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
Contents 9 10 10 12 16 16 17 .18 19 22 23 26 28 29 33 33 35 36 36 37 39 39 41 41 42 42 44 46 49 58 7n Preface
Chapter One. Subject-Matter of Mine Surveying. Historical Notes I.I. Subject-Matter
1.2. Brief Notes on History of Mine Surveying
Chapter Two. General Figure of the Earth, Systems of coordina-tes, 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
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
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
6 Contents 74 74 7~ 81 82 84 92 93 98 104 107 III III 112 116 121 121 122 133 134 137 137 138 140 142 142 143 148 150 154 155 157 167 167 181 185 188 188 193 195 218 221 Chapter Five. Horizontal Surveys of Underground Workings
5.1. General on Underground Mining Surveys 5.2. Horizontal Underground Surveys
5.3. Underground Reference Nets of Plan Control 5.4. Construction of Underground Reference Nets 5.5. Survey Nets
5.6. 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 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
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
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 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
7 Contents 228 229 234 238 238 238 260 262 263 264 266 269 270 272 272 274 275 280 283 287 290 291 295 295 296 300 303 305 306 309 309 309 311 315 318 324 324 325 327 328 334 336 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
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
Chapter Eleven. Rock Disturbance and Protection of Surface 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
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
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
Chapter Fourteen. Mine-Surveying Control of Geological Explo-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
8 Contents
340 345 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 349
349 350 351 351 353 355 356 358 358 360 362 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
Chapter One
Subject-Matter
of Mine
Surveying.
Historical
Notes
1.1. Subject-Matter
have increased drastically due to the realiza-tion of the latest achievements of science and engineering. There is a trend to form speciali-zed 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 stereo-photogrammetry). The prime task of mine-surveying service, as earlier, is however the compilation of plans of mining enterprises which are required for the normal exploita-tion of mineral deposits and represent the current state of deposits and underground or surface workings and structures and buil-dings on the land surface.Certain progress has been made recently in the methods and techniques of mine sur-veying. 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 instru-ments are finding ever wider use for direction assigning and control in vertical and horizon-tal workings, arrangement of equipment of vertical shafts, track laying in horizontal M odern mine surveying is a branch of the
mining science and industry which is concer-ned with surveys on the land surface and underground during the prospecting and extraction of mineral deposits and the const-ruction 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 be-come 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 mea-surements 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
11 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, high-precision optico-mechanical systems and electronic devices. Among many achieve-ments 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 stereophotogram-metric surveys of open-cast pits and under-ground workings, coded theodolites with direct input of measured results into electro-nic computers, special-purpose electroelectro-nic computers for mine surveying, desk calcula-tors, 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 speci-fied 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 sur-veying relates to the studies of mechanical processes in rock massifs and in the elements of working systems, which are induced by mineral extraction operations (mining geo-mechanics). The investigations of rock displa-cements and rock pressure have been espe-cially fruitful in the last 20-25 years. Regula-tions have been worked out for the protec-tion of surface structures, collieries and ore
mines against rock displacements. Methods have been developed for preliminary calcula-tions of land surface deformacalcula-tions in under-ground 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 thor-oughly 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 sur-veying is based on the concepts of fundamen-tal 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 sur-veying 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 explo-ring workings (pits, ditches, adits, etc.), makes the surveys of exploring workings, assaying points, seam outcrops, bedding elements of mineral deposits and enclosin2 rock: and
Ch. 1. Subject-Matter of Mine Surveying
12
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 pre-pare 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.
