On the Choice of Shaft Locations for Opening Up a Suite of Deposits

Acting Prof. G. E. Bakanov.

The grandiose development of the coal and mining-ore industry, outlined by the XVIII Congress of the VKP(b) in the third Stalin five-year plan, requires the construction of a large number of new mines both for the extraction of hard coals and of various ores, in which our immense socialist homeland is so rich.

For the swiftest fulfillment of tasks in the field of the mining industry, in the current five-year plan chiefly medium and small mines will be built, since with relatively small capital investments they ensure a more rapid commissioning. At the same time, since the third five-year plan provides for the broad development of high-quality metallurgy, in the coming years the extraction of ores containing rare metals will acquire considerable relative importance in the mining industry. By their nature, deposits of rare metals will to a considerable extent be worked by comparatively small mines. Therefore, in the years of the present five-year plan, new mine construction in the USSR will reach exceptionally colossal proportions.

The grandiose problems set by the third Stalin five-year plan, whose fulfillment will depend to a significant degree on the work of the mining industry, and the enormous scale of concerns connected with new mine construction, place before mining engineers and builders the following most important tasks:

a) The design of new mines must be carried out on the basis of the latest achievements of mining technology and the experience of the best Stakhanovites, striving for the most rational layout of the mine as a whole.

b) Speed methods of construction must be widely introduced, ensuring the building of mines in 10 months—one year, as L. M. Kaganovich indicated in his speech at the XVIII Congress of the VKP(b).

c) Mine construction must be carried out in exact accordance with the developed designs, both with respect to the mines themselves and with respect to the organization of their construction.

d) In the construction of new mines, local materials must be widely used both in the erection of surface structures and housing construction, and for the support of capital workings.

d) Mechanize all processes of driving workings and carry out thorough preliminary preparation for construction.

e) Take measures for the most rational use of monetary and material resources, mechanisms, and construction personnel, widely applying cyclic and Stakhanovite methods of work on the construction site itself.

As an example of an exemplary organization of construction work one may cite the construction of the mines “Proletarskaya-Krutaya,” “Kurakhovka,” and “Mushketovka” in the Donbass, built very recently. The methods of work and the results achieved by the builders at these mines must be widely popularized among the workers of newly constructed mines.

One of the elements of a rational layout of a mine is the correct choice of the location for sinking its shafts, intended for opening up and working the given deposit. Under the conditions of our socialist economy, the rational location for a mine should be considered to be one that ensures the lowest costs for the construction and operation of the mine, and also achieves good stability of the permanent workings, higher productivity of the enterprise, an early start of stoping production, the least losses of the useful mineral, and complete safety of work. Thus, when choosing the location for sinking a mine it is necessary to take into account the following factors:

a) the costs of driving shafts and crosscuts, constructing mine yards, headworks, and access roads;

b) the costs of haulage of the useful mineral, waste rock, stowing and support materials, the delivery of people to the workplace and back, hoisting of loads through the mine shaft, drainage, ventilation, and repair of permanent workings;

c) the productivity of the mine, the start of stoping production, and losses of the useful mineral;

d) the degree of safety of work and the stability of the main permanent workings (shafts, crosscuts, mine yards).

Many works in our mining-engineering literature are devoted to the question of choosing the location for sinking mine shafts. The principal among them are the works of Academician L. D. Shevyakov, R. E. Seletsky, Prof. A. M. Tseitlin, and A. E. Lokshin, V. V. Barolin, and D. N. Ogloblin. Therefore, in the present article we do not consider the question of choosing the location for sinking mine shafts as a whole, but touch only upon those elements which, in our opinion, have been insufficiently fully considered in the works of the above-mentioned authors. Specifically, in this work we consider two questions: finding the location for sinking a mine shaft across the strike of a suite that satisfies the minimum length of crosscuts, and the graphical determination of the position of the alignment corresponding to the least haulage work along the strike, when intra-mine—

initial delivery to the surface. We shall analyze the latter question as applied to deposits of irregular shape.

