J
ournal o
f
A
pp
Published Onli
n
http://dx.doi.or
g
Open Access
Stud
y
ABSTRA
C
This paper in
t
phasis on dis
c
nese Experi
m
sential for ca
l
calculates the
= 2.42 g, βr
=
moval system
Keywords: S
e
1. Introdu
c
Liquid metal
p
erimental F
a
PWR and B
W
a heat transfe
r
temperature
r
and high boil
i
tage of liqui
d
coefficient. T
h
a sodium-coo
ature makes
s
p
ossible as t
h
temperature
b
tures are bou
n
p
erature equi
p
residual heat
r
of sodium-co
o
Seismic fr
a
which is use
d
ment, and is
a
fragility is o
n
core damage
f
p
aper, seismi
c
three-dimensi
o
gility variabl
e
removal syst
e
p
iping is eval
u
*
Corresponding
a
p
lied Mathemat
i
n
e November 2
0
g
/10.4236/jamp
.
y
on S
e
Zhi
w
C
T
t
roduces the c
o
c
ussing quanti
z
m
ental Fast Re
a
l
culating seis
m
safety factors
=
0.36, βu = 0.
4
has high seis
m
e
ismic Fragili
t
c
tion
sodium is use
d
a
st Reactor (C
E
W
R. The greate
r
medium is t
h
r
ange, which
m
i
ng point is 8
d
sodium is i
h
erefore, the
s
l
ed fast reacto
r
s
tructure stiff
n
h
in as possibl
e
b
rings thermal
n
d to reduce
s
p
ment [1,2]. S
r
emoval syste
m
o
led fast react
o
a
gility analys
i
d
to evaluate r
e
a
key element
i
n
e of the two
f
requency (C
D
c
fragility anal
y
o
nal model o
f
e
s of piping o
f
e
m are
q
uanti
f
u
ated.
a
utho
r
.
i
cs and Physics
,
0
13 (http://ww
w
.2013.16016
e
ismic
F
w
ei Fu
1,2
, Ya
1
Nuclear a
n
2
Chi
n
o
nception of
s
z
ation
p
roces
s
a
cto
r
(CEFR)
m
ic fragility
p
and uncertain
t
4
4, HCLPF =
m
ic capacity.
t
y; Fragility P
a
d
as the coola
n
E
FR), which i
st advantage t
h
h
at it can keep
m
elting point
82.9˚C [1,2].
ts high ther
m
s
tructural com
m
r
are as follo
w
n
ess lower an
d
e
, and at the
s
expansion ef
f
s
eismic capac
i
o, the pipe o
f
m
with typic
a
or
is chosen to
i
s is a prob
a
e
al seismic ca
p
i
n seismic PS
A
parameters
u
D
F) by seismi
c
y
sis method i
s
f
system pipi
n
f
CEFR accid
e
f
ied, and the
,
2013, 1, 82-8
8
w
.scirp.org/jour
n
F
ragilit
y
h
ua Qiao
1
,
L
nd
Radiation S
a
n
a Institute of
A
Email:
*
fu
z
Receive
d
s
eismic fragili
t
s
of seismic fr
a
acciden
t
resid
u
p
arameters. Fi
n
t
ies of CEFR
p
0.65 g. The r
e
a
rameter; CE
F
n
t of China E
x
s different fo
r
m
h
at sodium is
a
liquid in a wi
d
is only 97.8
˚
A
nother adva
n
m
al conductivi
t
m
on features
o
w
s: high temp
e
d
pipe walls
a
s
ame time hi
g
f
ects. These fe
i
ty of high te
m
CEFR accide
n
a
l characteristi
c
study.
a
bilistic meth
o
p
acity of equi
p
A
, while seis
m
u
sed to quanti
f
c
events. In t
h
s
researched, t
h
n
g is build, f
r
e
nt residual he
capacity of t
h
8
n
al
/
jamp
)
y
Anal
y
L
ong Tang
2
,
fety Center of
M
A
tomic Energy,
B
z
hiwei@chinan
s
d
September 20
t
y, gives the
m
a
gility
p
aram
e
u
al heat remo
v
n
ally, combin
e
p
ipeline, and
o
e
sults show th
a
F
R Accident R
e
x
-
m
a
s
d
e
˚
C
n
-
t
y
o
f
e
r-
a
s
g
h
a-
m
-
n
t
c
s
o
d
p
-
m
ic
f
y
h
is
h
e
a-
e
at
h
e
2. Sei
s
2.1. C
o
The se
i
fined a
s
en val
u
leratio
n
tural o
seismi
c
rando
m
of-low
-
some
fa
a give
n
ter. T
h
modes,
ity par
a
tained.