compiles (together with geologists) the graph-ical documentation representing the shape and bedding conditions of a deposit. Mine-surveying 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 sur-veying: 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 fol-lowing operations: surveying of workings; assigning of directions to workings; compila-tion 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 cont-rol 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
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, archeo-logical findings, and other materials have given evidence that people of the antiquity were quite familiar with the art of construc-tion 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 under-ground surveying that has survived to our times belongs to Heron of Alexandria (lst century B. C.). These methods included va-rious measurements, plumbing, and construc-tion 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 of Mine Surveying 13
instruments and are sometimes used in modem mine-surveying practice. With the suspension compass and suspension semi-circle, 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 instru-ments 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 connec-tion triangles, method of symmetrical junc-tion, and the method of range lines with the use of the Weiss sleigh. Studies were carried In the 16th century A. D. when the
magne-tic needle compass came into use, mine surveying became more efficient and accur-ate. At that time, Agricola (Georg Bauer, 1494-1555), a famous German scientist, pub-lished 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 conten-ted 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 orienta-tion 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
Subject-Matter of Mine Surveyin
14 Ch
rock displacements in underground and open-cast mining. The movements of the Earth's surface under the effect of under-ground 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 subsi-dence 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 hypo-thesis 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 displace-ments was investigated by a number of researchers. 0. Donahue determined a num-ber of subsidence angles. A. Goldreich discov-ered 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 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 (Ger-many). 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 comp-leted in a number of countries. Gyrotheodo-lites have been employed efficiently for the orientation of underground surveying nets.
In the post-war years, many mine-sur-veying instruments were improved, and new instruments based on utterly nowel operating principles were developed, such as high-precision 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 sur-veys 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 mine-surveying problems in powerful electronic computers have been worked out.
Mine surveying is essentially an informa-tion 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
1.2. Brief Notes on History of Mine Surveying 15
the methods and techniques of underground surveys.
Another important stage in the develop-ment 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. Ba-khurin (1880-1940). He worked out a number of issues in the theory of errors and the method of least squares and their applica-tions 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 geomet-ric 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 sur-veying 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 sur-veying are being developed intensively. Mine-surveying problems are solved with wide use of electronic computers and automatic devices. deformations. One of the first methods was
proposed by Keinhorst and Bals and based on the assumption that a portion of work-ed-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 regula-tions 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 funda-mental 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 prob-lems, 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 theodo-lite 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 prepara-tion of mine plans by point coordinates were of extreme importance for further progress in
Chapter Two
General
Figure
of the Earth,
Systems
of Coordinates,
Control
and Survey
Underground
Nets
and Surface
Surveys
the Earth, this point is usually related to the general figure of the Earth which is under-stood 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 conti-nued 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 (obla-teness) 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 equa-torial and polar diameter. attains 42 km 2.1. General Figure 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 morpholo-gical 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 occu-pies 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
2.2. Geographic System of Coordinates 17
by the formula: a=(a-b)/a
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 trans-ferred in a country, is called a reference ellipsoid (local ellipsoid).
p I
Fig. 2.1 Ellipsoid of revolution of spheroid
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. geo-graphic latitude <p and geogeo-graphic longitude A. Geographic coordinates are reckoned respectively from the equatorial plane and Greenwich meridian (Fig. 2.2).
770 m. It has also been established by satel-lite 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 'dia-meters' 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
Ch. 2. Systems of Coordinates, Nets and Surface Surveys 18
In the general case, when the deviations of upright lines are neglected, geodetic and astronomic coordinates are replaced by the generalized concept of geographic coordi-nates.
In geographic coordinates, longitudes can be reckoned: (I) eastward and westward of the Greenwich meridian, from 00 to 180°, and are called respectively easterly and westerly longitudes; easterly longitudes are considered to be positive and westerly ones, negative or (2) only eastward of the Greenwich meridian, from 0° to 360°, and are always called easterly longitudes.
Latitudes may vary from 0° to 90° and are reckoned north and south of the equator. The former are considered positive and the latter, negative.
The longitude is the dihedral angle be-tween the plane of Greenwich (zero) meridian and the meridional plane of a point p and the latitude is the angle made by a vertical line in a point p to the plane of equator.
The plane passing through the centre of the Earth and perpendicular to the axis of rotation is called the equatorial plane. The plane passing through a vertical line and the axis of rotation of the Earth (or parallel to the latter) is the plane of a geographic ( astronomic) meridian. The lines of inter-section of the planes of geographic meridians with the Earth's surface are called meridians. The lines formed by the intersection of planes drawn perpendicular to the axis of rotation of the Earth with the Earth's surface are called parallels of latitudes, or simply parallels.