1. The shaft location corresponding to the minimum length of crosscuts

To solve this problem as applied to the conditions of a suite of seams or veins, we shall first consider this question in the presence of only one deposit. It is self-evident that the problem posed can be solved only in the case when the main shaft intersects the seam or vein. Therefore let us assume that shaft \(AB\) (Figs. 1 and 2) is sunk at point \(A\). Then, obviously, the length of the crosscuts is \(L = L_1 + L_2 \ldots\) (1), where \(L_1\) and \(L_2\) are the corresponding lengths of all crosscuts above point \(0\) and below it.

In the absence of a zero crosscut (Fig. 1), the quantity

\[ L_1 = l_1 + l_2 + \ldots + l_k = h \ctg \alpha + 2h \ctg \alpha + \ldots + kh \ctg \alpha = \]

\[ = \frac{1}{2}(1+k)kh \ctg \alpha . \]

Since

\[ k = \frac{z_1 - h}{h} = \frac{\rho \tg \alpha - h}{h}, \]

then

\[ L_1 = \frac{\rho}{2h}(\rho \tg \alpha - h) \tag{2} \]

The quantity \(L_2 = l_1 + l'_2 + \ldots + l'_n = h \ctg \alpha + 2h \ctg \alpha + \ldots + nh \ctg \alpha = {}^1/_2(1+n)nh \ctg \alpha\).

From the drawing (Fig. 1) it is seen that

\[ n = \frac{Z_2}{h} = \frac{H - Z_1}{h} = \]

\[ = \frac{H - \rho \tg \alpha}{h}, \]

therefore,

\[ L_2 = \frac{H + h - \rho \tg \alpha}{2h}(H - \rho \tg \alpha)\ctg \alpha \tag{2_1} \]

Substituting into equation (1) the found values \(L_1\) and \(L_2\), we obtain:

\[ L = \frac{\rho}{2h}(\rho \tg \alpha - h) + \frac{H - \rho \tg \alpha}{2h}(H + h - \rho \tg \alpha)\ctg \alpha \tag{3}. \]

Differentiating the length of the crosscuts \((L)\) with respect to the variable \((\rho)\) and equating the derivative found to 0, we obtain:

\[ \frac{dL}{d\rho} = \frac{1}{h}(2\rho \tg \alpha - H - h) = 0 \]

Fig. 1.

Fig. 2.

Fig. 3.

Hence we find that, in the present case, the least length of crosscuts will be obtained when

\[ \rho=\frac{H+h}{2\,\operatorname{tg}\alpha} \tag{4} \]

The same result, as is not difficult to verify, is obtained by finding the conditions for the minimum of the sum of the areas \(OMN=S_1\) and \(POB=S_2\) (Fig. 1)

\[ S=S_1+S_2=\frac{1}{2}(\rho-h\operatorname{ctg}\alpha)^2\operatorname{tg}\alpha+\frac{1}{2}(H-\rho\operatorname{tg}\alpha)^2\operatorname{ctg}\alpha. \]

\[ \frac{dS}{d\rho}=2\rho\operatorname{tg}\alpha-H-h=0,\quad \text{or}\quad \rho=\frac{H+h}{2\operatorname{tg}\alpha}. \]

As can be seen, the latter method is simpler, and therefore we shall use it below.

If there is a zero crosscut (Fig. 2), then

\[ S=S_1+S_2=\frac{1}{2}\rho^2\operatorname{tg}\alpha+\frac{1}{2}(H-\rho\operatorname{tg}\alpha)^2\operatorname{ctg}\alpha \]

\[ \frac{dS}{d\rho}=2\rho\operatorname{tg}\alpha-H=0 \quad \text{and} \]

\[ \rho=\frac{H}{2\operatorname{tg}\alpha} \tag{5} \]

The derivation made shows that, taking the value \(\rho\) equal to that found from equations (4) or (5), we can in each individual case easily find the place where the shaft to be sunk will have the least length of crosscuts. In this case (with a relatively uniform distribution of reserves along the dip), the minimum costs will also be obtained both for haulage of loads along the crosscuts and for ventilation of the shaft.

