Mine Surveying

First published

1989

Revised from the 1985 Russian edition

Translated from the Russian by V. Afanasyev

Ha allZAUUCKOM!l3blKe

Printed

in the Union

of Soviet Socia/ist Repub/ics

ISBN 5-03-000073-9

@ H3~aTeJIbCTBO «He~pa», 1985 @ English translation, Mir Publishers, 1989

Contents

Preface Chapter One. Subject-Matter of Mine Surveying. I.I. Subject-Matter 1.2. Brief Notes on History of Mine Surveying

9

Historical

Notes

Chapter Two. General Figure of the Earth, Systems of coordinates, Control and Survey Underground Nets and Surface Surveys 2.1. General Figure of the Earth 2.2. Geographic System of Coordinates 2.3. System of Plane Rectangular Coordinates 2.4. National System of Rectangular Coordinates 2.5. Geodetic Reference Nets 2.6. National Geodetic Nets 2.7. Geodetic Bridging Nets 2.8. Geodetic Survey Nets 2.9. General Data on Surveys

10 10 12

16 16 17 .18 19 22 23 26 28 29

Chapter Three. Graphical Documentation in Mine Surveying 3.1. General 3.2. Classification of Drawings and Rules of Mapping 3.3. Drawing Materials. Technology and Rules for Making and Storage of Mining Graphical Documentation 3.4. Mechanization ,of Graphical Work 3.5. Processes and Materials for Reproduction of Mining Graphical Documentation

33 33 35

Chapter Four. Connection Surveys 4.1. General 4.2. Orientation of Underground Survey via Horizontal or Inclined Adit 4.3. Geometric Orientation 4.4. Orientation down One Vertical Shaft 4.5. Sequence and Organization of Work for Orientation down One Vertical Shaft 4.6. Plumbing Surface Points onto Oriented Mine Level 4.7. Connection to Plumb Line Points in Orientation down One Vertical Shaft 4.8. Horizontal Connection Survey via Two Vertical Shafts 4.9. Horizontal Connection Survey with Use of Gyrocompasses 4.10. Vertical Connection Surveys

39 39

36 36

37

41 41 42

42 44

46 49 58 7n

Contents

6

Chapter 5.1. 5.2. 5.3. 5.4. 5.5. 5.6.

Five. Horizontal Surveys of Underground Workings General on Underground Mining Surveys Horizontal Underground Surveys Underground Reference Nets of Plan Control Construction of Underground Reference Nets Survey Nets Types of Station Points of Reference and Survey Nets. Their Fixation 5.7. Theodolites 5.8. Tests and Adjustments of Theodolites 5.9. Centring of Theodolites and Signals 5.10. Measurements of Horizontal Angles 5.11. Measurements of Inclination Angles 5.12. Measurements of Side Lengths of Theodolite Traverses 5.13. Distance Measurements by Light Range Finders 5.14. Detailed Survey of Underground Workings 5.15. Office Analysis of Results of Underground Theodolite Survey and Calculation of Point Coordinates 5.16. Accumulation of Errors in Underground Theodolite Surveys

74 74 7~

81

82 84 92 93 98 104 107 III III 112 116

Chapter Six. Vertical Surveys in Underground Workings 6.1. General 6.2. Levels 6.3. Levelling Staffs 6.4. Geometric Levelling in Underground Workings 6.5. Office Analysis of Results of Geometric Levelling 6.6. Errors in Geometric Levelling 6.7. Trigonometric Levelling 6.8. Errors in Trigonometric Levelling

121

Chapter Seven. Surveys of Preparatory and Stope Workings 7.1. General 7.2. Instruments for Surveys of Preparatory and Stope Workings 7.3. Surveys of Stope Workings in Coal Fields 7.4. Surveys of Underground Chambers and Cavities 7.5. Surveys of Preparatory Workings 7.6. Surveys of Blast Holes 7.7. Orientation of Sublevel Workings 7.8. Measurements of Mining Workings and Reserves of Mineral In Stocks

142

Chapter Eight. Special Surveys in Underground Workings 8.1. Assigning Directions to Underground Workings 8.2. Surveying of Workings Driven from Two Ends 8.3. Preliminary Estimation of Accuracy of Face Connection

167

Chapter Nine. Surveying in Mine Construction 9.1. General 9.2. Surveying at Mine Camp 9.3. Surveying in Construction of Mine Hoists 9.4. Survey Work During Sinking of Vertical Shafts 9.5. Survey Work for Arranging of Shaft Equipment

