Methodology for Locating the Displaced Limb of a Seam under the Conditions of the Prokopyevsk District of Kuzbass

A. A. Belitsky

Preface

The present work was completed in 1937 and submitted by the author as a dissertation for the degree of Candidate of Geological and Mineralogical Sciences. After the dissertation was defended on April 25, 1937, for reasons beyond the author’s control, it was not printed.

The geological part of this work was compiled from materials of 1935. Over four years, the mining operations of the Comrade Stalin Mine have made it possible to substantially refine the seam maps and sections provisionally compiled in 1935, especially for the Small Anticline. However, the new data did not introduce any fundamental changes; therefore this part of the work has been left by the author in its former form, all the more so because it is not of essential significance for the present work and is included only in order to set forth the method of geometric analysis of disjunctives by means of concrete examples.

It should be noted that the method developed by the author for locating the displaced limb of a seam was introduced into production in a timely manner and, by the present time, is already being successfully applied at several mines of the Prokopyevsk deposit of Kuzbass.

INTRODUCTION

One of the weakest points in the development of mine fields is mine tectonics, which in recent years has been attracting ever greater attention. It is of especially great importance for the Kuznetsk Basin, where at various times, in connection with the formation of mountain massifs along the periphery of the basin—on the east, the Kuznetsk Alatau, and on the west, the Salair Ridge—its productive deposits, especially along the margins, were gathered into rather steep folds and broken by a dense network of disjunctive disturbances of various types and various amplitudes.

These disjunctive disturbances greatly complicate the exploitation of deposits, since the loss of coal seams forces the work plan to be altered in the course of operations, delays the advance of preparatory workings, and entails a whole series of unproductive expenditures in searching for their displaced limbs.

Thanks to the broad scope of mining operations, in particular in the Prokopyevsk district of Kuzbass, mine workings reveal ever new disturbances almost every day. Most of these disturbances, during the ordinary exploration of mine fields from the surface, given the comparatively sparse network of exploratory workings, cannot be fully detected. Therefore such a disturbance is sometimes encountered by mine workings quite unexpectedly and, for its interpretation, requires new supplementary investigations.

Each time a new disturbance is encountered, the mine geologist is faced with the questions: where is the displaced limb of the seam located? Where and how should the mine working be directed most rationally? It is not always possible to answer these questions at once; sometimes, because of a whole series of difficulties arising in the investigation of the disjunctive disturbance encountered, the answer is delayed for entire months, as a result of which the mine workings are stopped for an indefinite period. Such a situation, especially at the present time, in connection with the Stakhanovite movement, which sets before mine geologists the task of ensuring the uninterrupted advance of mine workings, cannot be tolerated. On the other hand, this requires a careful study of the specific features of the tectonics of each district and, at the same time, the development of possibly simpler and sufficiently accurate methods for investigating individual disjunctive disturbances.

Of the comparatively small list of literature on the mine tectonics of Kuzbass, the works of Doctor of Geological Sciences, Professor M. A. Usov deserve special attention (10, 11, 12).

As a result of his many years of work in Kuzbass, he developed for the Kuznetsk Basin a classification of the principal forms of disjunctives, and also provided a whole series of extremely valuable indications, in both theoretical and practical respects, shedding light both on the genesis of disjunctive disturbances and, to some extent, on the methodology for searching for the displaced limb of a seam.

Among other works on the mine tectonics of Kuzbass, one may note: 1) the work of S. S. Rumyantsev (8) on the Kemerovo deposit, who was the first to approach this question from the standpoint of the strength of materials; 2) the work of Associate Professor P. F. Krasnikov (4) on the Prokopyevsk deposit, who succeeded, among other things, in establishing the “nodes” of intersection of disjunctives of different ages; 3) the geological-industrial sketches of the Prokopyevsk (5) and Osinniki deposits (9) that have appeared recently in print, as well as the third volume of Mineral Resources of the West Siberian Territory, devoted chiefly to the coals of the Kuznetsk Basin (7), where questions of mine tectonics are touched upon to one degree or another.

It must be noted, however, that all these works, while revealing the genesis and general regularities of the mine tectonics of individual districts, devote little attention to the methodology itself for searching for the displaced limb of a seam. Yet this question is of enormous practical importance, since the further the exploitation of a deposit proceeds, the more demanding it becomes for the mine geologist with respect to the correct, rapid, and rational solution of the question of the position of the displaced limb of a seam.

How poorly developed the questions of mine tectonics and the methodology for searching for the displaced limb of a seam still are may be seen, if only from the fact that in this field there exist two tendencies, almost unconnected with one another: on the one hand, the geological tendency, which in developing a methodology for the investigation of disjunctives in most cases does not make use of the mathematical method, as a result of which its conclusions are often far from sufficiently accurate for determining the position of the displaced limb of a seam; on the other hand, the mining-geometrical tendency, which also deals with mine tectonics and, in particular, precisely with determining the direction of displacement of the displaced limb of a seam, but makes poor use of geological data, as a result of which, in deciphering a concrete disturbance, it often encounters insurmountable difficulties.

The present work sets itself the task, using both methods—the geological and the mathematical—to make an attempt, on the basis of the specific features of the tectonics of Kuzbass, namely the predominance in it of the reverse-fault type of disturbance, to establish regularities with the aid of which, upon encountering a new disturbance, it would be possible comparatively easily and simply to determine the direction of displacement of the displaced limb of a seam. In addition, it may be supposed that the method we apply can have great significance also in solving more general problems of tectonics.

In the geological part, the author of the present work relies chiefly on material he collected during a year and a half of work as a mine geologist at the Coking I Mine named after Comrade Stalin, of the Prokopyevsk deposit. As for the mathematical method, here we made use of the conclusions of Prof. I. A. Molchanov (6), which are simpler than the usual methods of mine geometry, set forth, for example, in the fundamental work of A. E. Gutt (3).

The present work was carried out under the direct supervision of Prof. I. A. Molchanov and with the consultation of Prof. M. A. Usov, to whom I express my deep gratitude.

I. Main Features of the Structure of the Field of the Koksovaya Mine Area

1) General data

The area of the Koksovaya mine is located in the northeastern part of the Prokopyevsk deposit. On the north and partly on the west it is bounded by the channel of the Aba River; on the south the conventional boundary is drawn as a vertical plane passing along the axis of the central adit; the eastern boundary coincides with fault JJ on the eastern limb of the Maly Anticline (Fig. 1).

The total length along the strike is 2500–2600 m and across the strike of the seams—2200–2300 m.

The history of exploration of the Koksovaya mine area begins in 1920. In that year, engineer Gets (2) drove, in the field of the Koksovaya mine, a trench that intersected the entire series of seams of the western and eastern limbs of the Golubevsky Anticline. Subsequently, before the Koksovaya mine was laid out in 1929, five core boreholes were drilled in the area under the direction of engineer Lopushinsky: two of them were laid down at the site of the future shafts of the Skipovaya and Kletevaya mines, and the remaining three—on the western limb of the Golubevsky and on the eastern limb of the Abinsky anticlines. The deepest borehole, No. 1, had a depth of 274 m.

In 1934 and 1935 the geological bureau of the Koksovaya mine carried out exploration by zigzag trenches and by trenches in the southern part of the eastern limb of the Golubevsky Anticline, as a result of which the tectonic scheme of this limb was refined.

The Maly Anticline has been explored considerably better; it was attached to the Koksovaya mine area only in 1935. On it, several exploratory lines of core drilling were driven, as well as several exploratory lines of trenches, dudki, and shafts.

In addition, it should be noted that in the Koksovaya mine area the overlying horizons have already been illuminated by worked-out adits and mines: the northern part of the Golubevsky Anticline—by the Golubevsky adits down to the horizon of 265 m above the level of the Baltic Sea; the southern part of this anticline—by the Povarnikha mine, down to the same horizon; the southern part of the eastern limb of the Abinsky Anticline was worked by mine No. 2 down to the horizon of 232 m; along the western limb of the Maly Anticline, adit No. 11 is operating at the present time. Finally, one may note the crosscut “0” at the horizon of 265 m, in the plane of which the main crosscuts of the Koksovaya mine pass on the lower horizons (Figs. 1 and 2).

The Koksovaya Mine is the most powerful mine in the Soviet Union. Its designed capacity is 3 million tons per year. Its geological reserves, according to the latest calculations to a depth of 300 m, are estimated at 120 million tons¹). At present, two main crosscuts have been driven from it. One of them is located at the 215 m level; after passing through the Abinskaya and Golubevskaya anticlines, it has already intersected seam VI of the Interior of the Maly anticline. The total length of this crosscut is 1700 m. On this level, preparatory workings in some faces have advanced 600–800 m to the north and 400–500 m to the south. The second main crosscut was driven at the 165 m level, intersected the closure of the Moshchnyi seam of the Abinskaya anticline, and was then stopped.

The area of the Koksovaya Mine is composed of three comparatively narrow anticlines, strongly elongated in the NNW–SSE direction—the Abinskaya, Golubevskaya, and Maly anticlines—with the fifth and sixth synclines between them (Figs. 2 and 3). The western limb of the sixth syncline, owing to fault GG, is absent in the area of the Koksovaya Mine.

The dip of the fold limbs varies within the range of 60–70°. The distance between the axes of the anticlinal folds is from 750 to 950 m.

The axes of the folds in the area described are inclined toward the NW at the following angles:

Abinskaya anticline—16°, V syncline—15°, Golubevskaya anticline—16°, and Maly—25°.

The folds are complicated by a series of large and by a significant number of small faults, representing almost the entire range of tectonic forms according to the classification of Prof. M. A. Usov: conformable and nonconformable upthrows, direct and reverse thrusts, strike-slip faults, as well as bedding-plane displacements.

The strike of the major faults is close to the strike of the fold axes, and only among the minor faults are there fractures of diagonal and even transverse directions.

Let us also note a certain regularity in the distribution of faults along the limbs of the folds, especially well observed in the area of the Koksovaya Mine. The western limbs of the anticlinal folds have a comparatively undisturbed occurrence. By contrast, the eastern limbs, along the strike of the seams, have a whole series of small additional folds and are broken by a number of small longitudinal, diagonal, and transverse fractures. This regularity is characteristic of the entire Prokopyevsk deposit as well.

Tracing the faults from west to east, they may be characterized as follows.

2) Abinskaya Anticline.

The western limb, like most western limbs of anticlinal folds in the Prokopyevsk deposit, is comparatively—

¹) The numerical data are given according to materials from 1935. At present, both the reserves and the length of the mine workings have changed considerably.

relatively calm. Mining workings driven along this limb, within the mine boundaries at the 215 and 165 m levels, did not encounter disturbances. A drift driven along Seam IV Inner, with a total length of about 500 m, showed good persistence of the seam along the strike.

Conversely, the eastern limb of the Abinsk anticline is strongly disturbed. The densest network of disturbances in this limb is concentrated in the field of Mine No. 2. Here we have predominantly direct and discordant thrusts among the small disturbances, and concordant upthrows among the large disturbances.

The largest disturbance, I—I, passes through the Lutuginsky and Gorely seams (Figs. 2, 3, and 4). This disturbance, of the concordant upthrow type, has a diagonal strike in the field of Mine No. 2; it doubles the Gorely and Lutuginsky seams, with an insignificant horizontal length of seam displacement of about 20–25 m. Upon leaving the Lutuginsky seam, fault I—I changes its strike and again enters the Lutuginsky seam, but now from the floor; it doubles it a second time, with a horizontal length of seam displacement of about 300 m. Farther on the fault runs almost parallel to the strike of the seam and dies out north of the main crosscut of the Koksovaya Mine.

This disturbance is well recorded by the mine workings of Mine No. 2 at the 232 m level. Here it was encountered by the main drift of the Gorely seam and by the main crosscut of Mine No. 2. At the Koksovaya Mine this disturbance was encountered at the 215 m level in the main drift of the Lutuginsky seam and in the intermediate crosscuts between the Lutuginsky and Gorely seams. Thus, for example, the second southern intermediate crosscut of the Koksovaya Mine at the 215 m level, driven from the Lutuginsky seam to the Gorely seam 200 m south of the main crosscut, encountered the displaced limb of the Lutuginsky seam. Along the displaced limb of the Lutuginsky seam, drifts were driven: northward to the truncation of the seam—47 m, and southward to the pillar beneath the R.U. power station—60 m. The fault plane of this disturbance dips concordantly and more steeply than the seam; it has a dip angle of 66° while the seam dips at 55–63°.

It is interesting to note, in this disturbance, the character of the fault-plane manifestation. The fault plane of this disturbance was well exposed in the northern drift of the Lutuginsky seam from the second southern intermediate crosscut, where the seam began to be smoothly cut off 32 m from the beginning of the drift. Subsequently the drift was driven another 15 m; and since only coal was being extracted, while the side rocks remained untouched, over these 15 m the surface of the fault plane was exposed. It was represented by an almost ideal, magnificently polished plane. The rocks and coal proved to be completely undisturbed. The cutting occurred so neatly that, if it had not been possible to detect in the face a certain difference in dip and strike between the hanging and footwall sides of the seam, it would have been almost impossible to distinguish the fault plane from the bedding plane.

