Graphical interpretation deformation analysis of stability area using of strain analysis

Transcription

1 Acta Montanstca Slovaca Ročník 9(04), číslo, 3-40 Graphcal nterpretaton deformaton analyss of stablty area usng of stran analyss Slavomír Labant, Gabrel Wess, Jozef Zuzk and Mchal Baran The spatal changes of water constructon objects are surveyed by geodetc methods wthn the techncal and safety supervson of water constructons. To better understand the behavour of the area of nterest beneath the upper reservor of the pumped storage hydro power plant (PSHPP) Černy Váh, a deformaton analyss of ths area was realzed. The stablty or nstablty of the geodetc network ponts and the adjacent area was verfed. The estmatons of determned parameters of geodetc network were obtaned on the bass of stage adjustment of GNSS observatons, by applyng the LSM method, robust M-estmaton accordng to Huber and robust M-estmaton accordng to Hampel. The analyss of ncurred dscrepances (dfferences) n the poston of ponts, whether they are the results of accumulaton of measurement and systematc errors or they represent a local deformaton of the area, was the last objectve of ths paper. The analyss of the results obtaned from processng was performed by the method of fnte elements n the form of stran analyss, to present the dynamcs of the area underneath the water reservor. The results obtaned by applyng estmaton methods correspond to ther graphcal analyss. The use of Huber's and Hampel's robust M-estmates s an alternatve to the applcaton of LSM method, whch has a versatle use n practce, n varous areas of professonal dscplnes. Key words: Deformaton analyss, LSM, Huber s robust M-estmate, Hampel s robust M-estmate, Stran analyss Introducton The Earth surfaces, but also objects on and underneath t, are affected by external as well as nternal forces that deform these objects. Nowadays, modern Global Navgaton Satellte Systems (GNSS) are ncreasngly beng used for deformaton montorng of the Earth's surface and objects on t. The advantages of GNSS observatons, manly a great relablty, ndependence of the season, tme of measurement or drect vsblty between ponts are wdely used, whle the term observaton n real tme s gettng more and more nto the foreground. In the real-tme montorng, the measurements n epochs domnate n regard of the prce and protecton of nstrumentaton. The stablty montorng of dynamcally loaded water constructons s elaborated n the Techncal and Safety Supervson approved by the Mnstry of Envronment of the Slovak Republc. Detals about the safety of water constructons are specfed n the Act No. 364/004 Coll. on waters, amendng Act No. 37/990 Coll. of the Slovak Natonal Councl on offences, as amended by later regulatons (Water Act) [3]. Adjustment methods Methods of adjustment are based on the mnmum condton of some norm of the vector of correctons. The norm s a number assgned to each n-dmensonal vector that characterzes ts sze. Objectve functons of followng types are the most commonly used n geodesy [], []: n p p ρ ( v ) = v = mn. () = The p parameter specfes a specal type of an objectve functon [3]: The method of the mnmum sum of absolute values of correctons wth the parameter p= (L-norm) s expressed by the objectve functon: n ρ ( v ) = v = mn. () = Assoc. prof. MSc. Slavomír Labant, PhD., prof. MSc. Gabrel Wess, PhD., MSc. Mchal Baran, PhD., Insttute of Geodesy, Cartography and GIS, F BERG, Techncal Unversty of Košce, Letná 9, Košce, Slovak Republc, slavomr.labant@tuke.sk, gabrel.wess@tuke.sk, mchal.baran@tuke.sk MSc. Jozef Zuzk, PhD., Insttute of Busness and Management, F BERG, Techncal Unversty of Košce, Letná 9, Košce, Slovak Republc, jozef.zuzk@tuke.sk 3