188 188 193 195 218 221

121 122 133 134 137 137 138 140

142 143 148 150 154 155 157

167 181 185

7

Contents 9.6. Survey Work During Driving of Shaft Workings 9.7. Survey Work During Driving of Vertical Shafts by Special Methods 9.8. Survey Work During Deepening of Vertical Shafts

228 229 234

Chapter Ten. Surveying in Quarries 10.1. General 10.2. Reference and Survey Nets and Surveying Work 10.3. Mine-Surveying Coverage of Drilling and Blasting Work 10.4. Survey Work for Transport Servicing 10.5. Survey Work in Trenching 10.6. Survey Work in Open-Cast Mining with Conveyer Bridges 10.7. Calculations of Volumes of Extracted Overburden Rock and Mineral in Quarries 10.8. Reclamation of Land 10.9. Survey Work in Open-Cast Mining of Placer Deposits

238 238 238 260 262 263 264

Chapter Eleven. Rock Disturbance and Protection of Structures 11.1. Introductory Notes I 1.2. General Data on Rock Disturbance I 1.3. Rock Displacement Parameters I 1.4. Factors Responsible for Rock Displacement I 1.5. Monitoring Rock Displacement. Observation Stations I 1.6. Calculations of Rock Displacement I 1.7. Measures for Protecting Surface Structures I 1.8. Construction of Safety Pillars

266 269 270

Surface 272 272 274 275 280 283 287 290 291

Chapter Twelve. Stability of Quarry Flanks 12.1. Principal Causes and Kinds of Rock Deformation 12.2. Factors Affecting Flank Stability 12.3. Mine-Surveying Observations on Rock Mining Deformations in Open-Cast Mining 12.4. Stability of Working Benches and Flanks of Quarries 12.5. Measures for Controlling Landslides 12.6. Artificial Strengthening of Rock Massif

295 295 296

Chapter Thirteen. Mine-Surveying Control of Mining Safety 13.I. Role of Mine-Surveying Service in Mining Safety 13.2. Control of Mining Work near Old Workings 13.3. Examples of Calculation and Construction of Dangerous Zones 13.4. Construction of Zones of Elevated Rock Pressure 13.5. Construction of Dangerous Zones for Mining Work in Seams Liable to Coal, Gas and Rock Bursts

309 309 309 311 315

Chapter Fourteen. Mine-Surveying Control of Geological ration 14.1. Brief Data on Geological Exploration 14.2. Mine-Surveying Control of Geological Work 14.3. Topographic Basis of Geological Exploration 14.4. Transfer of Plan of Exploratory Workings into Nature 14.5. Layout of Exploratory Ditches 14.6. Geodetic Control of Geophysical Prospecting Methods

300 303 305 306

318

Explo324 324 325 327 328 334 336

8

Contents 14.7. Mine-Surveying Work in Geophysical Prospecting 14.8. Barometric Levelling of Geological Observation Objects Chapter Fifteen. Mine-Surveying Work for Mineral Extraction in Water Areas of Seas and Oceans 15.1. General 15.2. Brief Data on Geomorphology of Ocean Bottom Relief 15.3. Characteristics of Some Solid Minerals 15.4. Mine-Surveying Service of Geological Prospecting and Mining in Water Areas 15.5. Marine Mine-Surveying Reference Nets 15.6. Special Mine-Surveying Work in Water Areas 15.7. Routine Mine-Surveying Work in Water Areas 15.8. Determination of Plan Coordinates of Floating Vessels 15.9. Depth Measurements 15.10. Calculation of Volumes of Extracted Rock Index

340 345

349 349 350 351 351 353 355 356 358 358 360 362

Chapter One Subject-Matter of Historical

1.1. Subject-Matter M odern mine surveying is a branch of the mining science and industry which is concerned with surveys on the land surface and underground during the prospecting and extraction of mineral deposits and the construction of mining plants; the results of surveys are then used for plotting the plans of mining workings and bedding conditions of deposits and also for the solution of various problems of the mining geometry. At the early period of its existence, mine surveying could be characterized simply as underground geodesy. In some countries, it is still called in this way (for instance, 'geodesie souterraine' in France). In the course of its progress, however, mine surveying has become a complex discipline which includes not only the methods and techniques of the survey work (mine surveying proper), but also the estimation of the accuracy of measurements and calculations based on the method of least squares and the theory of probability; geodetic and mine-surveying instrumentation; mining geometry; studies of displacements and pressure of rocks (mining geomechanics),etc. All these aspects of mine surveying have the same objectives: to ensure safe and efficient exploitation of mineral deposits on the bases of the instrumental measurements performed under particular mining and geological conditions of a mining plant. Modern mine surveying has to cope with more diversified and complex problems. The quality and productivity of the survey work

