# Seismic Analysis Of Liquid Storage Tanks Biology Essay

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ABSTRACT: This study presents an idealization scheme for the analysis of rectangular storage tanks acted upon by earthquake excitations. Above and below ground tank, uses have been considered. A linear three-dimensional finite element analysis has been used to predict the natural frequencies. The analysis parameters are the ratio of height to length of the tank, the type of soil, level of water in the tank, and also the wall thickness. The results for top displacement and axial force components for a full tank above ground case have values greater than those in half- full (31%) and empty tank cases (75%). At the opposite of that, the underground tank demonstrate that top displacement and axial force components for an empty tank case have values greater than those in half- full (19%) and full tank cases (40%). The base shear for above ground tank case has values greater than those in underground tank cases (19% to 37%). The shear base for soil type 2 is greater than those in soil type 1(17% to 28%).

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## KEYWORDS: Seismic analysis, viscous dampers, rectangular tanks, finite element models, fluid-structure-soil interaction, time history, free vibration, ANSYS.

## 1. INTRODUCTION

The damage to storage tanks due to recent earthquakes has been extensively studied by (Jennings 1971, Hanson 1973, and Monos and Clough 1985). These tanks are mainly steel tanks whose failure modes are edge effects in the form of elephant foot buckling at the base. (Housner 1957) is the first who considers the hydrodynamic pressure distribution developed in rigid tanks during horizontal base excitation. He formulates a dynamic model for estimating the liquid response in seismically excited rigid, rectangular and circular tanks. The effect due to shell flexibility is later incorporated in the model by (Veletsos and Yang 1976), (Nash et al. 1978), (Haroun and Housner 1980). (Haroun and Tayel 1984) have investigated the effect of soil-structure interaction. (Veletsos and Tang 1986) and (Luft 1984) have considered the effect of vertical excitation on the hydrodynamic pressures. (Haroun and Chen 1989) have investigated the nonlinear sloshing behavior in rectangular tanks by considering large amplitude sloshing. The finite element analysis of the liquid-tank system is studied by (Haroun and Housner 1981). Several studies were also carried out to investigate that dynamic interaction between deformable wall of the tank and the liquid using finite element analysis. (ASCE 1984) comprehensively discusses the effect of fluid-structure interaction on the hydrodynamic pressures and (ASCE 1981) provides excellent guidelines for the analysis and design of liquid storage structures.

## 2. BASIC ASSUMPTIONS

The assumptions introduced in the present analysis are as follows:

the tank is symmetric in x-axis and symmetric in z-axis terms of geometry.

the material of the tank is linearly elastic, isotropic and homogeneous.

the contained liquid is inviscid, incompressible and in a non-rotational motion, within vessels having no net flow rate

the liquid represents solid elements.

the base is connected rigidly to the tank wall.

the soil medium is represented as a system of closely spaced independent linear springs, masses and dashpots.

the seismic effect parallel to z-axis and perpendicular on x-axis

The symbols of the geometric parameters used in this present paper are shown in Plate (1).

## Plate (1) Rectangular storage tank and coordinate system

## 3. DESCRIPTION OF STRUCTURE

The structure analyzed in the present study, shown in Plate (1), is a typical rectangular storage tank with a volume of 767.6m3. The contained liquid is assumed to be water with the density of 10kN/m3, Ew= 2.0684 x109 kN/m2 and Viscosity = 1.2379 x10-12kN/m.s, Ï…w= 0.19. The tank has a length of 12.6m, a width 6.3m, a height 12.6m and a shell thickness of 0.45m and is constructed from a concrete with Ec= 20x 106kN/m2, Ï…c= 0.15 and Ïc= 24kN/m3. The damping coefficient of the overall structure has been assumed equal to 5%. The soil has been chosen, according to (Prakash 1981) classification, four different models of soil types are carried out. The four types of soil are classified in Table (1).

## Table (1) Parametric studies of soil type

## No.

## Soil type

## Mass density

## kN.s2/m4

## Shear modules kN /m2

1

Loess at natural moisture

1.67

112892

2

Medium-sized gravel

1.8

58320

3

Medium-grained sand

1.65

42240

4

Fine-grained sand

1.65

19965

## 4. SEISMIC GROUND EXCITATION

In the present study a seismic ground motion, the ground acceleration has duration of 31.18sec and a peak ground acceleration (PGA) of 0.318g. A rectangular concrete tank has been analyzed due to north-south component El-Centro earthquake of Fig. (1), taken the first five seconds for analyzing models of tanks, which is assumed to act in the horizontal direction (z-axis).

