Behavior Of Liquid Storage Tanks Research Articles

Identification of the factors influencing the liquid sloshing wave height in a sloped bottom tank under horizontal excitation using PCA approach

The dynamic behavior of liquid storage tanks represents a pivotal research area concerning structural safety and reliability. Notably, sloped bottom tanks exhibit heightened sloshing with reduced liquid mass compared to rectangular counterparts. This study adopts a hybrid approach that seamlessly integrates the linear potential-flow theory, renowned for its analytical rigor in fluid dynamics modeling, with principal component analysis (PCA), a potent technique for dimensionality reduction and feature extraction. The hybrid methodology initially employs the linear potential-flow theory to simulate the fundamental fluid dynamics within sloped bottom tanks subjected to horizontal excitation. Subsequently, PCA is applied to the simulated data, identifying key components of liquid sloshing wave height variations. Through the analysis of these principal components, an accurate model of the maximum sloshing wave height is derived, achieving a close correlation with ANSYS simulation results, exhibiting a correlation coefficient of 0.98 and a mean absolute error of 2.5%. This approach uniquely facilitates the evaluation of the intricate interplay between multiple factors, including tank geometry and excitation frequency, on the dynamic characteristics of liquid sloshing waves in sloped bottom tanks. The findings emphasize the significant influence of tank height and tilt angle, with a sensitivity analysis indicating a 4.07% increase in maximum wave height per degree increase in tilt angle under specified experimental conditions. This comprehensive methodology not only enhances understanding of the complex liquid sloshing phenomenon but also provides precise theoretical and practical guidance for fluid sway control strategies. Future investigations will further expand the scope and elucidate the fundamental mechanisms governing liquid sloshing dynamics.

Liquid Sloshing in Soil-Supported Multiple Cylindrical Tanks Equipped with Baffle under Horizontal Excitation

The dynamic behavior of liquid storage tanks is one of the research issues about fluid–structure interaction problems. The analysis errors of the dynamics of multiple adjacent tanks can exist if neglecting soil–tank interaction since tanks are typically supported on flexible soil. In the present paper, the dynamics of a group of baffled cylindrical storage tanks supported on a circular surface foundation and undergoing horizontal excitation are analytically examined. For upper multiple tank–liquid–baffle subsystems, accurate solutions to the velocity potential for liquid sloshing are acquired according to the subdomain partition technique. A theoretical model is utilized to portray the continuous sloshing of each tank. For the soil–foundation subsystem, a lumped-parameter model is used to characterize the impacts of soil on upper-tank structures using Chebyshev complex polynomials that present the fitting results of horizontal, rocking, and coupling impedance functions. Then, a model of the soil–foundation–tank–liquid–baffle system is constructed on the basis of the substructure approach. The present sloshing frequencies, sloshing height, and hydrodynamic shear as well as the moment under rigid/soft soil foundations are compared to the available exact results and the numerical results to prove the validity of the present model. The error of the maximum sloshing height between the present and the numerical solutions is within 5.27%; the solution efficiency of system dynamics from the present model is 40–50 times faster than that from the ADINA model. A detailed parameter analysis of the dynamic characteristics and earthquake responses of the coupling system is presented. The research novelty is that an equivalent analytical model is presented, and it allows for investigating the dynamics of soil-supported multiple cylindrical tanks with a baffle, providing acceptable accuracy and high calculation efficiency.

Effects of Uncertain Soil Parameters on Seismic Responses of Fixed Base and Base-Isolated Liquid Storage Tanks

ABSTRACT Effects of soil-structure interaction (SSI) on the seismic performance of cylindrical ground-supported liquid storage tanks are studied. The present study attempts to investigate the effects of uncertainties, associated with the critical soil parameters, on the seismic behavior of liquid storage tanks. Random multi-layered soil models coupled with the fixed base liquid storage tank are developed and analyzed. Further, the tank structure is considered base-isolated with lead rubber bearing and analyzed with the same set of soil models, to investigate the seismic behavior of base-isolated tank under uncertain soil condition. A set of three ground motions are selected from a large suite through a mean spectral matching scheme for investigating the effect of soil uncertainties on the seismic response. Distributions of the peak seismic response quantities observed herein show that the uncertainties in soil parameters critically affect the seismic responses of fixed base and base-isolated liquid storage tanks. Sloshing displacement of fixed base and base-isolated tanks is affected by both uncertainty in the soil parameters and ground motion characteristics. Nevertheless, for ground-supported tank, relatively larger dispersion or variability of base shear and overturning moment, as compared to that of the sloshing response, is observed.

Seismic vulnerability assessment of base isolated liquid storage tanks under near-fault ground motions

This paper aims to develop the fragility curves of base isolated liquid storage tanks under near-fault ground motions. Liquid storage tanks are important lifeline structures for industrial plants, but the damages from the past earthquakes showed their vulnerability. The seismic isolation technique is a promising approach to reduce the seismic demand in liquid storage tanks. It should be considered that near-fault ground motions can damage base-isolated liquid storage tanks due to their characteristics such as pulses in their time history velocity. Therefore, it is important to assess the vulnerability of the liquid storage tanks under near-fault ground motion. Fragility curves are useful tools for structural engineers to evaluate seismic performance of structures. In this study, two types of liquid storage tanks, i.e., broad and slender, are considered. The fragility curves for both non-isolated tanks and base-isolated tanks by Friction Pendulum System are developed and compared. Six failure criteria have been considered for the fragility curves, including vertical displacement of convective mass, elastic buckling of tank wall, yielding of anchorages, elephant foot buckling, pipe-line fracture and base isolation displacement. Furthermore, the effect of the isolation period and the coefficient of friction on the fragility curves are investigated. The results show that the pipeline fracture and the tank’s wall buckling are the two most important parameters, which govern the behaviour of liquid storage tanks.

