GENERAL SURVEYING

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Gheorghe M.T. RadulescuGeneral Surveying

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<p>GHEORGHE M. T. RDULESCU</p> <p>GENERAL TOPOGRAPHYLECTURE NOTES</p> <p>2002</p> <p>FOREWORDThe presented lecture notes are addressed to the students of the Faculty of Mineral Resources and Environment, to those who attend a form of undergraduate or postgraduate specialization, to all those who in their design or execution activity find themselves in situations that require the help of topographic methods and instruments in order to solve the technical problems related with implementing an investment. This course represents the general part of TOPOGRAPHY, the direct side by which planimetric and leveling terrain surfaces are measured in order to be represented on topographic plans. Based on an experience of more than 20 years, I have elaborated this work starting from what I have learnt in the Faculty of Geodesy from Bucharest, from the prominent specialty teachers: the regretted N. Cristescu, M. Sebastian-Taub, M. Neamtu, E. Ulea, from my lifetime mentor Mr. Prof. Dr. Eng. Vasile Ursea, then passing to the collaboration within the specialty department in the Polytechnic Institute from ClujNapoca (during the years 1980-1985) together with the colleagues Ms. Viorica Balan and Mr. Gheorghe Bendea, and then continuing within the institution where I am working in the present. Being addressed also to those that chose a form pf specialization with reduced frequency (Distance Learning or Without Frequency) I have tried to give this work a didactical, explicit character, each relation being deduced starting from solutions in which the interrelation of the processed elements is presented. The Author</p> <p>II</p> <p>TABLE OF CONTENTSGHEORGHE M. T. RDULESCU..................................................................................I GENERAL TOPOGRAPHY.............................................................................................I LECTURE NOTES............................................................................................................I FOREWORD....................................................................................................................II TABLE OF CONTENTS................................................................................................III CHAPTER I.......................................................................................................................1 CHAPTER II THE SHAPE AND DIMENSIONS OF EARTH, PROJECTIONS, REPRESENTATIONS....................................................................................................17 CHAPTER III TOPOGRAPHIC ELEMENTS OF THE TERRAIN.....................26 CHAPTER IV ERROR ANALYSIS IN TERRESTRIAL MEASUREMENTS....38 CHAPTER V TOPOGRAPHIC INSTRUMENTS....................................................45 CHAPTER VI PLANIMETRIC SURVEYS..............................................................92 CHAPTER VII LEVELING SURVEYS..................................................................129 CHAPTER VIII PLANS AND MAPS......................................................................166</p> <p>III</p> <p>CHAPTER I1.1. TOPOGRAPHY THE SCIENCE OF TERRESTRIAL MEASUREMENTS1.1.a. THE ACTIVITY SPHERE OF TERRESTRIAL MEASUREMENTS The assembly of sciences that contribute to the measurement and representation of terrestrial surfaces establishes the science of terrestrial measurements. There can be distinguished three main goals of this science, from the following perspectives: Scientific: knowing the shape and dimensions of the Earth, as a planet; Direct practical: obtaining topographic plans and maps; Indirect-applicative practical: placing, directing and tracing the designed investments in the field, based on and comply with the execution project. The main branches of terrestrial measurements (Schema no.1) are: Geodesy: deals with studying the shape and dimensions of the Earth, or of some parts of it and with accurately determining the position of some points in the field, which, as a whole, form the geodetic control network. Because the surfaces that are operated on are large, the geodetic measurements take into account the terrestrial curvature. Topography: determines the position in the field of the natural and artificial details of the Earths surface, based on the points of the geodetic network, without taking into consideration the terrestrial curvature. Photogrammetry: by processing photographs (photograms) of the terrain, taken from plane or on the ground, it drafts plans and maps. Remote sensing: a set of techniques and technologies that allow the remote analysis of terrestrial surfaces, soil subsoil, from the qualitative and positional point of view, by processing the images taken in different regions of the electromagnetic spectrum. Cartography: studies the possibilities of passing from terrestrial surfaces which are curved, to projection ones which are plan, scaling down the obtained images and</p> <p>1</p> <p>representing them on maps, as well as the techniques of drafting, reproducing, printing, multiplying and depositing topographic maps.