nent b
a
under
a
In
F
ground
standa
r
One jo
b
under
a
2.2. S
e
The en
respon
d
in ter
m
y
sis for
Yan Chen
1
,
M
EP, Beijing,
C
B
eijing, China
s
c.cn
13
m
odel of seis
m
e
ters. Then, es
v
al system, a
n
ed
with quant
i
o
btains the sys
a
t: the
p
ipelin
e
e
sidual Heat
R
s
mic Fra
g
i
l
o
nception o
f
i
smic fragilit
y
s
the conditio
n
u
e of ground
m
n
or peak spe
c
r equipment
f
c
fragility is t
o
m
ness and un
c
-
probability-o
f
fa
ilure modes,
n
component i
n
h
e seismic fr
a
so for differ
e
a
meters, and
d
Figure 1 [3]
a
sed on dou
b
a
certain failur
e
F
i
g
ure 1, Am
acceleration
r
d deviations
w
b
of seismic
f
a
determined f
a
e
ismic Fragi
l
tire family of
d
ing to a parti
m
s of the be
s
Piping
Jiaxu Zuo
1*
C
hina
m
ic fragility a
n
tablishes 3D
m
n
d obtains the
i
tative metho
d
te
seismic f
r
e
of CEFR ac
c
R
emoval Syste
m
l
it
y
f
Seismic Fr
a
y
of a structu
r
n
al probabilit
y
m
otion value (
i
c
tral accelera
t
f
requencies)
[
o
obtain the
m
c
ertainty, and
f
-failure (HC
L
and further e
s
n
terms of a g
r
a
gility is corr
e
e
nt failures th
e
d
ifferent fragi
l
shows fragilit
y
b
le logarithm
i
e
mode.
is the best e
s
c
apacity, β
R
a
w
ith median v
f
ragility is to
a
ilure mode.
l
ity Model
fragility curv
e
cular failure
m
s
t estimate o
f
of CE
F
n
alysis, and
p
l
a
m
odel of
p
ipe
s
stresses whic
h
d
s of seismic
f
r
agility
p
aram
e
c
iden
t
residua
l
m
; 3D Model
a
gility
r
e or equipme
n
y
of its failure
i
.e., peak gro
u
t
ion at differe
n
[
3,4]. The pu
r
m
edia seismic
c
the high-co
n
L
PF) capacit
y
s
timate the ca
p
r
ound motion
e
sponded wit
h
e
re are differe
n
l
ity curves ca
n
y
curves for
a
i
c normal dis
s
timate of
t
h
e
a
nd β
U
are lo
g
alues 1.0 resp
obtain A
m
, β
R
e
s for an ele
m
m
ode can be e
x
f
the median
JAMP
FR
a
ces em-
s
of Chi-
h
are es-
f
ragility,
e
ters: A
m
l
heat re-
n
t is de-
at a giv-
u
nd acce-
n
t struc-
r
pose of
c
apacity,
n
fidence-
y
under
p
acity of
para
m
e-
h
failure
n
t fragil-
n
be ob-
a
compo-
tribution
e
median
g
arithmic
ectively.
R
and β
U
m
ent cor-
x
pressed
groun
d
Open Access
Fig
u
acceleration
c
Thus, the gro
u
[4]:
in which
R
e
values of 1.
0
randomness
a
median value
.
U
e
are logn
o
dard deviatio
n
the assumptio
fragility curv
e
ditional prob
a
leration is giv
f
in which Q is
dard Gaussia
n
brackets.
2.3. Fragilit
y
Quanti
f
Before you b
save the con
t
and graphic
f
u
re 1. Mean, m
e
c
apacity, Am,
u
nd accelerati
o
m
A
A
and
U
e
are
r
0
, representin
g
a
bout the med
i
.