The required location of the shaft can easily be found graphically. For this (Fig. 1) it is sufficient, on the line \(N_0K\), to set off from \(N_1\) a segment equal to \(\frac{H+h}{2}\), and from point \(K\) draw the line \(KA\), parallel to the bed or vein. The point \(A\), where the line \(AK\) intersects the surface, will be the required place for sinking the shaft. From the construction made in Fig. 1 it is seen that the segment

\[ N_1A=\rho=\frac{H+h}{2}\operatorname{ctg}\alpha=\frac{H+h}{2\operatorname{tg}\alpha}. \]

In the presence of a zero crosscut, the segment \(N_1K\) is taken equal to \(\frac{H}{2}\) (Fig. 2); otherwise the construction remains the same.

\(^{1)}\) \(H\) is the height of the shaft field along the dip; \(h\) is the height of a level. The other designations are shown in the figures.

Fig. 4.

Fig. 6.

Fig. 5.
a) \(\beta/H = 0.2\)
b) \(\beta/H = 1.2\).

The conclusions drawn for a single seam or a single vein make it possible to solve the posed problem for a suite of deposits.

Let us assume that a deposit consisting of several seams or veins having the same dip is opened up by shaft \(AB\) (Fig. 3) and by crosscuts \(l_1, l_2\), etc. (without the zero crosscut\(^1\)). Then, obviously, the sum of the areas of the triangles

\[ MNO=S_1 \quad \text{and} \quad POB=S_2 \]

will be

\[ S=S_1+S_2=\frac{1}{2}MN\cdot OM+\frac{1}{2}O_1B\cdot PB =\frac{1}{2}(\rho-h\,ctg\,\alpha)^2tg\,\alpha+\frac{1}{2}(H-\rho\,tg\,\alpha-\beta\,tg\,\alpha)^2ctg\,\alpha. \]

In equation (6) the following notation has been adopted:

\(\rho\)—the distance of the shaft from the outcrop beneath the overburden of the upper deposit;\(^2\)

\(H\)—the height of the shaft field along the dip; \(h\)—the height of a level;

\(\beta\)—the horizontal distance between the outermost deposits of the suite;

\(\alpha\)—the dip angle of the seams or veins.

Differentiating equation (6) and setting the derivative equal to zero, we obtain:

\[ \frac{dS}{d\rho}=2\rho\,tg\,\alpha-H-h+\beta\,tg\,\alpha=0 \tag{7} \]

From equation (7) it is evident that the least length of the crosscuts when opening up the suite will occur at

\[ \rho=\frac{H+h}{2\,tg\,\alpha}-\frac{\beta}{2} \tag{8} \]

If, for the quantity \(\rho\), we were to take the distance of the shaft from the outcrop beneath the overburden of the lower deposit, then it would not be difficult, in exactly the same way, to show that the minimum length of the crosscuts is attained at

\[ \rho=\frac{H+h}{2\,tg\,\alpha}+\frac{\beta}{2} \tag{9} \]

In the presence of a zero crosscut (Fig. 4), the sum of the areas of the triangles \(OMN\) and \(PO_1B\), equal to \(S=S_1+S_2\), is

\[ =\frac{1}{2}(MN\cdot OM+OB\cdot PB) =\frac{1}{2}\left[\rho^2tg\,\alpha+(H-\rho\,tg\,\alpha-\beta\,tg\,\alpha)ctg\,\alpha\right]. \]

The value of \(\rho\) satisfying the minimum length of the crosscuts is found from the equation:

\[ \frac{dS}{d\rho}=2\rho\,tg\,\alpha-H+\beta\,tg\,\alpha=0 \tag{10} \]

\(^1\) A very rare case in practice (author)

\(^2\) For deep occurrence—from the apex of the deposit.

