Response Of Liquid Storage Tanks Research Articles

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

Seismic response of the liquid storage tanks isolated by the elastomeric bearings and sliding systems is investigated under near-fault earthquake motions. The fault normal and parallel components of near-fault motion are applied in two horizontal directions of the tank. The continuous liquid mass of the tank is modeled as lumped masses known as sloshing mass, impulsive mass and rigid mass. The corresponding stiffness associated with these lumped masses has been worked out depending upon the properties of the tank wall and liquid mass. It is observed that the resultant response of the isolated tank is mainly governed by fault normal component with minor contribution from the fault parallel component. Further, a parametric study is also carried out to study the effects of important system parameters on the effectiveness of seismic isolation for liquid storage tanks. The various important parameters considered are: aspect ratio of tank, the period of isolation and the damping of isolation bearings. There exists an optimum value of isolation damping for which the base shear in the tank attains the minimum value under near-fault motion. The increase of damping beyond the optimum value will reduce the bearing and sloshing displacements but increases the base shear. A comparative performance of five isolation systems for liquid storage tanks is also studied under normal component of near-fault motion and found that the EDF type isolation system may be a better choice for design of isolated tank in near-fault locations. Finally, it is also observed that the satisfactory response can be obtained by analysing the base-isolated tanks under simple cycloidal pulse instead of complete acceleration history.

Effect of vertical acceleration on response of concrete rectangular liquid storage tanks

In this study, the response of concrete rectangular liquid storage tanks subjected to vertical ground acceleration is investigated. The importance of the vertical component of ground acceleration on the overall seismic behaviour of liquid storage tanks is evaluated. The combination of added mass and sequential method is proposed in which the flexibility of the tank wall is considered in the dynamic analysis. The time history response of the tank wall associated with the hydrodynamic pressure distribution is presented. Results show that the time history responses of liquid storage tanks by considering the flexibility of the tank wall in the calculation of hydrodynamic pressures are different from those obtained using the rigid wall assumption. The horizontal response of the tank under the assumed rigid wall boundary condition is more significant than that when wall flexibility is considered. It is concluded that the response of the tank wall due to vertical ground acceleration should be considered in the design.

Seismic response of base-isolated liquid storage tanks considering fluid–structure–soil interaction in time domain

The seismic response analysis of a base-isolated liquid storage tank on a half-space was examined using a coupling method that combines the finite elements and boundary elements. The coupled dynamic system that considers the base isolation system and soil–structure interaction effect is formulated in time domain to evaluate accurately the seismic response of a liquid storage tank. Finite elements for a structure and boundary elements for liquid are coupled using equilibrium and compatibility conditions. The base isolation system is modeled using the biaxial hysteretic element. The homogeneous half-space is idealized using the simple spring-dashpot model with frequency-independent coefficients. Some numerical examples are presented to demonstrate accuracy and applicability of the developed method. Consequently, a general numerical algorithm that can analyze the dynamic response of base-isolated liquid storage tanks on homogeneous half-space is developed in three-dimensional coordinates and dynamic response analysis is performed in time domain.

Wavelet‐based non‐stationary seismic rocking response of flexibly supported tanks

AbstractThe non‐stationary rocking response of liquid storage tanks under seismic base excitations including soil interaction has been developed based on the wavelet domain random vibration theory. The ground motion has been characterized through statistical functionals of wavelet coefficients of the ground acceleration history. The tank–liquid–foundation system is modelled as a multi‐degree‐of‐freedom (MDOF) system with both lateral and rocking motions of vibration of the foundation. The impulsive and convective modes of vibration of the liquid in the tank have been considered. The wavelet domain coupled dynamic equations are formulated and then solved to get the expressions of instantaneous power spectral density function (PSDF) in terms of functionals of input wavelet coefficients. The moments of the instantaneous PSDF are used to obtain the stochastic responses of the tank in the form of coefficients of hydrodynamic pressure, base shear and overturning base moment for the largest expected peak responses. Parametric variations are carried out to study the effects of various governing parameters like height of liquid in the tank, height–radius ratio of the tank, ratio of total liquid mass to mass of foundation, and shear wave velocity in the soil medium, on the responses of the tank. Copyright © 2003 John Wiley & Sons, Ltd.

