Fragility Analysis of the Reactor Steel Shaft Door Due to Accidental Extreme Overpressure

SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 23 | NUMBER: 2 | 2023 | DECEMBER © 2023 VSB - TECHNICAL UNIVERSITY OF OSTRAVA FACULTY OF CIVIL ENGINEERING 5 FRAGILITY ANALYSIS OF THE REACTOR STEEL SHAFT DOOR DUE TO ACCIDENTAL EXTREME OVERPRESSURE Ju aj KRÁLIK 1 , Joze BOČKAJ 1 1 Ins i u e o Fo ensic Enginee ing, Facul y o Ci il Enginee ing, Slo ak Uni e si y o Technology, Radlinského 11, 810 05 B a isla a, Slo akia ju aj.k alik@s uba.sk, joze .b[email p o ec ed]k DOI: 10.35181/ ces-2023-0008 Abs ac . This pape desc ibes he p obabilis ic nonlinea analysis o he he me ic s eel doo o he eac o sha ailu e due o ex eme p essu e and empe a u e. The p obabilis ic assessmen o NPP s uc u es o P obabilis ic Sa e y Analysis (PSA2) le el 2 o VVER 440/213 in he case o he echnology acciden s is p esen ed. The scena io o he ha d acciden in nuclea powe plan (NPP) and he me hodology o he calcula ion o he agili y cu e o he ailu e o e p essu e using he p obabilis ic sa e y assessmen PSA 2 le el is p esen ed. The nonlinea de e minis ic and p obabilis ic analysis based on he esponse su ace me hod (RSM) we e conside ed. Keywo ds Ansys, agili y, he me ic doo , nuclea sa e y, nonlinea analysis, p obabili y, PSA, RSM, echnology acciden . 1. In oduc ion The IAEA (In e na ional A omic Ene gy Agency) in Vienna [1] adop ed a la ge-scale p ojec "S ess Tes s o NPP", which de ines new equi emen s o he e i ica ion o he sa e y and eliabili y o NPP due o he acciden o NPP in Fukushima. Based on he ecommenda ions o he IAEA in Vienna [1], he p obabilis ic me hodology o he sa e y and eliabili y o he NPP s uc u es was accep ed o he p oblem o he sa e y o he c i ical s uc u es. The sa e y documen s o NRC [2], [3] and IAEA [1] ini ia e he equi emen s o e i y he he me ic s uc u es o NPP loaded by wo combina ions o he ex eme ac ions. Fi s ex eme loads a e conside ed o he p obabili y o exceedance 10-4 by yea and second o 10-2 by yea . O he ac ion e ec s a e conside ed as he cha ac e is ic loads du ing he acciden . In he case o he loss-o -coolan acciden (LOCA) he s eam p essu e expands om he eac o hall o he bubble condense [4]. The eac o and he bubble condense ein o ced s uc u es wi h s eel line a e he c i ical s uc u es o he NPP he me ic zone [4]. Nex , one om he c i ical echnology s uc u es a e he eac o he me ic co e s and doo s. Fig. 1: Sec ion plane o he NPP wi h eac o VVER440/213. The NPP wi h he eac o VVER440 consis o ou buildings – eac o building, leng hwise side building, c oss side building and u bine hall (Fig.1). The FEM model o he NPP was c ea ed in he so wa e ANSYS. Fig. 2: Scheme o he sa e y sys em o he he me ic zone. On he base o he global analysis o he sa e y o he NPP s uc u es unde he echnology acciden in SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 23 | NUMBER: 2 | 2023 | DECEMBER © 2023 VSB - TECHNICAL UNIVERSITY OF OSTRAVA FACULTY OF CIVIL ENGINEERING 6 acco dance wi h he in e na ional s anda ds [1], [5] he de ailed analysis o he he me ic co e , p o ec i e hood, and doo s. The sa e y scheme o he he me ic doo s and he he me ic zone a e p esen ed in Fig.2. The nonlinea analysis and he ull p obabilis ic analysis we e used as he inpu da a o he nex isk analysis o he NPP s uc u es in acco dance wi h he in e na ional s anda ds. Tab.1: The assumed scena ios o he acciden s in he he me ic zone The Commission NRC [2] uses he p obabilis ic isk assessmen (PRA) o es ima e isk by compu ing eal numbe s o de e mine wha can go w ong, how likely is i , and wha a e i s consequences. Thus, PRA p o ides