kennedy, b. a. (eds.)-surface mining-society for mining, metallurgy, and exploration (sme)1 (1990)

4.2 Feasibility Studies

GUILLERMO V. BORQUEZ JAMES V. THOMPSON

INTRODUCTION The purpose of a feasibility study is to demonstrate, on

paper, the technical and/or economic practicability of a project prior to execution. The initial effort in this section is to establish a feasibility study model and to show how to develop its capital and operating cost.

Generally, surface mining feasibility studies are only a part of a larger all-inclusive feasibility study that might include beneficiation and processing as well as infrastructure facilities. An exception to this might be a mine where the ore is shipped to a nearby custom processing facility. There are several examples of this type of operation in the uranium industry in the western United States.

The objective of the feasibility study is usually economic and the methods employed are somewhat independent of the mineral commodity. However, in a country which might have massive unemployment, ample inexpensive hydroelectric power, and no domestic petroleum production, the objective might be the utilization of domestic resources for the benefit of the country rather than hard line feasibility in the tradi- tional sense. For example, trolley operated haulage units might be selected regardless of the more favorable apparent economics of employing diesel trucks and imported oil.

BASIC DATA REQUIRED

General Obviously the location, elevation, climatic environment,

and local infrastructure should be known. The local infrastructure, including such items as housing, power and water availability, communications and transportation systems, labor availability and quality, is important advance information. Nature of the Ore Body

Once the local setting of the ore body has been ascer- tained, its general nature should be studied to determine: 1) placer deposit, open or confined area; 2) rippable waste and/ or ore; 3) hard rock waste and/or ore; and 4) geological vs. minable ore body. Geological vs. Minable Ore Body

Geological Ore Body: The geological ore body generally includes all the body of material that contains the valuable mineral to be mined. The geological ore body may contain high and low grade ore mnes that are not physically or economically minable, because of depth, isolation, or amount of included or covering waste.

Minable Ore Body: The minable ore body is that portion of the geological ore body that can be extracted at a profit. The limitations to the minable ore body may be stripping ratio, grade of ore, alteration of ore, depth, excessive water, or environmental considerations.

At the beginning of an operation, the minable ore body may not be completely delineated and, as operations proceed, more of the geological ore body becomes minable because of the learning curve, improved methods and equipment, and increases in the prices of the mineral product being mined.

Overall changes in technology and economics may also

cause the removal of ore from the minable category. A typical example of this was the vast reserves of wash and jigging ore on the US iron ranges in the North Central States. The advent of pellet technology and the resulting economic advantages in blast furnace operation brought about the aban- donment of iron ore reserves that could only be beneficiatied to an iron content in the low 50% Fe range.

Ore Reserves and Waste to Ore Ratios: In order to make a meaningful feasibility study of a site specific mining operation, it is necessary to have as much data as possible concerning ore reserves and the waste to ore ratio. While ore reserves are often based on surface trenching and pitting and at times indirect geophysical surveys, the most common exploration methods usually involve core drilling or air hole drilling.

A surface mining operation may produce any combination of the following products: ore, stripped waste, included waste that occurs between distinct bodies of ore, low grade material to be stockpiled for future treatment or treatment by a separate process,

It is, of course, necessary to quantify the amounts of each material to be mined and handled. Most copper mines in the southwest US will produce most of the above products and the same is true for some uranium mines and iron ore mines.

Selection of Mining Methods: While this subject is discussed in greater depth elsewhere in this volume, it is of course important to emphasize that the mining methods must be defined before a feasibility study can be undertaken. In some cases, for example in many placer operations, it is di5cult to separate mining from concentration. A bucket line dredge, cutterhead dredge, bucket wheel dredge, or simple dragline operation usually dredges the material directly to the processing plant, which is frequently on board the dredge or floating alongside in the dredge pond.

Stripping: Stripping is discussed in more detail elsewhere in this volume. Most ore bodies require the removal of a waste covering of various depth; frequently the stripping operation involves different methods and equipment. Many coal and phosphate deposits are stripped by a large dragline or shovel which casts the overburden in windrows to the side of the exposed ore. Many uranium deposits in the West, particularly in Wyoming, can be stripped by ripper and scraper. The general objective of stripping is to expose the ore with minimum transport of stripping material, if transportation is required. Removal can be accomplished by con- veyor systems, diesel, diesel-electric or trolley trucks, or even scrapers at times. Pit slurrying and pipeline systems can be used where conditions are favorable. It is generally undesir- able to crush and wet overburden material because of the slime problem. In the early days of California placer mining, hydraulic methods were employed for the removal of overburden but the resulting slime problem in river waters ultimately closed down these mines.

Ore Mining: The excavation of ore and its transportation to processing plant facilities may involve quite different methods and equipment than those employed in stripping. In the feasibility study, the ore mining portion may be considered separately if the amount of stripping is considerable

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and the nature of stripping waste is quite different than the ore. For example; soft ores such as the phosphate ores of Idaho can be removed by ripper and scraper, and in some western US uranium mines, the ore is removed from small lenses by very selective backhoe excavation.

Production ,Scheduling: The extent to which mining is planned and scheduled will depend upon the end use of the feasibility study. If the study is destined to aid in the decision to accept or reject a property, a conceptual plan can be developed to arrive at quantities of ore and waste for costing purposes. On the other hand, if the study will be used to obtain funding, detailed plans should be prepared. For feasibility studies, this may involve computer-assisted calculation of ore reserves and computer-prepared plans and sections of the pit at various stages in the life of the surface mine. Computer modeling might be used to develop production schedules on a yearly basis for the first five years of the mine and on a five-year basis thereafter.

Definitions: A feasibility study must adhere to some carefully defined terms and these should be set forth at the beginning of any feasibility study report. The following are some important definitions.

Frame of Time-A feasibility study should be based on data and estimates for a one-year frame of time. Economic factors developed in the study will ultimately be used in some kind of economic analysis and these are always on an annual basis. The study may involve projected production rates over a number of years, but often the preliminary effort is to develop a full production model first. The total frame of time will depend on the life of the ore body and the economic criteria selected for the evaluation.

Operations Scheduling-It is important to define the annual hours of scheduled operation. Most very large mines are scheduled to operate 365 days per year, three shifts per day. However, certain sections such as the administrative group in the mine office may only work a 40 hour week on day shift only. Drilling and blasting is frequently scheduled for only five days per week, and often for only one or two shifts per day. Certain maintenance functions are more heav- ily manned on day shift and some may be on a 40 hour week basis. Some large mines in the United States will plan a total shutdown for ten legal holidays, frequently to avoid the pre- mium pay required for operation during these periods. Labor is usually scheduled on a rotating shift basis and an effort is made to hold each employee to a 40 hour week. If the mine is to operate three shifts a day, seven days a week, it may be advantageous for the primary crusher to operate on the same schedule. From the standpoint of worker satisfac- tion, the best schedule is probably five days a week, two shifts per day. However, this can cause downstream difficulties. For very large mines, the storage necessary for 48 hours of mill consumption of primary crushed ore could be quite costly, particularly in severe winter climates.

It is not uncommon to schedule Monday day shift, both in the mine, primary crusher and concentrator, for scheduled maintenance, but this period is still part of overall scheduled time. A feasibility study should contain a table that outlines the mine schedule similar to the example shown in Table 1. The table should contain the following: scheduled days per year, scheduled shifts per day, scheduled legal holidays when the mine is shut down, average tons per day of stripping waste, average tons per day of ore, peak tonnage delivered to the primary crusher, and any other data pertinent to scheduling and production.

Factors Which Affect Productivity-Usually a mining feasibility study is concerned with a nonexistent operation. No

productivity criteria may be available, and frequently there is no similar experience in the area. The engineer works with judgment factors and, where possible, with experience from similar mines. The following are productivity factors and the definitions of these factors as they apply to feasibility studies. Operating mines may adopt different definitions.

Ovemll Job Eficiency-This is an hourly factor and it refers to the average number of minutes per hour that a machine or group of closely linked systems will operate while in service in the mine. Downtime during the hour is caused by the following: fueling and servicing of equipment; recess and lunch time, if lunch must come out of an eight hour shift; poor coordination of shovels, haulage vehicles; and crowding at the dump point.

Machinery manufacturers often talk about the 50-minute hour which results in an overall job efficiency of 83.5%. However, in many operations, a 45-minute hour and 75% overall job efficiency is more realistic.

Mechanical Avuilubility-This is a term that may cause some confusion. In a feasibility study the concern is the mechanical availability of a machine assigned to the job. A machine can be 100% available simply because it is not scheduled to perform work. Loss of mechanical availability refers to time when the machine is substantially out of operation for repairs during the period of time when it would normally be scheduled for production. Machinery manufacturers tend to be somewhat optimistic about this number, but if an overall number could be picked for all machines in an average surface mine, it would probably be about 85%.

Generally, mines which are scheduled for a high percentage of total annual hours will have lower mechanical availability of scheduled units because there was simply less unscheduled time for maintenance. It should be emphasized that mechanical availability is related to time lost for maintenance when the machine was scheduled for operation and does not consider maintenance done on unscheduled time.

One Wyoming uranium open pit mine can document the fact that when a seven-day-week operation is used, scraper availability drops to about 65%. This means that a larger scraper fleet must be scheduled. If a five-day-week is used, scraper fleet availability increases and fewer machines are scheduled.

Annual Outage Factor-Most mines are subject to some kind of loss of production that can only be measured on an annual basis. Examples are: 1) electrical storms and snow storms which knock out transmission lines and substations and block roads; 2) flash floods producing uncontrollable water in the pit, haulage road damage, and slides in the mine; 3) moving large units of equipment, such as draglines and shovels, which may have to be walked by trailing auxiliary power; 4) external causes, such as breakdowns in the transportation systems, strikes in some other segments of the industry, and local labor disturbances.

Without a backlog of experience, it is recommended that some figure be used for annual outage factor if for no other reason than to indicate that the items have not been overlooked. If a 95% factor is used, meaning that 5% of the scheduled time is lost, this would be about 18 days in a mine scheduled for operation 365 days per year. The 95% factor is probably too low for a mild dry climate with an adequate public power system such as in Arizona; however, in a region of severe winter climate and heavy snowfall, 95% is probably reasonable.

Production Utilization -This is the figure often confused with availability. The concern here is with the amount of time on an annual basis that the machine is actually pro-

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ductive. A machine may be 100% available, but it has no work to do.

For the purpose of feasibility studies, production utilization can be considered as the product of all of the foregoing. For example, if a mine is scheduled for six days per week, three shifts per day, minus ten legal holidays, 7,248 hours are scheduled for operation. The production utilization would be 0.75 (job efficiency) X 0.85 (mechanical availability) x 0.95 (annual outage factor) = 0.61.

The production utilization for the preceding example is 61% of scheduled time, or 7,248 X 0.61 = 4,421 hours for most machines. This is a conservative figure, and if actual operating experience closely related to the project under study is available, such information should be used in pref- erence.

Costing Hours-Operating and maintenance labor should be carried on a separate table as an annual cost and not assigned to each machine on an hourly basis. This will be discussed in more detail later. Ultimately, the annual use hours must be costed. The time lost in the overall job efficiency factor is not considered as free time and direct operating cost is calculated for the full hour. However, direct operating cost is not accruing during the downtime related to the mechanical availability factor. Also the machine is not accruing direct operating cost during periods of annual outage. The annual costing hours, for the example already discussed, are determined as follows:

Total scheduled hours 7,248 Mechanical downtime 1,087

(7,248 X 0.15) Annual outage (7,248 X 0.05) 362

Costing hours (rounded up) 5,800

The costing hours for each machine are multiplied by the number of machines or fraction thereof to arrive at total costing hours for the particular type of machine.

MACHINE SIZING, UTILIZATION AND SELECTION

This can be a major engineering effort involving computer programs and detailed studies, but information for such a study is seldom available in the preliminary feasibility phases. Much time can be wasted in detailed studies of equipment selection which affect the reliability of estimates to only a

loo

d 1X Effort -53% 2 X Effort -71% 3X Effort -82% 4X Ef for t -89%

1X Effort -53% 2 X Effort -71% 3X Effort -82% 4X Ef for t -89%

0 ' I I I 1x 2x 3x 4x

Feasibility study effort

Fig. 1. Reliability vs. effort (not an absolute analogy).

small degree (see Fig. 1, which is a hypothetical comparison of reliability vs. effort). It should be noted that many older open pit mines tend to get over-equipped and caution should be used when using equipment performance data from the large older mine as an example.

For the purposes of the discussion that follows, the reader is referred to Table 1. Using this information as a basis, equipment will be sized for a hypothetical operation in order to demonstrate the principles involved in preparing a feasibility study. Drilling and Blasting

Some engineers prefer to design elaborate drilling patterns for feasibility studies, but generally this effort is unnecessary. There is usually not enough information on hand to design such a drilling pattern unless a pilot mine with full scale benches has been operated. Considering the contingencies employed in a feasibility study, it would be necessary to know all of the factors which affect drilling and blasting.

The most important factors to know or to assume, in drilling and blasting, are a reasonable penetration rate for the size of drill hole selected and the powder factor. The

Table 1. Basic Criteria, Hypothetical Open Pit Mining

Annual tons of ore and waste combined* Annual legal holidays of total shutdown Scheduled operating days per weekt Annual scheduled operating days§ Scheduled shifts per day Scheduled hours per year, 302 x 24 Average daily tonnage 24 hr day (ore and waste) Average hourly tonnage Peak delivery to dumping points (1752 i 0.75) Overall job efficiency (45 min. hour)* Average mechanical availability of scheduled timet Annual outage factor

12,700,000 10 6

302 3

7,248 42,053

1,752 2,336 75% 85% 95%

It is assumed that ore and waste are of the same physical nature and that the haulage distance for both is the same.

§ 5 2 x 6 = 3 1 2 -10 = 302, however, 365 - 10 - = 03. In this case, 3 0 2 days have been assumed.

t Blasthole drilling scheduled 5 days, 2 shifts. t Blasthole drills 6 0 % and 80%.

FEASIBILITY STUDIES AND PROJECT FINANCING 399

Table 2. Selecting Number of Drills Required

Hole size Bench height Hole depth Total hole volume Percent of hole depth filled with explosive Volume of explosives Bulk density of explosives average Weight of explosives in hole Explosives factor, kg/t rock blasted Tons broken per hole Total tons ore and waste per year Total holes per year, 12,700,000 + 1,807 Total length of hole, 7,028 x 13.72 Drilling rate while drilling the hole Actual drilling time required, 96,424 + 25.9 Scheduled annual hours, 5 days, 2 shifts, 10 holidays

Overall job efficiency Mechanical availability Annual outage factor

Production utilization 0.60 x 0.80 x 0.95 Actual productive hours: 4,000 x .456 Drills required: 3,723 f 1,824 Drills in use or available Drills owned Costing hours: [4,000 - (4,000 x 0.20) - (4,000 x 0.05) x 2.051

22.86 cm 12.20 m 13.72 m 0.56 m3

60 % 0.34 m3 803 kg/m3 271 kg 0.15

1807 t 12.7 Mt

7,028 96424 m

3,723 hr 4,000 hr

25.9 m / h r

60% 80% 95%

45.6% 1,824 hr 2.05 2.0 3.0

6,150 hr

Note: Time lost from overall job efficiency is not free time because most of it is for drill movement nonoperating time due to mechanical availability and annual outage factors are not changed for direct operating cost.

penetration rate is the meters drilled per hour while actually drilling, and the powder factor is the quantity of explosives required per ton of rock broken. With these two factors, a reasonable estimate can be made of the number of drills required.

Table 2 gives a typical feasibility analysis of drill requirements. Many of the line items are assumptions based on experience and in some cases field observation. Referring to Table 2, the hole size selected was 22.86 cm. Generally, larger holes require less drilling but may not yield as good frag- mentation as a larger number of smaller holes. The hole depth is 13.72 m, 12.20 m is in the bench and 1.52 m is in the toe. The hole volume is 0.56 m3 and it will be filled to 60% of hole volume with explosives resulting in a total volume of 0.34 m’. These are arbitrary assumptions for a preliminary analysis.

The bulk density of the explosives is 803 kg/m3 and the weight of the explosive in the hole is 271 kg. This is a critical figure. The explosive factor is 0.15 kg of explosive per metric ton of material blasted and, therefore, each hole breaks 271 + 0.15 = 1 807 t. The total tons of ore and waste to be blasted each year is 12 700 OOO. The holes per year are 12 700 OOO -F 1 807 = 7 028 holes per year. The total length of holes is 7 028 x 13.72 = 96 424 m.

Next, it is necessary to develop production utilization. This is the product of assuming an overall job efficiency of 60%, a mechanical availability of 80%, and an annual outage factor of 95%, yielding a production utilization of 45.6%. The low overall job efficiency accounts for moving the drill from hole to hole and the low mechanical availability accounts for the rough usage that blast hole drills may en- counter.

The drilling in this example has been scheduled for two shifts per day, five days per week, minus ten legal holidays which results in 250 scheduled days or 4 OOO scheduled hours.

With production utilization of 45.6%, the actual drilling hours equal 1824. In this amount of actual drilling time,

96424 m of drilling must be accomplished in a year. As shown in Table 2, the drilling could be accomplished by 2.05 drills which means that two drills would be in use and that the operation would own three drills. The third drill could be a deferred purchase after the first year. The costing hours for the drills would be 6 150 hours as shown by the calculation at the bottom of Table 2.

Secondary Size Reduction This can be a costly activity. Every reasonable effort

should be made to avoid secondary blasting methods by perfecting better primary blasting. However, it is often necessary to do secondary lump breaking of some kind. The modem trend is away from explosive methods. Drop balls and similar devices tie up an expensive machine, which may be slow to move.