Mine Surveying. Notes

have increased drastically due to the realization of the latest achievements of science and engineering. There is a trend to form specialized mine-surveyor teams for making a particular kind of survey work at a number of mining plants (for instance, mine-surveying groups for the orientation of mines with the use of gyrocompasses or for surveying of open-cast pits by aerial and ground stereophotogrammetry). The prime task of minesurveying service, as earlier, is however the compilation of plans of mining enterprises which are required for the normal exploitation of mineral deposits and represent the current state of deposits and underground or surface workings and structures and buildings on the land surface. Certain progress has been made recently in the methods and techniques of mine surveying. New solutions have been proposed for the orientation and construction of underground reference nets. High-precision theodolites and light range finders have come into use for the construction of reference nets. New instruments and methods have been proposed for the surveys of quarries. Serious investigations have been completed in the field of mine surveying in the construction and reconstruction of mines. In particular, special methods have been suggested for the survey work during mounting of hoisting machines on tower head-frames and the construction of mine shafts. Laser instruments are finding ever wider use for direction assigning and control in vertical and horizontal workings, arrangement of equipment of vertical shafts, track laying in horizontal

1.1. Subject-Matter

workings, mounting of conveyers, laying of pipelines, etc. An essential progress has been done in the methods and instruments for plotting the mining graphical documentation and in the materials for making mine-surveying plans and sections. Field measurements and office work in mine surveying are now carried out with the use of diverse and rather intricate instruments and devices, in particular, highprecision optico-mechanical systems and electronic devices. Among many achievements in this field, it is worth to mention small-sized mine-surveying gyrocompasses, optical range finders, devices for measuring the curvature of boreholes, self-adjusting levels, apparatus for the stereophotogrammetric surveys of open-cast pits and underground workings, coded theodolites with direct input of measured results into electronic computers, special-purpose electronic computers for mine surveying, desk calculators, etc. Mine surveying also has to solve an important group of problems associated with the investigation of the configurations of lodes and their representation in special graphs and with the determination of the optimal regimes of extraction of minerals for obtaining the final product having the specified concentrations of useful and waste components. This branch of mine surveying, called mining geometry, helps the mine surveyor in controlling measures for the preservation of mineral deposits and efficient extraction of minerals. Another important concern of mine surveying relates to the studies of mechanical processesin rock massifs and in the elements of working systems, which are induced by mineral extraction operations (mining geomechanics).The investigations of rock displacements and rock pressure have been especially fruitful in the last 20-25 years. Regulations have been worked out for the protection of surface structures, collieries and ore

11

mines against rock displacements. Methods have been developed for preliminary calculations of land surface deformations in underground mining of coal fields, which have made it possible to introduce certain radical measures for the protection of structures against the harmful influence of underground workings. Conditions have been formulated for safe extraction of minerals from deposits beneath water basins. In open-cast mining, methods for the calculation of inclination angles of pit flanks and measures for artificial strengthening of slopes have been suggested. A division of mining geomechanics is concerned with the studies of the effects of rock bursts. The mechanisms of appearance of rock bursts have been investigated thoroughly on the scientific basis and measures for preventing them have been developed. Mine surveyors carry out the investigations of rock pressure in permanent, preparatory and stope workings in coal and ore deposits. As an engineering discipline, mine surveying is based on the concepts of fundamental sciences, such as mathematics, physics, mechanics, and philosophy. Measurements and calculations in mine surveying are carried out by the conventional techniques adopted in geodesy. Mine surveying is also associated closely with geodetic instrumentation, geology, mining, production management, etc. Mine surveyors have to participate in all stages of the operation of mining plants from the exploration of a mineral deposit and up to the abandonment of a mine after it has been worked out, and to perform specific survey work at all these stages. . Exploration of mineral deposits. In the exploration of mineral deposits, the mine surveyor makes land surveys, determines and transfers into nature the positions of exploring workings (pits, ditches, adits, etc.), makes the surveys of exploring workings, assaying points, seam outcrops, bedding elements of mineral deposits and enclosin2 rock: and

12

Ch.

