RESULTS OF CALCULATING THE OVERALL STABILITY OF THE PIT WALL OF THE FIRST BARANDATSKY OPEN PIT AT THE ITATSKOYE DEPOSIT

F. P. NIFANTOV, V. E. OLKHOVATENKO

(Presented by the scientific seminar of the Department of Hydrogeology and Engineering Geology)

The Itatskoye brown-coal deposit is one of the largest in the Kansk-Achinsk basin. On its territory it is planned to construct a number of large coal open pits with a capacity of 40–60 million tons of coal per year. In this connection, the problem of the stability of rocks in the walls of the future open pits acquires special significance. To resolve this problem, the Department of Hydrogeology and Engineering Geology of the Tomsk Polytechnic Institute, under an agreement with the Kuzbassuglegeologiya trust, carried out engineering-geological investigations on the territory of the First Barandatsky sector. In the course of the investigations, the engineering-geological properties of the rocks, their composition, and their textural and structural features were studied. Particular attention was devoted to investigating the density and strength of the rocks, which is necessary for calculating the stability of the walls of the projected open pits. The arithmetic mean values of the strength characteristics and unit weight of the rocks of the First Barandatsky sector are given in Table 1.

It is evident from the table presented that the Quaternary deposits and Cretaceous argillites are less strong. Jurassic sandstones, argillites, and siltstones are characterized by similar values of the angles of internal friction and cohesion.

Selection of the calculation scheme

At present there are many calculation schemes and methods for determining the stability of slopes and escarpments. The most substantiated of them are the methods of V. V. Sokolovsky and S. S. Golushkevich [3, 10, 11]. However, these methods require cumbersome computations and are little used in practice. Later the method of V. V. Sokolovsky was simplified by a number of authors [2, 5, 6], which makes it possible to determine comparatively quickly the shape of the surface of an equal-strength slope.

The second group consists of the methods of Prof. N. V. Ornatsky and Prof. N. M. Tsimbarevich, in which a planar slip surface is assumed, which is one of the shortcomings of these methods.

Among the methods of calculation by a circular-cylindrical slip surface, the methods of Fellenius and others are most widely used. The methods of this group are described in detail in the work of R. R. Chugaev, who, on the basis of their analysis, proposes his own method for calculating slope stability [15].

For slopes composed of heterogeneous rocks, the method of L. N. Bernatskii and the modified method of Yu. K. Malyushitskii [1, 5] are proposed, although G. L. Fisenko does not recommend applying the latter to deep open pits (more than 50–60 m); at the same time, for open pits up to 50–60 m deep this method gives quite satisfactory results.

Table 1

Values of the strength characteristics of the rocks of the First Barandatsky site

The simplest of all existing calculation methods are the methods of N. N. Maslov and M. N. Troitskaya, which are based on calculating slope angles from shear angles. Despite the simplicity of the calculations, the latter have no mathematical justification and are used as preliminary ones.

The principal drawback of many of the listed and other methods is that the rock mass is considered as an isotropic medium, whereas under natural conditions sedimentary rocks are more often anisotropic.

A special group of methods consists of the calculation schemes of the All-Union Scientific-Research Mine Surveying Institute (VNIMI), which to a considerable extent take into account the structural features and anisotropy of rocks [9]. The noted schemes were developed for various conditions of slope structure. Thus, for example, according to schemes I and II, the limiting height of a vertical slope composed of massive rocks is calculated, while according to schemes III and IV the stability of slopes of relatively small height is calculated when beds and weakening surfaces dip toward the excavation. The most acceptable for the conditions of the Barandatsky open pits of the Itatskoye deposit, evidently,

evidently, will be the fifth scheme, according to which the calculation is carried out when the strata dip gently or horizontally, and when the shear resistance of the rocks along bedding differs little from the shear resistance of the rocks along planes cutting the rock at an angle to, or normal to, the bedding.

Of the other methods for calculating slope stability, for the conditions of the Barandatsky open pits the method of a multilayer slope using the tables and graphs of I. S. Mukhin and A. I. Sragovich should also be considered suitable.

Below are presented the results of calculating the overall stability of the working wall of the future open pit by the selected methods for a depth of 140 m along exploration lines 71, 100, and 109, under the condition of complete preliminary drainage of the rocks in the walls and slopes of the future open pit.

As the initial characteristics, the arithmetic mean values of unit weight, angle of internal friction, and cohesion of the rocks were taken (Table 1). The latter, as the results of the investigations showed, differ only slightly from the guaranteed minimum values, which gives grounds for using them as design values at this stage of the investigations.