Solving this equation for \(\rho\), we obtain:

\[ \rho=\frac{H}{2\operatorname{tg}\alpha}-\frac{\beta}{2} \tag{11} \]

Likewise, as in the preceding case, taking as the value \(\rho\) the corresponding distance from the lower deposit, we find that the smallest length of crosscuts will occur when

\[ \rho=\frac{H}{2\operatorname{tg}\alpha}+\frac{\beta}{2} \tag{12} \]

Comparing the obtained equations (8), (9), (11), and (12) with equations (4) and (5), we arrive at the conclusion that the shaft having the minimum length of crosscuts for the entire suite is located at a distance \(\frac{\beta}{2}\) both from the shaft \(A_1B_1\), sunk according to the rule we established only for the upper deposit, and from the shaft \(A'_1B'_1\)—for the lower deposit (Figs. 3 and 4). Consequently, the required shaft for the whole suite passes through the point of intersection of the diagonals of the rectangle constructed on the shafts \(A_1B_1\) and \(A'_1B'_1\). Hence there follows a quite clear, very simple method for the graphical determination of the location for sinking the shaft \(AB\). However, such a determination can also be made by a still simpler method, using the construction shown in Figs. 1 and 2. For this it is sufficient, as indicated in Figs. 3 and 4, to find the point \(A_1\) or \(A'_1\), corresponding to the shaft location for the upper or lower deposit, and then from one of these points to lay off to the right or to the left (from point \(A_1\)—to the right, and from point \(A'_1\)—to the left) the segment \(A_1A\) or \(A'_1A\), equal to half the distance between the outer deposits of the suite, i.e. equal to \(\frac{\beta}{2}\). Point \(A\) will then be the required location for sinking the shaft having, for the given suite, the smallest length of crosscuts.

As can be seen from the drawings (Figs. 5a and 5b), the point \(A\) found by the indicated method when opening up a suite of deposits is not the only point at which the shaft has the smallest length of crosscuts. Around the shaft drawn through point \(A\), in the plane of its crosscuts, there is obtained an entire zone within which all shafts have a length of crosscuts equal to that of shaft \(AB\).

The width of this zone depends on the value of \(\frac{\beta}{H}\). The larger this ratio, the wider the zone, and conversely. In each individual case the extreme limits of such a zone can easily be established from the drawing after plotting shaft \(AB\) and all the crosscuts. In Fig. 5a they are within \(CD\), and in Fig. 5b within \(C_1D_1\). The existence of the established zone, when necessary, makes it possible to shift (within known limits) the location for sinking the shaft without increasing the length of the crosscuts.

This creates certain conveniences in choosing the shaft location on the basis of other factors, possibly without going beyond the minimum crosscuts.

If the veins or seams of the given suite dip at different angles (Fig. 6), varying within the limits from $\alpha_1$ to $\alpha_2$, then the condition for the minimum length of the crosscuts can be established as follows.

Let the shaft $AB$ open up a suite of seams, of which the uppermost lies at an angle $\alpha_1$, and the lowermost at an angle $\alpha_2$. Then, drawing the line $ND$, parallel to the lower seam, we see that $M=O\rho_1 tg\,\alpha_1$, $MO_1=\rho\,tg\,\alpha_2$ and $O_1O_2=\beta\,tg\,\alpha_2$. Consequently, the sum of the areas of the triangles $MON=S_1$ and $O_2PB=S_2$ will be:

\[ S=S_1+S_2=\frac{1}{2}\rho^2 tg\,\alpha_1+\frac{1}{2}(H-\rho\,tg\,\alpha_2-\beta\,tg\,\alpha_2)^2 ctg\,\alpha_2 \tag{13} \]

Equating the first derivative $\dfrac{dS}{d\rho}$ to zero and solving the resulting equation, we find the value of $(\rho)$ for which the length of the crosscuts will be minimal.

\[ \frac{dS}{d\rho}=\rho(tg\,\alpha_1+tg\,\alpha_2)-H+\beta\,tg\,\alpha_2=O \]

Hence

\[ \rho=\frac{H-\beta\,tg\,\alpha_2}{tg\,\alpha_1+tg\,\alpha_2} \tag{14} \]

For $\alpha_1=\alpha_2$ this equation, as was to be expected, has a form analogous to equation (11).

