13 A-Po Accuacy ff 1D Coodnates n te Netwok of Combned Leveng Tuckeš, S. 1 and Guev, J. 1 Unvesty of Banja Luka, Facuty of Actectua and Cv Engneeng, Depatment of Geodesy, Vojvode Stepe Stepanova 77/3, 78000 Banja Luka Repubc of Spska, B&H, Web ste: www.agfb.og, E-ma: svsnjc@agfb.og Unvesty of Begade, Facuty of Cv Engneeng, Depatment of Geodesy and Geonfomatcs, Bueva kaja Aeksanda 73, 11000 Begade Seba, Webste: www.gf.bg.ac.s, E-ma: jgucevc@gf.bg.ac.s Abstact Vetca postonng means detemnaton of a vetca poston (egt) of a pont eated to anote,.e. detemnaton of egt dffeences. In engneeng geodesy, te egt dffeences ae detemned by a combnaton of te geometca and tgonometc eveng. Estabsng of 1D geodetc netwok s pefomed accodng to a measuement pan, ceated by accuacy demands. It conssts of: seecton of nstuments and accessoes, defnng te accuacy condtons, defnng montong of data and conto of measuements. In ts pape we w pesent te actvtes on pepaaton, easaton and pocessng of measung quanttes, n ode to detemne te egt dffeences and pont egts of te opeatve poygon wtn te budng te gway codo Vc, segment Potej-Bjaa, sub-segment Zvov-Bjaa. Accuacy estmaton and te coce of te measung metod n te combned eveng netwok wee done foowng accuacy demands of egt eements wc ae a pat of te desgn estmaton. Key wods: Leveng, accuacy demands, toeance 1 INTRODUCTION Wen desgnng engneeng stuctues, te estabsment of a 1D netwok on te constucton ste s of cuca mpotance wtn te vetca spata ocasaton. Te accuacy and seecton of measuement metods, n suc a netwok s cacuated based on te equed accuacy of egt eements ncuded n te cacuaton of te desgn. Afte ts estabsment, 1D netwok becomes te bass of a cassca measung and makng egts dung te constucton and expotaton n te one of te stuctue. Te poject of 1D netwok on te constucton ste must take nto account eements tat affect ts sape, accuacy and metod of stabsaton. Tey ae pmay eements of te constucton ste poston, te stuctue poston (ove gound, undegound), type of stuctue, and quaty and ote specfc featues of te stuctue (Begov, A, 1990.). TS 4 Poste pesentatons INGEO 014 6 t Intenatona Confeence on Engneeng Suveyng Pague, Cec epubc, Ap 3-4, 014
14 INGEO 014 RESEARCH OBJECTIVE AND METHODS 1D netwok desgned fo speca needs conssts of a basc netwok of I ode, and netwoks of II and III ode f needed. Te eveng netwok poject soud ncude: evew pan o a map wt a te nfomaton about te exstng geodetc netwoks of te aea ncuded n te pocess of settng 1D netwok; metod of stabsaton; measuement pan, wc s deveoped accodng to te gven accuacy and cost anayss. Revew pan o map of geodetc netwok s made n te scae of 1:500 to 1:10 000, dependng on te se of te constucton ste. Taveses of te eveng netwok ae desgned aong man communcatons n te sape of a poygon o a system of noda ponts (Maov, K, 1978.). Ponts of 1D geodetc netwok (bencmaks) ae stabsed so tat tey can be easy used n te constucton and montong of te stuctue. Bencmaks can be of a dffeent desgn, but t s vey mpotant tat tey ae not destoyed o damaged. On age constucton stes damages ae fequent due to eatwoks, tanspotaton, and ote ccumstances, so t s necessay to pedct conto bencmaks paced outsde te one of constucton woks on te geoogcay stabe tean. Tey can be but n oontay o vetcay and made of cast on o aumnum..1 MEASUREMENT PLAN Detaed eaboaton of te measung metod s caed out on te bass of te defned accuacy of 1D coodnates of geodetc netwok ponts. Te