</p> <p>TE RRESTRIA L M EA SU REM EN TS</p> <p>G EO D E TIC A STRO N O M Y</p> <p>G EO D ET IC G RA V IM ETRY</p> <p>GE O D EO SY</p> <p>CA RTO G RA P H Y</p> <p>TO P O G RA P H Y</p> <p>P H O TO G RA M M ET RY</p> <p>REM O T E SE N SIN G CO SM ICA L ELIP SO ID P RA CTICA L M A TH EM A TICS A ERIA L D RA FT IN G CA RRY IN G O U T PLAN MAP E D ITIN G RE P RO D U CIN G P LA N P RO BLEM H EIG H T P RO BL EM G EN E RA L EN G IN E ERIN G T ERREST RIA L</p> <p>P LA N P RO BLEM P LA N IM ETRY</p> <p>H E IG H T P RO BLEM LEV ELLIN G</p> <p>D ESIG N EX ECU TO N I M O N ITO RIN G</p> <p>TRIA N G U LA TIO N</p> <p>TRILA TERA TIO N G EO D E TIC L E V E L LIN G G EO M E T RY M ETH O D S IN ST RU ME N T S</p> <p>O F SU P ERIO R O RD ER</p> <p>O F IN FERIO R O RD E R</p> <p>TRIG O N O ME T RY TRA V ERSIN G P LA N IM ETRIC TRA V ERSE L EV E LLIN G SU RV EY LEV EL LIN G TRA V ERSE</p> <p>P RE CISIO N TRA V ERSIN G</p> <p>P LA N IM ETRIC SU RV EY</p> <p>D RA FT IN G TO P O G RA P H IC P LA N S</p> <p>S ch e m a 1 . Th e co m pl e x o f a ppl i e d s ci e n ce s th a t fo rm th e te rre s tri a l m e a s u re m e n ts a n d th e i r i n te rde ce n de n pe</p> <p>2</p> <p>PHOTOINTERPRETATION</p> <p>T EH N ICA -E CO N O M ICA L STU D IES L</p> <p>1.1.b. THE OBJECT AND THE TOPOGRAPHIC APPLICATIONS IN CONSTRUCTIONS AND MINING Depending TOPOGRAPHY: GENERAL TOPOGRAPHY, which comprises: The study of general methods and instruments, used for different works; Measuring and representing terrestrial surfaces of limited extent on topographic plans and maps (the direct problem of topography). APPLIED TOPOGRAPHY (or engineering), which consists of: Ensuring maps, plans, profiles, bearing points, measurements and computations (that belong to the direct problem) for the design of different investments; Office and field works for applying the engineering projects and monitoring the time behavior of the terrains and constructions (the inverse problem of topography). General topography, as office science, precedes engineering topography. If the former has a universally valid character, the latter is profiled and adapted to the conditions and the domain that it is applied to. There are many applications of topography in different branches of economy (Schema 2). But we shall not discuss except those that are directly connected to the mining domain. Thus, in constructions, topography precedes, accompanies and follows the execution works, as we shall see: It offers graphical and numerical documentation (maps, plans, known coordinates benchmarks), which are necessary to study the design alternatives: In the phase of technical-economical studies, as well as of drafting the execution project integrated in the preceding aspect; The designed construction objects, as well as each composing element, are placed in the field in accordance to the project using topographic means. This on the solved problem, there exist two components of</p> <p>3</p> <p>kind of topographic operations are called tracing and refer to the accompanying aspect of execution works; Monitoring the behavior of the foundation terrain and of the construction elements during the execution is integrated in this category of topographic woks, too. After finishing the execution of the designed objectives, the above-mentioned activity is continued until it is found that the deformations in plan (horizontal displacements) and space (settling) have ceased. These topographic works are integrated in the following aspect of execution works. In mining topography also takes part in all phases of the activity: investigation, design, exploitation, monitoring. Investigation, phase of mining similar to that of technical-economical studies from constructions, is solved also through the contribution of topographic methods, which, besides the maps and plans of the studied area, based on geological laws, determines the position, shape and dimensions of the ore bodies that can be found in the terrestrial crust. In the opening and exploitation activity similar to the execution in the construction domain, the mining topography methods contribute to the good progress of the production processes. The main topographic operations in this study are: Topographic surveys of the mining perimeter; The exploitation of the opening works; Surveys aiming the spatial position of constructions and mining works, and their support with respect to the ore deposit; The correct placement of mining works; Tracing works under execution; Placing and verifying the position of important mechanical installations.</p> <p>As the process of exploitation of the ore deposit is carried on, the pressures in the mining works and the influence of the spaces exploited underground upon the main mining works and upon the surface are determined based on topographic measurements.