Basic principles of a method for determining the floor height in mining a suite of closely spaced steeply dipping seams
Abstract Generated abstract
The paper addresses the determination of level height when mining closely spaced, steeply dipping coal seams, a design parameter affecting production continuity, labor productivity, and mining cost. It critiques existing geometric formulas and variant approaches for insufficiently accounting for coal losses, mining-system differences, seam proximity, safety, production capacity, and preparation time for lower levels. The author proposes a combined variant, analytical, and graphical method that evaluates individual seams and mining systems, establishes technical limits, checks annual output and level-preparation constraints, and selects the suite-wide level height by minimizing projected extraction costs. The contribution is a structured procedure intended to support lower unit costs and improved productivity in complex Kuzbass-type deposits.
Full Text
BASIC PRINCIPLES OF THE METHOD FOR DETERMINING LEVEL HEIGHT IN THE MINING OF A SUITE OF CLOSELY SPACED STEEPLY DIPPING SEAMS
V. V. PROSKURIN
(Presented by the scientific conference of the Mining Operations Faculty)
Level height is one of the most important elements of a mine field; on it depend, first, the continuity of operation and the production capacity of the mine and, second, labor productivity and the cost of mining 1 metric ton of coal. Level height is an element of the mine field which, for any mining system, fixes the size of the extraction field along the dip of the seam.
The most advantageous basic dimensions of the elements of the mining system provide the conditions for attaining high technical and economic indicators in mine operation. Consequently, a correctly chosen level height must provide conditions for the steady growth of labor productivity and the reduction in the cost of mining 1 metric ton of coal, i.e., it must meet the tasks facing the coal industry and the national economy of the USSR.
The methods for determining level height have been developed theoretically quite insufficiently. Let us consider the recommendations proposed over the last 40 years.
Prof. B. I. Bokii, in A Practical Course in Mining Art, publ. 1914, gives the following formula for determining the level height without taking into account the dimensions of protective pillars and as applied to a separately taken seam:
\[ B=\frac{T}{2LP}, \tag{1} \]
where \(B\) is the inclined height of the level without the dimensions of protective pillars,
\(T\) is the annual output of the mine,
\(L\) is the magnitude of the annual advance of the working faces,
\(P\) is the productivity of the seam,
\(2\) denotes two wings.
To determine the full height by levels, the following formula was recommended:
\[ B_1 = B + K, \tag{2} \]
where \(B_1\) is the full inclined height of the level,
\(K\) is a quantity allowing for the size of the protective pillars left along the raise.
Over the course of forty years these formulas were improved and, in the book Foundations of the Theory of Designing Coal Mines by Academician L. D. Shevyakov, published in 1952, they are presented, as applied to a suite of seams, in a more developed form:
\[ h=\frac{A}{n_k n_e n_o L \Sigma P C}, \tag{3} \]
where \(h\) is the required inclined height of the level;
\(A\) is the annual output of the mine;
\(n_k\) is the number of wings being worked simultaneously;
\(n_e\) is the number of levels being worked simultaneously;
\(n_o\) is a coefficient allowing for the simultaneous working of seams;
\(L\) is the average annual advance of stoping operations on one wing of the field;
\(\Sigma P\) is the total productivity of the seams of the suite;
\(C\) is the extraction coefficient.
The determination of the inclined height of a level, both in Prof. B. I. Bokia’s formula (2) and in the modernized formula of Academician L. D. Shevyakov (3), is based on a logical geometrical interpretation: the volume of coal mined during a year, multiplied by its bulk density, is equal to the annual output of the mine. Taking two dimensions that define the area of the base of the prism as known, the third dimension—the inclined height of the level—is found.
The technical and economic essence of level height, as one of the basic elements of the mine field determining the technical-and-economic performance indicators of a mine, remained unaccounted for in formulas (2; 3).
Academician L. D. Shevyakov, in the book Foundations of the Theory of Designing Coal Mines (p. 186), recommends filling this gap in mining science by applying the method of variants. The essence of the recommendation is as follows: the designer, by assigning an arbitrary level height and, consequently, an arbitrary number of variants, must find such a level height as would correspond to the lowest costs per 1 t of industrial reserves contained in the level. In doing so, it is proposed to take into account: 1) the costs of driving the workings that prepare the level (shaft station, level crosscuts and drifts), and 2) the costs associated with delivery of loads along inclined workings, movement of people, hoisting of loads, drainage, and ventilation.