From this same disturbance develops disturbance II–II, which runs southwest along the Lutuginsky and Prokopyevsky seams and dies out at the Moshchny seam. This disturbance also belongs to the type of concordant upthrow. Owing to these two disturbances, the main crosscut of Mine No. 2 intersected the Lutuginsky seam three times (Fig. 4).

In addition to these two disturbances, in the field of Mine No. 2 there is also a whole series of smaller disturbances described in the work of Associate Professor P. F. Krasnikov. Therefore we shall permit ourselves not to dwell on them.

On the north of this limb only one disturbance deserves attention—the concordant upthrow III–III along the VI Vnutrenny seam. This upthrow is exposed at the 215 m level by the main drift of the VI Vnutrenny seam, by crosscuts along this seam, and by parallel drifts.

The strike of the dislocator is almost parallel to the strike of the seam, as a result of which the drift driven along the VI Vnutrenny seam followed the cut-off edge of the seam for a distance of 80 m. The dip of the dislocator and that of the seam are concordant. The dip angle of the dislocator is 75°, with a seam dip angle of 65°. The horizontal length of displacement of the seam is about 100 m.

For disturbance III–III it is necessary to note the very clean cutting of the seam by the dislocator. The plane of the dislocator, exposed by crosscuts, also proved to be well polished. The coal and the enclosing rocks are undisturbed.

3) Golubevsky Anticline.

On the western limb of the Golubevsky anticline only one disturbance can be noted: IV–IV, longitudinal, of the concordant upthrow type. It was established in the crosscut of the 265 m level and farther south in the drifts of the VI Vnutrenny seam at the 215 and 265 m levels. Owing to this same disturbance, the closure of the IV Vnutrenny seam in the crosscut of Mine 3–4 is complicated by a small duplication.

This disturbance develops due to a small additional fold in the closure part of the fifth syncline, the presence of which has been established by mine workings at the 265 m level.

The horizontal length of displacement of the VI Vnutrenny seam is 150–170 m, and of the IV Vnutrenny seam—25–30 m. The dislocator dips concordantly at an angle of 87°, with a seam dip angle of 70–75°. South of the closure of the IV Vnutrenny seam, disturbance IV–IV apparently dies out, since the mine workings of the central adit did not encounter this disturbance.

In addition to this principal disturbance, the mine workings of the Povarnikha Mine encountered an insignificant number of small disturbances, of the type of concordant upthrows and reverse thrusts. On this same limb, especially along the VI Vnutrenny seam, facts of intra-seam displacements have been recorded, causing pinches and swellings of the seam. It is possible that this same circumstance may explain the abnormal increase in thickness of the III Vnutrenny seam to 8.0 m,

especially north of the main crosscut of the Koksovaya mine. In general, however, this limb is comparatively calm, and the seams persist along the strike for a fairly great distance.

The eastern limb of the Golubevsky anticline, like the eastern limb of the Abinsky, is strongly disturbed. Among the largest disturbances not only of this limb but also of the entire area, it is necessary to note disturbance GG, of the type of an unconformable upthrow (Fig. 2). As a result of this disturbance, the reserves of this limb are reduced, since the displacer of disturbance GG dips in the direction opposite to the dip of the seams.

Disturbance GG was encountered by the main crosscut of the Central Adit at the 265 m level, 55 m east of the Moshchny seam. Owing to this disturbance, the crosscut of the Central Adit encountered, above the Moshchny seam, beyond disturbance GG, only the very cutoff of seam VI Inner of the eastern limb of the Golubevsky anticline.

At present, disturbance GG has been recorded by the main crosscut of the Koksovaya mine at the 215 m level, 15 m east of seam VI Inner; then by the face of the Gorely seam of the Povarnikha mine at the 265 m level, where the seam was finally cut off by this disturbance; and, finally, by the face of seam III Inner at the 215 m level, which, evidently, lies near the final cutoff, since the coal and the side rocks are strongly disturbed, and the seam proceeds extremely irregularly—at times swelling, at times, conversely, disappearing.

Disturbance GG has also been well traced on the surface by zigzag exploration, as a result of which seams I, II, III, and IV Inner have been traced up to their final cutoff by this disturbance.

The displacer of disturbance GG dips westward at an angle of 70°, while the seams dip eastward at an angle of 65–75°. The horizontal length of displacement, measured from the seam outcrops beneath the overburden, reaches 900 m.

For this disturbance it is of interest to note the character of the manifestation of the displacer. In the main crosscut of the Koksovaya mine, and also in the crosscut of the Central Adit, disturbance GG is represented by a crush zone about 30 m thick, which is expressed by a series of fan-like cracks diverging from bottom to top, passing through sandstone (Fig. 5). The sandstone between these cracks is strongly shattered, so that at a light touch of a pick it rapidly exfoliates and, falling, pulls large pieces of rock with it. Along the cracks, slickened vein clay was found in the form of interbeds 3 to 5 cm thick. In places there are deposits of calcite and even quartz. The surface of the cracks is irregular and wavy, as a result of which it is sometimes completely impossible to determine the elements of their attitude.

This crush zone greatly complicated the advance of the crosscut, since driving through it was possible only by hand, required heavy timbering, and throughout all

30 m, it was necessary to work under conditions of a strong inflow of water.

Among the other larger disturbances of this limb, mention should be made of the axial disturbance V—V, traced on the locks of the Lutuginsky, Gorely, and Prokopyevsky seams, at the 215 m level of the Koksovaya mine and the 265 m level of the Povarnikha mine, and also in the crosscut of the Central adit in the lock of the Moshchny seam. This disturbance stretches the locks along the axis. North of the Gorely seam, along the strike, it evidently dies out, since the locks of the Inner seams, worked by the Golubev adits, are not disturbed. It should also be noted that the lock of the Gorely seam at the 215 m level, undercut by the northern intermediate crosscut from the field drift, also proved to be undisturbed; evidently this disturbance also dies out with depth.

The dislocator of disturbance V—V dips westward at an angle of 80°, with the seams dipping eastward at an angle of 50–65°; i.e., this disturbance, like disturbance GG, belongs to the type of discordant upthrow.

Another, comparatively large disturbance on this limb deserves attention: VI—VI on seam II Inner, of the type of a concordant thrust (Figs. 6 and 7).

This disturbance was recorded at the southern end of the main drift on seam II Inner of the Golubev adits. It has been traced especially well at the 250 m level of the Koksovaya mine, where the central crosscut intersected seam II Inner twice, and then drifts were driven along it for a considerable distance. This same disturbance is also outlined on the surface by shallow boreholes.

However, despite such an abundance of points where this disturbance has been recorded, the elements of the occurrence of the dislocator are still unknown to us. Here, evidently, we again have an extremely precise cutting-off, since repeated searches for the fracture in the central crosscut of the 250 m level gave no positive results. From an analysis of the facts known to us regarding this disturbance, the following conclusion may be drawn. The disturbance is undoubtedly longitudinal, since it displaces only one seam—II Inner. The dislocator dips flatter than the seam, which is evident from the section in the plane of the central crosscut of the 250 m level (Fig. 7). The horizontal length of displacement of the seam, according to the data of shallow exploration drilling on the surface and the drifts of the 250 m level, is 200–250 m.

In addition to the disturbances described above, on this limb there are a large number of smaller diagonal disturbances, evidently apophyses of the main disturbance GG. The Inner seams proved to be especially strongly disturbed, where in individual sections, literally every five to ten meters, a new disturbance is encountered, though of small amplitude. All these disturbances, according to Prof. M. A. Usov’s classification, belong to the type of reverse thrusts. As will be shown below, we interpret them somewhat differently.

Among the large number of these small disturbances, three disturbances deserve attention: VII—VII, VIII—VIII, and XI—IX, which have been well traced by the mine workings of the Koksovaya mine (Fig. 2).

The dislocators of these disturbances generally have a diagonal strike from NW to SE, with a dip to the NE of 25–40°. The fractures run irregularly, often have a scalloped character, are mostly open and filled with vein clay, the thickness of which sometimes reaches 0.30–0.50 m. Veinlets of calcite and quartz, deposited by fracture waters, are not infrequently present along these fractures.

Disturbance VII—VII has been well traced by mine workings on the 215 m level. It cuts the Kharakternyi seam 165 m north of the main crosscut and, to the northwest, enters a field drift which, incidentally, undercuts the Kharakternyi seam. The horizontal length of displacement of the Kharakternyi seam is about 60 m. To the southeast this same disturbance displaces seams I, II, and III Vnutrennie and emerges at seam IV Vnutrennii, where it manifested itself in that it somewhat crumpled the coal seam and the side rocks.

Disturbance VIII—VIII, also traced on the 215 m level, cuts the Gorelyi seam 60 m north of the main crosscut and then, to the southeast, displaces the Kharakternyi seam and seams I, II, and III Vnutrennie, with a small horizontal length of displacement, on the order of 5–20 m. After emerging from seam III Vnutrennii, the fracture is lost between seams III and IV Vnutrennie. It is possible that it crossed seam IV Vnutrennii, but was not observed.

Disturbance IX—IX is analogous to the first two. It is well exposed in the southern intermediate crosscut on the 265 m level along seams I and II Vnutrennie. On the 215 m level this same disturbance was encountered at the end of the southern drift along seam III Vnutrennii, 70 m south of the intermediate crosscut, where seam III Vnutrennii was cut and shifted to the place of seam IV Vnutrennii. As a result of this disturbance, the drift driven along seam IV Vnutrennii imperceptibly passed into seam III Vnutrennii, while the intermediate crosscut driven 82 m from the southern intermediate crosscut from seam III Vnutrennii to seam IV Vnutrennii encountered seam II Vnutrennii. At present, the mine workings have undercut the downthrown limb of seam IV Vnutrennii and drifts have already been laid out along it. The horizontal length of displacement of seam IV Vnutrennii is 20 m.

In addition to these three disturbances, one more disturbance, X—X, of the same type was traced on the surface by trenches.

4) Small anticline.

Within the limits of the Small Anticline, on its eastern limb, only one large disturbance, JJ, can be noted; at present it has been adopted as the eastern boundary of the Koksovaya mine area. This disturbance is of the type of an unconformable reverse fault, analogous to disturbance GG. It has been recorded by two boreholes, Nos. 296 and 30, which—

which make it possible to determine its elements of occurrence. The fault plane dips westward at an angle of 77°, while the seams dip eastward at an angle of 67°.

Thus, using the tectonics of the Koksovaya mine as an example, we have shown a rather complex assemblage of disturbances in the Prokopyevsk district, which greatly complicates exploration, reserve calculation, and exploitation of this deposit. Therefore, the correct approach to the study of disjunctives and the determination of a rational method for searching for the displaced limb of a seam is of enormous practical importance. The following chapters of the present work are devoted to these questions.

II. Geological Methods for Investigating Disjunctives in a Mine Working.

Often mine workings cut disturbances that had not previously been encountered by development work and had not been recorded during drilling exploration of the mine field. If, in such a case, the displaced limb of the seam extends beyond the area of the face, then determining the displacement of the displaced limb of the seam, as well as the amplitude of this displacement, is a task of greater or lesser difficulty.

In order to decide in which direction the seam has been displaced relative to the plane of the face, it is necessary to study carefully the disjunctive encountered directly in the mine working. By studying and analyzing every detail of the disjunctive, it is sometimes possible to direct the mining operations correctly toward the displaced limb of the seam, without the use of exploratory workings or underground drilling.

The investigation of a disjunctive encountered in the face usually begins with determining the position and the elements of occurrence of the plane of the fault.

The difficulties in determining the position of the fault plane in the face depend on the angle at which the fault plane and the seam meet in the plane of the face, and also on the degree of disturbance of the seam and of the rocks adjacent to the fault plane. If the fault plane cuts the coal seam at a right angle or at an acute, but nevertheless considerable, angle (Fig. 8), then the line of intersection of the seam and the fault plane in the plane of the face is traced quite distinctly; and consequently, in this case, however poorly the fault plane may be expressed, and however strongly the coal seam and the rocks may be disturbed and crumpled, the position of the fault plane can be determined fairly easily.

However, in most cases in the Kuznetsk Basin, and in particular in the Prokopyevsk district, owing to the fact that the disjunctives are subordinate to a plicative structure and, consequently, cut the seams along strike and dip at very acute angles, the line of intersection of the seam with the fault plane over such a small—

area, as the area of the face, passes along the seam in the floor or in the roof of the latter.

Here two cases are possible in determining the fault plane.

1. If, with such a position of the lines of intersection of the seam with the fault, the face is not complicated by additional fractures, and the seam begins, along the strike, to be smoothly cut off—for example, from the roof—and at the same time the floor remains more or less undisturbed (Fig. 9), then the position of the fault in the face is also determined easily. In the present example it is clear that the fault passes in the roof of the seam. However, in this case, in addition to the obvious cutting-off of the seam from the roof, which we observe as the mine working advances forward, the fault can also be determined directly in the face, since the coal seam and the roof rocks adjoining the fault will be more disturbed than the floor of the seam.

2. If, however, the face is complicated by a whole series of additional fractures and the rocks are strongly crumpled, and to the same degree both in the floor and in the roof of the seam (Fig. 10), so that it is difficult to determine from which side the cutting-off is taking place, then in this case determination of the fault plane in the working is a very difficult matter.

