SOME RESULTS OF APPLYING THE METHOD OF GEOMETRIC ANALYSIS OF DISJUNCTS TO THE SEARCH FOR A DISPLACED WING OF A SEAM IN THE PROKOPYEVSK AREA OF KUZBASS

A. A. BELITSKY

Foreword

The present work was written in 1941 and accepted for publication in the Proceedings of the Institute, but for many reasons it has not been printed until now. Despite the fact that nine years have already passed, this work has not lost its relevance at the present time. During this period the method we developed for searching for the displaced wing of a seam was successfully applied by geologists of the Prokopyevsk area of Kuzbass, especially by V. A. Azimov, F. S. Denisov, and A. S. Zabrodin. Many years of experience in applying this method in the Prokopyevsk area enabled A. S. Zabrodin, first, to propose solutions of problems on a stereographic net, and second, to develop an original geometric classification of disjuncts. A. S. Zabrodin reported the results of his investigations at a meeting of mine geologists of the Kuzbassugol Combine in 1948.

It should be noted, however, that in recent years disjuncts of the reverse-fault type have been discovered in certain mines of the area, for which our method proved inapplicable. Yet this fact cannot diminish the significance of our method in general, and in particular for the Prokopyevsk area, since it concerns a small number of cases among many hundreds of correctly deciphered disjuncts. In addition, this work, in our opinion, is also of interest in connection with certain other questions of mine tectonics that are raised here incidentally and partially resolved. We are therefore convinced that the publication of this work will be of some benefit to the mine geologists of Kuzbass, as well as to the correct understanding of certain questions of the tectonics of the Prokopyevsk area.

Introduction

In coal basins with a complex structure, one of the important questions of mine geology is the search for the displaced wing of a seam. In such areas of Kuzbass as Prokopyevsk, Kiselevsk, Anzhersk, and others, owing to complex tectonics, mine workings encounter ruptures of seams almost daily. With the great variety of forms of disjuncts and the absence of simple regularities in their manifestation, each new disjunct requires an individual approach. If, at the same time, there are no reliable indications that make it possible to determine in what direction the seam has been displaced, then the mine working often comes to a halt for an indefinite time. The stoppage of a mine working because of the loss of a seam

coal greatly complicates exploitation of the deposit, forces the work plan to be rebuilt as operations proceed, and leads to irrational expenditures of funds.

Despite the obvious urgency of this question, a method for searching for the displaced wing of a seam has still hardly been developed. This can partly be explained by the fact that geologists began to engage systematically in mining geology proper only in the last ten to fifteen years. Before that, questions of mining geology at mines were dealt with almost exclusively by mine surveyors; it is therefore not surprising that in the mine-surveying literature, in textbooks and in individual works on mine geometry, much attention is devoted to the geometric analysis of disjuncts, and questions of searching for the displaced wing of a seam are also partly touched upon.

However, although mine surveyors have long been engaged with these questions (Gausse’s first classification of displacements appeared in 1903), their method for searching for the displaced wing of a seam also proved insufficiently developed, since the various rules for searching for the displaced wing of a seam set forth in mine geometry are valid only for simple disjuncts, in which the wings moved relative to one another either along the line of dip or along the line of rise of the displacer; such disjuncts, as is known, are encountered very rarely.

The principal shortcoming of the mine geometers, which prevented them from developing a more reliable method for searching for the displaced wing of a seam, is that, having become engrossed in geometry, they became detached from geology, forgetting that every disjunct is the result of a very complex tectonic process. Analyzing a disjunct apart from this process, considering it only as a geometric form, and thus tearing the particular away from the general—from the causes that give rise to this particular—they were compelled to base their analysis not on the direction of displacement of the wings of the disjunct relative to one another, but on the displacement, which they regard as the final result of movement.

It would be wrong, however, to assert that mine geometers completely ignore the relative direction of movement and do not understand its significance. On the contrary, where they succeed in determining this direction by a purely geometric route, they use it successfully to solve a number of practical problems, including the search for the displaced wing of a seam. Thus, in mine geometry the relative direction of movement is determined by a purely geometric route for translational cylindrical and complex displacements.

However, the geometric method of determining the direction of relative movement of the wings of a disjunct for the search for the displaced wing of a seam has very limited application, since in most cases in highly dislocated deposits—such as, for example, the Prokopyevsk and Kiselevsk deposits in Kuzbass—the most difficult task is the search for the displaced wing of a seam for a disturbance first encountered by a mine working, when the seam is known to us only on one side of the displacer, and the displacer itself can be studied only at one point, in the plane of the face. In such cases it is impossible to determine the relative movement of the wings of the disjunct by a geometric route, for even if this disturbance is a translational cylindrical one, knowing it only at one point, we shall be forced to approach it as a properly translational displacement.

As is known, in addition to the very limited geometric method, there exists a geological method, broader in its possibilities, for determining the relative direction of movement of the wings of disjuncts. This method, described in a number of works on structural geology [6; 9], consists in studying the surface of the displacer, on which, during move-

...of the wings relative to each other, the harder particles of the rock leave traces of their movement in the form of scratches, striations, grooves, and furrows. These traces of displacement, often observed on the surface of a fault and known under the general name of slickensides, may under certain conditions indicate the relative displacement of the wings of disjunctives.

This method is also known to mine surveyors, but they make almost no use of it. The reason is that, in their opinion [2; 3; 15], slickensides can be found only in rare cases. In addition, many still believe that even when slickensides can be found on the surface of a fault, it is almost entirely impossible to determine from them the relative direction of displacement, since the usually recommended method for this purpose—stroking the mirror of sliding by hand—does not in most cases give positive results.

That is why mine surveyors did not make relative displacement of the wings the basis of their analysis, and did not use it in searching for the displaced wing of a seam, although as early as 1907, as we shall see below, D. V. Frost [16] formulated a rule for finding the displaced wing of a seam for those cases in which the slickensides and the relative displacement of the wings of the disjunctives are known.

In 1935 a work by Prof. I. A. Molchanov [7] appeared in print. This work presents a geometric analysis of translational disjunctives, with the analysis based on the relative displacement of the wings of the disjunctives. This made it possible for the author of the present article to develop a new method for finding the displaced wing of a seam for such disturbances as are first intersected by a mine working, when the seam is known only on one side of the fault, and the fault itself is known only at one point, in the plane of the face.

In proposing this method, contrary to the opinions of mine surveyors, we considered that slickensides on fault planes can in most cases be found comparatively easily. But this is not all. If one does not confine oneself within the comparatively narrow limits of geometric analysis, but carries it out in close contact with, and on the basis of, already established geological regularities of a deposit or even of an entire basin, then, as it turns out, one can easily determine from the slickensides the relative direction of displacement, without resorting to the dubious method of stroking the mirror of sliding by hand.

An example of such a possibility is Kuzbass, where Acad. M. A. Usov [10; 11; 12; 13; 14] and a number of other researchers, as a result of studying the tectonics of the basin, came to the unanimous opinion that it is the consequence of tangential forces and therefore can only be reverse-fault in character. If we use this conclusion, it is clear that a striation found on the surface of a fault will also indicate the relative displacement of the wings, since we shall know in advance that the general movement of the wings of the disjunctives was only upward. If, however, we know the striation and are able from it to determine the relative direction of displacement, then the search for the displaced wing of a seam for newly encountered disturbances, when the seam is known only on one side of the fault, becomes the simplest problem, which can be solved in two ways.

1. Graphical method. For this purpose we depict the known wing of the seam and the fault in projections with numerical marks (Fig. 1). Then we superpose the plane of the fault \(ST\) on the plan and also find the superposed position of the line of intersection of the seam with the fault \(AA_1\). For this we use the method of rotating planes, known in descriptive geometry. As the axis of rotation we take the strike line of the fault \(ST\). The projection of any point belonging to the rotating pla-

the plane, upon rotation, will move along a line perpendicular to the axis of rotation. Therefore point \(A_1\) must move along the line \(A_0A_2\), perpendicular to the axis of rotation \(ST\), and when the plane of the fault is brought into coincidence with the plan it will occupy the position \(A_0\) at a distance from the axis equal to \(A_2A_0 = OK\). Thus we obtain the coincident position of the line of intersection of the seam with the fault, \(AA_0\), and of the plane of the fault, \(S_0T_0\).

Fig. 1

If now, knowing in advance the direction of relative displacement of the wings of the disjunctive dislocation at point \(A_0\), we draw a striation line at the angle known to us, then, obviously, the latter must indicate the direction in which to search for the displaced wing of the seam. If the striation lies between the lines \(AA_0\) and \(A_0T_0\), then the two wings form a gaping of the seam. If, however, the striation lies between the lines \(AA_0\) and \(A_0S_0\), then they form a doubling of the seam.