In the absence of a zero crosscut, the condition for the minimum length of the crosscuts is found from the equation:

\[ \begin{aligned} \frac{dS}{d\rho} &=\frac{dS_1}{d\rho}+\frac{dS_2}{d\rho} =\frac{d}{d\rho}\left(\frac{1}{2}M_1N_1.M_1O\right) +\frac{d}{d\rho}\left(1/2\,O_2B.BP\right)= \\ &=\frac{d}{d\rho}\left[\frac{1}{2}\left(\rho-hctg\,\alpha_1\right)^2 tg\,\alpha_1\right]+ \\ &\quad+\frac{d}{d\rho}\left[\frac{1}{2}\left(H-\rho\,tg\,\alpha_2-\beta\,tg\,\alpha_2\right)ctg\,\alpha_2\right] =\rho(tg\,\alpha_1+tg\,\alpha_2)-H-h+ \\ &\quad+\beta\,tg\,\alpha_2=0 \end{aligned} \]

Hence the sought value of $(\rho)$ will be

\[ \rho=\frac{H+h-\beta\,tg\,\alpha_2}{tg\,\alpha_1+tg\,\alpha_2} \tag{15} \]

When $H+h-\beta\,tg\,\alpha_2<0$, the mine shaft, over its entire depth, is located inside the suite.

If a synclinal or anticlinal fold is being opened up, it is self-evident that the smallest length of crosscuts would occur when the shaft is driven through the crest of the folds. However, in many cases, because of substantial losses of the useful mineral, such a shaft location cannot be adopted.

The equations obtained for determining the value \((\rho)\) make it possible, in each individual case, to find easily the position of the vertical shaft at which it will have the smallest length of crosscuts. Then, taking the remaining factors into account, the site for sinking the shaft can be finally selected.

2. Determination of the Site for Sinking a Shaft Along the Strike.

As was already indicated in the introductory part of the present article, in considering the question of choosing the site for sinking a shaft along the strike, we examine only the graphical method of determining the shaft corresponding to the least haulage work in irregular deposits. At the same time, a solution to this question is also given for the case in which it is necessary to take account of underground haulage to the surface.

The solution of this problem is based on the method proposed by Engineer V. V. Barolin in his article published in Gornyi zhurnal, 1927, No. 9. Unfortunately, in Engineer Barolin’s work the question of determining the site for sinking a shaft was not examined for irregular occurrence of deposits along the dip, if they are worked in several levels. In this case it is impossible to find a shaft corresponding to the minimum haulage work from the load diagram of only one drift, as recommended by Engineer V. V. Barolin. In addition, V. V. Barolin’s work does not provide a method for finding the shaft site when underground haulage to the surface is present. Thus, considering the method discussed in the above-mentioned article to be very simple and interesting, we, making use of it, set forth the solution of this problem in a more general form. As for surface haulage, the solution proposed by us is being presented in the literature for the first time.

Let us suppose that there is an ore deposit of irregular shape, which it is planned to work in three levels of height \(h\) m (Fig. 7). Let us further suppose that the shape of the ore body varies both along its strike and along the dip. Therefore, in this case it is impossible to represent the load on any one drift¹ in order to determine the place corresponding to the least work in hauling loads in the direction of the strike of the deposit. Consequently, we first construct load diagrams for all level drifts. For this purpose, we divide the reserves of each level into separate blocks, which

can be regarded as prismoids with bases whose areas are easily determined by a geometric method. And then, assuming that the reserves of such blocks are uniformly distributed over the corresponding sections of the drift, we construct for it a load diagram. In this way the loads of drifts I—I, II—II, and III—III, shown in Fig. 7, are obtained. To simplify the corresponding constructions in the indicated figure, the loads of the drifts are presented in a somewhat schematized form.

As a result of such a distribution of the reserves of the ore body, we obtain the loads: drift I—I—on the section \(ab—q'_1\), \(bc—q'_2\), \(cd—q'_3\); drift II—II—on the section \(a'b'—q''_1\), \(b'c'—q''_2\), \(c'd'—q''_3\); drift III—III on the section \(a''b''—q'''_1\), \(b''c''—q'''_2\), \(c''d''—q'''_3\). From these load diagrams of the individual drifts we construct the total load diagram of the line \(A'A'_1\), the projection of all the main drifts (I—I, II—II, III—III).