insigh s in o he s eng hs and weaknesses o he design and ope a ion o a nuclea powe plan . Fo he ype o NPP a PRA can es ima e h ee le els o isk: • A Le el 1 PRA es ima es he equency o acciden s ha cause damage o he nuclea eac o co e. This is commonly called co e damage equency (CDF). • A Le el 2 PRA, which s a s wi h he Le el 1 co e damage acciden s, es ima es he equency o acciden s ha elease adioac i i y om he nuclea powe plan . • A Le el 3 PRA, which s a s wi h he Le el 2 adioac i i y elease acciden s, es ima es he consequences in e ms o inju y o he public and damage o he en i onmen . The de ini ion o he agili y cu e o NPP gene ally ep esen s a c ucial s ep o he le el 2 p obabilis ic sa e y assessmen (PSA2), whe e he p obabili y o s uc u e ailu e can be e alua ed as he con olu ion o he agili y cu e wi h he load cu e. The assessmen o he s uc u al s eng h o he nuclea powe plan has acqui ed e en a g ea e impo ance in he amewo k o pos -Fukushima s ess es s whe e he assessmen o he sa e y ma gin and o -design condi ions [6]. 2. Scena io o he echnology acciden The p e ious analysis was achie ed o he o e p essu e alue o 100kPa due o design basic acciden (DBA), which co esponds o he loss o coolan acciden due o guillo ine cu ing o he coolan pipe [4]. When he ba bo age owe ope a es in he pa ial o ze o pe o mance he o e p essu e is equal o he 150 - 300 kPa. The ENEL p opose he maximum empe a u e in he eac o sha is equal abou o 1.800oC and in he con ainmen a ound he eac o sha is equal abou o 350oC [4]. The possibili y o he empe a u e inc easing o he con ainmen ailu e s a e is conside ed in he scena io oo. In he case o he ha d acciden he o e p essu e can be inc eased linea ly, and he in e nal and ex e nal empe a u e a e cons an . Th ee ypes o he scena ios we e conside ed (Tab.1). The c i ical was he acciden du ing 7 days wi h he o e p essu e 250kPa, in e nal empe a u e 150oC and ex e nal empe a u e -28oC. 3. Calcula ion model The echnology segmen s o he NPP he me ic zone a e made om he s eel. The he me ic s eel doo s ype A262 (wi h dimension 1600/900/150 mm) a e loca ed a he eac o sha . The s eel doo s ul il bo h he sealing and shielding unc ions. The echnology segmen s o he NPP he me ic zone a e made om he s eel (S235). Fig. 3: Scheme o he eac o sha he me ic doo - ype A262. Fig. 4: FEM model o he eac o sha he me ic doo . The s eel doo is i ed in he ame cas in conc e e and Type Du a ion O e p essu e in HZ [kPa] Ex eme empe a u es [oC] I. 1hou - 1day 150 127 II. 2hou s - 7days 250 150 III. 1yea - 80 - 120 SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 23 | NUMBER: 2 | 2023 | DECEMBER © 2023 VSB - TECHNICAL UNIVERSITY OF OSTRAVA FACULTY OF CIVIL ENGINEERING 7 sealed o he ame wi h double ubbe packing o 150 mm in wid h. The FEM model o he he me ic s eel doo is shown in Fig.4. The de ailed FEM model has 199.469 SOLID185 and CONTA173 elemen s. 4. Accep ance c i e ia In he case o he nonlinea analysis he he mal depended ma e ial p ope ies a e used ollowing he inpu da a o ma e ial 08CH18N10T de ined in s anda d CSN 413240, CSN 411700, CSN 413230, CSN 413240 and NTD SAI Sec ion II. The c i e ion o he max. s ess alues is limi ed by he H-M-H plas ic po en ial [4], [8] and [9]. The ailu e o he s eel s uc u e is limi ed by he max. s ain alues o by he s abili y o he nonlinea solu ion [10] and [11]. The s anda d STN EN 1993 1-2 [9] de ine ollowing cha ac e is ic alues o he s ain o he s uc u al s eel : - yield s ain , 0.02 ay    - ul ima e s ain , 0.15 au    - max. limi s ain , 0.20 ae    Fig. 5: S ess-s ain ela ionship o he s eel dependen on empe a u e. The s ess-s ain ela ionship