D. V. Frost [16], having this graphical construction in mind, as early as 1907 formulated the following rule for searching for the displaced wing of a seam: “the line of exploration and the line of intersection of the known part of the deposit with the fault will always be located on different sides of the slip line (the dip of the fault).” And indeed, if we examine projections with numerical elevations of normal faults (Fig. 2a) and reverse faults (Fig. 2b), it becomes clear that this rule is valid for any form of disjunctive dislocation.

Thus, for disjunctive dislocations on whose fault surfaces striation can be detected and the relative direction of displacement of the wings determined, D. V. Frost provided a comparatively simple graphical solution for searching for the displaced wing of a seam. However, as was already noted above, since it was considered difficult to detect striation and even more difficult to determine from it the relative direction of displacement of the wings, mining geometers in their practical work did not use this method, although it is appropriate to note here that in Kuzbass, for a long time, major specialists in mining geometry worked who dealt with the geometrization of a number of mine fields, the search for displaced wings of seams, and repeatedly conducted special courses in mining geometry for mine surveyors and geologists.

Fig. 2

1. The direction in which to search for the displaced wing of the seam under these conditions can also be determined by an analytical method, using the formulas of Prof. I. A. Molchanov.

Let us write down Prof. I. A. Molchanov’s formula, somewhat modified by us, for a complex diagonal disjunctive fault:

\[ l=H\left(\operatorname{ctg}\alpha+\operatorname{ctg}\beta\cos\omega \pm \frac{\operatorname{ctg}\gamma\sin\omega}{\sin\beta}\right), \tag{1} \]

where \(l\) is the apparent horizontal displacement of the seam, measured across its strike (Fig. 3). This quantity may be positive or negative; the following sign convention must be observed. The quantity \(l\) is always to be measured in the direction from the footwall wing of the seam toward the hanging wall; if this direction coincides with the dip of the seam, take the sign \((+)\); if it does not coincide, take the sign \((-)\). \(H\) is the vertical height of displacement; \(\alpha\) is the angle of dip of the seam; \(\beta\) is the angle of dip of the fault; \(\omega\) is the angle of intersection of the seam and the fault in plan. But since, when the seam and the fault meet in plan, two adjacent angles are formed, let us agree that for this angle we shall always take the vertex of that angle with respect to which the arrows indicating the dip of the fault and of the seam are directed toward one another. \(\gamma\) is the angle between the strike of the fault and the stroke (Figs. 4a and b). Here also there will be two adjacent angles. Let us agree to measure this angle from the hanging-wall side of the fault (Fig. 4a) counterclockwise, and from the footwall side (Fig. 4b) clockwise.

Fig. 3

Fig. 4

As for the sign before the third term on the right-hand side of formula (1), the following rule must be observed. If we turn the disjunctive fault shown on the plan so that the fault dips toward us, then, in the case where the seam dips to the right, the sign \((+)\) must be taken; if it dips to the left, the sign \((-)\) must be taken.

Analyzing formula (1) as applied to various forms of disjunctive faults, one may note that a positive value of \(l\) for conformable reverse faults corresponds to those disjunctive faults in which the wings, upon displacement, form a duplication of the seam (Fig. 3), while for nonconformable faults it corresponds to a gap in the seam (Fig. 5). If the value of \(l\) is negative, then, conversely, for conformable reverse faults there will correspond a gap in the seam (Fig. 6), and for nonconformable faults—a duplication of the seam (Fig. 7).

This dependence between the sign of \(l\) and the relative position of the wings with respect to one another is the basis for applying formula (1) in the search for the displaced wing of a seam. Indeed, if we are dealing with reverse faults, then the value \(H\) will always be positive,

and, consequently, depending on the sign before the quantity \(l\), the expression in parentheses must be either positive or negative. On the other hand, knowing the values of the angles \(\alpha, \beta, \omega\), and \(\gamma\), and substituting them into the expression in parentheses in formula (1), we can determine the sign of this expression and thereby determine the sign of the quantity \(l\). Knowing the sign before the quantity \(l\), we can easily determine the relative position of the wings with respect to one another.

At first glance this method appears more complicated than the graphical one. However, this is not so. For the expression in parentheses in formula (1), we have compiled a special graph (1). Using this graph, one can, without calculation, easily and simply determine the sign and absolute value of this expression. In addition, this method has the following advantages.

Fig. 5            Fig. 6            Fig. 7

1. Like any analytical method, it gives a more accurate result than the graphical method.

2. Using the analytical method, it seems possible, for each disjunctive separately, to easily verify the correctness of our conclusions, if for this purpose we take into account the errors that we permit in measuring the elements of bedding.

3. Using this method, after decoding the disjunctive, when the value of the quantity \(l\) is known, with the aid of the formulas of Prof. I. A. Molchanov we shall be able easily to calculate the vertical and inclined height of the displacement, as well as the full amplitude of the displacement.

This method of searching for the displaced wing of a seam was developed by us in 1936. Then, from 1937 to 1940, it was tested in the Prokopyevsk and partly in the Anzherka districts of Kuzbass. During this time, with the aid of this method, about two hundred disjunctives were decoded, and not a single case of an incorrect solution was recorded.

In January 1940, at a conference of mine geologists of Kuzbass, reports were heard by the chief geologist of the trust “Stalinugol,” V. A. Azimov, and the senior geologist of the mine named after I. V. Stalin, V. A. Monin, on the application of this method in the Prokopyevsk district.

In both reports this method was given a positive evaluation. The general opinion was that, under Kuzbass conditions, in the presence of sharply expressed facies variability of the enclosing rocks both in vertical and horizontal sections, and in the absence of marker horizons, this method gives a great production effect. At the same conference, a special instruction prepared by us was adopted on applying this method to the search for the displaced wing of a seam.

Thus, it may be considered that, as a result of the application of this method in production, it has received full recognition. Therefore we consider it necessary to dwell on some results of its application.

Specific Features of the Tectonics of the Prokopyevsk Area

The Prokopyevsk area, where our method is chiefly applied, is the most complex area of Kuzbass in tectonic terms. Situated on the southwestern margin of the basin, in the immediate vicinity of the foothills of the Salair, it was subjected to very intense dislocation, as a result of which the coal-bearing sequence of the area was gathered into numerous steep folds of northwestern strike, close to meridional, complicated by a large number of disjunctives. The latter represent almost the entire range of forms of disjunctives according to the classification of Academician M. A. Usov (Fig. 8): concordant and discordant normal faults, direct and reverse thrusts, strike-slip faults, and also bedding-plane displacements.

Fig. 8

Among the large number of disjunctives in this area, one may distinguish disjunctives of the first order, which take the form of concordant and discordant normal faults with a considerable displacement amplitude. The displacers of these disjunctives have a rather steep dip and cut the rock sequence along the strike at a very acute angle of 5–10°.

In addition to these disturbances, the coal-bearing deposits are broken by a dense network of disjunctives of the second and higher orders, with a considerably smaller displacement amplitude. The forms of these disjunctives are more diverse. Among them, concordant and discordant normal faults, direct and reverse thrusts, and also strike-slip faults are widely distributed.

In most cases the displacers of these disjunctives are conjugate with the displacers of first-order disjunctives, approaching them at a more or less acute angle. They evidently arose as a result of the release of stresses that were created in the flanks of first-order disjunctives, and therefore may be regarded as their apophyses.^1

The greatest difficulty for the exploitation of the deposit, and especially for the search for a displaced wing of a seam, is presented by disjunctives of the second and higher orders. These difficulties are due to the fact that most of these disjunctives cannot be recorded during ordinary exploration of mine fields from the surface; therefore mine workings cut them quite unexpectedly. In addition, in the presence of a dense network of these disjunctives it is often difficult to establish regularities in the distribution of their forms, since, on comparatively short segments of one and the same seam, all the forms of disjunctives occurring in the Prokopyevsk area can be observed.

Consequently, such disjunctives, when cut by a mine working, present a rather complex problem that must be solved quickly and with the least expenditure of resources. Let us see how this problem was solved before the appearance of our method.