The network of meridians and parallels applied on the surface of the Earth ellipsoid represents the coordinate axes of the geo-graphic system of coordinates.
If the geographic coordinates are determi-ned by astronomic observations (indepen-dently in any point on the Earth's surface), they are conventionally called astronomic geographic coordinates «p, /I.). The positions of points on the Earth's surface can also be determined by means of geographic coordi-nates obtained by geodetic observations and related to a normal to the ellipsoid surface; tt.ese are termed geodetic geographic coordi-nates and denoted as B (latitude) and L (longitude).
Since the surface of the geoid does not coincide with that of the ellipsoid, normals drawn to the surface of the latter turn out to deviate from the directions of upright lines. The magnitude of deviation may be equal to 3-4" on the average. Noting that the differe-nce of latitudes of 1" on the Earth's surface corresponds to a linear distance of 31 m, the positions of points on the Earth's surface, when given in astronomic and geodetic geographic Foordinates, may differ by 100 m on the average.
2.3. System of Plane Rectangular Coordinates
Geographic coordinates are expressed in angular values. They are inconvenient for engineering calculations in geodesy and mine surveying. Besides, the linear measurements of angular values turn out to be different in various portions of the Earth's surface. For these reasons, a system of plane rectangular coordinates seems to be more convenient for land and mine surveying and solving various engineering problems when their results should be plotted on maps and plans. Such a system can largely simplify topographic and mine surveying, adjustment of reference nets, calculations of coordinates of reference points, processing of the results of surveys, etc. The plane system of coordinates also ensures precise coincidence of plans of adjacent areas, etc.
The initial lines in a system of plane rectangular coordinates (Fig. 2.3) are two mutually perpendicular lines xx-yy lying in a horizontal plane and called respectively the axis of abscissae (x-axis) and the axis of ordinates (y-axis}. In contrast to
mathe-2.4. National System of Rectangular Coordinates 19
Fig. 2.3 System of plane rectangular coordinates
In land and mine surveying, the portions of the Earth's surface measuring up to 10 km in radius are considered to be flat (distortions along the length are not more than 1 cm and angular distortions, not more than 0.1"). The larger areas of the Earth's surface are depicted, to minimize distortions, in special projections in which the Earth ellipsoid is conventionally developed on a plane. In addition, the projection on a plane is done in such a way as to provide the coincidence of both geographic and rectangular coordi-nates.
matics, the axis of abscissae in land and mine surveying plans is arranged vertically and coincides with the direction of a meridian. The intersection of these axes is the origin of coordinates (point 0). The coordinate axes divide the plane of a drawing into four quadrants which are numbered clockwise beginning from the guadrant in the north-east section (see Fig. 2.3).
The abscissa x and ordinate y of points are the lengths of the perpendiculars drawn from these points onto the coordinate axes. The signs of coordinates depend on the quadrant in which the points are located. The abscissae of the points located in the first and fourth quadrant are positive and of those in the second and third quadrant are negative. The ordinates of the points in the first and second quadrant are positive and of those in the third and fourth quadrant are negative. ,.
2.4. National System
of Rectangular Coordinates When the territories of a substantial area are to be represented in topographic maps, the surface of the reference ellipsoid must be
20 Ch. 2. Systems of Coordinates, Nets and Surface Surveys
gular coordinates of points on a plane and the geographical coordinates on the reference ellipsoid.
2.4.1. Gauss Conformal Projection Among many requirements set forth to cartographic projections for topographic maps, the principal one is that projection distortions should not exceed the errors of corresponding geodetic measurements. This condition is approached most closely in the conformal projection proposed in 1820 by C. F. Gauss of Germany. It is based on the theory of plane conformal coordinates, which makes It possible to obtain almost undistor-ted images of the terrestrial ellipsoid on a plane.