2 Slavomír Labant, Gabrel Wess, Jozef Zuzk and Mchal Baran: Graphcal nterpretaton deformaton analyss of stablty area usng of stran analyss Least Squares Method (LSM) wth the parameter p= (L-norm) s expressed by the objectve functon: n ρ( v ) = v = mn. = The MINIMAX method wth the parameter for tolerance ntervals) s expressed by the objectve functon: p = ( ) = n ρ v v = mn. (4) = Identfyng and locatng of mstakes and systematc errors weghtng some of measured varables that would be ether cleaned or excludedd from fles enterng the adjustment procedure s the objectve of relable processng of measured varables pror to ther evaluaton. The LSM provdes an unbased and the best estmate only for normal dstrbutonn of errors n the set of measured varables. If the measured varables are weghted by systematc errors and mstakes (yawng values), the LSM s stll effectvely usable. Ths method also has the feature that larger errors of varables tres to decompose nto smaller parts, thereby unacceptably dstortng estmates of adjustment procedure [5], [6], [9], []. Defects wth the LSM led statstcs to seek methods whch are more resstant (robust) usng remote measurement. Experments have shown that robust estmates gve better results than the LSM. The majorty of robust adjustments used n geodesy modfy the exstng LSM to make t robust. When usng the robust LSM, the weght of measurement changes n each teraton usng the weght functon. When usng the robust methodd for estmaton, the mnmsed functon v T v s replaced wth the so-callecharactersng the loss functon [5], [9]: ρ( v ) = mn, whch generates the nfluence functon ψ ( v ) nfluencee of errors upon adjusted values. For ths functon, the followng s vald: n ( v ) ψ ( v ) = 0, where ψ (vv ) = ρ. (5) = v In order that the adjustment wll have the nature of a robust estmate, t s sutable to carry t out usng the teraton method wth varable weghng,.e.. that the weght p of observaton lj was determned n each teraton step as a correctve functon: ψ ( v ) p( v ) =, where p ( v ) s the weght functon. (6) v Ths prncple of soluton s teratve soluton wth gradually changng weghts measured varables p so that when a suffcentt number of teraton cycles (steps) were convergence correctons n the last step. The most used estmates are Huber s robust M-estmate, Hampel s robust M-estmate, for more nformaton and functon of estmates see [4]. Observatons and processng of geodetc network (L - norm measurements are defned by Ponts of the geodetc network are located around the crest of upper reservor of the hydro power plant Černy Váh n the area of the Natonal Park Low Tatras. PSHPP s used manly for hydraulc energy storage n tmes of reduced electrc system load, therefore preventng a wasteful shuttng down of thermal (or nuclear) power plants or reducng ther performance to the operatonal mnmum. The ssue of effcent use of hydropower s currently n the process of sustanable development of each country often addressng queston [9]. In relaton wth the soluton of the ssue, tt should also take nto account the natural characterr of the flood rsks that may endanger the subject area [0]. Geographc approach to flood rsk assessment provdes an approprate tool to present the obtaned results [5]. GNSS technology, n contrast to terrestral technologes, s not dependent on the drect vsblty between ponts. Therefore, t s not necessary to make forest paths through bushy or forest stand Fg.. The structure of the geodetng network n areas of ncreased protecton of nature. Seven reference ponts are monumented by heavy monumentaton around the reservor, labelled numercally n the range (Fg. ) ). The observatons were realzed n epochs Aprl 004, July 008 and October 0 for the purpose of deformaton montorng of stablty or nstablty of observedd ponts of the geodetc network. The network was realzed by GNSS vectors wth the structure of geodetc network n the shape of heptagon n each epoch. (3) 3

