Power Electric Mining Shovel & Dragline Pits
The determination of mining and stripping limits prior to undertaking exploitation by power-shovel methods requires careful engineering and often involves complicated computations.
Engineering Estimates
Stripping of overburden and capping in open-pit mining corresponds to development work in underground mining and, as previously pointed out, is a part of the ore-production cost. The cost of stripping is therefore an important factor in the calculations. The unit cost per cubic yard or per ton of stripping material to be removed will vary between wide limits, depending on the depth and character of the capping and overburden, topography, total volume and rate at which it is to be stripped, distance to the spoil dump and grade of track or truck roads, method of transportation, size, capacity, and type of excavating and haulage equipment, wage rates, and local costs of supplies and power.
The total volume of stripping will be that vertically above the limits of the ore pit plus that outside of the ore pit necessary to maintain safe strip-pit slopes and benches and provide working approaches to the pit. The strip-pit slopes will be governed by the character and depth of the capping or overburden and the direction of major planes of weakness, such as faults, bedding planes, and schistosity. The volume of stripping outside the ore-pit area and, hence, the stripping-ore ratio will increase rapidly with the depth of capping or overburden, especially if the surface rises away from the pit (see fig. 135). Since the stripping-ore ratio determines the stripping charge per ton of ore, it limits the grade of ore that can be mined profitably by open-pit methods and hence determines the boundary of the ore pit. Metal prices, which determine the grade of ore that can be mined profitably, are subject to wide fluctuations. Hence, it is evident that a careful appraisal of future market trends is as essential as precision in engineering calculations. Balancing of the various factors therefore often requires the use of cut-and-try methods.
Soderberg has discussed the estimates involved at the Utah copper pit, and the following is abstracted from his paper as a good example of the factors that must be considered and the methods to be used in making open-pit estimates.
Preparatory to making detailed ore estimates, the cut-off between commercial ore and waste must be determined; that is, a grade must be determined below which the material cannot be mined and meet its mining and treatment costs and show a profit. To arrive at this cut-off grade certain assumptions must necessarily be made, such as the selling price of copper, the estimated recovery in percent of gross content, and the cost of producing a pound of copper, which includes all costs other than stripping. The stripping cost is kept separate for reasons that will develop later. Table 54 is set up to illustrate the method used.
Under this set of conditions a copper content of 0.6 percent would be the point of cut-off; any grade under this would be waste and anything over should be classed as ore. Other tables should be made using other figures for doubtful assumptions to assist in establishing a safe cut-off figure.
At this stage it is convenient to set up a table of grades showing the amount of stripping any given grade of ore will carry. This is usually done as follows:
If it costs 40 cents to waste a cubic yard of overburden weighing 2 tons, ½ ton will cost 10 cents. It is then necessary to determine the grade of ore that will yield a return of 10 cents under the given conditions, assuming the average recovery to be 85 percent.
10 cents divided by 13.5 cents = 0.741
0.741 divided by .85 = .872
.872 divided by 2,000 (pounds per ton) = .0436 percent copper.
By adding this increment of grade (0.044) to the ore, it will support the removal of an additional half ton of waste for each addition, from which the following table may be set up:
From tables 53 and 54 graphs may be drawn from which it can be determined at a glance whether or not a certain block of material is ore or waste when the stripping ratio has been determined.
Dividends, of course, cannot be paid on a grade of ore at or near the point of cut-off; the average grade, therefore, must be well in excess of the cut-off grade, and no section of the ore body that will not pay its own way should be combined with higher grades for the purpose of increasing the reserve. Possible exceptions to this rule appear, of course, when a “horse” of waste or a small amount of low-grade material occurs that has to be removed in any case. These small quantities of waste may not be easily separated and may be milled at a loss (capacity permitting), which, however, will be smaller than the cost of removing the material as waste. In such cases, the low-grade tonnage is included in the ore reserve with its grade. The engineer’s judgment will guide him (after he has made a complete analysis of the ore body) in rounding out an estimate where so many variables are concerned. It is well to remember that material which at the time of the estimate is waste may come into the classification of ore by an increase in the price of copper, by an improvement in metallurgy, or by a lowering of costs with improved equipment.