It is necessary to avoid hasty conclusions, which may lead to an incorrect interpretation of the nature of the disturbance, prolong the investigation of the given disjunctive structure, or lead to irrational expenditures on searches for the displaced limb of the seam in the wrong direction.

Experience has shown that in this case the most correct approach, from a methodological point of view, is a comprehensive solution of the question; that is, the position of the fault in the face should be determined jointly and in dependence on the analysis of all details of the disjunctive structure.

The principal details of the disjunctive structure that may serve as criteria for determining the direction of displacement of the displaced limb of the seam may be considered to be:

1) the character of the manifestation of the fault,
2) drag folds,
3) the lithological composition of the rocks on the sides of the fault,
4) guide horizons, and
5) slickensides on the fault plane.

Let us examine each of these details separately.

1) Character of the manifestation of the fault.

In his works on the tectonics of the Kuznetsk Basin, M. A. Usov repeatedly noted a regularity in the character of the manifestation of a fault. This regularity is expressed in the fact that, in disjunctive structures of the type of concordant reverse fault and “direct thrust,” in most cases “the cutting-off of the seam occurs very neatly and the displacement itself proceeds smoothly, without any sharp deformations in the adjoining parts of the limbs of the disjunctive structure (10, 23). The surface—

the displacement planes of these disjunctives are distinguished by their smoothness, are often well polished, and are more or less regular.

This regularity in most cases is well maintained throughout the entire Prokopyevsk deposit and, in particular, in the field of the Koksovaya mine. As an example one may cite the disturbances described above in the Lutuginsky and VI Internal Abinsky seams, and the disturbance in the II Internal seam of the Golubevsky anticlines.

The explanation of this regularity may be found in the relation between the elements of occurrence of the seam and of the displacement plane. Most displacement planes of disjunctives of the type of concordant upthrow and direct thrust, dipping conformably with the seams, intersect them along strike and dip at a very acute angle of from 3 to 10° (Figs. 1, 2, 3, 4, 6, and 7). As a result, in seams split along a plane close to their bedding, no strong stresses arise; consequently the coal seam and the rocks on the flanks of the displacement plane undergo almost no deformation.

It is clear that if the displacement planes of these disjunctives intersect the seams along strike or dip at a more considerable angle, then considerably greater stresses will be created on the flanks of the displacement plane and, consequently, the coal seams and rocks will be more crumpled, while the surfaces of the displacement planes will be rough and wavy.

Thus, for example, the disturbance in the field of Mine No. 2 in the Kharakterny seam, of the type of direct thrust, well traced by the main crosscut at the 232 m level, has a diagonal strike (Fig. 2), intersecting the seam in horizontal section at an angle of 30°. Although the dip angles of the seam—38°—and of the displacement plane—35°—are almost identical, the coal seam and the rocks on the flanks of the displacement plane proved to be strongly disturbed, and the surface of the displacement plane became irregular and wavy.

The rocks and coal are still more deformed in disturbances of the type of discordant upthrow and reverse thrust. In this case, owing to the sharp friction manifested near the displacement plane during rupture and stretching of the seams, the rocks and coal on the flanks of the displacement plane are strongly deformed. For a discordant upthrow it is also of great importance that the displacement plane intersects the seams almost at a right angle. Here the stress increases still more, since the rupture surface becomes very uneven; therefore, during movement of the displaced parts of the disjunctive relative to one another, they have to level on their path projections of various sizes, as a result of which the rocks on the flanks of the displacement plane are deformed still more, forming entire zones of crumpled and broken rocks, similar to the zone that we described above in disturbance GG.

Thus, for longitudinal disturbances the character of manifestation of the displacement plane may serve as one of the criteria in determining the direction of displacement of the displaced limb of the seam, and

namely: a smooth cutting-off of the seam by a fracture and an undisturbed bedding of the rocks on the sides of the displacer will, most likely, indicate that the disjunctive disturbance encountered in the face may be assigned either to a concordant upthrow or to a direct thrust; consequently, in the horizontal section the seam will be doubled. Conversely, an uneven, wavy cutting-off of the seams by a fracture, strongly disturbed rocks on the sides of the displacer, and sometimes the presence of an entire crumpling zone should indicate that the given disjunctive may be assigned to a discordant upthrow or to a reverse thrust, and in the horizontal section the seam will be stretched.

It is clear that this conclusion will be valid in the case where horizontal movements are absent, or, in the extreme case, are insignificant.

2) Drag folds.

Drag folds, or turning-in of seams near a disturbance, are produced as a result of plastic deformation, chiefly of clayey rocks and of the coal seams enclosed between them. Since the turnings-in record the direction of movement of the moving mass, they are a very valuable criterion for determining the direction of displacement of the displaced limb of the seam.

Thus, for example, Fig. 10 presents a rather complex picture, where, as we indicated above, it is difficult even to determine the position of the displacer in the face. However, the clear turning-in of the seam observed by us in the face easily resolves the question of the position of the displacer in the face and, at the same time, makes it possible to determine the direction of displacement of the displaced limb of the seam. In the given case it is clear that the displacer cuts the seam discordantly and that the hanging wall of the disturbance moved upward. Obviously, here the most probable form of the disjunctive will be a discordant upthrow, and, consequently, the displaced limb of the seam at this horizon must be sought along the fracture, ahead of the face.

Sometimes the turning-in of the seam is not observed directly in the face, but the gentle dip of the seam at the displacer in the face, not corresponding to the normal dip of the seams of the given area, makes it possible to establish the presence of a turning-in. Thus, in Fig. 11 the roof of the seam at the displacer has a dip of 15°, whereas the normal dip of the given area is 75°; it is clear that here we have a distinct turning-in of the seam.

Often, as a result of drag, folds are formed, usually consisting of anticlines and synclines. In most cases these folds are overturned, and the steeper or overturned limb is directed toward the movement of the moving mass. These folds are especially well recorded in one of the sketches of the face along the level of seam I Inner, at the intersection by the level of disturbance VII—VII (Fig. 12). Here, in the plane of the face, two seams were found—I Inner and Kharakternyi, the normal distance between which is equal to

31 m. Both seams produced very characteristic drag folds; moreover, the 1st Internal seam produced a clearly expressed overturned anticlinal fold, the steep limb of which faces in the direction of displacement of the seam.

Thus, drag bends are of great importance in interpreting disjunctives. Therefore, when studying disjunctives in a mine working, the most serious attention must be paid to them.

As for slickensiding on the plane of the displacer, excellently analyzed by Willis (12), it may be described in the words of Prof. M. A. Usov (10, 25): “under the conditions of Kuzbass, with its weak rocks and generally plastic coals, these signs are less varied, being represented chiefly by bands and grooves that make it possible to judge mainly the bearing, and not the azimuth of the displacement that created these linear formations.”

Our few observations of slickensiding fully confirm this conclusion.

3) Lithological composition of the rocks in the walls of the displacer.

The lithological composition of the rocks may be of use in analyzing a disjunctive encountered at the face in two respects.

If the face is complex, as a result of which we cannot immediately determine the plane of the displacer, then it is possible to try to determine it by analyzing the lithological composition of the rocks in the plane of the face.

Let us suppose that, in a normal section, the seam has a banded sandstone in the roof and a sandy shale in the floor. Knowing the composition and structure of the rocks in the floor and roof of the seam, when analyzing the rocks in the plane of the face we find that in the floor of the seam there is the same sandy shale, while in the roof, instead of banded sandstone, there is argillite (Fig. 9).

In this case it is clear that the displacer cuts the seam from the roof, since in the face the rock of the seam floor has proved to be the same as in the normal section, whereas in the roof we have another rock, entirely unlike the normal roof rock of the seam.

If we know well the normal section of the enclosing rock mass, and if the composition and structure of the floor and roof of the seam are different, then the rock brought into the face as a result of displacement of the seam may prove to be a valuable criterion for searching for the displaced limb.

Let us imagine that, in the example described above, the structure, color, fracture, and other properties of the argillite are very characteristic of rocks lying stratigraphically above the seam; then it is clear that the seam must be sought to the left relative to the axis of the drift. Conversely, if this argillite were characteristic of rocks lying stratigraphically below the seam, then the seam must be sought to the right relative to the axis of the drift.

When using this criterion for locating the displaced limb of a seam, one must bear in mind the rather sharply manifested facies variability of the rocks in Kuzbass, as a result of which the rocks change their composition and structure along strike and dip. In this case, it is especially possible to recommend the study of rocks along crosscuts and drifts near the encountered disturbance, with the aim of determining the character and degree of facies variability of the rocks.

4) Guiding horizons.

Guiding horizons include the most characteristic interbeds, which are well persistent over great distances along the strike and dip of the rocks; for example: marker beds (companions)—coal seams of small thickness occurring in the roof or floor of the seam, interbeds of ferruginous rocks, conglomerates, horizons with flora and fauna, etc.

If one of such guiding horizons falls within the plane of the face, it will be the most reliable criterion in the search for the displaced limb of the seam. In the given case, knowing the normal distance between the seam and the guiding horizon encountered in the face, we can determine with sufficient accuracy not only the direction in which the displaced limb of the seam is located, but also the apparent horizontal amplitude of this displacement.

For example, Fig. 13 presents a sketch of a disturbance in seam II Inner, at horizon 215 m of the Coke Mine. Here, in the plane of the face, a marker bed was encountered, located between seams II and III Inner, i.e., in the floor of seam II Inner, and well persistent along strike. It is clear that in this case the displaced limb must be sought ahead and to the left of the axis of the drift.

If the normal distance between seam II Inner and the marker bed is equal to \(a\) (in this case 14 m), then the horizontal length of the disturbance will be equal to:

\[ x = \frac{a}{\operatorname{Sin}\alpha \operatorname{Sin}\Theta} \tag{1a} \]

Thus, by studying the disturbance directly in a mine working, we identify individual details of this disturbance which may, to one degree or another, serve as criteria in determining the direction of search for the displaced limb of the seam. However, it must be noted that not all these criteria are equally reliable, and they are not always present in the study of a given disjunctive disturbance.

Of the criteria enumerated above, the most reliable and important are the guiding horizons and the lithological composition of the country rocks. However, guiding horizons enter the investigator’s field of view in the face very rarely, while lithological—

composition, because of the sharp facies variability of the enclosing rocks, may lead the investigator to erroneous conclusions.

The question of determining the direction of displacement of the displaced limb of a seam may also be approached from another point of view—namely, from the standpoint of a geometrical analysis of the interrelations between the elements of occurrence of the seam and of the displacer. This method, in addition to the preceding one, as we shall see below, can yield very effective results.

III. Geometrical analysis of the principal forms of disjunctives.

1) General considerations.

Of all the variety of forms of disjunctives known to us in Kuzbass, and in particular in the Prokopyevsk district, we encounter—as has been established by the work of all geologists and especially by M. A. Usov—such forms of disjunctives as are due mainly to tangential stresses. Therefore, in all our further reasoning we shall proceed exclusively from the overthrust character of the disturbances in Kuzbass.

According to Prof. M. A. Usov’s classification of disjunctives, the following disjunctives occur in Kuzbass: concordant and discordant overthrust, concordant and discordant underthrust, direct and reverse upthrow, and direct downthrow (Fig. 14).

A concordant overthrust (a) is characterized by a concordant dip of the seam and of the displacer, the latter dipping more steeply than the former. Both in a vertical transverse section and in a horizontal section this form gives a duplication of the seam.

A discordant overthrust (b) is characterized by a discordant dip of the seam and of the displacer. This form of disjunctive, both in a vertical transverse section and in a horizontal section, gives a displacement of the seam along the displacer.

Concordant (d) and discordant (e) underthrusts differ from overthrusts in that, in the displacement of blocks relative to one another, the active limb of the disjunctive is not the hanging wall but the footwall; moreover, it moves not upward but downward. A distinction between these forms of disjunctives can be made only in the case when we are able to establish which of the displaced blocks was active, i.e., was in motion, and which remained in relative rest. To prove the actual displacement of the blocks is possible only in rare, exceptional cases. In the majority of cases one has to be satisfied merely with establishing the relative displacement of the blocks with respect to one another.

Under these conditions both types of disjunctives become completely identical and morphologically indistinguishable. Therefore, in what follows they may be considered together. Moreover, it must be noted that underthrusts in Kuzbass are generally encountered rarely, as a result of which they have been poorly studied.

Direct (в) and reverse (г) thrust faults have concordant dip of the seam and of the displacer, and in both forms of disjunctives the displacer dips more gently than the seam. Their difference, according to Prof. M. A. Usov, consists in the fact that in a reverse thrust the hanging wall is displaced upward, as it should be in a thrust, whereas in a direct one it is lowered downward, imitating in its form the phenomenon of a normal fault.

Prof. M. A. Usov explains the latter phenomenon by a bending of the plane of the displacer such that in section it acquires a reverse dip (10, 17). Without disputing the possibility of such an explanation, since curvature of planes in the vertical and horizontal directions is common in Kuzbass, we believe that the same phenomenon may be due both to the presence of an element of strike-slip displacement and to a special combination of the elements of attitude of the seam and the displacer, and in particular to the influence of the angle at which they meet.

As for the direct underthrust (з), with respect to this form of disjunctive one may say the same as for upthrow faults. This form is analogous to a direct thrust, differing from it in that in an underthrust the footwall moved from below upward. Morphologically they are likewise indistinguishable.