In this mode
l
o
rmally distri
b
n
s,
R
and
n and the equ
a
e
s for structur
e
a
bility of its fa
i
en by [5]:
ln(
)
'
m
a
A
f

called confid
n
cumulative
y
Analysis
V
f
ication Met
h
egin to form
a
t
ent as a sepa
r
f
iles separate
e
dian, 5% non
-
and two ra
n
o
n capacity, A
m
RU
ee
r
andom variab
g
, respectivel
y
i
an and the u
n
l
, we assume t
h
b
uted with l
o
U
, respecti
v
a
tion (1), we
c
e
s or equipme
n
ilure at a give
n
1
)
()
U
R
Q

ence and
1
distribution
V
ariables an
d
od
a
t your paper,
r
ate text file.
until after th
e
Z. W.
-
exceedance, a
n
n
dom variabl
e
, is given by (
(
les with medi
a
y
, the inhere
n
n
certainty in t
h
h
at both
R
ea
n
o
garithmic sta
n
v
ely. So due
t
c
an obtain easi
l
n
t, and the co
n
n
value of acc
(
2
1
[]
is the sta
n
of the term
i
d
Their
first write a
n
Keep your te
x
e
text has be
e
FU ET AL.
n
d 95% non-e
x
e
s.
1)
1)
a
n
n
t
h
e
nd
n
-
t
o
ly
n
-
e-
2
)
n
-
i
n
n
d
x
t
e
n
format
t
of har
d
graph.
the pa
p
In e
s
work i
n
the fac
acceler
specifi
e
level s
p
in whi
c
ground
fy the
strengt
h
And
related
as:
For
e
ture re
s
p
acity
f
Gen
e
x
ceedance fragi
l
t
ed and styled
.
d
returns to o
n
Do not add
a
p
er. Do
s
timating frag
n
terms of an
tor of safety.
ation capacit
y
e
d for design;
p
ecified for de
c
h A is the ac
t
. This relatio
n
conservatis
m
h
and the resp
o
so the media
n
to the media
n
A
e
quipment, th
s
ponse factor,
f
actor, as:
F
e
rally, the ele
m
l
ity curves for
a
.
Do not use
h
n
ly one retur
n
a
ny kind of p
a
i
lity paramet
e
intermediate
r
The factor o
f
y
above a refe
r
e.g., the safe
sign, A, is de
fi
SSE
A
FA
t
ual capacity
o
n
ship is typica
l
m
or factor
o
o
nse, as:
CR
FFF
n
factor of safe
n
ground acce
l
mm SSE
A
FA
e factor of s
a
equipment r
e
E
RS RE
C
F
FFF
m
ents which
c
a
component.
h
ard tabs, and
l
n
at the end o
f
a
gination any
w
e
rs, it is conv
e
r
andom variab
f
safety, F, o
n
r
ence level ea
r
shutdown ea
r
fi
ned as follow
o
n acceleratio
n
l
ly expanded
t
o
f safety in
b
ty, Fm, can b
e
l
eration capac
a
fety consists
o
e
sponse factor
C
c
an affect stru
JAMP
83
l
imit use
f
a pa
r
a-
w
here in
e
nient to
le called
n
ground
r
thquake
r
thquake
s [3,4]:
(3)
n
motion
t
o iden
t
i-
b
oth the
(4)
e
directly
c
ity, Am,
(5)
o
f struc-
and ca-
(6)
cture
r
e-
Z. W. FU ET AL.
Open Access JAMP
84
sponse involve ground motion (such as earthquake re-
sponse spectrum shape, horizontal direction peak re-
sponse, and vertical component response), damping,
modeling, mode combination, time history simulation,
foundation-structure interaction, and earthquake combi-
nation. The elements which can affect equipment re-
sponse, similar to the above, include qualification me-
thod, damping, modeling, mode combination, earthquake
combination. Note that in order to avoid duplicating,
earthquake combination only is considered in equipment
response [6,7].
The capacity factor FC for the equipment is the ratio of
the acceleration level at which the equipment ceases to
perform its intended function to the seismic design level.
And the factor FC can be calculated by the strength fac-
tor FS and the inelastic energy absorption factor Fμ, as (7)
[5].
CSμ
FFF (7)
The strength factor, FS, represents the ratio of ultimate
strength (or strength at loss-of-function) to the stress
calculated for acceleration at safety shutdown earthquake
(ASSE). In calculating the value of FS, the non-seismic
portion of the total load acting on the structure is sub-
tracted from the strength as follows:
N
S
TN
SP
FPP
(8)
where S is the strength of the structural element for the
specific failure mode, N
P is the normal operating load
(i.e., dead load, operating temperature load, etc.) and T
P
is the total load on the structure (i.e., sum of the seismic
load for SSE and the normal operating load). For higher
earthquake levels, other transients may have a high
probability of occurring simultaneously with the earth-
quake. The definition of in such cases should be ex-
tended to include the loads from these transients.
