On the Determination of Optimal Boundaries for Open-Pit Mining Operations

B. V. POLYAKOV

(Presented by the scientific seminar of the departments of bedded-deposit mining, ore-deposit mining, mine construction, safety engineering, and mine ventilation)

Open-pit mining of mineral deposits has a number of serious advantages over underground mining. This is convincingly demonstrated by Soviet mining practice, as well as by the mining practice of the technically most developed foreign countries \[3 and 4\]. The spread and improvement of open-pit mining of mineral deposits is an important reserve for increasing labor productivity in the Soviet mining industry and for improving the use of mineral resources—the basis of the industrial might of the Soviet Union.

The wealth of the mineral resources of our homeland, the presence of a powerful energy base, highly developed heavy machine building, and numerous well-trained technical personnel are extremely favorable to the development of open-pit mining operations. The number of reconstructed and newly built quarries for the extraction of the most varied minerals has increased noticeably in recent years. In the near future the volume of capital investment in open-pit mining of deposits will rise sharply \[1\]. In the interests of a more efficient expenditure of state funds, it is necessary, in particular, to further improve the design of quarries.

The most difficult and responsible task in designing a quarry is the establishment of the optimal boundaries of open-pit mining of a deposit, since in the theory and methodology of designing the ultimate contours of quarries there are still many gaps. This is especially apparent when solving the problem in its most general form, when a deposit of irregular shape or of limited extent along the strike, with mountainous relief of the earth’s surface, must be mined by open-pit and underground methods.

In each specific case of open-pit mining of mineral deposits there objectively exists a certain maximum permissible (limiting) value of the stripping ratio. The optimal boundaries of open-pit mining of a deposit are fixed on the topographic plan and geological sections by the ultimate contours of the quarry, which correspond to the appropriate stripping ratios.

At present, the ultimate depth of a quarry is taken to be the depth of the mineral seam; the stripping ratio for the co-

which has a limiting value [2,206]. However, a given value may correspond not to one, but to several near-horizon stripping ratios. Moreover, open-pit mining of a deposit may also be unacceptable when near-horizon stripping ratios are at the limiting value or even lower, if the value of the overall stripping ratio exceeds the limiting value. On the other hand, the limiting contours of an open pit cannot be established until the limiting value of the stripping ratio has been determined, while determination of the latter requires knowledge of the limiting contours of the open pit. In this connection, the problem of establishing the limiting contours of open pits under complex mining-and-geological conditions is often solved by the method of alternatives. In doing so, in our opinion, the following procedure should be followed:

1) approximate determination of the limiting value of the stripping ratio;

2) identification of the probable limiting contours of the open pit;

3) preparation of a preliminary design for development of the deposit in accordance with the probable limiting contours of the open pit, and a check determination of the limiting value of the stripping ratio;

4) comparison of the limiting values of the stripping ratio determined by the approximate and check calculations; repetition of the operations under items 1, 2, 3, and 4 when the discrepancy in these values exceeds the limits of accuracy of technical-and-economic calculations in mining: ±10–15%;

5) correction of the preliminarily established limiting contours of the open pit for organizational, technical, and other considerations.

The probable limiting contours of the open pit include the largest reserve of the mineral in such a way that the overall stripping ratio of any remainder of this reserve does not exceed the approximate limiting value. Obviously, the near-horizon stripping ratio characterizing the probable limiting contours of the open pit has an approximately limiting value.

If the limiting value of the stripping ratio determined by the preliminary design for development of the deposit, prepared in accordance with the probable limiting contours of the open pit, is equal (within the accuracy of the calculation) to the provisionally adopted value, then the probable limiting contours of the open pit pass into the category of preliminarily established ones.

In determining the limiting values of stripping ratios, only the principal factors affecting the optimal boundaries of open-pit mining are taken into account. Therefore, the limiting contours of the open pit established in accordance with the limiting value of the stripping ratio cannot be regarded otherwise than as preliminary, and are subject to correction on the basis of factors not previously taken into account and the possibilities of extracting the mineral without producing external stripping, while leaving part of it in the side pillars of the open pit.