The total load of the line \(A'A'_1\) is shown: section \(l_1—q_1\), \(l_2—q_2\), \(l_3—q_3\), etc., \(l_8—q_8\).

On the basis of the diagram constructed on the line \(A'A'_1\), we compute the diagrams of the work of tramming all loads to the point \(A_1\) and back—to the point \(A\). We construct these diagrams as follows. On the perpendicular to the straight line \(AA_1\), at a definite scale, we lay off the segment \(B'B = Q_1 = q_1 l_1\), and then in an analogous way we successively take the segments \(CD = Q_2 = q_2 l_2\); \(EF = Q_3 = q_3 l_3\); \(GI = Q_4 = q_4 l_4 \ldots\) and \(R_1S = Q_8 = q_8 l_8\). Connecting the points \(A, B, D, F \ldots P\) and \(S\) by straight lines, we obtain the figure \(ABDF \ldots SRA_1\), the area of which, as is not difficult to verify, represents the work of tramming all loads to the point \(A_1\). In order to deliver load \(Q_1\) to the point \(A_1\), it is necessary to expend work equal to \(\tfrac{1}{2}Q_1 l_1 + Q_1(AA_1-l_1)\). Meanwhile, the area of the trapezoid \(ABC_0A_1 = \tfrac{1}{2} B'B \cdot AB' + B'B \cdot B'A_1 = \tfrac{1}{2}Q_1 l_1 + Q_1(AA_1-l_1)\), i.e., the area of this trapezoid is equal to the work of tramming load \(Q_1\) to the point \(A_1\). In exactly the same way it can be shown that the area of the trapezoid \(BDD_0C_0\) is equal to the work of tramming load \(Q_2\) to the same point \(A_1\), etc. Consequently, the area of the figure indicated above, \(ABDFI \ldots SRA_1\), is indeed equal to the work of tramming the load \(Q=\sum_1^i Q_i\) to the right flank of the deposit, to the point \(A_1\).

We likewise construct the diagram \(A_1B_1D_1F_1 \ldots P_1S_1A\), whose area is equal to the work of tramming the loads \(Q_8, Q_7, Q_6 \ldots Q_2\) and \(Q_1\) to the left flank of the ore body, to the point \(A\). The point \(O_0\), the intersection of the lines \(ABDF \ldots PS_1\) and \(A_1B_1D_1F_1 \ldots P_1S_1\), will determine the position of the crosscut \(\varepsilon_1\varepsilon_1\) corresponding to the least work of underground tramming of ore and delivered waste rock (along drifts I—I, II—II, and III—III). This can readily be proved as follows. Suppose that the areas of the diagrams \(ABDF \ldots SA_1\), \(A_1B_1D_1F_1 \ldots S_1A\), and \(ABDFO_0F_1D_1B_1A_1\) are respectively equal to \(\omega_1\), \(\omega_2\), and \(\omega_3\). In this case, as can be seen in Fig. 7, the area \(\omega_3\) is smaller than the areas \(\omega_1\) and \(\omega_2\). Consequently, if the shaft were laid...

section along the strike

section along the dip

Fig. 7.

laid in the alignment passing through point \(A\) or \(A_1\), then the work of underground haulage would be considerably greater than for a shaft laid in the alignment \(\varepsilon_1 \varepsilon_1\), passing through point \(O_0\).¹ Next suppose that the shaft is moved from the alignment \(\varepsilon_1 \varepsilon_1\) to the right or to the left by an infinitesimally small amount \(dl\). With such a displacement the area \(\omega_3\) will increase by infinitesimally small areas \(d\omega\), situated to the right or to the left of point \(O_0\). Thus, by moving the shaft out of the plane \(\varepsilon_1 \varepsilon_1\), we shall increase the work of underground haulage of ore and rock. Consequently, the alignment \(\varepsilon_1 \varepsilon_1\), passing through point \(O_0\), corresponds to the minimum work of underground haulage for the given ore body.

