Fluid-Structure-Soil Interaction Analysis of Cylindrical Liquid Storage Structures

7/28/2019 Fluid-Structure-Soil Interaction Analysis of Cylindrical Liquid Storage Structures

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Fluid-Structure-Soil Interaction Analysis of

Cylindrical Liquid Storage Structures

Chung-Bang YUN andSoo-Hyuk CHANG / [email protected]@kaist. ac.kr

Korea Advanced Institute of Science & Technology, Taejon 305-701, Korea

Eiichi WATANABE / [email protected]

Kyoto University, Kyoto 606-8501, Japan

Abstract

A method is developed for fully coupled fluid-structure-soil interaction analyses of liquid storage

structures on/in a horizontally layered half space in the frequency domain. To capture the essenceof the fluid-structure interaction effect, the contained fluid is modeled using mixed finite elements

with two fields (displacement and pressure) approximation. On the other hand, the soil-structure

interaction effect is considered using finite elements and dynamic infinite elements. The present

finite/infinite elements method can be applied to the system with complex geometry of fluid region

and inhomogeneous near-field soil region. A couple of earthquake response analyses are carried out

on a RC tank on the ground and a real-scale embedded LNG tank. Numerical results indicate that

the SSI and embedment effects reduce member forces particularly on the structure at soft soil sites.

Key Words: fluid-structure-soil interaction, mixed fluid element, infinite element, large liquid tanks

Background and Objective of Research

A refined evaluation of seismic responses for large liquid storage structures is very important for

safety evaluation on existing facilities as well as aseismic design for new structures. The fluid-

structure interaction and soil-structure interaction are key factors in the dynamic analysis of those

structures. The objective of this study is to develop an efficient method for fluid-structure-soil

interaction analysis of large-scale liquid storage structures.

For the fluid-structure interaction analysis, three different finite element approaches may be

used to represent the fluid motion; i.e., Eulerian, Lagrangian and mixed methods. The velocity

potential (or pressure) is used to describe the behavior of the fluid in the Eulerian approach(1,2)

,

whereas the displacement field is used in the Lagrangian approach(3)

. In the mixed approaches(4,5,6)

,

both the displacement and pressure fields are included in the element formulation. The Lagrangianfluid elements have been widely used in commercial programs such as ADINA, ABAQUS and

ANSYS. The reduced integration technique is basically adopted to prevent the overestimation of

the volumetric stiffness of the fluid element. The spurious zero energy modes caused by the

reduced integration are removed by a combined usage of the rotational penalty and mass projection

techniques(3)

. However, this formulation requires physical insights into the behavior of the fluid

element. Accordingly, application of the approach has been limited to simple linear elements. On

the other hand, in the mixed element formulation, the reduced integral is not required and higher

order fluid elements can be easily developed. Besides, the mixed approach can be effectively used

for problems with complex geometries where the physical interpretation of the fluid motion is very

complicated. In this study, axisymmetric Q9/3 mixed fluid elements(6)

are used.

For the soil-structure interaction analysis, it is important to model the impedance of the far-field

soil region including the radiational damping effect. For the purpose, dynamic infinite elements(7)

developed by the present authors are used in modeling the unbounded multi-layered far-field soil
mailto:[email protected]:subway@kaistmailto:subway@kaistmailto:[email protected]


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medium, and the frequency dependant dynamic stiffness matrices are obtained. The equation of

motion for the coupled fluid-structure-soil interaction system is constructed in the frequency

domain using the substructured wave input technique( 7)

, in which the equivalent earthquake force

is evaluated along the interface between the near-field and far-field soil regions based on the resultsof the free-field analysis.

Methodology

This paper deals with long-scale cylindrical liquid tanks subjected to earthquake loading as shown

in Figure 1. The axisymmetric harmonic analysis method(6,7,8)

is employed for the axisymmetric

system subjected to non-axisymmetric 3-D loads. The contained fluid and far-field soil are

respectively discretized by Q9/3 mixed fluid elements and dynamic infinite elements, while the

structure and near-field soil are represented using conventional finite elements. Thus the fluid-

structure interaction and soil-structure interaction are directly included in the modeling.