Let us consider the influence of the angles at which the seam and the displacer meet on the form of disjunctives, making use of the conclusions from the geometric analysis of oblique disjunctives by Prof. I. A. Molchanov.

It should be noted that geologist-tectonists, and in part also mine surveyors, do not take into account, in analyzing the forms of disjunctives, the influence of the angle at which the seam and the displacer meet on the position of the displaced limb. This is not taken into account either by Prof. M. A. Usov or by other tectonists of Kuzbass. We do not find it in the classical works of Reid (15, 16), B. and R. Willis (13). The same is seen in Lahee (14), who in his Field Geology devotes much attention to questions of tectonics and illustrates them with excellent diagrams, borrowed in part from Reid (15) and other American authors. In examining an oblique normal fault (p. 196, Figs. 144, 145), he even falls into error, since it is easy to see that the line of displacement of the seam in the block diagrams he gives does not coincide with the line of dip of the displacer, but passes obliquely; consequently, the disturbance he considers is not a simple normal fault, with respect to which he makes all his constructions, but a normal strike-slip fault.

This question has not been analyzed with sufficient completeness even in mine geometry, since mine surveyors, in the precise analysis of disjunctives, operate not with the elements of attitude of the seam and the displacer, but with equations of planes in space, which, first, is cumbersome and inconvenient, and, second, is not illustrative.

In this respect the formulas derived by Prof. I. A. Molchanov, thanks to their simplicity and visual clarity, have undoubted advantages. But what is especially important is that they for the first time reveal the significance of the angle of meeting and introduce a new element into the methodology for investigating disjunctives.

2) Analysis of Simple Disjunctives

First of all, let us consider a thrust fault in its pure form, that is, such a form of disjunctive in which the fault plane dips concordantly with the dip of the seam, and the actual relative displacement of the limbs took place along the line of dip of the fault plane, with the hanging limb moving upward along the footwall; we shall conventionally call such disjunctives simple. Further, retaining the letter designations adopted by I. A. Molchanov (Fig. 17),¹ let us assume that: \(l\) is the visible horizontal displacement of the seam, measured across its strike; \(h_0\) is the vertical height of displacement; \(h_1\) is the inclined height of displacement; \(w\) is the subsidence of the seam; \(\alpha\) is the dip angle of the seam; \(\beta\) is the dip angle of the fault plane; \(\omega\) is the angle of intersection of the seam and the fault plane, with the convention 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 plane and of the seam are directed toward one another; \(x\) is a quantity characterizing the excess or deficiency of the visible horizontal displacement caused by the movement of the displaced limb of the seam along an oblique cut.

For oblique disjunctives that have no horizontal displacement, Prof. I. A. Molchanov (6,60) gives the following formula, applicable to all kinds of disturbances:

\[ l = h_0(\operatorname{Ctg}\alpha + \operatorname{Ctg}\beta \operatorname{Cos}\omega) \tag{16} \]

In this connection it is necessary to bear in mind the rule of signs given by Prof. I. A. Molchanov (6,61). “The magnitude of the visible horizontal displacement \(l\) should always be measured in the direction from the footwall limb of the seam toward the hanging-wall limb, and, if this direction coincides with the direction of dip of the seam, then \(l\) is to be taken with the sign \((+)\); if, however, it is directed opposite to the dip of the seam, then it is to be taken with the sign \((-)\); the angles \(\alpha\) and \(\beta\) are always to be considered positive.” The quantities \(h_0\) and \(h_1\) are to be considered positive in reverse faults and thrust faults, and negative in normal faults.

In discordant normal faults, in which the fault plane and the seam dip toward one another, the angle of intersection \(\omega\) is always acute; consequently, the expression in parentheses will always be a positive quantity. If, however, the seam and the fault plane dip concordantly, then \(\omega > 90^\circ\); consequently, \(\operatorname{Cos}\omega\) will be a negative quantity \((\operatorname{Cos}\omega < 0)\), and therefore the expression in parentheses may, depending on the magnitudes of the angles \(\alpha\) and \(\beta\), have different values.

If the fault plane and the seam dip concordantly, and \(\alpha > \beta\), i.e., if we have a thrust fault, then for corresponding values of \(\alpha\), \(\beta\), and \(\omega\) it may turn out that:

\[ \operatorname{Ctg}\alpha + \operatorname{Ctg}\beta \operatorname{Cos}\omega = 0 \tag{2} \]

¹ In the paper included in this same volume, I. A. Molchanov changed some designations, namely: \(h_0\) to \(H\); \(h_1\) to \(h\); and \(w\) to \(k\).

It is clear that in this case equality 1 becomes zero independently of the value of \(h_0\). This is possible only when the line of intersection of the seam and the displacer coincides with the line of displacement of the seam along the displacer. In the present case, for any value of \(h_0\), in a horizontal section we shall not have a visible break between the hanging and footwall limbs of the disturbance.

If, for this equality, we construct a block diagram, selecting the corresponding values of \(\alpha\), \(\beta\), and \(\omega\), we obtain Fig. 15. Here a mining working may pass through the disturbance without detecting the latter. In the limiting case it will encounter a more or less considerable zone of crushed coal with inclusions of fragments and even blocks of wall rocks, various bends, drag folds, and the like, which can affect only its rectilinearity.

For other values of \(\alpha\), \(\beta\), and \(\omega\), it may turn out that the quantity

\[ \operatorname{Ctg}\alpha + \operatorname{Ctg}\beta \operatorname{Cos}\omega > 0 \tag{3} \]

If we construct, for these values of \(\alpha\), \(\beta\), and \(\omega\), a block diagram (Fig. 16), we obtain the form of disjunctive disturbance which Prof. M. A. Usov calls a direct overthrust. In a horizontal section the seam will be doubled.

Finally, for the corresponding values of \(\alpha\), \(\beta\), and \(\omega\), it may turn out that the quantity

\[ \operatorname{Ctg}\alpha + \operatorname{Ctg}\beta \operatorname{Cos}\omega < 0 \tag{4} \]

This shows that the quantity 1 has changed its sign to the opposite one, and we obtain the form of disjunctive disturbance which Prof. M. A. Usov calls a reverse overthrust. In horizontal section this form of disjunctive disturbance gives a separation of the seams. The block diagram (Fig. 17) illustrates this case.

Consequently, the form in which overthrusts are manifested may be determined by a combination of the corresponding values of \(\alpha\), \(\beta\), and \(\omega\). This dependence is especially evident when, having selected values of \(\alpha\), \(\beta\), and \(\omega\) so that they correspond to a direct overthrust, we depict it in a projection with numerical elevations; then, on the same drawing, leaving the same \(\alpha\) and \(\beta\), we change \(\omega\) so as to obtain an expression corresponding to a reverse overthrust. As is seen from Fig. 18, it is sufficient to change the strike of the displacer \(KLK'L'\) to the strike \(EFE'F'\), that is, to change the angle of intersection \(\omega\), leaving the angles \(\alpha\) and \(\beta\) unchanged, for the hanging limb \(ABCD\) to move into the position \(MNOP\), thereby changing the form of the disjunctive disturbance from a direct overthrust to a reverse one.

From the analysis of expressions (3) and (4), as well as Figs. 15, 16, 17, and 18, the following conclusion may be drawn.

1. A direct overthrust may form when the hanging limb of the seam is displaced from below upward (Fig. 16). Therefore it is better to depict a direct overthrust not in orthogonal projection, as Prof. M. A. Usov proposes, but in the form of projections with numerical elevations. This method of depiction is more graphic and makes it easier to represent all the elements of the disjunctive disturbance in space.

1. In a direct thrust fault we have a normal displacement of the seam, that is, the visible horizontal displacement in the uplifted limb occurs in the direction of dip of the seam, and, consequently, \(l\) will be a positive quantity, although in the vertical transverse section it gives the impression of a normal fault (Fig. 14в).

2. In a reverse thrust fault we have an abnormal displacement of the seam, since the visible horizontal displacement occurs in the direction opposite to the dip of the seam, thus producing, on the plan, the impression of a normal fault (Fig. 14г).

3. Since a change in \(\omega\), with one and the same value of \(\alpha\) and \(\beta\), gives in one case a direct thrust fault and in the other a reverse thrust fault, it is quite probable that one and the same disturbance, cutting seams at different angles, may give in one of its parts a direct, and in another a reverse, thrust fault, having somewhere along the strike, between these two types of disjunctive disturbance, a point corresponding to expression (2), at which there will be no visible displacement of the seams in the horizontal section. In practice this is possible in two cases:

a) when the displacer intersects a suite of seams with a changing strike direction, but usually in this case the dip angle of the seams also changes;

b) when the displacer, bending, changes its strike and intersects the suite of seams at different angles. But in this case the displacement vector will no longer be normal to the strike direction of the displacer, but will form with it a certain angle \(\gamma\), not equal to \(90^\circ\); consequently, the simple disturbance passes into a complex one, and an element of strike-slip appears on the scene.

The author does not have the corresponding observations to illustrate the stated supposition by a practical example; however, it follows logically from the analysis carried out above. Nevertheless, if from this point of view one re-examines the correlation of disturbances, even within the limits of the Koksovaya mine section, then, probably, a number of such places will be found where direct and reverse thrust faults could be correlated.

1. A reverse and a direct thrust fault are one and the same genetic form of disjunctive disturbance. Their difference can be explained by the corresponding combinations of the angles \(\alpha\), \(\beta\), and \(\omega\).

On the basis of the geometrical analysis carried out above, the following rule may be derived for searching for the displaced limb of a seam in the case of thrust faults.

1. If the measured elements of occurrence give us expression (3), that is, the absolute values \(|\operatorname{Ctg}\alpha| > |\operatorname{Ctg}\beta \operatorname{Cos}\omega|\), then we shall necessarily have overlapping, and the seam must be sought upward from the footwall limb in the direction of dip of the seam, and from the hanging limb—in the direction of rise (Fig. 14в).

2. If, however, the absolute values \(|\operatorname{Ctg}\alpha| < |\operatorname{Ctg}\beta \operatorname{Cos}\omega|\), then we shall necessarily obtain a separation, and the seam must be sought ahead along the strike line of the displacer (Fig. 14г).

If we analyze in the same way concordant and

discordant normal faults, then here, despite the different forms of disjunctives, in both cases we shall obtain expression (3).

In the case of a discordant normal fault the angle \(\omega\) is always less than \(90^\circ\) and, consequently, \(\operatorname{Cos}\omega > 0\); therefore we obtain expression (3), since the sum of two positive quantities cannot be less than zero. Because the displacer and the seam dip discordantly, in the horizontal section there will always be a separation of the seams and, consequently, the displaced part of the seam must be sought, as in a reverse overthrust, ahead along the line of the displacer (Fig. 14b).

In the case of a concordant normal fault \(\alpha < \beta\) and \(\operatorname{Ctg}\alpha > \operatorname{Ctg}\beta\); consequently, for any value of \(\omega\), the absolute values \(|\operatorname{Ctg}\alpha| > |\operatorname{Ctg}\beta \operatorname{Cos}\omega|\); thus we shall always also obtain expression (3). Since in this case the displacer and the seam dip concordantly, in the horizontal section we shall necessarily have a convergence and, consequently, the rule for searching for the displaced limb will be the same as for a direct reverse overthrust (Fig. 14a).

On the basis of the analysis carried out above, we can construct a graph (Fig. 19) which will allow us, without any calculations, to determine the direction of search for the displaced limb of the seam for each particular value of \(\alpha\), \(\beta\), and \(\omega\).

On the abscissa axis of this graph we plot the seam dip angles \(\alpha\). On the ordinate axis we plot the absolute values \(\operatorname{Ctg}\alpha\). The graph will give a curve called a tangensoid.

On the same graph we construct the function

\[ y = \operatorname{Ctg}\beta \operatorname{Cos}\omega \tag{5} \]

For this purpose we take the value \(\operatorname{Ctg}\beta\) at every \(10^\circ\) and multiply them by \(\operatorname{Cos}\omega\) as the angle \(\omega\) varies from \(90^\circ\) to \(180^\circ\). As a result we obtain a family of curves—sinusoids—characterizing the change of the function \(y\) depending on the change of the angles \(\beta\) and \(\omega\).

Suppose that \(\alpha\), \(\beta\), and \(\omega\) are known to us. It is required, from the graph, to determine the direction of displacement of the displaced limb of the seam. Knowing \(\alpha\), we can find the corresponding ordinate; for this, from the point on the abscissa axis corresponding to the value of our \(\alpha\), in this case \(60^\circ\), we draw a line parallel to the ordinate axis until it intersects the curve—the tangensoid. The line \(AA'\) will be precisely the ordinate corresponding to the absolute value \(\operatorname{Ctg}60^\circ\). Through point \(A\) we draw a line parallel to the abscissa axis until it intersects the curve corresponding to our value of \(\beta\), in this case \(30^\circ\). From the drawing it is evident that \(AA' = BB'\). Obviously, the absolute values \(\operatorname{Ctg}\alpha\) at point \(A\), \(\operatorname{Ctg}\beta\), and \(\operatorname{Cos}\omega\) at point \(B\) satisfy equality (2), i.e., for the given values \(\alpha = 60^\circ\), \(\beta = 30^\circ\), and \(\omega = 109^\circ\), in the horizontal section there will be no visible displacement of the seam.