Coal losses, safety of work, the specific character of the mining systems intended for application on the seams (direction of advance of the stoping faces, their rate, closeness of seams, labor productivity of the face crew, etc.), i.e., the principal elements determining the technical-and-economic performance indicators of the mine and having substantial importance especially when establishing the level height for a suite of seams, remained unaccounted for in the recommendation.
With regard to the method for determining level height for a suite of steeply dipping seams, and all the more for thick seams, Academician L. D. Shevyakov indicates that this question requires “special detailed investigations.”
Table 1
Formulas and procedure for determining the optimal vertical height of a level for a suite of steeply dipping seams
Optimal vertical height of a level for seams No. 1, 2, …, \(n\) and panels I, II, m
Cost of extracting one ton of coal \((a)\) and the cost of extracting commercial reserves, projected onto \(1 \text{ m}^2\) of the vertical plane
\(\left(\dfrac{PC}{\sin \alpha}\,a\right)\), rub.
| Seams | Mining system | \(\gamma\)—specific gravity of all development and extraction work per panel, m\(^2\) | Productivity coefficient of extracting \(1\) m\(^2\) of coal seam \((PC)\), t/m\(^2\) | \(h_1\): \(a\) | \(h_1\): \(\dfrac{PC}{\sin x}\,a\) | \(h_2\): \(a\) | \(h_2\): \(\dfrac{PC}{\sin x}\,a\) | … | \(h_n\): \(a\) | \(h_n\): \(\dfrac{PC}{\sin x}\,a\) | \(h_n^{I}\): \(a\) | \(h_n^{I}\): \(\dfrac{PC}{\sin x}\,a\) | \(h_n^{II}\): \(a\) | \(h_n^{II}\): \(\dfrac{PC}{\sin x}\,a\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Seam 1 | L.S. | \(1.0\) | \(P_1C_1\) | \(a_1^1{}_{\min}\) | \(\dfrac{P_1C_1}{\sin x_1}\,a_1^1\) | \(a_1^{II}\) | \(\dfrac{P_1C_1}{\sin x_1}\,a_1^{II}\) | … | \(a_1^{[n-1]}\) | \(\dfrac{P_1C_1}{\sin x_1}\,a_1^{[n-1]}\) | \(a_1^{In}\) | \(\dfrac{P_1C_1}{\sin x_1}\,a_1^{In}\) | \(a_1^{IIn}\) | \(\dfrac{P_1C_1}{\sin x_1}\,a_1^{IIn}\) |
| Seam 2 | Sh. | \(1.0\) | \(P_2C_2\) | \(a_2^{I}\) | \(\dfrac{P_2C_2}{\sin x_2}\,a_2^{I}\) | \(a_2^{II}{}_{\min}\) | \(\dfrac{P_2C_2}{\sin x_2}\,a_2^{II}\) | … | \(a_2^{[n-1]}\) | \(\dfrac{P_2C_2}{\sin x_2}\,a_2^{[n-1]}\) | \(a_2^{In}\) | \(\dfrac{P_2C_2}{\sin x_2}\,a_2^{In}\) | \(a_2^{IIn}\) | \(\dfrac{P_2C_2}{\sin x_2}\,a_2^{IIn}\) |
| … | … | … | … | … | … | … | … | … | … | … | … | … | … | … |
