INVESTIGATION OF ERROR SOURCES MEASURING DEFORMATIONS OF ENGINEERING STRUCTURES BY GEODETIC METHODS Vladislovas Česlovas Aksaitauskas 1, Doatas Rekus, Alojyz Wasilewski 3 1, Deartet of Geodesy ad Cadastre, Faculty of Eviroetal Egieerig, Vilius Gediias Tecical Uiversity, Sauletekio al. 11, LT-13 Vilius, Lituaia E-ail: 1 Ceslovas.Aksaitauskas@vgtu.lt, gkk@vgtu.lt 3 Istitute of Geodesy, Uiversity of Waria ad Mazury i Olszty, Oczaowskiego 1, 1-957 Olszty-Kortowo, E-ail: 3 alekw@uw.edu.l Abstract. Moder costructio is caracterized by large-size objects, te colexity of egieerig structures ad a ig recisio of te joits ad kots of te costructio eleets. Due to te above caracteristics ad a extreely icreased ecaizatio degree, costructio tecology ad ature of te costructio egieerig equiet as caged, wile dead for ig accuracy icreased. I order to carry out te easureets as accurately as ossible, digital surveyig devices are used. Te ai art of te geodetic work i costructios is levelig. Usig digital levelig istruets for te recise levelig, te etodology of easureets cages due to te occurrece of te secific sources of error tat affect te structural egieerig easureets ad observatios of deforatios of egieerig structures. For tis urose, it is ecessary to erfor digital recisio ivestigatios of digital levels ad coded staffs of secific odels; recisio of digital levelig; ad tecical, geoetric ad etrological araeters of istruets. Keywords: coded staff, digital levelig, levelig error. Itroductio Digital levels easure ad save te eigt ad te distace to te staff at te ress of a butto, ad calculate te Costructio work starts ad fiises wit geodetic eigt of te oit. Te advatages iclude o readigs easureets, terefore geodetic easureets ad required, o coyig or writig dow ad o calculatio labelig are te ost iortat cooets of outig by ad. ad istallatio work i costructios ad deforatio Tis work cotais ivestigatios of levelig errors observatios. Moder costructios are distiguised by of digital level Wild NA33. Cages i levelig etodology ad sources of secific errors occur usig digital te size of costructio objects, colexity of egieerig structures ad ig recisio of coectors ad odes levels for recise levelig. of structural eleets. Tese eculiarities ad igly Tese cages ca affect costructio-egieerig icreased ecaizatio level caused cages i costructio tecology ad caracter of egieerig equi- odel of levels ad coded staffs ad digital levelig are easureets. Precisio ivestigatios of a articular et of costructio objects. Dead for recisio as ecessary. Digital ivestigatios of tecical, geoetrical greatly icreased. To reac a ig recisio of easureets, digital geodetic istruets are used. Large art eeded. ad etodological araeters of istruets are also of geodetic work i costructios is coosed of levelig. autoatic levels ad iact of teir accuracy o defor- Te scoe of tis work icludes resortig to digital Te digital levels rereseted a breaktroug i levellig teciques usig te iovative cocet of readig atio ad costructio easureets. a bar coded staff. Otical readigs are ot loger eeded. Readig syste recisio of te digital levels Exeriece sows tat wit digital levels tere is u to a 5% tie savig we coared wit covetioal Digital levels NA33 ca be used for a referred levels. Te ai reasos are te faster data cature as uber (1 to 99) of coded staff readigs (Aksaitauskas well as te sorter tie ad safer eas of data rocessig, taks to savig easured data o storage devices. readigs. It is ukow wat uber of readigs is oti- at al. 7). Te fial staff readig is based o tese 171