Consideration should be given to hydraulic hammers mounted on a controllable boom and on rubber tires with self-contained on-board power sources. However, the hydraulic hammer may be expensive and underutilized. A sec- ondhand or unused small dragline may be available which could be equipped with a drop ball, or a portable compressor and wagon drill might be used to drill a single hole in a large boulder for explosive breaking.

For the purpose of this example, a 0.40 m’/s compressor and a 1.18 cm track-mounted hammer drill has been selected. Such a unit can do other drilling jobs around the mine as well as secondary breaking. It is arbitrarily scheduled for 800 hours per year and there will be days when it is not used at all. Mechanical availability during scheduled time should be near 100%.

Loading Machines A typical open pit loading machine is the standard cable

operated dipper and boom shovel that has been in use for many years. A more modern piece of equipment with bucket capacities up to 15.3 m3 is the hydraulic front shovel. Since

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1970, front-end loaders have been perfected to the point where they can be used in coarse blasted rock and can be either rubber tired or crawler mounted. For the purposes of this discussion, Table 3 gives the data required to select the number of 7.65 m’ conventional shovels. The factors used in Table 3 are judgment factors, in part based on manufacturer’s information and in part on field observations.

Fill Factor: Fill factor is the percent of total capacity of the bucket that is actually filled during each pass into the muckpile. Coarse, poorly blasted ore usually gives a low fill factor. Finer ore and a relatively smooth bottom will give a high fill factor.

Actual Bucket Capacity: This is obtained by multiplying the fill factor by the bucket size.

Swing Time: Swing time is the time in seconds that it takes for the operator to crowd the bucket into the muckpile, pull out, turn, and dump into the haulage vehicle and return to the muckpile. The swing time for shovels is usually less than the similar cycle time for front-end loaders. However, this depends on the nature of the muckpile and the skill of the operator. Generally, conventional shovels will perform better in coarsely blasted rock than front-end loaders. Front shovels were first introduced in the mid 1960s and were mostly of European design. By the early 1980s most US manufacturers of excavating machinery were offering competitive designs. Sizes have ranged up to 19 m’, but the more common large size is about 15 m’. The advantages and disadvantages of front shovels compared to conventional cable operated shovels is hardly significant in a preliminary feasibility study. Many manufacturers make both types, and they have accumulated considerable operating data.

Continuous Capacity: The continuous passes per hour are determined from swing time and this multiplied by bucket capacity gives the hourly continuous production that would be expected. Continuous capacity is determined first and then discounted for production utilization later. See Table 3 for an example of this calculation.

Swell Factor and Bulk Density of Blasted Material: This is difficult to obtain even from operating mines. In the ex-

ample on Table 3, a swell factor of 0.67 has been employed, and this means that a bank m3 after blasting will have a volume of 1.49 m’. The weight of a bank m’ is 3.0 t, which means that the weight of a loose m3 would be 3.0 + 1.49 = 2.0 t. The tons per hour capacity of the loading machine at 80% lill factor on a continuous basis is then 6.12, giving a total of 1 571 t /h continuous capacity.

Production Utilization and Annual Shovel Capacity: Employing a 75% overall job efficiency, 85% mechanical availability, and 95% annual outage factor, the production utilization is 60.6%. The mining shovels are scheduled for three shifts per day, six days per week, minus 10 legal holidays which equals 302 days or 7,248 scheduled hours. When this is multiplied by the production utilization, the result is 4 392 hours of continuous production. Multiplying this number by the tons per hour capacity of the shovel, the annual capacity becomes 6 899 832 t. The annual production of ore and included waste is 12.7 Mt/a. Dividing the annual requirements by shovel capacity indicates that 1.84 shovels are required.

Two shovels would be in use, and rather than owning a third shovel, the operation could be equipped with a 9.18 m’ front-end loader, rubber tire mounted, which could back up the shovels and do other utility work. It can be noted in this calculation that the annual tonnage can safely be made when one shovel is shut down for short periods of time and production could be easy to sustain on an annual basis, if the front-end loader can be used as backup. To provide absolute assurance that loading will go on at all times, it would be necessary to equip the mine with more equipment than is justified when production is considered on an annual or even a weekly basis. Certainly, two shovels and a large front-end loader are adequate for the annual tonnage required.

Haulage Units For the purposes of this example, 77.1 t (85 st) rear dump

trucks will be used. The selection of an electric wheel or

Table 3. Selecting Boom and Dipper Type Shovel

Bucket size 7.65 m3 Fill factor, well blasted rock 80% Average bucket capacity 7.65 x 0.80 6.12 m3 Swing time 28 sec Passes per minute, continuous operation 60 + 28 2.1%

787 m3 m3 per hour continuous 6.12 x - x 60

Swell factor 0.67 Weight of bank m3 in place 3 t Loose m3 = 1 f 0.67 1.49 m3 Weight of loose ore 3 f 1.49 2.0 t/m3 Tons per pass, continuous 6.12 x 2 Tons per minute, continuous 12.24 x 2.14 Tons per hour, continuous 26.19 x 60 Annual tons to be loaded Annual shovel hours 12,700,000 f 1,571 Annual scheduled hours, 3 shifts, 6 days, 10 holidays

60 28

12.24 t 26.19 t 1571 t/h

8,084 hr 7,248 hr

12,700,000

Overall job efficiency 75% Mechanical availability 85% Annual outage factor 95%

Production utilization 75% x 85% x 95% 60.6% Productive hours 7,248 x 0.606 = 4,392 hr Shovels required 8,084 shovel hours f 4,392 1.84 Shovels in use 2.0 Costing hours [7,248 - (7,248 x .15) - (7,248 x .05)] x 1.84 = 10,669 hr

FEASIBILITY STUDIES AND PROJECT FINANCING 40 1

Table 4. Haulage Truck Selection, 854 (94st) Trucks

Cycle time continuous Trips per hour, continuous 60 -+ 12.5 Tons per hour continuous 4.8 x 85 Overall job efficiency Mechanical availability Annual outage factor Production utilization Scheduled hours per year (365 - 52 - 11) X 24 Productive hours 7,248 x 0.606 Annual production per truck year 4,392 x 408 Annual production required Trucks required 12,700,000 + 1,791,936 Trucks in use Trucks in fleet Costing hours [7,248 -(7,248 x .15) -(7,248 x

12.5 min 4.8

408 t/h 75% 85% 95%

60.6% 7,248 hrs 4,392 hrs

1,791,936 t 12,700,000

7.09 8.0 9.0

.05)] X 7.09 = 41,111 ~ ~ ~~ ~

Note: If trucks were capable of operating 100% of scheduled time only 4.29 trucks would be required. A fleet of eight trucks could in theory handle all the requirements without any spare, but if more than three trucks are out of service, the production schedule could not be met and a spare truck is provided to insure production if more than three trucks are out of service.

mechanical drive should be given careful study during the feasibility analysis.

Cycle Time: For the purpose of this example, it will be assumed that ore and waste are hauled the same distance (1 067 m one way) and that 12.7 Mt of combined ore and waste will have to be hauled each year.

The cycle time for trucks can be determined with greater reliability if an accurate profile is available over the haulage route. In the early phase of feasibility studies, this must be calculated from a hypothetical mining plan or assumed from limited information.

Manufacturer’s catalogs contain data from which the speed for loaded and empty trucks can be calculated for actual distances and grades.

A typical truck cycle might be:

Maneuvering for position at the shovel 1.0 min. Loading 3.0 min. Accelerating the loaded truck 1.0 min. Haulage to dumping point, 1 607 m away 2.5 min. Decelerate and dump 1.5 min. Return empty 1.5 min.

Total 12.5 min.

A critical portion of the cycle time is the time required to load the truck. In this example, the 77.1 t (85 st) truck might be somewhat large for a 7.65 m3 shovel because six passes might be considered excessive to some operators. How- ever, the 77.1 t (85 st) truck is an efficient unit and fewer truck drivers would be required.

The use of computer programs to optimize truck and shovel combinations is recommended for feasibility studies when adequate data is available.

Determining the Number of Haulage Units: Table 4 gives the calculations for determining the number of haulage units without necessarily optimizing the shovel-truck combination and without details of the haulage road profile. Support and Auxiliary Equipment

For the example under consideration, drills, shovels and trucks are the front line, regularly scheduled production equipment. Other support and auxiliary equipment is required as follows:

Rubber Tired Front-End Loader: In this example, a large front-end loader is proposed for emergency use when a reg-

ularly scheduled loading shovel is shut down for an extended period. This machine has a capacity of 9.18 m3 and its performance could be calculated in the same manner as the shovel in Table 3. It would probably have about the same fill factor, but its swing time or cycle time would be somewhat more. Depending upon conditions and the skill of the o p erator, it might have about 90% of the annual capacity of a 7.65 m3 shovel. As an alternative, the operation could be equipped with two smaller front-end loaders of lesser capacity.

The front-end loader is useful for removing isolated seg- regations of included waste or low grade ore. In any event, costing hours must be assigned to the front-end loader. Ar- bitrary scheduling might be one shift per day, six days per week, and with such light duty scheduling, its mechanical availability could be assumed to be 100% and the annual outage factor insignificant. When accounting for ten legal holidays and a six day work week, the scheduled annual days amount to 302, and the annual costing hours on a single shift basis will be 2,416 hours.

Rubber Tired Bulldozers: Where traction is no problem and there are no excessive lumps of very large coarse rock, a rubber tired bulldozer is very useful around an open pit mine. Compared to a track mounted dozer, the rubber tired bulldozer can be moved rapidly from one work site to the other.

Some of the duties which can be assigned to the rubber tired bulldozers are: 1) sweeping up fly rock around the shovel to keep a clear path for haulage trucks; 2) crowding the muckpile so that the dipper on the shovel may achieve a higher fill factor; 3) keeping a generally smooth haulage road in the immediate vicinity of the shovel, performing such dudes as filling chuck holes that may accumulate water; and 4) leveling wind rows on waste dump.

Before the development of the rubber tired bulldozer, a track mounted bulldozer would be assigned to a large shovel. Much of the time this machine was idling without much work to do. Since the development of rubber tired bulldozers, if the shovels are not too far apart, one rubber tired dozer may service two shovels. For the purposes of this example, two machines of the 231 kW class are assumed. Such a machine may be oversized for some of the duties but it would have the capacity for more rigorous duty when required. There should be one rubber tired dozer assigned to the two

402 SURFACE MINING

shovels and one other assigned to the waste dump. It may not be absolutely imperative that the waste dump station be constantly attended by one of the bulldozers. Backup is provided by a track mounted bulldozer and a motor grader, discussed later. The costing hours for the two bulldozers combined is about the same as the costing hours for the two shovels, which amounts to 10,612 per-year.

Track Mounted Bulldozers: The dozing power of a track mounted bulldozer exceeds that of the rubber tired machines and its principal duty would be in the pioneering of cuts for new benches and pit roads. In an emergency, it could be used on the waste dumps and around the shovels. For this example a machine in the 343 kW class is used, and if it were scheduled for use on day shift only, it should have almost a 100% mechanical availability during scheduled time and the annual outage factor would not be significant. The costing hours would be about 2,400 per year.

Motor Grader: A motor grader is indispensable for most open pit mines to properly maintain haulage roads. If the motor grader is scheduled for day shift only, six days per week, its mechanical availability should be almost 100% of scheduled time and the annual outage factor would be insignificant. The costing hours would be about 2,416. There are no tasks assigned to the motor grader that are so imperative that they cannot be delayed for minor maintenance purposes. In addition, both the rubber tired and track mounted bulldozer, and to a lesser extent, the front-end loader, can provide emergency backup for the motor grader.

Smaller Dump Trucks: There are frequent duties around a large open pit mine where smaller utility dump trucks can be used. In this example it is assumed that 32 t (35 st) trucks would be available for miscellaneous use. Among these uses are emergency use for ore haulage in case of unexpected multiple breakdowns of the main truck fleet and the haulage of road dressing material for the haulage roads. The total costing hours for the three trucks could be assumed to be about 2,400 hours.

Service Vehicles: Most surface mines find it necessary to sprinkle the haulage roads to control dust and, therefore, a water sprinkling truck is necessary. In a dry arid climate such as the southwestern United States, the truck may be used all year around; but in more humid northern climates, it might not be used for more than five or six months per year. Indeed, mud may be a greater problem than dust. For the purpose of this example, an arid dry climate is assumed and the sprinkling truck would be used for a few hours every day. For study purposes, assume 1,OOO hours per year.

Most surface mines will have a field fueling and lubrication truck and a field repair truck with welding, hard facing, and cutting equipment on board. Some large mines may also have a field tire changing truck, but in most locations in the United States, the major tire manufacturers have service organizations very close by that can dispatch a truck from their shop to the mine to perform this service.

Supervisors and engineering staff are usually provided with pickup trucks. Haulage of explosives and the loading of blastholes can often be contracted in United States mines.

All of the aforementioned vehicles, with the exception of pickup trucks, are generally underutilized. Even in a dry climate the sprinkling truck would probably be in use no more than about 1,200 hours per year. The same applies to fuel and repair trucks, and for both of these vehicles, a combined allowance of 2,000 hours per year would be adequate for this example. It will be assumed that the mine in the example being discussed here will be equipped with an explosives truck whose scheduled time would hardly exceed

600 hours per year. For this example, no tire changing truck would be provided.

For a mine that moves a total of 12 700 OOO t per year, there would probably be about eight pickup trucks for supervisors and engineers. Use of such vehicles will vary widely, but for the purposes of this example, it is assumed that the total usage would be about 10,OOO hours per year.

Pit Drainage and Lighting: These items may add significant cost to the mining operation. Many surface mines which do not have natural drainage may have to resort to pumping water from low points in the pit. For this example, it will be assumed that the mine is developed on a self- draining hillside location. If an open pit mine is to be developed on relatively flat terrain, a great deal of drilling and hole pumping may be required to obtain an estimate of the quantity of water to be removed. Accurate information can be difficult to obtain in the preliminary phases. With sufficient information, projections of water quantities can be made by competent geohydrologists. Complex problems can be en- countered where lakes must be drained, streams rerouted, and well points established around the active mining pit.

Most mines scheduling a night shift would have pit lighting. All of the equipment has attached headlights or floodlights. Most shovels and large blast hole drills are electrically operated, therefore, power is generally available in the pit and lights may be strung along the principal haulage loads. Portable floodlights can be placed in the shovel and dumping areas. Developing the equipment and cost for pit lighting is a straightforward engineering task and need not to be discussed in detail here. For the purpose of this example, it will be assumed that pit lighting is provided from the power distribution system in the mine.

Power Distribution: When shovels and blast hole drills are electrically powered, power distribution facilities from incoming power lines involve portable switch houses and trailing cables. While these units do not involve large operating costs, they are a significant item of capital cost. For the example being considered, three 1,OOO ampere switch houses and four trailing cables of at least 457 m (1,500 ft) capable of handling 8,OOO volts are assumed. Besides the secondary distribution system, the feasibility study must consider the requirements for incoming power and a loop around the pit, if necessary.

Radio Communication: Every mining operation today should make maximum use of two-way radio communications which is inexpensive in both capital cost and operating cost. A repeater station would be required which is located either on a high elevation of land or a tower so that maximum range may be obtained in the system. All supervisors’ trucks, haulage trucks, field service, repair trucks, and shovels should be equipped with a two-way radio unit. Other units such as the rubber tired bulldozer, motor grader, front-end loader, and water truck might be included.

MAINTENANCE FACILITIES

General Maintenance Concept for Feasibility Studies The ultimate objective of feasibility studies is usually

economic and involves the development of capital and operating cost. Many large mining operations will have central shops that perform all the maintenance for the mine, concentrator, processing plant, railroad, port facilities, and town site, as applicable, on a work order basis. The difficulty with this concept in a feasibility study is that it becomes necessary to prorate maintenance costs in order to determine a maintenance cost for the mining department.


The preferred method for feasibility studies is to assume that the mining department operates its own maintenance facility for the use of the mine. In some instances this might include the primary crusher. For this example, it will be assumed that the maintenance facility is solely for the mine and under the supervision of the mining department.

Nature of the Facilities Mine maintenance shops can vary from elaborate, fully

equipped, enclosed, and heated facilities to simple open shel- ter in a mild climate. The location of the mine, the sur- rounding infrastructure, and transportation facilities to and from the supply centers affect the nature of the shop. In a remote area, in the subarctic for example, the mine shop would have to be enclosed and heated with the equipment and parts inventory necessary to sustain the operation with the supply centers located thousands of miles away. In a remote tropical area, the structure might be in open shade but the facility would have to be fairly complete.

In remote areas the mine shop will have to carry a large inventory of spare parts, be capable of rebuilding engines, transmissions, and electrical components. A tire recapping shop may also be required.

In mining districts such as the northern US iron ranges and the southwestern copper mining districts, suppliers maintain service centers in medium to large communities within the district. Tire service is often provided on a contract basis. Major machinery companies that manufacture open pit mining machinery keep stocks of spare parts nearby and can usually provide engines and transmissions on an exchange basis.

From the foregoing discussion, it can be seen that maintenance facilities are affected by the local infrastructure and climate conditions. As stated in the beginning of this section, information concerning infrastructure and climatic conditions is essential in the preparation of a feasibility study. For the purposes of the example referred to herein, it is assumed that the maintenance shop is in a mild climate requiring some minimum enclosure and provisions for restricted space heating.

Sizing the Maintenance Facilities The maintenance facility usually involves a rectangular

building with numerous bays along one long side. These bays are usually equipped with roll-up doors that remain open most of the time, weather permitting. The building should be high enough so that it can accommodate a haulage truck with the bed raised to the maximum vertical position. It is desirable for the building to be equipped with an overruning bridge crane with the capacity to remove the largest engine. Heating can be provided on a spot basis with several types of heating devices.