3 Acta Montanstca Slovaca Ročník 9(04), číslo, 3-40 A Gauss Markov model (GMM) s the most commonly used method for adjustment of a general geodetc network, defned as follows [4], [7], [8], [0], []: v = AdCˆ dl = A( Cˆ C ) ( L L ), - functonal part, (7) Σ L = s0ql, - stochastc part, where: v s a vector of correctons of observed values, dl=l-l s a vector of auxlary observatons, dcˆ = Cˆ C s a vector of complements of adjusted values of determnng coordnates, A s a desgn matrx. The adjustment procedure conssts of the followng steps:. arrangement of the nput data,. defnton of model equatons, 3. auxlary calculatons, 4. creaton of a confguraton matrx, 5. calculaton of estmatons, 6. expresson of the accuracy of a geodetc network. Data of GPS and GNSS vectors that were measured and prmary processed by software were subsequently processed based on the Gauss-Markov estmaton model (GMM adjustment of ndrect measurements) as a GMM wth full rank. The pont 500 was selected as the reference pont of the geodetc network (monumented n the orgnal and most plan terran, GNSS recever remaned n the poston durng the whole measurement). Spatal orthogonal coordnates X, Y, Z and coordnate dfferences X j, Yj, Zj between ndvdual network ponts n ETRS89 were the result of processng. The observaton vector L consst of 3 x spatal vectors of observatons XYZj,.e. 3 x 33 of observaton components X j, Yj, Zj. The three-varant processng and adjustment of observatons and determned estmatons of adjusted coordnates was used for the processng of deformaton network observed n three epochs for functonal part of GMM ( τ = 04,08,) : ˆ 04 v A 0 dc dl ˆ 08 v= A dc dl, (8) 0 ˆ v A dc dl (99,) (99,54) (54,) Coordnate values of determned ponts of the network Ĉ are dependent on the used estmaton method of unknown parameters (LSM, robust M-estmaton accordng to Huber, robust M-estmaton accordng to Hampel). Estmates of adjusted coordnates Ĉ are presented n Tab.. Tab.. ETRS89 coordnates X, Y, Z from adjustment by the LSM method and robust M-estmaton accordng to Huber and Hampel LSM Huber Hampel Pont X ˆ ETRS89 Y ˆETRS89 Z ˆ ETRS 89 X ˆ ETRS89 Y ˆETRS89 Z ˆ ETRS 89 X ˆ ETRS89 Y ˆETRS89 Z ˆ ETRS 89 [m] [m] [m] [m] [m] [m] [m] [m] [m] (99,) 33

4 Slavomír Labant, Gabrel Wess, Jozef Zuzk and Mchal Baran: Graphcal nterpretaton deformaton analyss of stablty area usng of stran analyss Coordnate transformaton from ETRS89 to UTCN03 A global transformaton key s used for transformaton of ponts coordnates from the ETRS89 system nto the natonal mplementaton UTCN03 of the coordnate system UTCN, that apples to the whole terrtory of the SR and s defned by seven transformaton parameters determned by spatal smlarty transformaton by the Burša-Wolf s model [4]. Transformaton parameters for transton from the GRS 80 to the Bessel ellpsod 84 are [4]: translatons: T X = m, T Y = m, T Z = m, rotatons: R X = , scalng: m = 0.0 ppm. R Y = , R Z = , Cartesan spatal coordnates of ponts related to the Bessel ellpsod 84 from the GRS 80 ellpsod are