The essence of the Gauss conformal projection consists in that the terrestrial ellipsoid is enveloped by a tangent cylinder whose axis is perpendicular to the minor axis of the ellipsoid. With this arrangement of the cylinder, it touches the ellipsoid along a meridian which is a common line of both figures (Fig. 2.4). Other meridians, when transferred (projected) onto the cylinder, will be increased in length. With moving father from the tangent (central) meridian, i. e. from the centre of zone, lengths will be distorted more and more, and their distortions can be determined by the formula:
, y2 L\l=l
2R2
developed in a plane. This procedure cannot however be done without cutting and folding the spherical surface being developed. The problem is solved by using an auxiliary surface which can be easily developed in a plane, such as a cylinder or cone. The portions of the reference ellipsoid are projec-ted onto an auxiliary, geometrically regular surface (cylinder or cone) and this is then developed without folds and cuts. For more convenience, the auxiliary body is supposed to be tangent to the reference ellipsoid, and the network of meridians and parallels of the reference ellipsoid is transferred (projected} onto the surface of the body to form a cartographic grid on the map. Mter the cartographic grid has been transformed onto the auxiliary tangent figure, the latter is cut and developed in a plane. The method by which the image of the Earth's surface is transferred from the sphere onto the plane is called a cartographic projection.
Cartographic projections involve certain distortions of geographic objects relative to their shape on the reference ellipsoid. By the nature of distortion, modern cartographic projections can be divided into equiangular (equal-angle), equivalent (equal-area) and their derivatives. In equiangular projections, angles are not distorted, and therefore, projected figures retain their similarity to the original ones. In equivalent projections, the areas remain equal, but the angles are distorted, and therefore, the outlines of figures are distorted too. In derivative projec-tions, both angles and areas are distorted, but only moderately.
Cartographic projections are studied by mathematical cartography where they are considered on a formalized basis as certain analytical relationships between the coordi-nates of points on tM.e surface of a reference ellipsoid and the coordinates of their projec-tions on a plane. In the general form, these relationships can be written as x = f1 «p, 1..) and y = f2 «p, 1..); they correlate the
rectan-where 1 is the length of a section on the Earth ~phere; y is the length of an arc from the central meridian to the given section; and R is the Earth's radius.
With the use of the Gauss conformal projection, the surface of the terrestrial ellipsoid is represented on a sheet of paper in the form of individual figures as those shown in Fig. 2.5, which are called zones. As has been established, the optimal zone for trans-ferring onto a tangent cylinder is a spheroidal
2.4. National System of Rectangular Coordinates 21
dihedron included between two meridians with the longitude difference 6°. Thus, the surface of the Earth is divided into 60 zones, a tangent cylinder being drawn to the central (axial) meridian of each zone. The surface of the spheroid within the limits of a particular zone is projected conformally onto the surface of the cylinder.
of a zone (see Fig. 2.6). Ordinates calculated from this new origin are called reduced ordinates. If, for instance, the ordinates of two points of the eighth zone relative to the central meridian are Yl = 23730.00 m and Y2 = -102280.00 m, the reduced ordinates will be:
Yl = 23730.00 + 500000.00 = 523730.00 m Y2 = -102280.00 + 500000.00 = 397720.00 m
Since the same numerical coordinates may exist in all 60 zones, it has been agreed to relate the coordinates to a particular zone by 2.4.2. Zonal System
of Rectangular Coordinates
The origin of coordinates in each zone is taken at the intersection of the central meridian of that zone with the equator (Fig. 2.6). The central meridian is the x-axis, and the image of the terrestrial equator perpendicular to the central meridian is the y-axis. The x-coordinates of points to the north of the equator are considered positive and of those to the south, negative. The y-coordinates of points to the east of the central meridian are positive and of those to the west, negative.
The longitude of the central meridian is found by the formula: Lo = 6N -3°, where N is the zone number. The western boundary meridian of the. first zone coincides with the Greenwich meridian.