| Seam \((n-1)\) | H.S. | \(1.0\) | \(P_{n-1}C_{n-1}\) | \(a_{n-1}^{I}\) | \(\dfrac{P_{n-1}C_{n-1}}{\sin x_{n-1}}\,a_{n-1}^{I}\) | \(a_{n-1}^{II}\) | \(\dfrac{P_{n-1}C_{n-1}}{\sin x_{n-1}}\,a_{n-1}^{II}\) | … | \(a_{n-1}^{[n-1]}{}_{\min}\) | \(\dfrac{P_{n-1}C_{n-1}}{\sin x_{n-1}}\,a_{n-1}^{[n-1]}\) | \(a_{n-1}^{In}\) | \(\dfrac{P_{n-1}C_{n-1}}{\sin x_{n-1}}\,a_{n-1}^{In}\) | \(a_{n-1}^{IIn}\) | \(\dfrac{P_{n-1}C_{n-1}}{\sin x_{n-1}}\,a_{n-1}^{IIn}\) |
| Seam \(n\) | L.S. | \(\gamma_1\) | \(P_n^{I}C_n^{I}\) | \(a_{In}^{I}\) | \(\gamma_1\dfrac{P_n^{I}C_n^{I}}{\sin x_n^{I}}\,a_{In}^{I}\) | \(a_{In}^{II}\) | \(\gamma_1\dfrac{P_n^{I}C_n^{I}}{\sin x_n^{I}}\,a_{In}^{II}\) | … | \(a_{In}^{[n-1]}\) | \(\gamma_1\dfrac{P_n^{I}C_n^{I}}{\sin x_n^{I}}\,a_{In}^{[n-1]}\) | \(a_{In}^{In}{}_{\min}\) | \(\gamma_1\dfrac{P_n^{I}C_n^{I}}{\sin x_n^{I}}\,a_{In}^{In}\) | \(a_{In}^{IIn}\) | \(\gamma_1\dfrac{P_n^{I}C_n^{I}}{\sin x_n^{I}}\,a_{In}^{IIn}\) |
| Seam \(n\) | Sh. | \(\gamma_2\) | \(P_n^{II}C_n^{II}\) | \(a_{IIn}^{I}\) | \(\gamma_2\dfrac{P_n^{II}C_n^{II}}{\sin x_n^{II}}\,a_{IIn}^{I}\) | \(a_{IIn}^{II}\) | \(\gamma_2\dfrac{P_n^{II}C_n^{II}}{\sin x_n^{II}}\,a_{IIn}^{II}\) | … | \(a_{IIn}^{[n-1]}\) | \(\gamma_2\dfrac{P_n^{II}C_n^{II}}{\sin x_n^{II}}\,a_{IIn}^{[n-1]}\) | \(a_{IIn}^{In}\) | \(\gamma_2\dfrac{P_n^{II}C_n^{II}}{\sin x_n^{II}}\,a_{IIn}^{In}\) | \(a_{IIn}^{IIn}{}_{\min}\) | \(\gamma_2\dfrac{P_n^{II}C_n^{II}}{\sin x_n^{II}}\,a_{IIn}^{IIn}\) |
| Total | \(\displaystyle \sum_{1}^{n}\dfrac{PC}{\sin x}\,a\) | \(\displaystyle \sum_{1}^{n}\dfrac{PC}{\sin x}\,a\) | … | \(\displaystyle \sum_{1}^{n}\dfrac{PC}{\sin x}\,a\) | \(\displaystyle \sum_{1}^{n}\dfrac{PC}{\sin x}\,a\) | \(\displaystyle \sum_{1}^{n}\dfrac{PC}{\sin x}\,a\) |
\[ \min \sum_{1}^{n} i\,\frac{PC}{\sin x_i}\,a \]
determines the optimal vertical height of the level for the suite of seams \(h_i\).
Notes:
1) L.S. — system of mining by long pillars; Sh. — shield mining system; H.S. — system of mining by horizontal slices.
2) If it is planned to mine a seam using one mining system, then \(\gamma=1\); using two mining systems, \(\gamma=\gamma_1+\gamma_2\); using three mining systems, \(\gamma=\gamma_1+\gamma_2+\gamma_3\); \(n\) mining systems, \(\gamma=\gamma_1+\gamma_2+\cdots+\gamma_n\).
3) \(P_1, P_2, \ldots, P_n\) — productivity of seam No. 1, 2, …, \(n\), t/m\(^2\); \(P_1^{I}, P_1^{II}, \ldots, P_n^{I}, P_n^{II}\) — productivity of the seam in panel I, II, …, seam No. 1, …, \(n\), t/m\(^2\);
\(C_1, C_2, \ldots, C_n\) — extraction coefficient for seam No. 1, 2, …, \(n\); \(C_1^{I}, C_1^{II}, \ldots, C_n^{I}, C_n^{II}\) — extraction coefficient for seam No. 1, …, \(n\) in panel I, II.