A point that is never lost sight of is that the total cost of mining and stripping shall not exceed a reasonable underground cost. To determine this cost limit a series of trial sections was made up running normal to a tentative location of the stripping limits. On these sections detailed studies were made showing the ratio of ore to waste and the stripping limit for the particular section determined (see fig. 135 for a typical example of the problems involved). In this study it was necessary to determine the grade of the ore in each section and to ascertain just what amount of stripping could be moved and still show a commercial profit from the ore in question. Referring to the table of stripping ratios, it may be noted that under the costs and conditions upon which the table is based, ore having a grade of 0.82 percent copper can carry a stripping ratio of 3 to 1 or of 1½ cubic yards of waste to each ton of ore. At 40 cents per cubic yard this means a stripping cost of 60 cents per ton of ore. In some sections the average grade of ore is in excess of 1 percent copper and as far as grade is concerned could still show a profit for larger stripping ratios permitting the moving of the stripping limit to the increased ratio. But stripping costs in excess of 60 cents per ton under the conditions mentioned, together with other mining costs, exceed the probable underground mining cost; therefore, the maximum stripping ratio should not be greater than 3 to 1 and ore outside such limits should be classed as underground ore. Referring again to the section, it may be noted that the 0.6-percent ore line extends beyond the stripping limit, but such a grade is not considered profitable by underground mining and is therefore not included in ore-reserve calculations. When located within stripping limits, this grade can be classed as commercial ore and included in the reserve.
The study was continued for each section; the ultimate location of stripping limits was then finally laid out, and it was found that of the 625,000,000 tons of ore reserve developed to date, approximately 580,000,000 could be removed by open-cut methods. Possibly some 40 years hence, after open-cut methods have ceased to be profitable, there will be a “mop-up” job to win the remaining tonnage by caving methods. This will entail considerable development work, and plans that are being made for shoveling below the present scene of operations are being laid out to tie in with the possible underground operations.
In addition to the above factors that determine the choice between open-cut and underground methods is the practical side involving the necessity for mass production of a low-grade ore to make it of maximum commercial value. To this must be added the value of flexibility of control of production. To illustrate: If occasion should demand an immediate increase in production to 60,000 tons from a mine ordinarily producing 50,000 tons of ore per day, practically all that is involved in open-cut work is to take two shovels working on stripping and place them on ore. In underground work, to increase the number of ore faces 10 percent would present a serious problem.
Other issues involved that fix the limit to which open-cut operations can be carried are such factors as maximum degree of railroad curvatures, sufficient space for the efficient operation of power shovels, adjacent property rights, dump grounds for waste material, and above all the safe degree of over-all slope. Calculations of ore tonnages recoverable by open-cut methods and stripping are also dependent upon the slope.
The total ore removed to January 1, 1929, amounts to 175,007,974 tons having an average grade of 1.21 percent copper. During the same period 94,338,953 cubic yards of capping and low-grade material has been stripped and dumped in nearby gulches. This gives a stripping ratio to date of 1.1 tons of waste to 1 ton of ore, and is also the ratio being maintained at the present time. The final ratio is entirely dependent upon the ultimate over-all pit slope. Based upon a 40° slope this ratio will be approximately ½ to 1, but, if conditions make it necessary to use a much flatter slope, the ratio may be increased to equal amounts of waste and ore. These are general averages, as there are sections where the ratio reaches the maximum of 3 to 1, and it is in such places that slope is of paramount importance. When it is considered that in one section of the Utah Copper pit the question arose as to whether or not 38° instead of 40° should be used above a certain level and that the cost of removing this extra amount of waste would reach a sum of $2,000,000, it can readily be seen how vital a thing, at least to the Utah Copper Co., the ultimate over-all slope really is.
The individual bench slope—that is, the actual slope of one shovel face from the upper edge to the toe of the slope—is of less consideration. This is, of course, a function of the over-all slope, but while an individual bench might stand at 60° from the horizontal, it is not to be concluded that a face 1,500 feet high will stand at the same angle of repose. When the material in any part of the ore body gradually declines in grade from ore to waste, there is always the question as to where the limit of excavation will ultimately be, and it therefore becomes necessary to maintain the shovel terraces on the pit face where, for the time being at least, operations are suspended. This shovel bench can be maintained at a minimum width to accommodate a shovel and loading track—say 30 feet. The slope we are most concerned with is the aggregate made up of the individual bench slopes plus the width of benches. In other words, the over-all slopes would be the angle from the horizontal from the top edge of the excavation to the bottom toe of the excavation, and it is this angle that the Utah Copper Co. has tentatively set at 40°.
There always will be local variations. At some points the slopes will doubtless take the angle of repose of broken material, say 35°. With others a slope of 50° may be safe. Geological conditions will enter into this. For instance, where stripping is being done against a face of quartzite that is dipping toward the operations at 30° from the horizontal, this slope will doubtless turn out to be the dip of the beds. On the contrary, where the beds are dipping into the bench, say from the shovels, a much steeper slope can be maintained.
Investigations of open-cut metal-mining practices have been conducted by engineers of the Bureau of Mines for several years and are continuing. A bulletin is in course of preparation that will discuss the subject in much greater detail than is possible in the present bulletin. The data in table 55 have been compiled for the most part from reports previously published.