In order to eliminate negative ordinates, the origin of coordinates is transferred by
22 Ch. 2. Systems of Coordinates, Nets and Surface Surveys
In some cases, however, the x-axis can be temporarily oriented relative to the magnetic or astronomic meridian. In exceptional cases when the survey work is carried out in an uninhabited region, is not large in scope, and there are no triangulation points, the x-axis can be oriented by the direction of a magnetic needle, though orientation by the astronomic meridian is more preferable in such cases. Mine survey plans obtained with this orientation can be used for many years.
In contrast to magnetic declination, meri-dian convergence remains constant in time. In some kinds of mine surveying work, a condi-tional system of coordinates can be adopted, with the Ox-axis directed arbitrarily, for instance, along a line fixed by survey points. The conditional systems of coordinates are used in the mine survey servicing of construc-tion of shafts and hoisting complexes, orien-tation of mines via two shafts, and in a number of other cases.
writing the number of a zone before a coordinate.
In the cases considered above, the ordi-nates of points located, say, in a zone No.8, should be written as follows:
Yl = 8523730.00 m and Y2 = 8397720.00 m
An important problem in mine surveying is how to choose properly the directions of coordinate axes. In the Cartesian rectangular system, the Z-axis is always vertical and directed upward, whereas the axes Ox and Oy are perpendicular to each other and lie in the horizontal plane. The orientation of these two axes must not be arbitrary. If the direction of one of these axes is specified, this will uniquely determine the direction of the other axis. In land and mine surveying, the Ox-direction is usually chosen (oriented in the horizontal plane) so as to satisfy the following conditions:
(a) the direction of Ox-axis must be easily and precisely reproducible and
(b) the direction of Ox-axis at various mining enterprises must permit the coinci-dence of plans of individual mines and larger enterprises.
The following cases of orientation of the Ox-axis for mine surveying plans are pos-sible:
(a) orientation by a magnetic meridian;
(b) orientation by an astronomic meridian;
and .
(c) orientation by the central meridian within each zone of the national system of coordinates.
Orientation by (a) and (b) cannot satisfy the requirements given above, since the magnetic azimuth is not constant in time and space, and the astronomic azimuth is not constant in space. On the contrary, the central meridian retains its orientation and position within the limits of a zone. Thus, the orientation of the x-axis should be preferably done relative to the central meridian of a zone.
2.5. Geodetic Reference Nets
The mine survey servicing of mining enterprises is unfeasible without a network of reference points whose positions on the land are determined with a high precision.
The measurements on the surface and underground involve errors which are accu-mulated if surveys are being done on indivi-dual areas not associated with one another. When represented on general mine survey plans or topographic maps, these areas will then be distorted to such an extent that the results of surveys become useless. In that connection, mine surveying is carried out by the principle 'from the general to particular', i. e. by providing first a general geodetic net on the territory of a country and then reference survey nets for surveying of indivi-dual small isolated areas.
Points established on the surface and having precisely fixed coordinates are called reference (control) points. or base stations.
2.6. National Geodetic Nets
Points ensuring the correct horizontal repre-sentation of the land surface are called plan (planimetric) control points, or horizontal control points. Those which can characterize the vertical relief of the land surface are called elevation (height) control points. A system of reference (control) points established on the territory of a country makes up a geodetic net.
Geodetic nets can be divided into national nets, bridging (densification) nets, and survey nets. Mine survey nets on the territory of economic interests of mining enterprises consist of the P9ints of the national geodetic net and geodetic nets of mine surveying and topographic surveying carried out for servi-cing of mineral prospecting and construction and exploitation of mining enterprises.
Some kinds of geodetic work on the land surface are carried out by mine surveyors. They include: the development of the existing mine survey reference nets as required for the surveys of mines and quarries; surveys of the pay-ore areas of mining enterprises; perio-dical layout, survey and levelling during the construction of minIng enterprises and exp-loitation of deposits in order to reflect current variations on mine survey plans; surveys of rock dumps and stocks of mineral; surveys for determining the volume of earth-moving work, for the reconstruction of railway tracks and other structures; surveys for observing rock displacements, stability of structures, etc.