o he s eel (Fig.5) a e conside ed in acco dance wi h Eu ocode [9] and [10] on dependency o empe a u e le el o hea ing a es be ween 2 and 50K/min. In he case o he s eel he s ess-s ain diag am is di ided on ou egions. The s ess-s ain ela ions a e de ined in ollowing o m in egion I:   2 2 ,,,aay aya b c a a      , (1)  2 ,,,, ,ay ap ay ap a acE      ,  22 ,, ,aay ap bE cc     ,   2 ,, ,, , , , 2 ay ap aay ap ay ap cE         . and in egion III: ,,aay    . (2) 5. Nonlinea analysis The nonlinea analysis based on po en ial heo y conside ing he iso opic ma e ial p ope ies was made o he solid elemen s SOLID185 and CONTA173 elemen s [8] in he FEM model. The s eel is ypical iso opic ma e ial. The elas ic- plas ic beha iou o he iso opic ma e ials is desc ibed by he HMH yield c i e ion [8]. Consequen ly, he s ess-s ain ela ions a e ob ained om he ollowing ela ions:        pl el el Q dDdd Ddd            , (3) whe e ep D   is elas ic-plas ic ma ix in he o m :     T ee ep e T e QF DD DD FQ AD                   . (4) The ha dening pa ame e A depends on he yield unc ion and model o ha dening (iso opic o kinema ic). Hube -Mises-Hencky (HMH) de ine he yield unc ion in he o m:  eq T  , (5) whe e eq  is equi alen s ess in he poin and   o   is yield s ess depends on he ha dening. In he case o kinema ic ha dening by P age ( e sus Ziegle ) and he ideal Bauschinge ’s e ec is gi en 2 2 9 T AH E    . (6) The ha dening modulus H’ o his ma e ial is de ined in he o m: eq T pp eq eq dd Hdd    . (7) When his c i e ion is used wi h he iso opic ha dening op ion, he yield unc ion is gi en by:      0 T oep FM    , (8) whe e   oep is he e e ence yield s ess,  ep is he equi alen plas ic s ain and he ma ix [M] is diagonal. On he base o he elas ic-plas ic heo y and he HMH unc ion o plas ici y he ex eme s ain and s ess o he SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 23 | NUMBER: 2 | 2023 | DECEMBER © 2023 VSB - TECHNICAL UNIVERSITY OF OSTRAVA FACULTY OF CIVIL ENGINEERING 8 eac o he me ic doo o he acciden scena io ype II we e calcula ed. The ma ix [M] is de ined as ollows:  100000 010000 001000 000200 000020 000002 M           . (9) 6. P obabili y nonlinea assessmen The p obabilis ic me hods a e e y e ec i e o analyze o he sa e y and eliabili y o he s uc u es conside ing he unce ain ies o he inpu da a [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22] and [23]. The p obabili y analysis o he loss o he eac o co e in eg i y was [4], made o he o e p essu e loads om 250 kPa o 7000 kPa using he nonlinea solu ion o he s a ic equilib ium conside ing he geome ic and ma e ial nonlinea i ies o he s eel shell and beam elemen s. The p obabili y nonlinea analysis o he echnology segmen s is based on he p oposi ion ha he ela ion be ween he inpu and ou pu da a can be app oxima ed by he app oxima ion unc ion in he o m o he polynomial [7, 8]. The ull p obabilis ic assessmen was used o ge he p obabili y o echnology segmen ailu e. The sa e y o he echnology segmen s was de e mined by he sa e y unc ion SF in he o m [10] SF E R and 01SF, (10) whe e E is he ac ion unc ion and R is he esis ance unc ion. The eliabili y unc ion RF is de ined in he o m:  ,1 0RF g R E SF R E , (11) whe e  , g RE is he eliabili y unc ion. The p obabili y o ailu e can be de ined by he simple exp ession:    0 PPREPRE    . (12) The eliabili y unc ion RF can be exp essed gene ally as a unc ion o he s ochas ic pa ame e s X1, X2 o Xn, used in he calcula ion o R and E. 12 ( , ,..., ) n RF g X X X. (13) The ailu e unc ion g({X}) ep esen s he condi ion (capaci y ma gin) o he eliabili y, which can be ei he an explici o implici unc ion o he