In the absence at the shaft of intra-ore haulage on the surface, carried out in the direction of strike of the ore body, the most advantageous location for laying the shaft along the strike (from the point of view of the volume of underground haulage work) would be the plane \(\varepsilon_1 \varepsilon_1\), determined by the position of point \(O_0\) on the diagrams \(A S A_1\) and \(A_1 S_1 A\). With respect to the opening of the deposit shown in Fig. 7 and its exploitation, the location found for laying the shaft raises no objections (there is a relatively symmetrical two-wing field).

If the mined ore first goes to a concentrating mill located near the shaft, or goes directly to a plant situated near the shaft bins, then in choosing the location for laying the shafts it is necessary to take into account the work of hauling ore on the surface. Let us suppose that the alignment to which the mined ore is to go is located along the line \(\varepsilon_2 \varepsilon_2\) (the site of the concentrating mill or plant). Then, obviously, leaving the shaft in the plane \(\varepsilon_1 \varepsilon_1\), we would be forced to expend additional work on delivering the ore to the alignment \(\varepsilon_2 \varepsilon_2\), determined by the area of the rectangle \(ntt_1 n_1\). The side of this rectangle \(nn_1\) or \(tt_1\) represents the total ore reserve in tons, while \(nt\) or \(n_1t_1\) is the haulage distance in km or m. Therefore, in order to achieve minimum costs for hauling ore both underground and on the surface, it is necessary to shift the shaft somewhat toward the alignment \(\varepsilon_2 \varepsilon_2\) (Fig. 7). To find the alignment \(\varepsilon_3 \varepsilon_3\), corresponding to the least work of underground and surface haulage, we first determine the volume of surface-haulage work reduced to underground haulage. Since in most cases the cost of a unit of work (ruble-ton-meter or ton-kilometer) of surface haulage \((C_1)\) is somewhat less than that of underground haulage \((C_2)\), then, to obtain the reduced work of surface haulage, we reduce the actual number of its units in proportion to the ratio

\[ \frac{C_1}{C_2}. \]

The area of the rectangle \(ntxx_1\) is equal to the reduced work of haulage on the surface. Its side

\(nx = Q \dfrac{C_1}{C_2}\), where \(Q\) is the total reserve of ore obtained from the given deposit. (For finding the section \(\varepsilon_3 \varepsilon_3\), \(\dfrac{C_1}{C_2}=0.6\) is adopted.)

From the established value \(\dfrac{C_1}{C_2}Q\) we find the position of the plane \(\varepsilon_3 \varepsilon_3\), on which the shaft will be located that ensures the minimum haulage work both underground and on the surface. To do this, from the ordinates \(J J_1, E K_1 \ldots B P_1\) we choose the first (from the point \(O_0\)) which is greater than \(nx=\dfrac{C_1}{C_2}Q\), and lay off on it the value \(nx\) (from the points \(F_1, J D\), or \(B\)). Through the point \(\gamma_1\) (the lower end of the segment equal to the value \(nx\)) we draw a straight line parallel to the lines \(J O_0, F J\), or \(D F\), etc.—until it intersects the line \(O_0 J_1, J_1 K_1\), or \(K_1 N_1\)—at the point \(\gamma_2\), which determines the position of the plane \(\varepsilon_3 \varepsilon_3\), normal to the strike line of the ore deposit. In Fig. 7 the first ordinate which is greater than the value \(nx\) turned out to be the ordinate \(D N_1\). On it, from the point \(D\), the segment \(D \gamma_1\) is laid off, equal to the value \(nx=\dfrac{C_1}{C_2}Q\).