2.6. National Geodetic Nets
A national geodetic net may consist of triangulation, trilateration, polygonometric and levelling nets.
A plan (horizontal) geodetic reference net is mainly constructed by the method of trian-gulation, i. e. by laying out triangles on the land surface. In each triangle, all three angles are measured, which ensures a reliable con-trol of angular field measurements. For
deter-mining linear dimensions, the length of one side of a triangle is measured (taped) and the lengths of the other two sides are calculated. The triangles of a net are arranged in a certain order, and their shape should be close to equilateral where possible.
The vertexes of triangles are fixed on the land by special station markers fastened in the ground. A metallic or wooden beacon (tower) is constructed above a station mar-ker. It carries a cylinder at the top whose axis should be coincident with that of the marker. The cylinder serves as the sighting target when making observations from other points. The triangulation method makes it pos-sible to determine the horizontal (plan) coor-dinates for the vertexes of triangles. Triangu-lation rows which consist of triangles with an average side length of 20-25 km form first-class triangulation chains up to 200. km long (Fig. 2.7). Triangulation chains are laid off in submeridional and sublateral directions so as to form the closed polygons of a peripheral length up to 1000 km. The side lying at the intersection of several chains (ab in Fig. 2.7) is a common of these chains and called the initial side. Initial sides must be measured with a high accuracy. Since it is practically impossible to measure lines 20-25 km in length on the land surface, it is common practice to measure not an initial side, but a transverse side around 6 km long (ed in Fig. 2.7), which is called the triangulation base. In the base figure adbe, all interior angles are measured, and the length of the initial side is calculated by the known angles and the known length of the base line. In first-class triangulation, the latitude and lon-gitude of the points at the ends of the initial side and the astronomic azimuth of that side are additionally determined by astronomic observations.
The territory within polygons of first-class triangulation chains is filled in with a con-tinuous network of second-class triangula-tion triangles with the lengths of sides
ran-24 Ch. 2. Systems of Coordinates, Nets and Surface Surveys Class 1 chain
(i
/\ .~ .0= " : la u , 11 ~ b ~1 ~2 C!J3 ~4Fig. 2.7 Development of triangulation network: 1, 2, 3. 4-triangulation points of respectively first, second, third, and fourth class
built-up territories, a geodetic net consists of polygonometric traverses in the form of bro-ken lines representing closed or open poly-gons (Fig. 2.8). In that case, field work con-sists in measuring the angles in turning (change) points and the lengths of all poly-gonometric sides. Polypoly-gonometric nets are usually constructed by laying off the main and diagonal polygons having common change points (5 and 19 in Fig. 2.8). The required accuracy of polygonometric nets can be characterized by the data given in Table 2.2.
ging from 7 km to 20 km depending on the pattern of terrain. In second-class triangula-tion, base lines are measured in one of every 20-25 triangles. As in the first-class tri-angulation, the latitudes and longitudes and astronomic azimuth of base lines are deter-mined by astronomic observations. Further densification of a plan control geodetic net is carried out by third- and fourth-class triangulation. The characteristics of reference nets constructed by Ist-4th class triangula-tion are given in Table 2.1.
25
2.6. National Geodetic Nets
Table 2.1 Trian- gula-tion class Side length, km Mean angular error (by triangle misclosures), s Permissible triangular misclosure, m Mean measur-ing error of base (clos-ing) sides Mean measur-ing error of base 1 2 3
Fig. 2.8 Polygonometry: 5, 19-common junco tion points; K, L, M -triangulation points
Polygonometry as a method for the con-struction of geodetic nets has become popu-lar in recent years, with the appearance of high-precision light and ratio range finders,
which have largely facilitated linear mea-surements, the most labour-consuming pro-cedure in land and mine surveying.