Calculation of the overall stability of the wall of the planned open pit

According to the fifth calculation scheme of VNIMI, when calculating the overall stability of the walls of open pits composed of gently dipping strata toward the rock mass, the slip surface will pass in its upper part at an angle to the bedding, and in its lower part along the bedding of the rocks [9].

The magnitude of structural weakening of the rocks in calculations of open-pit walls is usually determined by the possible decrease in the value of rock cohesion in the mass according to the formula:

\[ K_{\mathrm{m}}=\frac{K_0}{1+a\ln(H/l)}, \]

where \(K_{\mathrm{m}}\) is the cohesion of the rock in the mass, t/m\(^2\);
\(K_0\) is the cohesion of a monolithic rock specimen, t/m\(^2\);
\(H\) is the total height of the wall, m;
\(l\) is the linear size of rock blocks bounded by cracks;
\(a\) is a coefficient depending on the nature of the fracturing of the rocks.

For the rocks investigated, which have cohesion \((K_0)\) less than 4 kg/cm\(^2\), according to VNIMI data the value of \(a\) may be taken as zero [9]. On this basis and according to the formula given above, the cohesion of the rock in the mass is taken equal to the cohesion of the rock in the lump, and the coefficient of structural weakening is taken equal to unity.

Taking this condition and the stage of investigation into account, in the calculations we shall use the weighted-average values of the design characteristics over the entire depth of the future open pit, given in Table 2.

Taking the data of Table 2 and the stability safety factor equal to 1.3, we obtain the final design values of the angle of internal friction and cohesion of the rocks (Table 3), according to which the calculations by the fifth VNIMI scheme were carried out.

The limiting height of a vertical slope is calculated by the formula:

\[ H_{90}=\frac{2\tilde{C}_{\mathrm{p}}}{\gamma}\cdot \operatorname{ctg}\left(45-\frac{\varphi_{\mathrm{p}}}{2}\right), \]

where \(H_{90}\) is the limiting height of a vertical slope, m;

\(\tilde c_{\mathrm{p}}\) is the calculated value of cohesion, t/m\(^2\);

\(\gamma\) is the weighted-average value of unit weight, t/m\(^3\);

\(\varphi_{\mathrm{p}}\) is the calculated value of the angle of internal friction in degrees.

Substituting the calculated characteristics into the above formula, we obtain a value of \(H_{90}\) equal, for line 71, to 5.72 m; for line 100, 5.2 m; and for line 109, 5.8 m.

Table 2

Table 3

Using the graph of the dependence of the wall inclination angle on depth (Fig. 1), proposed by VNIMI, we determine the scale of the graph and, through it, express the specified slope height. Then, from the graph, the wall inclination angle is determined for the given calculated angle of internal friction and specified slope height. Next, the graphical construction of the slope and check calculations are carried out; these reduce to finding the limiting height of a stable slope for the specified inclination angle and the calculated values of \(\varphi\) and \(c\). After performing the calculation for various depths, a graph is constructed of the dependence of the wall inclination angle on height. The calculation results are given in Table 4, from which it is seen that the overall wall inclination angle at a pit depth of 140 m and a safety factor of 1.3 is 29–31°.

Calculations by the method of a multilayer slope, using the graphs and tables of I. S. Mukhin and A. I. Sragovich [6], reduce to the following. The rock mass is divided into a number of computational layers, for which the calculated values of the angle of internal friction and cohesion are determined. Then, for each layer, the average unit weight of the rock is calculated, taking into account the overlying rocks. Next, using the graph for determining the coordinates of equal-strength slopes (Fig. 2), for the specified value of \(x\) and the angle of internal friction we find \(y\) and convert the coordinates to real conditions by the formulas:

\[ x=\frac{c}{\gamma}\cdot \bar{x}; \qquad y=\frac{c}{\gamma}\cdot y, \]

Fig. 1. Auxiliary chart for calculations of slope stability in slopes composed of homogeneous rocks (compiled by G. L. Fisenko)

Fig. 2. Shapes of equal-strength slopes in limiting-stressed homogeneous masses at \(\gamma = 1\), \(c = 1\), and various values of \(\varphi\) (after I. S. Mukhin and A. I. Sragovich)

Table 4

Calculated indicators and results of calculating the stability of the wall of the First Barandatsky open pit

Line 71

Itatsky seam

Line 109

Itatsky seam

Line 109

Itatsky seam

Fig. 3. Results of calculation by the method of a multilayer slope.
I — curve of the stable slope at a safety factor \(n = 1.0\); II — curve of the stable slope at a safety factor \(n = 1.3\); 1 — loams; 2 — clays; 3 — Cretaceous argillites; 4 — Jurassic aleurolites; 5 — Jurassic sandstones; 6 — Jurassic argillites; 7 — brown coal.

where \(x\) and \(y\) are coordinates for constructing the shapes of equal-strength slopes;
\(c\) is the cohesion of the rocks, t/m\(^2\);
\(\gamma\) is the unit weight of the rocks, t/m\(^3\).