In preparing a feasibility study it is important that sup- porting maintenance facilities not be overlooked. These include spaces for welding, electrical and instrumentation repair, and washdown. In remote areas requirements for oil reclaiming and components repair may be needed.

One of the important concepts to be developed during the preparation of the feasibility study is the amount of repair and maintenance work to be done at the mine. Because the cost of space and equipment can be significant and because the cost of downtime for equipment improperly maintained can become prohibitive to an operation, the repair and maintenance facilities should be developed in some detail during the feasibility process. See Table 5.

CAPITAL COSTS

Definition of Capital Costs A general definition of capital costs would be those items

of project cost that will be depreciated for capital recovery and tax purposes. Whether or not certain initial costs are capitalized or expensed is frequently influenced by management policy and income tax requirements. For example, the preproduction cost required to bring an open pit mine into production might be capitalized or expensed depending upon a particular company’s policy. As a general rule most mining companies would prefer to expense these items if it resulted in a tax advantage that was allowed by law.

Items Specifically Included in Capital Costs: Generally, capital costs include: 1) exploration and other preproduction cost depending on management policy; 2) mining machinery including freight, erection, and initial spare parts inventory; 3) permanent structures such as maintenance shops, mine offices, and warehouse; 4) all of the equipment and initial supplies in permanent structures; and 5 ) operating capital.

For a complete mining facility which might involve con- centrators, smelters, refineries, and other infrastructure, the list and definitions of capital costs would be more extensive.

Items Specifically Excluded fkom Capital Costs This category also depends upon management policy and tax matters but, in general, facilities located outside the immediate area of the mine are normally excluded from feasibility studies.

Types of Feasibility Study Estimates For the purpose of feasibility studies, four general types

of estimates have been devised for both capital and operating costs. A summary of these definitions is included in Table 6. Generally, feasibility studies restricted to mining only seldom become overly involved with these definitions. With the exception of more detailed design for permanent facilities, the definitions vary only slightly from Type I to Type IV. There is no difference in a quotation for equipment obtained for Type I or Type 11. Type I11 and Type IV might involve written equipment specifications. The feasibility study types are somewhat more applicable for complete feasibility studies that involve an entire project, not just the mining phase alone.

Mobile Mining Equipment. In the preparation of a mining feasibility study, one of

the most important items of capital cost is the list of mobile mining equipment. This list should include the following: 1) FOB factory cost of the machine fully equipped with all of the accessories required for the job; 2) dry weight of the machine; 3) export packing, if required; 4) installed diesel or electrical power, although not important for small vehicles; 5 ) freight from factory to job site, including actual deliveries to the job site; 6) import duties and special taxes; 7) job site erection cost; and 8) spare parts inventory.

Many of the above items are essential for operating cost calculations. The weight of the equipment may be required for freight calculations. In addition, if the weight and cost of a machine are known, a rough estimate can be made of the cost of another machine if its weight is known and if it is of the same order of complexity.

Most mining machinery in the United States originates in the middle west or the upper middle west, and inland freight charges in the United States can be estimated by contacting railroads and truck lines.

404 SURFACE MINING

Table 5. Major Items of Shop Equipment

Item Size QtY Unit Wt, kg

Overhead crane Shop supply air compressors Steam cleaner Forklift truck Welders, shop Welders, field Pipe/ bolt threader Band saw Hydraulic drill press Oil reclaiming unit Blacksmith anvil Pedestal grinder Work benches

Cleaning tanks

Tool lockers Welding booth Tire press Tire press Jib crane Engine positioner Transmission positioner Hydraulic puller Differential stand Hose reels, lube oil, air,

water, grease Barrel pumps Electrical test equipment Battery charge Injector pump tester Injector nozzle tester Sump pumps Grit blaster w/enclosure Chain hoists Miscellaneous tools Subtotal before sales tax

Subtotal before contingency Sales tax @

Contingency @ 10% Total

17.3 m3/min

1.8 t 400 amp 600 amp

15 cm pipe, 5 cm bolt

25 cm 190 L/hr

-

-

- 0.76 x 1.52 x 0.91

m high 0.91 x 3.05 x 0.91

m deep 36 compartments

3 room Light vehicle Heavy vehicle

0.9 t -

Light vehicles -

- 1.8 t

1 ea 1 ea 2,950 1 ea 410 1 ea 2,720 2 ea 365 2 ea 455 1 ea 2,270 1 ea 860 1 ea 455 1 ea 455 1 ea 230 1 ea 270 5 ea 270

2 ea 680

1 ea 1,360 1 ea 180 1 ea 180 1 ea 1,815 1 ea 1,000 1 ea 410 1 ea 410 1 ea 1,815 1 ea 365

4 ea 270 2 ea 270 lot 90 1 ea 45 1 ea 20 1 ea 20 2 ea 45 1 ea 320 5 ea 140

Import duties and other government assessments on overseas projects may require careful investigations. Even though foreign projects may be undertaken by mining organizations owned by the government, duties on imported equipment may be assessed.

Most large mining machinery arrives on the job in a knock-down condition. A large dragline, for example, can require many months to erect. Erection and start up of large mining machinery is usually under the supervision of a field engineer provided by the vendor. His service, if not included in the initial price of the machinery, will be an extra cost charged by the vendor.

Spare parts inventories can represent a significant capital cost; the cost of this inventory is an interest-bearing item. In the United States, where vendors maintain field service organizations, inventory may be kept to a minimum. On overseas projects, spare parts inventories are usually larger. Often an overseas project is being financed by some source of international funding and the tendency is to provide a large initial spare parts inventory since it may be difficult to

obtain government licenses to import spare parts once the project is operational.

For a preliminary feasibility study, 5% of the FOB factory cost of the machinery is adequate for estimating an initial stock of spare parts at US locations, but overseas projects may require as much as 10 to 20%.

Permanent Structures Usually the permanent structures for an open pit mine

are relatively simple architectural and structural designs. Unless the mine includes a crushing plant, the permanent facilities are usually a maintenance shop, mine office, warehouse, outdoor storage, fuel storage facilities, powder mag- azine and blasting material storage, and a changehouse. For a preliminary study, these facilities can be estimated by the square foot employing locally obtained unit costs. If the maintenance shop is to be equipped with an overhead crane, the building must be designed to include columns and crane rails for the support of the crane. Table 7 gives an example of a preliminary estimate for permanent structures for an


open pit mine. More detailed estimates, of course, require detailed design with quantity take offs.

OPERATING COST Operating costs for a feasibility study should be developed

for each element of cost. Caution should be exercised when using the operating costs o f existing mines. Criteria may be obtained from existing mines, but even a primary feasibility study should document each item and group of operating costs.

I f the feasibility study involves a surface mine only, the operating cost should include the highest level o f resident management. I f the feasibility study i s for an integrated mining, concentrating, and smelting operation, the operating cost estimate should include the highest level of management

directly related to the mine. This would generally be the office of the mine manager. Generally,front o 8 c e cost should not be prorated against the mining department.

Definitions Generally, operating costs include: 1) supervision and

labor, salaries and wages; 2) labor burden; 3) all expendable mining supplies; 4) operation of major mining equipment including maintenance parts; 5) electrical power; 6) allowance for mine department undistributed overhead such as office supplies, engineering supplies, and general maintenance supplies; and 7) local property taxes and insurances, in the case where the mine i s producing ore for direct shipment to other utilization points.

Items which are generally not included in a mining fea-

Table 6. Types of Feasibility Study Estimates5

Item Type I Type II Type 111 Type IV

Site Plant capacity Geographical location Maps and surveys Soil and foundations tests Site visits by project team

Process flowsheets Bench-scale tests Pilot plant tests Energy and material balances

Nature of facilities Equipment selection General arrangements, mechanical General arrangements, structural General arrangements, other Piping drawings Electrical drawings Specifications

Estimates prepared by Vendor quotations Civil work Mechanical work Structural work Piping and instrumentation Electrical work Indirect costs Contingency t

Labor rates Labor burden Power costs Fuel costs Expendable supplies Reagents Parts

Process

Facilities Design

Basis for Capital Cost Estimating

Operating Cost Determination

Economic Analysis D.C.F. Use of Estimates

Assumed Assumed None None Possibly

Assumed If available Not needed Not essential

Conceptual Hypothetical None None None None None None

Project Engr Previous Rough sketch % of machinery Rough sketch % of machinery $ per kW % of total 20-20% t

Assumed Assumed Assumed Assumed Assumed Assumed Assumed Not meaningful Comparison

rejection

Preliminary General If available None Recommended

Preliminary Recommended Recommended Preliminary

Possible Preliminary Minimum Outline Minimum None None Performance

Sr Estimators Single source Drawing estimate % of machinery Prelim drawings % of machinery $ per kW % of total 1520% t

Investigate Calculated Actual Verbal quote Verbal quote Verbal quote Verbal quote If requested Feasibility

Optimized Approximate Available Preliminary Essential

Optimized Essential Recommended Optimized

Probable Optimized Preliminary Outline Outline One-line One-line General

Sr Estimators Multiple Drawing estimate Man-hr/ton Takeoff /ton Take-off Take-off Calculated 15%t

Get contracts Calculated Actual Letter quote Letter quote Letter quote Letter quote If requested Budget

Finalized Specific Detailed Final Essential

Finalized Essential Essential Finalized

Actual Finalized Complete Preliminary Preliminary Some detail Some detail Detailed

Est Dept Competitive Ta ke-of f s Man-hr / ton* Take-off /ton* Ta ke-off * Take-off * Calculated 10%t

Get contracts* Calculated* Contract t Contract t Contract * Contract* Letter quote If requested Funding

* Often subject to subcontract bids. t In this definition the percentage assigned to contingencies is a judgment factor and is not to be interpreted as meaning that estimates are

t Contracts can be solicited if project is near-term. 5 Table courtesy of Kaiser Engineers.

necessarily accurate within this percentage range, nor is there an implied reference to any order of accuracy.

406 SURFACE MINING

Table 7. Estimated Capital Cost, Mine Maintenance Shop

Item

Total cost US$ x

1000

1 2 3 4 5 6 7 8 9

10 11 12 13 14

Structure 10,368 $m3 @ $62.21 m3 Shop equipment Fuel handling equipment Millwright labor and material, 20% of $946,000 Piping labor and material, 10% of $946,000 Electrical labor and material, 10% of $946,000 Subtotal-Equipment and installation, Lines 2 thru 6 Subtotal-Direct field cost, Line 1 + 7 Contractor’s Field O.H., Camp, Plant and Profit, 30% of line 8 Subtotal-Field constructed, Line 8 + 9 Engineering, Procurement, Construction Management, 12% of line 10 Total-Before contingency, Line 10 + 11 Contingency, 20% of Line 12 Total

$ 645 913

33 189 95 94

$1,324 $1,969

591 $2,560

307 $2,867

573 $3,440,

sibility study are: 1) nonresident management and sales costs; 2) income related or other taxes, because these are matters to be addressed in the economic analysis; 3) depreciation, interest, and royalties, which also are to be addressed in the economic analysis; and 4) transportation of ore beyond the local dumping points.

Basis for Direct Operating Cost Calculations Every attempt should be made to develop operating cost.

Unit cost from other mines can be used as a credibility check, but the engineer should develop costs specifically related to the project involved in the feasibility study. Many items are judgment factors applied by the engineer to indicate that the item was not overlooked, rather than to demonstrate absolute accuracy.

Supervision and Labor: Labor rates should be the current rates employed in the area. If there is no current mining activity in the area, the labor rates should reflect the local wage rate structure.

In a unionized mining area, the local labor unions will publish labor rates. In the United States, union wage scales may show very little percentage difference in rates between various categories. A high degree of skill may not show a large difference over unskilled employees. This is not true in some of the developing countries where skills are rewarded handsomely as compared to unskilled wages, and this differential can be a matter of several hundred percent.

Supervisory and engineering personnel are usually paid a monthly salary, and such rates are not difficult to obtain. Local precedents should be followed where possible. In a surface mining operation, most of the supervisors with some exceptions are engineering graduates. The wage scale for supervisors may be higher than for engineers. It is not unusual for the engineering staff to be rotated through supervisory positions, and often the distinction between supervisors and engineers is difficult to ascertain.

The most important item in developing the labor cost is the manning table. It is generally divided into three categories: 1) supervision, engineering, and clerical; 2) equipment operators; and 3) maintenance people.

The manning table should always be on an annual basis. In the example which has been used in this section, the total annual scheduled operating hours are 7,248. It is assumed that all labor is paid for 52 weeks per year, 40 hours per week, or 2,080 hours. However, an employee, if allowed two

weeks vacation and five days sick leave, in addition to the 10 legal holidays, only works 1,872 straight time hours. If a position such as a shovel operator must be manned for all scheduled hours, it will require 3.87 employees for two shovels. If the operation were fully scheduled at all times, or 8,760 hours per year, the position would require 4.7 employees. For this example, 4.5 employees should be used as an average because it may be assumed that there are excused absences and employees with long periods of service that may qualify them for more than two weeks vacation. For example, there are eight trucks in the active fleet and these trucks must be manned for 57,984 hours per year; dividing these hours by 1,872 indicates a requirement of 3.87 drivers per truck, or a theoretical requirement of about 31 drivers. To cover the aforementioned extended seniority vacations and excused absences, the total truck drivers who would be paid for 2,080 hours per year would be at least 35 in number.

Similar reasoning can be applied to other operations. Inasmuch as drilling and blasting is only scheduled for a five-day week, two shifts per day, the manning calculations would of course take this reduced schedule into account.

Unavoidable Overtime: Usually an effort is made to avoid all overtime by scheduling individuals in such a manner that no person works more than 40 hours per week. However, it is almost impossible to avoid some overtime. For a small mine scheduled for six days per week operation, the labor would probably be paid for six days, and in the United States, this would amount to at least time and a half for the sixth day or weekly pay for 52 hours. The manning table should be based on sufficient labor to avoid overtime, but for the purposes of a feasibility study, 10% can be added to direct hourly wages as a line item for large mines and 15% or more for small mines.

Labor Burden: Labor burden means fringe benefits. Cau- tion should be exercised when obtaining a factor for labor burden from existing operations. Such figures may contain items which, for a feasibility study, are covered elsewhere. In the example under consideration, sick leave, vacation, and holiday pay should not be a part of the labor burden because the employees are paid for holidays when the mine is not scheduled to operate and sick leave and vacations have been included in the calculation of the 1,872 hours per year that the average employee works. Overtime need not be in labor burden because it has already been accounted for as a line item on the manning table.


Labor burden usually consists of the following: 1) Stat- utory Burden: This includes items mandated by law, such as the employer’s contribution to Social Security, Workmen’s Compensation Insurance, Unemployment Insurance, and other costs that result from government action; 2) Benevolent Labor Burden: These are the items that an employer must pay to be competitive in the labor market to keep capable people. These include health insurance, group life insurance, pension plans, and other items directly related to wages and employment; 3) Union Enforced Burden: This includes items that may be the result of direct union negotiation.

Labor burden can be obtained from other operating companies and government agencies, but care should be exercised in identifying the included costs. As an approximation, true cash labor burden in the United States will be 25 to 35% of direct wages. However, it may be higher in some employee categories, and it can be higher in older operations that have many employees with many years of service. Overseas, it is not uncommon to find burdens of 50 to 100% or more. The best way to determine true cash labor burden is to make an actual investigation by contacting governmental authorities,

insurance companies, and whatever labor unions may be involved.

Manning the Operation: In Table 8 for the example under consideration, it will be noted that there are 12 supervisors for 126 employees and 12 clerical and engineering employees. There is one supervisor for each 9.5 employees. The ratio of operators to maintenance personnel is 1.68 to 1.0. This would be considered a good ratio; however in some operations, the ratio is one to one. A rough rule for feasibility studies is two operators to one maintenance employee.

More maintenance people will be required if on-site engine and transmission rebuilding is done and if tire shops capable of recapping tires are maintained. Older fleets of equipment may also require more maintenance personnel and the same is true if operation is scheduled for 100% of all time.

It is important when investigating operating mines to find out which people are classified as maintenance and which as operators.

In a feasibility study, the manning table need not be organized in a manner that distributes personnel by shift.

Table 8. Direct Operating Cost Supervision and Labor for a 14 Mt/a Open Pit Mine

Hourly or Annual Number of Annual Wage Cost

People Hours Paid $ $

Mine superintendent General mine foreman Drilling and blasting foreman Shift foreman Maintenance foreman Maintenance shift foreman Mining engineer-geologist Planning engineer-surveyor Draftsman-rodman Exploration driller Drill helper Tim, Mtc, Supply clerks Secretary Messenger, sampler, truck driver Janitor

Subtotal: Supervision Blasthole drill operators Drill helpers Lead man blasting Blasters helpers Shovel operators Heavy equipment operators Truck drivers

Electrician A Electrician B Mechanics A Mechanics B Field service men Maintenance labor Parts and tool room men

Subtotal: Maintenance Subtotal: Direct waees

Subtotal: Operators

1 3 1 3 1 3 1 1 2 1 1 3 1 1 1

24 2 3 1 3 8 12 35 64 3 3 8 8 4 8 4 38 126

-

-

-

Salary Salary Salary Salary Salary Salary Salary Salary Salary 2080 2080 2080 2080 2080 2080

50,000 40,000 35,000 35,000 40,000 30,000 35,000 30,000 25,000 12.00 9.00 8.00 7.00 7.00 6.00

2080 2080 2080 2080 2080 2080 2080 - 2080 2080 2080 2080 2080 2080 2080 -

11.00 9.00 9.00 8.00 12.00 10.00 8.00

12.00 11.00 10.00 9.00 8.00 7.00 8.00

Unavoidable overtiie, 10% of hourly labor (operators &I maintenance) Burden, 30% of all wages

Total

$ 50,000 120,000 35,000 105,000 40,000 90,000 35,000 30,000 50,000 24,960 18,720 49,920 14,560 14,560 12,480

$ 690,200 45,760 56,160 18,720 49,920 199,680 249,600 582,400

$1,202,240 74,880 68,640 166,400 149,760 66,560 116,480 66,560 709,280

$2,601,280 191,152 838,862

$3,63 1,734 $3,632,000 Round to nearest $1000

408

This is a matter which depends on experience and actual operations. It can generally be assumed that engineering and clerical help will work a 40 hour week on day shift. It can also be assumed that there will be more maintenance people on day shift than on the other two shifts. Drilling, blast hole loading, and blasting can probably be scheduled two shifts per day, five days a week. It is only important that the manning table have sufficient people. Only people operating production machinery should be distributed approximately equally on 3 shifts.

