나빈
(Nabin Raj Chaulagain)
1
선창호
(Chang-Ho Sun)
2
김익현
(Ick-Hyun Kim)
3†
-
정회원, 울산대학교 건설환경공학부 박사과정
()
-
정회원, 울산대학교 건설환경공학부 연구교수
()
-
정회원, 울산대학교 건설환경공학부 교수
()
Copyright © The Korea Institute for Structural Maintenance and Inspection
핵심용어
수평원통형 저장탱크, 구조물-유체 상호작용, 간이(간편)모델, 지진취약도곡선
Key words
Horizontal cylindrical tanks, fluid-structure interaction, simplified model, fragility curve
1. Introduction
Several studies have been done in the past for finding seismic response behavior of
cylindrical and rectangular storage tanks, however, there are very few studies regarding
the seismic response analysis of the horizontal and spherical storage tanks. Like
other storage structures, horizontal tanks also suffered the seismic damages on past
earthquake events. Horizontal cylindrical tanks are mostly used in the industrial
area with the purpose to store the chemicals and oils which are highly hazardous to
the environment and flammable upon its collapse of leakage. The consequence of the
failure of facilities in chemical plants will result in catastrophic damage like toxic
gas diffusion and fire hazards.
Seismic analysis of the chemical plant facilities can be done by finite element analysis
with different approaches that are by formulating a detailed 3D FSI model and a simplified
mechanical mass-spring model. Housner(1963) formulated the simplified mass-spring
model for the ground supported cylindrical tank. The modal superposition method was
adopted for seismic evaluation of the flexible cylindrical tanks by the finite element
approach with experimental verification(Haroun, 1980). Malhotra et al.(2000) have
proposed a simple procedure for analyzing the vertical cylindrical storage tank with
the account of impulsive and convective(sloshing) masses action in flexible tanks.
The remarkable study made by Karamanos et al.(2006) formulated the expressions for
calculating the dynamic properties of the spherical and horizontal storage tank system.
In their study, they investigated the effect of sloshing in the horizontal and spherical
tanks during earthquakes by SDOF representation of the storage system. In general,
it is important to know the seismic capacity of the critical facilities over the wide
range of earthquakes which can be obtained by formulating the seismic fragility curves
to each of the facilities of the industrial plant. Even though a number of studies
regarding seismic fragility assessment of cylindrical and rectangular tanks have been
done, yet seismic fragility of the horizontal cylindrical tank has not been developed
by formulating simplified finite element models.
This paper focuses on the seismic safety of the partially filled horizontal cylindrical
tank. Therefore, fragility analyses were performed with the simplified model at the
desired performance level. The overall study shows that seismic damage for the horizontal
storage system is more susceptible in the transverse direction.
2. Subject
2.1 Finite element model formulation
In this study, finite element analyses were made with two different approaches, namely
the FSI model and the simplified model. FSI analyses are performed in the FEM program
ANSYS(Canonsbug, 2012). Since the FSI model tends to represent the exact structure,
the structural components like saddles, tank wall, and contained fluid were modeled.
The tank wall is modeled by four-node shell element having six degrees of freedom
at each node called SHELL181. The supporting saddles were modeled by a 20-node solid
element called SOLID186.
The liquid inside the tank is modeled by the FLUID80 element which has three translational
degrees of freedom at each node. These elements are suitable to model as a liquid
inside the vessel without any flow rate. The behavior of the fluid is represented
by the Lagrangian approach and fluid is considered as incompressible, irrotational
and inviscid(Wilson and Khalvati, 1983). For the interaction between the shell and
the fluid element surface- to-surface contact by the element type CONTACT174 and TARGET170
supporting the Coulomb’s friction model was used.
The simplified model is formulated with the beam element connected with rigid and
convective links for impulsive and convective masses respectively. According to Eurocode
8(2006), the horizontal cylindrical tank should be analyzed for seismic actions along
the longitudinal and horizontal transverse direction. The approximate hydrodynamic
pressure generated by seismic actions in both longitudinal and transverse directions
can be obtained by considering an equivalent rectangular tank with the same depth
and volume as actual tank. Study made with this approach by converting the horizontal
tank into equivalent rectangular by Carluccio et al.(2008) agreed well with the base
shear component. According to Eurocode 8, the horizontal cylindrical tank can be equivalently
model as a rectangular tank for the H/R range between 0.5 to 1.6. H and R are the
liquid height and the radius of the horizontal tank, respectively. Therefore, in this
study the simplified model is prepared by converting the horizontal tank to equivalent
rectangular tank and transferring the liquid mass through convective mass and impulsive
mass using elastic and rigid links respectively. The validity of the partially filled
horizontal liquid storage tank is evaluated for the ground-based staged horizontal
tank is presented.
