ON SELECTING THE LOCATION FOR SINKING MINE HOISTING SHAFTS TAKING INTO ACCOUNT THE EFFECT OF MINERAL LOSSES IN PROTECTIVE PILLARS DURING THE OPENING OF DEPOSITS BY LEVEL CROSSCUTS

G. E. BAKANOV

(Presented by the scientific conference of the Mining-Operations Faculty)

Questions concerning the correct choice of the location for sinking mine hoisting shafts under the conditions of the Soviet socialist state are of great national-economic importance. The position of mine hoisting shafts in a number of cases substantially affects the costs of opening and developing deposits, the safety of work in the mine, the capacity of the enterprise, and the completeness of extraction of minerals during their mining. In connection with this, a large number of works by Soviet scientists and engineers have been devoted to the question of determining the location for sinking mine shafts. Among the earliest and more popular of these should be counted the work of L. D. Shevyakov [1], first published in the journal Inzhenernyi rabotnik, Nos. 3–4 for 1924. In this work the author set forth and substantiated a method for determining the location for sinking a shaft across the strike of a series of strata, proposed in 1917 by the mining engineer R. A. Seletsky. By this method, often referred to in the literature and in practice as the method of L. D. Shevyakov, the location for sinking a vertical shaft with level crosscuts is determined from the condition of the minimum work of haulage of the mineral along the crosscuts. In this connection it is established that the most advantageous location for sinking a shaft is one at which the following two inequalities are satisfied:

\[ \Sigma Q_{\text{right}} + Q_n > \Sigma Q_{\text{left}}, \tag{1} \]

\[ \Sigma Q_{\text{left}} + Q_n > \Sigma Q_{\text{right}}, \tag{2} \]

where \(\Sigma Q_{\text{right}}\) and \(\Sigma Q_{\text{left}}\) are the sums of the loads located to the right and to the left of the mine shaft;

\[ Q_n \]
is the load falling at the intersection of the mine shaft with the crosscut.

Having established the indicated dependence between the quantities \(Q_{\text{left}}\), \(Q_{\text{right}}\), and \(Q_n\), L. D. Shevyakov proposed [1, 39], when finding the “most advantageous” location for sinking a shaft, to use the rule: “…the shaft must be located so that it intersects the crosscut at the place of concentration of such a load which, being added to all the others situated to the left of it, will give a sum greater than the sum of all loads situated to the right of it, and, being added to the right-hand loads, will give a sum greater than the sum of the left-hand loads.”

From the rule given, it is evident that L. D. Shevyakov, in substantiating this method for determining the optimal location for sinking mine shafts, took into account only the volume of freight haulage along the main crosscuts. The length of the crosscuts, stowing transport along ventilation crosscuts, materials transport, ventilation costs, and mineral losses—factors that affect the location of mine shafts—were not taken into account in the work under consideration.

Fig. 1.

In 1926–1928, Professor P. K. Sobolevsky and mining engineer P. I. Panov [2] developed a graphical method for determining the location for sinking a mine shaft. By this method, as by the Shevyakov–Seletsky method considered above, the location corresponding to the minimum amount of work for delivering freight to the mine shaft is found. The essence of the method is as follows. Suppose that concentrated loads \(Q_1, Q_2 \ldots Q_k\) are located on the line \(MN\) (a crosscut, a drift) at distances \(l_1, l_2 \ldots l_{k-1}\) (Fig. 1). To the straight line \(CD\), parallel to \(MN\), perpendiculars are erected from points \(C\) and \(D\); on these, at a certain scale, the loads \(Q_1, Q_2 \ldots Q_k\) are laid off from point \(D\) in direct order (from left to right) and from point \(C\)—

in the reverse order. Through the points \(C, 1, 2 \ldots k - 1, k\) and the points \(D, k, k - 1 \ldots 2, 1\), straight lines are drawn, as shown in Fig. 1. Then through the points \(a_1, a'_2, a'_3 \ldots a'_6\) straight lines are drawn, respectively parallel to the rays \(C1;\ C2 \ldots Ck\), and through the points \(a_6, a''_5 \ldots a''_1\)—lines respectively parallel to the rays \(Dk,\ D(k - 1) \ldots D2,\ D1\). Since the tangents of the angles \(\alpha_1, \alpha_2 \ldots\) (Fig. 1) are proportional to the loads \(Q_1,\ (Q_1 + Q_2)\), the line \(a_1 a'_2 a'_3 \ldots a'_6 P\) characterizes the change in haulage work when moving the loads \(Q_i\) from point \(a_1\) to point \(a_6\) and beyond; the line \(a_6 a''_5 a''_4 a''_3 \ldots L\) characterizes the change in the work when moving the same loads from point \(a_6\) to point \(a_1\), and so on.