If, with the same values of \(\alpha\) and \(\beta\), the angle \(\omega < 109^\circ\), for example, \(\omega = 100^\circ\), then \(BB' > FE'\); thus, for the given case, we obtain expression (3). The displaced limb must be sought from the footwall limb in the direction of the seam dip, and from the hanging limb—in the direction of rise.

If, with the same values of $\alpha$ and $\beta$, the angle $\omega > 109^\circ$, for example, $\omega = 140^\circ$, then $FF' > BB'$ and, consequently, for the given case we obtain expression (4). The displaced limb of the seam must be sought ahead along the strike line of the dislocator.

For a conformable normal fault, owing to the fact that in the given case $\alpha < \beta$, the ordinate of the value $\operatorname{Ctg}\alpha$, for any value of $\omega$, will always be greater than the ordinate of the value $\operatorname{Ctg}\beta$ and $\operatorname{Cos}\omega$, and we shall obtain expression (3). For a discordant normal fault we shall likewise obtain expression (3), since here $\operatorname{Cos}\omega$ is always positive and, consequently, both ordinates will be added. The rule for searching for the displaced limb of the seam in the first case is the same as for a direct thrust fault, and in the second, owing to the discordant dip of the seam and the dislocator, the same as for a reverse thrust fault.

3) Analysis of complex disjunctives.

The preceding analysis was carried out for a particular, and therefore rare in nature, case. The most general case will not be thrust faults and normal faults, but thrust-strike-slip and normal-strike-slip faults; let us provisionally call such disjunctives complex. Here the displacement of the hanging limb of the seam occurs upward, but in an arbitrarily inclined direction.

In what follows, in the analysis of thrust- and normal-strike-slip faults, we shall introduce new conventional designations and terms (Fig. 20):

1) $R$ — the total amplitude of displacement,
2) $\lambda$ — the strike-slip element.

$\lambda$ may be a positive or negative quantity. We shall adhere to the sign convention for $\lambda$ proposed by I. A. Molchanov: if the plane of the dislocator is in front of the observer and dips toward him, then the direction of $\lambda$ to the right will be positive $(+)$, and to the left negative $(-)$.

3) $\gamma$ — the angle characterizing the strike-slip element. Naturally, this angle is formed by the direction of the hachuring and the strike of the dislocator, and it must be borne in mind that the angle $\gamma$ is measured counterclockwise from the positive direction of $\lambda$.

If the vector of the total displacement $R$ is resolved, by the parallelogram rule, into two components, then from triangle $ABC$ it is evident that the vertical component corresponds to the inclined height $h_1$, while the horizontal component corresponds to the strike-slip element $\lambda$ (Fig. 20).

Prof. I. A. Molchanov (6, 61) gives the following formula for this case:

$$ l = h_0 \left(\operatorname{Ctg}\alpha + \operatorname{Ctg}\beta \operatorname{Cos}\omega\right) \pm \lambda \operatorname{Sin}\omega \tag{6} $$

Let us note that the sign $(+)$ before the last term on the right-hand side of formula (6) is taken in the case when the subsidence of the seam, during the upward movement of the hanging limb, occurs in the direction of positive values of $\lambda$; otherwise the sign $(-)$ must be taken. Or, in other words:

if the dip of the seam is directed toward positive values of \(\lambda\), then the sign \((+)\) is taken in the formula; otherwise, \((-)\). From triangle ABC (Fig. 20) we obtain

\[ \lambda = h_1 \operatorname{Ctg}\gamma, \tag{7} \]

and from triangle EFK (Fig. 17)

\[ h_0 = h_1 \operatorname{Sin}\beta \tag{8} \]

or

\[ h_1 = \frac{h_0}{\operatorname{Sin}\beta}. \tag{9} \]

Substituting its value for \(h_1\) in formula (7), we obtain:

\[ \lambda = h_0 \frac{\operatorname{Ctg}\gamma}{\operatorname{Sin}\beta}. \tag{10} \]

If now, in equation (6), we substitute its value (10) for \(\lambda\) and carry out the transformation, the final formula will take the following form:

\[ l = h_0\left(\operatorname{Ctg}\alpha + \operatorname{Ctg}\beta \operatorname{Cos}\omega \pm \frac{\operatorname{Ctg}\gamma \operatorname{Sin}\omega}{\operatorname{Sin}\beta}\right). \tag{11} \]

The rule of signs remains the same.

Further analysis may be carried out in the same way as we did for simple disjunctives.

Let us again begin the analysis with overthrusts. Here, as before, \(\operatorname{Cos}\omega\) will always be negative, while \(\operatorname{Ctg}\gamma\) may be either positive or negative. If \(\gamma\) lies within the limits from \(0\) to \(90^\circ\), then \(\operatorname{Ctg}\gamma\) will be positive; if from \(90\) to \(180^\circ\), negative.

Let us write out from formula (11) the second factor, which we shall subject to analysis below:

\[ \operatorname{Ctg}\alpha + \operatorname{Ctg}\beta \operatorname{Cos}\omega \pm \frac{\operatorname{Ctg}\gamma \operatorname{Sin}\omega}{\operatorname{Sin}\beta} \tag{12} \]

Suppose that the quantities \(\alpha\), \(\beta\), and \(\omega\) give us expression (3). The dip of the seam is directed toward negative values of \(\lambda\); consequently, the sign before the third term will be \((-)\). The angle \(\gamma\) has proved to lie within the limits from \(90\) to \(180^\circ\). Then expression (12), presented for convenience of analysis in absolute values, will have the form:

\[ |\operatorname{Ctg}\alpha| - |\operatorname{Ctg}\beta \operatorname{Cos}\omega| + \left|\frac{\operatorname{Ctg}\gamma \operatorname{Sin}\omega}{\operatorname{Sin}\beta}\right| > 0 \tag{13} \]

In this case the displacement element will intensify the doubling of the seam, since the sign \((+)\) before the third term of expression (13) will further increase the absolute value of \(\operatorname{Ctg}\alpha\). The increase in doubling will be the greater, the closer \(\gamma\) is to \(180^\circ\).

If \(\gamma\) is closer to \(90^\circ\), then we shall have a strike-slip overthrust. If it is closer to \(180^\circ\), we shall have an overthrust strike-slip. Finally, there may be the particular case when \(\gamma = 180^\circ\); then \(\operatorname{Ctg}\gamma = \infty\) and \(h_0 = 0\). Formula (13) takes the form of an indeterminacy. Then we turn to the original formula (6) and obtain \(l = -\lambda \sin\omega\); consequently, we shall have a strike-slip, which Prof. I. A. Molchanov calls a negative strike-slip (Fig. 21a). It is clear that if \(\gamma = 90^\circ\), then in the given case a vertical displacement will occur, a case already analyzed by us above.

If, for the same values of \(\alpha\), \(\beta\), and \(\omega\), the value of \(\gamma\) lies within \(0\)—\(90^\circ\), then \(\operatorname{Ctg}\gamma\) will be positive, and, consequently, the absolute value of the third term of expression (13) will enter this expression with the sign \((-)\), that is:

\[ |\operatorname{Ctg}\alpha| - |\operatorname{Ctg}\beta \cos\omega| - \left|\frac{\operatorname{Ctg}\gamma \sin\omega}{\sin\beta}\right| \tag{14} \]

Here three cases are possible:

1.

\[ \left|\frac{\operatorname{Ctg}\gamma \sin\omega}{\sin\beta}\right| < |\operatorname{Ctg}\alpha| - |\operatorname{Ctg}\beta \cos\omega| \tag{15} \]

Then the absolute value of \(\operatorname{Ctg}\alpha\) remains greater than the sum of the absolute values of the other two terms of expression (14), and the arrangement of the seams remains the same as for expression (13), only reducing the doubling of the seam by a certain amount. Obviously, such a case is possible when the element of vertical displacement will considerably predominate over the element of strike-slip, that is, when \(\gamma\) is closer to \(90^\circ\).

2.

\[ \left|\frac{\operatorname{Ctg}\gamma \sin\omega}{\sin\beta}\right| = |\operatorname{Ctg}\alpha| - |\operatorname{Ctg}\beta \cos\omega| \tag{16} \]

In this case the form of the disjunctive disturbance will be the same as for expression (2). In a horizontal section we shall not observe a visible break of the seam: \(l = 0\).

3.

\[ \left|\frac{\operatorname{Ctg}\gamma \sin\omega}{\sin\beta}\right| > |\operatorname{Ctg}\alpha| - |\operatorname{Ctg}\beta \cos\omega| \tag{17} \]

In the given case the absolute value of \(\operatorname{Ctg}\alpha\) will prove smaller than the sum of the absolute values of the other two terms of expression (14), and the arrangement of the seams will be the same as for expression (4). Instead of the doubling of the seam expected according to the values of \(\alpha\), \(\beta\), and \(\omega\), we shall have its separation. This case is possible when the strike-slip element predominates over the element of vertical displacement, i.e., when \(\gamma\) is closer to \(0^\circ\).

Now let us assume that the combination of the magnitudes \(\alpha\), \(\beta\), and \(\omega\) gives us expression (4). The dip of the seam is likewise directed toward the side of negative values of \(\lambda\). The angle \(\gamma\) has proved to lie within \(0\)—\(90^\circ\). Then expression (12), represented in absolute values, will take the following form:

\[ |\operatorname{Ctg}\alpha| - |\operatorname{Ctg}\beta \cos\omega| - \left|\frac{\operatorname{Ctg}\beta \sin\omega}{\sin\gamma}\right| < 0 \tag{18} \]

Here, too, the shift element will intensify the separation of the seam, since the minus sign preceding the third term of expression (18) will reduce \(\operatorname{Ctg}\alpha\) still more. The increase in the separation of the seam will depend on \(\gamma\). If \(\gamma\) is closer to \(90^\circ\), then the increase in separation will be insignificant and, consequently, the form of the disjunctive disturbance will be a strike-slip thrust. If \(\gamma\) is closer to \(0^\circ\), then the separation of the seams increases considerably, and the form of the disjunctive disturbance will be a thrust strike-slip. Finally, in the present case it may be that \(\gamma = 0\); then in formula (6) \(h_0 = 0\), and, consequently, we obtain a shift called by Prof. I. A. Molchanov a positive shift (Fig. 21).

Now let us suppose that, for the given values of \(\alpha\), \(\beta\), and \(\omega\), the value of \(\gamma\) lies within the limits \(90\text{--}180^\circ\); then \(\operatorname{Ctg}\gamma\) will be negative, and therefore expression (18) will have the form:

\[ |\operatorname{Ctg}\alpha| - |\operatorname{Ctg}\beta \operatorname{Cos}\omega| + \left|\frac{\operatorname{Ctg}\gamma \operatorname{Sin}\omega}{\operatorname{Sin}\beta}\right| \tag{19} \]

Here, three cases are also possible:

1.

\[ \left|\frac{\operatorname{Ctg}\gamma \operatorname{Sin}\omega}{\operatorname{Sin}\beta}\right| < |\operatorname{Ctg}\beta \operatorname{Cos}\omega| - |\operatorname{Ctg}\alpha| \tag{20} \]

Here the sum of the first and third terms of expression (19) will be less than the second term. The disposition of the seams will remain the same as for expression (18), only the separation of the seams will be reduced by some amount. Such a case is possible when the value of \(\gamma\) is close to \(90^\circ\).

2.

\[ \left|\frac{\operatorname{Ctg}\gamma \operatorname{Sin}\omega}{\operatorname{Sin}\beta}\right| = |\operatorname{Ctg}\beta \operatorname{Cos}\omega| - |\operatorname{Ctg}\alpha| \tag{21} \]

Here the disposition of the seams will remain the same as for expression (2). In the horizontal section we shall not observe a visible break in the seam.

3.

\[ \left|\frac{\operatorname{Ctg}\gamma \operatorname{Sin}\omega}{\operatorname{Sin}\beta}\right| > |\operatorname{Ctg}\beta \operatorname{Cos}\omega| - |\operatorname{Ctg}\alpha| \tag{22} \]

Here the sum of the first and third terms of expression (19) will be greater than the second term, and the form of the disjunctive disturbance will be the same as for expression (3). Instead of the seam separation expected according to the values of \(\alpha\), \(\beta\), and \(\omega\), we shall have its joining. This case will be possible when \(\gamma\) is closer to \(180^\circ\).

In the same way one may analyze a discordant upthrow as well; here too we shall have four cases depending on the sign in the formula and the value of \(\gamma\). It should only be noted that in this case, in order to obtain joining of the seam, it is necessary to have a considerably greater absolute value of the third term of expression (12) than for concordant disturbances, since in the present case \(\cos\omega\) will always be positive and, consequently, the first two terms will be added.

Use of expression (12) for determining the direction of the search for the displaced limb of the seam can be considerably simplified. The first two terms of this expression are easily found on the graph (Fig. 19); for the third term one can likewise construct a graph, by means of which it is easy to find, for each particular value of \(\alpha\), \(\beta\), and \(\omega\), its absolute magnitude (Fig. 22).