1. Subject-Matter

compiles (together with geologists) the graphical documentation representing the shape and bedding conditions of a deposit. Minesurveying plans and sections plotted by the results of geological prospecting are used for the calculations of mineral reserves and design of mining plants. Design and construction of mining plants. At the stage of mining plant design, the mine surveyor participates in construction surveying: the determination of the boundaries of mine fields according to the current regulations on land allotment; design of working systems and surface structures; development of measures for the protection of surface and underground structures against harmful influence of underground workings; compilation of the graphs of work organization and plans of mining work for the periods of construction and exploitation of a mining plant; and the calculations of the losses and industrial reserves of minerals. At the stage of mining plant construction, the mine surveyor is engaged in a wide circle of problems associated with transferring the design data into nature (levelling of a pay-out area, layout of the centres and axes of shafts and mining complexes, location of roads, etc.). He performs control on the construction of hoisting complexes, sinking and equipment of shafts, driving of permanent workings, etc. Exploitation of deposits. The role of the mine surveyor at the stage of exploitation is extremely important and includes the following operations: surveying of workings; assigning of directions to workings; compilation of plans by the results of surveys; control of the mining work in accordance with the design specifications and safety regulations; surveys for the connection of surface and underground reference nets; continuous control of the completeness of mineral extraction; observations on rock displacements and rock pressure; development of measures for the protection of structures, natural objects and mining workings against the harmful effect of

of

Mine

Surveying

mining operations; reclamation of land; planning of the preparatory and stoping mining work; development of quarterly, annual and perspective plans of the mining work; and calculations of the balanced and industrial reserves, losses, and dilution of minerals. When a mine is to be abandoned, the mine surveyor has to determine whether the mineral has been extracted completely, to survey underground workings, and to prepare complementary mining plans. He also arranges the field books of underground surveys and mine orientations and prepares the main plans of the mining work for storage. 1.2. Brief Notes on History of Mine Surveying Mine surveying actually appeared as soon as Man learned to do the underground mining work. Historical manuscripts, archeological findings, and other materials have given evidence that people of the antiquity were quite familiar with the art of construction of fairly intricate mines and other underground objects. It may be referred, for instance, to a 3500-years old Egyptian parchment showing a mine, which has been found in Italy. It is also known that Romans drove an adit about 6 km long to drain water from a lake. More than 100 vertical and inclined shafts were sunk for driving the adit, some of them being to a depth more than 100 m. This is a clear evidence that Romans were experienced well in mine surveying. The first description of methods of underground surveying that has survived to our times belongs to Heron of Alexandria (lst century B. C.). These methods included various measurements, plumbing, and construction of chains of regular geometrical figures (for instance, similar triangles) on the surface and underground, by means of which it was possible to orient underground workings.

1.2.

Brief

Notes

on History

In the 16th century A. D. when the magnetic needle compass came into use, mine surveying became more efficient and accurate. At that time, Agricola (Georg Bauer, 1494-1555),a famous German scientist, published the book De re metallica libri XII where Chapter V was devoted to the surveys of mining workings by means of a compass with the circle divided into 12 sectors and by other methods. In particular, he described the method of measuring the depth of a mine or the length of an adit by means of an inclined cord and plumb bobs. Mine surveyors of those times still could not calculate the coordinates of the angular points of surveys. Initially, there were no survey plans, and the mine surveyor contented himself with making the same survey on the surface as underground (in a mine) and could decide on the development of the mining work relative to the boundaries of allotment by the positions of survey points on the surface. The plans of the mining work came into common use in Germany at a substantially later time, in the 17th century. At the end of that century, two kinds of the mining work plans were employed: those plotted in the plane of a seam or vein and those made as projections onto a vertical plane. The mining work plans of that period were however oriented by a magnetic meridian. Only from the mid of the 18th century when the phenomenon of magnetic declination was discovered (August Beyer, Von Bergbau Grundlicher Unterricht, 1749),mine surveyors were obliged to abandon the use of the magnetic meridian and change to the orientation of mine surveys by an astronomic meridian. In Germany, the compass with sight vanes was designed in the 16th century and the suspension compass, in the 17th century. These instruments (the latter in combination with a suspension semicircle) were for many centuries the most common mine-surveyor's