obtaned by spatal smlarty transformaton by the Burša-Wolf s model (or Molodenskj-Badekas model). The transformaton of Cartesan coordnates X,Y,Z to ellpsodal coordnates φ, λ and h s the next step. Converson of coordnates φ, λ and h to orthogonal planar coordnates of conform conc projecton n a general poston s realzed by Křovák s unverse projecton. A dgtal reference elevaton model wth the alphabetcal DVRM code wth the step of 600 x 600 m s used for converson of ellpsodal heghts determned n the ETRS89 and defned above the GRS80 ellpsod to normal heghts defned n The Baltc Vertcal Datum after adjustment (Bpv). Ths dgtal model was created by fttng the gravmetrc quas-geod GMSQ03B to ponts of The Natonal Spatal Network wth the known levelled heght determned n The Natonal Levellng Network []. As an alternatve of long calculatons of coordnate transformatons from the ETRS89 to the natonal mplementaton UTCN03 [7], [8] a sutable software that allows such a transformaton can be used, for example Leca Geo Offce. In ths way, also adjusted coordnates of ponts of all three epochs determned by the LSM and robust estmatons accordng to Huber and Hampel were transformed (Tab. ). τ t 04 t 08 t t Tab.. UTCN03 coordnates X, Y, h from adjustment by the LSM method and accordng to Huber and Hampel. LSM Huber Hampel Pont X UTCN03 Y UTCN03 h Bpv X UTCN03 Y UTCN03 h Bpv X UTCN03 Y UTCN03 h Bpv [m] [m] [m] [m] [m] [m] [m] [m] [m] Subsequently, transformed coordnates n the natonal mplementaton UTCN03 from all three adjustments and three epochs of observatons were used for the next presentaton of postonal and vertcal changes of ndvdual network ponts. graphcal vsualsatons (Fg. ) of postonal and vertcal changes of ponts from epochs 08 t, t to the epoch 04 t for all three methods of adjustment of observatons were created. The overall dsplacements of ponts corresponded to changes of coordnates presented n the deformaton analyss, coordnates of whch were determned by the LSM method and robust M-estmaton accordng to Huber and Hampel. Dfference of dsplacements s caused by dependence of cofactors on the sze of weghts of ndvdual methods. The analyss of the results obtaned from processng was performed by the method of fnte elements n the form of stran analyss, to present the dynamcs of the area underneath the water reservor (Stran analyss can be appled only to the homogenous envronment). 34

5 Acta Montanstca Slovaca Ročník 9(04), číslo, 3-40 epochs 04 t - t epochs 08 t - t Fg.. Horzontal and vertcal dsplacements between epochs 04 t - t and 08 t - t by method of processng LSM, Huber and Hampel Deformaton stran analyss The stran analyss s used to descrbe deformatons n the vcnty of pont. The spatal deformaton of object wth ts small surroundng can be expressed by coordnates [7]: τ, τ + Cˆ τ +,, Cˆ τ Cˆ τ τ + τ + C ˆ τ τ + = = ε + T (9) where: τ =04,08,; τ, τ + T s the vector of translaton parameters of the pont expressng ts spatal change τ + τ over the perod t= t t n all coordnate drectons: τ, τ + T X τ, τ + τ, τ + T = TY (0) τ, τ + T h If dsplacements are very small n comparson wth the sze of object, results n the deformaton tensor ε represent the tensor of overall deformaton n the followng form [4], [7]: ε = τ, τ + τ, τ + X X Y X h X X Y Y Y h Y X h Y = h h h τ, τ + ε ε ε XX YX hx ε ε ε XY YY hy ε Xh ε Yh, ε hh τ, τ + where X, Y and h are 3 components of the dsplacement vector Ĉ. Due to the asymmetry of deformaton tensor ε, t s possble to decompose t nto the symmetrcal and asymmetrcal part accordng to the followng equaton: T T ε = ej + ωj =.