Randomness and uncertainty are the two important
parameters in seismic fragility analysis, so when deter-
mining the safety factors the two parameters should be
determined too [7].
3. Stress Calculation of CEFR Accident
Residual Heat Removal System Piping
3.1. Basic Condition of the Piping
CEFR accident residual heat removal system has two
loops, and one loop mainly includes an independent heat
exchanger, an air heat exchanger and piping. The layout
of one loop is as Figure 2 [2].
The material of the piping is 304H, and the size of the
piping is as Figure 2. The piping material of argon sys-
tem for accident residual heat removal system is 304 L,
and the piping size is Φ48 × 4. The piping material of
sodium analysis and monitoring system for accident
Figure 2. Layout of one loop’s piping of CEFR accident
residual heat removal system.
residual heat removal system piping is 304 H, and the
size of double piping are Φ108 × 4.5 and Φ48 × 4.
3.2. Modeling for the Piping
The finite element method is used, and the AutoPIPE
software is chosen as analysis tool. The 3D continuous
pipeline is dispersed many space tube units, and the units
are connected by nodes. The connection points of equip-
ment and piping are taken as boundary conditions, and
the displacement is given according to the thermal ex-
pansion. The valves are simulated by valve units taking
account into the impact of the quality of electric head.
The treatment of double pipe is built two tubes, one of
which is a relatively small amount of displacement, the
pipeline where there is a shim in practice is connected
with the guide frame. The model of one loop is shown in
Figure 3.
3.3. Stress Calculation and the Selection of
Fragile Parts
To calculate the capacity factor of the piping, the stresses
generated by both normal operating conditions and safety
shutdown earthquake (SSE) load are needed, so the loads
should be applied to the model.
3.3.1. Determina t ion and Loading of Loads
Assumed that when the earthquake occurring, the reactor
is in normal operation condition, and the system is in the
normal standby condition, so the loads on the pipe can be
determined when the earthquake occurring.
1) Loads under normal operation condition
Loads under normal operation condition include pressure
0.402 MPa, weight, the constraint force and thermal load
of 485˚C. Put the combination of these loads to the mod-
el, then can get the stress N
σ.
Z. W. FU ET AL.
Open Access JAMP
85
Figure 3. Model of piping.
2) Loads under SSE condition
According to above assumption, loads under SSE con-
dition include the load caused by the SSE in addition to
the loads under normal operation condition. The load
caused by the SSE can be loaded by seismic response
spectrum, which comes from reference [2]. The spec-
trums used in the calculation are about four high levels
22.4 m, 26.6 m, 30.8 m and 35 m, and each level has
three response spectrums, two horizontal and one vertical.
The response spectrums about 5% damping are put in the
AutoPIPE software, then the seismic response spectrum
about SSE can be determined as Figure 4.
3.3.2. F r agile Points and Their Str e s s e s
When determining the fragile points, two methods are
used. One method is to choose the points where the stress
SSE
σ caused by the SSE load is the maximum, the other
is to choose the points where the stress NSSE
σ caused
by both the loads in the normal operation condition and
the SSE load is maximum. The points determined by the
two methods are often not the same point, because the
thermal expansion effects have been considered in the
design stage.
The SSE load and the combination of SSE load and
the normal loads loaded on the model one after another,
the points inside and outside the pipe where the stresses
are maximum are choose respectively as Figure 5 and
Figure 6. The fragile points and their stresses are shown
in Table 1.
4. Fragility Analysis and Calculation of
CEFR Piping
4.1. Calculation of Response Factor
Building structural response factor is calculated by NU-
REG0098 [8] factor median spectrum proportion and
RG1.60 [9] spectrum proportion, and the piping response
factor is calculated using the NUREG0098 median spec-
trum proportion and design floor response spectrum. The
calculated median factor and uncertainty are as follows:
Building located on the fifth floor structural response
median factor, randomness and uncertainty are SR
F1.0
,
RSR
β0.31, USR
β0.33.
Building located on the eighth floor structural response
median factor, randomness and uncertainty are SR
F0.7,
RSR USR
β0.31,β0.33.
When calculating the response factor of the pipe, the
response factor is only considered in damping factor, and
the randomness and uncertainty are only considered in
other factors. The calculated damping factors and uncer-
tainty are as follows:
The pipe located on the fifth floor damping factor and
uncertainty are D
F1.8
, UD
β0.22; The pipe located
on the eighth floor damping factor and uncertainty are
Z. W. FU ET AL.
Open Access JAMP
86
Figure 4. seismic response spectrum by SSE.