Fig. 2.

The points \(a_1, a_2 \ldots a_6\) are, respectively, the concentration points of the loads \(Q_1, Q_2 \ldots Q_6\). The amount of work for delivering the loads to any point between the points \(a_1, a_6\) and beyond them is determined by the ordinates of the broken line
\(L a''_2 b_2 b_3 b_4 b_5 a'_6 P\), where
\(a_2 b_2 = a_2 a''_2 + a_2 a'_2;\ a_3 b_3 = a_3 a''_3 + a_3 a'_3;\)
\(a_4 b_4 = a_4 a''_4 + a_4 a'_4\) and \(a_5 b_5 = a_5 a''_5 + a_5 a'_5\).

The scale \((\text{tm}/\text{mm})\) needed to determine the magnitude of the work is easily found by dividing \(Q_1 l_1\) by \(a_2 a'_2\), or \(Q_6 l_5\) by \(a_5 a''_5\).

The minimum haulage work, as is evident from the graph (Fig. 1), is obtained at point \(a_4\), where the load \(Q_4\) is concentrated; in Figure 2, it is between points \(a_3\) and \(a_4\). The same results are obtained when this problem is solved by the Shevyakov–Seletsky method. Nevertheless, the graphical method has

the advantage that it is visual and makes it possible, directly from the drawing, to judge the amount of additional work in transporting minerals to the mine shaft that may arise if the shaft is sunk in another place (not at point \(a_4\)—Fig. 1). Unfortunately, by the Sobolevsky–Panov method itself, as also by the Shevyakov–Seletsky method, the location of the mine shaft is found only from the condition of haulage of loads on the main crosscuts. This is the principal shortcoming of this method, limiting its application in practice.

A very interesting graphical method for determining the location of a mine shaft when opening deposits by capital or level crosscuts was proposed by A. M. Tseitlin and A. E. Lokshin [3].

Fig. 3.

In determining the location of the mine shaft by this method, account is taken of the costs for transporting the minerals, the waste rock extracted, the filling material delivered into the mine through the hoisting shaft, for driving the crosscuts, for ventilation of the mine, and for transporting people, materials, and equipment along the crosscuts. For this purpose the authors of the method proposed concentrating, at the points of intersection of the crosscuts with the veins or beds (points \(1, 2 \ldots 9\)—Fig. 3), not the loads to be moved along the crosscuts, as was recommended by L. D. Shevyakov, but the costs \(C_1, C_2, C_3 \ldots C_9\), per one \(m\), for transporting loads, driving the crosscuts, ventilation, etc. On the values \(C_1, C_2 \ldots C_n\), taken to a definite scale, a “force triangle” is constructed with its pole at point \(O\), lying on the perpendicular erected from the middle of the straight line \(a_1 a_{10}=\Sigma C_i\). The pole distance \(DO\), conventionally taken equal to 0.5 ruble, is chosen of any magnitude (at the discretion of the person constructing the graph). Through point \(1'\), the projection of point 1 onto the horizontal straight line \(MN\), a straight line \(A'1'_1\) is drawn, parallel to the ray \(a_1O\) of the “force triangle,” and the straight line \(1'_1 2'_1\), parallel to the ray \(a_2O\). Through points \(2'_1; 3'_1; 4'_1 \ldots 9'_1\), respectively, the straight lines \(2'_1 3'_1; 3'_1 4'_1; 4'_1 5'_1 \ldots 9'_1 B'\) are drawn, parallel to the rays \(a_3O, a_4O, a_5O \ldots a_{10}O\) (Fig. 3).

The horizontal straight line \(MN\) is located at a distance \(Z\) from the conventional level, where the magnitude \(Z\) expresses, in the adopted scale, the total

the costs for the items taken into account, if the mine shaft passes through point 1 (position \(\varepsilon \varepsilon\)). The horizontal straight line \(A''B''\) is determined by the position of the point (point \(4_1'\)—Fig. 3) corresponding to the minimum of the costs \(Z_0\), calculated for the same items as were taken into account in determining the value \(Z\).

The points of intersection of the crosscuts with the beds or veins (points \(1, 2, 3 \ldots n\)—Fig. 3) are numbered in the sequence in which they are projected onto the line \(MN\).