On the basis of the accuracy of calculating mineral reserves and taking account of the specific situation, the designer may adopt a limiting pit depth 10–15% greater or smaller than the preliminarily established one, without resorting to additional calculations. Taking into account the difference in the rates of development of open-pit and underground mining technology, in the construction periods of open pits and mines, in the intensity of open-pit and underground mining, and also in the extraction of low-grade ores, the depth of the open pit should be increased. The basis for decreasing it may be the coordination of calendar plans for the development

open-pit and underground working of the deposit, the desire to avoid economic loss from the demolition of existing large buildings and structures and special expenditures for diverting the river channel, etc.

For convenience and clarity in establishing the limiting contours of an open pit under complex mining-and-geological conditions, it is advisable to use a diagram of bench-by-bench reserves of the useful mineral and of the actual and allowable volumes of overburden. To construct the diagram it is sufficient to have the graphic materials ordinarily needed in designing open pits.

The diagram of bench-by-bench volumes is constructed in a rectangular coordinate system. Downward along the vertical axis, segments are laid off successively, proportional to the differences in elevations of adjacent bench plans. Through the ends of these segments, horizontals are drawn. On the latter, to the left of the vertical axis the corresponding bench-by-bench reserves of the useful mineral are laid off, and to the right the corresponding actual and allowable bench-by-bench volumes of overburden. The magnitudes of the bench-by-bench reserves of the useful mineral and of the actual volumes of overburden are found by measurements on vertical geological sections of the deposit, either directly or after simple graphical constructions, and are laid off on the diagram as segments at a definite, preferably identical, scale. The magnitudes of the allowable bench-by-bench volumes of overburden are found by multiplying the bench-by-bench reserves of the useful mineral by the assigned limiting value of the stripping ratio. Connecting, by a smooth curve, the ends of the segments proportional to like quantities gives the graphs of the change with depth in the bench-by-bench reserves of the useful mineral and in the actual and allowable bench-by-bench volumes of overburden.

The diagram of bench-by-bench volumes makes it possible to identify benches with the limiting value of the stripping ratio, which are fixed on the diagram by the points of intersection of the graphs of the actual and allowable bench-by-bench volumes of overburden, and to analyze (by comparing the corresponding areas of the diagram) the advisability of limiting open-pit mining by one bench or another. The convenience of using the diagram, and also the practical advisability of solving the problem of the optimal boundaries of open-pit workings in the procedure proposed by us, are best judged from an example.

A coal seam of normal thickness of ten meters, dipping almost in accordance with the slope of the ravine, is to be mined by open pit. In the weathering zone (up to twenty meters from the ground surface) the coal is oxidized and has no industrial value.

Establishing the optimal boundaries for the open-pit mining of the seam reduces to finding the limiting contours of the open pit on the characteristic transverse geological sections of the seam (Fig. 1). We neglect the uncovering of the seam at the ends of the open pit, taking into account the very considerable length of the latter. Next we specify the slope angles of the pit walls \((\beta)\) and an approximate limiting coefficient for external overburden. For the example under consideration, we take the value of the latter as seven.

We construct a diagram of the bench-by-bench reserves of the useful mineral, expressed in cubic meters, and of the actual and approximately allowable volumes of external overburden (Fig. 2).

The reserves of the bench \((-20\ \mathrm{m})\) are proportional to the segment \(\overline{a_1 b_1}\) (Fig. 1), those of the bench \((-40\ \mathrm{m})\) to the segment \(a_2 b_2\), and so on. Laying off these segments on the corresponding horizontals to the left of the depth axis (Fig. 2) and con—

joining the ends of them with a curve, we obtain the graph of the variation of the bench reserves \(AOB\).

The actual bench volumes of overburden on the side of the hanging wall of the seam are proportional to the segments \(c_1d_1, c_2d_2\ldots\); on the side of the footwall—to the segments \(e_6f_6, e_7f_7\ldots\), which are found by means of known graphical constructions (Fig. 1).

Fig. 1. Cross section of the seam

Fig. 2. Diagram of bench volumes

Plotting these segments on the corresponding horizons to the right of the elevation axis (Fig. 2) and joining their ends with a curve, we obtain the graph of the actual variation with depth of the bench volumes of overburden \(CDE\). In the example under consideration, overburden on the side of the footwall is absent down to the horizon \((-80\ \text{m})\), but then increases rapidly. Coal of the oxidized zone down to a depth of \(20\ \text{m}\) is included in the volume of initial overburden.