of Mine

Surveying

13

instruments and are sometimes used in modem mine-surveying practice. With the suspension compass and suspension semicircle, it was easier to construct underground surveying nets; instead of a number of triangles, it was now sufficient to layout a broken line in an underground working by means of a cord. Practical mine surveying was given a strong impetus in the 1840's when work was undertaken to drive long adits near Freiberg and Harz in Germany. Prof. Weissbach and mine surveyor H. Borchers, who participated in the work, proved the applicability of theodolites and level instruments for mine surveying. These adits had a large length, intersected many mines, and were driven from many points by meeting faces. To perform this work, a detailed triangulation was carried out on the surface, which provided a single coordination network for all the mines involved. Levelling surveys carried out together with triangulation made it possible to relate all points to a single elevation system. Roughly at the same time, the methods of precise orientation of underground surveys were developed. In the 19th century, theodolites and levelling instruments came into wide use in mine-surveying practice in Germany. New mine-surveyor's instruments appeared, such as box compass, mirror compass, projecting plates, and large-Iength tapes for measuring the depths of mine shafts. In the second half of the 19th and the beginning of the 2Oth century, well equipped works for ~aking mine-surveyor's instruments were put into operation in Germany (Hildebrandt, Fennel, Zeiss). New methods of mine surveying and estimation of observed results were developed, in particular, the method of connection surveys with connection triangles, method of symmetrical junction, and the method of range lines with the use of the Weiss sleigh. Studies were carried

14

Ch

Subject-Matter

out on the effect of air currents on the positions of plumb bobs in the orientation of deep shafts (Wilski's hypothesis). In the first half of the 2Oth century, gyroscopic instruments came into use for the orientation of underground surveying nets. The first attempts for mine orientation by gyroscopes were undertaken in 1913-14 in Poland and Germany. At the beginning of the 192O's,a mine-surveying gyroscope was designed and manufactured in Germany, but turned out to be inefficient. Wide application of gyroscopic orientation dates to 1947 (Germany). The earlier makes of mine-surveying gyroscopes had certain drawbacks (large mass and dimensions, uncertain readings, etc.). In recent years, successful work on the design of gyrocompasses, gyrotheodolites and gyroscopic attachments has been completed in a number of countries. Gyrotheodolites have been employed efficiently for the orientation of underground surveying nets. In the post-war years, many mine-surveying instruments were improved, and new instruments based on utterly nowel operating principles were developed, such as highprecision theodolites, self-adjusting levels, coded theodolites, optical and radio range finders, and laser instruments. Much work has been done on the development of instruments for stereophotogrammetric surveys which are finding wide use in many countries for underground surveying. In recent time, the mine-surveying office work has been largely mechanized by the application of desk calculators, electronic computers, etc. Programs for solving minesurveying problems in powerful electronic computers have been worked out. Mine surveying is essentially an information science,and accordingly it has started to widely employ various automatic systems for data collection, storage, processing and transmission. In modern mine surveying, there is a strong trend to increase the observations on

of Mine

Surveyin

rock displacements in underground and open-cast mining. The movements of the Earth's surface under the effect of underground workings were noticed already in the 15th and 16th centuries, but attracted a keen interest of mine surveyors in the 18th century and especially in the 19th century in Belgium where the mining work began to endanger surface buildings and water-supply system in Liege. In the second half of the 19th century, the investigations of the laws of rock subsidence and caving were started, which resulted in the hypothesis of normals proposed by Toilliez in 1838. Another hypothesis was suggested by Gonot in 1858, according to which the displacement of a worked-up rock layer proceeded along the normals to the seam. In 1885, H. Fayol proposed the hypothesis of cupola based on the idea that the zone of rock subsidence was confined by a cupola (dome-shaped) space. At the end of the last century, J. Jicinsky marked in his works that the process of rock displacement should be influenced by the thickness of a seam, dipping angle, depth of the mining work, and properties of overlying rock. Of large significance for understanding properly the process of rock subsidence was the hypothesis suggested by R. Hausse (the end of the 19th century), which considered two zones of rock subsidence: the cave-in zone and bend zone. In the first quarter of this century, the problem of rock displacements was investigated by a number of researchers. 0. Donahue determined a number of subsidenceangles. A. Goldreich discovered certain differences in the subsidence of bed rock and detrital deposits. H. Briggs found the correlations between the angles of rupture and the compression and rupture resistance of rocks and established that subsidence angles in hard and brittle rocks are steeper than in those having a lower strength. In recent time, much attention has been given to the methods of prediction of rock

1.2.