The broken line \(A'1'2_1'3_1'4_1'5_1'6_1'7_1'8_1'9_1'B'\) characterizes the change in costs (for the factors taken into account) arising with a change in the site of the mine shaft. That this is so can easily be verified. In order that the straight line \(1'A'\) actually determine the change in costs arising from shifting the mine shaft to the left from point \(1'\), its angular coefficient \(\tg \alpha_1\) must numerically be equal to \(\sum C_i\), since, as the mine is shifted from point \(1'\) to the left, the costs increase by \(\sum C_i\) with each meter. By construction, the straight line \(1'A'\) is parallel to the straight line \(a_1O\). Consequently, its angular coefficient \(\tg \alpha_1\) is equal to \(\tg \alpha_1'\), the angular coefficient of the straight line \(a_1O\). But, as is seen from the drawing (Fig. 3),

\[ \tg \alpha_1'=\frac{0.5\sum C_i}{DO}=\frac{0.5\sum C_i}{0.5}=\sum C_i. \]

Hence

\[ \tg \alpha_1=\tg \alpha_1'=\sum C_i. \]

This is what had to be proved.

If the mine is shifted by one m to the right from point \(1'\), then the costs decrease by \((\sum C_i-2C_1)\). Then \(\tg \alpha_2\), the angular coefficient of the straight line \(1'2_1'\), if it expresses the change in costs when the mine is shifted between points \(1'\)—\(2_1'\), must be equal to \(\sum C_i-2C_1\). Since, by construction, the straight line \(1'2_1'\) is parallel to the straight line \(a_2O\), then \(\tg \alpha_2=\tg \alpha_2'=\)

\[ =\frac{0.5\sum C_i-C_1}{DO}=\frac{0.5\sum C_i-C_1}{0.5}=\sum C_i-2C_1. \]

The results obtained show that the straight lines \(A'1'\) and \(1'2_1'\) do indeed express the change in the costs taken into account when the mine is shifted between the points \(2_1'\), \(A'\), and so on. In an analogous way it can be proved that the other elements \((2_1'3_1'; 3_1'4_1' \ldots 9_1'B')\) of the broken line \(A'1'2_1'3_1'\ldots 8_1'9_1'B'\), constructed by the method indicated above, possess the same properties as the elements \(A'1'\) and \(1'2_1'\).

If the straight line \(A''B''\) is taken as the axis of abscissas, then the ordinate of any point of the line \(A'1'2_1'3_1'\ldots 8_1'9_1'B'\) will, on a certain scale, represent the increment of costs \((\Delta Z_0)\) that arises if the mine shaft is moved from the position \(\varepsilon_0\varepsilon_0\), corresponding to the minimum of costs, to another point.

The scale of the increments \((\Delta Z_0)\) depends on the linear scale of the cross-section of the series being opened, on the scale adopted for the values \((C_i)\) when constructing the “force triangle,” and on the dimensions of the pole distance \((DO)\). To find this scale, it is sufficient to set off on the straight line \(MN\), from point \(1'\), a segment \(1'K\) of any magnitude (preferably 100; 200; 50 m—on the scale), determine for point \(K\) the length of the ordinate \(\Delta Z=K'L\), and divide by it the product \(1'K\sum C_i\). Then the required scale is

\[ m_{\Delta Z_0}=\frac{1'K\sum C_i}{\Delta Z}\left(\frac{\text{m}\cdot\text{rub}/\text{m}}{\text{mm}}=\text{rub}/\text{mm}\right). \]

As is seen from the graph (Fig. 3), the costs associated with the location of the mine shaft attain their minimum value if the mine shaft passes through point 4. When the shaft is shifted to the right or left from this point, the costs increase according to the law of the line \(A'1'2_1'3_1'\ldots 8_1'9_1'B'\). If the shaft is laid on the footwall (point \(B\)) or hanging-wall (point \(A\)) side

(beyond the zone of rock displacement), then the increment in costs for the first case will be \(\Delta_1\), and for the second, \(\Delta_2\).

To construct the graph \(A' 1'_1 2'_1 3'_1 \ldots 8'_1 9'_1 B'\), the costs \(C_1, C_2 \ldots C_n\) are first calculated and a “force triangle” is constructed (on a specified scale). The graph is then constructed as indicated above. The quantities \(C_1, C_2 \ldots C_n\) are calculated as shown in Table 1. This table is compiled for the case when, in determining the location for sinking the shaft, the costs of transporting minerals along the main crosscuts, transporting filling and materials along the ventilation crosscuts, driving the crosscuts, and ventilating the mine are taken into account. In drawing up this table, \(c_0\) and \(c'_0\) denote the cost of a unit of clean haulage work along the main (\(c_0\)) and ventilation (\(c'_0\)) crosscuts; \(c_{kv}\) denotes the cost of one linear meter of crosscut in rubles. The other letter designations adopted here are clear from the explanations given in the table itself. In compiling the table, ventilation expenses (per one linear meter of crosscut) are calculated depending on the quantity of air delivered to points \(1, 2 \ldots 9\), the depression, the life of the levels, and the cost of electric power. The costs of driving crosscuts are included in the table for points located at the intersections of level crosscuts with the extreme seams (or veins) of the series being opened (points 1; 3; 4; 6; 7; 9—Fig. 3). At each such point, crosscuts are taken into account in the amount of the cost of half a linear meter of them [3].