## Figure (1) Accelerogram N-S El Centro earthquake, 18-May-1940

## 5. SOIL-STRUCTURE INTERACTION

According to (Clough 2003), the soil-structure interaction (SSI) effects on the dynamic response of a rectangular tank can be taken into account by modeling each of the physical degrees-of freedom, i.e. horizontal and vertical, of the surrounding soil system as discrete system with six degrees-of-freedom. The constants of all the discrete elements are computed as listed in Table 2.

## Table (2) Soil properties of all concrete models considered in the analysis

Soil type

unit

soil type 1

soil type 2

soil type 3

soil type 4

## Directions

## r

m

0.5085

0.5085

0.5085

0.5085

## Gs

kN/m

112892

58320

42240

19965

## ð›Žs

## -

0.45

0.2

0.3

0.35

Vertical

## Ks

kN/m2

417495.1

148278.6

122737.4

62475.1

## Cs

kN.s/m

542.0

335.3

305.1

208.4

## ms

kN.s2/m

0.33

0.36

0.36

0.33

Horizontal

## Ks

kN/m

346811.0

159921.2

123092.0

59554.0

## Cs

kN.s/m

298.0

210.1

184.3

122.8

## ms

kN.s2/m

0.06

0.07

0.07

0.06

## 6. FEM MODEL

The numerical analysis of the rectangular storage tank structure is performed on the basis of detailed FEM model developed with the help of the routines available in the ANSYS Finite Element program (ANSYS 2008), as shown in Plate (2). The rectangular storage tank is modeled by 26485 or 19093 respectively, for the two cases of tank considered in this work, i.e. the underground tank and the tank above ground, four-noded shell elements (SHELL63) with six DOFs per node. The eight node solid fluid element (FLUID80), with three DOFs per node, has been chosen to model the incompressible fluid content. A total of 4368 or 8736 FLUID80 elements are used, respectively, for the three levels of tank fullness considered in this work, i.e. empty, half full and full. In order to satisfy the continuity conditions between the fluid and solid media at the rectangular tank boundary, the coincident nodes of the fluid and shell elements are constrained to be coupled in the direction normal to the interface, while relative movements are allowed to occur in the tangential directions. The uniaxial "tension only" behavior of the braces is simulated by means of the 3-D spar elements LINK10, which feature a bilinear stiffness matrix, i.e. the stiffness is removed if the element goes into compression. The viscous fluid damper devices are modeled using the 1-D non-linear damper elements COMBIN37. Finally, concentrated mass elements (MASS21) and linear spring-damper elements (COMBIN14) are used to model the discrete elements for the simulation of soil-structure interaction. The above FEM rectangular tank model is numerically analyzed by means of a full transient linear analysis. The governing equations of motion can be expressed in matrix form as (Chopra 1996).

(1)

with [M], and being the mass, damping and stiffness matrices of the structure, respectively, an influence coefficient matrix, and the ground acceleration. Eq. (1) is integrated directly in time using the Newmark-Î² method.

## Plat (2) Finite element rectangular tank model

## 7. NUMERICAL STUDY

The seismic response of the rectangular liquid storage tank above ground and underground is investigated by performing two types of analyses: (i) modal analysis and (ii) time domain analysis. The problem is solved for four types of soil.

## 7.1 Modal Analysis

The first step in the dynamic analysis of any structural system is to determine the free vibration response such as natural frequencies and mode shapes, which are important in calculating the seismic response of the liquid storage tanks. The Block Lanczos method is used in ANSYS for the Eigenvalue and Eigenvector extractions to calculate natural frequencies including the fluid modes (Hallquist 1998).

## 7.1.1 Effect of Tank Height to Length Ratio Variation

For this purpose, two cases of storage tanks are considered, the tank above ground and buried tank, for each case it has been used empty and completely full tanks. The results of natural frequencies are given in Fig.(2) and (3) for empty and completely full tanks, after using four different types of soil, it has been observed that weakest the soil (having low shear modules (Gs)), for this reason the natural frequencies getting less for the weakest soil, that become clear in soil type No. 4.