al ad ow a readig recisio is cagig deedig o te uber of readigs (Krikstaois 1, Aksaitauskas at al. 7). Readig syste recisio of te digital level NA33 No. 946 was ivestigated usig a 47 log base fixed by teoral etal stakes. Readigs were erfored ito two staffs set at distaces of 14 ad 33. Air teerature i te sade was easured by a teroeter. Usig a easureet rogra MEASURE ONLY, te easureets ito te closer ad furter stadig staffs were ade. Eac cycle cotaied differet uber of readigs,, wic was altered fro to 9. Te easureet data was autoatically corrected for te Eart curvature error. O te followig day, te secod cycles of easureets were calculated. Suarized recisio idexes of te exerietal easureets are rovided i Tables 1 ad ad Figs 1,, 3 ad 4. Te readig recisio deeds o te distace to a staff. recisio results were calculated usig te followig weigts (Krikstaois 1): i i. (1) Assue tat is equal to.1. Te corresodig weigts are: 3 1, σ i σi ai 3 1, ai ai Accordig to te weigt average forula: σi 3 1. () σi σ i ~ a i σ, i a ai a, ai a (3) a i ai a i Table. Suarized recisio idexes of te exerietal easureets (secod day) d 14. d 33. Precisio, σ a a σ a a.3..31.3.44.3 3.3.18.18.5.43.6 4.38..45.6.34.68 5..14.3.3.36.68 6..16.4.3.8.6 7.3.1.33.5.16.41 8..1.35.6.16.41 9.1.13.4.1.16.4 ~ σ.1,1,8,6,4, a. a.3 ~ σ.3 a.94 a.17 3 4 5 6 7 8 9 (d14 ) (d14 ) (d33 ) (d33 ) Table 1. Suarized recisio idexes of te exerietal easureets (first day) σ d 14. a d 33. a σ a a.3..31.3.48.67 3.1.18.18.7.44.77 4.5.4.84.6.34.7 5..14.3.4.36.81 6..16.4.3.8.69 7.3.1.33.1.16.41 8..1.35..16.45 9.1.14.43.1.16.47 ~ σ. a.8 a.37 ~ σ. 4 a.96 a.11 Precisio, Fig 1. Graical exressio of suarized recisio idexes of te exerietal easureets (first day),6,5,4,3,,1 3 4 5 6 7 8 9 (d14 ) (d33 ) Fig. Graical exressio of suarized recisio idexes of te exerietal easureets (first day) 17
Precisio,8,7,6,5,4,3,,1 3 4 5 6 7 8 9 Ivestigatio of te icolete tilt coesatio of te digital level Icolete coesatio of a level was exaied levelig te sae statio wit lyig ad agled levels. For tis urose te level was laced strictly i te iddle betwee te staffs tat were fixed o built oles, ad te eigt differece was easured at te followig bubble ositio of te serical level (Fig 5) (Krikstaois 1). d14 d33 d33 d 33 Fig 3. Graical exressio of suarized recisio idexes of te exerietal easureets (secod day) Precisio,5,4,3,,1 3 4 5 6 7 8 9 d14 d33 Fig 4. Graical exressio of suarized recisio idexes of te exerietal easureets (secod day) Results of a researc based o a siilar etodology are ublised by Krikstaois (Kriskaois 1). Oeratio efficiecy deeded o te work duratio i a levelig statio, wic, i tur, deeded o te selectio of otial uber of readigs i a coded staff. No direct deedecy betwee te uber of readigs ad readig recisio was observed. Te readig recisio deeded o te distace to a staff. A correlatio betwee a stadard deviatio of te readig average obtaied by te digital level Wild NA33 ad te uber of readigs was week. Based o tat, it was suggested tat readig uber exceedig five is uecessary. Based o our two days researc (Figs 1-4), te best recisio results are obtaied we 7. We > 7, a iroveet of te recisio results is isigificat. Terefore, te uber of readigs of sould ot be less te 7, altoug tis would decrease te levelig efficiecy (Becker 1994, 1999). a b c d e Fig 5. Positios of te serical level bubble wile testig a level coesator: a bubble i te iddle of te aoule, b ad c at te logitudial icliatio, d ad e at te trasverse icliatio. Te of te averages of eigt