s ochas ic pa ame e s and can be single (de ined on one c oss-sec ion) o complex (de ined on se e al c oss-sec ions, e.g., on a complex ini e elemen model). In he case o he nonlinea analysis he co ec solu ion o he elas ic-plas ic beha io o he s uc u es is de e mined by he unc ion plas ici y. The HMH unc ion o he plas ici y was used o he nonlinea solu ion o he s eel echnology segmen s. This plas ici y unc ion is de ined in he o m: y R  and e E  , (14) whe e he e ec i e s ess e  (Von Mises s ess) is de ined as ollows  1 2 222 12 21 31 1 2 e        . (15) The ailu e o he s eel echnology segmen s in he ame o he PSA analysis is de ined by he ul ilimi e alues o he maximal s ain de o ma ion. This ailu e unc ion is de ined in he o m: ,ay R    and e E  , (16) whe e he e ec i e s ain e  (Von Mises s ain) is de ined as ollows  1 2 222 12 21 31 11 12 e          , (17) whe e   is he e ec i e Poisson cons an . The ailu e p obabili y is calcula ed om he e alua ion o he s a is ical pa ame e s and heo e ical model o he p obabili y dis ibu ion o he eliabili y unc ion Z = g(X) using he simula ion me hods. The ailu e p obabili y is de ined as he bes es ima ion on he base o nume ical simula ions in he o m:  1 10 N i i pIgX N    , (18) whe e N in he numbe o simula ions, g(.) is he ailu e unc ion, I[.] is he unc ion wi h alue 1, i he condi ion in he squa e b acke is ul illed, o he wise is equal 0. The ull p obabilis ic analysis esul om he nonlinea analysis o he se ies simula ed cases conside ed he unce ain ies o he inpu da a. The a ious simula ion me hods (di ec , modi ied o app oxima ion me hods) can be used o he conside a ion o he in luences o he unce ain y o he inpu da a [4]. In case o he nonlinea analysis o he ull FEM model he app oxima ion me hod RSM (Response su ace me hod) is he mos e ec i e me hod [8]. The RSM me hod assumes ha i is possible o de ine he dependency be ween he a iable inpu and he ou pu da a h ough he app oxima ion unc ions in he ollowing o m: 1 2 11 1 NNNN oiiiii ijij ii iji Yc cX cX cXX         , (19) whe e co is he index o he cons an membe ; ci a e he indices o he linea membe and cij he indices o he SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 23 | NUMBER: 2 | 2023 | DECEMBER © 2023 VSB - TECHNICAL UNIVERSITY OF OSTRAVA FACULTY OF CIVIL ENGINEERING 9 quad a ic membe , which a e gi en o p ede e mined schemes o he op imal dis ibu ion o he a iables o o using he eg ession analysis a e calcula ing he esponse. App oxima e polynomial coe icien s a e gi en om he condi ion o he e o minimum, usually by he "Cen al Composi e Design Sampling" (CCD) me hod o he "Box- Behnken Ma ix Sampling" (BBM) me hod [8]. On base o expe imen al design, he unknown coe icien s a e de e mined due o he andom a iables selec ed wi hin he expe imen al egion. The unce ain y in he andom a iables can be de ined in he model by a ying in he a bi a y amoun p oducing he whole expe imen al egion. The o al ec o o he de o ma ion pa ame e s { s} in he FEM is de ined o he s h-simula ion in he o m:       1 ,,,, sGNs ssss KEF FGQPT     , (20) and he s ain ec o     s ss B  , (21) whe e   GN K is he nonlinea s i ness ma ix depending on he a iable pa ame e s and s EF  , F is he HMH yield unc ion de ined in he s ess componen s,   F is he ec o o he gene al o ces depending on he a iable pa ame e s ,,and s ss s GQP T o he s h-simula ion. 7. Unce ain ies o he inpu da a The unce ain ies a e coming om he ollowing sou ces [4], [7], [10] and [14]:  Pa ame e s o ma e ial p ope ies. Based on expe imen s wi h conc e e elemen s he s anda d de ia ion is 11.1%. In case o o he ma e ials his alue is abou 5%.  