4) \(x_1, x_2, \ldots, x_n\) — dip angle of seam No. 1, 2, …, \(n\); \(x_n^{I}, x_n^{II}\) — the same in panel I, II; \(a_1^{I}, a_1^{II}, \ldots, a_1^{[n-1]}\) — cost of extracting one ton of coal from seam No. 1 in variants I, II, …, \([n-1]\); \(a_2^{I}, a_2^{II}, \ldots, a_2^{[n-1]}\) — the same for seam No. 2.
(p. 184). Thus, among the methods for determining the level height for a suite of steeply dipping seams, in the theoretical arsenal of mining science there still remains, in its sole form, the modernized formula (3).
Applying formula (3), for example, to the conditions of the “Koksovaya” mine in Prokopyevsk, we obtain a vertical level height on the order of 30–35 m, which, for economic and practical reasons, is entirely unacceptable.
Consequently, the problem reduces to finding not only such a level height as would ensure the conditions for achieving the mine’s established annual production capacity, but also such a level height as would simultaneously ensure the conditions for attaining high technical-and-economic indicators for the mine. And these conditions can be provided by a properly selected mining system and the principal dimensions of its elements.
In this respect, as applied to the mining of ore deposits, a significant step in the theoretical development of the problem of establishing level height was made by Cand. Tech. Sci., Assoc. Prof. G. E. Bakanov. In his published work (Izv. TPI, vol. 79), he gives, in general form, an analytical expression for determining the optimum level height \((h_0)\) for mining systems, of the form:
\[ A_1 h_0^4 + A_2 h_0^3 + A_3 h_0^2 + A_4 h_0 + A_5 = 0, \tag{4} \]
where \(A_{1\ldots 5}\) are constants for a particular mine field.
It is known that Kuzbass is rich in deposits represented by closely spaced steeply dipping seams, varying in thickness and dip angle, and that for mining such seams, several systems are often used simultaneously within the suite. The basic principles of a method for establishing the optimum level height for the entire suite of closely spaced steeply dipping seams, and for the general case in which different systems are applied simultaneously on the seams of the suite, have not been developed theoretically. The development of this question is set as the task of the present work.
The richest Prokopyevsk-Kiselevsk deposit of Kuzbass is represented by closely spaced steeply dipping seams and is characterized by sharp folding. The selection of level height in the design of the mines now operating in the Prokopyevsk-Kiselevsk district of Kuzbass was carried out empirically. This is well demonstrated by the level heights adopted in the district over the last 25 years: 50, 70, 80, and 100 m. In individual sections of some mines (the “Chernaya Gora” mine) the vertical level height reaches 140 m; at the “Severnaya” mine in the Kemerovo district it has been adopted as 150 m.
Let us consider the principal requirements that must be met by the level height when mining a suite of closely spaced steeply dipping seams. Practice has shown that they reduce to the following:
1) the level height must satisfy the conditions that would ensure the established annual production capacity of the mine;
2) the level height must be such that conditions are ensured for the timely preparation of the lower level for stoping operations;
3) the level height must be optimal for the entire complex of seams composing the suite and for the complex of mining systems planned for application, i.e., such that conditions are ensured for attaining, over the level as a whole, higher labor productivity and a lower cost of mining 1 t of coal.
In solving the problem posed, the following parameters and conditions are taken as known (fixed) initial assumptions for the calculation:
1) the established annual production capacity of the mine;
2) the length of the mine field along the strike;
3) the practically “unlimited” occurrence of the seams of the suite in depth;
4) the availability to the designer of initial data for all seams of the suite, quite sufficient for selecting (for each seam) the mining system.
Taking into account the diversity of requirements for establishing the height of a level and the incommensurable quantities that must be taken into account, we recommend observing the following sequence in the stages of calculation.
-
Specify for each seam of the suite the mining system, and, for certain seams having nonuniform conditions of occurrence, also for individual sections.
-
Establish the order of mining the seams in the suite. In doing so, special account should be taken of contiguous seams, bypassed seams, seams hazardous with respect to sudden outbursts of coal and gas, and also the directions of advance of the stoping operations along the seams (down the dip or along the strike).
