.9:1 7.4:1 5.8:1 4.2:1 2.7:1 1.1:1

*Excludes stripping cost.

At stripping cost of $0.95 per tonne of waste.

()Indicates negative value.

ReferenceTaylor, H.K., 1972, General Background Theory of Cutoff Grades, Transactions (Section A: Mining Industry), Institution of Mining and Metallurgy, Vol. 81, pp. A160A179.