equed geodetc measuements ae caed out based on te measung pan, wc s made by a gven accuacy and ncudes: seecton of nstuments and accessoes, defnng tems of accuacy and defnng data fo measuement montong and conto..1.1 A-po accuacy assessment of 1D coodnates In ode to nvestgate wete usng cetan metods of measuement te equed accuacy may be aceved and unde wc ccumstances, t s pevousy necessay to pefom te anayss of te metod. Ts anayss soud detemne te souces of eos n measung, te accuacy wt wc t s necessay to pefom cetan actvtes n te measuement pocess, as we as wat ae te optons fo emnatng o educng te mpact of systematc eos wt te wokng metod o by makng appopate coectons. A-po assessment of accuacy s pefomed fo a specfc type of eveng based on detemnng te vaues of some eementay eos. Te expessons fo te a-po assessment of accuacy of egt dffeences ncude: assessment of accuacy of geometc eveng, assessment of accuacy of tgonometc eveng. A-po assessment of accuacy of geometc eveng s pefomed statng fom te ndvdua souces of eos n te expesson fo te mean squaed eo of egt dffeence at te staton (Mk, R., 1991., p.33)): 1 o DR d M n. (1) Te egt dffeence between two bencmaks s cacuated as: H 1... n. Fo a omogeneous accuacy:... 1 n mean squaed eo of egt dffeence between two bencmaks fom n statons, s cacuated accodng to te expesson:
Tuckeš, S, et a.: Accuacy of 1D coodnates n te netwok... 15 H n. () If we stat fom appoxmate vaues of cetan souces of eos: 0 m - andom eo of dvson of od; 0. 05 - andom efacton; 0. 5 - andom eo n od eadngs; M 7 m - od-pa scae eo; 9 m - ounded eadngs eo (Mk, 1991 and nkov, 1973.), mean squaed eo of egt dffeence at te staton of one eveng sde (measued twce n ) fo dffeent engts of ne of sgt D, wt a maxmum egt dffeence at te staton 1 m s cacuated n Tabe 1. o DR Tabe 1 Vaues of egt dffeence eos D (m) 10 5 50 (mm) n = 0.04 0.05 0.07 n H (mm) 5 0.10 0.1 0.17 10 0.14 0.17 0.4 0 0.0 0.4 0.33 30 0.4 0.9 0.41 50 0.31 0.37 0.53 Assessment of accuacy of tgonometc eveng s pefomed statng fom te expesson used fo detemnaton of egt dffeence based on te obseved ent dstances (Maov, 1978): B D H m A D ctga A B 1 k A D ctga. (3) D H m If due to te cuvatue of te eat s suface and pont egts D ctg A membes ae consdeed neggbe fo te engts ess tan 1000 m, te mean squaed eo of egt dffeence s found by appyng te pncpe of eo tansfe on te expesson (3) 4 D D ctg D 4 k, (4) sn 4 wee: - standad devaton of egt dffeence, - standad devaton of te measued ent dstance, D - standad devaton of te measued engt, k - standad devaton of te efacton coeffcent, - standad devaton of te measued nstument egt, - standad devaton of te measued sgna egt. Te mpacts of standad devatons D, and do not depend on te engt D. Te mpacts of standad devatons and k depend on te engt D and ae age fo onge dstances. Te expesson (4) can be smpfed f te fst membe s eft out, wc s neggbe, t emans tat te accuacy of egt dffeence detemnaton by usng tgonometc eveng: 4 D D 4 k (5) sn 4 If te egt dffeence H s detemned on te bass of ecpoca measuement 1 and ten te mean squaed eo of ecpocay detemned egt dffeence s:
16 INGEO 014 1 1 H 1 4 4 (6) o fo omogenous accuacy 1 and wt smutaneousy detemned egt dffeences te mpact of efacton can be negected, and tus we ave: 1 1 D 1 1 H 4 sn (7) Te queston s: Wc nstument soud be used fo measung ent dstances, knowng tat t s necessay to detemne egt dffeence wt accuacy 5 mm and wee, 3 mm. Tabe Vaues ent dstance eos D (m) 100 300 500 550 ( ) 11.67 3.89.33.1 Tabe sows tat te mpact of eo depends on engt D, and s age fo onge dstances, wc must be taken nto account n te seecton of nstuments and accessoes..1. Wegts of egt dffeence Wegts of egt dffeence ae detemned statng fom te expesson: k P, (8) H H wee k s abtay constant, and H s mean squaed eo of a cetan egt dffeence n te tavese of geometc eveng accodng to te expesson and fo tgonometc eveng accodng to te expesson 7.. ADJUSTMENT 1D COORDINATES OF THE LEVELLING NETWORK Detemnatons of 1D coodnates ae adjust by te metod of east squaes. Te measued vaues n te netwok ae: egt dffeences between te ponts of opeatng poygon of te 1D netwok. Hegt dffeences of basc 1D netwok, wt a mean eo of ess tan 0.3 mm/km s detemned by usng te geometc eveng, and egt dffeences of netwok II and III fo wc accuacy of te ode of 5 mm s expected can be detemned usng tgonometc eveng fo te engts of ess tan 550 m. Te measued vaues n te adjustment ae ndependent vaues. H 3 RESEARCH AREA Fgue 1 Poston of Codo Vc fom Budapest to te Coatan pot of Poe Codo Vc s panned to connect te aeas sout of Budapest, va Osjek n Coata, wt Saajevo and Mosta n Bosna and Heegovna and te Coatan pot of Poce (Fg. 1). Te Codo Vc n B&H s dvded nto 13 sectons wt te tota engt of 334 km. Fo te woks on te poject fo te constucton of Codo Vc motoway, secton: Potej-Bjaa, subsecton Zvov-Bjaa, a geodetc netwok was estabsed desgned fo 1D mak ponts of
G1 Tuckeš, S, et a.: Accuacy of 1D coodnates n te netwok... 17 te stuctue, geomety conto dung constucton and geomety conto of te pefomed woks. 1D netwok soud meet sevea puposes, so te ponts of te netwok ae stabsed at a suffcent dstance fom te stuctue so tey ae not damaged and te stabty s not teatened. 4 PROCESSING OF RESULTS Taveses of te 1D netwok ae desgned n te fom of fou poygons of geometc eveng (G1, G, G3 and G4) and tee poygons of tgonometc eveng (T1, T and T3) (Fg..) 1D netwok s a geodetc bass fo makng and montong te stuctue subsdence n 1D pane and t s stabsed on te foundatons of enfoced concete coumns. 4.1 MEASUREMENT PLAN In accodance wt te paametes obtaned fom te a-po assessment of accuacy, measuement s panned n two pats. Te measuement pan n te 1D netwok nvoves measuement of geometc and tgonometc eveng wt te connecton of poygons. In te pat of te poygon of geometc eveng, measuement was conducted wt LEICA DNA03 dgta eve, wc as te decaed measuement accuacy of 0.3 mm/km wt nva bacode ods. Te eve s tested and as a cetfcate of cabaton. Measuements wee taken fom te mdde wt te maxmum engt of te ne of sgt of 5 m. Te condtons dung measuement wtn te geometca eveng ncude: befoe te measuement tempeng of nstuments and accessoes soud be pefomed; dung measuement, nstument and tpod soud be potected fom dect sungt; measuements soud be pefomed n te peod of sotem, so tat te condtons on bot ods ae about te same; and aso te dvsons of te od beow 0.50 m and ove.5 m soud not be ead. In ode to aceve an accuacy of 0.3 mm/km, te measuement pocedue mpes te measuement back and fot, fom te mdde, wt te cange n te nstument egt and wt te maxmum engt of te ne of sgt of 30 m. Montong and conto of measuements wee caed out at te staton and wtn te poygon of geometc eveng. In te tgonometc eveng, te measuement was pefomed wt te tota staton LEICA TC003, wc as te decaed measuement accuacy (0.5")/1 mm + 1 ppm. Measuements wee pefomed among a te ponts vsbe fom te staton tat connected