Brief Notes

on History

deformations. One of the first methods was proposed by Keinhorst and Bals and based on the assumption that a portion of worked-out area confined by subsidence angles acted by a definite law on each point of the Earth's surface. The progress of mine surveying owes much to the contributions of Russian and Soviet scientists. The first in Russia mining regulations were issued by v. Tatishchev in 1734. In 1763, M. Lomonosov published his book On M easurements of M ines, the first publication in the country which dealt thoroughly with all aspects of mine surveying of that time and was a part of the fundamental work Principles of M etallurgy or Mining. Lomonosov gave the descriptions of the suspension compass and suspension semi-circle, measuring rod, instruments for plotting mine-surveying drawings, etc. and solutions of various mine-surveying problems, in particular, the method of location of the surface of a vertical shaft to be connected to a system of horizontal underground workings. In 1773, a mining school was founded in St. Petersburg (now the Leningrad Mining Institute). It had a mine-surveying class where students obtained profound training in the subject. A major event in the history of mine surveying in this country was the publication, in 1847, of the book The Art of Mine Surveying written by P. Olyshev, professor of the St. Petersburg mining school (1817-1896). The author gave the description of a theodolite with an eccentric telescope and of a geodetic level, proposed the procedure for the calculation of the coordinates of theodolite traverses, and solved the problem of driving an underground working by meeting faces. The introduction of theodolite surveys into the mine-surveying practice and the preparation of mine plans by point coordinates were of extreme importance for further progress in

of Mine

Surveying

15

the methods and techniques of underground surveys. Another important stage in the development of mine surveying is associated with the name of Prof. V. Bauman (1867-1923),author of a number of fundamental works, such as A Course in the Art of Mine Surveying (in three volumes), On the Problem of Faults. Shifts and Other Types of Displacement of Veins and Seams. On the Problem of Evaluation of M ineral and Ore Deposits, etc. An exceptionally great contribution to the mine-surveying science was done by I. Bakhurin (1880-1940).He worked out a number of issues in the theory of errors and the method of least squares and their applications for the estimation of accuracy and equation of mine surveys. Bakhurin was concerned with practically all aspects of mine surveying: survey control of workings driven by meeting faces;theory of cumulative errors in underground polygons; theory of random errors and method of least squares; theory of physical (in particular magnetic) and geometric orientation of mines; errors of orientation via one or two vertical shafts; mine-surveying instrumentation; rock displacements; etc. The results of his studies were~ummarized in the book A Course of Mine-Surveying Art (1932). The progress of mine surveying in this country is also associated with the name of Prof. P. Sobolevsky (1868-1949) who is responsible for a new branch of mine surveying which has later formed into an individual discipline, mining geometry. The development of mine surveying in recent time, and especially in the last two or three decades of the total scientific and engineering progress, has been associated with the improvement of existing and design of principally novel instruments, systems and techniques of field and office work. The scientific and applied aspects of mine surveying are being developed intensively. Minesurveying problems are solved with wide use of electronic computers and automatic devices.

Chapter Two General

2.1. General

Figure Control

Figure

of the Earth, Systems of Coordinates, and Survey Underground Nets and Surface Surveys

of the

Earth

The physical surface of the Earth is far from having a simple shape. Of the total area of the Earth's surface equal to 510 mln kIn2, 71 per cent fall on the bottom of seas and oceans and 29 per cent, on the land. Both the oceanic bottom and the continents have an intricate relief, especially the former. As has been found by investigations, the Ocean in some places has depths more than 10 kIn. Some regions of the land reach altitudes up to 7-8 km. The analysis of the depth of the Ocean and altitudes of the land on the basis of l-kIn height intervals has demonstrated that their distribution has two distinct peaks: one at altitudes of loo m above the level of the Ocean and the other at roughly 4.5 kIn below that level. It has been concluded on that basis that the surface of the Earth consists of two sharply distinct morphological elements: continents and oceans, the natural boundary between these elements being at a depth around 1.5 km below the level of the ocean. Further, the local irregularities of the surface relief make the shape of the Earth's surface extremely complicated so that the figure of the Earth can hardly be described mathematically. Noting that the surface of water of the Ocean has a rather simple shape and occupies almost 3/4 of the Earth's surface, it would be reasonable to assume the figure of the Earth as the body confined by the water surface of the Ocean. When determining the position of a point on the physical surface of

the Earth, this point is usually related to the general figure of the Earth which is understood in geodesy and mine surveying as the figure obtained by mental continuation of the still water surface of the Ocean. The surface obtained in this way is called the level surface. Its principal property consists in that the potential of the force of gravity on that surface is the same in all points, i. e. the surface is always perpendicular to an upright (vertical) line, and therefore, is horizontal everywhere. In the general case, it is possible to draw an infinite number of level surfaces at different distances from the Earth's centre, but one of these surfaces, i. e. that coinciding with the mean level of the Ocean and continued at that level under the continents, forms a figure that is taken as the general figure of the Earth and called the geoid. Since the direction of an upright line may depend on a number of factors, the geoid has a complicated structure. The principal among these factors is that the force of terrestrial attraction is variable, since the Earth's radius diminishes at the poles and since the rocks of the Earth's mantle have different density. The variations in the force of gravity are mainly due to the former reason (smaller radii of the Earth at the poles), though the latter reason may have an essential effect in some cases. The geoid has flattened portions (oblateness) near the poles, and its shape is too complicated for mathematical description. The results of satellite observations have shown that the oblateness, expressed as the difference between the lengths of an equatorial and polar diameter. attains 42 km

2.2.

