Králik Juraj

Scenario Scenario of possible accidentsof possible accidents Scenario Scenario of possible accidentsof possible accidents

22

Brief look atBrief look at the principal problems of the principal problems of PSA 3 level analysisPSA 3 level analysis Brief look atBrief look at the principal problems of the principal problems of PSA 3 level analysisPSA 3 level analysis

Nonlinear analysis Nonlinear analysis of the concrete containmentof the concrete containment Nonlinear analysis Nonlinear analysis of the concrete containmentof the concrete containment

Probability analysis Probability analysis of the concrete containment failure using of the concrete containment failure using RSM methodRSM method Probability analysis Probability analysis of the concrete containment failure using of the concrete containment failure using RSM methodRSM method

ConclusionsConclusions ConclusionsConclusions

FE - modelFE - model of the NPP structures of the NPP structures FE - modelFE - model of the NPP structures of the NPP structures

MonitoringMonitoring of NPP and definition of the of NPP and definition of the investigation tasksinvestigation tasks MonitoringMonitoring of NPP and definition of the of NPP and definition of the investigation tasksinvestigation tasks

26 April 1986

Chernobyl power plant in 2003 with the sarcophagus containment

structureAerial view of the damaged core on

May 3, 1986. Roof of the turbine hall

is damaged (image center). Roof of

the adjacent reactor 3 (image lower

left) shows minor fire damage.

The battle to contain the contamination and avert a greater catastrophe ultimately involved over 500,000 workers and cost an estimated 18 billion rubles. A 2006 report predicted 30,000 to 60,000 cancer deaths as a result of Chernobyl fallout. 33

Unit 1 und 3

Hydrogen burn inside the

reactor service floor

Destruction of the steel-frame

roof

Reinforced concrete reactor

building seems undamaged

Spectacular but minor safety

relevant

2. Accident progression

44

PCCV Model after the Structural Failure Mode Test

The design pressure is 0.39 MPa. *** Failure pressure is 1.42 MPa

55

Definition fo the Definition fo the scenario for LOCAscenario for LOCA loads loads Definition fo the Definition fo the scenario for LOCAscenario for LOCA loads loads

Program Program ANSYS ANSYS and own programs and own programs CREEP, SHRINK and CRACKCREEP, SHRINK and CRACK Program Program ANSYS ANSYS and own programs and own programs CREEP, SHRINK and CRACKCREEP, SHRINK and CRACK

Consideration of the longConsideration of the long-term-term influence of the influence of the temperature, creep temperature, creep

and shrinkageand shrinkage of concrete after 20 yearsof concrete after 20 years

Consideration of the longConsideration of the long-term-term influence of the influence of the temperature, creep temperature, creep

and shrinkageand shrinkage of concrete after 20 yearsof concrete after 20 years

Consideration of the Consideration of the soil-structure interactionsoil-structure interaction, the influence of the soil, the influence of the soil

consolidation after 20 yearsconsolidation after 20 years

Consideration of the Consideration of the soil-structure interactionsoil-structure interaction, the influence of the soil, the influence of the soil

consolidation after 20 yearsconsolidation after 20 years

Investigation of the Investigation of the concrete cracking and crushing concrete cracking and crushing Investigation of the Investigation of the concrete cracking and crushing concrete cracking and crushing

CheckingChecking of calculation model and its of calculation model and its accuracyaccuracy CheckingChecking of calculation model and its of calculation model and its accuracyaccuracy

66

88

Definition PSA 3 levelDefinition PSA 3 level

Systematic study of the possibilities of the Systematic study of the possibilities of the penetration hermetic zone penetration hermetic zone due to due to

accident of the various technology segments considering the accident of the various technology segments considering the uncertainties of uncertainties of

the structures and accident posibilities. the structures and accident posibilities.

Aim of the PSA 3 levelAim of the PSA 3 level

Definition of Definition of failure pression failure pression ppuu and its and its probability distribution probability distribution in in

dependency of all posibility uncertainties dependency of all posibility uncertainties ((action effects and structure action effects and structure

resistanceresistance))

Three sourses of uncertainties for PSA 3 levelThree sourses of uncertainties for PSA 3 level

1. Definition of 1. Definition of plant damage states plant damage states (PDS)(PDS)

2. 2. SimulationSimulation of the problem, including of the problem, including eventevent treetree construction and models construction and models

3. Input 3. Input datadata used to feed models used to feed models

Each PDS consists of a collection of Each PDS consists of a collection of core damage sequencescore damage sequences, which are , which are

expected to behave similarly following the onset of core damage. expected to behave similarly following the onset of core damage.