( εj + εj ) +.( ε j εj ) () where the symmetrcal part of deformaton tensor ε s referred to as the stran tensor e j and asymmetrcal part of deformaton tensor ε represents the rotaton ω j. Tensor dagonal elements e are referred to as the tensle stran and characterze a dlataton n the approprate drecton. Off-dagonal elements are referred to as shear strans and characterze changes n angles between approprate nput lnes. Graphcal nterpretaton of elements of the stran tensor e j () on the example of cube (Fg. 3) wth edges of unform lengths that s plotted by thn lnes and ts deformed shape by thck lne wth desgnaton of relevant changes due to the deformaton. () 35

6 Slavomír Labant, Gabrel Wess, Jozef Zuzk and Mchal Baran: Graphcal nterpretaton deformaton analyss of stablty area usng of stran analyss The rotatonal component ω j can be splt nto two parts: the component dependent on the poston ω j and ndependent on the o poston ω j. The computatonal procedure of components of the stran tensor e j s a matter of smple transformaton for any drecton. Stran analysss of the DN ponts n the XY plane Deformaton stran analyss can be used not only for analyss of D (or 3D) physcal changes n the entre montored area, but also for ts ndvdual parts, whle results of these stran analyses are more trustworthy. The smaller parts of the area of trangular shape n the total number of 5 (Fg. 4) were created by sutable trples of ponts of the geodetc network around the crest of upper Fg. 3. Geometrcal nterpre reservor of the PSHPPP Černy Váh. The spatal dsplacement of the -th pont for the montored perod can be expressed by the followng equaton [4], [7]: X exx exy 0 ωxy XY = X Tx (,) = + Y eyx. e yy ωyx 0 + Y, Ty X where Y are the po ont coordnates n the. epoch of analyss and the vector of deformato on parameters: T θ = ( e xx exy eyy ωxy Tx Ty (,6) ) T (3) ncludes all remanng unknownn ponts from the equaton (3). Vector XY represents a dsplacement of pont and ts surroundngs n the drecton of coordnate axes: XY = F θ, (4) where F s the matrx of coeffcents contanng pont coordnates of the second epoch: X Y 0 Y 0 F =. (,6) 0 X Y 0 (5) X For ndvdual areas of trangular shape, t s possble to express deformaton parameters θ bndng Legend: locaton of the to three ponts. By mathematcal expresson of θ from trangular shape area, the equaton (5) and by addton of ther weghts Q, -I. V.- the number of trang Fg. 4. Parts of the area around the the followng relaton can be defned: θ = ( F T Q F ) T F XY. XY Q XY etaton of stran elements () centre of gravty of gular shaped area. e PSHPP Černy Váh (6) LSM Huber Hampel area part I. II. III. IV. V. I. II. III. IV. V. I. II. III. IV. V. Tab. 3. Deformaton parameters of the stran analyss 04/ and 08/. e xy e yy ω xy [µstran] [µstran] [ ] 04/ 08/ 04/ 08/ 04/ 08/ e xx [µstran] 04/ 08/ -7,9-5,90 7,36 4,873-5,533-6,67 4,307 4,9 3,355-3,355-3,560 6,36 9,746 8,96-4,86-3,770 9,57 8,004 6,60-6,577-3,560 7,533 9,746 6,005-4,86-3,770 8,7 5,54 6,643-3,3 T x T y [m] [m] 04/ 08/ 04/ 08/ -5,94-4,43 35,573 -,858-7,946 -,49 0,04 0,04-0,040 0,03 4,35 -,36-9,45-6,7,359,478-0,0-0,008 0,03 0,07-5,36 0,9 358,588 64,785 9,96 0,40-0,009-0,00 0,050 0,05 8,63-9,934-6,89-7,408-4,637 -,488-0,09-0,03-0,05 0,006 4,538-3,07 -, -9,060 0,977 -,7-0,007 0,007 0,005 0,000-6,35 0,795 3,003-4,79-7,9 3,755 0,035-0,06-0,033 0,06 3,576-8,0300 -,58-0,86,95,664-0,05-0,0 0,0 0,03-35,656 4,77 358,84 8,084,8,456-0,009-0,005 0,047 0,03 30,585-3,408-5, -4,7-4,505 -,49-0,07-0,06-0,054 0,009 6,35-3,6533-0,85-7,03,99 -,39-0,0 0,0 0,004-0,00-6,35 -,775 3,003-4,79-7,9 3,08 0,035-0,03-0,033 0,06 3,576-4,0 -,58-0,86,95,47-0,05-0,000 0,0 0,03-35,656 4,77 358,84 8,084,8,456-0,009-0,005 0,047 0,03 3,786-0,3833-5, -6,674-4,57 -,05-0,06-0,05-0,054 0,009 7,53 -,089-0,85-9,060,509 -,06-0,03 0,007 0,004 0,000 36