Machinery Operation: In Tables 2, 3, and 4 and the text that follows these tables, annual costing hours have been assigned. These are the hours of actual machinery operation that must be paid for. Table 9 provides calculations for determining the annual cost of mining machinery. Costing hours are multiplied by the hourly cost of the machinery exclusive of operating and maintenance labor.

It may be desirable to present a table that gives the hourly operating cost of each piece of mobile mining equipment by categories such as fuel, lubrication, engine supplies, tires, repair parts, and electrical power. In a mining feasibility study, such items as taxes, insurances, depreciation, and interest should not appear on this table because these items are more appropriately covered elsewhere, particularly in the section on economic analysis.

Details of operating costs are not always easy to obtain. The best source of information would be the records of an operating open pit mine that is similar to the mine being studied. Machinery manufacturers can frequently provide cost breakdowns. A word of caution is necessary concerning maintenance costs obtained from equipment manufacturers. These costs invariably include maintenance labor and in the example under consideration here this item is carried on the mining department manning table. It is therefore necessary to factor out maintenance labor cost from the maintenance figure provided by vendors. In the United States, labor is generally one-half to two-thirds of the maintenance cost and

the remainder would be parts, but in overseas situations, particularly where duty is charged on imported parts, the labor portion may be only 10 to 25%.

The table showing the breakdown of hourly cost for each machine, particularly on overseas jobs, can be quite valuable. It is a guide for logistics calculations because it provides information on parts and supply quantities to be transported and stored.

The hourly cost of machines in an open pit mine varies widely. Older fleets may cost more, and new fleets considerably less. The figures obtained from vendors are usually averages and should be adjusted, if necessary, employing judgment factors.

The annual cost of operating mining machinery is the result of costing hours multiplied by hourly operating cost with the aforementioned exclusions.

For small mines that do not have redundant equipment and for large mines that prefer to keep maintenance forces at a low level, a line item should be added to the machinery cost table for rental of equipment during major breakdowns and for off-site maintenance contracts. This is a judgment factor; but for small mines it could be as high as 25% of the total machinery operating cost, and for large mines it will be in the range of 10 to 15%. To a certain extent, this is a contingency factor.

Drilling Supplies: The hourly operating cost for blast hole drills is not intended to include drill bits. These are included in Table 10. The life of drill bits depends on numerous factors, most of which might not be known in a preliminary feasibility study. If air hole drilling with rotary drills or down-the-hole hammers have been used in the exploration program, some idea might be obtained about the possible bit consumption. Also, operating mines with similar ore and waste could be a source of such information. Vendors of drill bits can be a valuable source of information if first hand knowledge is not available from on-site drilling of the deposit or from similar mining operations.

Table 9. Annual Cost of Mobile Mining Machinery

Total Annual Cost per Annual Costing Hourt cost *

Major Items of Machinery Hours* $ $ x 1000

Blasthole drills, exclusive of bits 6150

7.6 m3 shovels 9915 77 t haulage trucks 45290 9 m3 rubber tire front-end loader 2416 230 kw rubber tire bulldozer 10612 345 kw truck-mounted bulldozer 2400 Motor grader 2400 32 t small dump trucks 2400 Service vehicles, ANFO. fuel, repair 3800 Supervisors pickup trucks 10000 30 m3 front-end loader 800

Subtotal 96958 Allowance for rental equipment 10% Allowance for less than expected productivity, 10%

Secondary drill rig 800

Total

75.00 2 1 .oo

11 5.00 42.00 48.00 25.00 41.00 17.00 2 1 .oo 12.00 8.00

12.00

46 1 17

1,140 1,902

116 265

98 46 50 46 80 10

$4,226 422 423

$5,071

*See Tables 2, 3, and 4 and text. t Exclusive of operating and maintenance labor.

$ Rounded to nearest $1000.

Direct operating cost, no ownership cost included Information obtained mostly from vendors and represents averages. Costs should be updated.

FEASIBILITY STUDIES AND PROJECT FINANCING

Table 10. Annual Cost of Drilling and Blasting Supplies

Annual cost

$ x 1000

Drill bits 97000 m i 300 m/bit x $4000/bit Slurry 0.025 kg/t x $1.43/kg x 12,700,000 t ANFO 0.165 kg/t x $0.804/kg x 12,700,000 t Blasting cord 451000 m @ $0.25/m Boosters 1.0 kglhole x 7028 hole x $1.43/kg Secondary blasting @ 8% of above total including bits

1,293 454

1,684 113

10 283

Total $3,837

409

Explosives: In Table 10, the cost of explosives is tabulated. This is a straightforward calculation and the most important information is the powder factor. From the powder factor and the annual tons to be blasted, the explosives cost can be determined. What the explosive mix will be is a matter of judgment and, again, an operating mine with similar ore and waste would be the best source of information. Manu- facturers of explosives and the literature they publish are also good sources.

Undistributed Mining Department Overhead This item is frequently overlooked. It is recommended that this be developed in some detail as shown in Table 11. The item is referred to as undistributed because it represents those costs

not directly assignable to labor burden, machine operation, or explosives. This item is most often forgotten by engineers who make operating cost estimates by the unit cost method. Usually unit costs are available for drilling and blasting, loading, hauling, etc., but none of these costs contain department overhead. A percentage factor can be applied for overhead, but it is risky and at times not very convincing.

Reliability of Estimates and Credibility Checks Most mining engineers with some experience have certain

credibility checks that they can apply to operating cost calculations. For example, in the United States, wages and burden should be about 40% (plus or minus 10%) of the

Table 11. Undistributed Mining Department Overhead

Annual cost

$

Mine office heat, 200 m2 @ $30/m2/yr Electric power, 200 m2 @ $30/m2/yr Telephone, 12 outlets @ $300/yr/outlet, basic Water and sewage, inside employees 12 @ $50 Office supplies, $300 yr, all staff employees, 24 x $300 Engineering supplies, $600 x 4 employees Repair office and engineering equipment 24 employees x $150 Safety and Training supplies 126 employees x $50 Equipment usage during training 500 hr @ $40 hr Radio service 35 units @ $150 yr/unit Crew bus* 230 days x 105 km x $1.24/km Office building maintenance allowance 200 mz x $1 5.00/m2 LD phone and telex allowance $300/month x 12 mos Professional costt, 12 professionals @ $1000/yr each Exploration drilling, 1400 hr @ $75/rig hour Assaying $1.0 per hole 7000 blastholes + 3000 Exploration boreholes @ $10.00 each

6,000 6,000 3,600

600 7,200 2,400 3,600 6,300

20,000 5,300

30,000 3,000 3,600

12,000 105,000 100,000

Subtotal, Mine and Engineering offices $314,600 Heat, 1000 mz @ $22/m2/yrS Electric power 1000 m2 @ $35/m2§ Telephone, 4 outlets @ $300/yr/outlet Water and sewage, 38 employees @ $50/yr each Small tool replacement allowance, 34 employees x $300 yr Undistributed maintenance supplies $3.00 machine hour Repair shop equipment $300/employee, 34 employees Shop building maintenance 1000 m2 @ $10.00/m2

Subtotal, Maintenance shop

22,000 35,000

1,200 1,900

10,200 29 1,000

10,200 10,000

381,500 Total $696,100

* Assume a subsidized crew bus and mileage cost covers depreciation, tax, insurance, etc t Publications and professional activity such as AIME. $ Lower heat level than office building. 5 Higher power use than office building.

410 SURFACE MINING

Table 12. Summary of Direct Cost Mining Department

cost of Material

Annual Cost Moved $ x 1000 $/t

Supervision, labor and burden Mobile machinery Drilling and blasting supplies Undistributed overhead Local taxes (non-income related) and insurance*

Total before contingency Contingencyt, 20%

Total Annual Tons Material Moved: 12,700,000

0.29 0.40 0.30 0.05 0.06 $1.10 0.22 $1.32

3,632 5,071 3,837 696 720

3,956 2,791 6,747

* Unless firm data is available, use 3% of total mining department capital cost which, in this example, would be about $24,000.000 x 0.03 =

t In this definition the percentage assigned to contingencies is a judgment factor and is not to be interpreted as meaning that estimates are $720,000.

necessarily accurate within this percentage range, nor is there an implied reference to any order of accuracy.

direct operating cost of an open pit mine. There are always special circumstances that would change this percentage. The direct operating cost of mining machinery will depend on such things as fuel, remoteness of the operation, etc., but it will amount to about 37% (plus or minus 10%) of the direct operating cost. Blasting supplies can vary widely. For explosives alone the percentage is 12 to 15% in most instances. Explosives can be very expensive overseas. Undistributed mining department overhead will vary widely, but it is about 10%. See Table 12.

Production in terms of total tons of material per man shift in the mining department is a good credibility check. Unless there are unusual circumstances or a very small mine is involved, less than 200 t of total material moved per man shift is unacceptable. The study should be reviewed for under- estimation of machine capacity and too many employees. Two hundred to three hundred tons per man shift is in the acceptable range, 300 to 400 t is good, and 400 to 600 t is excellent and achievable in many operations. It is important

to note that this figure is based on total tons of material moved and this includes ore and waste, and the total number of employees in the mining department.

ECONOMIC ANALYSIS Economic analysis is not very meaningful if the mine is

a part of a larger integrated concentrating and smelting complex. If the mine sells raw ore with no beneficiation except primary crushing, then the mine becomes an economic unit generating revenue.

The details of discounted cash flow analysis, sensitivity analysis, and payout time are discussed later in this work. However, a simple spot cash flow analysis is frequently helpful. An example is given in Table 13. This procedure is used only to indicate whether or not a project is in the range of profitability. The analysis is for some nth year in the future when the project has reached design production and over- come initial start-up difficulties. Such an analysis assumes constant dollars. It can be used for preliminary comparison

Table 13. Spot Cash Flow Analysis for Preliminary Feasibility Studies.

Annual $ x 1000

Gross revenue 12.7 Mt @ $2.64/t Less direct operating cost 12.7 mt x $1.32/t Operating profit Depreciation $24,000,000 + 8 years Interest @ 15% on 75% of investment, 0.15 x .75 x $24,000,000 Depletion 15% of gross revenuet 0.15 x $33,528,000 Before tax profit All income-related taxes, assume 50% After tax profit Add back depletion Net profit Add back depreciation Cash flow$ Payout time, $24,000,000 f $13,334,000 = 1.8 years

ROE $10.334.000 f 6,000,000 172% ROI $10,334,000 + 24,000,000 43%

33,528 16,764 21,336 -3,000 -2,700 -5,029 10,610 5,305 5,305 5,029 10,334 3,000 13,334

* Assume a mining contract delivering ore to the buyer's crusher from a deposit owned by the mining contractor. Assume all material moved is

t Some foreign countries have no provision for depletion. See US tax laws on depletion. t Assume no investment credit or tax holiday.

ore.

FEASIBILITY STUDIES AND PROJECT FINANCING 41 1

of alternates such as shovels and trucks vs. bucket wheel excavators and conveyors. More sophisticated programs are adapted to a computer program.

ECONOMIC VIABILITY-CASH FLOW ANALYSIS Feasibility studies may have many different purposes.

However, in many cases the final objective will be to serve as a reliable document to be presented to a lender. Therefore, the economic viability of the mining venture must be dem- onstrated in the feasibility study.

The main test of the overall economic viability, from a lender’s point of view, is through cash flow analysis. “A cash flow forecast that extends at least through the life of the proposed loans-and preferably for some additional years- should be prepared under the costing and marketing assumptions justified elsewhere in the report.” (Gibbs and Sroka, 1978.)

The final decision on alternate choices, either of different mining projects or changes in parameters, such as production rates, methods, etc., is based on a rational continuous process, namely economic analysis.

Principles of an Economic Model In general, an economic model for investment decisions

should consider four important principles as given by Haynes and Massie, 1969.

The Incremental Principle: A decision is sound if it increases revenue more than costs, or if it reduces costs more than revenue. This seems obvious; however, its application is not obvious at all, and using average costs as the basis for the decision model could lead to error, or at least it does not present a complete picture of the investment alternatives.

The Principle of Time Perspective: A decision should take into account both the short and long term effects on revenues and costs, giving appropriate weight to the most relevant time periods.

The Opportunity Cost Principle: Decision making involves a careful measurement of costs. The company must evaluate the opportunity cost of investing in the proposed project as compared to other investment possibilities (Joy, 1980).

The Discounting Principle: If a decision affects costs and revenues at future dates, it is necessary to discount these costs and revenues to present values before a valid comparison of alternatives is possible.

The four principles, previously mentioned, are the frame- work of economic analysis which will interrelate the areas of mineral resources, technology for recovering the resources, the annual capacity of the proposed mine operation, the capital investment required, the estimated operating costs, and the profitability criteria for the final investment decision.

In the final analysis, the evaluation of the profitability of the investment is measured by the difference between the summation of the present value of the expected proceeds over future years vs. the capital invested today. This could be simply expressed by P. Value of Cash flow = P. Value of Investment i- P. Value of Profit.

In summary the economic analysis in the feasibility study is performed by formulating a model which should include the following elements: 1) evaluation of the main variables; mineral reserves, production rates, recoveries, cost estimations, prices of the commodity, regulatory and environmental factors; 2) profitability criteria; 3) cash flow projection model; and 4) test of the cash flow model.

Evaluation of the Main Variables Several major variables are involved in the economics

models. These variables are classified either as Industry Stim- ulant Group, Economic Stimulant Group, or Regulatory Stimulant Group (Beasley and Pfleider, 1972; Pfleider, 1980).

The Industry Stimulant Group model contains: 1) mineral reserves, tonnage and grades (cut-off and average); 2) production rate and grade, corrected for dilution; 3) alternative mining, mineral processing, and metals recovery methods; 4) anticipated product recoveries in the mining, processing and metals recovery steps. And, for each of the above set of variables: 1) operating and overhead costs; 2) transportation and sales expenses; 3) capital costs for mine, plant and infrastructure; and 4) working capital requirements.

The Economic Stimulant Group model consists of: 1) market prices of products; 2) equity-loan ratios; and 3) interest rates and payback times of loans.

The Regulatory Stimulant Group model variables are: 1) depreciation and amortization rates; 2) depletion allowances, if any; 3) royalties and/or profit splits; 4) tax rates for ad valorem, property, production, profits, custom duties, transfer of dividends; and 5 ) tax moratoriums, investment credits.

Some of these variables have already been described in detail elsewhere in this chapter; however, they are repeated here with the objective of presenting an overall view of all the factors involved in the economic analysis.

While the Industry Stimulant Group has its impact in the design and estimating phase, the Economic Stimulant Group (market prices and loan arrangements) and the Reg- ulatory Stimulant Group (representing taxing structures) are of equal or perhaps greater importance because the firm has only limited or no control over these variables.

In general, the main objective of the Economic Model is to estimate the annual return. However, in this process the projected return is dependent upon two t y p of parameters identified by Wells (1978) as “nondiscretionary and discretionary parameters.” Discretionary parameters include mining and beneficiation methods, annual production capacity, sequence of mining, cut-off grade, design of the mine, processing plant, and facilities required to obtain an efficient production. Nondiscretionary parameters are those which the firm cannot control directly, such as selling price of the product, basic costs of labor and supplies, taxes, regulations, etc.

Profitability Criteria Used in the Evaluation The criteria to be selected for the evaluation will depend

on the investment objective of the parties concerned in the mining venture. Several profitability criteria are widely used by the mining industry, financial institutions, and government agencies to evaluate individual projects and to compare alternates between mutually exclusive mining ventures. There are two general groups of profitability criteria: 1) Non-discounted cash flow-payback period and average internal rate of return; 2) Discounted cash pow-Hoskold Formula, Net Present Value (NPV), Internal Rate of Return (IRR or ROR), Profitability Index (PI), Payback Period.

For evaluation purposes, the discounted cash flows are the only profitability criteria used, since the time value of money is the most important principle in the evaluation process. The following is a brief review of the profitability criterion of this group.

The Hoskold Formula has been used since 1877; however, its use is limited today. It calculates present value by discounting future annual income at a risk rate while building

412 SURFACE MINING

a sinking fund to repay investment at a safe rate. The present value (Pv) is calculated by the following formula:

A PV = r

(R”- 1 ) + rl

where PV is present value, A is annuity (annual cash flow), r is safe discount rate, rl is risk rate, n is number of years, R is (1 + r).

Net Present Value (NPV) has been widely used since the 1960s. It calculates net present value by discounting estimated annual cash flows to a common point of time at a selected discount rate considering the risk of the investment.

Cash Flow (CF) Net present value (NPY) = c -

1-0 ( 1 + k)‘ where k is discount rate, t is number of years.