When a new disjunctive was encountered, the face was subjected to a thorough investigation. Special attention was paid to marker horizons, drag folds, and comparison of the lithological composition of the rocks

^1 Subsequently we established that the dense network of disjunctives of the second and higher orders formed as a result of the release of stresses along the planes of cleavage cracks.

in the walls of the dislocator. If it proved possible to discover guiding horizons—markers (thin coal seams occurring in the roof or floor of the seam), interbeds of iron-bearing rocks, conglomerates, horizons with flora and fauna, and so forth—then one determined not only the direction in which it was necessary to search for the displaced wing of the seam, but also, with sufficient accuracy, the amplitude of displacement. If it proved possible to discover in the face drag folds, i.e., bends of the seams near the disturbance, or to establish beyond the disturbance the rocks of the hanging or footwall side, then on the basis of these data it was easy to determine the direction of the mine working toward the displaced wing of the seam. In short, if, as a result of studying the face, some geological criterion was found that directly or indirectly indicated the direction of movement of the displaced wing of the seam, then the problem of searching for the displaced wing of the seam was solved comparatively simply.

It must be noted, however, that by no means are all these criteria equally reliable, and they are not always present when studying a disjunct in a mine working. The Kuznetsk Basin is, in general, very poor in guiding horizons, and therefore they very rarely come within the investigator’s field of view in the face. Drag folds also occur infrequently; moreover, within the small area of the face of a mine working it is sometimes impossible to detect them. As for the lithological composition of the rocks in the walls of the dislocator, owing to the sharp facies variability of the rocks of Kuzbass, this criterion can easily lead the investigator to erroneous conclusions. Therefore it has to be applied in searching for the displaced wing of a seam with great caution, and only in those cases when the rocks of the seam floor and roof differ sharply from one another and, in addition, there is confidence that, both along the strike and along the dip of the seam, they retain their composition at least over short distances.

Usually, in those cases when, as a result of a thorough study of the disjunct in the face, it is not possible to establish reliable geological criteria, recourse was had to searches for the displaced wing of the seam by means of prospecting workings—raises, small-section crosscuts, winzes, and underground boreholes. In this case, when the directions of the exploratory mine workings were assigned, it was assumed that all disjuncts are simple, i.e., such that the displaced wings move relative to one another either along the line of dip of the dislocator—reverse faults and normal faults—or along the line of strike of the dislocator—strike-slip faults.

Such an approach to disjuncts opened up great possibilities for searching for the displaced wing of a seam. It was enough to determine the form of the disjunct in the face, since from the geometric mutual arrangement of the wings of disjuncts it is easy to find the displaced wing of the seam. Academician M. A. Usov repeatedly pointed to this possibility. In one of his remarkable works on the mine tectonics of Kuzbass [11] he writes: “Concordant reverse faults are very convenient from an industrial standpoint, for in both vertical and horizontal section the seam appears duplicated over a certain extent, which increases the coal reserves; moreover, searches for the displaced wing of the disturbance present no particular difficulties and can be carried out on the same horizon where the seam was cut by a crosscut, in the shortest direction to the other side of the fracture.”

P. F. Krasnikov most clearly formulated the search for the displaced wing of a seam on this basis; in his work on the Prokopyevsk region [4], characterizing a concordant reverse fault, he wrote: “This form is characterized by the fact that the dislocator dips in the same direction as the seam or suite intersected by it, having, in comparison with the seam, a steeper dip… Both in vertical transverse and in horizontal

sections of the seam wing overlap one another, which is why this form of dislocation is very convenient for exploitation.

In connection with this, it should be noted that the search for the other wing of a conformable fault presents no special difficulties and may be carried out as follows.

1. Smooth truncation by a fracture dipping more steeply than the seam indicates a conformable fault as the most probable form of the encountered disturbance.

2. Having proceeded along the seam intersected by the fault plane to the end of the truncation of the seam, one must go by crosscut to the other side of the fracture in order to find, in the shortest direction, the displaced wing of the seam.

In a similar way he formulates the rules for searching for the displaced wing of a seam also for the other disjunctives.

It should be noted, however, that even with such a simplified and, as we shall see below, quite incorrect conception of the character of the movement of the wings of disjunctives in Kuzbass, and especially in the Prokopyevsk area, this method of searching for the displaced wing of a seam could be applied only to faults, since conformable and nonconformable faults are easily distinguishable in the face. As for direct and reverse thrusts, even in this case it was impossible to apply this method to them, since from the relationship between the elements of the attitude of the seam and of the displacement plane it is impossible to distinguish a direct thrust from a reverse one. Both these forms of disjunctives, as is known, are characterized by conformable dip of the seam and the displacement plane; moreover, in both direct and reverse thrusts the displacement plane has a gentler dip than the seam.

The verification and application of our method have shown with complete obviousness that in Kuzbass, and especially in the Prokopyevsk area, we are dealing not with simple but with complex disjunctives, in which the displaced wings have moved relative to one another in an arbitrarily inclined direction. Such disjunctives are more correctly called not faults and thrusts, but fault- or thrust-slip displacements, since here the total amplitude of displacement \(R\) (Fig. 9) can be resolved into two elements: \(h\)—the fault element—and \(\lambda\)—the slip element. It is obvious that the absolute magnitudes \(h\) and \(\lambda\) will depend on the value of the angle \(\gamma\). The closer the angle \(\gamma\) approaches \(0\) or \(180^\circ\), the more the slip element \(\lambda\) will increase, while the fault element \(h\) will decrease. Conversely, the closer the angle \(\gamma\) approaches \(90^\circ\), the more the slip element \(\lambda\) will decrease and the fault element \(h\) will increase.

Fig. 9

Among our numerous observations, only a few cases have been recorded by hatching where the angle \(\gamma\) exceeded \(45\text{–}50^\circ\) or was less than \(130\text{–}135^\circ\). In most cases the value of the angle \(\gamma\) varied within the limits \(10\text{–}50^\circ\) and \(170\text{–}130^\circ\). Thus the slip element almost always predominated over the fault element. It is clear that, for such values of the angle \(\gamma\), irrespective of the form of the disjunctive, the position of the wings relative to the displacement-plane line will be influenced by the direction of displacement of the seam wings.

Let us examine this with an example. Suppose that the encountered disturbance has the elements of attitude of a conformable fault (Fig. 10). If, in this case, the angle \(\gamma = 90^\circ\), then we shall have a simple conformable fault and, consequently, the displaced wing of the seam should occupy position \(MM\). Here the magnitude of the apparent horizontal displacement \(l\) at the given horizon is formed...

only at the expense of the upthrow element, and it is obvious that, for one and the same value of the vertical height of the disjunctive fault, the value \(l\) will depend on the dip angle of the seam.

If the angle \(\gamma > 90^\circ\), then here a strike-slip element already appears, and in the present case \(\lambda\) will coincide with the dip of the seam; consequently, the value \(l\) will increase still more. The displaced wing of the seam will occupy the position NN.

For a value of the angle \(\gamma < 90^\circ\), the strike-slip element \(\lambda\) will be directed to the other side, against the dip of the seam and, consequently, the value \(l\) will decrease. Here three cases are possible.

Fig. 10

1. The value of the angle \(\gamma\) is close to \(90^\circ\). The value \(\gamma\) will be insignificant. The value \(l\) still remains positive, but the duplication of the seam decreases. The displaced wing of the seam occupies the position HH.

2. The value of the angle \(\gamma\) is such that \(l = 0\). Such a form of disjunctive fault is possible in the case when the line of displacement of the seam along the dislocator coincides with the line of intersection of the seam with the dislocator; in this case there will be no visible rupture of the seam in the horizontal section. The displaced wing of the seam will occupy the position AA.

3. The value of the angle \(\gamma\) is closer to 0. Here the magnitude of the strike-slip element \(\lambda\) is so large that \(l\) becomes negative and, instead of duplication of the seam wings, a gap between them is obtained. The displaced wing occupies the position PP.

From the analyzed example of a complex concordant upthrow it is evident that, not only for thrust faults but in general for any form of disjunctive fault, it is impossible to determine the position of the displaced wing of a seam from the mutual relation of the bedding elements of the seam and the dislocator, since, depending on the value of the angle \(\gamma\), the arrangement of the seam wings may be different.

This is why the method of searching for the displaced wing of a seam based on an incorrect notion of the character of the movement of the seam wings relative to one another cannot be applied in Kuzbass, since in reality we are dealing not with simple but with complex disjunctive faults. Moreover, at present the mine geologists themselves, from their own personal experience, have already become convinced of the erroneousness of this method.

Our method, alongside reliable geological criteria, or even more so in their absence, makes it possible to solve the problem of searching for the displaced wing of a seam for complex disjunctive faults in a completely objective and, at the same time, easy and simple manner.

In the following chapter, from the numerous decoded disjunctive faults in the mines of the Prokopyevsk district, we give only the most interesting examples, which vividly illustrate the effectiveness of our method.