## Above ground Underground

## Figure (2) Fundamental natural frequencies versus aspect ratio (Ht/lx) variation of empty tank

## Above ground Underground

## Figure (3) Fundamental natural frequencies versus aspect ratio (Ht/lx) variation of full tank

In comparing the results between the two cases of the tanks (the tank above ground and buried tank), it has been found that the buried tank has natural frequencies less than the tank above ground, because the mass of the tank will increase and that will make the natural frequencies getting less. It is also noticed by examining these tables and plots, that the natural frequencies of the empty tank are much larger than those of the full tanks regardless of the type of soil.

## 7.1.2 Effect of Liquid Height to Tank Length Ratio Variation

To demonstrate the effect of liquid height variation (HL/Ht), two cases of the tanks (the tank above ground and buried tank) were considered for this purpose. The resulting natural frequencies are given in Fig.(4) for above ground and buried tanks respectively.

## Above ground Underground

## Figure (4) Fundamental natural frequencies versus filling ratio (HL/Ht)

It can be observed from these tables and plots that, as the level of fluid in the tank increases, the natural frequencies decrease for both cases of tanks and for all four types of the soil. This behavior is obvious since the mass of the structure system increases with the level of fluid.

## 7.1.3 Effect of Wall Thickness Variation

To demonstrate the effect of wall thickness variation, empty tank and completely full tank, is studied for the free vibration characteristics when its wall thickness varies from 450mm to 1350mm with one type of the surrounding soil (soil type 1), and also for two cases (above ground and buried tank).

## Above ground Underground

## Figure (5) Effect of thickness variation on natural frequencies of empty tank

## Above ground Underground

## Figure (6) Effect of thickness variation on natural frequencies of full tank

The resulting natural frequencies are given in Fig.(5) and (6). It can be seen clearly from these results that, the natural frequencies increases when the thickness of the wall increases without changing the height of the tank (the wall stiffness increases with increasing its thickness).

## 7.2 Time Domain Analysis

A time history analysis using the first five seconds of the north-south component of the 1940 El Centro earthquake was used for the linear elastic model. Peak ground acceleration values were adjusted to 0.318g. Model time history analysis under linear elastic, small deformation assumptions included evaluation of water surface profiles top displacements, axial force, and resulting base shear. The following sections summarize results.

The four sets of figures drawn for the different two types of surrounding soil are assumed (soil type 1, and 2 as mentioned in article (5)), with different levels of water (full, half -full, and empty tank) are considered, as shown in Figs.((7) - (10)). The plots presented for earthquake response of the rectangular tank above ground demonstrate that top displacement and axial force components for a full tank case have values greater than those in half- full (31%) and empty tank cases (75%). At the opposite of that, the underground rectangular tank demonstrate that top displacement and axial force components for an empty tank case have values greater than those in half- full (19%) and full tank cases (40%).

It is also interesting to notice that the base shear for above ground tank case have values greater than those in underground tank cases (19% to 37%). The shear base for soil type 2 is greater than those in soil type 1(17% to 28%). It is found that the surrounding soil type has a significant influence on the tank response, as shown in Fig.(11) and (12).

## Soil type 1 Soil type 2

## Figure (7) Plot of the top displacement-versus wall height ratio above the base (tank above ground)

## Soil type 1 Soil type 2

## Figure (8) Plot of the top displacement-versus wall height ratio above the base (buried tank)

## Soil type 1 Soil type 2

## Figure (9) Axial Force- wall height ratio for relationships above the base in long wall

## Soil type 1 Soil type 2

## Figure (10) Axial Force- wall height ratio for relationships above the base in long wall

## Soil type 1 Soil type 2

## Figure (11) Plot of base shear-height of water (tank above ground)

## Soil type 1 Soil type 2

## Figure (12) Plot of base shear-height of water (buried tank)

## 8. CONCLUSIONS

It is concluded that the soil tank interaction is represented by an elastic half-space medium. Variations of the properties of surrounding soil medium are found to have an important influence on the free and forced vibrational response (seismic excitation) for the storage tanks.

The frequencies in the above ground tank are greater than those for buried tank nearly (26% to 27%), and the frequencies in type 1 case have values greater than those in type 2 nearly (29% to 31%).

The shear base for above ground tank have values greater than those in underground tank by ratio (19% to 37%), The shear base for soil type 2 is greater than those in soil type 1 by ratio (17% to 28%). It is found that the surrounding soil type has a significant influence on the tank response.

It is also found that, the natural frequency is proportional to the wall thickness of the tank. This behavior is related to the fact that the dynamic stiffness of a tank is a function of its wall thickness.