Research Note MODELING OF VERTICAL MOVEMENTS OF BUILDINGS WITH MAT FOUNDATION * C. T. CELIK * *

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1 Iranan Journal of Scence & Technology, Transacton B, Engneerng, Vol. 32, No. B5, pp Prnted n The Islamc Republc of Iran, 28 Shraz Unversty Research Note MODELING OF VERTICAL MOVEMENTS OF BUILDINGS WITH MAT FOUNDATION * C. T. CELIK * * Dept. of Geodesy and Photogrammetry Engneerng, Ngde Unversty, Ngde, Turkey Emal:ctcelk@ngde.edu.tr Abstract A developed model was appled to dsplacement vectors acqured from a project that montored the vertcal movements of a buldng n the man campus of Ngde Unversty. The estmated subsdence and ts correspondng standard devaton errors by the model are mm ±.53 mm for block 1, mm ±.35 mm for block 2, and mm ±.54 mm for block 3, respectvely. The tlt angle s estmated and ts correspondng standard errors are ± 2.39, ± 1.95, and ± 4.64 arc second for Block 1, Block 2, and Block 3 respectvely over a perod of one year. Results showed that the model produced n ths paper can be used to estmate the vertcal movements of a buldng wth a Mat foundaton. Keywords Vertcal deformaton montorng, buldng settlement, modelng, least square adjustment 1. INTRODUCTION Deformaton montorng by geodetc surveyng methods s a powerful technque for both natural and manmade features. Partcularly, montorng deformatons of engneerng structures such as dams, brdges, plants, and buldngs where large human actvtes take place can be a crtcal ssue for the predcton of possble hazardous events. Montorng deformaton by geodetc methods conssts of four stages: specfcaton, desgn, mplementaton, and analyss [1]. In the specfcaton stage a number of ssues need to be posed concernng the magntude and confdence level of the movement, selecton of constant or varable accuracy for ponts, and requrements for drecton of the movement. In the second stage, four sub stages of the desgn are dstngushed [2]. Under the specfcatons made, an optmum confguraton of statons and a measurement plan are sought [3], [4]. Measurement technques are manly dvded nto two groups; geodetc and non-geodetc technques [5]. Geodetc measurements can be analyzed by varous methods. Two-epoch and mult-epoch analyss need to be dstngushed. One method of mult-epoch analyss s performed based on two-epoch analyss. It s carred out between the frst epoch and the current one [6]. Several researchers have developed analyss methods ncludng Bonn, Delft, Fredercton, Hafa-Tel Avv, Hanover, Karlsruhe, Munch I-II, Stuttgart, and Warsaw I approaches. A summary of these methods was gven by [7], [8]. Absolute or relatve networks can be chosen accordng to the feature of the movement under queston. In montorng natural features such as faults, a relatve movement s requred; n man-made structures such as dams, brdges, and buldngs, an absolute network s preferable to a relatve one. The Global Congruency Test [3] s appled to both networks to verfy f the absolute network has mantaned ts shape and to search for a reference network consstng of ponts that have a mnmum confguraton defect n relatve networks [1]. After determnng the reference ponts, a Receved by the edtors November 8, 26; Accepted January 8, 28. Correspondng author