— Approximately permissible bench-adjacent volumes of overburden \((c_i g_i)\) are proportional to the bench-adjacent commercial reserves of coal \((a_i b_i)\) and to the limiting stripping ratio: \(c_i g_i = 7 a_i b_i\). Laying off, on the corresponding benches, to the right of the depth axis (Fig. 2), the segments \(c_1 d_1, c_2 g_2 \ldots\) and joining their ends with a curve, we obtain a graph of the variation with depth of the approximately permissible bench-adjacent volumes of overburden \(GQH\).

The ordinate of the intersection of the graphs of actual and permissible volumes of overburden at point \(N\) gives the probable limiting depth of the open pit: 118 m. The pit contour \(STUVW\) corresponding to this depth approaches the limiting one. The equality of the actual and permissible volumes of overburden, proportional to the segment \(\overline{MN}\) (Fig. 2), for a given coal reserve \(\overline{IM}\), indicates that at a depth of 118 m the bench-adjacent stripping ratio reaches the approximately accepted limiting value

\[ \frac{\overline{MN}}{\overline{IM}} = 7 . \]

A reduction of stripping ratios below the specified value on deep benches is excluded by the nature of the variation in bench-adjacent coal reserves and actual volumes of overburden: the former remain approximately constant, while the latter increase steadily and rapidly. Hence open-pit operations beyond the pit contour with a bottom elevation of \((-118\ \text{m})\) are unacceptable. However, they can very well be applied at lesser depths, since the coal reserves contained between the bench \((-118\ \text{m})\) and any overlying bench, up to the surface, can be extracted with a stripping ratio not exceeding the specified limiting value. This is clearly seen by comparing the areas \(CNMLKA\) and \(LGNM\) of the diagram, the first of which is considerably smaller than the second. The ratios of these areas to the area \(IKLM\), equivalent to the reserves of the pit field down to a depth of 118 m, give the actual and permissible values of the gross stripping ratio.

Let us note that with a greater depth of weathering, for example 60 m, open-pit operations with a limiting value of the stripping ratio equal to seven would be inexpedient, despite the presence of bench-adjacent stripping ratios even with smaller values. In this case the magnitude of the gross stripping ratio would exceed the permissible value owing to an increase in the volume of initial overburden. This is easy to see from a comparison of the areas \(POACDNM\) and \(PQNM\) of the diagram.

If, in a preliminary design for the open-pit mining of the seam down to the bench \(-118\ \text{m}\), the limiting value of the stripping ratio is determined to be eight instead of the accepted seven, then, with the accuracy of economic calculations in mining \((\pm 10\text{–}15\%)\), the contour \(STUVW\) should be regarded as the limiting one, established in advance.

To avoid the inrush of storm and flood waters into the open pit from the ravine, we limit stripping operations by the bench \((-110\ \text{m})\). In this case the limiting depth of stripping decreases by less than 10%, which is certainly permissible. For the specified limiting stripping ratio equal to seven, the limiting stripping depth of 110 m corresponds not to a ten-meter but to a nine-meter seam thickness. Such deviations in seam thickness are practically quite possible.

Further development of this seam, which has a thickness of ten meters, without carrying out stripping is impossible because of the conditions for placing the equipment. Thus, as the limiting one in this given—

in this case it is necessary to recognize the contour of the open pit as \(XYZRW\). Obviously, this contour is subject to correction when it is coordinated with the contours of the open pit on adjacent profiles.

The conditions for identifying the optimal boundaries of open-pit operations are highly varied. In each specific example of finding the limiting contours of an open pit, its own details are inevitable. However, the general procedure recommended by us for solving this problem should, to some extent, always be maintained.

REFERENCES

1. Directives of the Twentieth Congress of the CPSU on the Sixth Five-Year Plan for the Development of the National Economy of the USSR for 1956–1960.

2. Gorodetskii P. I. Fundamentals of Designing Mining Enterprises. Metallurgizdat, 1955.

3. For Further Technical Progress in the Mining Industry, Gornyi Zhurnal, No. 3, 1956.

4. Plea for better Quarry Practice, Mine Quarry Eng., 1946, Vol. 11, No. 6.