Some Results of Applying the Method

Our method first began to be applied in the Prokopyevsk area of Kuzbass in the summer of 1937. We began by testing it on known and previously decoded disjunctives. Examining these disjunctives, we found striations on the surfaces of the displacers, measured the angle $\gamma$ from them, and then, for the given disjunctive, established by formula (1) the mutual position of the wings of the seam relative to the displacer. In this way, during the very first month of our work at the Stalin, 3–3 bis, Molotov, and Voroshilov mines, we examined about 30 disjunctives, and in all cases there was complete agreement between our conclusions and the actual mutual position of the wings of the seam.

Already at the beginning of testing this method it became clear to us that it gives positive results, and therefore we immediately decided to apply it to the deciphering of new disturbances. For this purpose the geological department of the Stalin mine proposed that we decipher a disturbance along seam VI Inner of the western limb of the Muraveinik anticline, encountered by the main drift at the 215 m level, 150 m south of the main crosscut of the mine. This disturbance (Fig. 11) had the attitude elements of a concordant reverse fault. The strike azimuth of the displacer was $297^\circ$, the dip angle $55^\circ$; the strike azimuth of the seam was $344^\circ$, and the dip angle $45^\circ$.

Fig. 11

Before proposing this disturbance to us, the mine geologists examined it in detail at the working face. The results of this investigation did not make it possible to determine the location of the displaced wing of the seam, since the lithological composition of the rocks in the floor and roof of seam VI Inner is homogeneous, and no other geological criteria were found at the face. However, regarding this disturbance as a simple disjunctive, they came to the conclusion that there would be a duplication of the seam here and, consequently, that the displaced wing should be sought to the west of the drift face. This conclusion was also supported by borehole No. 271, which intersected seam VI Inner at this level 160 m south of the disturbance; thus, if from the point where this borehole intersects the seam the latter is projected parallel to the seam located in the footwall of the disjunctive, it will approach the disjunctive from the western side of the working face.

When we were asked to apply our method to this disturbance, the mine geologists had already formed a definite opinion as to the direction in which it was necessary to look for the displaced wing of the seam. We re-examined the disturbance, and on the surface of the displacer we found well-expressed striations. The angle $\gamma$ proved to be equal to $40^\circ$, while the angle $\omega$, taken from the mine workings plan, was $134^\circ$. Consequently, we obtained all the data necessary for the solution by formula (1). We present this solution.

Given: \(\alpha = 45^\circ,\ \beta = 55^\circ,\ \omega = 134^\circ\), and \(\gamma = 40^\circ\).

Substitute these quantities into the expression standing in parentheses in formula (1):

\[ \operatorname{ctg} 45^\circ - \operatorname{ctg} 55^\circ \cos 134^\circ - \frac{\operatorname{ctg} 40^\circ \sin 134^\circ}{\sin 55^\circ}. \]

In this case, according to our rule of signs, before the third term of this expression it is necessary to take the sign \((-)\), since, if we look at the dislocator from the side of the hanging wall of the disjunctive fault, the seam dips to the left.

Then, from the table of natural trigonometric values, we write out:

\[ \begin{aligned} \operatorname{ctg} 45^\circ &= 1.000, & \operatorname{ctg} 40^\circ &= 1.192,\\ \operatorname{ctg} 55^\circ &= 0.700, & \sin 134^\circ &= 0.719,\\ \cos 134^\circ &= -0.695, & \sin 55^\circ &= 0.819. \end{aligned} \]

We determine the numerical values of the individual terms:

\[ \begin{aligned} 1.\quad &\operatorname{ctg} 45^\circ = 1.000,\\ 2.\quad &\operatorname{ctg} 55^\circ \cos 134^\circ = 0.700(-0.695) = -0.486,\\ 3.\quad &\frac{\operatorname{ctg} 40^\circ \sin 134^\circ}{\sin 55^\circ} = \frac{1.192 \cdot 0.719}{0.819} = 1.045. \end{aligned} \]

Now, substituting these quantities into our expression, we find:

\[ 1.000 - 0.486 - 1.045 = -0.531. \]

As applied to this disjunctive fault, the expression standing in parentheses in formula (1) proved to be negative; consequently, the quantity \(l\) is also negative. We already know that a negative value of \(l\) for conformable upthrow faults corresponds to a gaping of the wings of the seam, and therefore the displaced wing of the seam must be sought not to the west, but to the east of the working face. It is clear that this disjunctive fault is not simple, but complex, with a predominance of the strike-slip element over the upthrow element; moreover, in this case the strike-slip element is directed against the dip of the seam, which caused the separation of the wings. Therefore this disjunctive fault should more correctly be called not simply a conformable upthrow fault, but a conformable upthrow–strike-slip fault.

Thus, our conclusion was directly opposite to the conclusion of the mine geologists; however, they did not agree with it and decided to drill horizontal borehole No. 82 to the west of the working face. From Fig. 11 it is seen that borehole No. 82, drilled to a depth of 32.6 m, did not encounter the displaced wing of the seam. It became clear that our solution was correct; nevertheless, the geological department of the mine decided to drill another borehole, No. 83, supposing that the seam might pass somewhat east of borehole No. 82. But borehole No. 83 as well, drilled to a depth of 22.4 m, did not meet the seam. Then nothing remained but to drill borehole No. 85 east of the working face, which, after 6 m, cut the displaced wing of the seam.

Thus, owing to an entirely incorrect idea of the nature of the movement of the wings of disjunctive faults relative to one another, funds were wasted on drilling two boreholes, delaying the working face for more than a month, whereas our method immediately indicated the correct direction in which the displaced wing of the seam had to be sought.

Among the large number of our observations in the Prokopyevsk district of Kuzbass there are many cases similar to the disjunctive fault analyzed here, when, owing to the movement of the hanging wall of the disturbance against the dip of the seam, a conformable upthrow fault produces gaping instead of duplication of the seam, and a nonconformable upthrow fault produces duplication of the seam instead of gaping. In the latter case, by our method it is likewise easy to find the displaced wings of the seam.

Thus, in the Voroshilov Mine, in the Burnt seam of Mine No. 5-North, several disjuncts with elements of occurrence of an oblique reverse fault were encountered by an adit. In one of these disjuncts (Fig. 12a) we discovered striation; the measured angle \(\gamma\) proved to be equal to \(20^\circ\). The strike azimuth of the displacer of this disjunct was \(210^\circ\). The dip angle

Fig. 12

of the displacer was \(48^\circ\). The strike azimuth of the seam was \(150^\circ\), and the dip angle of the seam was \(52^\circ\). Thus, we obtained all the data necessary to determine the direction in which to search for the displaced wing of the seam by formula (1).

Given: \(\alpha = 52^\circ,\ \beta = 48^\circ,\ \omega = 50^\circ,\ \gamma = 20^\circ\).

As in the first case, after carrying out all the necessary calculations, we obtain

\[ 0.781 + 0.579 - 2.820 = -1.460. \]

Consequently, the expression standing in the brackets of formula (1) has turned out to be negative; this means that the value \(l\) will also be negative. And we know from the preceding discussion that, for an obliquely dipping reverse-fault disturbance, a negative value of \(l\) always corresponds to duplication of the seam; therefore the displaced wing of the seam must be sought west of the working face. As can be seen from Fig. 2, our solution proved to be correct. Here, too, we are dealing not with a simple but with a complex disjunct. It would be more correct to call it an oblique reverse strike-slip fault.

From the point of view of the application of our method, a very interesting disjunct is the one reported at the conference of mine geologists of Kuzbass in January 1940 by V. A. Mosnin, senior geologist of the Stalin Mine. This disjunct was encountered by a furnace along seam VI of the Inner western wing of the “Muraveinik” anticline, 20 m up the rise of the seam from the southern main adit of the 215 m level. This disjunct had elements of occurrence of an oblique reverse fault (Fig. 13). The strike azimuth of the displacer was \(148^\circ\), the dip angle \(66^\circ\). The strike azimuth of the seam was \(242^\circ\), and the dip angle \(55^\circ\).

For this disjunct it was necessary to find the displaced wing of the seam quickly. As can be seen from Fig. 13, at the very face of the furnace a considerable turning-in of the seam toward the displacer of the disjunct was observed. In general, in the Kuzbass, turnings-in of the seam toward the displacers of disjuncts are a fairly reliable criterion for determining the direction in which to search for the displaced

wing of the seam; therefore, in this case the mine geologist had grounds for directing the working east of the furnace face, since the nature of the seam’s turning indicated precisely this direction. However, during examination of the surface of the dislocator, striation was found,

Fig. 13

on which an angle \(\gamma\) equal to \(140^\circ\) was measured. Thus it became possible to solve this disjunctive disturbance by our method as well.