Internal Rate of Return (IRR) or (ROR) is the calculated rate that makes the present value of cash inflow equal to that of cash outlays, or

= o Cash Flow (CF) Internal rate of return ( IRR) = c

1-0 ( 1 + IRR)’ where t is number of years.

Profitability Index (PI) is defined as the present value of future cash flow divided by the initial investment. This criterion is also called the benefit-cd ratir: and is used in the capital rationing situation. This is the situation where a budget constraint is imposed, and the firm may not invest in all acceptable projects.

4 Cash Flow (CF)

where k is discount rate, t is number of years. Payback Period represents the number of years required

in the cash flow analysis for the accumulated cash flow to equal investments. This is measured either from the initiation of the project or from the start of the operations. This criterion is especially useful for mining ventures with high risk or short life. Normally the payback period is expected to be one to three years for high risk projects, and six to ten years for low risk projects.

The selection of the criterion for the evaluation of the mining property will depend upon the criteria best suited for the investment objective. However, there is a trend to use the present value and rate of return techniques for economic analysis. These techniques, in conjunction with sensitivity and risk analysis, are good analytical tools for simulating the impact of the uncertainty on the profitability measurement, either present value or rate of return. These simulation techniques will be treated in more detail later in this section.

Rate of Return Vs. Present Value The Internal Rate of Return (IRR or ROR) is easy to

understand because it has intuitive economic meaning. It works well on simple accept/reject problems but its main drawback could be that it may not give the best selection criteria for complex accept/reject problems (multiple rates), mutually exclusive of choices and capital rationing.

The Net Present Value (NPV) is relatively easy to calculate. It is considered by many people as the best method for mutually exclusive ranking problems and for accept/ reject decisions. Its main disadvantages could be that some-

times it is not easy to understand the concept and it may not work well for capital rationing situations. In the latter case, the profitability index (PI) works better than net present value (NPV).

Probably the most troublesome part of the net present value calculation is the estimation of the discount rate, which will convert the cash flows projected to the net present value at a given point in time.

Various financial treatises give details for estimating the discount rate; however, in this section, the authors provide an overview of one method for estimating the discount rate using the equation known as Capital Asset Pricing Model, CAPM (Joy, 1980).

The interest rate or discount rate (K,) may be estimated by the following linear equation.

K, = K, + (K, - K,,) Beta, where K, is the interest rate required for X investment, K,/ is the risk-free interest rate, K, is the interest rate at market value, Beta, is the investment risk for X investment. “In principle, K,/ is observable in the market place and K, can be estimated. The interest rate for US Bonds is usually taken as a basis to estimate the risk-free rate (K,/) for long term investments.”

“The most common method of estimating Beta, is by regression analysis. Rates of return on the firm’s stock, Re, and rates of return on a market index, Rm values are sta- tistically related by the straight-line equation called market model.” (Joy, 1980.)

Re = a + Beta, Rm About five years of monthly rate of return are used to

estimate Beta,. Further discussion of this model is beyond the scope of this work. Nevertheless, to complete our overview, we add the following values: 1 ) For a risk-free investment, Beta, = 0; 2) For K, = K,, Beta, = 1. 3) For K, = 1.4 K,, Beta, = 2.

Cash Flow Model Financial treatises give several reasons for using cash flow

in the evaluation of investment alternatives. The three main reasons for using cash flow in the evaluation of mining investment are summarized as follows: 1) Cash flow yields a better measurement of the net economic benefit associated with the mining venture; 2) Cash flow avoids accounting ambiguities; 3) Mining companies are permitted depletion allowances in addition to the depreciation allowances. These noncash expenditures are tax deduction items that are added back into the cash flow stream.

The cash flow after tax stream consists of four main parts: Net Cash Flow = A - B + C - D

where A is gross income, B is cost deductions, C is noncash expenditure, D is capital expenditure. A typical format for estimating annual cash flow is presented in Table 13a.

Test of the Cash Flow Model Evaluation In the evaluation of a mining project, we consider three

basic elements for discriminating between alternatives. These elements are: 1) project cash flow estimations; 2) appropriate discount rate; and 3) profitability criteria for the decision making process consistent with the objectives of the firm.

Regardless of the methodology used to develop the estimate of the profitability of the project, the fact is that the result is subject to a level of uncertainty. This level will depend upon the degree of reliability of each of the variables involved in the calculation. The uncertainty is due to the


Table 13a. General Format for Estimating Annual Cash Flow

Gross Income (A) Gross value of production

- Value of royalties payment* $ = Gross income from mine property

Cost Deductions (9) - Mine operating costs - Milling operating costs - Environmental and reclamation costs - Deferred exploration - Ore development - Deferred pre-production development - Interest on loan* - Net taxable loss carried forward* - Depreciation - Other undistributable costs*

Net Income $ = Net income before taxes and depletion - State and local taxes = Net income before depletion - Depletion - Federal income taxes

$ = Net income after taxes and depletion

Non-Cash Expenditures (C) (Add back) + Depreciation + Depletion + Deferred exploration + Deferred pre-production development + Net tax loss carried forward*

$ = Net Cash Inflow

Capital expenditures (D) - Exploration costs - Pre-Production costs - Plant and equipment

- initial - replacement

- Payment on loan principal*

Cash Flow $ = Net Cash Flow * If any deduction is applicable.

fact that the projections of future cash flows as predicted by the model, are only at best, good estimates. These estimates are obtained from data and conditions as known at the time of the model formulation.

In order to evaluate the effect of changes in values of variables incorporated in the model on the profitability criteria, two techniques are generally used. One is the simulation using the Monte Carlo technique or risk analysis simulation, and the other is sensitivity analysis. With the advent of the computer and rapid simulation programs, there is an increasing application of these techniques.

Sensitivity Analysis: Sensitivity analysis varies the range of a single variable at a time. The procedure is repeated for the other variables. In this fashion the most sensitive parameters of the model are detected. The process for testing the sensitivity of the model consists of changing one variable and holding constant the others at their estimated most likely value. The variation for the single value will range from its minimum to its maximum estimated value. The effect, in either present value or rate of return, is recorded in a matrix form with the main parameters and their respective changes in values.

Simulation Using Risk Analysis: Risk analysis'is a systematic analysis of the risk associated with various dependent

variables to develop a final expected distribution of the profitability measurement. This distribution is used for the decision making process of the investment alternative.

This technique is also known as probabilistic Analysis. It simulates numerous variations in the range of all the main variables at the same time. The simulation is carried out by computer programs using randomly selected values from given statistical distributions.

This approach is widely used today. Its general application in evaluation of projects was originally proposed by D.B. Hertz in 1964. The main feature of the technique is that it gives the decision makers a schedule indicating the frequency distribution of the profitability criteria and their respective relative probability of occurrence. At the same time, it will indicate if the investment has any chance of being a total loss.

When the feasibility study is performed with the objective of selecting a mining venture between various alternate investments, risk analysis is a powerful analytical tool for identifying in a realistic way the alternate that offers the greater economic comparative advantage in line with the objectives of the firm.

Often, the alternates differ in location, tonnage and grade distribution, size of equipment, operating costs, life of op-

414 SURFACE MINING

eration and equipment, etc. The main factors for discriminating between these types of alternatives are the estimation of capital and operating costs. These costs are deterministic events by the nature of their development.

The cost estimation of a new mining venture, regardless of the detail contained in the estimates, is subject to a level of uncertainty. This uncertainty is, in fact, a pervasive feature of the cost estimating process because of the lack of complete knowledge about the conditions or efficiency of the future operation. A search in the technical literature shows that there are several good descriptions of the risk analysis method.

The main concept and elements are summarized here to present a comprehensive overview of the analysis. It is hoped that the description will give the reader some insight for practical applications of this technique for the evaluation of mineral deposits or other selection of alternatives in the mineral industry.

Type of Risk in Mine Evaluations Risk is inherent in the decision to invest capital for con-

verting mineral resources into future expected profit or, simply stated, in mining jargon, there is always a risk in the process of converting mineral resources into ore.

There are two types of risk in mine evaluations: 1) risk inherent to the physical characteristics of the mineral body, and 2) risk associated with future events.

Risk Inherent to the Physical Characteristics of the Min- eral Body: The mineral reserves obtained from the geologic model contain a level of uncertainty, depending upon the amount of exploration data used as a basis for the model. This is due to the fact that the reserves estimation is based upon a small, physically known fraction of the mineral body. Therefore, the tonnage and grade of the entire deposit are inferred from a relatively small sample. Consequently, the specific mineral content, based on the information available at the time of the study, is limited by the sample population and the geometry of the mineral body.

The advent of geostatistics permits us to greatly reduce this uncertainty. Geostatistics reveals a great deal about the idiosyncrasies of mineral distribution and its spatial location. Consequently, the reliability of the in situ reserves estimations are considerably improved. It should be emphasized that by far the most important factors in the reliability of the reserves estimates are good core recoveries, good sampling, and good assaying procedures. It would be a fallacy to use a sophisticated geostatistical model with questionable data base. Therefore, in a complete feasibility study, it is essential to review the sampling procedures and confirm the reported assays.

The expected mill head grade will depend upon the grade distribution of the deposit, the economic constraints imposed to define the limit of the ore body, and the proposed mining plan. However, this grade will be subject to variation due to dilution as a consequence of the following factors: geometry of the ore body, mining practice and unknown geological factors at the time of the study.

Risk Associated with Future Events: In general, a mineral deposit takes three to seven years to bring into production after the firm has made the investment decision. Depending upon reserves, it will take another 10 to 30 years to exploit the ore body considered in the evaluation. During this period many events could happen that will affect the following parameters: price of the commodity, initial and replacement capital costs, operating cost, taxation policies, and change in government policies regarding partial or total

ownership of the mineral properties. In the life of the properties, including the development period, there is the possi- bility that all the main parameters involved in the evaluation could deviate from the original estimates. Several combinations of variations in parameters could occur and these variations will affect the profitability estimate of the property under evaluation.

Procedure for Simulation by Risk Analysis The process of performing a systematic risk analysis for

the measurement of profit associated with changes of the main dependent variables consists of three main elements: 1) estimation of the basic values of the main variables; 2) estimation of the probability of occurrence of each estimated value; and 3) selection, at random, of one value from the probability distribution for each variable. The general methodology to be used is illustrated in Fig. 2.

Estimates of the Basic Values of the Main Variables: Up to this point, the basic values of the main variables have been established with the formulation of the geological model (including cut-off grade, average grade, and tonnage), revenue forecast, and the development of capital and operating costs. A typical schedule of the basic values of the main variables is as follows:

1. Total tonnage at given cutoff grade, number of tons. 2. Average in situ grade, percent. 3. Dilution, percent. 4. Average mill head grade, percent. 5. Annual mining rate, number of tons. 6. Metallurgical recovery, percent. 7. Estimated annual revenue, dollars. 8. Estimated capital costs, dollars. 9. Estimated operating costs, dollars.

Estimates of the Probability of Occurrence of Each Basic Value: The estimation of the probability of occurrence of each basic value is the step that is most likely to trouble the mine evaluators. However, there are three general ways of approaching the estimation: 1) mathematical probability, 2) inferred probability, and 3) subjective probability.

Mathematical Probability-is the generation of stochastic variates for several distributions, such as normal, uniform, binominal, and is easily manipulated by a computer program. Naylor, et al., (1966) provide formulas and programs for generating the probability distribution.

Inferred Probability-by fitting curves has been suggested by Harris (1970) when there is historical or other data available and when the probability distribution law is unknown. He suggests that, “The estimate be made by the fitting of a polynomial of some unspecified degree to the data or the grouping of data into class intervals, and then calculating the relative frequencies for each class.”

Subjective Probabilities-are typically cases where there are components for which there is no historical information applicable for the fitting of a probability distribution. The estimation of capital and operating costs are some of these components. A general procedure for forming a subjective probability distribution is given in the following section.

The estimation of the average value of each component is expanded to represent the possible range of variation of the basic values and the likelihood that these values will be reached. The range could be estimated with some degree of confidence by experienced engineers involved in developing the basic values of the cost components of the feasibility study. The degree of confidence is directly related to the

Next Page

Chapter 5 Planning and

5.1 Definition of Mining

Design of

Parameters

Surface Mines

Robert Laurich, Editor

DAVID ARMSTRONG

INTRODUCTION Many 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 affedng 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 HEIGHT The bench height is the vertical distance between each

horizontal level of the pit. The elements of a bench are illustrated in Fig. 1. Unless geologic conditions dictate other- wise, 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.

The 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 SLOPES The 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., 457, 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 orien- tation within the pit. Fig. 2 illustrates how the pit slopes may vary in the 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

Fig. 1. Bench cross section. Fig. 2. Example of pit slopes varying in a deposit.

459

460

Fig. 3. Pit designed with a 45’ pit slope.

1 I I

in the pit. The overall pit slope used for design must be flatter to allow for the road system in the ultimate pit.

Figs. 3 and 4 show the need to design the pit with a lesser slope to allow for roads. The pit in Fig. 3 has been designed with a 45’ angle for the pit walls. The pit in Fig. 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.

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 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.

1 I I I I I I 1

Fig. 4. Pit designed with a 45” interramp slope and a road system.

PLANNING AND DESIGN OF SURFACE MINES 46 1

1 I I I 1 I 1

Fig. 5. Pit designed with a 38’ overall slope to allow for a 45’ interramp slope and a road sys-

tem.

Fig. 6 shows a vertical section of a pit wall from Fig. 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.

CUTOFF GRADE As 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

A

ORKMlyAL QROUWD SURFACE

A SURFACE mrEncEpr OF HI WALL

o SURFACE mrnncEP1 OF THE HTWALL

C ROADS ARE lllcLUOED

F ROADS ARE NOT MICLWED

Fig. 6. Vertical section through a pit wall.

462 SURFACE MINING

Fig. 7. Relative pit sizes using different levels of costs.

r S U U FACE r

c o s t s / / / / /

/ / T'\ \ \ ' depreciation 1

/ \ \ \ B \,minimum profit / /

/ k-- - - - -d /

/ /

/ / c o s t s

\ \ \

\ c \\ \, , depreciation

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 refine- ment.

Depreciation is used in the calculation for the purpose of setting the pit size. As shown in Fig. 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.

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. 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

Table 1. Calculation of Breakeven Cutoff Grade

Head Grade 0.80% Cu 0.70% Cu Recovery 85% Cu 85% Cu Recoverable Copper 6.80 Kg 5.95 Kg