differeces for te level used i te first class levelig sould ot exceed.5 or.5 er level tilt iute (Krikštaois 1). Icolete coesatio of te level tilt was ivestigated we te distace betwee te staffs was 3.95 ad 15.63. A readig obtaied by digital levels is a average of several (i tis case 5) readigs. I tis ivestigatio, four easureet sectios were ade i total wile cagig te level eigt wit eac sectio. Te results of te easureets are give i Table. Te averages of te eigt differeces ad te differeces of tese averages fro te average of te eigt differece obtaied at te bubble ositio i te iddle of te level aoules were calculated [3]. Table 3. Ivestigatio of te icolete tilt coesatio of te digital level. Sectio No. Heigt differeces bubble i te iddle at te logitudial icliatio at te trasverse icliatio of te aoule 5 +5 5 +5 1 3 4 5 6 Level NA33 No. 946 s 3.95 1 1.51178 1.5111 1.5177 1.5185 1.5189 1.51176 1.5113 1.5181 1.5183 1.5197 3 1.51179 1.5111 1.518 1.5186 1.51388 4 1.51179 1.511 1.5184 1.5177 1.5189 5 1.51178 1.511 1.5175 1.5184 1.513 173
Cotiued Table 3 1 3 4 5 6 1.51178 1.5111 1.5179 1.5183 1.5193 () +.33 +.1 +.5 +.15 s 3.95 1 1.646 1.64 1.648 1.644 1.643 1.648 1.641 1.644 1.64 1.638 3 1.646 1.646 1.646 1.637 1.64 4 1.645 1.648 1.646 1.641 1.645 5 1.643 1.643 1.643 1.638 1.64 1.645 1.644 1.645 1.64 1.64 ().1..5.3 Level NA33 No. 943 s 3.95 1 1.51183 1.5177 1.5185 1.5186 1.5175 1.5118 1.5188 1.5198 1.519 1.5191 3 1.51179 1.519 1.5193 1.5189 1.5184 4 1.51183 1.5177 1.5131 1.5184 1.519 5 1.5119 1.518 1.518 1.5183 1.5186 1.51183 1.518 1.519 1.5186 1.5186 ().1 +.9 +.3 +.3 s 3.95 1 1.646 1.634 1.646 1.64 1.637 1.646 1.64 1.64 1.643 1.64 3 1.636 1.645 1.643 1.643 1.641 4 1.643 1.635 1.646 1.64 1.638 5 1.641 1.636 1.645 1.64 1.635 1.64 1.638 1.644 1.64 1.638 ().4.. +.4 It was foud tat tese digital levels eet te requireets for te first-class istruets. Te obtaied (i Table 3) of te averages of eigt differeces did ot exceed.5 or.5 er level tilt iute. Deteriatio of te average square error of te digital level NA33 Te average square error of te levelig usig serical level was deteried by te level exaier ЭУ No. 145. A scale value of te easurig disk of te exaier was µ 1. Serical levels of te levelig istruet were cecked before te study. At te begiig of te easureets, te level was laced o te exaier wile targetig te telescoe alog te bar. Te bubble of te serical level was cetered ad te easureet disk readig l was oted. A easureet screw was tured util te level iclied by -3. Usig te sae screw te level bubble was retured to te ceter of te aoule ad te disc readig was oted agai. Oe easureet sectio was coosed of 1 bubble ceterigs ad te sae aout of readigs. Four sectios were ileeted, eac tie rotatig te level telescoe by 9. Readig averages of eac sectio l vid ad readig deviatios ν were calculated. Mea square error of te levelig was calculated accordig te followig equatio (Krikštaois 1): k v 1 (4), k ( 1 ) ere k te uber of sectios; te uber of readigs i te sectio; ad l ax idicate te quality of te serical level of te levelig istruet. Te results of tis ivestigatio are reseted i Table 4. Te ea square error ad te value l ax for te levels used i te first-class levelig work sould ot exceed 3 (Krikštaois ). Te obtaied results were as follows: Level NA33 No. 946 v k( 1 ) 81 4 (1 1) 8.8, (5) l ax l ave l 3ave 4.6.3.1 (6) Level NA33 No. 943 v k( 1 ) 1918 ( 4 (1 1) 7.3, (7) l ax l 3ave l ave 36.3 11.9 4.4. (8) Te erfored ivestigatio as revealed quite ig l ax values, but tey all were witi te erissible