Variable friction pendulum system for seismic isolation of liquid storage tanks

doi:10.1016/j.nucengdes.2007.10.011

Nuclear Engineering and Design

Volume 238, Issue 6, June 2008, Pages 1304-1315

https://doi.org/10.1016/j.nucengdes.2007.10.011 Get rights and content

Abstract

Earthquake response of liquid storage steel tanks isolated with variable friction pendulum system (VFPS) is investigated under normal component of six recorded near-fault ground motions. The continuous liquid mass of the tank is modeled as lumped masses known as sloshing mass, impulsive mass and rigid mass. The corresponding stiffness constants associated with these lumped masses are worked out depending upon the properties of the tank wall and liquid mass. The governing equations of motion of the tanks isolated with variable friction pendulum system are derived and solved by Newmark's step-by-step method assuming linear variation of acceleration over small time interval. In order to verify the effectiveness of the VFPS in tanks, the seismic response of tanks isolated with VFPS is compared with that of the same tanks isolated using the conventional friction pendulum system (FPS). Furthermore, a parametric study is also carried out to critically examine the behaviour of tanks isolated with VFPS. The various important parameters considered are the tank aspect ratio, the isolation period and initial time period of the VFPS. In addition, the seismic response of tanks isolated with VFPS under trigonometric cycloidal pulses is also investigated. From these investigations, it is concluded that with the installation of VFPS in tanks, the seismic response of tanks during near-fault ground motions can be controlled within a desirable range. Finally, it is also observed that the response of tanks isolated with VFPS under the near-fault ground motions and trigonometric cycloidal pulses matches well only when the isolation period reaches high values.

Introduction

Liquid storage tanks are lifeline structures and strategically very important, since they have vital use in industries and nuclear power plants. Unlike most structures (such as buildings or bridges), the weight of storage tanks varies in time because of variable liquid storage level, and they may contain low-temperature (e.g., LNG) or corrosive substances. Recent years have seen a number of occurrences of catastrophic failures of liquid storage tanks due to severe, impulsive, seismic events such as the 1994 Northridge earthquake in California, the 1995 Kobe earthquake in Japan and 1999 Chi-Chi earthquake in Taiwan. Such failures have been due to the number of causes with the most common being buckling of tank wall due to excessive development of compressive stresses in the wall, failure of piping system and uplift of the anchorage system. Failures of storage tanks not only instantly disrupts essential infrastructure but can also cause fires or environmental contamination when flammable materials or hazardous chemicals leak. Consequently, protection of liquid storage tanks against severe seismic events has become crucial. For over three decades, seismic isolation technology has been recognized as one of the promising alternatives for protecting liquid storage tanks against severe earthquakes. The main concept in isolation is to increase the fundamental period of structural vibration beyond the energy containing period of earthquake ground motions. The other purpose of an isolation system is to provide an additional means of energy dissipation, thereby, reducing the transmitted acceleration into the superstructure. The innovative design approach aims mainly at the isolation of a structure from the supporting ground, generally in the horizontal direction, in order to reduce the transmission of the earthquake motion to the structure.

A number of authors have discussed the effectiveness of base isolation for aseismic design of liquid storage tanks. Malhotra (1997) investigated the seismic response of base-isolated tanks and found that isolation was effective in reducing the response of the tanks over traditional fixed base tank without any significant change in sloshing displacement. Shenton III and Hampton (1999) investigated the seismic response of isolated elevated tanks and found that seismic isolation is effective in reducing the tower drift, base shear, overturning moment, and tank wall pressure for the full range of tank capacities. Wang et al. (2001) investigated the response of liquid storage tanks isolated by friction pendulum system (FPS) and observed that the isolation was effective in reducing the response of the tanks. Shrimali and Jangid (2002) investigated the seismic response of liquid storage tanks isolated by lead–rubber bearings under bi-directional earthquake excitation and observed that the seismic response of isolated tanks is insensitive to interaction effect of the bearing forces. Shrimali and Jangid (2004) presented the earthquake analysis of base-isolated liquid storage tanks using linear theory of base isolation. Jadhav and Jangid (2006) investigated the seismic response of liquid storage tanks isolated by elastomeric bearings and sliding systems under near-fault ground motions and observed that both elastomeric and sliding systems were effective in reducing the earthquake forces of the liquid storage tanks. In spite of the above studies, there have not been many attempts to investigate the dynamic behaviour of liquid storage tanks under near-fault ground motions. Consequently, the effects of these motions on liquid storage tanks are not yet understood fully.