The PDS set includes The PDS set includes 69 possible combinations 69 possible combinations of PDS parameter values. It of PDS parameter values. It

should be noted that not all of the possible combinations of PDS parameter should be noted that not all of the possible combinations of PDS parameter

values need to be considered. The grouping diagram for core damage sequences values need to be considered. The grouping diagram for core damage sequences

in the full power state is shown in follow schemein the full power state is shown in follow scheme

99

1111

Four main source of Accident progression Four main source of Accident progression

1.1. Large LOCA (2x Large LOCA (2x 500mm) 500mm)

2.2. Transients or small LOCA (Transients or small LOCA (13mm, 13mm, 32mm, 32mm, 71mm )71mm )

3.3. Interfacing LOCAInterfacing LOCA

4.4. Open reactor (or fuel pool)Open reactor (or fuel pool)

CTMT and EWST pressure in time

020406080

100120140160180200220240

0 319 618 948 1264 1636 2030 2948

Time [min]

Pre

ss

ure

[k

Pa

]

CTMT

EWST

CTMT and EWST pressure in time

020406080

100120140160180200220240

0 319 618 948 1264 1636 2030 2948

Time [min]

Pre

ss

ure

[k

Pa

]

CTMT

EWST

ppmax max = 135,5kPa= 135,5kPappmax max = 135,5kPa= 135,5kPa

ppmax max = 222,7kPa= 222,7kPappmax max = 222,7kPa= 222,7kPa

CTMT and EWST pressure

0

40

80

120

160

200

240

0,00 0,10 0,34 0,55 0,81 1,03

Time [min]

Pre

ssu

re [

kP

a]

CTMT

EWST

CTMT and EWST pressure

0

40

80

120

160

200

240

0,00 0,10 0,34 0,55 0,81 1,03

Time [min]

Pre

ssu

re [

kP

a]

CTMT

EWST

1212

pp = 87kPa= 87kPapp = 87kPa= 87kPa

CTMT and EWST temperature in time

0

20

40

60

80

100

120

140

160

180

0 319 618 948 1264 1636 2030 2948

Time [min]

Te

mp

era

ture

[o

C]

Box PG

HN

CTMT and EWST temperature in time

0

20

40

60

80

100

120

140

160

180

0 319 618 948 1264 1636 2030 2948

Time [min]

Te

mp

era

ture

[o

C]

Box PG

HN

TTmax max = 156= 156ooCCTTmax max = 156= 156ooCC

TTmax max = 149= 149ooCCTTmax max = 149= 149ooCC

CTMT and EWST temperature

0

30

60

90

120

150

180

0,00 1,03 8,81 40,38 83,02 129,03

Time [min]

Tem

per

atu

re [

oC

]

CTMT

EWST

CTMT and EWST temperature

0

30

60

90

120

150

180

0,00 1,03 8,81 40,38 83,02 129,03

Time [min]

Tem

per

atu

re [

oC

]

CTMT

EWST

1313

TT = 60= 60ooCCTT = 60= 60ooCC

1515

EWSTEWST

Steel corrosion

11,211,311,411,511,611,711,811,912,012,1

0 5 10 15 20 25 30 35Time [years]

Dia

me

ter

[mm

] Sommer

Faraday

Steel corrosion

11,211,311,411,511,611,711,811,912,012,1

0 5 10 15 20 25 30 35Time [years]

Dia

me

ter

[mm

] Sommer

Faraday

t

tcorrot

o

dttiDD 0232.0 t

tcorrot

o

dttiDD 0232.0 D(t) = Do A tcorrBD(t) = Do A tcorrB

Faraday’s law Sommer’s law

2020

NPP V1 Jaslovské Bohunice

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

0 10 20 30 40 50 60 70 80 90

Steam pressure [kPa]

Dis

plac

emen

t [m

m]

S7_exp

S7_num

S9_exp

S9_num

S8_exp

S8_num

NPP V1 Jaslovské Bohunice

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

0 10 20 30 40 50 60 70 80 90

Steam pressure [kPa]

Dis

plac

emen

t [m

m]

S7_exp

S7_num

S9_exp

S9_num

S8_exp

S8_num

2121

IInn tthhiiss mmooddeell tthhee bbiilliinneeaarr ssttrreessss--ssttrraaiinn ddiiaaggrraamm ffoorr ccoonnccrreettee aanndd KKuuppffeerr''ss bbiiddiimmeennssiioonnaall

ffaaiilluurree ccrriitteerriioonn ooff ccoonnccrreettee iiss ccoonnssiiddeerreedd.. TThhee ssttrreessss--ssttrraaiinn ddiiaaggrraamm iiss iinnttrroodduucceedd iinn tthhee

mmooddiiffiieedd ffoorrmm iinnttoo tthhee EENNVV 11999922--11--11 ((11999911))

-- iinn ccoommpprreessssiioonn 0 cu

.2.1

..

