CHARACTERISTICS OF NONSTATIONARY PARASEISMIC KINEMATIC EXCITATIONS IN THE REGION OF POLKOWICE

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1 A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N T The Silesin University of Tehnology No. 3/ 2009 CHARACTERISTICS OF NONSTATIONARY PARASEISMIC KINEMATIC EXCITATIONS IN THE REGION OF POLKOWICE Zigniew LIPSKI * * Dr.; Fulty of Civil Engineering, The Silesin University of Tehnology, Akdemik 5, Gliwie, Polnd E-mil ddress: zigniew.lipski@polsl.pl Reeived: ; Revised: ; Aepted: A s t r t The pper presents the results of n nlysis of nonsttionry kinemti exittions generted y qukes due to mining tivities in Polkowie in the Copper-Mining Distrit of Legni nd Głogów, ffeting dynmilly uilding strutures in the town. Their time-nd-spetrl properties deide out the intensity of dynmi response of the supporting struture of uildings. In the nlysis Gor s trnsformtion ws pplied, sed on whih the vlues of eighteen rndom vriles were lulted, hrterizing time-nd-spetrl properties of these exittions. In every one of them two segments were diserned, the initil nd the fundmentl one, whih were hrterized with respet to the durility of the segments, the oundry frequenies of the evolving nds nd extreme vlues of elertion. In the oordinte system time-frequeny those res hve een seprted, nd extreme trnsient hrmonious omponents of exittions did our. Sixty-four mining qukes whih ourred in the region of Polkowie hve een nlyzed, for whih horizontl, orthogonl omponents of the elerogrms were reorded with n extreme vlue of elertion of t lest 0.25 m/s 2. A syntheti speifition of otined results hrterizing the time-nd-spetrl properties of kinemti exittions hs een presented. S t r e s z z e n i e W pry przedstwiono wyniki nlizy niestjonrnośi wymuszeń kinemtyznyh generownyh przez wstrząsy górnize w Polkowih w Legniko-Głogowskim Okręgu Miedziowym. Stnowią one oiążeni dynmizne zudowy miejskiej i ih włsnośi zsowo-widmowe deydują o poziomie odpowiedzi dynmiznej konstrukji nośnyh udynków. W nlizie wykorzystno trnsformję Gor. N jej podstwie olizono wrtośi osiemnstu zmiennyh losowyh, z pomoą któryh shrkteryzowne zostły włsnośi zsowo-widmowe wymuszeń. W kżdym z nih wyróżniono dw segmenty: pozątkowy i podstwowy. Niestjonrnośi wymuszeń shrkteryzowno z pomoą: zsów trwni segmentów, zęstotliwośi grniznyh ewoluująyh psm orz ekstremlnyh wrtośi przyspieszeń. Wydzielono tkże oszry w ukłdzie współrzędnyh zs zęstotliwość, w któryh pojwiją się ekstremlne, krótkotrwłe skłdowe hrmonizne wymuszeń. Anlizowno 64 wstrząsy górnize z terenu Polkowi, dl któryh zrejestrowno poziome, ortogonlne skłdowe kelerogrmów o ekstremlnej wrtośi przyspieszeni o njmniej 0.25 m/s 2. Podno syntetyzne zestwienie uzysknyh wyników hrkteryzująyh zsowo-widmowe włsnośi wymuszeń kinemtyznyh. K e y w o r d s : Mining qukes; Kinemti exittions; Time-spetrl properties, Gor s representtion. 1. INTRODUCTION The elerogrms nd seismogrms reorded in regions ffeted, mong others, y qukes due to mining tivities provide n imge of elsti wves propgted in the lithosphere. Geophysil investigtions indite tht in these wves re frgments onneted with longitudinl wves to e distinguished [1] denoted s P, trnsverse wves, denoted s S, nd Ryleigh s wves, i.e. surfe wves, whih susequently reh the mesuring sttions. In speil ses the imges of these wves re distintly reognizle [2-4]. The question rises, wht effet do delys of the respetive groups of wves exert on the dynmi retion of the supporting strutures of the uildings exposed to suh qukes. Bsing on dynmi nlyses rried out so fr [5-7] onerning uildings situted in the Copper- Mining Region of Legni nd Głogów it my e stted 3/2009 A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N T 41

2 Z. L i p s k i tht the dynmi response of these strutures in the initil stge of exittions is usully rther smll, ut inreses in the ourse of further exittions, rehing eventully the ourrene of extreme fields of stresses nd dynmi displements, fter whih they gin fde out. In se of kinemti exittions with low or high dominting frequeny nds [2,4] the struturl dynmi responses depend on their spetrl properties. These qulittive regulrities re onneted with nonsttionry stte of these kinemti exittions [8], euse their time-spetrl properties hnge due to vrious kinds of elsti wves propgting in the lminr roky medium nd their sequentil pproh to the uildings. Thus we my sy tht the prolem of nonsttionry exittions generted y mining qukes hs from the viewpoint of the dynmis of the onstrution of uildings two spets, generl nd n pplile one. The former one onsists in the reognition of the spetrl properties evolving in the ourse of eh kinemti exittion together with their numeril hrteristis. The ltter spet omprises the wy nd instruments pplied in the nlysis, tking into ount the nonsttionrity nd onsequenes onerning numeril nlysis sing on the history lods method ffeting the strutures exposed to prseismi exittions. The present pper provides results of nonsttionry kinemti exittions nlysis reorded in Polkowie. The im of this nlysis ws to reognize nd to hrterize numerilly desried phenomenon in form of n essile speifition of representtive exittions. It my e n underlie of nlysis of their dynmi effet on vrious kinds of uilding strutures. 2. THEORETICAL FUNDAMENTALS AND MEASUREMENT DATA The pper nlyzes the signls whih re disrete elertions in time, onneted with virtions in the susoil generted y qukes due to mining tivities. It hs een ssumed tht the respetive exittions re the result of ertin rndom proesses. The set of their vlues t the moment t omprises smples of rndom vriles x t, i.e. the vlues of elerogrms t this moment t. Their vrines (1) in the set of the reliztion of the proesses nd the vlues of the orreltion funtion (1) depend on time in ompline with the formule [9]: (1) (1) where: E[.] the verging opertor in the set of ll the reliztions of the proess t stedy vlue of t. The ssumptions (1) nd (1) determine the nonsttionry hrter of the elerogrms in wider sense [9]. So-lled time-frequeny representtion of signls ws pplied in the nlysis of the nonsttionry stte. The generl im of its pplition ws highly urte joint mplitudinl-frequeny deomposition of signls s funtions of time, i.e. representtion of the vriility of the mplitudes, frequeny nd phses of their omponents. Usully, however, the evolution of the funtion of spetrl power density is determined in time [9]. For this purpose Gor s trnsformtion ws used, owing, first of ll, to its suffiient ury, omprtively simple lgorithm of numeril lultions nd file reliztion in the omputer system Mtl 7.5. Generlly Gor s trnsformtion my e defined [9] s the representtion of nonsttionry signl s the sum of si funtion, resulting from n ssumed prototype funtion due to shifting it long the xes of time nd frequeny y multiplying it with the omplex hrmoni signls. Gor s time-frequeny trnsformtion of ontinuous signl x(t) is defined y the formul (2) where: g m,n (t) - window funtion of the synthesis g(t) with n energy equl to 1, shifted in time y m Δt nd frequeny y n Δf, m,n oeffiients of deomposition, γ(t) window funtion of the nlysis, iorthogonl to the window funtion of the synthesis g(t), (the sterisk denotes onjugte omplex funtion), Δt, Δf shift in the domin of time nd frequeny, respetively. The funtion of the synthesis ought to hrterize onentrtion of energy in the domin of time nd frequeny. This ondition ensures n dequte resolution of the trnsformotion in oth domins. The modules of Gor s trnsformotion, i.e. the resulting Gor s time-frequeny representtions were lulted y mens of the formul (3) 42 A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N T 3/2009

3 CHARACTERISTICS OF NONSTATIONARY PARASEISMIC KINEMATIC EXCITATIONS IN THE REGION OF POLKOWICE Anlogilly to Fourier s trnsformotion, the funtion S x (mδt,nδf) my e ompred with the spetrl power density rting. The formule (2) hve lso disrete version, not quoted here. It ws relized y mens of progrm tken down in the Mtl 7.5. As the window of the synthesis Cheyshev polynomils were pplied, inditing onentrtion of energy round the entrl frequeny, s well s inonsiderle errors. The window funtions of the nlysis were lulted numerilly mking use of n dequte lgorithm [9]. For prtil resons the results of the nlysis of the elerogrms, i.e. the vlues of Gor s representtions, hve een visulized y mens of mps in the deiel sle. As referene level hrmoni signl with n mplitude of ref = 0.01 m/s 2 ws ssumed, dpted to the urrently nlyzed omponent frequeny of the elerogrm nd the window length of the nlysis γ(t). These mps were pplied prtiulrly for the purpose of ssessing the durtion nd oundry frequenies of the evolving spetrum nds of the Gor s representtions. All the prmeters hrterizing the nonsttionrity of kinemti exittions re onsidered to e rndom vriles with n unknown distriution of proility. In the ourse of nlyzing their empiril densities of proility, onsiderle irregulrities hve een deteted in the form of two lol extremes, symmetry et. Therefore, their distriution funtions were pplied, sing on whih the quntiles of the rndom vriles orders of 0.1; 0.5 nd 0.9 were lulted. The set of the nlyzed kinemti exittions, i.e. elerogrms, omprised 64 pirs of signls in the form of horizontl, orthogonl omponents of elertion of the virtions in the soil, used y mining qukes in the region of Polkowie. They resulted from four mesuring sttions situted in vrious prts of the town. The qukes were seleted from out 640, ourring in the yers nd in Polkowie nd its neighorhood. They were hrterized y pek elertions exeeding 0.25 m/s 2. Their entire durtion omprised point on the time xis of the rrivl of signl t the mesuring sttion, ending eyond the lst lol extremum mounting to e = 0.1 m/s 2. The speifition of these qukes ws pulished in [10] nd will not e quoted here gin. Figure 1. Mps of Gor s time-frequeny representtions of the elerogrms ) omponent X, ) omponent Y 3. RESULTS OF THE ANALYSIS The mps of Gor s representtions permitted synthetil visuliztion of the time-frequeny evolution of the spetrl power density of these signls. Exemplry digrms for oth horizontl omponents of the elertion of the virtions ourring on Jnury 25 th, 2000 hve een presented in Fig. 1, together with the deiel sles. The distriution of the representtion, prtiulrly their lol extremes indites distint evolution of the spetrum in the ourse of exittion. Their initil prt is loted in nd whose oundries re distintly higher thn those of the susequent frgment of the signl. Also oth omponents of the digrms re similr, euse they re imges of the sme progress of virtions generted in the lithosphere nd hve een reorded synhronilly in seleted orthogonl diretions. It ought to e stressed tht this hrteristi imge of the time-frequeny representtion of exittions onerned 56 shoks reorded t vrious mesuring sttions. The remining eight shoks displyed different distriution of representtions long the time xis, they required prt nd individul time-frequeny nlysis. The evolution of the spetrum of kinemti exittions is still more distintly visile in Figs. 2-. Here the pek vlues of elertions re lolized in those points in whih Gor s representtions hieve lol extremes. These digrms hve een plotted independently for the omponents X nd Y of set of kinemti exittions, exluding untypil ones. Fig. 2 sets off the effet of the evolution of the pek vlues of elertions, tking into ount their dependene on the frequeny. Two zones n e distinguished, viz. the first segment hrterized y pek vlues of elertions lolized in the higher nd in ontrdistintion to the seond segment, in whih these vlues pper in the lower nd. It is lso evident tht the pek vlues wne with the pssge of the time of exittions. e C I V I L E N G I N E E R I N G 3/2009 A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N T 43

4 Z. L i p s k i Figure 3. Loliztion of the ends of segments No. 1 ), No. 2 ), No. 2 ) t the time xis Figure 2. Digrms of the lol extremes of kinemti exittions, ) omponents X, ) omponents Y. Figure 4. Frequenies in the lower nds of segments: ) No. 1, ) No. 2, ) No. 2 Figure 5. Frequenies in the upper nds of segments: ) No. 1, ) No. 2, ) No A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N T 3/2009

5 CHARACTERISTICS OF NONSTATIONARY PARASEISMIC KINEMATIC EXCITATIONS IN THE REGION OF POLKOWICE e C I V I L E N G I N E E R I N G Figure 6. Loliztion of the lol extremes of Gor s representtions on the time xis in segments: ) No. 1, ) No. 2, ) No. 2 Figure 7. Loliztion of the lol extremes of Gor s representtions on the frequeny xis in segments: ) No. 1, ) No. 2, ) No. 2 Gor s representtions onerning set of 56 mining onussions were nlyzed in detil sing on the ssumptions quoted elow. The omponents X nd Y were nlyzed jointly due to the similrity of the mps of vlues of the representtions nd euse they onstitute the imge of one resultnt exittion. For eh kinemti exittion two fundmentl segments hve een distinguished, the initil one No. 1 nd the si one, No. 2, the ltter hve een divided dditionlly into two prts susegments nd. The durtion nd dominting frequeny nds of the respetive segments of kinemti exittions hve een ssessed sing on mps nlogil to those presented in Fig. 1 where the level of 7 db in Gor s representtion is onspiuous, orresponding to the rtio of the pek vlues of elertions of the omponents of exittion to the pek vlue of the referene signl ref = 0.01 m/s 2 mounting to 5. The isoline of the vlues 7 db permitted to red off in the mps the mentioned prmeters of the exittions segments. In the nlysis use ws lso mde of the vlues nd position of the lol extremes of Gor s representtion in the segments 1 nd 2,. In the zones determined y them the lol extremes of elertion of the omponents of kinemti exittion hve een lulted. Altogether 18 rndom vriles were nlyzed, hrterizing the nonsttionrity of kinemti exittions. The lssified distriution funtions of the mentioned rndom vriles hve een presented in Figs The respetive olors onern the respetive segments. The vlues of quntiles of the order 0.1; 0.5 (medin) i 0.9 hve denoted, s well s their loliztion. These were pplied to determine the oundries in the domin of time nd frequeny of the seleted segments of kinemti exittions. The vlues of the quntiles of rndom vriles lulted sing on empiril distriution funtions hve een gthered in Tle 1. Fig. 8 visulizes the time-frequeny properties of kinemti exittions, tking into ount the ssessed prmeters. Denoted time oundries of the segments re: the first one is ommened y quntile of order 0.1, segments No. 1 nd No. 2 divide the medins nd the lst one is ompleted y quntile of order 0.9. The oundries of segments nds hve een plotted too: the upper one s quntile of order 0.9, the ottom one s quntile of order 0.1, pproximted y mens of spline funtions. Inside the segments nds those res hve een mrked in whih the mximum of Gor s representtions, eing the imge of the lol omponents dominting in the segments of exittions re lolized. Their lower nd upper oundries hve een depited, wheres the 3/2009 A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N T 45

6 Z. L i p s k i Tle 1. Vlues of the prmeters hrterizing rndom vriles No. Rndom vrile Vlue of quntile End time, segment No.1 [s] End time, segm. No.2 [s] End time, segm. No.2 [s] Lower frequeny, segm. No.1 [Hz] Lower frequeny, segm. No.2 [Hz] Lower frequeny, segm. No.2 [Hz] Upper frequeny, segm. No.1 [Hz] Upper frequeny, segm. No.2 [Hz] Upper frequeny, segm. No.2 [Hz] Pek vlue Time oordinte of Gor s representtion mximum, segm. No.1 [s] Time oordinte of Gor s representtion mximum, segm. No.2 [s] Time oordinte of Gor s representtion mximum, segm. No.2 [s] Frequeny oordinte of Gor s representtion mximum, segm. No.1 [Hz] Frequeny oordinte of Gor s representtion mximum, segm. No.2 [Hz] Frequeny oordinte of Gor s representtion mximum, segm. No.2 [Hz] Pek vlue of elertion, segm. No. 1 [m/s 2 ] Pek vlue of elertion, segm. No. 2 [m/s 2 ] Pek vlue of elertion, segm. No. 2 [m/s 2 ] oundry points on the time xis orrespond to quntiles of order 0.1 (segment No. 1) or order 0.9 (segment No. 2). The immedite points re identil with the oundries of segments. The ssumption of indited oundries of the segments mens tht inside the re denoted y them there were 80% of the results onerning the nlyzed exittions in the domin of time nd s mny in the domin of frequenies. Beyond this re there were results onerning smples of rndom vriles, whih were rther improle. The evolution digrm in Fig. 8 illustrtes the vrition of the properties of kinemti exittions, whih in their initil phse onstitute high-frequeny signls with nd of Hz, dominting in nd Hz. The durtion of this segment mounts to out 0.7 s nd my inlude pek elertions rehing 0.59 m/s 2 with proility of 90% nd extreme oserved vlues not exeeding 1.24 m/s 2.The si segment No. 2 lsts from out 0.7 s to out 3.45 s. Beyond this limit in out 10% of ses the kinemti exittions re longer. Two susegments my e distinguished, their oundry eing the point on the time xis t 2 = 1.35 s. The nds of these susegments re defined y the oundries Hz nd Hz. The lower oundries re in their se muh lower thn in the initil segment. The dominnt res of the segment 2 re omprised within nds Hz nd Hz, they re distintly shifted towrds lower frequenies in reltion to the initil segment. Dominting zones of segment No. 2 orrespond with elertions of 0.72 or 0.19 m/s 2 with proility of eing exeeded mounting to 10%. The extreme mesured vlues did not exeed nd m/s 2, respetively. Chnges of the ottom oundries of nds inside segment No. 2 re rther smll in ontrdistintion to the upper ound- 46 A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N T 3/2009

7 CHARACTERISTICS OF NONSTATIONARY PARASEISMIC KINEMATIC EXCITATIONS IN THE REGION OF POLKOWICE ACKNOWLEDGEMENTS The investigtions presented in this pper hve een rried out sed on the results of seismologil nd dynmi mesurements rried out y the Mining Plnt Rudn KGHM Polsk Miedź in Polkowie. e C I V I L E N G I N E E R I N G REFERENCES Figure 8. Time-frequeny hrteristis of kinemti exittions segments ry. Vlues of the pek vlues of elertion fde quikly in the ourse of their durtion. In susegment No. 2 they re t lest out 2.5 times lower thn in prt No CONCLUSIONS Presented nlysis of the nonsttionrity of kinemti exittions permitted to expose the time-frequeny properties nd express them y mens of the ssumed prmeters. Their nonsttionrity is quite evident nd my not e disregrded y ssuming sttionrity of elerogrms sed on mesurements of qukes due to mining tivities. Mentioned properties of exittions re of essentil importne from the viewpoint of the effets of these qukes on uilding strutures. The initil segments of exittions, eing high-frequeny signls, do not ffet onsiderly uildings with low si frequenies of their nturl spetrum [2, 4, 8]. It is only the si segments whih intensify this effet mrkedly. The ltter is, however, omprtively short nd quikly fdes out in the ourse of its durtion. It my e sid tht this onstitutes generl nd qulittive justifition of the frequently desried regulrity, mintining tht mining qukes in spite of high pek vlues of elertion ffet the uilding development of towns only to smll degree, without using lrger dmges in the strutures of the uildings. [1] Giowiz J., Kijko A.; An introdution to mining seismology. Ademi Press, Sn Diego, 1994 [2] Cholewiki A., Szul J.; Prolemy zezpiezni udynków n oddziływni wstrząsów górnizyh. (Prolems of uildings protetion ginst the mining tremors influene) Górnitwo i Środowisko, Główny Instytut Górnitw, Ktowie, Wyd. Spejlne, nr V/2007, p (in Polish) [3] Zemty Z.; Rokurst indued ground motion omprtive study. Soil Dynmis nd Erthquke Engineering 24, 2004, pp [4] Zemty Z.; Non-sttionry rndom virtions of sher em under high frequeny seismi effets. Soil Dynmis nd Erthquke Engineering 27, 2007, p [5] Ajdukiewiz A., Kliszzewiz A., Lipski Z., Poremski G.; Anlysis of Existing Lrge-Pnel Conrete Buildings Sujeted to Pr-Seismi Influenes in Mining Region, Proeedings of FIB-Symposium, Conrete Strutures in Seismi Regions, Athens, 2003, p [6] Wwrzynek A., Lipski Z., Pilśnik J.; Oen zgrożeni niskiej zudowy mieszklnej w rejonie Polkowi oddziływnimi prsejsmiznymi. (An ssessment of hzrds for low prtment houses in the region of Polkowie due to prseismi phenomen). Inżynieri i Budownitwo, nr 10/2003, p (in Polish) [7] Ttr T.; Dziłnie drgń powierzhniowyh wywołnyh wstrząsmi górnizymi n niską trdyyjną zudowę mieszklną. (Impt of surfe virtions generted y mining qukes on low, trditionl, residentil development). Zeszyty Nuk. Pol. Krkowskiej, seri Inżynieri Lądow nr 74, Krków, 2002 (in Polish) [8] Lipski Z.; Sttistil hrteristis of some seleted prmeters of prseismi kinemti exittions in uildings. Slovk Journl of Civil Engin., Brtislv, 3/2006, p [9] Zieliński T.; Cyfrowe przetwrznie sygnłów. Od teorii do zstosowń. (Numeril proessing of signls. From theory to pplitions), Wydwnitw Komunikji i Łąznośi, Wrszw, 2005 (in Polish) 3/2009 A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N T 47

8 Z. L i p s k i [10] Lipski Z.; Chrteristis of prseismi lods from the viewpoint of the rnge of uilding nlysis. Arhiteture Civil Engineering Environment, vol.1 No. 4/2008, The Silesin University of Tehnology, Gliwie, p A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N T 3/2009