Assessmen o mechanical cha ac e is ics e o ac o s a e abou 8-12%, i depends on he cons uc ion ma e ial di e ences used o he di e en uni s wi h VVER 440/213. In some cases, i can be conse a i e, in o he cases non-conse a i e impac .  Unce ain ies in he nume ical esul s in he alue o 10-15%. In his a ea we can ake in o conside a ion he s eel line wi h he conc e e elemen s.  Unce ain ies a ising om he empe a u es impac in he alue o 10%.  O he calcula ions assump ions 3-5%. The mean alues and s anda d de ia ions we e de ined in acco dance o he expe imen al es and design alues o he ma e ial p ope ies and he ac ion e ec s [6 and 8] (see Tab.3). Based on he esul s om he simula ed nonlinea analysis o he echnology segmen s and he a iabili y o he inpu pa ame e s 106 Mon e Ca lo simula ions we e pe o med in he sys em ANSYS [8]. Tab.2: Va iabili y o inpu pa ame e s. Quan i y Cha ac . alue Va ia ble Type Mean  De ia [%] Min. alue Max. alue Ma e ial S eng h F k a N 1.10 6.6 0.77 1.35 Ac ion e ec s Dead load G k g a N 1 5 0.81 1.20 Li e load Qk q a GU 0.64 22.6 0.23 1.36 P essu e LOCA p k p a N 1 8 0.70 1.33 Tempe a u e T k a GU 0.67 14.2 0.40 1.15 Model unce ain ies Ac ion E k e a N 1 5 0.81 1.19 Resis ance R k a N 1 5 0.81 1.20 8. P obabili y nonlinea analysis o he eac o doo The calcula ion o he p obabili y o he eac o doo ailu e is based on he esul s o he nonlinea analysis o a ious le el o he acciden p essu e and mean alues o he ma e ial p ope ies. The c i ical a ea o he echnology segmen s de ined om he nonlinea de e minis ic analysis a e he mechanical closu es. The CCD me hod o he RSM app oxima ion is based on 45 nonlinea simula ions depending on he 6 a iable inpu da a. The nonlinea solu ion o he one simula ion consis s abou he 50 o 150 i e a ions depending on he scope o he plas ic de o ma ions in he calcula ed s uc u es. The sensi i i y analysis gi es us he in o ma ion abou he in luences o he a iable p ope ies o he inpu da a o he ou pu da a. These analyses a e based on he co ela ion’s ma ixes. 9. F agili y cu es o ailu e p essu e The PSA app oach o he e alua ion o p obabilis ic p essu e capaci y in ol es limi s a e analyses [4], [7], [10] and [11]. The limi s a es should ep esen possible ailu e modes o he con inemen unc ions. The con ainmen [4] may ail a di e en loca ions unde di e en ailu e modes. Conside wo ailu e modes A and B, each wi h n agili y cu es and espec i e p obabili ies pi (i = 1,…, n) and qj (j = 1,…, n). Then he union C = AB, he agili y FCij (x) is gi en by           Cij Ai Bj Ai Bj F xFxFxFxFx, (22) whe e he subsc ip s i and j indica e one o he n agili y cu es o he ailu e modes and x deno e a speci ic alue o he p essu e wi hin he con ainmen . The p obabili y pij associa ed wi h agili y cu e FCij.(x) is gi en by pi. qj i he median capaci ies o he ailu e modes a e independen . The esul o he in e sec ion e m in (22) is FAj(x), FBj(x) when he andomness in he ailu e mode capaci ies is independen and min [FAi.(x), FBj.(x)] when he ailu e SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 23 | NUMBER: 2 | 2023 | DECEMBER © 2023 VSB - TECHNICAL UNIVERSITY OF OSTRAVA FACULTY OF CIVIL ENGINEERING 10 modes a e pe ec ly dependen . The ollowing is and he consequence o an acciden depends on he o al leak a ea. Mul iple leaks a di e en loca ions o he con ainmen (e.g., bellows, ha ch, and ai lock) may con ibu e o he o al leak a ea. Using he me hodology desc ibed abo e, we can ob ain he agili y cu es o leak a each loca ion. Fo a gi en acciden sequence, he induced acciden p essu e p obabili y dis ibu ion, h ( x ), is known. This is con ol ed wi h he agili y cu e o each leak