Given: \(\alpha = 55^\circ,\ \beta = 66^\circ,\ \omega = 14^\circ\), and \(\gamma = 140^\circ\).

As before, we substitute these quantities into the expression standing in parentheses in formula (1), and, after carrying out all the necessary calculations, obtain:

\[ 0.700 + 0.432 - 0.315 = 0.817. \]

Thus, the expression standing in parentheses in formula (1) proved to be positive; consequently, the value \(l\) is also positive. From the preceding we know that a positive value of \(l\) for a discordant upthrow corresponds to gaping of the wings of the seam, and therefore the displaced wing of the seam must be sought west of the furnace face.

Thus two opposite conclusions were obtained. The turns of the seam toward the dislocator of the disjunctive disturbance indicated the necessity of turning the working eastward, while our method indicated westward relative to the furnace face.

This disjunctive disturbance was encountered in November 1939, when our method had already proved itself favorably on a large number of disturbances. Geologist V. A. Monin, from his own experience, had become convinced of its effectiveness; therefore he directed the furnace not to the east, but to the west, i.e., in the direction indicated by our method. As can be seen from the figure, he was not mistaken: after several meters the furnace encountered the displaced wing of the seam.

As for the turns of the seam, they were probably caused by the large disturbance JJ, which in this place, for a distance of more than 500 m along the strike, passes directly along the floor of the seam. Owing to this disturbance, the coal in the floor is strongly crumpled, and the thickness of the seam, as a result of stretching, decreased in places by more than half.

The three examples analyzed quite convincingly illustrate the significance of our method for searching for the displaced wing of a seam. But this is not its only merit. Application of this method made it possible, incidentally, to resolve and pose a whole series of very important questions concerning the nature of the tectonics of the Prokopyevsk area.

Thus, among geologists of the Prokopyevsk area there was a very widespread opinion about the presence in the area of so-called hinged disjunctive disturbances. These included, for example, the disturbance encountered by seams VI and IV Internal on the western wing of the small anticline of the Stalin Mine (Fig. 14a). This disjunctive disturbance, well traced by the main crosscuts and principal kvershlags of the mine at the 265 horizon.

and 215 m, proved interesting in that, while cutting two seams at once, it forms different types of disjunctive disturbance in each of them: in seam VI Internal—a direct thrust (Fig. 14b), and in seam IV Internal—a concordant reverse fault (Fig. 14c). From this it was concluded that somewhere between the seams, along the strike of the displacer, there is a center around which both wings turned relative to each other through a certain angle; in this process the hanging wall of seam VI Internal moved downward, while that of IV Internal moved upward.

In making this conclusion, an incorrect conception of the nature of the movement of the wings of the disjunctive disturbance relative to each other again played its negative role. The geologists regarded this disjunctive disturbance as simple, whereas in fact it proved to be complex. Moreover, owing to certain works on the mine tectonics of Kuzbass (4; 8; 11; 12; 13; 14), it was considered that a direct thrust is formed only when the hanging wall of the disturbance is lowered, whereas as early as 1936 we proved [1] that this form of disjunctive disturbance can also be formed when the hanging wall is displaced upward.

Fig. 14

Analysis of this disjunctive disturbance by our method made it possible to draw another conclusion. The fact is that the angle \(\gamma\) measured by us for seam VI Internal proved to be \(42^\circ\), and for seam IV Internal—\(20^\circ\). Consequently, in the present case the hanging wings of both seams not only rose upward, but at the same time, and to a more considerable degree, were displaced along the strike of the displacer. In this case the displacement of the hanging wing of the disjunctive disturbance took place in the direction of the dip of the seams; for this reason, in seam VI Internal a doubling of the seam resulted, although, judging from the relationship of the elements of occurrence of the seam and the displacer, in the case of a simple disjunctive disturbance a reverse thrust could have formed here, which, as we know, produces a gap in the seam.

This circumstance, too, was not taken into account by the geologists of the Prokopyevsk district. In reality, as follows from our observations by means of hatching, here there is not a hinged disturbance but an ordinary reverse-fault–strike-slip disturbance.

The application of our method, moreover, makes it possible to establish the form of a thrust in complex disjunctive disturbances, which has not only theoretical but also very great practical significance.

We have already noted that, in contrast to reverse faults, it is impossible to establish the form of thrusts from the relationship between the elements of occurrence of the seam and the displacer. In the presence of complex disjunctive disturbances, direct and reverse thrusts are also difficult to distinguish by the relative position of the wings of the seam with respect to the displacer, since, at small values of the angle \(\gamma\) and with the corresponding direction of displacement of the displaced wing of the seam, in a direct thrust a gap in the seam may form instead of a doubling, and in a reverse thrust a doubling of the seam may form instead of a gap.

Thus, the form of a thrust can be established only for simple disjunctive disturbances. In other words, if we are able, in each individual

In this case, if we reduce complex faults to simple ones and then reconstruct what the relative position of the wings of the seam with respect to the displacer must be, we shall then be able to determine the form of any disjunct, including a thrust.

This problem—the reduction of complex disjuncts to simple ones—is very easily solved with the aid of the formula for a complex diagonal disjunct already known to us.

Let us write this formula again:

\[ l=H\left(\operatorname{ctg}\alpha+\operatorname{ctg}\beta\cos\omega \pm \frac{\operatorname{ctg}\gamma\sin\omega}{\sin\beta}\right). \]

If we turn to the derivation of this formula (7), we shall see that the first two terms of the expression in parentheses characterize a simple disjunct, when displacement of the wings occurred only along the dip line of the displacer; the third term of this expression takes into account the horizontal component in the displacement of the wings in an arbitrarily inclined direction. Consequently, the first two terms of this expression will always indicate the vertical component of the movement of the wings of the fault, while the sum of all three terms will indicate the direction in which we must search for the displaced wing of the seam.

Let us examine this in a concrete example.

At the I. V. Stalin mine, in the southern main crosscut on the 215 m horizon, along the Prokopyevsky II seam of the western wing of the Golubevskaya anticline, a disjunct with elements of thrust occurrence was encountered (Fig. 15). The azimuth of strike of the displacer of this fault is 320°. The azimuth of strike of the seam is 345°. The remaining data had the following values: \(\alpha=75^\circ\), \(\beta=60^\circ\), \(\omega=155^\circ\), and \(\gamma=170^\circ\).

Fig. 15

After the calculations already known to us, we obtained the following final result:

\[ 0.268-0.523+1.156=0.901. \]

Here the sum of all three terms gives us a positive value, which corresponds, for concordant reverse faults, to duplication of the seam. Having thus established the relative position of the wings of the seam with respect to the displacer of this disjunct, as can be seen from Fig. 15, the mine working toward the displaced wing of the seam was laid out correctly.

However, the first two terms of this expression give us a negative value. This allows us to conclude that, if this dislocation were simple, i.e., if the angle \(\gamma\) were equal to \(90^\circ\), then in the present case there would be gaping of the wings and, consequently, this dislocation must be assigned to a reverse overthrust–strike-slip fault. Thus, by applying our method, one can easily determine the form of overthrusts as well.

Here it is appropriate to note that mine geologists, even in the Prokopyevsk district, still do not take into account the slip element when determining the form of overthrusts, as a result of which they often name them incorrectly. From this point of view it is necessary to revise the old determinations and establish the actual forms of the overthrusts.

Further, it should be noted that, with the aid of our method, it proved possible to demonstrate the erroneousness of distinguishing, in the Prokopyevsk district, the so-called transverse normal faults, to which the transverse disjunctives on the western wing of the “Muraveinik” anticline are usually assigned (Fig. 16).

Some geologists, for example B. S. Krupennikov, even distinguish them as a special type of disjunctives of the Prokopyevsk district. Thus, in one of

Fig. 16

his works [5], having these disjunctives in mind, he writes: “And, finally, the least studied third type of dislocations—transverse normal faults, traced both by mine workings and fixed by exploration”...

M. A. Usov [14] likewise assigns these dislocations to normal faults, and at the same time gives a very original explanation of their formation. Considering the structure of this anticline, he writes: “It is evident from the structure that, during tangential movement, the southwestern wing of the anticline and of the reverse fault was raised the most. And when, following this main onset of compression, extension followed as a natural reaction, then, being quite considerable in this phase, it was reflected first of all and chiefly on this raised wing. The latter began to slide, under the influence of its own weight, downward along the displacer of the reverse fault; and since the displacement was uneven, dying out toward the closure of the anticline, the wing was broken by transverse cracks, dipping to the south, into blocks which gradually subsided relative to one another in this direction.”