Horizontally LayeredFar-Field Soil

Inhomogeneous

Near-Field Soile

AxisymmetricStructures

Mixed Fluid Elements

Model Employed

r

Liquid

AxisymmetricSolid Elements

EquivalentEarthquake Load

Dynamic Infinite Elements

Problem Considered

Node for displacement

Node for pressure

Homogeneous

Far-Field Soil

Incident Plane Body Waves

Figure 1. Fluid-structure-soil interaction system and its modeling

Mixed fluid elements for modeling contained fluid

Treating the fluid as an elastic material without shear resistance, the equilibrium equation in the

fluid region( ) and the boundary condition on the free surface(f f ) can be represented as

0=+ ffp u&& in f , = ugp f on f (1)

where is the displacement vector of the fluid; is the elevation of the free surface;f

u u is the

hydrodynamic pressure in the fluid; is the gradient differential operator; is the mass density

of the fluid; and gis the gravitational acceleration. The equation of motion for the contained fluid

can be obtained from Eq 1 using the mixed fluid element with displacement and pressure variables.

Then by condensing out the pressure variables, the equation can be obtained only for the nodal

displacement vector as

f

fd

0dKKdM =++ ffff )( && (2)

where is the fluid mass matrix; and K and are stiffness matrices associated withfM

fK


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sloshing and compressibility of the liquid(9)

, respectively. In this study, the Q9/3 cylindrical mixed

element(6)

(i.e., nine nodes for displacement and three nodes for pressure as shown in Figure 1) is

utilized to model the nearly incompressible fluid. Although the element can not enforce the

continuity of pressure along interfaces between elements, many studies reported that the elementpasses the multiple element patch tests and has the O(h2) convergence rate of the stress

(6).

Dynamic infinite elements for modeling far-field soil

The displacement field of an infinite element in the far-field soil region, ( ; )u x% , is expressed as

)();(~

);(~ = qxNxu in e (3)

where ;( ; ) [ , , ]d s b =N x N N N% % % % q d s b=T T T

T, ,

b

( ; )

; is position vector; and is nodal

displacement vector, while and are respectively amplitude vectors of the side and bubble

modes shown in Figure 2. The shape functions

x d

s

N x% are complex-valued and contain multiple

wave functions which are obtained from the approximate solutions for horizontally layered half-

space medium in the frequency domain.(7) Typical shape functions for the horizontal infinite

elements are shown in Figure 2.

The mass and stiffness matrices can be computed by a similar procedure to the one for the finite

element formulation as

( ) ( ; ) ( ; )e

T ed

= M N x N x% % % , ( ) ( ; ) ( ; )e T ed

= x DB x% % %K B (4)

where the integrations in the infinite domain are carried out using the Gauss-Laguerre integration

scheme. Then the dynamic stiffness matrix )(~

S for the far-field soil region is constructed as

)(~

)(~

)(~ 2 = MKS (5)

It is noted that the dynamic stiffness matrix is dependent on the excitation frequency since the

shape functions are defined as functions of the frequency.

-10

+1

-10

+1

-Im{N11(,)}Re{N11(,)}

- 10

+1

- 10

+1

- Im{N21(,)}Re{N21(,)}

(a) Nodal modes

+1

0-1

+1

0-1

Re{ }NS,12(,) -Im{ }NS,12 (,)

+1

0-1

+1

0-1

Re{ }Nb,22(,) -Im{ }Nb,22(,)

(b) Side mode (c) Bubble mode

Figure 2. Example shape functions of a 3-node horizontal infinite element


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Fluid-Structure-Soil Interaction System for Earthquake Loading

The equation of motion for a fully coupled fluid-structure-soil system subjected to ground

motion is constructed in the frequency domain from Eqs (2) and (5) using the substructured wave

input technique(7) as

( ) ( ) 0 ( ) 0

( ) ( ) ( ) ( ) ( ) 0 ( )

0 ( ) ( ) ( ) ( ) ( )

ff fn f

nf nn nn en n c

eqk

ne ee ee e e

u

+ = +

S S u

S S S S u

S S S u a

) )

&&

%

(6)

where the subscript f denotes degrees of freedom in the fluid region; the subscript n represents

those in the structure and in the near-field soil except for the interface(e ) between the near-field

and far-field soil regions; the subscript e denotes those one ; is circular frequency; ,

and

)( S

)(S )(~

S represent the dynamic stiffness matrices obtained from fluid elements, finiteelements and infinite elements respectively; u ( )c & is the earthquake input used as a control

motion in the free field analysis; and denotes the coefficient vector

&

e

)(eqkea(8)

for the equivalent

earthquake force along . In the free-field analysis, the response of the multi-layered soil

medium is computed along the interface(

e

) considering the effects of the ground motion

amplification and the nonlinear soil behavior.