loca ion o ob ain he p obabili y o leak om ha loca ion ( P Li) . I is unde s ood ha he e is no b eak o con ainmen up u e a his p essu e. Fig. 6: Family o agili y cu es showing modelling unce ain y.    0 1 Li b l phxFxFxdx     , (23) he e  b Fx is he agili y o b eak a he loca ion and  l Fx is he agili y o leak. The leak is o each loca ion speci ied as a andom a iable wi h a p obabili y dis ibu ion. The p obabili y o eac o co e ailu e is calcula ed om he p obabili y o he eliabili y unc ion RF in he o m, P = P ( RF < 0), (24) whe e he eliabili y condi ion RF is de ined depending on a conc e e ailu e condi ion , 1e a y RF    , (25) whe e he ailu e unc ion was conside ed in he o m (16). The agili y cu e o he ailu e p essu e was de e mined using 45 p obabilis ic simula ions using he RSM app oxima ion me hod wi h he expe imen al design CCD o 10 6 Mon e Ca lo simula ions o each model and 5 le el o he o e p essu e. The a ious p obabilis ic calcula ions o 5 cons an le el o o e p essu e nex o he a iable o e p essu e o gauss and uni o m dis ibu ion we e aken ou . The ailu e c i e ion o he s eel s uc u es using HMH (Von Mises) plas ic c i e ion wi h he mul ilinea kinema ic ha dening s ess-s ain ela ions o he a ious le el o he empe a u es and he deg ada ion o he s eng h we e conside ed. The unce ain y o he inpu da a ( ab.2) and he esul s o he nonlinea analysis o he echnological s uc u es o a ious le el o he acciden p essu e we e aken. Fig. 7: F agili y cu es o he s eel eac o sha doo . Fig. 8: F agili y cu es o he conc e e ame abou he eac o sha doo . The idealized agili y cu es o he eac o sha doo a e p esen ed in Fig.7. In case o he ein o ced s uc u e ame abou o he doo he idealized agili y cu es a e p esen ed in Fig.8. 10. Conclusion This epo is based on me hodology o he p obabilis ic analysis o s uc u es o he me ic zone o NPP wi h eac o VVER440/213 de ailed desc ibed in wo k [4]. The nonlinea p obabilis ic analysis o he eac o sha doo ailu e is in acco dance wi h he equi emen s IAEA [1] and NRC [2], expe iences om he simila analysis NPP in ab oad [21], new knowledges om he p obabilis ic analysis o s uc u es [7], [10], [11], [12], [14] and ou expe iences om he p e ious analysis [4]. These analyses go ou om he p e ious esul s o he moni o ing o ma e ial p ope ies [4], and NPP s uc u es, as well as om he esul s o he esis ance analysis o he impo an s uc u al componen s om he poin o he ini ia ed acciden s. The s uc u es we e analysed on impac o he ex eme load’s si ua ion de ined in he scena ios o he in e nal acciden s. Acco ding o he nonlinea de e minis ic analysis we e SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 23 | NUMBER: 2 | 2023 | DECEMBER © 2023 VSB - TECHNICAL UNIVERSITY OF OSTRAVA FACULTY OF CIVIL ENGINEERING 11 de ined he mos c i ical s uc u al componen s o which he alues o he ailu e p essu e o he acciden a e de e mined on base o he bes es ima ion. We p opose om he supposi ion ha he loss o con ainmen in eg i y occu and he pe o mance o he NPP can be unsa e. The c i ical elemen s we e iden i ied aking in o conside a ion also unce ain ies o he inpu da a in he esul s. The nonlinea analysis o he loss o he con ainmen in eg i y was made o he o e p essu e loads om 250kPa using he nonlinea solu ion o he s a ic equilib ium conside ing he geome ic and ma e ial nonlinea i ies o he s eel shell and solid elemen s. The nonlinea analyses we e pe o med in he ANSYS p og am using he HMH plas ic condi ion [8]. The s anda d STN EN 1993 1-2 [9] de ine ollowing cha ac e is ic alues o he s ain o he s uc u al s eel - yield s ain and ul ima e s ain. The p obabili y analysis o he loss o