Dynamic Analysis of Liquid Storage Tanks with Sliding Systems

Dynamic response of liquid storage tanks isolated by the sliding systems is investigated under real earthquake ground motion. The frictional force of sliding systems is modelled by conventional and hysteretic models. The continuous liquid mass is lumped as convective mass, impulsive mass and rigid mass. The corresponding stiffness associated with these lumped masses is worked out depending upon the properties of the tank wall and liquid mass. The governing equations of motion of the tank with sliding system are derived and solved by Newmark's step-by-step method with iterations. The frictional force mobilized at the interface of the sliding system is assumed to be velocity dependent. For comparative study, the seismic response of isolated liquid storage tank obtained by the conventional model is compared with the corresponding response obtained by the hysteretic model. In order to measure the effectiveness of isolation system, the seismic response of isolated tank is compared with that of the non-isolated tank. A parametric study is also conducted to study the effects of aspect ratio of tank on the effectiveness of seismic isolation of liquid storage tanks. It is found that the sliding systems are quite effective in reducing the earthquake response of liquid storage tanks. In addition, the conventional and the hysteretic model of the sliding system predict the same seismic response of liquid storage tanks. However, the conventional model is relatively more computationally efficient as compared to the hysteretic model.

Response of Base‐Isolated Liquid Storage Tanks

Seismic response of liquid storage tanks isolated by elastomeric bearings and sliding system is investigated under real earthquake ground motions. The continuous liquid mass of the tank is modeled as lumped masses known as sloshing mass, impulsive mass and rigid mass. The coupled differential equations of motion of the system are derived and solved in the incremental form using Newmark′s step‐by‐step method with iterations. The seismic response of isolated tank is studied to investigate the comparative effectiveness of various isolation systems. A parametric study is also carried out to study the effect of important system parameters on the effectiveness of seismic isolation for liquid storage tanks. The various important parameters considered are: (i) aspect ratio of the tank and (ii) the time period of the isolation systems. It was observed that both elastomeric and sliding systems are found to be effective in reducing the earthquake forces of the liquid storage tanks. However, the elastomeric bearing with lead core is found to perform better in comparison to other systems. Further, an approximate model is proposed for evaluation of seismic response of base‐isolated liquid storage tanks. A comparison of the seismic response evaluated by the proposed approximate method and an exact approach is made under different isolation systems and system parameters. It was observed that the proposed approximate analysis provides satisfactory response estimates of the base‐isolated liquid storage tanks under earthquake excitation.

A COMPARATIVE STUDY OF PERFORMANCE OF VARIOUS ISOLATION SYSTEMS FOR LIQUID STORAGE TANKS

A comparative study of performance of various isolation systems for liquid storage tanks is investigated under real earthquake ground motions. The various base isolation systems considered are the laminated rubber bearings (with and without lead core) and sliding isolation systems (with and without restoring force). The isolated liquid storage tank is idealized with three-degrees-of-freedom associated with convective, impulsive and rigid mass under uni-directional earthquake excitation. Since the force-deformation behaviour of the isolation systems is non-linear, as a result, the equations of motion are solved numerically by step-by-step method. In order to measure the effectiveness of the isolation systems, the seismic response of the isolated liquid storage tanks is compared with the corresponding response of non-isolated tanks. Further, the effectiveness of the isolation is also explored for wide range of practical liquid storage tanks considering the influence of tank aspect ratio. It is observed that the isolation systems are quite effective in attenuating the earthquake acceleration transmitted to the tank, which reduces the design seismic forces significantly. Further, it is also found that the sliding type isolation systems are more effective in controlling the response of liquid storage tanks in comparison to the elastomeric bearings. Among the various sliding systems, the resilient-friction base isolator is found to be most effective for seismic isolation of the tanks.