2.2 Modeling
2.2.1 3D -FSI Finite Element Model
The structure analyzed in the present study is the typical ground-supported horizontal
cylindrical storage tank with a volume of 188 m$^3$. The liquid volume in the tank
is 85%. The liquid contained in the tank is butane of density of 603 kg/m$^3$. The
subdivision of the finite element and boundary element of the tank considered is presented
in Fig. 1. The geometrical properties of the storage system are given in Table 1 and the material properties are given in Table 2.
Table 1. Geometrical properties of the horizontal tank
|
Length of the tank
|
15 m
|
|
External diameter
|
4 m
|
|
Thickness of the tank wall
|
0.012 m
|
|
Thickness of the saddles
|
0.02 m
|
|
Width of the steel saddles
|
3.4 m
|
Table 2. Mechanical properties of the horizontal tank
|
Design strength of the steel tank
|
360 MPa
|
|
Design Strength of the supporting saddles
|
230 MPa
|
|
Sonic velocity of the liquid
|
1,616 m/s
|
|
Poisson's ratio of steel
|
0.3
|
|
Density of steel
|
7,850 kg/m$^3$
|
|
Young modulus of the steel
|
2ⅹ1011 N/m$^2$
|
Fig. 1. Finite element idealization for the 3D detailed model
2.2.2 Simplified Finite Element Model
The simplified model is developed as two mass system as recommended by literature(Karamanos
et al., 2006). Finite element software SAP2000 is used to form the analysis of the
simplified model. The simplified 2D model is prepared in such a way that the wall
of the tank is modeled by beam elements with equivalent stiffness. In the current
study, the liquid depth is 3.17m and the radius is 2m, therefore H/R ratio is 1.58.
The two equivalent tank models were created of equal volume with the original cylindrical
tank for evaluating the longitudinal and transverse seismic effects separately. Both
equivalent models have the same liquid volume and depth, but different tank sizes.
The dynamic properties of the equivalent tanks are calculated based on the IITK-GSDMA
guidelines(Barton and Parker, 1987]. The equivalent simplified mass-spring models
of rectangular tanks are shown in Fig. 2. The liquid element in the horizontal tank is represented by the mass-spring system.
The calculated dynamic properties for the tanks are presented in Table 3.
Fig. 2. Equivalent model for simplified analysis of rectangular storage tank
Table 3. Parameters of the simplified models in both directions
|
Parameters
|
Longitudinal
|
Transverse
|
Remarks
|
|
$m_{c}/m$
|
0.729
|
0.328
|
- 'm' represents mass
- 'h' represents height
- subscript 'c' represents
convective
- subscript 'i' represents
impulsive
- superscript (') represents
tank wall
|
|
$m_{i}/m$
|
0.243
|
0.671
|
|
$h_{c}/h$
|
0.517
|
0.659
|
|
$h_{i}/h$
|
0.375
|
0.481
|
|
$h_{c}^{'}/h$
|
2.620
|
0.75
|
|
$h_{i}^{'}/h$
|
1.92
|
0.55
|
2.3 Time history Analyses
2.3.1 3D detailed model
The seismic responses of the horizontal tank under bi- directional ground excitations
were observed. The horizontal ground motions were applied simultaneously in longitudinal
and transverse axes.
The past earthquake records are not enough and suitable for seismic analyses, hence
a set of artificial ground motions were developed and used in this study to find the
seismic analyses. The ground acceleration for the total duration of 20sec was developed
along with the longitudinal and transverse directions with peak ground acceleration(PGA)
of 0.154g. Fourteen random seismic excitations compatible to the design response spectrum
specified in the Korea seismic design code were generated. To generate the artificial
ground motions the stationary process is multiplied by the envelope function, the
envelope function is taken from the seismic design code with a short period of 0.02sec
and a long period of 3.0sec, the time step size of 0.01sec is used. Artificial ground
motions are generated using the program SIMQKE. The matched random ground motions
with the target spectrum are shown in Fig. 3.
Fig. 3. Design response spectrum with matched cases
Time history analyses were carried with the modal superposition technique. To characterize
the convective and impulsive responses along with the time domain the time step of
0.01sec was used. More than 200 modes were utilized so that the ratio of accumulated
mass to the total mass becomes more than 90% to capture the convective and impulsive
responses in the analyses. The time history results of the detailed 3D model are presented
in Table 4. Fig. 4 and 5 illustrate the time history response of the detailed 3D model.