he conc e e con ainmen in eg i y was made o he o e p essu e loads om 250kPa o 7.000kPa using he nonlinea solu ion o he s a ic equilib ium. The unce ain ies o he loads le el ( empe a u e, dead and li e loads), he ma e ial model o he s eel s uc u es as well as he inaccu acy o he calcula ion model and he nume ical me hods [4] we e conside ed in he app oxima ion RSM me hod o CCD expe imen al design and 106 Mon e Ca lo simula ions. This epo is based on he me hodology o he p obabilis ic analysis o s uc u es o he he me ic zone o NPP wi h eac o VVER44/213 de ailed desc ibed in he wo k [4]. The unce ain ies o he loads le el, he ma e ial model o he s eel s uc u es as well as he inaccu acy o he calcula ion model and he nume ical me hods we e conside ed in he app oxima ion RSM me hod o CCD expe imen al design and 106 Mon e Ca lo simula ions [7] and [8]. One om he c i ical echnology segmen s o he con ainmen is he he me ic s eel doo ype A252 wi h he ailu e p essu e pu.0,05 = 4.78MPa. The mean alue o p essu e capaci y o he s eel doo ype A252 is pu.0,50= 5.88MPa, he uppe bound o 95% is pu.0,95= 6.75Ma. These agili y cu es (Fig.7, 8) a e he inpu da a o he ollowing isk analysis o he NPP. Acknowledgmen s The p ojec was ealized wi h he inancial suppo o he G an Agency o he Slo ak Republic (VEGA). The p ojec egis a ion numbe is VEGA No. 1-0453-20. Re e ences [1] IAEA/TA-2488. Guidelines o WWER 440/213 Con ainmen E alua ion, TC P ojec RER/9/035, WWER-SC-l70, Rep. o Consul ans Mee ing, Vienna, augus 1996. [2] NRC, RG 1.200, An App oach o De e mining he Technical Adequacy o P obabilis ic Risk Assessmen Resul s o Risk-In o med Ac i i ies, U.S. Nuclea Regula o y Commission, Washing on, DC. 2009. [3] NUREG/CR-4839, Me hods o Ex e nal E en Sc eening Quan i ica ion: Risk Me hods In eg a ion and E alua ion P og am (RMIEP) Me hods De elopmen , Repo , Sandia Na ional Labo a o ies and U.S. Nuclea Regula o y Commission, 1992. [4] KRÁLIK, J. Risk Assessmen o NPP Sa e y in Case o Eme gency Si ua ions on Technology, In: Monog aph “Recen Imp o emen s o Powe Plan s Managemen and Technology”, Ed. A.B.Nikolic, Z.S.Janda, Pp. 69-96, Pub. INTECH, Sep . 2017, ISBN 978-953-51-3357-5. [5] ASME, Sec ion III, Di . 1, Appendix F, “Rules o E alua ion o Se ice Loadings wi h Le el D Se ice Limi s,” Ame ican Socie y o Mechanical Enginee s, 1998.NRA SR, The s ess es s o Nuclea Powe Plan s Slo akia, ÚJD B a isla a, Sep embe 2011. [6] HALDAR, A. S. MAHADEVAN, P obabili y, Reliabili y and S a is ical Me hods in Enginee ing Design, John Wiley & Sons, New Yo k, 2000. [7] KOHNKE, P. ANSYS, Theo y, SAS IP Inc. Canonsbu g, 2008. [8] STN EN 1993-1-2. Eu ocode 3: Design o s eel s uc u es. Pa 1-2 Gene al ules — S uc u al i e design. [9] HANBOOK 5. Implemen a ion o Eu ocodes Reliabili y Backg ounds. Design o Buildings o he Fi e Si ua ion. De elopmen o Skills Facili a ing Implemen a ion o Eu ocodes. Leona do Da Vinci Pilo P ojec CZ/02/B/F/PP-134007. P ague, CR, 2005. [10] MELCHERS, R. E. S uc u al Reliabili y: Analysis and P edic ion, John Wiley & Sons, Chiches e , 1999, U.K. [11] NOVÁK, D. e al. Small-sample P obabilis ic Asses- smen – so wa e FReET, ICASP 9, 9 h In e na ional Con e ence on Applica ions o S a is ics and P obabili y in Ci il Enginee ing, San F ancisco, USA, July 6-9, 2003, pp. 91-96. [12] NOVÁK, D. BERGMEISTER, K. PUKL, R. ČERVENKA, V., S uc u al assessmen and eliabili y analysis o exis ing enginee ing s uc u es, Theo e ical backg ound. S uc u e and in as uc u e enginee ing, Vol. 9, No. 2, 2009, pp. 267-275. [13] SÝKORA, M. M. HOLICKÝ, Assessmen o Unce ain ies in Mechanical Models, In: Applied Mechanics and Ma