Let us plot the function

\[ y = C \operatorname{tg}\gamma \operatorname{Sin}\omega \tag{23} \]

On the graph there will be obtained, as in the preceding case, a family of curves (sinusoids), which will characterize the change of the function \(y\) as \(\gamma\) and \(\omega\) vary. The absolute magnitudes of any point taken on one of these curves will be expressed by the ordinate. If we take the corresponding points on the ordinate and divide their absolute magnitudes by \(\operatorname{Sin}\beta\), the values of which will be located on the axis of abscissas, then we shall obtain a new family of tangent curves, which will characterize the change of the absolute magnitude of expression (23) as \(\beta\) varies, i.e., on these curves we shall obtain the required quantity.

Suppose that \(\gamma\), \(\omega\), and \(\beta\) are known; it is required to determine from the graph the expression

\[ x = \frac{C \operatorname{tg}\gamma \operatorname{Sin}\omega}{\operatorname{Sin}\beta} \tag{24} \]

For greater clarity let us take a numerical example.

Let \(\gamma = 30^\circ;\ \omega = 150;\ \beta = 50^\circ.\)

On the graph we find on the axis of abscissas the point corresponding to

\[ \operatorname{Sin}150^\circ = \operatorname{Sin}30^\circ. \]

From this point \(A'\) we draw a line parallel to the ordinate axis until it intersects the curve \(\gamma = 30^\circ\). The intersection point \(A\) will correspond to the absolute value of the numerator of expression (24).

\[ \operatorname{Ctg}30^\circ \operatorname{Sin}30^\circ = 0.865. \]

Next we carry point \(A\) to the right, onto a line parallel to the \(Y\)-axis. If it does not coincide with the origin of some curve characterizing our sought quantity, then by interpolation we draw a curve, relative to the nearest curve, until it intersects the value \(\operatorname{Sin}50^\circ\). The ordinate of the intersection point will give us the absolute magnitude of expression (24). In the present case this point will correspond to point \(B\), and we obtain

\[ \frac{\operatorname{Ctg}30^\circ \operatorname{Sin}30^\circ}{\operatorname{Sin}50^\circ} = \frac{0.885}{0.643} = 1.137 \]

The two graphs constructed above (Fig. 19 and Fig. 22) may be combined into one graph (Fig. 23), and the first family of curves, as is evident from the graph, can characterize both

function (5), and function (23). It is clear that for practical work it is more convenient to use the latter graph.

Thus, from the graph the absolute values of the terms of formula (11) are easily determined. Using the analysis made of the relationships among these terms, i.e., ultimately, the sign with which each of these three terms must be taken, it is easy also to determine the sign of their algebraic sum. The sign of this sum, in turn, determines the sign of the quantity \(l\). If, as in the Kuzbass, the prevailing form of disjunctives is reverse faults and overthrusts, in which the hanging walls move upward, then the sign of \(h_1\) will always be \((+)\); therefore the sign of \(l\) will be identical with the sign of expression (12). Consequently, if for expression (12) we obtain the sign \((+)\), then \(l\) will also be positive, and therefore the position of the seam in the hanging wall of the disjunctives must be sought in the direction of dip of the seam. If, however, in expression (12) we obtain the sign \((-)\), then \(l\) will be negative, and the position of the seam in the hanging wall of the disjunctives must be sought in the direction opposite to the dip of the seam.

The angles \(\alpha\), \(\beta\), and \(\omega\) can always be taken directly from the face; as for \(\gamma\), it can be determined from the striation, if such is present on the plane of the displacer. It is necessary, however, to make the reservation that striation is not always present on the plane of the displacer; or, owing to the presence of several phases of tectogenesis, the original striation may be obscured by the appearance of a new one, which already has a different angle \(\gamma\).

Sometimes it is possible to determine the angle \(\gamma\) even without striation, from two conjugate planes of displacers, one of which is the apophysis of the other. Such “branching” disjunctives are very widespread in the Kuzbass, and therefore the indicated method for determining the direction of the relative displacement of the wings is of especially great importance; we shall dwell on it in the next chapter.

IV. Analysis of the Tectonics of the Koksovaya Mine

1) General Provisions

In the preceding chapters, when determining the direction in which to search for the displaced wing of a seam, we proceeded from an analysis of disjunctives directly in a mine working, without relation to the tectonics of the entire deposit or of a separate part of it. However, for the correct interpretation of disjunctives it is necessary to consider them in close connection with the general tectonics of the deposit, since on the basis of its regularities one can predetermine the predominant forms of disjunctives and thereby considerably facilitate the search for the displaced wing of a seam.

Let us try, from this point of view, to analyze the tectonics of the eastern wing of the Golubevsky anticline, applying here the methodology presented above.

According to geological investigations, the tectonics of the Prokopyevsk deposit is conditioned by the western pressure, dominant in this area, from the side of the Salair Ridge. As a result of this pressure, on the corresponding limbs of the folds the main fault lines were laid down, chiefly of an overthrust character, with considerable amplitudes of displacement. The planes of these faults have a rather steep dip of 70–85° and intersect the strike of the series at a very acute angle of 5–10° (Fig. 1).

These fault planes were formed most readily on the eastern limbs of anticlinal folds, where, owing to the discordant dip of the displacers and the beds, discordant overthrusts arose. The western limbs of the anticlinal folds proved to be less disturbed, and only in the western part of the deposit were fault planes also established in places on them; moreover, because in this case they dip conformably with, and more steeply than, the beds, concordant overthrusts arose on these limbs.

In addition to the principal fault planes, along their flanks we encounter a series of second-order disjunctives, with a considerably smaller amplitude of displacement. In most cases the planes of the displacers of these disturbances are conjugate with the principal fault planes, approaching them at a more or less acute angle. The forms of these disjunctives vary. However, in most cases, despite all the apparent complexity and chaotic nature of the elements of occurrence at first glance, it is possible to distinguish the principal patterns of disturbance, governed by one and the same laws.

These disjunctives are apophyses of the principal fault lines. They arose as a result of the release of stresses that were created in the flanks of the principal fault lines, and the movement of individual blocks along the planes of the second-order displacers was in close connection with, and in direct dependence on, the movement of the entire mass of the hanging wall of the principal faults. Consequently, from them—or, more precisely, by considering the major disturbances in connection with them—it is possible to reconstruct the genesis of the dislocations of the given area, or even of the entire deposit.

Having made these brief but necessary observations concerning the tectonics of the entire Prokopyevsk district, we shall now proceed to the main task of the present chapter: the analysis of the tectonics of the eastern limb of the Golubevsky anticline.

On the eastern limb of the Golubevsky anticline, the principal disturbances are disturbances GG and, in part, V—V. True, the latter is of considerably smaller amplitude and, as we have already noted earlier, at the 215 m horizon it dies out, not reaching the closure of the Gorely bed. Therefore it is of no great importance in the creation of a dense network of disjunctives on this limb.

If we turn to the tectonics of the entire eastern limb of the Golubevsky anticline (Fig. 24), enclosed between two

called the principal dislocations GG and V—V, then, with a fairly dense network of various disturbances of this limb, four characteristic disturbances of the second order may be distinguished, namely VII—VII, VIII—VIII, IX—IX, and X—X.

The displacers of these disturbances have a diagonal strike—285°—and form with the disturbance GG a considerable angle, reaching up to 40°. The displacers of these disturbances dip conformably with the seams, and, consequently, opposite to the dip of the plane of the displacer GG; moreover their dip is considerably gentler than the dip of the seams, varying within the range 35–55°. In horizontal section they produce a separation of the seams.

These disturbances do not intersect the disturbance GG. They are confined exclusively to the hanging wall of the latter and adjoin the main fracture, gradually merging with it. It follows from this that these disturbances were formed simultaneously with the disturbance GG, and arose during the movement of the entire mass of the hanging wall along the rupture plane GG. Therefore the planes of the displacers of disturbances VII—VII, VIII—VIII, IX—IX, and X—X may be regarded as mutually conjugate with GG.

The movement of blocks enclosed between the fractures of the second order and GG could occur only simultaneously along two mutually conjugate planes of displacers, and, consequently, the direction of their movement must coincide with the line of intersection of these planes. In the present case each block moved in the direction of the line of intersection of the plane of the displacer GG and the plane of the displacer of the corresponding apophyseal disturbance. Thus the line of intersection of the planes of the displacers is a complete analogue of slickenside striation, and from it we can determine the angle \(\gamma\), or \(\gamma \pm 180^\circ\). If this is so, then, using the formulas of I. A. Molchanov, we can determine not only the character but also the amplitude of the relative displacement of these blocks.

2) Methods for determining the angle \(\gamma\).

Let us consider disturbance IX—IX, taking any seam displaced by this disturbance, for example IV Internal. The angles \(\alpha\) and \(\beta\) are known to us. The quantities \(l\) and \(\omega\) are determined from the plan. The angle \(\gamma\), characterizing the direction of the striation, is determined from the two conjugate planes of the displacers IX—IX and GG (Fig. 25a).

The angle of intersection of the displacers GG and IX—IX is 40°; the dip angle of the displacer GG is \(\beta_1 = 70^\circ\), that of the displacer IX—IX is \(\beta_2 = 40^\circ\). We construct a second horizontal section at an arbitrarily chosen distance below the plane of the plan. To do this, we draw two parallel lines KK and LL (Fig. 25b) at a distance \(r\) (on the scale of the plan) from one another and then, taking arbitrary points \(s\) and \(t\) on the line KK, we lay off from them the dips of the displacers \(\beta_1\) and \(\beta_2\). We obtain the offsets \(a_1\) and \(a_2\). Then, at a distance \(a_1\) from the trace of the displacer GG of the given horizon and \(a_2\) from the trace of the displacer IX—IX, we construct the projections of the traces of these displacers on the planes

of the lower horizon \(IX'—IX'—G'G'\). If we now connect points \(IX\) and \(IX'\), we obtain the line of intersection of the displacers \(GG\) and \(IX—IX\). If we take the line of intersection of the planes as the line of movement of the block along the plane \(IX—IX\), then, obviously, the angle \(IX\,IX\,IX'^{1}\) will be \(\gamma'\), i.e., the horizontal projection of the angle \(\gamma\). Knowing \(\gamma'\), we can easily find the true magnitude \(\gamma\). For this purpose, from point \(IX'\) we drop to the trace of the displacer \(IX—IX\) the perpendicular \(IX'E\), and from point \(E\) draw, at the angle \(\beta=40^\circ\), the line \(EK=EIX'\). Then from point \(K\) draw a perpendicular to line \(EK\) until it intersects the extension of line \(EIX'\) at point \(n\). It is now not difficult to see that \(\angle EIXn\) is the true magnitude of the angle \(\gamma\), since \(EIXnK\) is nothing other than the development of the dihedral angles \(BA_1C\) and \(AA_1D\) (Fig. 26) onto the horizontal plane and, consequently, \(\angle EIXn\) corresponds to \(\angle ADC\). Measuring \(\angle EIXn\) with a protractor, we find that it is equal to \(38^\circ\), but since \(\gamma\) is counted counterclockwise from positive values of \(\lambda\), in the present case we shall finally have:

\[ \gamma = 180^\circ - 38^\circ = 142^\circ{}^{1}) \]

The angle \(\gamma\), if we know \(\gamma'\), can also be found analytically. For this, Prof. I. A. Molchanov (6, 66) gives the following formula:

\[ \operatorname{Tg}\gamma=\frac{\operatorname{Tg}\gamma'}{\operatorname{Cos}\beta} \tag{25} \]

Let us find the value of \(\gamma\) for the displacer \(IX—IX\), using formula (25).

The angle \(\beta\) is known to us—\(40^\circ\). We measure the angle \(\gamma'\) with a protractor in Fig. 25a: \(\angle IX\,IX\,IX'=\angle\gamma'=31^\circ\).

From the table of natural trigonometric values we write out:

\[ \operatorname{Cos}\beta=0.766,\qquad \operatorname{Tg}\gamma'=0.600. \]

Then

\[ \operatorname{Tg}\gamma=\frac{0.600}{0.766}=0.785,\quad \text{or } \gamma=38^\circ. \]

But, taking into account the rule for counting the angle \(\gamma\), we finally obtain

\[ \gamma=180^\circ-38^\circ=142^\circ. \]

We have already arrived at the conclusion that the block \(IX—IX\) moved simultaneously and in the same direction as the hanging wall of the disturbance \(GG\). Then, obviously, the line of intersection \(IX—IX'\) may also be taken as the line of movement of the hanging wall of disturbance \(a\); consequently, \(\angle IX'IXF=\gamma'_g\), i.e., \(\gamma'_g\) is the horizontal projection of the angle \(\gamma_g\) of this disturbance. Carrying out the same construction as in the first case, we find that the true magnitude is

\[ \gamma_g=25^\circ. \]

\(^{1}\) Assuming the movement of the hanging wall upward.

Here also, knowing \(\gamma_g\) and \(\beta\), one can, using formula (25), determine \(\gamma_g\) analytically.

\[ \beta = 70^\circ. \]
We also measure the angle \(\gamma_g\) in Fig. 25a:

\[ IX'IX\, g = \gamma'_g = 9^\circ. \]

From the table of natural trigonometric values we write out:

\[ \operatorname{Ctg}\beta = 0.342;\qquad \operatorname{Tg}\gamma'_g = 0.158. \]

Then

\[ \operatorname{Tg}\gamma_g = \frac{0.158}{0.342} = 0.468, \]

or

\[ \gamma_g = 25^\circ. \]

Thus, having two conjugate planes of the dislocator, we can always find the angle \(\gamma'\) graphically; and knowing the latter, we can determine the true value \(\gamma\) either graphically or analytically.