2 544 C. T. Celk combned adjustment s requred to compare the estmated parameters. Ths s done by applyng one set of parameters for the reference ponts and two sets of parameters for the rest of the ponts n the network. From the result of the combned adjustment, a dsplacement vector whose sgnfcance s to be tested s obtaned. Sgnfcant movements are then formulated to ft a deformaton model. A number of models have been mposed on montored structures such as dams, brdges etc. Skal ny [9] studed to montor the foundaton of the Arkerejske Palaty buldng of the Suzdal Kremln. However, few studes have been done on modelng vertcal movements of buldngs wth Mat foundatons. The am of ths paper s to develop a model for the estmaton of vertcal movements of a buldng wth a Mat foundaton. A dsplacement vector from the project has been used n modelng and the results presented. Ths paper develops a model to estmate overall mode of deformaton, n addton to ndvdual pont deformaton gven by the dsplacement vector from the project below. 2. PROJECT: MONITORING VERTICAL MOVEMENTS OF BUILDINGS ON THE CAMPUS OF NIGDE UNIVERSITY The man am of ths project was to determne the vertcal movements of the buldngs on the campus. A reference network wth 5 statons was used to serve absolute reference ponts, nne ponts were set to the Presdental Buldng, and 17 ponts set to the Faculty of Arts and Scence Buldng as object ponts whose movements were to be montored (Fg. 1). N3 N4 N5 N2 R6 R7 R5 PB R8 R3 R4 R9 R1 FE1 Block 2 FE11 FE9 FE8 FE7 FE6 FE12 FASB FE13 Block 1 FE3 FE14 FE1 FE15 FE2 Block 3 FE17 FE5 FE4 FE16 N1 Fg. 1. Locaton of reference (N ) and object ponts (R, and FE ) nstalled n the campus Precse levelng was appled to perform measurements usng a Pentax AFL-32 level wth an SM5 parallel glass plate and 2m nvar staff. Two measurement campagns on 26 July, 23 and on 24 July, 24 were performed. 3. MODELING VERTICAL MOVEMENTS OF A BUILDING WITH MAT FOUNDATION A model to estmate the overall mode of deformaton of the body under queston has been developed n ths secton. A secton of a buldng at a gven tme t 1 can be assumed as a 2-D plane surface consderng ts basement. A 2-D plane surface was assumed snce the buldng was constructed wth a Mat foundaton. The secton may be tlted and subsdzed by some magntude due to settlement wthn the perod of two Iranan Journal of Scence & Technology, Volume 32, Number B5 October 28

3 Modelng of vertcal movement of buldng 545 epochs. To obtan the tlt angle α and the magntude of subsdence a, a model can be set up as follows (Fg. 2) d + v = a + S α C = σh + σh (1) d ' sn( ), d = h ' h, where h and h ' are the heghts of ponts and. S j s the dstance between and j. σ h and σ h ' are standard devatons of h and h '. The relatonshp between the angle α and the dsplacement dfference can be formulated from Fgs. 1a, 1b, 1c, and Eq. (1) can be lnearzed by Taylor s expanson. S assumed to be a constant, therefore, Eq. (1) can be rewrtten as d 2 2 ' j s Where v d = a + S sn( α ) + da + S cos( α) dα d ' ' (2) α = α + dα a = a, da + da, dx = dα b = a + 1 S cos( α ) 1 α = P = Cd (3) M M ' S' sn( ) d, A, vd = Adx b, The lnearzed form s now obtaned. The soluton to Eq. (3) s a well-known least square adjustment problem [1]. T 1 T T 1 ( A PA) A Pb, C = ( A ) dx = PA dx (4) z The plane assumed at tme t 1 x, y, z y, z j a j -α S j j x d S j *sn(α) ' (a) -α S j j α s the angle caused by vertcal movement y The plane at tme t 2 due to vertcal movement ' -α (b) y, z S j j j ' (c) Fg. 2. A model of vertcal movement of a buldng wth mat foundaton Ths model was set up for the data acqured from the project. The Faculty of Arts and Scence Buldng conssts of three blocks constructed at dfferent tmes. FE1, FE2, FE3, FE4, FE5, FE6, FE7, and FE13 ponts are from Block1, FE8, FE9, FE1, FE11, and FE12 ponts are from Block 2, and fnally FE14, FE15, FE16, and FE17 ponts are from Block 3 (Fg. 1). Dsplacement vectors for the three blocks, and dstances between ponts and j, were taken from the project as nputs to the gven model (Table 1). October 28 Iranan Journal of Scence & Technology, Volume 32, Number B5

4 546 C. T. Celk Table 1. Dsplacement vector dh and ts standard devaton error from the combned adjustment and dstances Blocks dh =h -h S dh to j S j (m) number 1 FE FE1-FE1. FE FE1-FE FE FE1-FE FE FE1-FE FE FE1-FE FE FE1-FE FE FE1-FE FE FE8-FE8. FE9-2.4 FE8-FE FE FE8-FE FE FE8-FE FE FE8-FE FE FE14. FE FE FE FE FE FE The outputs are the subsdence a and tlt angle α 4. RESULTS & CONCLUSIONS Dsplacement vector, ts assocated varance-covarance matrx from a combned-adjustment, and dstances between the base pont and another pont n each block were used n the model to estmate overall mode of deformaton (Table 1). Fgure 3 llustrates the vertcal movements estmated for the three blocks of the Faculty of Arts and Scence Buldng n the campus, and the estmated magntude of subsdence, tlt angles and ther correspondng standard devaton errors are tabulated n Table 2. Table 2. Estmated subsdence, tlt angle and correspondng standard devaton errors Block number Subsdance Standard error(subs) Estmated angle (Second of arc) Standard devaton error (Second of Arc) These estmated subsdence and tlt angles are based on the base pont FE1, FE8, and FE14 for Block 1, Block 2, and Block 3 respectvely. A postve tlt angle represents antclockwse rotaton from a horzontal level (from the assumed 2-D plane) and a negatve one represents the clockwse rotaton of the plane. The tlt angle arc second for Block 1 s postve due to the base pont. From Fg. 3, t seems that all the estmated tlt angles are consstent wth one another. A comparson of dsplacements between the model-based subsdence and tlt angles and those from the combned-adjustment were tabulated n Table 3. For Block 1, Block 2 and Block 3, the model can precsely represent the overall mode of deformaton wth standard devaton errors ±.3 and ±.6 mm respectvely. Iranan Journal of Scence & Technology, Volume 32, Number B5 October 28