Table 4. Time history responses with 3D model
|
Responses
|
Direction
|
Convective
|
Impulsive
|
Total (SRSS)
|
|
Base Shear
(kN)
|
Longitudinal
|
2.73
|
110.69
|
110.72
|
|
Transverse
|
35.60
|
275.89
|
278.17
|
|
Overturning Moment
(k-Nm)
|
Longitudinal
|
6.86
|
552.87
|
552.91
|
|
Transverse
|
70.97
|
649.99
|
653.85
|
Fig. 4. Response of base shear
From time-history results, it can be concluded that the effect of the convective component
is less as compared to the impulsive component. To observe the liquid sloshing behavior
in earthquake, the total vibration time is extended up to 30s even though the actual
vibration stops at 20 s. As it can be seen in Figure 4 and 5 that the sloshing(convective) reaction continues even after the 20s where the impulsive
reaction stops. It should be noticed that the impulsive response occurs earlier than
the convective response. Figure 4 and 5 illustrate that the sloshing phenomena start after the peak response of the impulsive
component. Furthermore, in the case of the horizontal tank the transverse seismic
action is comparatively higher than the longitudinal as expected. The transverse base
shear is almost 2.5 times higher than the longitudinal base shear. Similarly, the
transverse overturning moment is 14% higher than the longitudinal overturning moment.
This illustrates that the transverse directional seismic results are higher than the
longitudinal directional seismic results.
Fig. 5. Response of overturning moment
2.3.2 Simplified model
In the simplified fluid-structure interaction model, the impulsive and convective
masses at their respective heights, together with the associated stiffness and the
spring topology are modeled. The dynamic properties of the simplified model are illustrated
in Table 3. The damping ratio of 5% is used for the impulsive mode and 0.5% is used for the
convective one.
The mass of the liquid is 96.615 t corresponding to the filling ratio of 85% and the
mass of the tank is 27.81 t. This filling ratio corresponds to the fluid height to
radius ratio(H/R) of 1.58. For the excitation in the longitudinal direction, the impulsive
mass corresponding to 24 t is 25% of the liquid mass and 72 t is 75% of the liquid
mass. Similarly, for the transverse direction, the impulsive mass corresponding to
65t is 67% of the liquid mass and the convective mass corresponding to 31 t is 33%
of the liquid mass.
Table 5 illustrates the seismic base shear and overturning moment results for the simplified
model. The difference in base shear results for the 3D FSI model and simplified one
is 11% for longitudinal direction and 6% in the transverse direction. Similarly, for
the overturning moment the difference is 16% and 0.4%. As the seismic analysis results
compare favorably, the simplified model here can represent the FSI model for further
fragility analysis.
Table 5. Time history responses of simplified model
|
Responses
|
Direction
|
Results
|
|
Base Shear
(kN)
|
Longitudinal
|
124.15
|
|
Transverse
|
263.72
|
|
Overturning Moment
(k-Nm)
|
Longitudinal
|
479.43
|
|
Transverse
|
680.18
|
2.4 Seismic Performance Evaluation
2.4.1 Limit states
The seismic performance of the horizontal cylindrical tank is evaluated by time history
analyses. In addition to 14 artificial ground excitations as mentioned above a set
of 18 natural earthquake records were selected from the Pacific Earthquake Engineering
Research(PEER) ground motion database as shown in Table 6. The selected ground motions include the bi-directional horizontal ground motions.
Table 6 shows the magnitudes and PGA in longitudinal and transverse directions for all the
selected set of ground motions. Each record was scaled to 10 sets of ground motions
of a gradual increase in intensity level.
