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
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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
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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
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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
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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

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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
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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.
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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.