Now, knowing \(\alpha, \beta, \omega, \gamma\), and \(l\), we can determine the absolute magnitudes of all the remaining elements characterizing the disturbance \(IX—IX\), namely \(R, h_0, h_1\), and \(\lambda\).

3) Determination of the basic elements for the disturbance IX—IX.

For seam IV Inner we find that \(l = -20\) ¹), \(\alpha = 65^\circ\), \(\omega = 130^\circ\). The dip angle of the dislocator \(IX—IX\) is \(\beta = 40^\circ\), \(\gamma = 142^\circ\).

To determine the absolute value \(R\), we shall use the formula of Prof. I. A. Molchanov (6, 65).

\[ R = \frac{l} {\operatorname{Ctg}\alpha \operatorname{Sin}\beta \operatorname{Sin}\gamma + \operatorname{Cos}\beta \operatorname{Cos}\omega \operatorname{Sin}\gamma \pm \operatorname{Sin}\omega \operatorname{Cos}\gamma}. \tag{26} \]

In the present case the sign before the third term in the denominator of formula (26) must be taken as \((-)\), since the dip of seam IV Inner is directed toward negative values of \(\lambda\).

From the table of natural trigonometric values we write out:

\[ \begin{aligned} \operatorname{Ctg}\alpha &= 0.466; & \operatorname{Ctg}\beta &= 1.192; & \operatorname{Ctg}\gamma &= -1.280,\\ \operatorname{Cos}\omega &= -0.643; & \operatorname{Cos}\beta &= 0.766; & \operatorname{Cos}\gamma &= -0.788,\\ \operatorname{Sin}\omega &= 0.766; & \operatorname{Sin}\beta &= 0.643; & \operatorname{Sin}\gamma &= 0.616. \end{aligned} \]

We determine the numerical values of the individual terms:

\[ \begin{aligned} 1.\quad & \operatorname{Ctg}\alpha \operatorname{Sin}\beta \operatorname{Sin}\gamma = 0.466 \cdot 0.643 \cdot 0.616 = 0.184,\\ 2.\quad & \operatorname{Cos}\beta \operatorname{Cos}\omega \operatorname{Sin}\gamma = 0.766(-0.643)\cdot 0.616 = -0.303,\\ 3.\quad & \operatorname{Sin}\omega \operatorname{Cos}\gamma = 0.766(-0.788) = -0.604,\\ 4.\quad & \operatorname{Ctg}\beta \operatorname{Cos}\omega = 1.192(-0.643) = -0.766,\\ 5.\quad & \frac{\operatorname{Ctg}\gamma \operatorname{Sin}\omega}{\sin\beta} = \frac{(-1.280)\cdot 0.766}{0.643} = -1.525. \end{aligned} \]

¹) In the present case, measuring \(l\) from the lying wall to the hanging wall, we go against the dip of the seam; consequently, according to the sign rule, before \(l\) one must take the sign \((-)\).

Using formula (26), we find:

\[ R=\frac{-20}{0.184-0.303+0.604}=\frac{-20}{0.485}=-41.2\ \text{m}. \]

We have obtained the value \(R\) with the sign \((-)\), which is absurd, since \(R\) can only be a positive quantity. Negative values of \(R\) show that the movement along the line of intersection occurred in the opposite direction, i.e., \(\gamma\) should be equal not to \(142^\circ\), as we first found graphically and then analytically, but to \(142^\circ+180^\circ=322^\circ\), i.e., the position of the vector \(R\) will be not in the second but in the fourth quadrant, and, consequently, the movement was not upward but downward.

Judging by the character of the disturbance IX—IX, it may be assigned either to a reverse fault or to a normal fault. As we see, the mathematical analysis of this form of disjunctive brings us precisely to a normal fault, since the value \(R\) will be positive only if we take \(\gamma=322^\circ\). Then \(\sin \gamma\) will be negative, \(\cos \gamma\) positive; therefore all the signs in the denominator of formula (26) will change to the opposite ones, and, consequently, the value \(R\) will be positive, i.e.,

\[ R=\frac{-20}{-0.184+0.303-0.604}=\frac{-20}{-0.485}=41.2\ \text{m}. \]

Now, applying formulas (11, 9, and 10), we determine the remaining elements of this disturbance:

\[ h_0=\frac{-20}{0.466-0.766+1.525}=\frac{-20}{1.225}=-16.3\ \text{m}; \]

\[ h_1=\frac{-16.3}{0.643}=-25.3\ \text{m};\quad \lambda=\frac{(-16.3)(-1.280)}{0.643}=32.5\ \text{m}, \]

Whence we conclude that this form of disjunctive is a positive normal strike-slip fault with elements \(h_1=-25.3\ \text{m}\) and \(\lambda=32.5\ \text{m}\).

That in the present case we are dealing with normal faults is also indicated by the open character of the fissures of these disturbances, since in the mine workings that intersected these fissures, divergence of the walls from \(0.1\) to \(0.5\ \text{m}\) was everywhere recorded, with the fissures filled with characteristic vein clay and fragments of the wall rocks. In the same way, all the principal elements may also be determined for disturbance GG.

Determination of the principal elements of disturbance GG.

For the VI Inner seam we find that \(l=125\ \text{m}\), \(\alpha=65^\circ\), \(\omega=10^\circ\). The dip angle of the displacer GG is \(\beta=70^\circ\), \(\gamma=25^\circ\).

In the present case, measuring \(l\) from the footwall to the hanging wall, we proceed along the dip of the seam; consequently, according to the sign rule, a sign \((+)\) must be placed before \(l\). As for the sign before

by the third term of formula (26), then here one must take the sign (−), since the arrow indicating the dip of seam VI Internal is directed toward negative values of \(\lambda\).

Also using formula (26), from a table of natural trigonometric values we write:

\[ \begin{aligned} \operatorname{Ctg}\alpha &= 0.466; & \operatorname{Ctg}\beta &= 0.364; & \operatorname{Ctg}\gamma &= 2.144 \\ \operatorname{Cos}\omega &= 0.985; & \operatorname{Cos}\beta &= 0.342; & \operatorname{Cos}\gamma &= 0.906 \\ \operatorname{Sin}\omega &= 0.174; & \operatorname{Sin}\beta &= 0.940; & \operatorname{Sin}\gamma &= 0.422 \end{aligned} \]

We determine the numerical values of the individual terms:

\[ \begin{aligned} 1.\quad &\operatorname{Ctg}\alpha \operatorname{Sin}\beta \operatorname{Sin}\gamma = 0.466 \cdot 0.940 \cdot 0.422 = 0.185 \\ 2.\quad &\operatorname{Cos}\beta \operatorname{Cos}\omega \operatorname{Sin}\gamma = 0.342 \cdot 0.985 \cdot 0.422 = 0.145 \\ 3.\quad &\operatorname{Sin}\omega \operatorname{Cos}\gamma = 0.174 \cdot 0.906 = 0.158 \\ 4.\quad &\operatorname{Ctg}\beta \operatorname{Cos}\omega = 0.364 \cdot 0.985 = 0.359 \\ 5.\quad &\frac{\operatorname{Ctg}\gamma \operatorname{Sin}\omega}{\operatorname{Sin}\beta} = \frac{2.144 \cdot 0.174}{0.940} = 0.397 \end{aligned} \]

Substituting into formulas 9, 10, and 11 the numerical values in place of the trigonometric quantities, we obtain:

\[ R = \frac{125}{0.185 + 0.145 - 0.158} = \frac{125}{0.172} = 725\ \text{m} \]

\[ h_0 = \frac{125}{0.466 + 0.359 - 0.397} = \frac{125}{0.428} = 292\ \text{m} \]

\[ h_1 = \frac{292}{0.940} = 310\ \text{m};\quad \lambda = \frac{292 \cdot 2.144}{0.940} = 665\ \text{m}. \]

From this we conclude that the disturbance GG is a positive reverse fault–strike-slip fault with elements \(h_0 = 292\) m and \(\lambda = 665\) m, the magnitude of the horizontal displacement being more than twice the magnitude of the vertical displacement.

Thus, analysis of the disturbance GG has led us to a reverse fault–strike-slip fault with a significant predominance of horizontal displacement over vertical displacement. But this is not all—this same analysis allows us to judge not only the magnitude of the principal elements of the disturbance GG, but also the direction in which the hanging wall of this disturbance moved. Indeed, the positive value of \(\lambda\) quite definitely indicates that the hanging wall of the disturbance GG moved in the direction from NW to SE, i.e., in a direction opposite to the dip of the seams.

Having arrived at this conclusion, we can easily explain the occurrence of normal faults in this wall as well. In the present case, disturbances VII—VII, VIII—VIII, IX—IX, and X—X break the hanging wall of disturbance GG into blocks bounded on four sides by the planes of displacers. Since these disturbances are apophyses of disturbance GG and were formed simultaneously with the formation of

the latter, then, obeying the general movement of the hanging wall of the fault GG, on the one hand, and on the other—the movement along their displacement planes, were raised relative to one another in such a way that each preceding block, counting from the NW to the SE, lagged somewhat in its upward movement in relation to the following one, thus producing a telescopic protrusion of each succeeding block from beneath the preceding one. Such lagging of the blocks, with the general upward movement of the entire hanging wall, caused the formation of these forms of disjunctives, which do not represent typical faults, but by their morphological features must be assigned to them.

Thus, by using the method set forth, it is possible to establish not only the form of the disjunctives and their mutual relation, but also the principal elements \(R\), \(h_0\), \(h_1\), and \(\lambda\), characterizing the amplitude of the actual relative displacement of the displaced parts of the seam.

It is understandable that second-order disturbances, as a result of the release of stresses arising along their sides, will in turn create apophyses, i.e., third-order disturbances. Such disturbances, generally having a small amplitude, are encountered very often in mines and greatly complicate the conduct of mining operations. For them, using this same method, it is also possible to determine all the principal elements characterizing the given disjunctive.

Conclusion.

In the present work the author, using material collected by him while working as a mine geologist at the Koksovaya I Mine named after Comrade Stalin, in the Prokopyevsk district, investigates the principal forms of disjunctives encountered in the Kuznetsk Basin in the search for the displaced limb of a seam.

The author comes to the conclusion that, as a result of careful study of a disturbance directly in a mine working, by analyzing geological criteria, it is sometimes possible from them to determine the position of the displaced limb of a seam. However, these criteria are not always present in disjunctives and are not always reliable, especially in complex disturbances and under conditions of sharp facies variability of the Kuzbass rocks. In this case, along with geological criteria, it is necessary to resort to geometrical analysis of disjunctives. With such a combined analysis of disjunctives, it is often possible to determine the direction in which to search for the displaced limb of a seam without the use of exploratory workings or underground drilling.

In his investigations the author used, chiefly, the method of geometrical analysis of translational disjunctives proposed by Prof. I. A. Molchanov, by means of which he analyzes the principal forms of disjunctives first for vertical, and then also for arbitrarily inclined displacement of the displaced limb of the seam.

As a result of such an analysis, the author establishes regularities by means of which, in most cases, it is possible simply and easily to determine the position of the displaced limb of a seam. For this it is necessary to know the basic elements entering into the above-mentioned formulas, namely: the angle of dip of the seam ($\alpha$), the angle of dip of the displacer ($\beta$), the angle of intersection in the horizontal section of the seam and the displacer ($\omega$), and the angle formed by the striation on the plane of the displacer with its strike ($\gamma$). To simplify the use of these formulas, the author has compiled special graphs both for simple and for complex disjunctives, by which, without calculation, using the arguments $\alpha$, $\beta$, $\omega$, and $\gamma$, one can easily find the necessary quantities entering into this formula.

The advantage of this method also consists in the fact that, if the elements of occurrence of the seam and the displacer, as well as the angle $\gamma$, are determined with sufficient reliability, then the position of the displaced limb of the seam can be determined knowing the disjunctive at only one point. This is especially important in the case of thrusts, where even with one and the same dip of the seam and of the displacer we may expect either a doubling or a separation of the seam along the displacer. Thanks to this method, we can determine the form of the thrust and thereby establish the position of the displaced part of the seam.

The most serious difficulty in determining the displaced limb of a seam by this method is the determination of the angle $\gamma$, since striation is not always present on the plane of the displacer, or else, owing to the fact that in Kuzbass there were several phases of tectogenesis, the original striation is often obscured by the appearance of a new one having already another angle $\gamma$. In this case, if we have two conjugate planes of the displacer, one of which is the apophysis of the other, the author gives a more reliable method for determining the angle $\gamma$.

In addition, in the course of carrying out the present work, the author arrived at conclusions that change our ideas concerning certain forms of disjunctives, on the one hand, and concerning the genesis of the tectonics of the Prokopyevsk district, on the other.

1. Thus, until now it has been considered that, in a direct thrust, the hanging limb of the fault descends from above downward; moreover, Prof. M. A. Usov explains the formation of this form of disjunctive by the bending of the plane of the displacer in the hinge of a fold, as a result of which this fault gives, on one limb, an upthrow and, on the other, a direct thrust.