liit, i.e. below 3". By tis, te levels are i accordace wit te requireets raised for te first-class levelig. Deteriatio of te colliatio error of te digital levels A digital level autoatically coesates for te colliatio error digitally erforig readigs i coded staffs, if suc error is defied ad saved i te eory of te istruet. Tey ave te absolute colliatio error abscoll ad te variable error colldif, wic deeds o eteorological coditios. Iitial value of te abscoll set by a aufacturer is equal to zero secods. Te colliatio error of tese levels ca be adjusted usig aiteace rogra CHECK&ADJUST. By settig u tis rogra, readigs are autoatically coesated for te Eart curvature errors. Ceckig is ade by reeatig te levelig of a 45 5 legt site lie AB, wic is fixed by etal oles. Te lie is divided ito tree equal sectios. Te lie cotais oits 1 ad, wic are locatios of te levelig statios (Krikstaois, ). 174
Table 4. Exale of te calculatio of te levelig ea square error usig te level NA33 No. 946 Exaier ЭУ Nr.145 µ 1" cotaiig a serical level Sectios 1 3 4 l 1 v 1 v 1 l v v L 3 v 3 v 3 l 4 v 4 v 4 1-5 65-4 - 4 5-4 576 36 1 1 4 4 5 5 5 33 4 16 4 5 5 36-4 16 18 4 9 46 11 11 39-1 1 5-4 16 35 43 3 9 19-1 1 3 4 16 4 7 49 45 5 5 9 9 81 37 8 64 38 3 9 4 4 4 16 3 3 9 4 5 5 46 6 36 6 6 36 34 5 5 9-6 36 48 8 64 4 8-1 1 37 4 45 5 5 35 6 36 l 1vid v 1 v 1 l vid v v l 3vid v 3 v 3 l 4 vid v 4 v 4 35.3 +3 895 4.4 +4 58.3 +7 567 8.8 +1 759 I te statio 1, readig a 1 ad distace d 1 are set to te closer-stadig staff. Te, readig a ad distace d are set to te furter-stadig staff. Measureet sequece i te statio is as follows: b, d 3 ad a, d 4. If abscoll ad durig te ceckig colldif cost, te two eigt differeces ca be calculated: AB ( a1 b1 ) tgcolldif, ( d1 d ) (9) AB ( b a ) tgcolldif, ( d 3 d 4 ) (1) Startig te ceckig, i.e. uttig ito te rogra CHECK&ADJUST, abscoll value fro te eory of te level ca be see i te istruet dislay. After erforig easureets i bot statios, te variable colliatio error colldif ad te ew absolute colliatio error abscoll are calculated. Bot values, i secods, are sow i te dislay. Te ew absolute colliatio error is equal to te su of te old ad te ewly deteried variable colliatio error. Te absolute colliatio error abscoll, takig ito accout colldif value, ca be set to a ew value or left as te old value. If te abscoll value is too large (> ), it ca be reduced or reoved by adjustig te ositio of te iddle orizotal reticle. After cofirig te adjustet of te reticle ositio, te level calculates te correct readig a. Visual readig to te staff wit cetietric stes laced i oit A is ade witout ovig te level stadig i te oit. If te istruet is well adjusted, te calculated ad te visually set readigs are idetical. If te differece betwee te readigs is larger ta 3 for te 3 distace (colldif ), orizotal reticle sould be adjusted. After te adjustet of te orizotal reticle, te colliatio error is ceck agai. Durig te oral easureet coditios, stadard deviatio of te error is about ± (Aksaitauskas et al. 7). Ivestigatios of colldif daily variatios of te digital levels NA33 No.946 ad No.943 were erfored at Vilius Gediias Tecical Uiversity. Two 175 istruets, reviously used by Istitute of Geodesy for te levelig of te geodesic vertical grid, were used for tese ivestigatios. Te etodology develoed by Krikštaois was alied. A base AB of 45 was selected. Te ed oits of te base were fixed usig etal stakes were coded staffs were fixedly (usig suorts) istalled. Te base was te divided ito tree equal sectios. Bot levels were laced at oits 