THE CONCEPTION OF MONITORING THE SUPERFICIAL DEFORMATION LOCATED ON THE UNSTABLE FOUNDATION WITH THE USAGE OF GPS TECHNOLOGY

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1 HE CONCEPION OF MONIORING HE SUPERFICIL DEFORMION LOCED ON HE UNSBLE FOUNDION WIH HE USGE OF GPS ECHNOLOG Waldemar Kamń Inttute of Geode Facult of Geode and Land ManagementUnert of Warma and Maur n Oltn Poland btract: In th paper a new method for montorng urface deformaton preented. heoretcal conderaton are upplemented an eample of practcal applcaton.. Introducton he deformaton meaurement ncludng the earth urface deformaton preent problem n the modern engneerng geode. he montorng of deformaton located on the untable foundaton and agned n untable reference tem epecall mportant problem. he untable foundaton defned a urface that can be nfluenced b moement together wth the engneerng obect located on t. he problem of deformaton agnng tll preent becaue a lot of buldng netment are tuated at ct centre net to etng buldng. he earth wor amng at creaton of for eample underground mult-tore car par can caue the moement of area urroundng the buldng area ncludng the local reference tem and at the ame tme can nfluence on the etng buldng caung the tran and mutual dplacement. he author of one paper Wśnew 989 propoed a concept of determnng the parameter of poton and hape of foundaton plate. In th paper the concepton of montorng earth urface deformaton located on the untable foundaton wth uage of GPS technolog preented more nformaton n paper Kamń 8. he formula olng the problem ncludng the aurac anal defned b the coarance matr are preented. he emprcal tet were made. he nterpretaton of nteretng reult comng from the tet encourage to conduct further and more detaled theoretcal and emprcal anale.. he Concept Deelopment Let u aume that a frequentl the cae n engneerng practce the reference urface plane Ω whoe fragment n an local co-ordnate tem hown n Fg..

2 Θ S Ω Ω Fgure Let u further aume that after conductng an ntal meaurement at tme moment t 3 we obtaned a urface Θ whoe repreentaton plane Ω. he plane Ω defned n an ntantaneou reference tem. Performng control meaurement at tme moment t t t 3 we get repectel urface Θ and plane Ω 3. In fgure denote the dtance between an rregular urface Θ reultng e.g. from uneen eleaton ettlement of pont and the optmum plane Ω at an pont 3 - the moment of meaurement. Dtance determned b the leat quare method can be treated a the length of ector [ ] - component of the ector whch perpendcular to plane Ω and whch determne ntantaneou poton of the plane n an untable reference tem. In order to carr out further pecalt anale the coordnate of a pont determned n the meaurement.e. n the tem hould then b recalculated to the reference tem. he coordnate can be recalculated wth the ue of a 6-parameter tranformaton wth the followng parameter: - [ ] tranlaton ector of the centre of the reference tem - R [ ] ector of the angle of rotaton around the a of the reference tem. he 6-parameter tranformaton uuall carred out aordng to the followng prncple:

3 3 R Χ. he relatonhp [ ] denote a ector of coordnate of the -th pont n an untable ntantaneou reference tem of the -th current meaurement. Formula. eld the followng equaton for an nddual pont:. Ung GPS technolog n the geodetc meaurement whoe am to determne urface deformaton equaton of correcton between pont and can be hown n the followng form ob ob ob.3 Carrng out the tranformaton for a par of pont the relatonhp. hould be nerted nto the relatonhp.3. Hence ob ob ob..4 It hould be ponted out that uch ubttuton reult n the dappearance of the tranlaton ector of the centre of the ntantaneou tem [ ]. Wth the reult of

4 meaurement made n arou epoch on untable ground one cannot determne a ector of tranlaton between untable reference tem whch determne the optmum plane. Let u conder the dfference n coordnate een n the penultmate column of relatonhp.4 determned for an par of pont a. It appear from the theoretcal aumpton adopted earler that relatonhp whch and denote the alttude of pont determne multaneoul dtance of the ntantaneou urface wrte that and. Θ from the ntantaneou optmum plane n and Ω. We can alo meaurement are carred out at arou moment n tme the followng dfference hould be condered further.5 where [ ] and ]. [. he dfference hown n the relatonhp.5 can be treated a dplacement repreented onl b angle of rotaton and tran of the obect. umng that angle of rotaton n partcular meaurement epoch wll hae low alue the followng can be wrtten.6 and repectel for coordnate dfference.7 Hence equaton.8 can alo be wrtten n the followng form 4