-
Find the limiting maximum technically possible vertical height of the level \((h_t)\) for each seam of the suite. In doing so, special account should be taken of the proximity of seams, the mining systems adopted for use, the directions of advance of the stoping faces, and also the tendency of the coals to spontaneous combustion (in terms of observing the periods for preventive siltation of worked-out areas).
-
Determine by economic calculation the optimum height of the level for each seam or its individual section, taking into account the mining system adopted for use.
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Determine the optimum vertical height of the level \((h_0)\) for the entire suite of steeply dipping seams, using the calculation method presented in Table 1.
-
Check whether the optimum height of the level thus determined satisfies the established annual production capacity of the mine. For the check, the following formula may be used:
\[ h_A = \frac{A}{ \dfrac{L_1 P_1 C_1}{\sin \alpha_1} + \dfrac{L_2 P_2 C_2}{\sin \alpha_2} +\ldots+ \dfrac{L_n P_n C_n}{\sin \alpha_n} }, \tag{5} \]
where \(h\) is the vertical height of the level, m;
\(A\) is the established annual production capacity of the mine, t;
\(L_1, L_2 \ldots L_n\) is the rate of advance of the stoping faces on seam No. \(1, 2, \ldots n\), m/year;
\(P_1, P_2 \ldots P_n\) is the productivity of seam No. \(1, 2, \ldots n\), t/m\(^2\);
\(C_1, C_2 \ldots C_n\) is the coal extraction coefficient for seam No. \(1, 2, \ldots n\);
\(\alpha_1, \alpha_2 \ldots \alpha_n\) is the dip angle of seam No. \(1, 2, \ldots n\).
- Check whether the optimum height of the level thus determined satisfies the timely preparation of this level for stoping operations.
Initial assumption:
\[ t_{\mathrm{er}} = t_{\mathrm{pe}} + t_r, \tag{6} \]
where \(t_{\mathrm{er}}\) is the calculated service life of a level, years;
\(t_{\mathrm{pe}}\) is the time required to prepare the level for stoping operations, years;
\(t_r\) is reserve time, years.
But
\[ t_{\mathrm{er}} = \frac{Z_e}{A}. \tag{7} \]
\[ Z_e = \frac{P_1 C_1}{\sin \alpha_1} + \frac{P_2 C_2}{\sin \alpha_2} +\cdots+ \frac{P_n C_n}{\sin \alpha_n} \, h_n S. \tag{8} \]
Whence
\[ h_n = \frac{(t_{\mathrm{pe}}+t_r)A} {\left( \frac{P_1 C_1}{\sin \alpha_1} + \frac{P_2 C_2}{\sin \alpha_2} +\cdots+ \frac{P_n C_n}{\sin \alpha_n} \right)S}, \tag{9} \]
where \(Z_e\) is the commercial reserves of the level, \(t\);
\(h_n\) is the vertical height of the level that ensures the conditions for the timely preparation of this level for stoping operations, \(m\);
\(S\) is the length of the mine field along the strike, \(m\).
Plotting the extreme limiting values of the heights of levels \((h_A, h_n, h_t)\) on the graph strictly delimits the area of investigation for the economic comparison of variants (Fig. 1). Thus, the propose-
Labels visible in the figure: \(h_n\), \(h_t\), \(h_A\), “area \(h_0\),” \(\alpha_1(\min)\), \(\alpha_2(\min)\), \(\alpha_3(\min)\), \(\alpha_4(\min)\), \(\alpha_1\), \(\alpha_2\), \(\alpha_3\), \(\alpha_4\), \(h_3\), \(h_t\), \(h_n\), \(h_0\), \(m n\), and \(\sum^n P C \alpha / \sin \alpha\).
Fig. 1. Determination of the optimum vertical height of a level for a suite of closely spaced steeply dipping seams.
… the basic principles of the method for determining the level height for mining a suite of steeply dipping seams simultaneously as a complex combine elements of the variant method and elements of analytical and graphical calculation methods. In scientific terms, this method is new, since it simultaneously takes into account: a) the complex of seams making up the suite; b) the complex of mining systems intended for use, and the share of their participation in stoping production; c) the established production capacity of the mine; d) the time required to prepare the lower-lying level. Its practical significance consists in the fact that the method makes it possible, for specific sections, to find such a level height as would provide conditions for achieving a lower cost of producing 1 t of coal and higher labor productivity for the level as a whole.