e ials, Vol. 378, pp 13-18, © TTP, Swi ze land, 2013. SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 23 | NUMBER: 2 | 2023 | DECEMBER © 2023 VSB - TECHNICAL UNIVERSITY OF OSTRAVA FACULTY OF CIVIL ENGINEERING 12 [14] KALA, Z. Sensi i i y analysis o s eel plane ames wi h ini ial impe ec ions, Enginee ing S uc u es, 33, 8, pp.2342-2349, 2011. [15] KALA, Z. J. KALA, Sensi i i y Analysis o S abili y P oblems o S eel Columns using Shell Fini e Elemen s and Nonlinea Compu a ion Me hods, In p oc. Enginee ing mechanics 2011, 17 h In e na ional Con e ence, ISBN 978-80-87012-33-8, S a ka, 2011. [16] KONEČNÝ, P. e al. Towa ds Pa allel Compu ing using he Simula ion-based Reliabili y Assessmen Me hod. In. P oceedings o he Fi s In e na ional Con e ence on Pa allel, Dis ibu ed and G id Compu ing o Enginee ing, Ci il Comp P ess, p. 542-549. ISBN 978-1-905088-29-4, 2009. [17] KREJSA, M. J. KRÁLIK. P obabilis ic Compu a- ional Me hods in S uc u al Failu e Analysis, Jou nal o Mul iscale Modelling, Vol. 6, No. 2 (5 pages), Impe ial College P ess, DOI: 10.1142/S1756973715500067, 2015. [18] KREJSA, M. e al. P obabilis ic Calcula ion Using Pa allel Compu ing, In Enginee ing mechanics 2016, 22nd In e na ional con e ence. S a ka, ČR, 9. - 12. 5. 2016. 1s . ed. P ague, ITAM AS CR, 2016, p. 347- 350. ISSN 1805-8248. ISBN 978-80-87012-59-8. [19] KREJSA, M. e al. P obabilis ic a igue analysis o exis ing s eel s uc u e. In 4 h In e na ional Scien i ic Con e ence - SPACE 2019, EDP Sciences, Londyn, 2020, ISSN 2261-236X. [20] VEJVODA, S., KERŠNER, Z., NOVÁK, D. & TEPLÝ, B. P obabilis ic Sa e y Assessmen o he S eam Gene a o Co e , In P oc. o he 17 h In e na ional Con e ence on S uc u al Mechanics in Reac o Technology (SMiRT 17), P ague, Czech Republic, Augus 17-22, 2003, in CD, M04-4, 10 pp. [21] KRÁL, P. e al. Using he in e se iden i ica ion o pa ame e s o a nonlinea conc e e ma e ial model o analysis o RC s uc u al elemen . In AIP Con e ence P oceedings, 2019, Vol. 2116, 4 pp. ISSN 0094- 243X. [22] SUCHARDOVÁ, P., BERNATÍK, A., SUCHARDA, O. Assessmen o loss esul s by means o mul i - C i e ia analysis. In: Ad ances in Sa e y, Reliabili y and Risk Managemen - P oc. o he Eu opean Sa e y and Reliabili y Con e ence, ESREL 2011. London: CRC P ess-Taylo & F ancis g oup, pp. 1563-1570. ISBN 978-0-415-68379-1. Abou Au ho s Ju aj KRÁLIK was bo n in B a isla a, Slo akia. He ecei ed his Ph.D. om Facul y o Ci il Enginee ing Slo ak Uni e si y o Technology in B a isla a in 1990. He is p o esso o Applied Mechanics in Facul y o Ci il Enginee ing STU in B a isla a. He is Au ho ized Ci il Enginee , Fo ensic Expe in Ci il Enginee ing and Au ho ized Expe o Sa e y Con ol o Nuclea Powe Plan s. His esea ch in e es s include - S a ics and dynamics o he ci il enginee ing s uc u es, Ea hquake enginee ing, Nonlinea mechanics o s eel and ein o ced conc e e s uc u es, Sa e y and eliabili y o he Nuclea Powe Plan s, Soil-s uc u e and Fluid-s uc u e in e ac ion and o he s. He is he au ho o he ollowing publica ions: Books and ex books: 23, Jou nals: 115, Con e ences: 430, P ojec s and expe ’s epo s: 185. Ci a ion in esea ch pape s: Scopus - 238 ci a ions (h - index 11), Web o Science - 182 ci a ions (h -index 8). Scopus Au ho ID: 57000998100, RESEARCH ID: F- 9699-2017 and ORCID ID: 0000-0002-3706-6041. Joze BOČKAJ was bo n in Dolný Kubín, Slo akia. He ecei ed his Ing. om Facul y o Ci il Enginee ing Uni e si y o Technology in Žilina in 2020. He is doc o al s uden in Facul y o Ci il Enginee ing STU in B a isla a. His esea ch in e es s include – Building cons uc ions, The mal mechanics, Fluid mechanics, Wind enginee ing.