poygons of geometca eveng. Te nstument as been tested and as a cetfcate of cabaton. Te condtons dung te measuement wtn tgonometc eveng ncude: befoe te measuement, te nstument and accessoes wee subjected to extena condtons fo about af an ou; dung te measuement, te nstument was potected fom dect sungt; measung nstument egt and psm was caed wt te tape tat ad te cetfcate of cabaton. Te measuement pocedue mpes measuements n bot postons of teescope wt 5 eadngs eac. Te measued vaues ae coected fo te mpact of atmospec paametes, cuvatue of te Eat's suface and te effect of efacton. Tansfeng egts fom bencmaks but n te foundatons of enfoced concete coumns to teads fo foced centeng on te coumn ( t ), was caed out wt te ep of geometc eveng. T3 T5 K5L703 G4 T1 T3 T0 T18 K5L7039 T16 T19 T17 K5L700 G3 T14 T15 T1 T11 T9 G T T10 T6 T8 geometc eveng T3 T13 tgonometc eveng K5L7017 Fgue Dagam of measued vaues T1 T5 T4 T1 T7 G1 T K5L7016
18 INGEO 014 4. CALCULATION OF 1D COORDINATES OF THE LEVELLING NETWORK Te 1D geodetc netwok s compsed of a tota of 8 ponts of wc 3 ae stabsed on enfoced meta pates and 5 poygon ponts. Cacuaton of 1D coodnates was pefomed by adjustment accodng to te metod of east squaes. Te wegts of egt dffeences wee detemned n accodance wt te expesson (8), fo eac measued vaue. Te stocastc mode s set up fo te case wen te measued vaues ae stocastcay ndependent,.e. wen a te eements outsde te man dagona covaance matx of te measued vaues ae eo. Vetca geodetc Datum s defned n te oca 1D system wt te egts of poygon ponts K5L7016 and K5L703 (Fg. ). Te accuacy of detemnng te coodnate s n te ange fom 0.09 mm to 0.81 mm and te aveage accuacy s 0.43 mm. Tems of efeence ave been equed accuacy of 1 mm, wc confms tat te pocedue descbed above s aceved equements accuacy. 5 CONCLUSION In geodetc pactce, fo sovng te pobem of 1D poston n engneeng and tecnca feds, te egts ae most often detemned by te metod of geometc and tgonometc eveng. Te seecton of te measuement metod s n te functon of te equed accuacy and feasbty condtons of sutabe metods fo easaton of 1D geodetc netwok. If dffeent measuement metods ae used fo egt dffeences, te pocessng of te measued vaues n te stocastc mode nvoves te use of dffeent expessons fo cacuatng te mean squaed eo of te measued vaue tat depend on te type and dstbuton of measuement esuts as we as te nvoved coectons n te measuement esuts. Te accuacy of measung egt dffeences s adjusted wt appopate pocessng of te measuement esuts, by enteng te equed coectons n te esuts of measuements and tus te most appopate vaue fo 0 s seected. Wtn te eased 1D poygon, te a-po accuacy assessment s apped and te seecton of nstuments and accessoes s caed out. Sgma a-po s 1 and sgma a- posteo fom pefomed measuements s ˆ 0 =1.11. Vaue of te test ypotess of te goba mode s 1.4 wc compaed wt te vaue of te test statstcs of te goba mode fo te adopted eve of sgnfcance 0.05 s 1.6 and pesents te adequacy of te mode fo 0.1 mm 0.55 mm and 0. mm. GeomLev TgLev Dst 0 REFERENCES MRKI, R.: Geodetska metoogja (Geodetc metoogy), Nauna knjga, ISBN 863410661, Beogad, 1991. INKLOVI, N.: Anaa petodna ocena tacnost metoda pecn geodetsk meenja (Te anayss and a-po accuacy assessment of pecse geodetc measuements), Nauna knjga, Beogad, 1973. BEGOVI, A.: Inženjeska geodeja 1 (Engneeng Geodesy), Nauna knjga, Beogad, 1990. MIHAILOVI, K., Geodeja II (Geodesy), II deo. Unvetet u Beogadu. Nauna knjga, Beogad, 1978.