The advantage of the Zeitlin—Lokshin method is its simplicity, clarity, and sufficient accuracy. By this method all the principal factors affecting the costs associated with the shaft location are taken into account (apart from the terrain relief and the transportation of ore or coal on the surface). True, R. A. Seletsky later showed in his work [4] that, using inequalities (1) and (2)—\(\sum Q_{prav} + Q_n > \sum Q_{lev}\) and \(\sum Q_{lev} + Q_n > \sum Q_{prav}\)—one can find the optimal location for sinking the shaft while taking into account not only the volume of haulage on the main crosscuts. For this, as in the graphical method of Zeitlin—Lokshin, it is sufficient, for points \(1; 2; 3 \ldots 9\) (Fig. 3), to find the values \(C_1, C_2 \ldots C_9\) and to substitute into inequalities (1), (2), instead of the values \(Q_i\), the values \(C_i\), found as shown in Table 1. Then the optimal location for sinking the shaft will be at the point at which the inequalities are satisfied:

\[ \sum C_{prav} + C_n > \sum C_{lev}, \tag{3} \]

\[ \sum C_{lev} + C_n > \sum C_{prav}. \tag{4} \]

The location corresponding to the minimum of costs, determined in this way, coincides with that which was found graphically in Fig. 3. However, if it is not required to draw the graph of the change in costs or of the work for haulage of loads, but only to find the point (the location of the shaft) corresponding to the minimum of these quantities, then it is not at all necessary to select the values \(C_i\) or \(Q_i\) in order to compose inequalities (1) and (2) or (3) and (4). For this it is sufficient to plot the values \(C_i\) or \(Q_i\), on any scale, on a straight line, as was done in the “force triangle” (Fig. 3), to find on it the point \(D\)—the midpoint of this straight line, equal to \(\sum C_i\) or \(\sum Q_i\)—and to establish the ordinal number of the first segment expressing \(C\) or \(Q\) that passes through point \(D\) in the direction of point \(a_{10}\). It is quite obvious that the number of this segment will correspond to the number of the desired point determining the optimal position of the shaft according to the elements taken into account (according to \(C\) or according to \(Q\)). If the midpoint of the straight line \(a_1 a_{10}\) (Fig. 3) coincides with the boundary of two segments defining the quantities \(C\) or \(Q\), then obviously the optimal location for sinking the shaft will be at any place

Table 1

between the points at which these \(C\) or \(Q\) are concentrated. As can be seen, such a method of solving the problem is much simpler than selecting points at which inequalities (1), (2) or (3), (4) would be satisfied.

For practical purposes it is much more important to have a graph of the variation in costs associated with moving the mine shaft. The availability of such a graph greatly facilitates the task of finding the truly optimal location for the mine shaft. This is precisely the advantage of the graphical method considered.

The methods of Lokshin—Tseitlin [3] and Seletsky [4] take into account almost all the principal factors influencing the costs associated with the location of the sinking of a capital shaft. However, neither in these methods nor in the other methods considered is any account at all taken of the influence of the location of the shafts on losses of minerals. On the contrary, the location of the shaft found from the elements that were taken into account by Shevyakov, Panov and Seletsky, Tseitlin and Lokshin, in most cases lies near the greatest concentration of the mineral. When the shaft is located in such a place, it becomes necessary to leave a large quantity of the mineral in protective pillars. Since such pillars, when the mine is liquidated, are recovered only by 50–65%, the presence at a mine of large protective pillars causes large losses of minerals (coal, ore, and others). In a number of cases this inflicts serious economic damage on our state. Therefore, when selecting the location for sinking shafts, this very important factor cannot be disregarded. The previously proposed methods for determining the optimal location for sinking shafts did not take this circumstance into account. This is a serious shortcoming of them. In a number of cases, the location for sinking the shaft found by one of the methods considered above as optimal is in reality not only not optimal, but, on the contrary, often proves to be the least advantageous because of large losses of minerals in near-shaft pillars.