Through the point \(\gamma_1\) a straight line is drawn parallel to the line \(DF\) until it intersects the straight line \(N_1 K_1\) at the point \(\gamma_2\), which determines the position of the required plane (section) \(\varepsilon_3 \varepsilon_3\). A shaft located in this section will indeed give the least haulage work (underground and surface). This is not difficult to verify directly from the drawing shown in Fig. 7. Suppose that the shaft from the section \(\varepsilon_3 \varepsilon_3\) is shifted somewhat to the left. Then a small area will be added to the underground haulage, determined by the trapezoid \(\gamma_2 \gamma_3 \gamma_4 \gamma_5\), while on the reduced surface haulage it will be decreased by the area of the rectangle \(m \gamma_6 \gamma_7 m_2\). Since the height and the base \(\gamma_2 \gamma_3\) of the trapezoid are equal to the height and base \(m m_2\) of the rectangle, while its other base \(\gamma_4 \gamma_5 > m m_2\), the area of the “added” trapezoid is greater than that of the “subtracted” rectangle. Hence it is seen that when the shaft is moved to the left from the plane \(\varepsilon_3 \varepsilon_3\), the total haulage work of the loads increases (because of the more rapid increase in underground haulage work). In exactly the same way it can be proved that when the shaft is moved to the right, an increase in work will also be observed (as a result of the more intensive growth of the reduced surface haulage work). Consequently, the position of the section \(\varepsilon_3 \varepsilon_3\) corresponds to the minimum haulage work.

The proposed method for determining the location of a shaft corresponding to the least haulage work along the strike may be applied both to irregular deposits consisting of a single deposit body and to several more or less regular veins and seams having either different lengths or a sufficiently complex relative arrangement along the strike.

d) Mechanize all processes of driving workings and carry out thorough preliminary preparation for construction.

e) Take measures for the most rational use of monetary and material resources, mechanisms, and construction personnel, widely applying cyclic and Stakhanovite methods of work at the construction site itself.

As an example of a model organization of construction work, one may cite the construction of the mines “Proletarskaya-Krutaya,” “Kurakhovka,” and “Mushketovka” in the Donbass, built in very recent times. The methods of work and the results achieved by the builders at these mines must be widely popularized among the workers of newly built mines.

One of the elements of the rational layout of a mine is the correct choice of the location for sinking its shafts, intended for opening up and developing the given deposit. Under the conditions of our socialist economy, the rational location for establishing a mine must be regarded as one at which the least expenditures for the construction and operation of the mine are ensured, and also good stability of the capital workings, higher productivity of the enterprise, a rapid start of stoping extraction, the least losses of the mineral, and complete safety of work are achieved. Thus, when choosing the location for establishing a mine, it is necessary to take into account the following factors:

a) the costs of sinking shafts and staple shafts, constructing mine yards, surface structures, and approach roads;

b) the costs of haulage of the mineral, barren rock, packing and support materials, transportation of people to the workplace and back, hoisting of loads through the mine shaft, water drainage, ventilation, and repair of capital workings;

c) the productivity of the mine, the beginning of stoping extraction, and losses of the mineral;

d) the degree of work safety and the stability of the main capital workings (shafts, staple shafts, mine yards).

Many works in our mining-engineering literature have been devoted to the question of choosing the location for establishing mines. The principal among them are the works of Academician L. D. Shevyakov, R. E. Selesko, Prof. A. M. Tseitlin and A. E. Lokshin, V. V. Barolin and D. N. Ogloblin. Therefore, in the present article we do not examine the question of choosing the location for establishing mines as a whole, but touch only upon those elements which, in our opinion, were not considered sufficiently fully in the works of the above-mentioned authors. Specifically, in this work we consider two questions: finding the location for establishing a mine across the strike of a suite, satisfying the minimum length of staple shafts, and the graphical determination of the position of an alignment corresponding to the least haulage work along the strike, when intra-mine [[unclear: word cut off at page edge]]

with the regular occurrence of a significant number of seams, so many concentrated loads may appear on the projection of the crosscuts that they will have to be reduced to a distributed load. In the case of relatively regular, flat-lying deposits, it is, of course, more correct to regard the distribution of reserves on the crosscuts as concentrated; but under such conditions (when choosing the location for a shaft by extension), there is no need to carry out rather complicated constructions, since the problem itself is solved here much more simply. Therefore, when constructing the diagrams \(A S A_1\) and \(A_1 S_1 A\) as applied to irregularly shaped deposits, in our opinion it is much more convenient and simpler to use distributed reserves.

1. The alignments are arranged normal to the line of strike of the ore body. ↩↩