Near-fault ground motion can introduce more devastating response to isolated structures than an equal or larger (higher peak ground acceleration) far-field ground motion (Loh et al., 2002). Such strong response especially large isolator displacement will lead to very large isolators, costly flexible connections for utilities and an extensive and expensive loss of space for a seismic gap or moat. Moreover, if the seismic gap is inadequate to accommodate such large isolator displacement, then the resulting impact response can be undesirable (Nagarajaiah and Sun, 2001). To reduce this displacement, supplementary dampers are often prescribed. However, additional damping may also increase the internal motion of the superstructure as well as increase accelerations, thus defeating many gains for which base isolation is intended. Therefore, control of large isolator displacement has been of special concern in recent research. This concern profoundly influenced seismic isolation design requirements in the 1997 Uniform Building Code (ICBO, 1997). In the earlier code, there were no near-fault effects but in the recent code, near-fault effects viz. source type and distance dependent near-fault factors to the customary design spectrum have been introduced. However, it is believed that these factors are not sufficient to solve the problem consistently, because they pay little attention to the physical characteristics of near-fault ground motions. In view of this, it is necessary to conduct the reliable numerical studies on the behaviour of base-isolated liquid storage tanks under near-fault ground motions in order to control the large isolator displacement as well as to provide assistance to current research and engineering practice.

In this paper, the seismic response of liquid storage slender and broad tanks isolated with variable friction pendulum system (VFPS) is investigated under near-fault ground motions. The specific objectives of the present study may be summarized as: (i) to study the dynamic behaviour of liquid storage tanks isolated with VFPS under near-fault ground motions, (ii) to compare the seismic response of liquid storage tanks isolated with VFPS and FPS in order to measure the effectiveness of VFPS, (iii) to investigate the influence of important parameters on the response of liquid storage tanks isolated with VFPS through a parametric study. The important parameters considered are the tank aspect ratio, the isolation period and initial time period of the VFPS and (iv) to study the seismic response of liquid storage tanks isolated with VFPS under trigonometric cycloidal pulses.

Section snippets

Near-fault ground motions

Seismologists have identified the forward directivity and fling-step as the primary characteristics of near-fault ground motions. These characteristics make near-fault earthquakes unique compared to far-field ground motions. The fling-step usually induces only limited inertial demands on structures due to the long-period nature of the static displacement. On the other hand, ground motions that are influenced by forward-directivity effects can be very damaging to structures. Forward-directivity

Modeling and idealization

The model considered for the base-isolated cylindrical liquid storage tanks is shown in Fig. 2 in which the VFPS is installed between base and foundation of the tank. The contained liquid is considered as incompressible, inviscid and has irrotational flow. During the base excitation, the entire tank liquid mass vibrates in three distinct patterns such as sloshing or convective mass (i.e., top liquid mass controlling the free liquid surface), impulsive mass (i.e., intermediate liquid mass

Variable friction pendulum system

The VFPS is very similar to FPS in regards of details as shown in Fig. 3(a). The difference between FPS and VFPS is that the friction coefficient of FPS is considered to be constant whereas the friction coefficient of VFPS is varied in form of curve as shown in Fig. 3(b). The equation to define the curve for friction coefficient of VFPS is shown as follows: $μ = (μ_{0} + a_{1} | x_{b} |) e^{- a_{2} | x_{b} |}$ where μ₀ is the initial value of friction coefficient; a₁ and a₂ are the parameters that describe the variation of