Per Tonne costs Per tonne ore Per kg Cu Per tonne ore Per kg Cu

Mining Processing General &

Depreciation

Freight, Smelting

Administrative

Total

Refining Total

Value @ $1.75/Kg

Net value

Cutoff grade

~~~

$1.00 3.00

1 .oo 1.40

$ 6.40 -

5.10 $11.50

911.90

$ 0.40

$1.00 3.00

1 .oo 1.40 -

$0.94 $ 6.40 $1.08

.75 4.46 .75 $ 1.69 $10.86 $1.83

1.75 10.4 1 1.75

- -

- $ 0.06 ($0.45) ($0.08)

0.753% Cu (by interpolation)

PLANNING AND DESIGN OF SURFACE MINES 463

1.0-

0.8 - Y p;:

% ”

6 3 0 . 6 - 0

; 0.4-

0.2-

L

1.01 ’ 0.8

0.2

0 I I I 1 I i 4 5 6 7 8 9

$Cost s Per Tonne of Ore

Fig. 8. Cutoff grades for different costs and metal prices.

Price (S Per k g Copper)

Fig. 9. Relationship of mining and milling cutoff grades.

41

3: 1

2:1

1:1.

0

41 -1 3: 1

2:1

1:1.

/- / /

Ore Grade (% Copper)

Fig. 10. Strip ratios for different ore grades and metal prices.

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 1 is the calculation of the mining cutoff grade for a copper project with the following parameters:

30

$300,000,000

$1.00 $0.95 $3.00 $1.00

$0.75

85%

kt/d (33,000 st pd) of ore mined for 20 years capital cost (including replacement capital) mining cost per tonne of ore mining cost per tonne of waste processing cost per tonne of ore general and administrative (G&A) cost per tonne of ore freight, smelter, and refining (FSR) cost per kilogram of copper overall copper recovery

The results are shown graphically in Fig. 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. 9.

STRIP RATIO The 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 1 ( A - B ) / C

where:

A = revenue per tonne of ore B = production cost per tonne of ore (including all costs

C = stripping cost per tonne of waste

In certain studies a minimum profit requirement is in-

to the point of sale, excluding stripping)

cluded in the formula.

BESR = [ A - ( B + D ) ] / C

where:

D = minimum profit per tonne of ore.

Table 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. 10.

REFERENCE Taylor, H.K., 1972, “General Background Theory of Cutoff

Grades,” Trunsuctions (Section A: Mining Industry), Institution of Mining and Metallurgy, Vol. 81, pp. A160-Al79.

464 SURFACE MINING

Table 2. Calculation of Breakeven Strip Ratios

Head Grade (96 CU) 1 .o 0.9 0.8 0.7 0.6 0.5

7.65 6.80 5.95 5.10 4.25 Kg Cu recovered 8.50 per tonne ore

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

COSTS: Mining' $ 1.00 Milling 3.00 G&A 1 .oo

f 5.00 f 0.59 f 5.00 0 0.65 f 5.00 f 0.74 f 5.00 S 0.84 f 5.00 S 0.98 f 5.00 S 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 f 1.40 $10.10 f 1.49 $ 9.46 $ 1.59 f 8.83 0 1.73 f 8.19 f 1.93 -------- -- -- -

Depreciation 0.20 1.40 1.40 0.16 1.40 0.19 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 Net 2.10 Ratiot 2.2:l

@ $2.00/kg Cu Value $17.00 Net 4.22 Ratiot 4.4: 1

@ $2.25/kg Cu Value $19.13 Net 6.35 Ratiot 6.7:l

@ $2.50/kg Cu Value $21.25 Net 8.47 Ratiot 8.9: 1

$13.39 1.25 1.3: 1

$15.30 3.16 3.3:l

$17.21 5.07 5.3:l

$19.13 6.99 7.4: 1

$11.90 .40

0.4: 1

$13.60 2.10 2.2:l

$1 5.30 3.80 4.0: 1

$17.00 5.50 5.8:l

$10.41 (0.45) -

$11.90 1.04 1.1:l

$13.39 2.53 2.7:l

$14.88 4.02 4.2:l

$8.93 (1.30) -

$10.20 (0.03) -

$11.48 1.25 1.3:l

$12.75 2.52 2.7:l

$7.44 (2.15) -

$8.50 (1.09) -

$9.56 (0.03) -

$10.63 1.04 1.1:l

~~ ~~

* Excludes stripping cost. t A t stripping cost of $0.95 per tonne of waste. ( ) Indicates negative value.

5.2 Ultimate Pit Definition

INTRODUCTION There are probably as many ways of designing an ultimate

open pit as there are engineers doing the design work. The methods differ by the size of the deposit, the quantity and quality of the data, the availability of computer assistance, and the assumptions of the engineer.

As the first step for long or short-range planning, the limits of the open pit must be set. The limits define the amount of ore minable, the metal content, and the associated amount of waste to be moved during the life of the operation. The size, geometry, and location of the ultimate pit are important in planning tailings areas, waste dumps, access roads, concentrating plants, and all other surface facilities. Knowledge gained from designing the ultimate pit also aids in guiding future exploration work.

In designing the ultimate pit, the engineer will assign values to the physical and economic parameters discussed in the previous section. The ultimate pit limit will represent the maximum boundary of all material meeting these criteria. The material contained in the pit will meet two objectives.

1. A block will not be mined unless it can pay all costs for its mining, processing, and marketing and for stripping the waste above the block.

2. For conservation of resources, any block meeting the first objective will be included in the pit.

The result of these objectives is the design that will maximize the total profit of the pit based on the physical and economic parameters used. As these parameters change in the future, the pit design may also change. Because the values of the parameters are not uniquely known at the time of design, the engineer may wish to design the pit for a range of values to determine the most important factors and their effect on the ultimate pit limit.

MANUAL DESIGN The manual method of designing pits involves consid-

erable time and judgment on the part of the engineer. The usual method of manual design starts with the three types of vertical sections shown in Fig. 1:

1. Cross sections spaced at regular intervals parallel to each other and normal to the long axis of the ore body. These will provide most of the pit definition and may number from

LOWS axis OF O R E ~ O D Y - - I

CROSS SEC Ti0 NS

10 to perhaps 30, depending on the size and shape of the deposit and on the information available.

2. A longitudinal section along the long axis of the ore body to help define the pit limits at the ends of the ore body.

3. Radial sections to help define the pit limits at the ends of the ore body.

Each section should show ore grades, surface topography, geology (if needed to set the pit limits), structural controls (if needed to set the pit limits), and any other information that will limit the pit (e.g., ownership boundaries).

The stripping ratio is used to set the pit limits on each section. The pit limits are placed on each section independently using the proper pit slope angle.

The pit limits are placed on the section at a point where the grade of ore can pay for mining the waste above it. When a line for the pit limit has been drawn on the section, the grade of the ore along the line is calculated and the lengths of the ore and waste are measured. The ratio of the waste and ore is calculated and compared to the breakeven stripping ratio for the grade of ore along the pit limit. If the calculated stripping ratio is less than the allowable stripping ratio, the pit limit is expanded. If the calculated stripping ratio is greater, the pit limit is contracted. This process continues on the section until the pit limit is set at a point where the calculated and breakeven stripping ratios are equal.

In Fig. 2, the grade on the right side of the pit was estimated to be 0.6% Cu. At a price of $2.25 per kg of copper, the breakeven stripping ratio from Fig. 3 is 1.3:l. The line for the pit limit was found using the required pit slope and located at the point that gave a waste:ore ratio of 1.3:l. At the limit

Length of waste (XY) - 1.3 Length of ore (YZ) 1

- -

On the left side of the section, the pit limit for the 0.7% Cu grade was similarly determined using a breakeven stripping ratio of 1.7:l. If the grade of the ore changed as the pit limit line was moved, the breakeven stripping ratio to use would also change.

The pit limits are established on the longitudinal section in the same manner with the same stripping ratio curves. The pit limits for the radial section are handled with a different stripping ratio curve, however. As shown in Fig. 4, the cross sections and the longitudinal section represent a slice along the pit wall with the base the same length as the

Fig. 1. Types of vertical sections used for a manual pit design. Fig. 2. Pit limits shown on section.

465

466 SURFACE MINING

/ /

/

1 M I I I I I

.5 .6 .7 .8 .9 1.0 Ore Grade (% Copper)

Fig. 3. Strip ratios for different ore grades and metal prices.

surface intercept. The radial section represents a narrow portion of the pit at the base and a much wider portion at the surface intercept. The allowable stripping ratios must be adjusted downward for the radial sections before the pit limit can be set.

The next step in the manual design is to transfer the pit limits from each section to a single plan map of the deposit. The elevation and location of the pit bottom and the surface intercepts from each section are transferred. If a pit slope change occurred on a section, its position is also transferred.

The resultant plan map will show a very irregular pattern of the elevation and outline of the pit bottom and of the surface intercepts. The bottom must be manually smoothed to conform to the section information.

Starting with the smoothed pit bottom, the engineer will develop the outline for each bench at the point midway between the bench toe and crest. The engineer manually expands the pit from the bottom with the following criteria:

1. The breakeven stripping ratios for adjacent sections may need to be averaged.

Fig. 4. Segments influenced by vertical sections.

2. The allowable pit slopes must be obeyed. If the road system is designed at the same time, the interramp angle is used. If the preliminary design does not show the roads, the outline for the bench midpoints will be based on the flatter overall pit slope that allows for roads.

3. Possible unstable patterns in the pit should be avoided. These would include any bulges into the pit.

4. Simple geometric patterns on each bench make the designing easier.

When the pit plan has been developed, the results should be reviewed to determine if the breakeven stripping ratios have been satisfied. The pit can be divided into sectors on the pit plan and each sector checked for the waste:ore ratio. Two ways the stripping ratios for each sector can be checked are:

1. The pit limits from the pit plan maps can be transferred back to the sections and the stripping ratio can then be calculated from the sections.

2. The bench outlines can be transferred to each individual bench map. The ore and waste lengths are measured along the bench outline for each sector. The results for each bench are combined to calculate the stripping ratio for that sector. The ore grade for the sector is the weighted average (by length) of the grade of the ore along the pit limit for each bench.

The total reserves for the pit and the average stripping ratio are determined by accumulating the values from each bench. On each bench the ore tonnes above the breakeven cutoff grade are measured and the average grade of the ore is calculated. The tonnes of waste are also measured. The total of the tonnes of ore and the total of the tonnes of waste on each bench give the average stripping ratio for the pit.

COMPUTER METHODS As should be appreciated, the manual design of a pit gets

the planning engineer closely involved with the design and increases the engineer’s knowledge of the deposit. The procedure is cumbersome, though, and is difficult to use on large or complex deposits. Because of the lengthiness of the procedure, the number of alternatives that can be examined is limited. As more information is gathered or if any of the design parameters change, the entire process may have to be repeated. Another drawback to the method of manual design is that the pit may be well designed on each section, but,

SE6hlENT REPRESENTED c ~ o s s s E c ~ ~ o u ~ z BY CROSSSECTfON

RADIAL SECTfON

REPRESENTED BY RADIAL SECTfOW


when the sections are joined and the pit is smoothed, the result may not yield the best overall pit.

The growth of computer usage has allowed engineers to handle greater amounts of data and to examine more pit alternatives than with manual methods. The computer has proved to be an excellent tool for storing, retrieving, processing, and displaying data from mining projects. Computer applications have been developed to take much of the burden of pit design from the engineer.

The computer efforts can be divided into two groupings: 1. Computer-assisted methods. The calculations are done

by the computer under the direct guidance of the engineer. The computer does not do the entire design but only does the brunt of the calculation work with the engineer con- trolling the process. Examples would be the two-dimensional Lerchs-Grossman technique and the three-dimensional design using an incremental pit expansion method.

2. Automated methods. These are capable of designing the ultimate pit for a given set of economic and physical constraints without intervention by the engineer. One category of automated methods contains the mathematically optimal techniques using linear programming, dynamic programming, or network flows. A second category has the heuristic methods, such as the floating cone method that produces an acceptable pit, but not necessarily an optimal one. As the cost of computer processing decreases, better automated methods will be forthcoming.

Another characteristic differentiating the types of computerized methods is the use of either a whole or partial block for mining. In a whole block method, each block is mined either as a unit or left intact; in a partial block method, a portion of each block can be mined. Each type has certain advantages:

1. Accuracy-With the use of partial blocks, the tonnage of small volumes can be calculated quite accurately. The overall tonnage of the pit may be accurate using a whole block method, but, the accuracy is less for smaller volumes.

2. Physical constraints-The desired pit slopes and pit boundaries are approximated by the mined blocks. The use of whole blocks may result in pit walls that are unacceptable in terms of operations and slope stability. Some whole block techniques may assume the block size is a function of the pit slope and some may not allow the slope to vary in the pit. Smoothing is usually required for an ultimate pit designed using whole blocks.

3. Cost-When properly used, whole block methods have generally proven to be less costly in terms of computer costs than partial block methods. As a result, several pit configurations can be quickly analyzed with a whole block method to give a good basis for a more detailed partial block analysis.

LERCHEGROSSMAN METHOD The two-dimensional Lerchs-Grossman method will de-

sign on a vertical section the pit outline giving the maximum net profit. The method is appealing because it eliminates the trial-and-error process of manually designing the pit on each section. The method is also convenient for computer processing.

Like the manual method, the Lerchs-Grossman method designs the pit on vertical sections. The results must still be transferred to a pit plan map and manually smoothed and checked. Even though the pit is optimal on each section, the ultimate pit resulting from the smoothing is probably not optimal.

The example in Fig. 5 represents a vertical section through a block model of the deposit. Each square represents the net value of a block if it were independently mined and processed. Blocks with a positive net value have been shaded in the figure. The block size has been set in the example so that the pit profile will move up or down only one block at most as it moves sideways. Step 1

Add the values down each column of blocks and enter these numbers into the corresponding blocks in Fig. 6. This is the upper value in each block of Fig. 6 and represents the cumulative value of the material from each block to the surface.

Step 2 Start with the top block in the left column and work

down each column. Put an arrow in the block pointing to the highest value in:

1. the block one to the left and one above, 2. the block one to the left, 3. the block one to the left and one below. Calculate the bottom value for the block by adding the

top value to the bottom value of the block the arrow points to. The bottom value in each block represents the total net value of the material in the block, the blocks in the column, and the blocks in the pit profile to the left of the block. Blocks marked with an X cannot be mined unless more columns are added.

Step 3 Scan the top row for the maximum total value. This is

the total net return of the optimal pit. For the example, the optimal pit would have a value of $13. Trace the arrows back to get the outline of the pit. Fig. 7 shows the pit outlined on the section. Note that even though the block on row 6 at column 6 has the highest net value in the deposit it is not in the pit. To mine it would lower the value of the pit.

Fig. 5. Vertical section showing the net value of each block.

468 SURFACE MINING

I 2 3 c 5 6 7 8 9 1 0 1 1

Fig. 6. Section after the search procedure.

Fig. 7. Optimal pit outline.

INCREMENTAL PIT EXPANSION The incremental pit expansion technique is a trial-and-

error process guided by the engineer. Although this method will not necessarily produce an optimal pit, in the hands of a skillful engineer it is a very powerful tool. Either whole or partial blocks can be used.

The engineer will digitize the outline of a new pit bottom or an expansion to a pit wall. The computer projects this shape upwards in conformance with the pit slopes to be used. The resulting expansion should be graphically shown to the engineer for confirmation that the increment is as expected.

If the expansion is agreeable to the engineer, a tabulation is done for the material in the increment. The shape of the expansion at the midpoint of each bench is used with the block values for the bench to calculate the grade, tonnes of ore, tonnes of waste, revenues, and costs of the increment. If the increment meets the criteria of the engineer, it is kept in the pit and another outline is digitized. In this manner, the size of the pit gradually grows as the engineer outlines each increment and decides if it meets the design criteria.

To be most effective, the design should progress from the upper benches downward and from the higher grade areas outward on each bench. This is to ensure that only those blocks that can pay for themselves will be included in the pit.

FLOATING CONE METHOD The most popular automated method has been the float-

ing cone method. The concept is similar to the incremental pit expansion but the manual intervention can be minimized or eliminated.

Instead of a digitized bottom, one block or a group of blocks forms the base of the expansion. If the grade of the base is above the mining cutoff grade, the expansion is projected upward to the top level of the model as in Fig. 8. The

resulting cone is formed using the appropriate pit slope an- gles.

All blocks that are encompassed by the cone (and are not considered previously mined) are tabulated for the costs of mining and processing and for the revenues derived from the ore. If the total revenues are greater than the total costs for the blocks in the cone, the cone has a positive net value and is economic to mine. The surface topography is then altered to reflect the simulated mining of the cone. The topography is left unchanged unless the cone value is positive.

A second block is then examined, as shown in Fig. 9. Assuming the first cone had a positive value and was included in the pit, only the blocks in the shaded portion need be tabulated.

Fig. 8. Cone centered on a base block.

469

Fig. 9. Cone formed by a second base block.

Each block in the deposit is examined in turn as a base block of a cone. For a large model, this can be a costly process. The resulting pit is also dependent on the pattern in which the next base block is chosen. For example, a base block on an upper level may not have been economic when initially examined. If part of the waste covering it is stripped by mining a cone from a lower level, the block should again be checked before another block from a lower level is used as a base block. This is necessary to make each cone pay for itself.

Because of this potential problem, an engineer can in- tervene in the process. The engineer can define a smaller volume in which all base blocks will be checked by the computer. From the results of the cones in this smaller volume, the engineer can specify another volume to check. With this added control, the selection sequence of base blocks is less of a problem.

REFERENCES Barnes, M. P., 1980, Computer-Assisted Mineral Appraisal and Fea-

sibility, AIME, New York. Kim, Y. C., 1978, “Ultimate Pit Limit Design Methodologies Using

Computer Models-The State of the Art,” Mining Engineering,

Koskiniemi, B. C., 1977, “Hand Methods in Open-Pit Mine Planning and Design,” Open Pit Mine Planning and Design. J. T. Crawford and W. A. Hustrulid, eds., AIME, New York, pp. 187-194.

Lerchs, H., and Grossman, I. F., 1965, “Optimum Design of Open- Pit Mines,” Transactions, Canadian Institute of Mining and Me- tallurgy, Vol. 68, pp. 17-24.

Miller, V. J., and Hoe, H. L., 1982, “Mineralization Modeling and Ore Reserve Estimation,” Engineering and Mining Journal, Vol.

Soderberg, A., and Rausch, D. O., 1968, “Pit Planning and Layout,” Surface Mining, E. P. Pfleider, ed., AIME, New York, pp. 141- 165.

Pana, M.T., and Davey, R. K., 1973, “Pit Planning and Design,” SME Mining Engineering Handbook, A. B. Cummins and I. A. Given, ed., AIME, New York, pp. 17.1-17.19.

Pana, M.T., and Davey, R. K., 1973a, “Open-Pit Mine Design,” SME Mining Engineering Handbook, A. B. Cummins and I. A. Given, ed., AIME, New York, pp. 30.7-30.19.

Taylor, H.K., 1972, “General Background Theory of Cutoff Grades,” Transactions (Section A: Mining Industry), Institution of Mining and Metallurgy, Vol. 81, pp. A160-AI79.

Vol. 30, NO. 10, pp. 1454-1459.

183, NO. 6, pp.66-74.

5.3 Open Pit Optimization

JEFF WHITTLE

INTRODUCTION Computer hardware, and to a lesser extent software, has

for the last 20 years consistently advanced at a rate which has exceeded all expectations. As a result, calculations which were difficult or impossible to do only a few years ago can now easily be completed on a computer small enough to fit on a desk and costing only a few months’ salary. What is more, the calculations can be done by users with very little knowledge of computers.

Pit optimization is a field which has benefitted greatly from this process in recent years, and we can now go far beyond simple optimization of a pit outline. Thorough sensitivity work, which has often only received lip service in the past, can now be carried out routinely on every ore body that is examined. Management can be offered the real pos- sibility of trading profit for reduced corporate risk in an explicit manner.

Pit optimization was touched upon briefly in the previous section, but we will now go into it in much more detail and describe what can be done at the time of writing (early 1990). There will undoubtedly be further developments.