2

k

kfc ,,

c

)0035.0,0022.0( cuc ((55))

--iinn tteennssiioonn mt

)/).(2exp(. tmttf SShheeaarr mmoodduulluuss iiss rreedduucceedd aafftteerr ccrraacckkiinngg aaccccoorrddiinngg ttoo tthhee llaaww ddeerriivveedd bbyy KKoollmmaarr..

IInn tthhiiss mmooddeell tthhee bbiilliinneeaarr ssttrreessss--ssttrraaiinn ddiiaaggrraamm ffoorr ccoonnccrreettee aanndd KKuuppffeerr''ss bbiiddiimmeennssiioonnaall

ffaaiilluurree ccrriitteerriioonn ooff ccoonnccrreettee iiss ccoonnssiiddeerreedd.. TThhee ssttrreessss--ssttrraaiinn ddiiaaggrraamm iiss iinnttrroodduucceedd iinn tthhee

mmooddiiffiieedd ffoorrmm iinnttoo tthhee EENNVV 11999922--11--11 ((11999911))

-- iinn ccoommpprreessssiioonn 0 cu

.2.1

..

2

k

kfc ,,

c

)0035.0,0022.0( cuc ((55))

--iinn tteennssiioonn mt

)/).(2exp(. tmttf SShheeaarr mmoodduulluuss iiss rreedduucceedd aafftteerr ccrraacckkiinngg aaccccoorrddiinngg ttoo tthhee llaaww ddeerriivveedd bbyy KKoollmmaarr..

efcf

loading

eq

t

ef etf

efcf

c cu cm

tm

loading

unloading

efcf

loading

eq

t

ef etf

efcf

c cu cm

tm

loading

unloading

2323

In this model is considered the bilinear stress-strain diagram for concrete and Kupfer's

bidimensional failure criterion of concrete (see fig.6). The failure function is

- In compression-compression state

cefc f

a

af .

.1

.65.3.12

,

2

1

c

ca

- In tension-compression state

eccefc rff . ,

c

cec fr 13278.5.1

,

9,0ecr - In tension-tension state

ettef rfft

. , BA

BAAret .

.1 ,

AxKB . , cc fx 2 ,

0.1 xret , .12,0 xret

c2efc f

a1

a65.31f

Compressive Failure

Fig.6 Bidimensional conrete model

TensilFailure2

1

c

ca

fc

effc

1c2c

fc

2424

The matrix of material stiffness is diagonal l in the case of concrete cracking in one

direction. If c is the orientation angle of the principal direction of the relative deformation

in the concrete layer and s is the reinforcement orientation, we can get a global matrix of a

constitution relation for lth layer in the form

n

j

ls

ls

Tls

lc

lc

Tlc

lcr

1

TDTTDTD ,

where Tc , Ts are the transformation matrices for the concrete and steel elements.

s

lzx

s

lyz

lxy

ly

llx

lxy

l

lx

lxy

llx

l

l

k

Gk

G

G

EBEB

EBEB

00000

00000

00000

000000

0000

0000

D,

lx

lxy

ly

lyl

EE

EB

2

,

2525Shell91

Concrete - Ec = 16,4Gpa, = 0,2, fc= -43Mpa, ft= 2Mpa Steel - Es = 201Gpa, = 0,3, fs= 670Mpa Concrete - Ec = 16,4Gpa, = 0,2, fc= -43Mpa, ft= 2Mpa Steel - Es = 201Gpa, = 0,3, fs= 670Mpa

65

9

9

2x23,5

Plate D3

0

10

20

30

40

50

60

0 5 10 15 20Displacement w [mm]

Fo

rce

F [

kN]

Experiment

Numerical

Plate D3

0

10

20

30

40

50

60

0 5 10 15 20Displacement w [mm]

Fo

rce

F [

kN]