The optimal location for sinking a shaft, taking into account, along with other factors, also losses of coal or ore in protective pillars, can be found as follows. Having constructed the graph of the variation in costs \(A'1'_1 2'_1 3'_1 \ldots 8'_1 9'_1 B'\), as was done in Fig. 3, one must below the straight line \(A''B''\) construct a graph showing how the economic damage from leaving protective pillars will vary if the mine shaft is moved from position \(AA''\) to position \(BB''\) (through positions \(\varepsilon\varepsilon\), \(\varepsilon_0\varepsilon_0\), etc.). In constructing this graph it is necessary to be guided by the following. If the mine shaft is sunk at point \(A\), located outside the zone of displacement of the rocks of the hanging wall (position of the mine shaft \(AA''\)), or at point \(B\)—outside the zone of displacement of the rocks of the footwall (position of the mine shaft \(BB''\)), then protective pillars around the mine shafts are not left. Consequently, when the mine shafts are located at point \(A\) or \(B\), the economic damage from the loss of minerals in near-shaft pillars will be equal to zero, and the end points of the graph showing the change in economic damage (Fig. 4, \(a\) and \(b\)) will coincide with the line \(A''B''\) at points \(A''\) and \(B''\).

At other points (\(m''_1\); \(n''_1 \ldots 1''_1\); \(2''_1\), etc.) the ordinates of the graph \(A''m''_1 n''_1 o''_1 1''_1 2''_1 \ldots 8''_1 B''\) relative to the abscissa axis \(A''B''\) are determined by the value of the mineral, its reserves in the protective pillars, and the conditions for extracting these reserves when the pillars are recovered. In Fig. 4, \(a\) and \(b\), it is seen that if the mine shaft is located on the line \(\varepsilon_0\varepsilon_0\), then the ordinate, expressing on a definite scale the economic damage from losses of the mineral in the pillars, is equal to the segment \(4'_1 4''_1\); if the shaft passes through \(n\) or point \(8\), then the ordinate will be \(n'' n''_1\) or \(8'' 8''_1\). The ordinates of the graph \(A''m''_1 n''_1 o''_1 1''_1 2''_1 \ldots 8''_1 B''\) are taken on the same scale as in constructing the po-

the ordinates of the graph \(A' m' n' 1' 2'_1' \ldots 8_1' B'\) have been obtained. How this scale is determined was indicated when considering the Lyukshin–Tseitlin method (Fig. 3). Having thus constructed, on the same scale, the graphs \(A' m' n' \ldots 1' 2'_1' \ldots 8_1' B'\) and \(A'' m_1'' n_1'' o_1'' 1_1'' \ldots 8_1'' B''\), we obtain a visual representation of how the costs will change as the shaft location changes, and how the economic damage from the loss of the mineral in the protective pillars will change at the same time. From this it is easy to find where the truly optimal location for the mine hoisting shaft lies. Such a location falls where there is the smallest distance between the lines \(A' 1' 2_1' \ldots 8_1' B'\) and \(A'' 1_1'' 2_1'' \ldots 8_1'' B''\) (Fig. 4 a and b). For the case shown in Fig. 4a, the smallest distance between the indicated lines falls on the segment \(8_1' 8_1''\). Such an absolute sum of the ordinates of points \(8_1'\) and \(8_1''\) (relative to \(A'' B''\)) would be obtained if the mine shaft passed through point 8, although here, as is clear from the drawing, on the lower deposit it would be necessary to have a protective pillar around the mine shaft. In Fig. 4b the graphs are constructed for deposits with the same reserves and the same bedding elements, but with a more valuable mineral than in the case considered above. If in the first case the profitability of industrial use of the mineral \((d)\) was taken as 3 rubles/t, then in the second it is taken as equal to 12 rubles/t. For this case the smallest sum of ordinates is equal to the segments \(B' B''\) and \(8_1' 8_1''\), which would be obtained if the mine shaft were sunk at point \(B\) (outside the zone of displacement of the rocks of the footwall) or if it passed through point 8. When sinking the shaft at point \(B\), the need to provide a protective pillar around the mine shaft is eliminated; if it passes through point 8, then, as noted above, a pillar will have to be left on the lower deposit. Economically, both positions of the mine shaft are almost equivalent. Moreover, in this case the entire interval from \(8_1' 8_1''\) to \(B' B''\) has almost identical absolute sums of the ordinates of the graphs \(A' \ldots 1' 2' \ldots B'\) and \(A'' \ldots 1_1'' 2_1'' \ldots B''\). Consequently, for the given dimensions of the deposit, its bedding elements and the value of the mineral, and for the adopted dimensions of the protective pillars and the conditions of mining them, all points of shaft location between points 8 and \(B\) are, economically, almost equivalent.