Table 6. Earthquake records for input ground motions
|
S. N
|
Earthquake
|
Magnitude
|
Station
|
PGA(g)
|
|
X(g)
|
Y(g)
|
|
1
|
Azna,USA
|
4.92
|
Pinyon Flat
|
0.079
|
0.131
|
|
2
|
Gulf of Aqaba,Israel
|
7.2
|
Eilat
|
0.092
|
0.080
|
|
3
|
Borrego Mtn
|
6.63
|
El Centro Array #9
|
0.132
|
0.057
|
|
4
|
Coalinga-01, USA
|
6.36
|
Parkfield - Fault Zone 11
|
0.078
|
0.087
|
|
5
|
Dursunbey,Turkey
|
5.34
|
Dursunbey
|
0.223
|
0.287
|
|
6
|
Corinth,Greece
|
6.6
|
Corinth
|
0.236
|
0.296
|
|
7
|
Kocaeli,Turkey
|
7.51
|
Fatih
|
0.188
|
0.161
|
|
8
|
Morgan Hill,USA
|
6.19
|
Halls Valley
|
0.156
|
0.312
|
|
9
|
Kobe, Japan
|
6.9
|
Nishi-Akashi
|
0.483
|
0.464
|
|
10
|
Imperial Valley-02, USA
|
6.95
|
El Centro Array #9
|
0.280
|
0.210
|
|
11
|
Imperial Valley-06, USA
|
6.53
|
Delta
|
0.235
|
0.349
|
|
12
|
Chi-Chi, Taiwan-04
|
6.2
|
HWA051
|
0.014
|
0.015
|
|
13
|
Parkfield,USA
|
6.19
|
Cholame - Shandon Array #5
|
0.145
|
0.443
|
|
14
|
Northridge-01, USA
|
6.69
|
Hollywood - Willoughby Ave
|
0.135
|
0.250
|
|
15
|
Coalinga-01, USA
|
6.36
|
Cantua Creek School
|
0.225
|
0.288
|
|
16
|
Chichi,Taiwan
|
5.28
|
CHY002
|
0.147
|
0.024
|
|
17
|
San Fernando,USA
|
6.61
|
Castaic - Old Ridge Route
|
0.320
|
0.275
|
|
18
|
Tabas,Iran
|
7.35
|
Ferdows
|
0.093
|
0.104
|
The seismic performance of the tank considered should be done by developing the fragility
curves. The non-anchored tanks and pipe connected tanks are susceptible to damage
due to lateral movement and rotation of the tank to saddle(Sezen and Whittaker, 2004).
On the other hand, those with anchored base and rigidly connected saddles may be susceptible
to buckling of the tank wall(Burgos et al., 2018).
Therefore, to evaluate the fragility curves, the engineering demand parameters, EDPs,
need to be defined. With the overview of the past failure history of the horizontal
tanks, the EDPs shown in Table 7 have been assumed in this study: overturning moment and sliding failure(Sezen and
Whittaker, 2006). Once the EDPs are selected, the performance of the tank will be
determined by assigning the limit state threshold values for each defined EDPs. In
the horizontal cylindrical tank, the seismic fragility curves should be developed
for both longitudinal and transverse directions. Overturning fragility is computed
based on the design limit values for overturning in longitudinal and transverse directions,
and sliding fragility is computed based on maximum horizontal base shear.
Table 7. EDPs and limit states for fragility evaluation of horizontal tanks
|
Failure mode
|
EDP
|
Limit state
|
Threshold values
|
|
Overturning
|
Overturning moment
|
Overturning moment limit
|
6788.82(L)
1556(T)
|
|
Sliding
|
Base shear
|
Base shear
($F_{sliding}=\mu\times W$)
|
460 kN
|
2.4.2 Fragility analysis results
Seismic fragility curves of the examined ground-supported horizontal cylindrical tank
are shown in Fig. 6 and 7. Table 8 lists the median and standard deviation of ln(PGA) for fragility functions of defined
limit states. From the fragility curves, it is possible to see that the transverse
direction is weak against earthquake. The performance point for the sliding of the
horizontal tank is 0.3g PGA and failure probability is 90% at 0.5g PGA along the transverse
direction. Similarly, the performance point is 0.5g PGA and failure probability of
90% is at 0.7g PGA along the longitudinal direction. On the other hand, the performance
point for the overturning of the horizontal tank considered in this study is 0.5g
PGA and failure probability is 90% at 1g PGA along the transverse direction. Similarly,
the performance point is 1g PGA and failure probability is 90% at 2.5g PGA along the
longitudinal direction.
Fig. 6. Fragility curve of sliding
Fig. 7. Fragility curve of overturning
3. Conclusions
In this study, seismic analyses of the ground supported horizontal tank were performed
using a 3D detailed model and a simplified one. And the fragility curves were developed
for limit states of overturning and sliding. The following conclusions are drawn from
the study.
(1) The liquid inside the tank will continue to slosh even after the earthquake vibration
stops and the peak responses of the impulsive component and convective component vary.
The peak of the impulsive component reaches earlier than the convective component
during earthquake vibration.
(2) Seismic response results of the simplified model and the 3D FSI one show agreeable
results, therefore the simplified model can be used for developing seismic fragility
curves for horizontal cylindrical tanks.
(3) When the design level earthquake (0.154 g horizontal PGA) occurs, the probability
of the damage by overturning and sliding is almost 0 %.
(4) The considered horizontal tank will not likely receive any damage from earthquakes
of 0.3 g or less PGA.
(5) The performance point of the overturning of the tank is higher than that of sliding.
(6) Fragility curves for the desired limit states show that seismic damage for the
horizontal tank is susceptible along the transverse direction.
Acknowledgement
This research is supported by Korean Environment Industry and Technology Institute
(KEITI) through The Chemical Accident Prevention Technology Development Project (201700
2050001), funded by Korea Ministry of Environment (MOE).
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