Experiment

Numerical

2626

Non-linear containment analysis

0

20

40

60

80

100

120

0 50 100 150 200 250 300

Overpressure in HZ [kPa]

Uti

liza

tio

n o

f s

ec

tio

n [

%]

with steel liner

without steel liner

Non-linear containment analysis

0

20

40

60

80

100

120

0 50 100 150 200 250 300

Overpressure in HZ [kPa]

Uti

liza

tio

n o

f s

ec

tio

n [

%]

with steel liner

without steel liner

210kPa210kPa260kPa260kPa

3131

The reliability condition is defined in the form

SF = R - E ≥ 0, various in the form relative SF = R / Ed -1 ≥ 0

where R is the capacity of structure, E - the load action.

The reliability of the shell structure is defined depending on concrete

failure condition for layered shell as follow

R = Fui (pvar(t,) ; up ; ) + up ,

where pvar(t,) is the variable strain vector

The total strain vector for l th load level

gvar , Tvar , pvar and evar are the variable defined by histograms

3333

var var var var var, , . , . , . .l l l lg th pt t g t T t p e

Input quantities

V a r i a b l e c o n s t a n t s

Elasticity modul

evar

Tempe-rature

Tvar

Live load

gvar

Failure criterium

fvar

Mean value 1 1 1 1

Standard deviation σ

0,111 0,10 0,10 0,15

var var var var var, , . , . , . .l l l lg th pt t g t T t p e

3434

1 1 1

ˆ .NRV NRV NRV

o i i ij i ji i j

Y c c X c X X

1 1 1

ˆ .NRV NRV NRV

o i i ij i ji i j

Y c c X c X X

3535

( ) ( ) ( ) ( )f f E R E Rp dp f x x dx x f x dx

where where ffEE(x), f(x), fRR(x) (x) are the density functions and are the density functions and EE(x)(x),, RR(x) (x) are the distribution are the distribution

functions of action functions of action EE and resistance and resistance RR

Probability of failureProbability of failure

Aproximation and simulationAproximation and simulation

Number of variability input : 4Number of variability input : 4 Number of simulations CCD : 25Number of simulations CCD : 25

Intelligent System Design Lab.Intelligent System Design Lab.

Original System

x1

x

2-1 0

1

1

0

-1

DOE and Experiments

Black BoxedSystem

Black BoxedSystem

Input

1x

2x

Response

y

RS Model

20 i i ii i ii i jy c c x c x c x x 20 i i ii i ii i jy c c x c x c x x

RSM : Response Surface MethodRSM : Response Surface Method : Response Surface Model: Response Surface Model

3636

1 1 1

ˆ .NRV NRV NRV

o i i ij i ji i j

Y c c X c X X

Central Composite DesignCentral Composite Design Box-Behnken MatrixBox-Behnken Matrix

3737

Number of variability input : 4Number of variability input : 4Number of simulations CCD : 25Number of simulations CCD : 25

Number of variability input : 4Number of variability input : 4Number of simulations BBM : 25Number of simulations BBM : 25

AproximaAproximationtion met methodshods - RS - RSMM : :

AdvantagesAdvantages

• • reduction of simulation quantitiesreduction of simulation quantities

• • posibilities to use the posibilities to use the „design experiments“ „design experiments“ or or „„regresion analysis”regresion analysis”

• • independence of simulationsindependence of simulations

DisadvantagesDisadvantages

• • Number of simulation increase with the number of input simplesNumber of simulation increase with the number of input simples

• • Non acceptable for non continuous problemsNon acceptable for non continuous problems

3838

3939

PPmm=320kPa=320kPaModel without deqradation SF=83,4%Model without deqradation SF=83,4%

Model with deqradation SF=94,8%Model with deqradation SF=94,8%

4040

Pressure pPressure pmm=260 kPa=260 kPa

Pressure pPressure pmm=320 kPa=320 kPa

4141

Probability of the containment failure is less as 10-6 for overpressure 320kPa

and the original model without degradation effects.

Probability of the containment failure is equal to 1,375.10-4 for overpressure 320

kPa considering degradation effects.

The The degradationdegradation - the bottom EWST plate and wall vertical microcracks – - the bottom EWST plate and wall vertical microcracks –

decrease the safety of CTMT structure, but not significant decrease the safety of CTMT structure, but not significant (about 15%)

The RSM method is very effective method for nonlinear problems on robust

FE- models.

Králik Juraj

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