The erroneousness in the interpretation of these disjunctives also follows from an incorrect conception of the movement of the wings of the disjunctives relative to one another. If they were simple, then they could be regarded as normal-fault disjunctives. In reality, however, they proved to be complex.

Until now these disjunctives were known only from the old workings of adit No. 10 at the 265 m level. In recent years they were opened by the workings of the I. V. Stalin mine at the 215 m level, where we were able, on two displacers along Seam VI Internal, to observe clearly expressed slickensiding and to measure the angle from it. One

one of these disjuncts was encountered by the southern main drift 150 m from the main crosscut of the mine and was described by us in detail at the beginning of this chapter (Fig. 11). Another disjunct (Fig. 17) was encountered by the northern drift, 200 m from the same crosscut.

As we already know from the description of the first disjunct, the angle \(\gamma\) proved here to be \(40^\circ\); in the second it is \(50^\circ\). Thus, in both cases the horizontal component is directed opposite to the dip of the seam, as a result of which the hanging walls of these disjuncts moved not in a westerly direction, as would have been expected for a simple disjunct, but in an easterly direction. This latter circumstance was not taken into account by many geologists in determining the form of these disjuncts¹. In reality they are not faults, but reverse-strike-slip faults; moreover, the strike-slip element, as in many other disjuncts of the Prokopyevsk area, here played the leading role in the direction of movement of the wings of the disjunct relative to one another.

As a result of applying our method, one further conclusion suggests itself, extremely important both theoretically and practically. This conclusion concerns the age of that phase of tectogenesis which created the dense network of disjuncts in the Prokopyevsk area.

Fig. 17

M. A. Usov [14] distinguishes the following phases of tectogenesis that took part in forming the present structure of Kuzbass: Sudetic, Asturian, Saalian, Austric, Pfalzian, Lower and Upper Kimmerian, Laramian, and Rissian. The first four phases, being the earliest, manifested themselves very weakly and therefore were almost not reflected in the folded structure of the basin. On the contrary, the subsequent phases played the leading role. Thus, M. A. Usov [14] writes that “the folded structures of Kuzbass were formed in two principal phases of tectogenesis: the Pfalzian and the Upper Kimmerian,” and then “in the subsequent powerful Laramian phase of tectogenesis the folds in the weaker and more mobile zones, chiefly along the western periphery, were twisted out.”

Then M. A. Usov notes that later phases of tectogenesis also manifested themselves in Kuzbass, among which the Rissian phase was the most sharply expressed.

M. A. Usov links the formation of tangential disjuncts with the folded structure; at the same time he indicates that some of them were initiated in earlier phases, but that they were formed chiefly in connection with the twisting-out of folds in the Laramian phase.

Thus, the tectonic history of Kuzbass was extremely complex and varied. Taking this into account, at the beginning of the application of our method we feared that the disjunctives formed in the early phases of tectogenesis might later, in later phases, have undergone repeated movements, thereby erasing the primary striation and creating a new one, possibly even of the opposite direction; all the more so since such additional movements were indicated, among others, by M. A. Usov, who wrote [14]: “...the disjunctive displacers, even the largest ones... were not cemented by anagenetic solutions, and additional movements occurred along them in the later phases of tectogenesis. Of these the sharpest, according to the available data, was the Rissian, when the mountain systems of the West Siberian region acquired their modern aspect—in particular the Kuznetsk Alatau, which borders Kuzbass from the east and south.”

If, after the formation of the disjunctives, movements took place that did not coincide in direction with the preceding phase, then obviously, in most cases, the striation that we now observe on the surfaces of the displacers would not correspond to the true movement of the wings of the disjunctives relative to one another, and then our method would prove untenable. However, up to now, among the large number of disjunctives deciphered by this method, incorrect solutions have been recorded in relatively few cases, and all of them relate to disjunctives of the reverse-fault type; consequently, we are dealing with primary striation.

It is precisely this last circumstance that compels us to raise the question of the age of the phase of tectogenesis that created the dense network of disjunctives in the Prokopyevsk area. Of course, it is difficult to say, on the basis of our observations of striation alone, exactly which phase this was. For this, more extensive observations are necessary. Nevertheless, it may be said that either these disjunctives were formed in one of the latest phases, after which there were no appreciable movements—at least none that would have caused additional movements of the wings—or, in the subsequent phases, movement proceeded in the same direction.

It may be hoped that, in combination with other observations of regional geology, in the future, when we succeed in detecting striation on the main fault lines, it will be possible to establish not only this phase, but also to determine with sufficient accuracy the direction of the stress that caused them.¹

Finally, it is necessary once again to note that, as a result of applying our method, it was possible to reveal the actual direction of motion of the wings of the disjunctives relative to one another. All the disjunctives in the Prokopyevsk area proved to be complex, with the strike-slip element predominating over the reverse-fault elements. This made it possible to refine the principal forms of the Kuzbass disjunctives established by Academician M. A. Usov, and to introduce certain corrections into the earlier views on the tectonics of the Prokopyevsk area.

Methodology of observations and processing of materials

When applying our method to the search for the displaced wing of a seam, it is necessary to know the angles $\alpha$, $\beta$, $\omega$, and $\gamma$. The angles $\alpha$ and $\beta$ are determined at the face of the working by ordinary measurement with a mining compass. The angle $\omega$ is taken either from the plan or is calculated from the azimuths of the strike of the seam and the displacer. The angle $\gamma$ is measured directly on the surface of the displacer.

¹ At present there is every reason to suppose that the formation of the disjunctive disturbances of the Prokopyevsk–Kiselevsk area should be connected with the movement of the Salair Ridge in a northeastern direction.

It is clear that the final result when solving by formula (1) will depend on the correctness and thoroughness of the measurements of these angles. Carelessness in measurements, a gross error, and failure to observe the necessary conditions may lead to an undeserved discrediting of the method itself. Therefore special attention must be paid to the measurement of these angles and to the method of observations on the elements of the attitude of the seam and of the dislocator, as well as to the hatching.

Experience in applying our method in the Prokopyevsk area has shown that the dip angle of the seam must be measured in a sector no farther than 100 m from the disjunctive fault. At the disjunctive fault itself it is not recommended to measure the dip angle of the seam, since, as a result of the seam being turned toward the dislocator, and also of crushing and fracturing of the floor and roof rocks, the dip angle of the seam is strongly distorted. This angle must be measured both along the floor and along the roof of the seam, and at least 8–10 times in different places. The final dip angle of the seam must be calculated as the arithmetic mean of these measurements.

Often, under the conditions of an operating mine, there may be mine workings along this seam on other levels, above and below the given one. In this case it is necessary to make an accurate transverse section and then use it to check the dip angle of the seam measured with the mining compass.

Measuring the dip angle of the dislocator presents especially great difficulties. In general, the surface of the dislocator is not an ideal plane, especially in the Prokopyevsk area, where it is often considerably curved. Therefore one cannot confine oneself to measuring at only one point of the dislocator. Our experience has shown that, in order to measure the dip angle of the dislocator, it is necessary to expose as large a part of its surface as possible, make a series of measurements on it, and then, just as for determining the dip angle of the seam, calculate its arithmetic mean value.

However, when measuring the dip angle of curved dislocators at only one place, a large error may be made; therefore this angle must be measured in several places. Usually it is possible to measure it at least in two places—in the face and in the wall of the working, since at acute angles of intersection the working always passes for some distance along the strike of the dislocator. If, in doing so, it turns out that the surface of the dislocator is strongly curved and the difference between the minimum and maximum measurement exceeds 12°, then the face of the working should be advanced somewhat farther along the strike of the dislocator, thereby exposing the surface of the dislocator in a new place, and only after this should the arithmetic mean value of this angle finally be derived.

The angle $\omega$ is taken from the plan or is calculated from the strike azimuths of the seam and of the dislocator measured in the mine working. Therefore, along with measuring the dip angles of the seam and of the dislocator, their strike azimuths are also measured; moreover, for the final solution it is likewise necessary to take the computed arithmetic mean values. As a check on the measured strike azimuths of the seam, the strike of the drift may be used; as for the dislocator, in the case when there are two points of intersection of the dislocator in the drift—in the face and in the wall of the drift—the measured strike azimuths of the dislocator can be checked by a graphical construction, for which it is necessary to connect on the plan the points of intersection of the dislocator with the drift.