THE MEANING OF PIT OPTIMIZATION The first thing to realize is that any feasible pit outline

has a dollar value which can, in theory, be calculated. By feasible, here, we mean that no wall slope is steeper

than the rock can support after allowing for the insertion of haul roads and safety berms. That is, we are talking about overall pit slopes.

To calculate the dollar value we must decide on a mining sequence and then conceptually mine out the pit, progressively accumulating the revenues and costs as we go. If we wish to allow for the time value of money-that is the fact that a dollar we receive today is more valuable than one that we (might) receive next year-then we must discount the revenues and costs by a factor which increases with time.

The second thing to realize is that in doing this calculation we have, in effect, allocated a value to every cubic meter or to every block of rock. What is more, we have allocated these values without taking any account of the mining which has gone before, except that the value may depend on the position

-

100

E

Fig. 1. Simplified ore body.

of the block and the effect that its position has on haulage distances.

Current computer optimization techniques attempt to find the feasible pit outline which has the maximum total dollar value. The good ones guarantee that there is no single block or combination of blocks which can be added to or subtracted from the outline to produce an increase in total outline value. That is, they guarantee the absolute mathematical maximum. They also exclude any block combinations which have a zero value.

Once we have fixed the block values and the slopes, we have fixed the optimal outline, and it is important to make the point that there is only one optimal outline. If we assume that there are two outlines of the same value, then it is easy to show that the two taken together would produce an outline of higher value. Consequently the assumption of the existence of two different optimal outlines of equal value is false.

If the block values increase then, in general, the optimal pit gets bigger. If the slopes increase then, in general, the optimal pit gets deeper.

Of course, we have to know the pit outline in order to calculate the values of the blocks, particularly if the time value of money is important. Conversely, we have to know the block values in order to find the optimal outline. We therefore have a chicken and egg situation, and we will return to this.

A SIMPLE EXAMPLE Let us assume that we have a flat topography and a

vertical rectangular ore body of constant grade as is shown in Fig. 1. Let us further assume that the ore body is sufficiently long in strike for end effects to be ignored. Under these circumstances, we only have to concern ourselves with a section.

In this simplified case there are eight possible pit outlines that we can consider, and the tonnages for these outlines are given in Table 1.

If we assume that ore is worth $2.00 per tonne after all mining and processing costs have been paid, and that waste costs $1.00 per tonne to remove, then we obtain the values shown in Table 2 for the possible pit outlines.

When plotted against pit tonnage, these values produce the graph in Fig. 2. With these very simple assumptions the outline with the highest value is number five.

There are other things that we can learn from this curve.

Table 1. Tonnages for the Possible Pit Outlines

Pit Ore Waste Total

1 500 100 600 2 1000 400 1400 3 1500 900 2400 4 2000 1600 3600 5 2500 2500 5000 6 3000 3600 6600 7 3500 4900 8400 8 4000 6400 10400

470

47 1

value value ainnn , ----- I

0 1 I 1 I I J 0 2000 4000 6000 8000 io .ooo tonnes

Fig. 2. Relationship between pit tonnage and value.

I tonnes

Fig. 3. The effect of small design changes at different points on the tonnage/value curve.

Firstly, outlines four and six have values which are close to that of outline five, and this is not just an artefact of this particular ore body. For any continuous ore body, as the pit is expanded towards optimality, the last shell which is added will have only a small positive value. If it had a large one, there would probably be another positive shell to follow. This means that in this case, and in the vast majority of real ore bodies, the curve of value against tonnage is smooth and surprisingly flat at the peak. It is common to find that a 10% range of pit tonnage covers only a 1% range of pit value. The trick is to find the peak, and good optimizers guarantee to do this.

Secondly, consider Fig. 3. If we are working without an optimizer and doing a detailed design for a realistically complex ore body, then we might be working away from the peak at ‘A’, where changes in pit tonnage can have a significant effect on the value of the pit. In fact, generations of mining engineers have learned that a series of small adjustments, involving a great deal of work, can significantly affect the profitability of the mine. Contrast this with starting from an optimized outline at ‘B’. From this point, providing that ore and waste are kept in step with each other, it is difficult to go wrong. Certainly there is no need to experiment with small adjustments. Since, with modem software, we can plot this graph for real ore bodies, we can actually find out how much freedom of movement we have before we start the detailed design. In other words, designs based on optimized outlines are very much easier to do.

THE EFFECTS OF SCHEDULING ON THE OPTIMAL OUTLINE

When we schedule a pit, we plan the sequence in which various parts of it will be mined and the time interval in which each is to be mined. This affects the value of the mine

Table 2. Values of the pits if ore is worth $2 per tonne and if waste costs $1 per tonne.

Pit Value ~~

900 1600 2100 2400 2500 2400 2100 1600

because it determines when various items of revenue and expenditure will occur. This is important because the dollar we have today is more valuable to us than the dollar that we are going to receive or spend in a year’s time. There are various reasons for this:

0 Delayed revenue may increase our need to borrow funds and pay interest, thus reducing the effective revenue;

0 Delayed revenue may not eventuate-one of the risk factors;

Delayed expenditure may reduce our need to borrow funds and pay interest, thus reducing the effective expenditure;

Something unexpected may go wrong with the operation-another risk factor; etc.

The standard way to allow for this is to discount next year’s dollar by a certain percentage and to apply that idea cumulatively into the future. Thus we discount future revenues and costs by a particular discount rate and reduce them all to a net present value.

There are two discount rates. The notional discount rate is applied to actual revenues and costs which are likely to occur. That is, revenues and costs which follow the inflation rate. Thus the notional rate (typically 20%) includes an allowance for inflation. It is correct to use this, provided that we inflate our revenues and costs for future years. However, we are then in the position of guessing at the future inflation rate and then guessing at a figure to correct for it! It is easier to work out revenues and costs in today’s dollars and then to use the real discount rate (typically lo%), which does not allow for inflation.

In what we will call worst case mining, each bench is mined completely before the next bench is started. Waste at the top of the outer shells is mined early, and the cost is discounted less than the revenue from the corresponding ore which is mined much later. This can make the outer shells uneconomic. The optimal pit for worst case mining is thus generally smaller than is indicated by simple optimization using today’s costs and revenues. This can easily be seen by referring to Fig. 1.

In what we will call best case mining, each shell is mined in turn and thus the related ore and waste is mined in approximately the same time period. In this case, the optimal pit is usually close to the one obtained by simple optimization. Unfortunately, if we try to mine each shell separately, mining costs usually increase and cancel out some of the gains.

In small pits, worst case mining may be the only possi- bility. The larger the pit, the more opportunity there is for creative sequencing, and the closer it is possible to get to best case mining.

472 SURFACE MINING

PRODUCTION OF A DETAILED DESIGN FROM AN OPTIMAL OUTLINE

The precise method used in creating a detailed pit design depends on the tools which are available. It may be done entirely by hand, or with varying degrees of computer assistance.

Whatever the method, the aim is to produce a detailed design which deviates as little as possible from the outline provided by optimization. Where deviation is unavoidable, we try to balance extra tonnage in one place with reduced tonnage in another. The resultant design should in most cases contain ore and waste tonnages very similar to those contained by the optimal outline. If it is not possible to achieve this, then it may be that the slopes were not set correctly for the optimization. For example, insufficient allowance may have been made for the effect of haul roads.

While all reasonable steps should be made to follow the optimal outline, the shape of the graph shown in Fig. 2 should be borne in mind. Provided that waste is not included without the ore which it uncovers, small deviations from the outline have little or no effect on the pit value. A useful concept is to say that the spirit of the outline should be followed rather than the detail. Certainly the square edges of the blocks on the outer surface of the outline are irrelevant. As a starting point, a smooth line should be drawn through them as is shown in Fig. 4. Remember that the block edges are artefacts, they do not represent geological or grade boundaries.

The achievement of the necessary minimum mining widths at the bottom of the pit is often cited as a problem with pit optimization. This problem is more apparent than real in that, for large disseminated or near horizontal ore bodies, the necessary adjustments at the bottom of the pit are usually easy, whereas, for steeply dipping reef structures, it may be possible to put extra constraints into the optimization so as to ensure the necessary width. In the remaining cases, some loss of pit value will be involved in adjusting the bottom of the pit, but it should never exceed 1 or 2%.

THE AVAILABLE OPTIMIZATION METHODS All currently available methods of optimization attempt

to find the optimal outline in terms of a block model. That is, they try to find the list of blocks which has the maximum total value while still obeying the slope constraints.

The enormity of this problem is seldom appreciated. Trial and Error

Consider a trivial model with only one section and 10 benches of 10 blocks. If we take a very simple-minded approach, each of the 100 blocks can either be mined or not, so there are 2IM or lom alternatives, many of them not feasible. Even if a computer could assess a million alternatives a second, it would still take three million times the current age of the universe to find the best one!

If the allowable slope is one block up or down at each column change, and we use this information to ensure that we try only feasible alternatives, the number of alternatives is reduced to 10 X 39 or 200,000. A computer could easily assess this number of alternatives. However, if we extend the model to 10 sections, the number of alternatives rises to 10 x 2% or about 10'' again, and we still have only 1000 blocks, which is insufficient for serious work.

Put simply, trial and error is useless. Floating Cone

The floating cone method has been popular because it is easy to program and easy to understand. It works by searching through the block model for ore blocks and then assessing the value of the inverted cones which have to be mined to expose them. If the value of a cone is positive, it is mined out and all the blocks it includes are changed to air blocks. The search then continues.

Unfortunately, this simple-minded approach rarely finds the optimal pit because of two distinct problems; one causes it to omit profitable ore from the pit and the other causes it to include non-profitable ore.

The first occurs because it cannot try all possible combinations of ore blocks, as that would be a trial and error process, and we have seen that that is computationally un- reasonable. Most pits are viable in part at least because numbers of ore blocks combine to pay for the stripping of waste above them, when no individual block or even close group of blocks can do so. The floating cone method cannot detect this co-operation between different parts of the ore body if neither part is viable in its own right.

The second occurs for slightly more technical reasons. In Fig. 5 there are three small ore bodies and their corresponding waste volumes, with their values and costs shown. A floating cone program will examine A and will find that the corresponding cone has a total value of (40-20-30) = -10, and so is not worth mining. It will then examine B, will find a cone of value (200-80-30) = +90 and will convert it to air, leaving the values shown in Fig. 6

If a floating cone program is to work correctly, whenever it converts a cone to air, it should start searching again at the top of the model. However, this is computationally very expensive so that most programs continue their search down- wards and would consider C next.

At this time the cone for C has a total value of (40-50+40-20) = +lo, so that the program mines it. This should not happen, because some of the value of ore body A is being used to help pay for the mining of waste

Optimal Yock outline Det3iled design outline

Fig. 4. Smoothing out the block outline. Fig. 5. Ore and waste values before floating cone run.


Fig. 6. Ore and waste values after the removal of ore body B and its corresponding waste.

(the -50 region) which is below it. The true optimal pit in this case includes A and B, but not C.

Apart from being easy to understand and program, the one advantage that the floating cone method has over other methods is that, if instead of using just one block the program uses a disk of blocks as its starting point, then this can ensure a particular minimum mining width at the bottom of the pit.

Two-Dimensional Lerchs-Grossmann Method In 1965 Lerchs and Grossmann gave two different

methods for open pit optimization in the same paper. Oqe works on a single section at a time. It only handles slopes which are one block up or down and one across, so that the block proportions have to be chosen so as to create the required slopes. This method is easy to program and is reliable in what it does, but, since sections are optimized independently, there is no guarantee that successive sections can be joined up in a feasible manner. Consequently a good deal of manual adjustment is usually required to produce a detailed design. The end result is erratic and unlikely to be truly optimal.

Two later variants of this method exist. One (Johnson, Sharp, 1971) uses the two-dimensional method both along sections and across them, in an attempt to join them up. The other (Koenigsberg, 1982) uses a similar idea but works in both directions at once. Both are restricted to slopes which are defined by the block proportions and neither honors even these slopes at 45" to section. This last point is best illustrated by running the programs on a model which contains only one (very valuable) ore block. The resulting pit is diamond shaped rather than circular, with slopes correct in the E-W and N-S directions, but much too steep in between.

Three-Dimensional Lerchs-Grossmann and Network Flow

The second method given by Lerchs and Grossmann (1965) was based on a graph theory method, and Johnson ( 1968) published a network flow method of optimizing a pit. Both guarantee to find the optimum in three dimensions regardless of block proportions. Both, naturqlly, give the same result.

Both are difficult to program for a production environment where there are large numbers of blocks. Nevertheless this has been achieved and programs are now available which

can run on any computer from a PC upwards. Most of these use the Lerchs-Grossmann method.

Because these programs guarantee to find the sub-set of blocks with the absolute maximum value consistent with the slope constraints, the alterations to the pit outline caused by small slope or block value changes are reliable indicators of the effect of such changes. This has opened up the field of real sensitivity analysis, where the effects of slope, price and cost changes can be measured accurately. With other methods, only the crudest sensitivity work is possible.

This has led to the development of programs which au- tomate some aspects of sensitivity analysis to the point where graphs of net present value against, say, total pit tonnage, can easily be plotted. Further mention of this will be made later.

CALCULATING BLOCK VALUES The correct calculation of block values is essential for

any optimization. If the block values are wrong, the optimized pit outline will also be wrong.

For optimization purposes, there are two basic rules which must be followed when calculating the value of a block. The First Rule

Calculate the block value on the assumption that it HAS been uncovered and that it WILL be mined.

No allowance for assumed stripping ratios should be made, because stripping is precisely what pit optimization works out. If a stripping ratio is assumed when calculating the block values, the result of the optimization is being pre- judged.

Similarly, take no notice of any pre-conceived breakeven cutoff. The use of a breakeven cutoff can be helpful in manual pit design; it is inappropriate for optimized pit design. A consequence of this is that a block model in which only rock containing grades above a breakeven cutoff is designated as ore, is also inappropriate for pit Optimization.

The only relevant cutoff in this context is that grade at which the revenue from recovered product will just pay for the cost of processing and any extra mining cost which is only applicable to ore. Second Rule

Include any on-going cost which would stop if mining were stopped.

This is because, when the optimization program is adding a block to the pit outline, it is effectively extending the life of the mine. It must therefore pay for all the costs involved in extending the life of the mine.

Incremental costs such as fuel costs, wages, etc. must obviously be included in the cost of mining or processing, whichever is involved.

Overhead costs WHICH WILL STOP IF MINING STOPS must also be included. If the mine throughput is to be limited by the overall mining capacity, then these overheads should be included in the mining costs. If the throughput is to be limited by the processing capacity, then these overheads should be included in the processing cost, because only the addition of an ore block extends the life of the mine.

Nonrecoverable upfront costs, such as the cost of building access roads, should not be included in the costs used in optimization. Although these may be paid for with a loan which is to be repaid over a number of years, these repay- ments will be required whether mining continues or not. If the value of the optimized pit is less than the nonrecoverable upfront costs, then the mine should not be proceeded with.

474

Fig. 7. Undiscounted, best case, and 40 worst case NPV plotted against pit ton-

nage. 30.

2 0 .

BLOCK SIZES Again, re-blocking should be done by adding values and There are four block sizes which are relevant in this work. not by averaging grades.

For Outlining the Ore Body The size of the block that is needed for outlining the ore

body depends on the shape and size of the ore body and on the particular computer modelling package that is being used. It may be quite small, which can lead to a model consisting of millions of blocks.

For Calculating Block Values The value of blocks should be calculated with a block

size which is similar to the selective mining size. That is, a parcel of rock should not be so small that it could not be mined separately, nor so large that grades are artificially smoothed. This block is sometimes bigger than that needed for outlining the ore body, requiring blocks to be combined and their grades averaged.

For Designing a Pit There is now considerable experience in pit design using

optimization techniques and, assuming that the pit occupies most of the width and length of the model and that the outline is not too convoluted, then a full model of 100,000 to 200,000 blocks is usually more than sufficient for pit design purposes. This leads to a block size which may be bigger than that for calculating values.

If it is necessary to re-block the value model, then it should be done by adding component block values and NOT by averaging grades.

For Sensitivity Work If we want to do a series of optimizations using, say,

different product prices so as to plot a graph of pit value against price, a model of 20,000 to 50,000 blocks will give just the same shape of graph with a very small shift of absolute value. Thus, most optimizations for sensitivity work can be done very quickly and this approach generally leads to a much more thorough sensitivity analysis.

SENSITIVITY WORK Although an optimized block outline and the correspond-

ing detailed design are not the same, they do have a close relationship and, provided a good optimizer is used, are very similar in value. Consequently, when comparing two designs, the difference in value between the two optimal block outlines will be very similar to the difference in value between the two detailed designs. This means that sensitivity work can be carried out without doing any detailed designs at all.

Also, because a good optimizer produces a result which is objective and single-valued, it is quite reasonable to take note of small value differences due to, say, changing the slopes by a few degrees. This is not true when designs are done by hand, because an engineer will probably produce different designs on different days, without any change of slope.

During sensitivity work, we explore the economic and slope sensitivity of the mine. We sort out the general scale of mining and hence the operating costs. We decide approximately where the haul roads are to go and adjust the slopes in these regions to the average slope.

This requires a large number of quick optimization runs. However, it is probably the most valuable part of the whole design exercise because it inevitably leads to a much better understanding of the ore body and its economics. Graphs can be prepared which show how various characteristics of the mine, such as value or tonnage, are related to product price, costs, etc.

Probably the most significant graph is the one shown in Fig. 7. This relates net present value (NPV) to total pit tonnage for a given throughput and product price.