Fig. 4 a and b.

In Figure 5 (a and b) the investigated graphs are given for the same deposits, interchanged in position (the lower deposit is the more productive one—\(m_2 = 2\) m). For the case where \(d = 3\) rubles/t, the equivalent intervals with respect to the location—

Figures 4–7 have been reduced by a factor of two; the scales have changed accordingly: length 1:7500; costs—750 thousand rubles per cm.

the mine shafts are between points 1—4 and at point \(B\). If \(d = 12\) rubles/t (Fig. 5 b), then, all other conditions being equal, the only advantageous location for the mine shaft is point \(B\), situated on the footwall side of the suite.

If deposits arranged in the same way as in Figs. 5 a and 6 a have doubled thicknesses \((m_1 = 2\ \text{m},\ m_2 = 4\ \text{m})\), then, with the same value of the mineral,

Fig. 5 a and b.

the diagram of the economic efficiency of the locations for hoisting shafts will look as shown in Fig. 6 b. From this diagram it is evident that, under these conditions, the economically most advantageous location for the hoisting shaft is likewise point \(B\) (on the footwall side of the suite).

Fig. 6 a and b.

Figure 7 (a and b) shows a suite of deposits having a flatter dip \((40^\circ)\) than in the preceding figures (4—6), where there were presented

the syncline, dipping at an angle of \(70^\circ\). In this figure, as in Figs. 4–6, two diagrams \(A'1'_1 2'_1 \ldots 8'_1 B' B'' 8''_1 \ldots 2''_1 1''_1 A''\) are plotted. The upper one is for the case when \(d = 3\) rubles/t, and the lower one for \(d = 12\) rubles/t. In both cases, as is clear from these diagrams, the optimum site for sinking the shaft lies on the line \(33''_1\) (the height of the diagram \(3'_1 3''_1\)). The site corresponding to the minimum costs, determined by the graph \(A'1'_1 2'_1 \ldots 8'_1 B'\), lies at point 4 (the position of the shaft \(e_0 e_0\)). However, the ordinates of the central part of the upper diagram (Fig. 7 a) differ very little from one another. Therefore all positions of the shafts from point 2 to point 5 are practically equivalent. If the character of the mineral corresponds to the conditions of the lower diagram (Fig. 7 b), then the equivalent sections lie between points 2–3 and 6–7.

Thickness of the upper deposit \(m_1 = 1\) m, of the lower \(m_2 = 2\) m. Length of the mine field \(L = 950\) m. Scales: length 1:3750, costs 1 cm = 375 thousand rubles. Cost of mining ore by systems with backfilling \(C_2\) rubles/t. Cost of ore under ordinary conditions \(C_1 = C - 2\) rubles/t.

Fig. 7 a and b.

The examples considered (Figs. 4–7) show that the more valuable the mineral whose extraction is being designed, and the greater the thickness of its deposits, the less advantageous is a shaft that intersects a suite of veins or seams. Here it is often more advantageous to place the shaft completely in the country rocks, especially in the rocks of the footwall (Figs. 4 b and 5 b). Shafts intersecting suites are more expedient in the development of thin deposits of less valuable minerals. However, even in this case, as is readily seen from the figures given (4 a and 5 a), the most advantageous position of the shaft rarely coincides with the place where the minimum costs are obtained according to the graph \(A'1'_1 2'_1 \ldots 8'_1 B'\) (at the point coinciding with the straight line \(A''B''\)). This, however, all depends on a combination of a whole series of mining-geological and techno-economic factors: the thickness of the deposits, the conditions of their exploitation, the value of the mineral, the cost of crosscuts and haulage of the extracted mineral raw material, and the costs of ventilation of work-

flow, etc. In constructing the diagram \(A'1'2'_1 \ldots 8'_1B'B''8''_1 \ldots 2''_1 1''A''\), all these factors are taken into account, and this makes it possible, under specific conditions, to find from such a diagram the truly optimal location for the mine shaft.

With inclined and flat dipping of deposits, cases in which it is advantageous to use shafts crossing the series occur much more often than with steep dipping. This is clearly seen even from the drawing (Fig. 7). Here, on both diagrams (for \(d = 3\) rubles/t and \(d = 12\) rubles/t), their lower portions are located directly beneath the deposits. This is an indication of the advantage of shafts that cross the series and pass through the points beneath which the diagrams have the smallest heights.