Non-linear seismic response of base-isolated liquid storage tanks to bi-directional excitation

Seismic response of the liquid storage tanks isolated by lead-rubber bearings is investigated for bi-directional earthquake excitation (i.e. two horizontal components). The biaxial force-deformation behaviour of the bearings is considered as bi-linear modelled by coupled non-linear differential equations. The continuous liquid mass of the tank is modelled as lumped masses known as convective mass, impulsive mass and rigid mass. The corresponding stiffness associated with these lumped masses has been worked out depending upon the properties of the tank wall and liquid mass. Since the force-deformation behaviour of the bearings is non-linear, as a result, the seismic response is obtained by the Newmark's step-by-step method. The seismic responses of two types of the isolated tanks (i.e. slender and broad) are investigated under several recorded earthquake ground to study the effects of bi-directional interaction. Further, a parametric study is also carried out to study the effects of important system parameters on the effectiveness of seismic isolation for liquid storage tanks. The various important parameters considered are: (i) the period of isolation, (ii) the damping of isolation bearings and (iii) the yield strength level of the bearings. It has been observed that the seismic response of isolated tank is found to be insensitive to interaction effect of the bearing forces. Further, there exists an optimum value of isolation damping for which the base shear in the tank attains the minimum value. Therefore, increasing the bearing damping beyond a certain value may decrease the bearing and sloshing displacements but it may increase the base shear.

Seismic response of liquid storage tanks isolated by sliding bearings

The response of liquid storage tanks isolated by the sliding systems is investigated under two horizontal components of real earthquake ground motion. The continuous liquid mass is lumped as convective mass, impulsive mass and rigid mass. The corresponding stiffness associated with these lumped masses is calculated depending upon the properties of the tank wall and liquid mass. The governing equations of motion of the tank with a sliding system are derived and solved by Newmark's step-by-step method with iterations. The frictional forces mobilized at the interface of the sliding system are assumed to be velocity dependent and their interaction in two horizontal directions is duly considered. A parametric study is also conducted to study the effects of important system parameters on the effectiveness of seismic isolation of the liquid storage tanks. The various parameters considered are (i) the period of isolation (ii) the damping of isolation bearings and (iii) the coefficient of friction of sliding bearings. It has been found that the bi-directional interaction of frictional forces has noticeable effects and if these effects are ignored then the sliding base displacements will be underestimated which can be crucial from the design point of view. Further, the dependence of the friction coefficient on relative velocity of the sliding bearings has no significant effects on the peak response of the isolated liquid storage tanks.

Non‐stationary seismic response of tanks with soil interaction by wavelets

AbstractA wavelet‐based random vibration theory has been developed for the non‐stationary seismic response of liquid storage tanks including soil interaction. The ground motion process has been characterized via estimates of statistical functionals of wavelet coefficients obtained from a single time history of ground accelerations. The tank–liquid–soil system has been modelled as a two‐degree‐of‐freedom (2‐DOF) system. The wavelet domain equations have been formulated and the wavelet coefficients of the required response state are obtained by solving two linear simultaneous algebraic equations. The explicit expression for the instantaneous power spectral density function (PSDF) in terms of the functionals of the input wavelet coefficients has been obtained. The moments of this PSDF are used to estimate the expected pseudo‐spectral acceleration (PSA) response of the tank. Parametric variations are carried out to study the effects of tank height, foundation natural frequency, shear wave velocity of soil and ratio of the mass of tank (including liquid) to the mass of foundation on the PSA responses of tanks. Copyright © 2001 John Wiley & Sons, Ltd.