Another popular method for the construc-tion of planimetric geodetic nets is trilatera-tion. Its essence reduces to the construction of a network of triangles (as in triangulation) and measuring of the lengths of their sides (rather than angles). The latter are calculated from the known lengths of three sides. With the known angles and the measured length of one side (which is taken as the base line), the lengths of the other sides are calculated, after which the coordinates of trilateration points are determined. In trilateration, lengths are measured by means of range finders which can ensure a high accuracy of linear measure-ments (up to 1/400000).
The elevation (height) control of various land and mine survey operations is ensured by levelling nets which may be of class I, II,
26 Ch. 2. Systems of Coordinates. Nets and Surface Surveys To be performed with highest precision s.JL IO.JL 20JL II III IV 500-600 150-200 25
errors do not exceed 0.05 mm per kilometre of the levelling line.
Second-class levelling is carried out by running polygons connected to the points of first-class levelling and attaining a length of 500-600 km. The main object of second-class levelling is to provide the precise basis for third- and fourth-class levelling. In levelling nets of class II, the perimeters of polygons and the lengths of level lines should not exceed 40 km and the lengths of lines be-tween junction points, 10 km. In third-class levelling lines, the lengths of lines between higher-class levelling points shoud not exceed 15 km and of those between junction points, 5 kill. The lines of levels should be connected with one another at every 3 km in built-up territories or at every 5 km in free territories.
The height marks of triangulation and polygonometric points of all classes and of points of local plan reference nets are per-rnitted to be determined by class IV levelling. Trigonometric levelling is permissible for the determination of the heights of reference net points in exceptional cases, such as in moun-tainous regions.
The levelling lines of all classes are fixed on the land by means of ground and wall bench marks. The bench marks in the levelling nets of class I, II and III must be spaced at intervals of 5- 7 km. Fourth-class levelling is done by wall and ground bench marks and polygonometric stations. Wall and ground bench marks are established with intervals not more than 300 ill in built-up areas and not more than 0.5-2 kill in free territories. In levelling lines run through settlements, at least one bench or wall mark should be established in a settlement.
III and IV. First- and second-class levelling nets are the main basis for establishing the general system of elevations for the entire territory of the country. Third- and fourth-class levelling nets are the basis for topo-graphic surveys and for the solution of va-rious problems associated with geodetic and mine survey servicing of civil and industrial construction objects. The general characte-ristics of national levelling reference nets are given in Table 2.3. The permissible misclo-sure (mm) of traverses in local geodetic reference nets constructed by technical level-ling is equal to 50JL ' where L is the length of a traverse line, km.
Fundamental bench marks of a natural levelling net should be established with a density ensuring that every subdivision map plotted on a scale 1/5000 include at least one bench mark. With topographic surveys on a scale 1/2000, the density of fundamental bench marks should be such as to allow one bench mark for one-four map sheets.
First-class levelling is carried on the land along the directions essential for the national economy and defence of the country and relates to the most precise kinds of geodetic work. Accordingly, it must be carried out with the use of the most precise instruments. In modern levelling, random and systematic
2.7. Geodetic Bridging Nets
Geodetic bridging (densification) nets are developed on the basis of geodetic net points and serve for the surveys of land surface on
27 2.7. Geodetic Bridging Nets
Table 2.4 Second order First order Parameter 0.25-3.0 1/20000 :1: 40" :1:10" 3 0.5-5.0 1/500000 ::!:20" ::!:5" 5 0.25-3.0 1/10000 20° 3 0.5-5.0 1/20000 20° 5 3 9 0.80-0.30 15 0.12-0.60 Triangulation
Side length of triangles, km
Maximum relative error for base side Maximum misclosure of triangle
Mean measuring error from triangle misclosures Maximum length of chain of triangles, km Trilateration
Side length of triangles, km
Maximum relative error of side measurement Minimum angle of triangles
Maximum length of chain of triangles, km Polygonometry
Maximum length of traverses, km
Maximum perimeter of polygonometric traverses in free networks, km
Length of side of traverse, km
Maximum length of traverse from nodal point to highest-class or highest-order point, km
Maximum number of sides in traverse Maximum relative misclosure of traverse Mean measuring error of traverse
3 15 110000 :t5" 2 15 1/5000 :t10"
scales 1/5000 to 1/500 and for performing various kinds of mine survey work.