The mine-siting location found by the method of L. D. Shevyakov [1] or P. K. Sobolevskii [2] is always at the point of greatest concentration of the mineral. It is usually obtained near the thickest deposits. Therefore, if the location thus found is adopted for sinking the mine, a large amount of mineral must be left in protective pillars. To avoid this, the question of the position of the hoisting shaft must be reconsidered, and the most advantageous location for it must be sought by the method of alternatives. Therefore, in such cases there is no need to seek the location for the mine shaft according to the conditions of haulage of loads, as is done by inequalities (1) and (2) or by the graph (Figs. 1, 2).

The mine-shaft location determined by the Lokshin–Tseitlin method [3] or by the method of R. A. Seletskii [4], although it deviates somewhat from the position corresponding to the minimum haulage work of loads on crosscuts (because allowance is made for the costs of driving the crosscuts), is nevertheless obtained rather close to it (point 4—Figures 4–7). When the mine shaft is located at this place, it also becomes necessary to leave a large quantity of ore or coal in shaft-adjacent pillars. How expedient this is must be examined by considering other alternatives that provide either for the complete elimination of pillars or for some reduction in their size. For this reason, these methods of determining the mine location also do not give an exhaustive solution to the problem under consideration. They do not take into account the economic loss from losses of minerals arising from incomplete extraction of protective pillars.

The method proposed here provides for constructing a graph showing the change in costs with displacement of the mine-siting location \((A'1'2'_1 \ldots 8'_1B'\)—Figs. 4–7) and a graph of the economic loss from mineral losses in protective pillars for various positions of the hoisting mine shaft \((A''1''_1 2''_1 \ldots 8''_1B'')\). The combination of these two graphs forms the diagram \(A'1'_1 2'_1 8'_1B'B''8''_1 \ldots 2''_1 1''A''\) (Figures 4–7), which characterizes the degree of economy of the various points where the mine shaft may be located in the cross section of the series from point \(A\) to point \(B\) (within the zone of rock movement on the hanging and footwall sides of the series—with a reserve equal to the protective berm). Having constructed such a diagram, one can easily find the location for the mine shaft that will be the most advantageous in all respects.

In constructing the graph \(A''1''_1 2''_1 \ldots 8''_1B''\), the economic loss from leaving protective pillars of the mineral can be calculated as recommended in the book by P. I. Gorodetskii, Design of Mining Enterprises [5, 376], or in the Handbook of Ore Mining [6, 148 and 149].

In particular, in P. I. Gorodetskii’s book the absolute magnitude of the economic loss is calculated from three elements:

1) from the increase in the cost of mining the mineral when extracting pillars

\[ S_1 = (c_1 - c)\, k_u Q_u; \tag{5} \]

2) from the increase in depreciation of fixed assets in connection with the reduction in the extractable reserves of the mineral

\[ S_2=K\frac{(k-k_c)Q_c}{kQ}; \tag{6} \]

3) from the decrease in the economic efficiency of working the deposit (or mine field)

\[ S_3=d(k-k_c)Q_c. \tag{7} \]

In all,

\[ S=S_1+S_2+S_3. \tag{8} \]

In equations (5–7) the following notation is adopted:
\(Q_c\)—reserves of the mineral in the protective pillar;
\(k\)—coefficient of extraction of the mineral under ordinary mining conditions;
\(k_c\)—coefficient of extraction of the mineral when mining the pillar;
\(c\)—cost of mining the mineral under ordinary conditions, rubles/t;
\(c_1\)—cost of mining the mineral from the pillar, rubles/t;
\(K\)—capital expenditures on facilities amortized over the life of the mine, rubles;
\(d\)—index of profitability of the industrial utilization of the mineral, rubles/t, and
\(Q\)—balance reserves of the deposit or mine field, t.

If the protective pillar is not mined at all (is completely left during mine closure), then the coefficient \(k_c=0\) and the quantity \(S_1=0\). Then the economic loss from leaving such a pillar is

\[ S=S_2+S_3=\frac{KQ_c}{Q}+dkQ_c. \tag{9} \]