</p> <p>4</p> <p>M A T H E M A T I C S H Y SIC S P</p> <p>E R RO R T H E O R Y</p> <p>IT</p> <p>GE O GR A P H Y GE O L O GY</p> <p>GE O D E SY</p> <p>T O P O GR A P H Y P H O T O GR A M M E T RY C H E M IST R Y</p> <p>CO N ST RU CT IO N S M IN IN G LA N D RECLA M A T IO N LA N D REGIST ER SYLVICU LT U RE GEO LO GY GEO GRA PH Y GEO PH YSICS GEO M O RPH GY O LO H YD RO GRA PH Y O CEA N O GRA PH Y SYST EM A T IZ A T IO N U RBA N ISM SEISM O LO GY VO LCA N O LO GY PO LLU T IO N A N A LYSIS N A VA L A N D A IR N A VIGA T IO N A RCH A EO LO GY D EFEN SE SPO RT A T H LET ICS S</p> <p>S che m a 2 . The ma in s cie nce s tha t to po g ra phy a nd pho to g ra mme try ha v e direindire ct co nne ctio n with ct o r</p> <p>5</p> <p>1.2. THE PRINCIPLES OF THE TECHNICAL SCIENCE IN TOPOGRAPHYThe importance of topography as applied science is undeniable. All this, in the case in which the execution precision of topographic works is respected and is correlated to that of the works they are applied on. In the same way, the leading role of topography in different application domains should not be neglected, since it implies great responsibility. In order to correspond to these requirements, the topographic works should be executed respecting the technological discipline, concisely reflected by the following principles: 1. VERIFYING THE OPERATION: At least one verification is needed for every topographic work. 2. VERIFYING THE MEASURED DATA: When the operations in field are finished, the data taken during that measurement cycle will be verified. 3. THE NECESSARY PRECISION: The precision of the topographic tracing or measurement works will be given by the execution precision of the designed objective. 4. APPLYING AUTOMATED CALCULUS: Data processing is performed, if it is possible, by using means of automated calculus. 5. THE PERIODIC VERIFICATION OF INSTRUMENTS: In order to maintain over time the functional qualities of the topographic instruments (especially the optical ones), their periodic verification and rectification is required.</p> <p>6</p> <p>6. FAVORABLE METEOROLOGICAL AND NATURAL CONDITIONS: There will be performed no work in the field, except if the meteorological and natural conditions are favorable to the chosen methods and devices. In case of emergencies, there will be taken such operation measures that the influence of the environment to be minimal. 7. THE PROFITABLENESS OF TOPOGRAPHIC WORKS: The choice of methods and instruments used in a topographic operation should depend on the necessary working precision. 8. GEOMETRIZING THE MEASURED AREA: The terrain cannot be measured as it is, so it is geometrized. In the choice of the points by which topographic surface is geometrized, it is essential that the scaled down image (the plan, the map) obtained as final product to be complete, corresponding to the requirements of the beneficiary, but not to contain more elements than necessary. 9. AVOINDING LAUNCING INTO THE WORK: Before beginning a topographic work, there should be drafted a rational activity schedule, which should be respected along the entire period of execution of the work. 10. RESPECTING THE SAFETY MEASURES OF THE WORK: In order to avoid any possibility of accident or sickness, the safety measures of the topographic work and those specific to the domain that is operated within (mine, construction site, etc.) should be respected. One should work only being completely healthy. Schema no. 3 synthetically presents the main measurement and tracing topographic operations. As it can be seen, two types of angles are used: horizontal and vertical, and two distances: horizontal and vertical (heights). A clear distinction should be made between the measurement and tracing operations. In the first case, the linear or angular ratio under which a series of points existing in the field is to be found is recorded,</p> <p>7</p> <p>whereas in the second case, one or more dimensional measures are applied in the field, in order to obtain a new topographic point.</p> <p>GENERAL MEASUREM ENTMeasured elements</p> <p>ENGINEERING</p> <p>TOPOGRAPHYTRACINGCompu tations Known Unknown elements elementsMeasur Points Measur Points es es Traced Measured Traced</p> <p>Known Unknown elements elementsMeasur Points Measur Points es es</p> <p>Schema</p> <p>Schema</p> <p>Compu tations</p> <p>D</p> <p>Distances</p> <p>D</p> <p>l0</p> <p>A B</p> <p>DAB</p> <p>A</p> <p>D A B D B n A l0 l0 l0 B l1 n0 l1 xlCII A</p> <p>D B C</p> <p>Particularities of topographic operations</p> <p>D =n A A 0 1 DB l l B =n - 1 B 0 DA l l l0 D= A D A ---------D B B ---2I = IB - IA</p> <p>A C</p> <p>-</p> <p>BA</p> <p>D BA</p> <p>n = ---D --- 0 l l1= D - n 0 .l</p> <p>n l1</p> <p>S A B</p> <p>A</p> <p>Horizontal angles</p> <p>-</p> <p>SCC</p> <p>I A</p> <p>CA</p> <p>CII B</p> <p>I B</p> <p>B</p> <p>C C II = IIB - IIA A D B CB C I +CII = ------- --2I = g - I 100 V II = II - g VI 300 +II = ------- --2</p> <p>A C</p> <p>-</p> <p>B S</p> <p>CIA</p> <p>CII A</p> <p>A CIA CII A CIB CII B</p> <p> B</p> <p>D AB</p> <p>I CB = IA- C II = II - CB A C</p> <p>Vertical angles</p> <p>-</p> <p>A B</p> <p>i</p> <p>I V II V</p> <p>i VI B VII</p> <p>A C</p> <p>-</p> <p>B i</p> <p>I V</p> <p>i B i</p> <p>II V</p> <p>A A A Z B Z BB Horizontal comparison plan b B A Z Level B Z surface B</p> <p>A A C a bB Z AB</p> <p>I V I V I</p> <p>I V= g - 100 V=- g 300</p> <p>Heights</p> <p>ZA</p> <p>-</p> <p>a A Z A</p> <p>Z A A = a Z B- b b Z= A -A Z Z B BZ aB</p> <p>ZB A ZB</p> <p>B</p> <p>A ZA</p> <p>ZB</p> <p>a b</p> <p>-A BZ =Z = a A Z B b-</p> <p>8</p> <p>1.3. LENGTH AND SURFACE...</p>