Effects of wall flexibility on the dynamic response of liquid storage tanks

A knowledge of the free vibration characteristics of tank — liquid systems is essential in order to predict dynamic responses. It has been demonstrated that in a dynamic situation impulsive forces are significant because of the elastic compliance of the tank wall. In this paper, the effects of wall flexibility on the dynamic response of liquid storage tanks is considered. Variational principles are used to obtain a functional describing coupled oscillations between a linear elastic body and a liquid of small wave heights. A complementary Rayleigh's quotient has been introduced to obtain coupled natural frequencies and the dynamic pressure distribution in the axisymmetric natural modes of vibration. Both low frequencies (liquid sloshing mode) and high frequencies (tank bulging mode) have been included in this study.

Boundary Element Method for Fluid-Structure Interaction Problems in Liquid Storage Tanks

Abstract The dynamic response of liquid storage tank, including the hydrodynamic interactions, subjected to earthquake excitations is studied by the combinations of boundary element method and finite element procedure in this paper. The tank wall and inviscid fluid domain are treated as two substructures of the total system-coupled through the hydrodynamic pressures. The boundary element method is employed to determine the hydrodynamic pressures associated with small amplitude excitations and negligible surface wave effects in fluid domain which are expressed as the frequency-dependent terms related with the natural vibration modes of elastic tank alone. These terms are incorporated into the finite element formulation of elastic tank in frequency domain and the generalized displacements are computed by synthesizing their complex frequency response using Fast-Fourier Transform procedure. Thus, the hydrodynamic interactions between the elastic flexible tank wall and the fluid are then solved. To demonstrate the accuracy and validity of the solution procedure developed herein, numerical examples are analyzed. Good correlations between the computed results with the referenced solutions in literature can be noted. The effects of fluid compressibility and tank flexibility are also evaluated in this work. Finally, the dynamic response of liquid storage tank due to seismic excitations is also analyzed.

Behavior of Unanchored Fluid-Filled Tanks Subjected to Ground Excitation

An analysis developed for the response of liquid storage tanks under horizontal base excitation is employed and numerical results are obtained for unanchored tanks. These results are compared and found to be in good agreement with experimental data. Base uplift is shown to cause a dramatic reduction in the effective beam-type stiffness of a tank, which in turn reduces the tank response frequency and changes the developed hydrodynamic loads significantly. Based on these results, an explanation is provided for some great qualitative and quantitative differences in the behavior of a tank, resulting from its base fixity condition alone.

Rocking Response of Liquid Storage Tanks

A comprehensive analysis is made of the dynamic response of liquid containing, upright circular cylindrical tanks to a rocking base motion of arbitrary temporal variation. Both rigid and flexible tanks are examined. Critical response quantities for rigid tanks are evaluated over wide ranges of the parameters involved and the results presented in a form convenient for use in practical applications. The interrelationship of the responses of the system to rocking and lateral base motions of the same temporal variation is established, and it is shown that some of the effects of base rocking may be determined from available data concerning the response of laterally excited tanks. Additionally, the well‐known mechanical model for a laterally excited tank is generalized to permit consideration of the effects of base rocking. The influence of tank flexibility is evaluated by an extension of a simple approximate technique proposed previously for laterally excited tanks.

Nonlinear Analysis of Liquid-Filled Tank

Recent developments related to the analysis and design of liquid storage tanks are surveyed. Different aspects of the problem are examined. Background for finite element formulation is also outlined. A numerical tank model which accounts for the lateral pressure loading is developed to provide an understanding of this effect on the behavior of liquid storage tanks. This lateral pressure loading is simulated via an equivalent hydrostatic approach in which the follower force effect is accounted. Results show that the tank model collapses at a critical load 20% lower than the classical prediction. It also shows that the axial stress is basically dominated by cos θ mode. Higher order modes, are significant in the hoop stress profile which is nonlinear in character. The observed “elephant-foot buckle” and the “ovalling” response of liquid storage tanks in many tank failures during earthquakes can be predicted with these nonlinear methodologies.