Without disputing the possibility of such formation of thrusts, the author shows on block diagrams and models that a direct thrust may also be formed in another way, namely, by displacement of the hanging limb from below upward.

1. Until now it has been considered that in the Prokopyevsk district of Kuzbass normal faults are entirely absent. However, as a result of a geometrical analysis of the eastern limb of the Golubeevka anticline, the author proved the presence of normal faults in this district. True, this form of disjunctive cannot be recognized as an ordinary normal fault, since the subsidence of the hanging limb of the fault occurred as a result of—

...the absence of lagging of individual blocks enclosed on all four sides by displacement planes, with a general rise of these blocks from below upward. It should be noted that these disturbances have hitherto been regarded as thrusts.

1. In addition, from a geometrical analysis of the disturbances and their genesis, the author concludes that in these disturbances, during the displacement of the hanging and footwall limbs relative to one another, the element of horizontal movement considerably predominated over the vertical one; moreover, the movement of the hanging limb of disturbance GG proceeded in the direction from NW to SE. Thus the author defines disturbance GG as a reverse strike-slip fault, whereas until now this disturbance had been considered a reverse fault.

LITERATURE

1. Butov, P. I. and Yavorsky, V. I.—The Kuznetsk Coal Basin, Transactions of the Geological Committee, issue 177, 1927.

2. Getz, A. M.—The Prokopyevsk and Kiselevsk coal deposits of the Kuzbass. Kuznetsk Basin. Library of the Mining Journal No. 2, 1924; 167–192.

3. Gutt, A. E.—Course in Mining Geometry—Kharkov, 1932.

4. Krasnikov, P. F.—The principal forms of dislocations of the Prokopyevsk Mine of the Kuzbass. Collection on the Geology of Siberia. Tomsk, 1933, 51–78.

5. Kutashev, I. D., Adler, Yu. F. and others.—Geological-industrial description of the Prokopyevsk, Kiselevsk, and Afoninsk districts. 1934.

6. Molchanov, I. A.—Geometrical analysis of translational disjunctives. Mine-Surveying Collection. Vol. II. Tomsk, 1935.

7. Mineral Resources of the West Siberian Territory. Vol. III. Coals. 1935.

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

9. Stanov, V. V., Dorofeev, P. I., Verkhov, V. A. and Podbelsky, G. N.—Geological-industrial description of the Osinniki district of the Kuzbass. Novosibirsk, 1935.

10. Usov, M. A.—Forms of disjunctive dislocations in the mines of the Kuzbass. Collection on the Geology of Siberia. Tomsk, 1933; 2–50.

11. The same.—Tectonics of the Kuzbass. Problems of Soviet Geology. 1935, No. 2, 113–133.

12. The same.—Composition and tectonics of the deposit of the southern district of the Kuzbass. Novonikolaevsk. 1924.

13. Willis, B. and Willis, R.—Structural Geology. Translation, Baku; 1932.

14. Lahee, F. H.—Field Geology, 1923.

15. Reid, H. F.—Report of the Committee on the Nomenclature of Faults. Geol. Soc. Am. Bull., 24. 163–186, 1913.

16. Reid, H. F.—Geometry of Faults—Bull. Geol. Soc. of Am. XX, 1909.

Explanation of the Figures

Fig. 1. Geological structure of the Prokopyevsk district of Kuzbass (after I. D. Kutashev, Yu. F. Adler, et al., 1934). A—the Abinsk anticline; B—the Golubevka anticline; C—the Maly anticline.

Fig. 2. Structure of the 215 m level of the site of the Koksovaya mine, Prokopyevsk district, Kuzbass. A—the Abinsk anticline; B—the Golubevka anticline; C—the Maly anticline; thin double lines following the strike of the seams—drifts; across the strike—crosscuts; EF—the main crosscut of the Koksovaya mine; MN—the main crosscut of Mine No. 2; OP—the crosscut of Mine 3–4 (central adit).

Fig. 3. Vertical section in the plane of the main crosscut of the Koksovaya mine. A—the Abinsk anticline; B—the Golubevka anticline; C—the Maly anticline.

Fig. 4. Vertical section in the plane of the main crosscut of Mine No. 2.

Fig. 5. Crumpling zone of fault GG (sketch of the southern wall of the main crosscut, level 215).

Fig. 6. Tracing from the mine-surveying plan of the 250 m level of the eastern limb of the Golubevka anticline: 1—Kharakterny seam; 2—Inner I seam; 3—Inner II seam; 4—Inner III seam; 5—Inner IV seam; VI–VI—fault crack; AA—central crosscut.

Fig. 7. Vertical section in the plane of the central crosscut of the 250 m level of the eastern limb of the Golubevka anticline: 1—Kharakterny seam; 2—Inner I seam; 3—Inner II seam; 4—Inner III seam; 5—Inner IV seam.

Fig. 8. Geological sketches of faces: 1—fault crack; 2/a—Kharakterny seam; 2/b—Inner VI seam.

Fig. 9. Geological sketch of the face in transverse-vertical (I) and horizontal (II) sections (the scale of the horizontal section is half that of the vertical section), on the Inner I seam. 1. Fault crack. 2. Sandy shale. 3. Argillite. 4. Banded sandstone.

Fig. 10. Sketch of the face in transverse-vertical (I) and horizontal (II) sections (the scale of the horizontal section is half that of the vertical section), on the Inner II seam.

Fig. 11 and 12. Sketches of the face: 1—fault crack; 2—Inner III seam; 3—Inner I seam; 4—Kharakterny seam.

Fig. 13. Sketch of the face along the Inner II seam in transverse-vertical (I) and horizontal (II) sections; b—Inner II seam; v—guide bed;

\[ \frac{a}{\sin \alpha} \]

—the horizontal distance between the Inner II seam and guide bed b;

\[ \Theta \]

—the acute angle of intersection of the seam by the dislocator.

Fig. 14. Transverse-vertical (I) and horizontal (II) sections of the principal types of disjunctive dislocations: 1—crack; 2—hanging-wall seam; 3—footwall seam; AB—the horizontal plane, and CD—the vertical plane of sections (after M. A. Usov).

Fig. 15. Block diagram and projection of the upthrown limb onto the horizontal plane P of the thrust at \( \operatorname{Ctg}\alpha + \operatorname{Ctg}\beta \operatorname{Cos}\omega = 0 \); EN—the seam of the hanging wall; LK—the seam of the footwall; HH—the plane of the dislocator; EE—the line of intersection of the seam with the dislocator; \( \alpha \)—angle of dip of the seam; \( \beta \)—angle of dip of the dislocator; \( \omega \)—angle of intersection of the seam and the dislocator.

Fig. 16. Block diagram and projection of the upthrown limb onto the horizontal plane P of the thrust at \( \operatorname{Ctg}\alpha + \operatorname{Ctg}\beta \operatorname{Cos}\omega > 0 \). The designations are the same as in Fig. 15.

Fig. 17. Block diagram (I) and projection of the upthrown limb onto the horizontal plane (II) of the thrust at \( \operatorname{Ctg}\alpha + \operatorname{Ctg}\beta \operatorname{Cos}\omega < 0 \). \( h_1 \)—inclined height, \( h_0 \)—ver-

vertical height of displacement, \(l\)—visible horizontal displacement, \(w\)—subsidence of the seam. The remaining designations are the same as in Fig. 15.

Fig. 18. Projection with numerical marks. ABCD—the position of the hanging wall at the strike of the fractures KL—K′L′ and angle \(\omega = 110^\circ\); the form of the disjunctive is a direct overthrust. We leave the same angles \(\alpha\) and \(\beta\), but change the angle \(\omega = 150^\circ\); in this case the fracture takes the position EF—E′F′, and the hanging wall—MNOP; the form of the disjunctive has changed from a direct overthrust to a reverse one; NP and BD are lines of intersection, NG and BG are lines of displacement.

Fig. 19. Graph for determining the direction of prospecting for the displaced limb of a seam for simple disjunctives.

Fig. 20. Elements of a complex disjunctive. F—the plane of the displacer; R—the full amplitude of displacement; \(\lambda\)—element of shift; \(\gamma\)—the angle formed by the direction of the line of displacement and the strike of the displacer; \(h_1\) and \(h_0\)—the same as in Fig. 17.

Fig. 21. Horizontal section of shifts: a—negative shift; b—positive shift; 1—fracture of the disturbance; 2—hanging wall; 3—footwall.

Fig. 22. Graph for determining the direction of prospecting for the displaced limb of a seam for complex disjunctives.

Fig. 23. Summary graph for determining the direction of prospecting for the displaced limb of a seam.

Fig. 24. Structure of the Golubevsky anticline of the 215 m horizon.

Fig. 25. Graphical method for determining the angle \(\gamma\): a) IX—IX and GG—traces of the displacers on the plane of the plan; IX′—IX′ and G′G′—traces of the displacers on a horizontal plane below the plane of the plan at a distance \(r\); IX—IX′—line of intersection of the displacers; \(\angle E\) IX—IX′ \(= \gamma_2' = 30^\circ\)—horizontal projection of the angle \(\gamma\) for the IX IX disturbance; \(\angle\) IX′ IXF \(= \gamma'_g = 10^\circ\)—horizontal projection of the angle \(\gamma\) for the GG disturbance; \(\angle\) LÉIXn \(= \gamma_2 38^\circ\) for the IX—IX disturbance; \(\angle\) MIXF \(= \gamma_g = 25^\circ\) for the GG disturbance; the remaining lines are auxiliary in the construction.

b) Auxiliary drawing for determining the inclinations \(a_1\) and \(a_2\)

KK—horizon of the plan

LL—projected horizon at a distance

\(\beta_1\)—70° angle of dip of the GG displacer

\(\beta_2\)—40° of the XI—IX displacer

Fig. 26. Elements of a complex disjunctive: AD, AC, and \(\lambda_1\)—projections onto the horizontal plane Q of the elements R, \(h_1\), and \(\angle \gamma\).

Legend.

• \(H_2\) Bezugolnaya suite
• \(H_1^3\) Anzherka (Balakhonka) suite
• \(H_1^2\) Anzherka (Balakhonka) suite
• \(H_1^1\) Anzherka (Balakhonka) suite
• \(H_0\) Ostrog suite
• \(C_1\) Lower Carboniferous
• \(D_2\) Middle Devonian
• Fault lines

Fig. 1

Fig. 2

Visible annotations in the diagram include the following seam names and labels: Moshchnyi, Prokopyevskii, Gorelyi, Kharakternyi, Lutuginskii, Berezovskii, Provodnik, Internal I, Internal II, Internal III, Internal IV, and Srednii.

Fig. 4

Legend:

1—Provodnik; 2—Moshchnyi; 3—Gorelyi; 4—Prokopyevskii; 5—Lutuginskii; 6—Srednii; 7—Kharakternyi; 8—Internal I; 9—Internal II; 10—Internal III; 11—Internal IV.

Fig. 3

Fig. 5

1 — Coal; 2 — Sandstone; 3 — Difference of the characteristic beds; 4 — Argillite sandy; 5 — Argillite silty; 6 — Clayey shales; 7 — Sandstone; 8 — Fractures; 9 — Sandy shales.

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Visible annotations: I; II; A—B; “along AB”; 1, 2, 3, 4, 5.

Fig. 10

Visible annotations: I; II; A—B; “along AB”; 1.

Fig. 13

Visible annotations: I; II; A—B; “along AB”; $\dfrac{a}{\sin d}$; 1, 6, 8, 9.

Fig. 11

Visible annotations: 1, 2, 3.

Fig. 12

Visible annotations: 1, 3, 4.

Fig. 14

Fig. 15

Fig. 16

Fig. 17

Fig. 18

Fig. 19.

Labels visible in the graph: \(\beta = 20^\circ\), \(\beta = 30^\circ\), \(\beta = 40^\circ\), \(\beta = 50^\circ\), \(\beta = 60^\circ\), \(\beta = 70^\circ\), \(\beta = 80^\circ\); \(\cos \alpha\); \(\operatorname{ctg}\alpha\).

Fig. 20.

Labels visible in the diagram: \(h_1\), \(h_2\), \(R\), \(R_1\), \(a\), \(b\), \(n\).

Fig. 21.

a — normal fault
b — reverse fault

Labels visible in the diagram: 1, 2, 3.

Fig. 22

Fig. 26

Fig. 23

Fig. 25

Visible labels in the construction diagram: \(g\), \(g_1\), \(g_2\), \(g'\), \(g''\), \(q\), \(k\), \(m\), \(x\), \(y\), \(x_1\), \(x'\), \(a\), \(b\), \(c\), \(d\), \(e\), \(\alpha\), \(\beta\), \(\varphi\), \(0^\circ\).

Fig. 24

Visible scale marks: 0, 50, 100, 200, 300.

Visible seam and working labels in the plan include:

• IV Inner
• Inner I
• Inner II
• Prokopyevsk
• Dutrovsky [[unclear]]
• Complex
• Coking
• Inner I
• Inner II
• Inner III
• Inner IV

Other visible mine-plan inscriptions include several shaft and working designations, partly unclear: [[unclear: multiple abbreviated labels and numerical marks on the mine plan]].