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 considerable 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. 5.2.1:

Figure 5.2.1.

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 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. 5.2.2, 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. 5.2.3 is 1.3:1. 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 1.3:1. At the limit

Figure 5.2.2.

Figure 5.2.3.

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 1.7:1. 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. 5.2.4, the cross sections and the longitudinal section represent a slice along the pit wall with the base the same length as the 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.

Figure 5.2.4.

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.
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, 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 controlling 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.

Lerchs-Grossman Method

The two-dimensional Lerchs-Grossman method will design 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. 5.2.5 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.

Figure 5.2.5.

Step 1

Add the values down each column of blocks and enter these numbers into the corresponding blocks in Fig. 5.2.6. This is the upper value in each block of Fig. 5.2.6 and represents the cumulative value of the material from each block to the surface.

Figure 5.2.6.

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. Figure 5.2.7 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.

Figure 5.2.7.

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 floating 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. 5.2.8. The resulting cone is formed using the appropriate pit slope angles.

Figure 5.2.8.

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. 5.2.9. Assuming the first cone had a positive value and was included in the pit, only the blocks in the shaded portion need be tabulated.

Figure 5.2.9.

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 intervene 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 Feasibility, AIME, New York.

Kim, Y.C., 1978, “Ultimate Pit Limit Design Methodologies Using Computer Models—The State of the Art,” Mining Engineering, Vol. 30, No. 10, pp. 1454–1459.

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 Metallurgy, Vol. 68, pp. 17–24.

Miller, V.J., and Hoe, H.L., 1982, “Mineralization Modeling and Ore Reserve Estimation,” Engineering and Mining Journal, Vol. 183, No. 6, pp. 66–74.

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–A179.

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