5 5 ob ob ob or n the matr notaton l.9 n whch: - ector of correcton nown matrce of coeffcent [ ] ob ob ob l - ector of free term and - etmated alue. Becaue there are no reference pont n the method free adutment hould be emploed n the oluton of the problem. 3. dutment of the Oberaton Reult he unnown can be determned b the leat quare method. he adutment problem ha the followng form l P mn ϕ 3. where P a matr of weght of the meaurement reult. Seeng the mnmum of the obecte functon P ϕ wth reference to unnown and eld the followng relatonhp ϕ ϕ 3. Hence Pl Pl 3.3 Soluton the relatonhp 3.3 a ector of unnown ] [ wth the followng form

6 Pl 3.4 Pl where notaton [ ] denote g nere of the matr. Determnaton of the coarance matr of aduted parameter for D P reult n P C DC D l C m l P C where the matr of cofactor m 3.5 Q ha the followng form Q 3.6 m P / f f n-rd the number of degree of freedom; n number of oberaton r number of unnown d networ defect. 4. n Eample of Practcal pplcaton he followng eperment wa conducted n order to erf the propoed method of adutment. From the meaurement of a III cla net conducted b GPS technolog at Łoman. Repeca. Walewet al. 995 a fragment Fg. ha been elected and ued for thorough practcal tetng of the propoed method of determnaton of dplacement and tran of terran. 6

7 Fgure he followng ector are the ought parameter [ S S S S S S S ] S S and [ ]. he component of ector hown n Fg. hae been treated a the ntal meaurement and aduted b the method propoed n th paper. Subequentl mulatng the moement of the urface under tud b the alue preented n able the data were tranformed wth the ue of the relatonhp.. h produced four arant of the networ Varant number Parameter of tranformaton [m] [m] [m] I II III IV able Followng the tranformaton of coordnate for each of the analed arant the ector component were calculated producng the current meaurement reult. 7

8 able and 3 how the reult of adutment obtaned n the calculaton. able how the angle of rotaton and ther mean error a well a the dfference between the reult produced n partcular arant and the prmar reult. Etmaton reult Varant number m m Ẑ m W P W P W P Intal meaurement I II III IV P ntal meaurement W dcued arant able n anal of the alue hown n able reeal that arant I II and III whch repreent the current meaurement the dfference n the angle of rotaton aume the alue wthn the nteral < >. herefore the concluon can be drawn that the net pont dd not retan tablt n the aumed reference tem and were dplaced. In arant IV onl the dfference allow for upcon regardng the dplacement of the net pont. In able 3 are howng component of the ector tran dfference between coordnate. 8

9 Varant W P 3 Stran 3 3 W P I II III IV able 3 he reult of adutment hown n able 3 how that urface tran ourred n arant I II III wherea the reult of calculaton preented n arant IV do not ndcate the poblt of an tran. he data hown n the table allow for certan generalaton concernng the analed eample. he reult hown n arant I II and III ndcate that a dplacement of the net pont and tran of the urface under tud hae ourred. he reult obtaned n arant IV ndcate that onl dplacement hae ourred n the tud area. 5. Concluon he eample preented aboe doe not prode ground for general concluon. he reult obtaned from calculaton wth the ue of the propoed method are an encouragement to conduct further more detaled theoretcal and emprcal tude. Reference. Kamń W. 8 Bollettno d Geodea e Scence ffn N.. Repeca. Walew. nn 995 III cla net Łoman obect. 3. Wśnew. 989 he dea of determnaton of parameter of locaton and hape of fundamental plate on the ba of free leelng. Materal from VI Scentfc-echncal Seon Current centfc and techncal problem of geodetc wor. Gdań Sobeewo 6-7 October In Polh Correpondng author contact Waldemar Kamń waldemar.amn@uwm.edu.pl Inttute of Geode Unert of Warma and Maur n Oltn Poland 9