Table 1. Fragile points and their stresses.
Loads Point
Outside tube
(MPa)
Inside tube
(MPa)
SSE
σ N
σ SSE
σN
σ
SSE load G37/8th floor)52 123 59 97
Normal loads
+ SSE load G35(5th floor)16 249 59 97
Figure 5. Points of inside/outside tube where stress by SSE load is maximum.
Figure 6. Points of inside/outside tube where stress by normal loads and SSE load is maximum.
D
F1.6, UD
β0.24.
So the piping response median factors and uncertainty
are as follows:
The pipe located on the fifth floor median factor and
uncertainty are RER REURE
F1.8,β0.18,β0.26 .
The pipe located on the eighth floor median factor and
uncertainty are RER REU RE
F1.6,β0.18,β0.28 .
4.2. Calculation of Capacity Factor
The pipe material is 304 H, according to the reference [5],
the median material yield strength is 37 ksi (255 MPa),
and the uncertainty is 0.13; the median limit strength is
84 ksi (579 MPa), and the uncertainty is 0.07. According
to the standard of ASME [10], the normal loads + SSE
load should belong to the C condition, and the allowable
limit is 2.25 times allowable yield strength, but not more
than 1.8 times ultimate strength.
The pipe failure is the ductility failure, inelastic energy
absorption should be considered. The inelastic energy
absorption factor is choose form reference [11], Fμ =
1.25, then the uncertainty is calculated, Uμ
β = 0.1. The
strength factors of the pipe are calculated by eq-8, where
the strength is 574 MPa, PN is N
σ, and TN
PP
is
SSE
σ. The calculated strength factor, capacity factor and
uncertainty are shown in Table 2.
4.3. Fragility Analysis and Calculation for Piping
According to above equations and data, the fragility
0
1
2
3
4
5
6
0 10203040
acceleration g
frequency Hz
X
Y
Z
Z. W. FU ET AL.
Open Access JAMP
87
Table 2. Quantification results of capacity factor, strength factor and uncertainty.
loads points
Outside tube (MPa) Inside tube (MPa)
S
F C
F C
U
β S
F C
F C
U
β
SSE load G37(8th floor) 8.67 10.83 0.16 8.08 10.1 0.16
Normal loads + SSE load G35(5th floor) 20.31 25.38 0.16 8.08 10.1 0.16
Figure 7. Fragility curves of the piping.
parameters of the lower capacity point conservatively
selected as the fragility parameters of piping, the final
fragility parameters of piping are as follow:
mmSSE
A4A2F2.
g

22
ββ β0.36
RRSRRRE

222
ββββ 0.44
UUSRUREUC

U
R1.65β
1.65β
50 m
HCLPF 0.65Aee
g

Figure 7 shows the fragility curves of piping accord-
ing to the calculated fragility parameters.
5. Conclusions
This paper studies the analysis method of seismic fragil-
ity, and using the method to calculate the seismic fragili-
ty parameters for the piping of CEFR accident residual
heat removal system. The main results are as follows:
1) The calculated seismic fragility parameters for the
piping of CEFR accident residual heat removal system
are Am = 2.42 g, βr = 0.36 and βu = 0.44, and the HCLPF
capacity is 0.65 g.
2) Compared with CEFR SSE, the results indicate that
the piping of CEFR accident residual heat removal sys-
tem has stronger seismic capacity.
3) This paper has used the NUREG0098 reference
spectrum, rather than the actual site probability hazard
curve, which must cause the calculated results different
from actual values.
4) In this paper, the data of some safety factors and
uncertainty are recommended by references, and these
data are different form real data of power plant, which is
the focus of future research too.
6. Acknowledgements
Thanks for Professor Zhang Donghui, Professor Zhang
Chunming and senior engineer Li Tieping who have
given important guidance and help. At the same time this
paper is sponsored by Large-scale Advanced Pressurized
Water Reactor Power Plant project of National Science
and Technology Major Project (2013ZX06002001).
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00.5 11.5 22.5 3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
P eak Ground Accel erationa/g
*
Conditional Probability of Failure
HCLP F
o
95%Confidance
50%Confidance
Mean
5%Confidance
Z. W. FU ET AL.
Open Access JAMP
88
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