Planimetric geodetic bridging nets can be constructed as analytical nets or polygono-metric nets of the first or second order. Their main characteristics are given in Table 2.4.
Analytical nets can be formed by triangu-lation as a continuous network or chains of triangles or intersections (bearings). Analy-tical bridging nets of the first order can be developed on the basis of geodetic reference nets of classes I, 2, 3 and 4; those of the second order can be developed on the basis of reference nets of all classes and a first-order analytical net. The analytical nets of the first order may have the sides from 0.5 km to 5 km long and those of the second order, from 0.25 km to 3 km long. The angles
of triangles should be not smaller than 30°, and the number of triangles in a chain should be not more than 10.
If the territory to be surveyed has no available points of geodetic plan control (of any class), it is permissible to develop the independent survey nets of the first or second order for land and mine surveying. In that case, it is required to measure at least two base sides separated from each other by at least 10 triangles.
The polygonometry of the first and second order can be developed in the form of indi-vidual traverses or a system of traverses with junction points belonging to the national geodetic reference net or first-order analytical net.
Of special significance are approach mine surveying points in reference nets. The
ap-28 Ch. 2. Systems of Coordinates. Nets and Surface Surveys
proach points must ensure the possibility of running a hanging traverse with the number of sides not more than three to a mine shaft. Approach points should be located at distances not more than 300 m from the collar of a shaft. It is possible to use the points of triangulation, trilateration and po-lygonometric nets of class 1-4 or of first-order analytical nets as approach points. The pay-ore area of a mining enterprise should have at least three elevation bench marks with their heights measured by levelling of a class not worse than four.
Table 2.5 Contour interval height, m Level line length in technical levelling, km Levelline length in trigonometric levelling, km 0.5 1.0 2.0 5.0 3 10 15 2 5
and on territories where linear measure-ments are complicated, the base points of a survey net can be deterniined analytically by constructing a chain of triangles; by the methods of intersections and resections; or by constructing a central system of geodetic rectangles.
The angles in triangles should, as a rule, be not smaller than 30°. Side lengths should be not less than 150 m. A direct intersection is made from three points and a resection, by four initial points. The misclosures of tri-angles should be not more than I '. The relative error of initial sides in triangle chains should not exceed 1/2000. In closed areas, the base points of a survey net can be deterniined conveniently by running individual theodo-lite traverses or a system of theodotheodo-lite tra-verses in which the points of a geodetic reference net serve as junction points.
Elevation survey nets are constructed by geometric, technical and trigonometric (geodetic) levelling. Geometric levelling is usually employed in areas with the height of contour interval of relief up to I m and trigonometric levelling, with greater contour interval heights. The lengths of level lines supported by the levelling points of class I-IV and of closed level lines should not exceed the values given in Table 2.5.
2.8. Geodetic Survey Nets
Planimetric and elevation survey nets are constructed on the basis of points of a geodetic reference net. In exceptional cases, when the area to be surveyed is not more than 20 km2 for surveys on a scale of 1/5000 or 10 km2, 1/2000, they can be based on the points of a survey net only.
Planimetric survey nets are developed by running theodolite, tacheometric or plane-table traverses or can be constructed analy-tically.
The number of points of a survey net is determined by the scale of a survey map and should be equal, together with the points of a geodetic reference net, to at least four points per square kilometre of the territory for a scale 1/5000, 10 points for a scale 1/2000 or 16 points for a scale 1/1000. The errors of the location of survey net points relative to the nearest points of a geodetic reference net should not exceed the accuracy of a surveying scale (i. e. should be not more than:!: 0.1 mm on the scale of the map).
Survey nets consist of base points and additional points, i. e. points determined in the survey net proper. Each survey sheet should include at least three base points fixed by fundamental marks for a scale of 1/5000, at least two such points for a scale 1/2000 or one point for a scale 1/1000. In open areas