7 Acta Montanstca Slovaca Ročník 9(04), číslo, 3-40 The stran analyss for a par of epoch - and - was performed n the Matlab 7..0 software for pont coordnates determned by usng the LSM method and robust M-estmatons accordng to Huber and Hampel (Tab. 3). Graphcal nterpretaton of the stran analyss In addton to numercal nterpretatons of the result of stran analyss, t s also possble to nterpret them n a graphcal way, and therefore t s possble to obtan clear nformaton on deformatons that occurred wthn the montored localty [4], [3], [7]: dlataton (a proportonal planar deformaton of the area) expresses the proportonal change of the area between two examned epochs for the montored area: = e xx + e yy, (7) postve values represent expanson of the area part and negatve values represent compresson of the area part for the montored perod, whch can be graphcally dsplayed n the form of crcles wth a radus n the unt of µstran, proportonal shear deformaton γ : ( e e ) + (. e ), γ = (8) xx yy xy expresses proportonal changes of real angles for the montored perod. It can be graphcally nterpreted by usng solnes wth numercal data n µstran, the sze of horzontal dsplacements h can be dsplayed by solnes from values: h = T x + T y. (9) Character of deformatons of the montored area can be complemented by addtonal parameters [3]: the sze of the major, maxmum tensle deformaton (dlataton, expanson) e : e = 0,5.( + ) [µstran], (0) γ the sze of the major, mnmum tensle deformaton (compresson) e : e = 0,5.( ) [µstran], () γ the bearng of the axs of maxmum tensle deformaton e σ : e σ = 0,5. arctg(. e /( e e )) [ ], () e xy xx yy the bearng of the axs of shear deformaton σ γ : σ γ = σ e ± π / 4 [ ]. (3) Indvdual calculated parameters of the stran analyss for the parts of area of trangular shape determned from results adjusted by usng the above estmaton methods of unknown parameters are presented n Tab. 3. Tab. 3. Values of proportonal planar, proportonal shear deformaton and horzontal dsplacements. τ t LSM Huber Hampel γ h γ h γ h [µstran] [µstran] [mm] [µstran] [µstran] [mm] [µstran] [µstran] [mm] I. 7,66 6,48 57,30 8,443 56,04 48,04 8,443 56,04 48,04 II. -,34 37,554 8,3 -,837 33,0 9,03 -,837 33,0 9,03 III. 353, ,757 50, , ,755 47, , ,755 47,677 IV. -,583 70,58 55,09-5,706 75,784 60,080-6,95 77,07 59,804 V. -8,867 8,07 8,703-3,574 0,800 3,000-3,54,088 3,740 I. -7,047 9,587 9,43,957 30,557 37,037-6,747,507 9,48 II. -,850,054 8,9 -,90 5,5 5,65-4,858 8,764 5,37 III. 48,68 83,58 5,004 67,34 95,333 3,07 67,34 95,333 3,07 IV. 6,784 37,38 3,637 3,73 4,963 7,950 8,840 38,306 6,55 V. -,45 8,436 7,377-3,60 7,30,70 -,38 7,098 6,606 37

8 Slavomír Labant, L Gabrel Wess, W Jozef Zuzzk and Mchal Baran: B Graphcall nterpretaton deeformaton analysss of stablty areea usng of stran anaalyss he area Fg. 5. crcles dsplayed n orrange represeent compresson of the trangular shapeed part of th d frrom Tab. 3) and a red crcles expanson of the area (postve values of (negatvee values of dlataton dlatatonn from Tab. 3). Blue chaan-dotted crccles represent the sze of prroportonal shhear deformaton for the perod 04 t - t andd 08t - t relatted to the cenntre of gravty y of that areaa (Tab. 3 - γ).. The radus sze s of crcles s dependent onn the sze of prresented results n unts of µstan. µ 04 e epochs t - t epochs 08t - t Fg. 5. Proportonall planar and sheaar deformatons dsplayed d by crclee by method of prrocessng LSM, H Huber and Hampeel Tab.. 5 present the graphcal reepresentaton of translaton ns h by solnes wth the basc ntervall of 0 mm relateed to the centrre of gravty of o that area (T Tab. 3). Huber Hampel epochs 08t - t epochs 04t - t LSM H dsplaccements dsplayedd by solnes by method m of processsng LSM, Huber and Hampel Fg. 6. Horzontal 38

9 Acta Montanstca Slovaca Ročník 9(04), číslo, 3-40 Concluson The present artcle provdes an overall processng of the geodetc network and the deformaton analyss of the area around and underneath the upper reservor of the pumped storage hydro power plant (PSHPP) Černy Váh n the The analyss was realzed based on the stage adjustment of GNSS vectors, by applyng three selected methods of processng and adjustment of geodetc network wth the estmaton of unknown parameters. The LSM method, robust M-estmaton accordng to Huber and robust M-estmaton accordng to Humpel represented the selected methods of estmatons. In the present study, the estmatons of parameters of the st and nd order of network structures and ther statstcal assessment n the area of deformaton montorng were solved. For ths purpose, a local geodetc network of reference ponts was surveyed by usng GNSS technology n the localty of the pumped storage hydro power plant (PSHPP) Černy Váh. The measurements were realzed n three epochs (Aprl 004, July 008 and October 0) n a suffcent tme nterval. In the artcle was the examnaton of ncurred dfferences of adjusted coordnates of ponts n the deformaton network resultng from the use of dfferent methods for processng of measurements. However, dsplacement of the pont 5005 was demonstrated by all three methods. Other dfferences were dentfed as the result of the effect of systematc and measurement errors. A graphcal testng usng absolute and relatve confdence ellpsods that confrmed the results obtaned by processng was also realzed. The stran analyss of the geodetc network was also performed n the process of deformaton analyss, for the dentfcaton and transparent descrpton of spatal changes n the montored area underneath and around the water reservor, for the selected perod. The whole processng was performed n the Matlab 7..0 that was also used as the vsualsaton nstrument for the presentaton of estmatons of results obtaned from the geodetc network of the area. References [] Btterer, L.: Adjustment calculus (Vyrovnávací počet). ŽU Žlna, 006, 80 p., ISBN [] Böhm, J., Radouch, V., Hampacher, M.: Error theory and adjustment calculus (Teore chyb a vyrovnavací počet). nd edton, Praha: Geodetc and cartographc enterprse, 990, 46 p., ISBN [3] Böhm, J., Radouch, V.: Adjustment calculus (Vyrovnávací počet). Praha, Kartografe, 978, 50 p., ISBN [4] Caspary, W. F.: Concepts of network and deformaton analyss. st edton, Kensngthon: School of surveyng. The Unversty of New South Wales, 987, 87 p., ISBN [5] Gaňová, L., Zeleňáková, M., Purcz, P., Kuzevčová, Ž., Hlavatá, H.: A ranfall dstrbuton and ther nfluence on flood generaton n the eastern Slovaka. Acta Unverstats Agrculturae et Slvculturae Mendelanae Brunenss. 6, 03, 6, , ISSN Avalable at: [6] Gašncová S., Gašnec J., Staňková H., Černota P.: Comparson of LSM and alternatve estmaton methods of the processng results of geodetc measurements. SDMG 0: Proceedngs of the 8th conference: Praha, Ostrava, VŠB-TU, 0, 40-50, ISBN [7] Gašnec J., Gašncová S., Černota P., Staňková H.: Uses of Terrestral Laser Sannng n Mntorng of Ground Ice wthn Dobšnská Ice Cave. Journal of the Polsh Mneral Engneerng Socety, 30,, 0, 3-4, ISSN Avalable at: [8] Gašnec, J. Gašncová, S., Gergeľová, M.: Creaton of Spatal Model of Dobšnská Ice Cave and ts Connecton nto the Natonal Coordnate Reference System UTCN03. Geodetc and cartographc horzon. 58, 0, 9, 8-3, ISSN Avalable at: [9] Gergeľová, M., Kuzevčová, Ž., Kuzevč, Š.: A GIS based assessment of hydropower potental n Hornád basn. Acta Montanstca Slovaca. 8, 03,, 9-00, ISSN Avalable at: [0] Gergeľová, M., Kuzevčová, Ž., Kuzevč, Š., Sabolová, J.: Hydrodynamc modelng and GIS tools appled n urban areas. Acta Montanstca Slovaca. 8, 03, 4, 6-33, ISSN Avalable at: [] Jäger, R., Müller, T. Saler, H., Schwäble, R.: Klasssche und Robuste Ausglechungsverfahren. Wchmann, Hedelberg, 005, 340 p., ISBN

10 Slavomír Labant, Gabrel Wess, Jozef Zuzk and Mchal Baran: Graphcal nterpretaton deformaton analyss of stablty area usng of stran analyss [] Klobušak, M., Letmannová K., Feranc, D.: Implementaton of mandatory transformatons natonal reference coordnate and elevaton systems to ETRS89. [onlne, cted 0.3.0]. Avalable at: [3] Kolcun, Š., Sütt, J.: Deformaton analyss of the area around Jaslovské Bohunce. Acta Montanstca Slovaca. 5, 000,, 7-76, ISSN Avalable at: [4] Labant, S., Wess, G., Kukučka, P.: Robust adjustment of a geodetc network measured by satellte technology n the Dargovských Hrdnov suburb. Acta Montanstca Slovaca. 6, 0, 3, 9-37, ISSN Avalable at: [5] Mxtaj, L., Wess, E., Wess, R., Kukučka, P.: Impact of acquston on fnancal ndcators of mnng. SGEM 03. 3th Internatonal Multdscplnary Scentfc Geoconference Scence and Technologes n Geology, Exploraton and Mnng. Conference proceedngs,, 6-, June, 03, Albena, Bulgara, Albena, STEF9 Technology Ltd., 03, , ISBN [6] Naščáková, J., Wess, E., Červenka, P., Mxtaj, L., Wess, R.: A support of the renewable source energy utlzaton and condtons for the bogass staton nvestment. Acta Montanstca Slovaca. 4, 009, 4, 33-39, ISSN Avalable at: [7] Sabová, J., Jakub, V.: Geodetc deformaton montorng. st edton. Košce: Edtor centre and edtoral offce AMS, F BERG, Techncal Unversty of Košce, 007, 8 p., ISBN [8] Sabová, J., Pukanská, K.: Expanson of local geodetc pont feld and ts qualty. GeoScence Engneerng. 58, 0, 3, 47-5, ISSN Avalable at: pdf [9] Sokol Š., Bajtala M., Ježko J., Černota P.: Testng the Accuracy of Determnng 3D Cartesan Coordnates Usng the Measurng Staton S8 Trmble DR Plus ROBOTIC. Journal of the Polsh Mneral Engneerng Socety, 33,, 04, 85 90, ISSN Avalable at: [0] Sütt, J., Wess, G.: 3D geodetc montorng slope deformatons. Acta Montanstca Slovaca., 996,, 09-6, ISSN Avalable at: [] Vávrová, V., Wess, E., Červenka, P., Ferencz, V., Naščáková, J.: Possbltes and problems of usng pupllary reflex for subconscous detecton of consumer preferences. Metalurgja. 53, 04,, 85-88, ISSN Avalable at: [] Wess, G., Sütt J.: Geodetc local network I (Geodetcké lokálne sete). Štrofek, 997, 88 p., ISBN [3] Act No. 364/004 Coll., on waters, amendng Act No. 37/990 Coll. of the Slovak Natonal Councl on offences, as amended by later regulatons (Water Act). [4] Decree no. 75/0 Offce of Geodesy, Cartography and Cadastre of the Slovak Republc of 5 March 0, amendng and supplementng Decree of the Offce of Geodesy, Cartography and Cadastre of the Slovak Republc no. 300/009 Coll., mplementng no. 5/995 Coll., of the Natonal Councl of the Slovak Republc about geodesy and cartography, as amended by later regulatons. 40