Example Analyses and Discussions

Flexible RC tank on a layered half-space

In order to gain insight of the fluid-structure-soil interaction effect on the member forces of a liquid

storage tank, a dynamic analysis is carried out for a structure depicted in Figure 4 under various

soil conditions. The structure is located on a horizontal soil layer with an underlying bedrock.

Three values of the shear wave velocity for the soil layer are considered in this investigation; i.e.,

500m/s, 800m/s, and 5000m/s. The other material properties for the structure and soil regions are

given in Figure 4. An acceleration time history with PGA of 0.14g, which is compatible with the

Korean design response spectrum for a rock site, is simulated for the earthquake input as in Figure

4. The control acceleration is assigned at the top of the bedrock as a horizontal outcrop motion.

Thus, the seismic motion can be amplified on the ground surface depending on the properties of the

horizontal soil layer.

Member forces are calculated along the vertical shell, and their maximum values are plotted in

Figure 5. For the purpose of comparison, the maximum member forces are also computed usingANSYS program

(10)for the same structure but on a fixed base. A fully coupled fluid-structure-soil

interaction analysis cannot be carried out by ANSYS program. In the present ANSYS analysis, the

input ground acceleration at the fixed base is prepared for each soil condition by carrying out the

free-field analysis using SHAKE91 program.(11)

Thus, the solution by ANSYS can be considered as

the response for the same input ground motion but excluding the soil-structure interaction effect.

Two sets of the results for a rigid soil condition by the present and ANSYS analyses (in Figure 5a)

are found in good agreements, which confirms the accuracy of the present analysis. The results for

the softer soil conditions in Figure 5 indicate that the member forces on the shell reduce

considerably as the soil stiffness decreases. This result re-confirms that accurate dynamic analysis

of a large liquid storage tank considering the soil-structure interaction may yield cost-effective

cross-section for the structure.


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LNG storage tank embedded in a multi-layered half-space

For the sake of demonstrating the applicability, a seismic response analysis is performed for a real-

scale LNG storage tank embedded in a multi-layered ground as shown in Figure 6. It is located at a

reclaimed area, where the soil condition is very soft. The same simulated acceleration record shownin Figure 4 is used as the horizontal rock outcropping control motion. Figure 6 depicts the absolute

maximum member forces along the vertical shell in comparison with those obtained using an

Eulerian approach for modeling the fluid(2)

. It can be observed that the present method using the

mixed fluid element yields almost identical structural responses to those using the Eulerian

approach.

Research OutputA method for seismic response analysis of cylindrical liquid storage structures on/in horizontally

layered half-space is developed. To capture the essence of fluid-structure-soil interaction effects

effectively, axisymmetric mixed finite elements with displacement and pressure variables are

employed to model the contained fluid, while the structure and soil medium are represented by theaxisymmetric harmonic finite elements and dynamic infinite elements.

The results of a seismic response analysis for a liquid storage tank on a horizontal layer with a

bedrock indicate that accurate dynamic analysis of a large liquid storage tank including the soil-

structure interaction effects may yield cost-effective cross-sections particularly for those at soft soil

sites. A seismic analysis on a real-scale LNG storage tank embedded in layered half-space shows

that the maximum member forces along the shell are in good agreements with those obtained

utilizing an Eulerian approach for fluid modeling.

The present finite element based formulation incorporating the mixed fluid elements and the

dynamic infinite elements can effectively be used for the fluid-structure-soil interaction problem

with complex geometry and inhomogeneous soil configuration.

References

1. A.S. Veletsos and Y. Tang, Soil-structure interaction effects for laterally excited liquid storage tanks,Earthquake Eng. & Structural Dyn., Vol. 19, 1990, pp. 473-496.