When measuring the elements of the attitude of the seam and of the dislocator, the methods recommended in courses of mining geometry [3; 4; 5] also give good results. It is especially necessary to note the method of intersecting cords, with the aid of which it is possible to measure with sufficient accuracy in

elements of occurrence in a mine working even with considerable curvature of the displacement surface.

It is especially important, when using our method, to find striation on the displacement surface. The experience of our observations in the Prokopyevsk area has shown that it can be detected comparatively easily on the polished slickenside surface of most displacers. However, in different rocks it manifests itself differently. Thus, in clayey rocks the striation is expressed mainly by scratches, sometimes continuous, but more often discontinuous. Much more rarely shallow furrows are encountered. In sandy rocks it is expressed in most cases by furrows, sometimes passing into wide grooves resembling, in outward appearance, ripple marks. In sandy rocks the striation is usually coarsely expressed, whereas in clayey rocks the scratches and furrows are represented by slender lines, clearly visible on the glossy surface of the displacer.

It should, however, be borne in mind that only in rare cases is it possible to detect striation at once. In most cases, for this purpose it is necessary to expose as large an area of the displacer as possible, and, where possible, in different places. Our experience has shown that the surface of the displacer must be exposed very carefully, especially in clayey rocks, since when exposing the displacer with a pick one can easily destroy the striation. Nor should dust and dirt be wiped off the exposed surface of the displacer with one’s hands or sleeves, for, especially in clayey rocks, the striation can easily be rubbed out. It is better, where possible, to use compressed air for this purpose.

When exposing the surface of the displacer, one must carefully see to it that pieces of coal knocked off at the contact with the displacer do not disturb its polishing. If the crack is filled with compressed vein clay, whose surface is also sometimes well polished, it is first necessary carefully to expose its surface, on which it is often possible to observe very good striation, and then, having stripped it from the displacer, to check the striation directly on the plane of the displacer.

After striation has been detected on the surface of the displacer, the angle $\gamma$ should be measured. For this, the most clearly expressed stria is selected, and in order that it be still more clearly visible, a line may additionally be drawn along it with a pencil. Next, the exact strike line of the displacer is marked with a compass; this line forms the angle $\gamma$ with the marked stria. Then this angle is measured directly on the surface of the displacer with an ordinary protractor.

The angle $\gamma$ must likewise be measured several times, where possible in different places—in the walls and at the face of the working—and then the arithmetic mean is calculated, which is taken for the subsequent calculations.

The processing of the results of observations reduces to calculating the arithmetic mean values of the angles $\alpha$, $\beta$, and $\gamma$, after which one may proceed to determining the direction of search for the displaced wing of the seam and the form of the disjunctive by formula (1). A table of measurements of these angles, as well as the actual solution of formula (1), must be given on the geological sketch of the given disjunctive. On the sketch of the working face and on the plan, the places where measurements of these angles were made should be marked.

Fig. 18

In addition, it is recommended that on the seam map, near each fault plane where striation was measured, the horizontal projection of the stria be shown by an arrow. The latter can be determined by the following formula

\[ \operatorname{tg}\gamma'=\operatorname{tg}\gamma\cos\beta, \tag{2} \]

where \(\gamma'\) is the projection of the angle onto the horizontal plane (Fig. 18).

Conditions for applying the method

The chief condition for applying our method in searches for the displaced wing of a seam, as we have already noted above, is the determination of the character of the tectonics of the given area. In this connection, it can find wide application only when, as a result of a tectonic investigation, it has been established that only reverse-fault or only normal-fault disjunctives occur in the area. If both kinds are present, when it is impossible to determine them in advance, our method cannot be applied, since for normal-fault disjunctives all the regularities we have derived, on which searches for the displaced wing of a seam are based, have the opposite meaning.

In addition, this method can find application when striation can be detected on the surface of the fault plane. At the same time there must be certainty that this striation corresponds to the primary direction of movement of the wings of the disjunctives.

Fig. 19

The testing and application of this method over a number of years in the Prokopyevsk district of Kuzbass have also enabled us to discover the error that we made in measuring the elements of occurrence, and, consequently, to calculate that absolute value of \(\operatorname{tg}\gamma'\) at which drawing conclusions about the direction of searches for the displaced wing of a seam becomes dangerous.

From our experience we concluded that, in measurements of the angles \(\alpha\) and \(\gamma\), an error of \(\pm 3^\circ\) may be allowed, while in measurements of the angles \(\beta\) and \(\omega\) this error increases to \(\pm 5^\circ\).

If the absolute value of the expression enclosed in parentheses in (1) falls within these errors, then we do not recommend using our method to decide the question of the direction of searches for the displaced wing of a seam.

Let us examine this with examples.

At the I. V. Stalin mine, in seam II of the Inner western wing of the small anticline, at the 215 m level, a disjunctive was encountered (Fig. 19). After studying it at the working face, we obtained the following data:

\[ \alpha=45^\circ,\quad \beta=70^\circ,\quad \omega=133^\circ\quad \text{and}\quad \gamma=42^\circ. \]

Substituting these values into the expression enclosed in parentheses in formula (1), and carrying out the necessary calculations, we obtain:

\[ 1{,}000-0{,}248+0{,}860=1{,}612. \]

The expression in parentheses in formula (1) turned out to be positive; consequently, this disjunctive should have a doubling of the seam.

Now let us see whether the obtained value exceeds the possible total error that we allow in measuring the elements of occurrence. For this purpose we shall take the most unfavorable case, when all the errors reduce the obtained value, i.e., let us assume:

\[ \alpha = 45^\circ + 3^\circ = 48^\circ,\quad \beta = 70^\circ - 5^\circ = 65^\circ, \]

\[ \omega = 133^\circ + 5^\circ = 138^\circ,\quad \gamma = 42^\circ + 3^\circ = 45^\circ. \]

Solving the preceding example with these data, we find

\[ 0.900 - 0.346 + 0.737 = 1.291. \]

Thus, even taking possible errors into account, the expression in parentheses in formula (1) has remained positive. Consequently, our initial conclusion about a doubling of the seam in this disjunctive is correct, and we may now confidently lay out a mine working toward the displaced wing of the seam.

Let us examine a second example, in which the absolute value of the expression in parentheses in formula (1) is obtained within the limits of the permissible errors.

This example also concerns a disjunctive along seam II, the Inner seam, which was encountered on the western limb of the Small anticline (Fig. 20). Here the data proved to be as follows:

\[ \alpha = 80^\circ,\quad \beta = 64^\circ,\quad \omega = 11^\circ \ \text{and}\ \gamma = 165^\circ. \]

By the preceding method, substituting these values into the expression in parentheses in formula (1), we find

\[ 0.176 + 0.479 - 0.793 = -0.138. \]

We have obtained a negative value. A negative value of the expression in parentheses in formula (1), for a nonconcordant reverse-fault disjunctive, corresponds to a gap between the wings of the seam. Consequently, the displaced wing of the seam must be located to the southwest of the face of the working.

Fig. 20

Now, just as in the preceding example, let us see whether the obtained value exceeds the possible total error. For this purpose we shall take the same most unfavorable case, i.e., let us assume:

\[ \alpha = 80^\circ - 3^\circ = 77^\circ,\quad \beta = 64^\circ - 5^\circ = 59^\circ, \]

\[ \omega = 11^\circ - 5^\circ = 6^\circ,\quad \gamma = 165^\circ - 3^\circ = 162^\circ. \]

Solving the preceding example now with the new data, we obtain

\[ 0.231 + 0.597 - 0.371 = 0.457. \]

Thus, taking into account the possible total error that we allow in measuring the elements of occurrence, we obtain a positive value. A positive value of the expression in parentheses in formula (1), for a nonconcordant reverse-fault disjunctive, corres—

corresponds to a doubling of the seam. Consequently, in the present case, on the basis of this method it is impossible to decide where the displaced wing of the seam is located, since the value obtained lies within the limits of permissible errors.

Such are the conditions for applying our method to searches for the displaced wing of a seam. All these conditions exist in the Prokopyevsk area. Judging from the testing of this method in other areas of Kuzbass, in particular in the Anzhero-Sudzhensk area, it may be assumed that they exist throughout the entire Kuznetsk Basin.

We believe that, given these conditions, our method may find application in other coal basins as well, and also in searches for the displaced wing of a vein in ore deposits. It should only be recommended that this method first be tested on already deciphered disjunctive faults, and only after that be used to search for the displaced wing of new disjunctive faults.

Conclusion

The present work summarizes the results of testing the application of the method of geometric analysis of disjunctive faults to searches for the displaced wing of seams in the Prokopyevsk area of Kuzbass.