Geographic

System

of

17

Coordinates

by the formula: a=(a-b)/a

Fig. 2.1

Ellipsoid

pI of revolution

of spheroid

770 m. It has also been established by satellite observations that the Earth has a pyriform (pear-Iike) shape: the South pole has turned out to be nearer by 45 km to the Earth's centre than the North pole. In addition, the South pole is located 25 m 80 cm below the surface of oblated sphere, whereas the North pole protrudes by 18 m 90 cm above that surface. Measurements have also demonstrated that the Earth has 'recesses'and 'ridges' which are traced clearly against the profile of the complicated figure of the geoid. The largest 'recesses'are located to the south-west of India (depth 59 m) and near the Antarctic continent (30 m). The highest ridges are located near New Guinea (57 m) and in France (35 m). It has also been established that the Earth's equator is not circular, but elliptical with one of its 'diameters' being larger by 200 m than the other. In view of these circumstances, the idea of using the geoid as the basis for geodetic calculations has been renounced. Among regular mathematical surfaces, the one that can approximate most closely the geoid surface is an ellipsoid of revolution obtained by the rotation of an ellipse on its minor axis. This figure is called the Earth's ellipsoid, or spheroid. The dimensions of the Earth's ellipsoid (Fig. 2.1) can be characterized by the lengths of its major and minor half-axes, a and b, and by the oblateness a which can be deteri:nined 2-1270

When plotting the portions of the Earth's surface on maps and plans, an important matter is to choose the proper dimensions for the ellipsoid which will approximate the geoid and onto whose surface the physical surface of the Earth with all its natural and artificial details will be projected. Many attempts have been made to determine the dimensions of an ellipsoid to approximate most closely the geoid (the first in 1800 by J.-B.J. Delambre, a French mathematician). An ellipsoid of particular dimensions and oriented uniquely in the Earth's body, onto whose surface the results of topographic, geodetic and mine surveying work are transferred in a country, is called a reference ellipsoid (local ellipsoid). 2.2. Geographic System of Coordinates The positions of points on the surface of the Earth or spheroid are determined by means of geographic coordinates, i. e. geographic latitude . "'

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58

Ch. 4. Connection

can be used for checking. The discrepancy between them must be within the accuracy of calculations. If other methods have not been used for orientation, connection survey via two vertical shafts must be carried out twice. The final result is taken as the arithmetic mean of two procedures. It is recommended to make the connection survey via two vertical shafts in combination with gyroscopic orientation of the sides adjoining the plummets. An example of calculation for orientation via two vertical shafts is given in Tables 4.4 and 4.5. If a mine field is opened by three or more vertical shafts connected by underground workings, it is recommended to make connection survey through the shafts with the use of redundant measurements. 4.9.

Horizontal Connection Survey with Use of Gyrocompasses

The wire of a plummet hanging in a shaft is subject to the action of a number of factors which tend to deviate it from the vertical position. The most important among these factors are air currents in the shaft and underground workings, and abundant water drip (downpour). These factors have been investigated and can be accounted for by special formulae. These factors have however become less important with the appearance of gyroscopic instruments which can determine the direction angles of any traverse side in a mine with an accuracy to 10-20". In that connection, geometric methods of orientation now have only a limited application, mainly in the construction of new mines. Repeated orientations in exploited mines are mostly carried out by means of gyrocompasses. Further, the essential disadvantage of geometric orientation via a single shaft by means of two plummets is that the distance between the plummets is too short and a direction angle