The diagrams \(A'1'2'_1\ldots 8'_1B'B''8''_1\ldots 2''_1 1''A''\) shown in Figs. 4–7 were compiled for deposits 950 m long with a vertical height of 240 m, a horizontal thickness of 1–2 and 2–4 m (as indicated in the figures), a volumetric weight of the mineral of 3 t/m\(^3\), and vein dip angles of 70 and 40°. The calculations for constructing the diagrams were made with a mine-level height of 80 m; \(k=0.9\), the difference \(k-k_c=0.3\); the difference \(c_1-c=2\) rubles/t; \(K=3.5\)–5 million rubles; dilution of the mineral when working the veins of 5%; the cost of clear extraction on main crosscuts of 1 ruble/km·t, on ventilation crosscuts—1.1 rubles/km·t; the cost of crosscuts of 180 rubles/linear m, mine shafts (hoisting and ventilation) of 5 and 4 thousand rubles/linear m, and shaft stations of 350 thousand rubles/station (for the adopted mining conditions). The volumes of protective pillars were determined in accordance with the adopted angles of displacement of the rocks, shown in Figs. 4–7 (more fully in Fig. 4). The diagrams \(A''1''_1 2''_1\ldots 8''_1 B''\) were constructed on the same scale as the diagrams \(A'1'_1 2'_1\ldots 8'_1 B'\). The diagram \(A'1'_1 2'_1\ldots 8'_1 B'\) in Fig. 4 was constructed for \(\sum C_i=10650\) rubles/m (transport of filling material on the ventilation crosscuts is provided); in Figs. 5–7—for \(\sum C_i=7400\), and in Fig. 6b—for \(\sum C_i=9300\) (in the last two cases, without filling).

The diagrams \(A'1'2'_1\ldots 8'_1B'\), presented in Figs. 4–7, do not express the absolute costs that change with the shifting of mine shafts. They show only increments in costs as compared with those that would have been incurred if the mine shaft were located in position \(\varepsilon_o\varepsilon_o\) and passed through point 4. In order to judge the degree of economy of individual variants, it is sometimes important to know the absolute amount of costs for these variants. For this it is sufficient to calculate the value \(Z_o\) (Fig. 3), drop onto it the abscissa \(A''B''\) (Fig. 4), and, with respect to this abscissa, construct the diagram \(A''1''_1 2''_1\ldots 8''_1B''\). In Fig. 8 the diagram \(A'1'2'_1\ldots 8'_1B'B''\ldots\) is plotted...

… \(1_1''A''\), the ordinates of which show the absolute sum of expenditures and the amount of economic damage from the pillars left behind, depending on the location chosen for the mine shaft. The diagram was constructed under the same conditions as were adopted for constructing the diagram shown in Fig. 4b. The value \(Z_o\) was determined by calculation as 500 thousand rubles (according to the data given above). From this diagram it is evident that the character of the relationships under consideration here has remained the same as in the diagram 4b.

Fig. 8.

If, over the extent from point \(A\) to point \(B\) (Figs. 4–8), the surface relief undergoes substantial changes, then, as the mine shaft is moved between these points, the expenditures for driving the shaft itself, for hoisting the minerals, and for drainage will also change. By plotting on the diagram the line \(A' 1'_2 \ldots 8'_1 B'\), \(B_1' 8_1'' \ldots 2_1'' 1_1'' A''\), showing the increments (positive or negative) of expenditure for these elements, we obtain a diagram that gives a complete representation of the economy of the various points (between \(A\) and \(B\)) where the main shaft can be driven for opening the suite of deposits shown in the figures. In constructing this line one may also take into account the costs of transporting the mineral on the surface, if they may be of substantial significance.

The method considered in the present work for determining the location of hoisting shafts of mines, taking into account the influence of losses of minerals in protective pillars, is, in our opinion, sufficiently simple, clear, and correct. Such a formulation of the question in selecting the location of mines is of great national economic importance, since it makes it possible to develop more rationally deposits of minerals that are of great importance for the national economy of the Soviet Union.

LITERATURE

1. Shevyakov L. D. On the question of selecting the location for sinking a mine. Collection of articles on mining, publication of Soyuzugol, 1930.

2. Ogloblin D. I. Selection of the location for sinking a mine, ONTI, 1935.

3. Tseitlin A. M., Lokshin A. E. On the selection of the location for sinking a mine when opening deposits by main or level crosscuts. Proceedings of the First Conference on the Rationalization of the Coal Industry, 1930.

4. Seletskii R. A. A method for the rational selection of the location for sinking a mine when opening a suite of seams by a central mine and level crosscuts. Proceedings of the First Conference on the Rationalization of the Coal Industry, 1930.

5. Gorodetskii P. I. Design of Mining Enterprises, Metallurgizdat, 1949.

6. Handbook of Ore Mining, book 1, Metallurgizdat, 1952.

7. Shevyakov L. D. Determination of the location for sinking the hoisting shaft of a mine, Ugletekhizdat, 1947.