2. J-M. Kim, C-B. Yun and S-H. Chang, Fluid-structure-soil interaction analysis for embedded cylindricalliquid storage structure, Proceedings of the Fourth Asia-Pacific Conference on ComputationalMechanics, Singapore, Dec. 15-17, 1999, pp.749-754.

3. Y-S. Kim and C-B. Yun, A spurious free four-node displacement-based fluid element for fluid-structure

interaction analysis,Engineering Structures, Vol. 19, No. 8, 1997, pp. 665-678.4. T.J.R. Hughes, W.K. Liu and T.K. Zimmermann, Lagrangian-Eulerian finite element formulation for

incompressible viscous flows, Comput. Meths. Appl. Mech. Engrg., Vol. 29, 1981, pp.329-349.5. J. Donea, S. Giuliani and J.P. Halleux, An arbitrary Lagrangian-Eulerian finite element method for

transient dynamic fluid-structure interactions, Comput. Meths. Appl. Mech. Engrg., Vol. 33, 1982,

pp.689-723.6. O.C. Zienkiewicz and R.L. Taylor, The Finite Element Methods: Volume 1. Basic Formulation and

Linear Problems, Fourth edition, McGraw-Hill, 1989.7. C-B. Yun, J-M. Kim and C-H. Hyun, Axisymmetric elastodynamic infinite elements for multi-layered

half-space,Int. J. for Numerical Methods in Eng., Vol. 38, 1995, pp. 3723-3743.8. C-B. Yun and J-M. Kim, KIESSI-AX3D: A computer program for soil-structure interaction analysis

using finite and infinite element techniques, Research Rep., Dept. of Civil Eng., Korea Advanced

Institute of Science & Technology, 1996.9. C-B. Yun, S-H. Chang and J-M. Kim, 3-D axisymmetric fluid-structure-soil interaction analysis using

mixed-fluid element and infinite element, Proceedings of the 14th

Engineering MechanicsConference(CD-Rom), Austin, Texas, USA, May 21-24, 2000

10. ANSYS Inc.,ANSYS 5.5, Users Reference Manual, 1999.

11. P.B. Schnabel, J. Lysmer, and H.B. Seed, SHAKE91 -- A computer program for earthquake responseanalysis of horizontally layered sites, Earthquake Engineering Research Center, University ofCalifornia, Berkeley, California, 1991.


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Nz

Nt

Ntz

Ntz

Bedrock

(s=2.5Mg/m3, Vs=5000m/sec s=0.2, h=2%)

50m H=40m

R=30m

20m

Compliant Soil

C.L.

(s=2.5Mg/m3, s=0.2, h=2%)

3m

RC Shell

c=2.6Mg/m3

,Es=30MPa,

c=0.2,h=2%

0.8m

Water

PGA=0.14g

20 30

Time (sec)

r

d

z

10

104m Figure 4. RC liquid storage tank and its meshes of finite and infinite elements

(Vs of compliant soil: Three cases with 500, 800, and 5,000 m/sec)

0 2000 4000 6000 8000

Member force (KN/m)

0

10

20

30

40

50

Heightfromf

luidbottom(

m)

0 2000 4000 6000 8000

Member force (KN/m )

0

10

20

30

40

50

Heightfromf

luidbottom(

m)

0 2000 4000 6000 8000

Member force (KN/m)

0

10

20

30

40

50

Heightfromf

luidbottom(

m)

SSI Effectwith without

tN z {

zN S U

tzN .

(a) Vs=5,000 m/s (b) Vs=800 m/s (c) Vs=500 m/s

Figure 5. Maximum member force profiles for a RC liquid storage tank shown in Figure 4

(Nt at , N0o = z at 0o = , and Ntz at )90o =

0 2000 4000 600

Nt (kN/m)0

0

10

20

30

40

50

Heightfromf

luidbottom(

m)

0 2000 4000 6000 8000 10000

Ntz (kN/m)

0

10

20

30

40

50

Eulerian

Approach(2)

Present study

(a) Geometry and finite/infinite element modeling (b) Maximum member forces

Figure 6. A real-scale embedded LNG storage tank and maximum member forces

Documents

Fluid-Structure-Soil Interaction Analysis of Cylindrical Liquid Storage Structures