First, a set of optimal outlines is prepared, where each is optimal for a different product price. For some fixed product price, each of the outlines is then scheduled as though it was to be the limiting pit. If an automated practical scheduling scheme is available, it should be used. In producing Fig. 7, two limiting schedules have been used. Best case

0 2 4 6 8 10 Total Pit Tonnage (Millions)

12


scheduling involves mining with many small pushbacks or cutbacks. Although in no sense a practical schedule, it indicates the highest possible NPV. Worst case scheduling involves completing the mining of each bench before starting the next. This is usually practical, but produces the lowest possible NPV.

The NPV for any practical mining schedule must lie somewhere between the two lower curves, with smaller pits tending towards the bottom curve and larger pits providing opportunities to get nearer to the middle curve.

This graph, which can be plotted for different product prices, is the single-most useful presentation known to the writer. It is meaningful to engineers, accountants, and management alike and can usefully be discussed in committee. It allows profit and corporate risk, in the form of mine life (pit tonnage), to be related and traded explicitly. Once a pit size has been chosen, it is easy to use the corresponding pit outline as a starting point for the detailed design.

This graph can be prepared by using any good optimizer and by doing a lot of work. However, software now exists which will produce the data for it automatically and quickly.

CONCLUSION We have seen how good pit optimizers can be used not

only to help design ultimate pit outlines, but also to carry out sensitivity analysis to an extent which is not possible without them.

Pit optimization is a tool which, used properly, can greatly speed and ease the process of pit design and can significantly increase the value of most pits. It can also be used to reduce the corporate risk involved in mining.

REFERENCE LIST Johnson, T.B., 1968, “Optimum Open Pit Mine Scheduling,” Ph.D. Diss. University of California, Berkeley, CA, 120 pp.

Johnson, T.B., and Sharpe, R.W., 1971, “Three Dimensional Dy- namic Programming Method for Optimal Ultimate Pit Design,” Report of Investigation 7553, US Bureau of Mines.

Koenigsberg, E., 1982, “The Optimum Contours of an Open Pit Mine: An Application of Dynamic Programming,” Proceedings, 17th APCOM Symposium, AIME, New York, pp. 274-287.

Lerchs, H., and Grossmann, I.F., 1965, “Optimum Design of Open Pit Mines,” CZM Bulletin, Canadian Institute of Mining and Me- tallurgy, Vol. 58, January.

5.4 Optimum Production Scheduling

ERNEST L. BOHNET

The objective of production scheduling is to maximize the net present value and return on investment that can be derived from the extraction, concentration, and sale of some commodity from an ore deposit. The method and sequence of extraction, and the cutoff grade and production strategy will be affected by the following primary factors:

1. Location and distribution of the ore in respect to topography and elevation;

2. Mineral types, physical characteristics, and grade / tonnage distribution;

3. Direct operating expenses associated with mining, processing, and converting the commodity into a salable

4. Initial and replacement capital costs needed to com-

5. Indirect costs such as taxes and royalties; 6. Commodity recovery factors and value; 7. Market and capital constraints; 8. Political and environmental considerations. The procedure used to establish the optimal mining

schedule can be divided into three stages. Tfe first defines the extraction order or mining sequence, the second defines a cutoff grade strategy that varies through time and will be optimal for a given set of production parameters, and the third defines which combination of production rates of the mine, mill, and refinery will be optimal, within the limits placed by logistical, financial, marketing, and other constraints.

In order to develop an optimum production schedule, a sequence or extraction order inside of the so-called ultimate pit must first be determined. The extraction sequence depends on two subsets of parameters. The first deals with the strip ratio associated with recovering the ore, the grade of that ore, and the physical location of that ore in respect to availability through time.

The second subset of parameters consists of costs associated with starting and maintaining the whole operation. Direct operating costs can be used to define a breakeven cutoff grade and strip ratio, but the objective of mine planning is to devise a strategy that will optimize the total investment. Operating at breakeven cutoffs and strip ratios is only optimal for the final phase at the end of the mine life.

Before the mine production planning commences, a great deal of work has already been completed in exploration and modeling the deposit. From this work, a number of tentative assumptions have been made, including the most probable mining method and hence, the bench height, type, and approximate size of the loading equipment and the mining selectivity. Other test work and assumptions will also have been made regarding the type of process needed to recover the commodity. These parameters will be used to estimate the most probable range of mining and processing costs.

The design of the mining phases can be accomplished by rough manual approximation after review of the bench plans and cross sections, or analytically by computer techniques. Each method has advantages and disadvantages as applied by an experienced engineer, but the method chosen is determined by the accuracy requirements and available funding. If the study objective is very preliminary, with little basic

form;

mence and maintain the operation;

data available, then manual methods can be justified. If the study is to be a sound basis for investment and development of the mine, and a great deal of information has been col- lected, then a very thorough computer analysis is warranted.

Computer designed phases can be determined by feeding the data developed and stored in a computer block model into a set of programs that can be used to calculate an economic phase limit. The objective is to develop three dimensional equal profit potential surfaces throughout the mineral deposit. Each surface has to be sufficiently spaced apart to allow adequate room for mining the slices between the surfaces. Since the distance between equal profit potential surfaces will vary, some manual adjustments will be required, as well as the addition of haul roads out of a phase and if required, access left for the next phase. See Fig. 1.

Manual methods depend on having an experienced engineer review the bench plans and cross sections through the deposit to visually pick out the higher grade targets that have reasonable strip ratios. For example, it would be incorrect to first target high grade areas for mining having very high strip ratios that reduce the net value of the recovered ore below the net value of medium grade ore in another area with much less stripping. The manual method is only a first step estimate and, therefore, it will not be as accurate as a computerized technique.

Computerized pit limit determinations can be made using the 2-D Lerchs-Grossman method, or three-dimensional techniques, such as the floating cone or the 3-D Borgmann pit design method. The results of the last two systems are nearly the same, the difference being that the floating cone is a computerized trial-and-error method while the Borg- mann is an analytical method.

The strategy used in developing the Computerized pit phases is to use higher costs or lower commodity prices in the initial phase and then, for each successive phase, lower costs or higher commodity prices are used. The net effect of this strategy is that the initial phase will have a high breakeven cutoff grade and high net value per ton of ore mined, and each following phase will have a lower cutoff grade and net value per ton of ore.

The accuracy of the estimated costs, recoveries, and commodity price parameters need only be reasonably precise, since they are only used to determine the location of the ores with the relative highest to lowest net values.

Cost estimates needed for determining the extraction sequence can be broken down into three distinct major categories: (1) costs per ton of material mined; (2) costs per ton of ore treated; and (3) costs per pound of commodity produced.

The costs per ton of material mined include the direct mining costs per ton for the drilling, blasting, loading, hauling, ancillary equipment, and mine general and administrative functions. The cost per ton of the capital and replacement expenditures for mine mobile equipment related to the total material mined is also included because the major mobile mining equipment is consumed in approximate direct pro- portion to the amount of material handled by the equipment, unlike the major initial capital cost components of the plant and infrastructure. The plant components that are replaced

476

477

WIDTH ADJUSTED TO

ENSURE S U F F I C I E N T

M I N I N G SPACE.

r . ( 2 0 0 - 3 0 0 F E E T ) '.. ACCESS RAMPS AND HAUL ROADS

PHASE I

PHASE 1 1

PHASE 1 x 1 Fig. 1. Internal pit phases: typical pit cross section.

PHASE I DESIGNED USING A 0 . 8 0 % COPPER CUTOFF

CONTAINS ORE O F H IGHEST NET VALUE.

PHASE I 1 DESIGNED USING A 0 . 6 0 % COPPER CUTOFF CONTAINS ORE O F MEDIUM NET VALUE.

PHASE I 1 1 DESIGNED USING A 0.30% CDPPER CUTOFF

CONTAINS ORE OF THE LOWEST NET VALUE,

AND ORE I N LAST F I N I T E S L I C E I N P I T WALL

CONTAINS ORE OF ZERO NET VALUE

or repaired are usually included in the operating maintenance costs per ton of ore, and are not related to the total tonnage moved in the mine.

The depreciation cost to cover mobile surface mine equipment purchase and replacement will usually be in the range of $0.15 to $0.25 per ton of material mined. The magnitude of the cost will depend on the size, type, and anticipated life of the equipment, the mine production level, the haulage distances, and the work schedule.

The most important reason for including mine mobile equipment depreciation is that the method of producing three-dimensional equal profit surfaces in the ore deposit must consider all relevant costs per ton of material mined. If the equipment depreciation were not included, then the cost per ton of material mined will be understated and the phase design will tend to move out into higher stripping ratio areas. This would not matter if the relative strip ratios were equal in all directions around the pit perimeter, but this is rarely so. In most mineral deposits, there will be areas of high and low strip ratios, so moving too far out into a high strip ratio area will lower the net value of the phase, and the 3-D surface generated will no longer be of equal value.

The significance of this costing philosophy can be realized in mining operations where the direct operating costs per ton of material are low relative to the mine equipment depreciation costs per ton of material.

As an example, compare two surface mining operations, one located in the Philippines, the other in Alaska. The net value of a mining increment in each of the pit walls is compared.

Direct mining cost/ton

Gross value/ton of ore

Indicated breakeven strip

Philippines Alaska

of material $0.25 $0.80

f.0.b. mine $3.00 $3.00

ratio 12-1= 11:l 3.75-1=2.75:1

If W0.20/ton of material is added for mobile mine equipment depreciation: breakeven strip ratio 5.67:l 2.00: 1

% change 48% 27%

In summary, the net value of the ore in an incremental slice has to be sufficient to carry all direct operating costs and the initial and replacement expenditures for mobile mine equipment. If the mine equipment depreciation is not included, areas with a much higher breakeven strip ratio will be incorporated into the mine phase, resulting in an over- statement of the net value of ore derived from those high strip ratio areas in the phase.

The second cost collection area is the cost per ton of ore treated and includes expenditures applied to the ore once it has left the mine area. These costs are not related to the total quantity of material removed from the surface mine, but only applicable to the ore tonnage to be treated. Direct costs applied would be:

1. Extra costs associated with transporting the ore to treatment facilities;

2. Crushing and grinding costs; 3. Concentrating cost; and 4. Overhead costs to cover site and head office admin-

istrative and general expenditures as well as marketing, sales, and property management costs.

The third cost category is the expenditures incurred per unit of salable commodity(ies) produced. This would cover the sums spent for concentrate handling and transportation, smelting, and refining, and any royalties or taxes that relate to gross revenues rather than profits.

In addition, a certain amount could be inserted into this category to ensure a minimum profit per pound of salable product.

In order to determine the quantity of salable product, recoveries have to be estimated for the concentrating, smelt-

47%

ing, and refining processes. Recoveries should be based on pilot plant results or on recoveries obtained at mines with similar ores and processes.

Gross revenues are determined from the quantity of salable commodity produced multiplied by a specified commodity price.

There are specific reasons for including some costs and excluding others in the determination of the mining limits. The best manner to justify the inclusion or exclusion of a cost parameter is to first answer the question of what factors are reasonably known or unknown. The quantity of minable ore reserves, the strip ratio, and the associated cost per ton of ore for capital are not known at the commencement of the design. Reasonable estimates can be made as to:

1. Mining cost per ton of material; 2. Mining equipment depreciation or cost of the mining

equipment consumed per ton of material mined; 3. Ore treatment costs; 4. General overhead costs per ton of ore; 5. Anticipated recoveries; 6. Direct charges per pound of salable product; 7. Commodity price; and 8. Minimum profit expected per pound of commodity

produced. Using these estimated factors, a breakeven cutoff grade

can be determined and the final pit limits and total minable ore reserves determined for the breakeven cutoff grade. From these basic parameters, optimization routines can be applied in order to determine the best extraction sequence.

Table 1 illustrates an example of typical base economic parameters used to determine phase increments in a copper mine. If the values were used without modification, the ultimate pit limits would be determined. Since the objective is to define internal phases of higher net value, either an artificial cost is added to the cost per unit of salable product or the commodity value is lowered.

In selecting the economic parameters governing the size of the first phase, the objective is to establish a phase that contains sufficient ore reserves for about a five-year period. This interval would correspond to the payback period and, therefore, it is important to locate the ore with the highest net value during the initial mining sequence.

For example, to try to design the initial phase, an artificial cost of $0.50 per pound of copper could be added or subtracted from the commodity price so that the ore cutoff would be raised to 0.80% and only material above this cutoff would be classified as ore and generate funds to pay for the removal of waste. The objective will be to generate a series of phases spaced sufficiently apart for practical mining, commencing with an initial phase that roughly corresponds to the payback period, followed by a series of progressively larger phases out to the ultimate pit boundary. The variations in costs and the number of phases are determined by combining judgment with a trial-and-error method. One computerized technique that can provide guidance in selecting the various phases and economic parameters is the 2-D Lerchs-Grossman method. By selecting a few typical sections through the ore deposit, relatively inexpensive 2-D pit limits can be determined for various economic parameters. These results can then be used to set the variable costs needed to determine the pit limits using 3-D computer techniques.

The preceding discussion has described the method used to define the internal pit phases. This is the first stage in defining the optimum production and cutoff grade strategy. The second step is the determination of the optimum cutoff grade strategy to be used from one phase to the next, for a defined trial production rate. Only cutoff grades equal to, or less than, the cutoff grade for a particular phase can be used for determining the optimum cutoff grade. If an attempt is made to use a higher cutoff grade, the physical shape of the phase will no longer be valid since the pit wall location depended on revenues from a specified amount of ore that

Table 1. Basic Economic Parameters Used to Determine a Sequence of Phases (Copper Mine Example)

a. Direct mining costs per ton of material: Mobile mining equipment depreciation per ton of material: Total costs for category (a), per ton of material mined:

b. Ore treatment costs per ton of ore: General and overhead costs per ton of ore: Total costs for category (b), per ton of ore processed:

c. Smelting, refining, and transportation costs per Ib of copper: Insurance, property taxes, and royalties per Ib of copper: Total costs for category (c), per Ib of copper recovered:

d. Plant, smelting, and refining recoveries:

e. Commodity price per Ib of copper recovered:

(A minimum profit or variable cost can be added to this total)

(This value can be varied to expand or contract phases)

(a) + (b)

100 Breakeven cutoff equals: 2000(d)[(e) - (c)]

$0.80 $0.20 $1 .OO

$3.00 $0.75 $3.75

$0.35 $0.05 $0.40

-

-

-

85% or 0.85

$1.25

= 0.33%

(b)

100 Internal cutoff grade equals: 2000(d)[(e) - (c)] = 0.26%


will no longer be available. That is, previous low grade ore blocks will now be waste with negative revenues.

In the situation where low grade rock has to be removed from the pit to expose ore, a lower cutoff grade can be used to determine if that low grade material should be processed. This lower cutoff grade is called the internal cutoff grade and is determined by ignoring the mining cost in the breakeven cutoff grade calculation.

The optimum cutoff grade will usually start at a somewhat higher level than the breakeven cutoff grade and will be reduced in time to equal the internal breakeven cutoff grade. The higher the production level, or for a marginal deposit, the less difference there will be between the optimum and breakeven cutoff grades.

The optimum production level can be determined on a strictly economic basis, but with large ore deposits, other constraints such as mining logistics, marketing, and financing will provide limits.

The best strategy can be determined graphically by varying the production rate and cutoff grade for a number of combinations. Fig. 2 illustrates the results from twelve strategies: three production rates and four cutoff grade alternatives. For example, if three pit phases were determined using breakeven cutoff grades of 0.80, 0.60, and 0.30% copper, then four alternative cutoff grade strategies could be:

Cutoff grades used inside of each phase

0.80 0.60 0.30 Alternative phase phase phase

1 0.8 0.6 0.30 2 0.6 0.6 0.30 3 0.45 0.45 0.30 4 0.30 0.30 0.30

These cutoff strategies can then be applied to each of the three alternative production rates.

A second, more rigorous method to determine the best mine/mill/refinery production rate and cutoff strategy is to use the approach presented by K. F. Lane. Lane’s method considers the constraints placed on the operation by the mine, mill, and refinery (or market). Utilizing the grade/tonnage curves for each of the phases developed in the previous stage and combining this with the three categories of costs, plus a fixed cost per year, the optimum cutoff grade strategy on a net present value basis can then be determined, for a given set of production parameters of the mine, mill, and refinery (market). This analysis is more accurate than a graphic solution since the program will fluctuate the cutoff grades through time to match the unique physical distribution of the ore in the various increments.

In order to develop a practical extraction sequence using this method, a scheduling program has to be first applied to the phases to define the progressive mining sequence. This allows the program to recognize the internal stripping variations and permits the progressive removal of material from more than one phase simultaneously; it permits prestripping of an outer phase as ore is being drawn from an internal phase.

900-

v) 0 .. X

In (L 6 6 0 0 -

-I

n w

> z

3 0 0 -

I I I I 0 . 3 0 0.45 0 . 6 0 0.80

CUTOFF GRADE ( % COPPER1

OPTIMUM I N I T I A L CUTOFF GRADE

3 0 . 0 0 0 T P D = 0 . 7 8 % COPPER 4 5 , 0 0 O T P D = 0.59% COPPER 6 0 . 0 0 0 T P D = 0 . 5 6 % COPPER

Fig. 2. Graphic solution to maximize NPV (NPV vs. production rate and cutoff grade alternatives).

In order to determine the optimum production capacities of the mine, mill, and refinery that will maximize the net present value, a trial-and-error method is used. Initial capital costs estimates are subtracted from the NPV to allow ranking of the various production rate alternatives.

Lane’s method allows the mine planner to readily try more alternatives and complete sensitivity analyses on commodity price, recoveries, and other cost parameters.

The preceding discussion has outlined the procedures that can be used to determine the optimum production schedule and cutoff grade strategy. The completed analysis will serve to guide the engineer in detailing the production schedule for both short and long range plans. In cases where the operation is in existence, the same analysis can be completed so that fluctuations in commodity values and costs can be quantified and the plan altered accordingly to optimize the extraction strategy.

It should be noted that in following through the procedures outlined, the basic pit design should be completed first with few or no constraints. The design can then be modified and the costs resulting from constraints can then be quantified. Constraints may be the number of working faces needed for a particular production rate, waste dump locations, drainage routes, property boundaries, ore delivery points, market capacity, environmental constraints, and the availability of personnel, equipment, and financing.

Designing the best and most practical production schedule for each unique ore deposit is a complex task, and only by using a logical procedure that isolates and provides a solution for one set of variables at a time can a satisfactory and optimum solution be determined.

kennedy, b. a. (eds.)-surface mining-society for mining, metallurgy, and exploration (sme)1 (1990)

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