5 Modelng of vertcal movement of buldng 547 Block2 FE8 FE14 FE1 Block1 Block3 26 July July 24 Subsdence (1 mm) Tlt angles are1 tmes exaggerated, and subsdence scale s 1:1. Fg. 3. Vertcal movements of the faculty of arts and scence buldng Table 3. Model errors Block Number Pont ID d(m) from model d(m) from dsplacement Error FE FE FE FE FE FE FE FE FE FE FE FE FE FE FE FE Standard devaton error of the model For Block 1, ±2.2 mm standard devaton error may suggest that Mat foundaton of Block 1 was not movng rgdly. The Block 1 buldng s the oldest among others constructed n Snce then t has been settlng. Lttle or no movement was antcpated for Block 1. However, mm subsdence ndcates that the settlement s stll n progress. The Block 2 constructon s relatvely new n comparson wth Block 1 and old n comparson wth Block 3. Therefore, t s expected that a larger magntude of subsdence occurs to Block 3. It s demonstrated that the model produced n ths paper can accurately reflect vertcal movements of a buldng wth Mat foundaton only, and so ths model may be used for buldngs wth MAT foundaton. Acknowledgments- The author would lke to thank the Research Fund of Ngde Unversty for fundng the FEB -21/28 numbered project. October 28 Iranan Journal of Scence & Technology, Volume 32, Number B5

6 548 C. T. Celk REFERENCES 1. Dodson, A. H. (1993). Analyss of control networks and ther applcaton to deformaton montorng. In: Kenne TJM, Perte G (Eds.) Engneerng Surveyng Technology. Unversty of Glasgow, London, pp Graferend, E. W. (1974). Optmzaton of geodetc networks. Internatonal Symposum on Problems Related to the Redefnton of North Amercan Geodetc Networks. The Unversty of New Brunswck, Canada. 3. Kuang, S. L. (1991). Optmzaton and desgn of montorng shames. Ph.D. dssertaton. Department of Surveyng Engneerng, Techncal Report No. 157, Unversty of New Brunswck, Canada. 4. Kaplan, M. O., Ayan, T. & Erol, S. (24). The effects of geodetc confguraton of the network n deformaton analyss. FIG workng Week, May 22-27, Athens, Greece. 5. Erol, S., Erol, B. & Ayan, T. (24). A general revew of deformaton montorng technques and a case study: analysng deformatons usng GPS/levellng. XXth ISPRS Congress, Istanbul. 6. Caspary, W. F. (1987). Concept of network and deformaton analyss. Monograph11, School of Surveyng, The Unversty of New South Wales, Kesngton, Australa. 7. Heck, B., Kok, J. J., Welh, W. M., Baumer, R., Chrazanowsky, A., Chen, Y. Q. & Secord, J. (1983). Report of the FIG-workng group on the analyss of deformaton measurements by geodetc methods. Budapest. 8. Chen, Young-q (1983). Analyss of deformaton surveys ---a generalsed method. TR. 94 UNB, Canada. 9. Skal ny, V. S., Kosygn, E. V. & Sorochan, E. A. (22). The montorng of deformaton process of the foundatons of the buldng Arkerejske Palaty of the Suzdal Kremln. Fundamenty Mekhanka Gruntov, No. 2, pp Cross, P. A., (1994). Advanced least squares appled to poston fxng. Workng Papers No. 4, Unversty of East London, London. Iranan Journal of Scence & Technology, Volume 32, Number B5 October 28