Surveys

cannot be transferred underground with a sufficiently high accuracy. A practical merit of gyroscopic orientation is that the direction angle of one or several sides of an underground survey net can be determined with a high accuracy in any place of the mine field and at any distance from the shafts. These circumstances have predetermined wide popularity of the connection survey method in which the coordinates x. y of an initial point of an underground polygon are determined by means of a plummet sunk into the shaft, (the problem of projection), and direction angles are then measured by the gyroscopic method. Under production conditions, the problems of centring and projection are tackled separately and in the following sequence. The projection problem is solved by means of a plummet hung in the vertical shaft. The method and equipment in this case are essentially the same as in orientation via a single shaft by means of two plummets. It should be noted, however, that, since the direction angle of the initial traverse side will then be determined by the gyroscopic method, the projection can be carried out in a simplified way without spending time for the stabilization of a plummet, determination of its central positions on scales,etc. on the surface and in the mine. A polygonometric traverse of an accuracy of not less than second-order is run on the surface from the initial side 31-32 to the centring point, i. e. the plummet point ° (Fig. 4.12). The angle ~A at a point A and the distance from that point to the plumb line 0, IAO' are measured in the shaft; the direction angle of a side A-B (IlAB) is then determined by the gyroscopic method. The direction angle of a side O-A is calculated by the formula: IlAO = IlAB -~A :J: 180° (4.28) and the coordinates of the first point (A) of an underground side, by the formulae:

4.9.

Horizontal

Connection

Survey

by Gyrocompasses

59

4.9.1. Theoretical Principles of Gyroscopic Orientation

Level950 m Fig. 4.12 Solving projection problem for determining initial point coordinates of underground polygon

XA =

Xo +

loAcosuoA

(4.29)

YA = YO+ loAsin aoA This method is used especially widely at mining enterprises with large mine fields and block-type vertical shafts located at a distance of 5-6 km from the main shafts. The connection survey made by this method increases substantially the accuracy and reliability of the survey reference net in the entire wing of a mine.

Mine surveying has in recent time become less labour-consuming and more accurate due to the appearance of reliable small-sized and explosion-proof gyrocompasses. The operating principle of a mine-surveying gyrocompass is based on the daily rotation of the Earth and the property of a free gyroscope to rotate freely in three mutually perpendicular planes (Fig. 4. 13). A gyroscope is called balanced if its centre of gravity coincides with the suspension point O (the point of intersection of the three axes). Balanced gyroscopes in which there is no friction in the suspension supports are called free. Free gyroscopes can exist only theoretically. Practically, the centre of gravity is always displaced somewhat relative to the suspension axis and there always is friction, though slight, in suspension supports. A free gyroscope (Fig. 4.13a) comprises a massive spinning disc, or rotor 2, which is suspended in two gimbals. The rotor is mounted in the inner gimbal 4 and outer gimbal 7 on bearings 1,3, and 5. This system allows the rotor to rotate freely on the

(a)

y

Fig. 4.13

Free gyroscope (a) and pendulum gyrocompass (b)

60

Ch. 4. Connection

Surveys

principal (spin) axis x, rotation axis of the inner gimbal y (sensitivity axis), and rotation axis of the outer gimbal z (precession axis). As the disc is rotating simultaneously on the three axes, the suspension point O remains immobile, and the x axis acquires stability and do~s not react to rotation of a base 6, in other words it retains a stable orientation in space. If the moment of an external force is applied to the x axis of a quickly rotating gyroscope, this axis turns (precesses)in the plane perpendicular to the force applied. The angular velocity of precession, O>pr'is directly proportional to the moment of external force M ex and inversely proportional to the rotating velocity H of the gyroscope:

E Fig.

4.14

Components

of Earth's

,x rotation

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102

Ch. 5. Horizontal

Surveys

of Underground

Workings

III

(b) III

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--

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Fig. 5.21

Measurement

of horizontal

angle by eccentric

The measurements of horizontal angles in underground workings with the angles of dip more than 300 are made only by the method of sets under the provision of the following additional conditions: I. If a repeating theodolite is employed, its limb must be locked for the entire time of measurements. 2. The theodolite for measuring horizontal angles must be provided with a striding level and permit plumbing of its vertical axis of rotation before each set. 3. The alidade of the theodolite should always be rotated in one direction only. 5.10.4.

Measurements of Horizontal Angles by Means of Eccentric- Telescope Theodolites

telescope

is shown in Fig. 5.210 and with the circle at left, in Fig. 5.21b. In order to measure the angle between the directions II-I and 1I-111, for instance, with the circle at right, the telescope is sighted successively on signals I and III. In that case, the horizontal axis of rotation of the telescope moves from position II-I into 1I-2, i.e. its setting is changed by an angle 13" and therefore, the angle 13,will be measured instead of 13.Similarly, with the circle at left, the angle 13! will be measured instead of 13. As may be seen in Fig. 5.21, the exterior angles ~

~Receiving

stage

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level

5000 dia ~r~or

level

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30000 Fig. 9.18

Geometrical

elements of single-rope

17500

mine hoist

205

9.3. Surveying in Construction of Mine Hoists

by the formulae: