Modeling Of Ground Motions For Tbilisi Region With Site Effects

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1 Modelg O Goud Moos Fo Tbls Rego Wh Se Eecs Paaa Rekvava Keeva Mdva Geoga Naoal ssocao o Egeeg Sesmology ad Eahquake Egeeg Tbls Geoga ekvavapaaa@yahoo.com mdvak@yahoo.com Keywods: Sesmc Goud Moo Respose Specum. BSTRCT The ulzao o me hsoes o eahquake goud moo has gow cosdeably he eld o eahquake egeeg. I s vey ulkely howeve ha ecodgs o eahquake goud moo wll be avalable o all ses ad codos o ees. Hece hee s a eed o ece mehods o he smulao o sog goud moo o a gve ego. Due o lack o he eal sog goud moo ecods he objecve o hs eseach s o develop a mehodology o apd geeao o hozoal ad vecal compoes o eahquake goud moo a ay se o Tbls ego (wh 50 km). The model developed hs sudy povdes smulao o goud moo ove a wde age o magudes ad dsaces a 8 eahquake souce s zoes o Tbls ego. The eseach cludes hee ma opcs: () he sochasc smulao o eahquake goud moo a a gve se o he cy o Tbls; () he esmao o acceleao me hsoes a a gve se usg he dec mehod o egeeg sesmology cosdeg sol codos based o he heoy o he eleced waves ad () calculao o hozoal ad vecal acceleao espose specum o ma ses o Tbls eoy. The obaed esuls he ems o acceleao espose speca ad specal dyamc coeces ca be wdely appled he pacce o eahquake egeeg Geoga. Ioduco I he pacce o eahquake egeeg a eahquake eec quaavely s classed accodg o he sesmc scale ad by he buldg code. Fo hs pupose ae used Peak Goud cceleao (PG) Peak Goud elocy (PG) ad Peak Goud Dsplaceme (PGD) he sesmc scale. I he buldg code he sesmc aco usually s epeseed by a elasc acceleao espose specum ad he acceleao me-hsoes. I should be oed ha each eahquake epeses dvdual pocess whch s geeaed ude cea geogaphc ad geologcal codos s desucve eec s o all depeds o he sesmc souce magude ad he epceal dsace. The elasc acceleao espose specum shape depeds o he eahquake geeao mechasm ad goud espose he se o ees. Theeoe he elasc acceleao espose speca deed accodg o he ecoded acceleogams dee egos de om each ohe ad elec oly local se codos. The me-hsoes dyamc aalyss povdes he evaluao o sesmc demad o sucues usg he ecoded ad acal o smulaed acceleogams ha gves omao o eahquake esy s equecy ad duao.e. does o exclude me aco as occus he espose specum aalyss. Poceedg om he egulaos o sesmc aco basc cocepo gve [] seleco o he elasc espose specum shape he couy o pa o he couy s possble om 4-4

2 he cea couy Naoal aexes ha ae woked ou by local uhoes. I accodace wh he ecommedaos suggesed by Euocode 8 [] deep geologcal daa o he cosuco se should be cosdeed ad he hozoal ad vecal elasc espose speca should be compued akg o accou he sesmc souces ad he eahquake magudes geeaed om hem. I geeal lack o he sog eahquake ecods sasc package ceaes cea poblems o he elasc espose speca ad he dyamc coece specal cuves elaboao. I should be oed ha a example o such poblems s Tbls he capal o Geoga. Fo Tbls ego (wh 50 km) ecods o he sog eahquakes daa ae lmed. Dug las 00 yeas a he eoy o Tbls cy abou huded weak eahquakes ook place. Local sog eahquake occued oly o pl 5 00 ude he ceal pa o he cy wh magude M=4.5 ad ecoded o he bedock peak hozoal acceleao o 0g whch was ampled o he age o 0.0 o 0.30g due o dyamc espose o suace sol deposs. I s evde ha o he bass o he weak ad ae eahquakes eal ecods omao o he sesmc aco speced egoal model s mpossble. I such codos he mos saghowad pocedue s o geeae goud moo me-hsoes usg o egoal eahquake souces zoes paamees ad classcao accodg o he sols sesmologcal ad geologcal popees avalable o he eoy o Tbls. he same me accodg o he Geoga Buldg Code [] Tbls s locaed he sesmc zoe o esy 8 degee by he MSK-64 wh a maxmum hozoal acceleao equals 0.7g ad a eu peod o eahquakes 500 yeas (%/ 50 yeas). The specal dyamc coece s deemed o gouds o had (I) medum (II) ad so (III) caegoes ad whou specal vesgaos s maxmum value o all hee caegoes gouds equals.5. I should be oed ha om he eahquake souce zoes o Tbls ego a he eoy o he cy hee ae expeced he eahquakes wh magudes M=5.0_7.0 ad coespodg sesmc geeaed kemacs o shg as evese ad dexal ske slp [3]. Theeoe s ecessay o dee moe pecsely he specal cuves o dyamc coece cosdeg sesmologcal ad geologcal popees o he gouds wh he cy ad adjace aea. Ude such codos s mpoa o smulae egoal sesmc aco he om o he acceleao o me-hsoes ad o elaboae he elasc espose speca ad he heecompoe specal cuves o dyamc coece o vaous ses o Tbls. Thee ae seveal models he leaue o umecal smulao o eahquake goud moo. The goud moo smulao models ca be classed o wo caegoes: geophyscal models ad egeeg models whch esmae he goud moo udameally dee ways [34]. The objecve o hs sudy s o develop a mehodology o smulao goud moos ad evaluao he acceleao espose speca ad he hee compoes specal cuves o dyamc coece a ay se o Tbls eoy cosdeg he egoal sesmologcal chaacescs ad geologcal codos o he se o ees. The poposed appoach cludes hee ma opcs: () he sochasc smulao o eahquake goud moo a a gve se o he cy o Tbls; () esmao o acceleao me hsoes a a gve se usg he dec mehod o egeeg sesmology akg o accou a sol popees based o he heoy o he mulple eleced waves () calculao o he hozoal ad vecal elasc espose speca ad coespodg he specal cuves o dyamc coece o ma ses o Tbls eoy. Sochasc Smulao o Eahquake Goud Moo 4-43

3 Fo smulao o possble sesmc goud mouos o he eoy o Tbls cy hs pape s employed he dscee osaoay Gaussa sochasc pocess epeseed as [5] g () = E () X () () (=3) whee g () deemes o goud acceleao he deco o hee pcpal ohogoal axses wh zeo coss coelao bewee o compoes; E () s he deemsc omalzed evelope uco o modulag uco; X () epeses a ypcal ealzao o he saoay leed wheose pocess. Nomalzed saoay adom uco wh zeo mea ad u-vaace s chaacezed by K() uco o coelao as K()=e - j (cos j + j / j s j ) () whee scoelaocoece chaacezg badwdh o he pocess ; s ccula pocess equecy; j epeses a odal umbe o pocess. The modulag uco E () s deed ems o so-called Belag mpulse ad wh E () max = s gve by () E ε exp( ε) (3) whee cools he shape o he evelope uco ad deemes he eecve duao ad pocess osaoay. Geealzg he om Eq. he hozoal ad vecal compoes o he pocess ca be we as g( ) exp( ) x ( ) ( ) exp( ) x( ) g ( ) 3 exp( ) x3( ) g3 (4) whee s a mea squae value o acceleao he deco o pcpal axses ad deoes adom pocess esy ha s deed by s vaace; k da ae coecve acos o he value o he hozoal ad vecal compoes whch ae accodgly equal o ad 0.7. Thus he omulao Eq.4 s compleely deemed wh xed values o doma equecy j usg hee paamees: ad whch ae depeded o egoal sesmologcal ad geologcal codos o he smple om o he eahquake magude hypoceal dsace doma equecy ad goud chaacescs a he se. O he bass o poposed sochasc goud moo model omulaed Eq.4 he sowae package CCSIM [3] was developed whch allows o geeae he mulple acal acceleogams o he pedced eahquakes. 4-44

4 Paamees Esmao Fo esmao o he maxmum macosesmc esy ITb o he expeced eahquake o he eoy o Tbls cy om he eahquake souces zoes o Tbls ego he wo vaous expessos ae appled [6]: o small eahquakes (M s <6) I Tb =.5M s 3.4lgR+3. (5) o sog eahquakes (M s >=6) I Tb =.5M s 4.7lgR+4.0 (6) whee M s s suace-wave magude; R= ( +h ) / s hypoceal dsace; s epceal dsace; h-ocal deph. The esulg equao o lage hozoal values o peak hozoal acceleao s deed by [7] ad log PG h = M s -logr-0.003k+0.8p (7) h 4.5 (8) whee p s 0 o 50-pecele values ad o 84-pecele. Fo he deemao o doma peod T o goud moo empcal elaos bewee he suace-wave magude o he eahquake ad a hypoceal dsace deved o shallowocus ea-souce eahquakes ude a aveage sol se codos ae calculaed by he ollowg omula [8] lgt=0.5m s +0.5lgR+C +C ±0. (9) whee C s paamee o aul mechasm (C =-0. o evese C =0 o ske slp C =0.- o dexal ske slp); C coece o luece o ake o cosdeao acos ha s equal o.; Duao o he esve phase o goud moo s compued by lgd=0.5m s +0.50lgR+C +C +C 3 ±0.30 (0) whee C s paamee o aul mechasm (C =-0.5 o evese C =0.0 o ske slp C =-0. o dexal ske slp; C =-0.5 o had goud; C =0 o medum goud; C =0.5 o so goud; a mea value o ao C 3 s equal o.3. The calculaed paamees o he bodele eoy o Tbls cy ae lsed Table. I should be oed ha o compuao o PG has bee used 84-pecele. O he bass o empcal daa he moe esve hozoal compoe o PG h s obaed.8 mes geae ha ohe oe ad he vecal compoe s /3 o he maxmum hozoal compoe. Fo 0 ses o Tbls cy eoy (350 squae klomees Fg.) wee also deemed mmum hypoceal dsaces PG o % ad % pobables o beg exceeded 50 yeas values o he doma peods ad duao o oscllao. s a llusao Table 4-45

5 ae gve paamees geeaed om he hgh poeal sesmc geeag zoe #3 whch s suaed o he oh-wes o Tbls ego. Noe ha values o PG Table coespod o % pobably o beg exceeded 50 yeas ad ae by 5% less ha compued o % pobably o beg exceeded 50 yeas. Fg.. Locao o he ses o he eoy o he cy Table. Quaave Chaacescs o he Pedced Goud Moo o he Bodele o Tbls Cy Zoe # R (km) I TB (deg) T (sec) D (sec) PG h (m/sec ) PG h (m/sec ) PG h3 (m/sec ) Fom ocus wh M= Fom ocus wh M= Fom ocus wh M= Fom ocus wh M= Fom ocus wh M= Table. Quaave Chaacescs o he Pedced Goud Moo o he Cocee Ses o Tbls Cy Zo e # M Paamees Se # The ma paamee usg he expesso: R m km PG h m/sec PG h m/sec PG h3 m/sec T sec D sec ω jo he goud moo model has bee deemed based o he Eq.9 j =π/t j () The value o he coelao degee chaacezg paamee was evaluaed based o he 4-46

6 aalyss o he eahquakes ecods daa [3] depedg o ad o (x) (y) da 3(z) compoes cosss o j =0.04 j ; j =0.53 j ; j3 =0.4 j ; () The mea squae value o acceleao was acceped cosdeg ha =PG /3 =3 (3) The paamee s deemed o he bass o he gve duao o esve oscllaos above-meoed ecods ad s equal o j = 0.0 j (4) Thus calculaed paamees ae epeseed Table 3 bu mea squae values o he hozoal ad vecal acceleaos o eahquake geeaed om he hgh poeal sesmc geeag zoe #3 ae gve Table 4. Table 3. Paamees o Geaao o Regoal Syhec cceleogams Zoe ¹ Table 4. Mea Squae alues o acceleaos o Cocee Ses Mea squae value o accele ao m/sec j sec - Pobably o exceedg 50 yeas j sec - j sec - j3 sec - Se # j sec - d=0.04t j sec Fom ocus wh M= Fom ocus wh M= Fom ocus wh M= Fom ocus wh M= Fom ocus wh M= % / % / % / % / % /

7 % / Deemao o Mullaye Goud Moo Based o he Theoy o Mulple Releced Waves Mehod o he mulple eleced waves gves a possbly o deeme o a cocee eoy by geologc pole coomy o aual laws o sesmc oscllao o he mullaye goud suace ude moo o ockbed as oudao accodg a law o gve acceleogam. Fo aalycal dawg o acceleogam o he goud ee suace oscllao le cosde a wave pcue a ay me he goud aea wh dee hckess ad hozoal bodele. I s assumed ha he goud s elasc ad waves ae popagaed he vecal deco (Fg. ). I he om o sesmc luece hs case s used ecoded o he ockbed acceleogam om he daabase o goud moos wh kow eahquake [3]. Fg.. Desg model o ohomogeeous goud I he Fg. ae acceped ollowg desgaos: () s value o acceleao's wave uco a he me o he boom level o he -h laye; () s value o acceleao's wave uco a he me o he op level o he -h laye; 0 ( ) s acceleogam o he level o had ock. Fo ay -h laye o goud he wave equao o shea oscllaos ca be we as [9]: ( ) s ( ) 0 y whee () s he acceleao o goud laye pacles; s he me; y epeses he coodae o goud pacles he vecal deco; s s he velocy o he shea wave popagao. Soluo o he equao (4.) s gve by (6) whee s he aco o eaco ude passg o wave om --h o -h laye; he aco o wave eleco o he bodele bewee ad - layes; epeses he (5) 4-48

8 4-49 me o wave passage he -h laye s ( H / whee H ad s ae accodgly he hckess o goud laye ad he velocy o he shea wave popagao he -h laye). ad acos ae deed by s s s / (7) / s s s s (8) whee s a desy o -h goud laye. Hece ally soluo o he dec poblem o egeeg sesmology ca be epeseed by he ecue elaos as [9]: (9) Oscllao o he pacles om he boom o -h laye o he level o y ca be calculaed accodg o s s y y H y / / (0) Thus he developed algohm o soluo he dec poblem o egeeg sesmology s ealzed by he sowae package GFRT [3]. Smulao Resuls o Tbls Cy Ses The sowae CCIM was used o geeao o he hozoal ad vecal compoes o syhec acceleogams coespodg possble sesmc souce zoes o Tbls ego gve Table. Dscee sep o he smulaed acceleogams was ake equal o 0.04T. Whe assessg he pobablsc mea elasc espose speca ad he dyamc coece specal cuves o all ses whch ae peseed Fg. he equed umbe o ealzaos was educed o each syhec acceleogam up o 0 ealzaos. The mos ovel aspec o hs exeso s elaboao o pope hee compoes dyamc coece specal cuves whch ae compued o 50 yeas exposue me ad % ad % pobables o exceedg. s a example Fg. 3 shows pas o he pobablsc mea elasc acceleao espose speca o 5% dampg ad he coespodg specal cuve o dyamc coece o syhec moo geeaed om he souce zoe ¹3 o se ¹8 o so sol chaacescs o % 50 yeas. Usg he sowae GFRT a luece o a ypcal eahquake ad local geologcal codos upo omg he elasc acceleao espose speca o he abovemeoed ses was suded. Wh ha ad vew om he daa se [3] was seleced ve ecoded o

9 he bedock acceleogams (EL Ceo Saa Babaa-980 Moeego Ful ad Tbls ) whch ae dee om each ohe by paamees o PG doma peod (T) ad duao (D) bu by he magude ad epceal dsace ae close o pedcable eahquakes chaacescs o Tbls ego. Fg. 3. Geeaed om zoe #3 o se #8 xyz compoes o acceleao espose speca (a) ad specal cuves o dyamc coece Fg. 4. Thee compoes acceleao espose speca (a) ad specal cuves o dyamc coece (b) o se #8 esulg om he acceleogam calculaed a he ee suace om ecodg "Tbls- 00" o he deph z=-43.m Cosdeg he sol pole popees (hckess desy shea wave velocy) o hese ses eceved om geologcal es o he bass o he abovemeoed ecoded goud moos wee calculaed he hee-compoes o me-hsoes o he goud suace o he ses. The a he al phase o aalyss he hee compoes o elasc acceleao espose 4-50

10 speca ad specal cuves o dyamc coece have bee ploed. Fg.4 dsplays he eec o local sol codo o he dyamc coece o he cocee se ¹8 ude aco o Tbls-00 ecods. ccodg o he obaed esuls he value o he amplcao aco as ao o he maxmum acceleaos o he goud suace ad o he bedock was compued. The aalyss shows ha he gve sol popees o he ses ude vesgao he amplcao acos ae chaged om.5 o.6. Summay The complex appoach o smulao goud moo ad cosuco o he hozoal ad vecal elasc espose speca ad coespodg dyamc coece specal cuves ae poposed whch accou o he locao o he eahquake souce zoes ad sesmologcal ad geologcal chaacescs o he Tbls ego ad cocee cosuco ses. Based o he empcal elaos ad chaacescs o he eahquake souce zoes he values o mea acceleaos o goud moo o %/ ad % pobables o beg exceeded 50 yeas expeced he ses o Tbls cy has bee deemed ad appopae pobablsc hozoal ad vecal elasc espose speca ad specal dyamc coeces ae calculaed (ca be used sesmc desg ad aalyss o sucues). O he eoy ude examao o he cocee cosuco ses esul o expemeal eseach he dyamc paamees o sol geologcal layes ae deemed ad based o he heoy o mulple eleced waves he goud moo o he ses o Tbls cy hozoal ad vecal elasc espose speca ad specal dyamc coeces ae calculaed he coeced shapes cosdeg he local ses codos o II ad III caegoy o sol ae cosuced whch ca be wdely appled he pacce o eahquake egeeg Geoga. kcowledgeme The desgaed pojec has bee ullled by acal suppo o Geoga Naoal Scece Foudao (Ga #GNSF/ST08/7-484). y dea hs publcao s possessed by he auhos ad may o epese he opo o Geoga Naoal Scece Foudao sel. Reeeces [] Euocode 8: Desg o sucue o eahquake essace-pa :Geeal ules sesmc acos ad ules o buldgs. Euopea Sadad EN 998-:004. [] Buldg Code: Eahquake Egeeg PN Geoga Msy o Ecoomc Developme Tbls Geoga 009. [3] Rekvava P. ad Mdva K. Elaboao o he Sesmc Iluece Spaal Models o Peomace- Based Desg Cosdeg Sesmologcal ad Egeeg-Geologcal Codos o Tbls Rego Teoy Geoga Naoal Scece Foudao Ga N GNSF/ST08/ [4] Rezaea S. ad De Kuegha. Sochasc Modelg ad Smulao o Goud Moos o Peomace-Based Eahquake Egeeg PEER Repo 00/0 Uvesy o Caloa Bekeley 00. [5] Rekvava P. ad Mdva K. Modelg o Eahquake Goud Moo o Tbls Rego. Global Joual o Reseaches Egeeg. Revoluos Egeeg 0(3) [6] Javakhshvl Z. aazaashvl O. Bukashvl N. Iepeao Macosesmc alley o Geoga. Joual o Geoga Geophyscal Socey [7] Sm P. zumza. Javakhshvl Z. eev S. Maye-Rosa D. Balassaa S. ad Cheldze T. The Dgal cceleogaph Newok he Caucasus. Eahquake Hazad ad Sesmc Rsk Reduco [8] Mkhalova N.N. ad pkaev F.F. Some Coelao Relaos bewee Paamees o Sesmc Moo. Joual O Eahquake Pedco Resech 5()

11 [9] Napevadze Sh.G. Some Poblems o Egeeg SesmologyMeceeba Publshg Tbls Geoga