The results of the calculations are shown in Fig. 3 and given in Table 4. It is evident from the table that the pit-wall inclination angles obtained by this method, with a stability safety factor of 1.3, are: for Quaternary clays, 40–43°; Quaternary loams, 39°; Cretaceous argillites and siltstones, 24–27°; Jurassic siltstones, 24–29°; Jurassic argillites, 25–26°; Jurassic sandstones, 27–31°; and brown coals, 32–33°. For many types of rocks in the overburden sequence, the slope angles calculated by both methods proved to be close. The exceptions are the angles obtained for the Quaternary sequence and for shallow-lying Jurassic argillites, where the discrepancies proved significant (Table 4).

The high slope angles for the Quaternary sequence (39–43°) obtained by the multilayer-slope method should evidently be regarded as improbable. Therefore, in the course of designing the open pit, for these deposits and for the weathered zone of Jurassic and Cretaceous rocks, the overall pit-wall slope angle should be taken as no greater than 30°, as obtained from the VNIMI calculation scheme.

During the period of detailed investigations and calculations at the stage of preparing the design assignment and working drawings for the open pit, special attention must be given to studying the properties of weakened rocks, in particular silts and interbeds of coaly argillites; to determining the degree of variability of strength characteristics in the pit walls; and to carrying out more complete calculations of wall stability, taking into account the action of all natural and mining-engineering conditions that affect the stability of rocks in the walls and benches of the open pit.

REFERENCES

1. L. N. Bernatskii, Conditions of Stability of Earth Masses. Transizdat, 1925.

2. N. I. Golovanov. Stability of slopes of earth structures according to the theory of limiting equilibrium. Collection of Works of IGDA, Ukrainian SSR, No. 4 (13), 1956.

3. S. S. Golushkevich. The Plane Problem of the Theory of Limiting Equilibrium of a Granular Medium. Gostekhizdat, 1948.

4. P. I. Kozhevnikov. On calculations of slopes for stability. In: Collection of Articles of Glavshakhtoproekt–Tsentrgiproshakht, Ministry of Coal Industry of the USSR. Open-Pit Mining of Coal Deposits. Ugletekhizdat, 1955.

5. Yu. N. Malyshevskii. Conditions of Stability of Pit Walls. Kiev, 1957.

6. I. S. Mukhin, A. I. Sragovich. Construction of Limiting Contours of Equal-Stable Slopes. Akademizdat, 1954.

7. M. L. Rudakov, A. P. Li. Physico-mechanical properties of rocks and wall inclination angles of certain open pits in Kazakhstan. Proceedings of PGI, Ural Branch of the Academy of Sciences of the USSR, issue 57, 1961.

8. M. L. Rudakov, I. I. Popov, A. P. Li. Prevention of Landslides in Open Pits. Gosgortekhizdat, 1960.

9. Guidelines for Determining Optimum Inclination Angles of Pit Walls and Waste-Dump Slopes. VNIMI Publishing House, 1962.

10. V. V. Sokolovskii. Plane limiting equilibrium of rocks. Proceedings of the Academy of Sciences of the USSR, Department of Technical Sciences, No. 9, 1948.

11. V. V. Sokolovskii. Statics of a Granular Medium. Akademizdat, 1942.

12. G. L. Fisenko. Determination of Slope Angles of the Walls of the Korkino Coal Open Pits. Ugletekhizdat, 1953.

13. G. L. Fisenko. Stability of the Walls of Coal Open Pits. Ugletekhizdat, 1956.

14. N. M. Tsimbarevich. Mechanics of Rocks. Ugletekhizdat, 1948.

15. R. R. Chugaev. Calculation of the Stability of Earth Slopes and Concrete Dams on a Rock Foundation by the Method of Circular-Cylindrical Surfaces. Gosenergoizdat, 1963.