Governing equations of motion

The governing equations of motion of isolated liquid storage tank subjected to uni-directional near-fault ground motion are expressed in the matrix form as $[M] {\ddot{x}} + [C] {\dot{x}} + [K] {x} + {F} = - [M] {r} {\ddot{u}}_{g}$ where {x} = {x_c, x_i, x_b}^T and {F} = {0, 0, F_x}^T are the relative displacement and frictional force vectors, respectively; x_c = u_c − u_b is the displacement of the sloshing mass relative to bearing displacement; x_i = u_i − u_b is the displacement of the impulsive mass relative to bearing displacement; x_b = u_b − u_g is the

Numerical study

The seismic response of liquid storage tanks isolated with VFPS under normal component of six near-fault ground motions is investigated. For comparative and detailed parametric study, two different types of tanks, namely, the broad and slender tanks are considered. The tank parameters such as damping ratio of convective mass, ξ_c and the impulsive mass, ξ_j are taken as 0.5% and 2%, respectively. The tank wall considered is made of steel with a modulus of elasticity of E = 200 GPa and mass density, ρ

Behaviour of liquid storage tank isolated with VFPS under trigonometric cycloidal pulses

It was shown that the near-fault ground motions come in large variations which make a consistent evaluation of near-fault effects difficult and cumbersome. If simple cycloidal pulses can be found that represent the impulsive characteristics of near-fault ground motions with reasonable accuracy, the process of response evaluation or prediction is significantly facilitated. Furthermore, the study of simple pulses along with real ground motions provides a more transparent picture of near-fault

Conclusions

The seismic response of liquid storage tanks isolated with variable friction pendulum system is investigated under six recorded near-fault ground motions. The normal component of six near-fault ground motions is utilized as input to study the variation of base shear, sloshing displacement, impulsive displacement and isolator displacement. The comparison of the seismic response of liquid storage tanks isolated with VFPS and FPS is made in order to verify the effectiveness of VFPS. Further, a

References (20)

F.-G. Fan et al.
Multi-story base-isolated buildings under a harmonic ground motion—Part II: sensitivity analysis
Nucl. Eng. Des.
(1990)
N.S. Kim et al.
Pseudodynamic test for evaluation of seismic performance of base-isolated liquid storage tanks
Eng. Struct.
(1995)
M.K. Shrimali et al.
Non-linear seismic response of base-isolated liquid storage tanks to bi-directional excitation
Nucl. Eng. Des.
(2002)
M.K. Shrimali et al.
Seismic analysis of base-isolated liquid storage tank
J. Sound Vib.
(2004)
B. Alavi et al.
Behavior of moment-resisting frame structures subjected to near-fault ground motions
Earthquake Eng. Struct. Dyn.
(2004)
J.F. Hall et al.
Near-source ground motion and its effects on flexible buildings
Earthquake Spectra
(1995)
M.A. Haroun
Vibration studies and test of liquid storage tanks
Earthquake Eng. Struct. Dyn.
(1983)
International Conference of Building Officials, 1997. Uniform Building Code, Earthquake regulations for seismic...
M.B. Jadhav et al.
Response of base-isolated liquid storage tanks to near-fault motions
Struct. Eng. Mech.
(2006)
R.S. Jangid et al.
Base isolation for near-fault motions
Earthquake Eng. Struct. Dyn.
(2001)

There are more references available in the full text version of this article.

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Variable friction pendulum system for seismic isolation of liquid storage tanks

Abstract

Introduction

Section snippets

Near-fault ground motions

Modeling and idealization

Variable friction pendulum system

Governing equations of motion

Numerical study

Behaviour of liquid storage tank isolated with VFPS under trigonometric cycloidal pulses

Conclusions

Nucl. Eng. Des.

Eng. Struct.

Nucl. Eng. Des.

J. Sound Vib.

Behavior of moment-resisting frame structures subjected to near-fault ground motions

Earthquake Eng. Struct. Dyn.

Near-source ground motion and its effects on flexible buildings

Earthquake Spectra

Vibration studies and test of liquid storage tanks

Earthquake Eng. Struct. Dyn.

Response of base-isolated liquid storage tanks to near-fault motions

Struct. Eng. Mech.

Base isolation for near-fault motions

Earthquake Eng. Struct. Dyn.