In the first three years alone of applying this method, more than 200 disjunctive faults were deciphered, and not a single case of an incorrect solution was recorded. Later it was established that there is a small number of disjunctive faults to which our method proved inapplicable. These are disjunctive faults of the upthrow type, which have a very limited distribution in the area. Therefore, in the Prokopyevsk area our method has gained recognition and is now being successfully used in some mines to search for the displaced wing of a seam.

Taking into account the positive results of this method, the conference of mine geologists of Kuzbass in January 1940 heard reports by the chief geologist of the Stalinu-gol trust, V. A. Azimov, and by the former senior geologist of the I. V. Stalin mine, V. A. Monin, on the results of its application in the Prokopyevsk area of Kuzbass. In both reports this method was given a positive assessment; therefore the conference recommended it for the other areas of Kuzbass and, in addition, adopted for practical guidance the special instruction that we had drawn up.

Thus, it may be considered that this method has justified itself. Its application made it possible to find the displaced wings of seams comparatively easily, quickly, and correctly, which, for the complex structure of some areas of Kuzbass and the variety of forms of disjunctive faults, is of great practical importance.

However, the positive significance of this method lies not only in its use for searching for the displaced wing of a seam. At the same time, it was also possible to resolve and pose a whole series of very important questions concerning the nature of the tectonics of the Prokopyevsk area. Among them the most serious are the following.

1. Our numerous observations of slickenside striation have shown that all disjunctive faults of the Prokopyevsk area are complex—such that the movement of the wings takes place, although upward, in an arbitrarily inclined direction. In this case the element of horizontal displacement almost always predominates over the element of vertical displacement, since the angle between the striation and the strike of the displacer in the overwhelming majority of cases varies within the limits of 10–50° and 170–130°. Therefore such disjunctive faults should more correctly be called not upthrows, overthrusts, and strike-slip faults, but upthrow- and overthrust-strike-slip faults.

1. Among the Prokopyevsk geologists there was a widespread opinion that hinged disjunctives were present in the area. These disjunctives were distinguished on the grounds that sometimes one and the same displacer, intersecting two seams at the same time, displaces one of the seams upward—a conformable reverse fault—and the other downward—a direct thrust. Since these forms of disjunctives were regarded by them as simple, they concluded that somewhere between the seams, along the strike of the displacer, there is a center around which both wings of the disjunctive rotated relative to one another through a certain angle; in this process the hanging wall along one seam rose upward, and along the other descended downward.

Using a concrete example of such a disjunctive, we prove that these are not rotational but ordinary reverse-fault–strike-slip disjunctives, and that in the given case the hanging wings of this disjunctive along both seams not only rose upward, but at the same time, and to a more considerable degree, were displaced along the strike of the displacer, owing to which a false impression is created of the lowering of the hanging wall in a direct thrust-strike-slip.

1. By applying, in the search for the displaced wing of a seam, the formula for a complex diagonal disjunctive, we can correctly determine the form of the thrust. This is of great importance because, unlike reverse faults, the form of thrusts cannot be established from the mutual relationship of the bedding elements of the seam and the displacer. Moreover, in complex disturbances, direct and reverse thrust-strike-slips are also difficult to distinguish by the mutual position of the broken parts of the seam relative to the displacer, since at acute angles between the slickenlines and the strike of the displacer, in a direct thrust-strike-slip, instead of a duplication a gap in the seam may form, while in a reverse thrust-strike-slip, instead of a gap, a duplication of the seam may form.

2. With the aid of our method it was also possible to prove the erroneousness of distinguishing, in the Prokopyevsk area, the so-called transverse normal faults. We established that these disjunctives in reality have the form of reverse-fault–strike-slips, or upthrow-strike-slips; that the existing position of the broken parts of the seams relative to the displacer, on the basis of which they had been assigned to normal faults, is due to the strike-slip element, which in the given case played the leading role in the direction of movement of the wings of the disjunctive.

3. The results of applying our method in the Prokopyevsk area enabled us to raise the question of the age of that phase of tectogenesis which created the dense network of disjunctives in the area.

Taking into account the complex tectonic history of Kuzbass, where Academician M. A. Usov [14] counts nine phases of tectogenesis, at the beginning of applying our method we feared that repeated movements in later phases might obscure the primary slickenlines and create new ones of a different direction. In that case our method would have proved untenable; however, these fears turned out to be unfounded, since the overwhelming majority of the disjunctives deciphered by this method proved to have been correctly solved; consequently, we are dealing with primary slickenlines.

The latter gave us the right to raise the question of the age of the disjunctive dislocations of the Prokopyevsk area. While not resolving it concretely, we nevertheless express the most probable supposition: that they either formed in one of the latest phases of tectogenesis, after which there were no longer any appreciable movements, or, in the subsequent phases, the movement occurred in the same direction.

Such are our conclusions. Undoubtedly, they will have some significance for a correct understanding of the tectonics of the Prokopyevsk area. At the same time they will also have practical significance, since a correct understanding of the tectonics is one of the basic conditions for successful searches for the displaced wing of a seam.

In addition, in the present work we also dwell on the method of observations of the elements of the attitude of the seam and of the displacer, and on striation. In doing so, we emphasize that the final result in solving by the formula of a complex diagonal disjunct will depend on the correctness and care with which the angles are measured; therefore we recommend making measurements at different places and then computing their arithmetic mean values.

Finally, we draw special attention to the conditions for applying our method. These conditions are as follows:

1. Our method can be applied only in the case when it has been established that, in the given area, there is only a general upthrow or only a general downthrow character of the disjuncts. If both types are present, and when it is impossible to determine them in advance, we do not recommend applying this method for searching for the displaced wing of a seam, since in that case it is impossible to determine from the striation the direction of movement of the wings of the fault.

2. When striation can be found on the surface of the displacer and there is confidence that it corresponds to the primary direction of movement of the wings of the disjunct.

3. When the absolute value of the expression standing in parentheses in the formula of the complex diagonal disjunct exceeds the error that we allow in measuring the elements of attitude.

All these conditions are present in the Prokopyevsk area; there is every reason to suppose that they are also present in other areas of Kuzbass. As for the application of this method in other basins, we recommend first testing it on already deciphered disjuncts and only after that applying it to searches for the displaced wing of a seam when new disjuncts are encountered.

REFERENCES

1. Beditskii A. A.—A method for searching for the displaced wing of a seam under the conditions of the Prokopyevsk area of Kuzbass, Proceedings of the Tomsk Industrial Institute named after S. M. Kirov, vol. 60, issue 1, Tomsk, 1939.

2. Gutt A. E.—A course in mining geometry, Kharkov, 1932.

3. Dalinkevich M. A.—Mining geometry, Leningrad, 1924.

4. Krasnikov P. F.—The principal forms of dislocations of the Prokopyevsk mine of Kuzbass, Collection on the Geology of Siberia, Tomsk, 1933.

5. Krupennikov B. S.—The Prokopyevsk and Kiselevsk-Afoninsk districts, Minerals of the West-Siberian Territory, vol. III. Coals, Novosibirsk, 1935.

6. Lees Ch. K.—Structural geology, ONTI, 1935.

7. Molchanov I. A.—Geometrical analysis of translational disjuncts, Mine-Surveying Collection, vol. II, Tomsk, 1935.

8. Rumyantsev S. S.—Tectonic disturbances observed along the northwestern margin of Kuzbass, and their explanation (an experiment in applying the theory of strength of materials to tectonics), Mining Journal, Nos. 10 and 11, 1928.

9. Willis B. and Willis R.—Structural geology, Baku, 1932.

10. Usov M. A.—Composition and tectonics of the deposit of the southern district of Kuzbass, Novonikolaevsk, 1924.

11. The same—Forms of disjunctive dislocations in the mines of Kuzbass, Collection on the Geology of Siberia, Tomsk, 1933.

12. The same—Tectonics of Kuzbass, Problems of Soviet Geology, No. 2, 1935.

13. The same—Geological sketch of Kuzbass, Minerals of the West-Siberian Territory, vol. III, Coals, Novosibirsk, 1935.

14. The same—Tectonics of Kuzbass, Bulletin of the West-Siberian Geological Administration, No. 5, 1940.

15. Ushakov I. N.—Mining geometry, ONTI, 1937.

16. Frost D. V.—A graphical method for solving mine-surveying problems, Proceedings of the Tomsk Technological Institute, vol. VIII, 5, 1907.

1. M. A. Usov was misled with regard to these disjuncts by the geologist Yu. A. Urban, who reported to him that he had allegedly observed vertical striations here on the surface of the displacers, which does not correspond to reality. ↩