1 ad. Measureets were erfored every alf a our. Te easureet cycles were ade cagig laceet of te level witout ovig te triod. Air teerature, easured i te sade by a teroeter H-, varied u to 4 ºC. I order to acieve as uifor easureet coditios ad objective results as ossible, te easureets usig bot levels were erfored sequetially at te sae cosistecy. Te easureets of oe cycle by eac level lasted about 5 iutes. Te largest teerature variatio durig oe cycle did ot exceed.5 ºC. Fig 6. Teerature variatios durig colldif easureets by te level NA33 No.943
Fig 7. Teerature variatios durig colldif easureets by te level NA33 No.946 3. Te erfored ivestigatio as revealed quite ig l ax values, but tey did ot exceed te erissible liit, i.e. 3". Cosequetly, te levels eet te requireets raised for te first-class levelig. 4. Te variability rofile of colldif for bot istruets, i.e. NA33 No.943 ad NA33 No.946, was siilar, altoug te agle values differed u to 6. A sligt iact fro air teerature for colldif variatios was also observed. 5. Te colldif values cage; terefore, if te surroudig air teerature cages, a ew absolute colliatio error abscoll sould be set ad saved i te eory of te istruet. I order to reduce te iact of te colliatio error for te easureet results, te error values sould be set at teerature closest to a average air teerature at wic te furter easureets will be ade. 6. Durig te easureets i a statio we all distaces to te staffs are absolutely equal ad colldif value is stable, colldif does ot ave ay iact o te easured eigt differece. Refereces Fig 8. colldif variatio durig a day Coclusios 1. Te erfored ivestigatio of te readig syste recisio of te levels NA33 sows tat te readig recisio deeds o te distace betwee te istruet ad te staff. Tis ivestigatio sows tat te ost recise idicators are obtaied we 7. We > 7, te a iroveet of te recisio results is isigificat. Terefore, te uber of readigs of sould ot be less te 7, altoug tis would decrease te levelig efficiecy.. Studyig te icolete tilt coesatio of te digital levels NA33 it was foud tat tese digital levels eet te requireets for te first-class istruets. Te obtaied of te averages of eigt differeces did ot exceed.5 or.5 er level tilt iute. Aksaitauskas, A.; Rekus, D.; Wasilevsky, A. 7. Iact of digital level Wild NA33 error ivestigatios o costructio egieerig easureets, i 9 t Iteratioal oder buildig aterials, structures ad teciques. May 16 18, 7, Vilius, Lituaia. Vilius: Tecika, 111 1114. Becker, J. M.; Adersso, B.; Eriksso, P. O.; Nordquist, A. 1994. A ew geeratio of levellig istruets: NA ad NA3, i FIG XX. Iteratioal cogress, Melboure, Australia, 94 35. Becker, J. M. 1999. History ad evolutio of eigt deteriatio teciques esecially i Swede, i Geodesy Surveyig i te Future, Te Iortace of Heigts, Gävle, Swede, 43 57. Krikštaois, B.. Matavių aalogiiais ir skaiteiiais ivelyrais tiksluo tyriai [Measureets of aalogue ad digital recisio levels studies]. Geodezija ir kartografija 6(): 69 7. Krikštaois, B.. Skaiteiio ivelyro Wild NA33 atskaitos sisteos yatuų tyriai [Digital levels Wild NA33 caracteristics of te referece syste]. Geodezija ir kartografija 8(): 39 44. Krikštaois, B. 1. Geodeziių vertikalių tiklų sudaryo skaiteiiais ivelyrais aalizė [Geodetic vertical etwork akig wit digital levels aalysis]. Doctor disertatio. VILNIUS: Tecika, 1. 36. Zakarevičius, A. 1974. Niveliacijos tiklų išlygitų dydžių tiksluo įvertiio klausiai [Levelig etworks of sizes to couterbalace te accuracy of te evaluatio questios]. Geodezijos darbai 7: 38 48. 176