Effect of MetaFoundation on the Seismic Responses of Liquid Storage Tanks

Cylindrical liquid storage tanks are vital lifeline structures, playing a critical role in industry and human life. Damages to these structures during previous earthquakes indicate their vulnerability against seismic events. A novel strategy to reduce the seismic demands in the structures is the use of metamaterials, being periodically placed in the foundation, called MetaFoundation (MF). The periodic configuration of metamaterials can create a stop band, leading to a decrease in wave propagation in the foundation. The aim of this paper is to study the effect of MF on the dynamic behaviour of liquid storage tanks. To that end, the governing equations of motion of the liquid storage tank equipped with MF are derived and solved in the time domain to obtain the time history of the responses under a set of ground motions. Then, the peak responses of tanks, mounted on MF, are compared with the corresponding responses in the fixed base condition. Besides, a parametric study is performed to assess the effect of the predominant frequency of earthquakes, the number of layers of metamaterials, the thickness of soft material, and the damping ratios of soft material on the performance of the MF. The obtained results indicate that the MF improves the dynamic behaviour of the squat tank, in which the mean ratio of responses using MF to the ones in the fixed base conditions equals 0.551 for impulsive displacement, overturning moment, and base shear.

Evaluation of the seismic response of liquid storage tanks

The paper presents a few case studies on the seismic response behavior of liquid storage tanks (LSTs), for which not much literature is available. They include (i) the comparison between responses obtained by the 2D-FE analysis and analysis performed according to the procedure recommended by ACI 350.3 for different PGA levels of ground motions; (ii) the comparison between the variations of sloshing heights, base shear, and overturning moment with the PGA obtained by the 2D- and 3D-FE analyses; (iii) the effect of bi- and tri-directional earthquake interactions on different responses; and (iv) the effect of angle of incidence of the earthquake on those responses. The numerical study is conducted with a square tank of size 6 m

Non-Contact Water Level Response Measurement of a Tubular Level Gauge Using Image Signals.

The occurrence of excessive fluid sloshing during an earthquake can damage structures used to store fluids and can induce secondary disasters, such as environmental destruction and human casualties, due to discharge of the stored fluids. Thus, to prevent such disasters, it is important to accurately predict the sloshing behavior of liquid storage tanks. Tubular level gauges, which visually show the fluid level of a liquid storage tank, are easy to install and economical compared to other water level gauges. They directly show the fluid level and can be applied for various fluids because they can be constructed with various materials according to the fluid characteristics and the intended use. Therefore, in this study, the shaking table test was conducted to verify the validity of the method for measuring the water level response of the tubular level gauge installed on a liquid storage tank using image signals. In addition, image enhancement methods were applied to distinguish between the float installed in the tubular level gauge and the gray level of the background.

An innovative isolation system for improving the seismic behaviour of liquid storage tanks

Abstract The current study proposes a new vertical seismic isolation of an aboveground liquid storage tank (AST) and theoretically and numerically evaluates its effectiveness for a comprehensive practical range of tank geometries. In the proposed system, the forces in the vertical direction caused by the overturning moment are isolated as an alternative to the common horizontal system used for shear base isolation of ASTs. The equations of motion for a liquid tank equipped in the proposed system were extracted using the mass-spring simplified model of contained liquid. A parametric study was performed by employing the non-linear solution of the governing equations and the effectiveness of the proposed system for all AST aspect ratios is discussed. The numerical results show that the overturning moment of the tanks equipped with the proposed isolation system decreased significantly with respect to the corresponding fully anchored tanks. The results of the parametric study on the tank aspect ratio and liquid height indicate that the proposed system is more efficient for slender tanks than for broad tanks.

Strengthening of Cylindrical Steel Water Tank Under the Seismic Loading

Cylindrical steel tanks are widely used to water store and for cooling in nuclear power plants. The seismic behaviour of liquid storage tanks is very complicated due to the hydrodynamic pressures of the fluids in them. In this paper, the epoxy-carbon coating method is suggested to improve of seismic performance of cylindrical steel tanks. Composite epoxy-carbon materials are widely used for winding thin walled cylindrical steel structures. After tank had coated with epoxy–carbon composite material, it was observed that Equivalent (von-Mises) stresses significantly decreased. The maximum hoop stress in the unprotected tank is 81.92 MPa, while the maximum stress is reduced to 44.77 MPa after it was coated with the epoxy-carbon.

Seismic Behavior of Liquid Storage Tanks Using Complex and Simple Analytical Models

Performance-based seismic evaluation is usually done by considering simplified models for the liquid storage tanks therefore, it is important to validate those simplified models before conducting such evaluation. The purpose of this study is to compare the seismic response results of the FSI (fluid-structure interaction) model and the simplified models for the cylindrical liquid storage tanks and to verify the applicability of the simplified models for estimating failure probability. Seismic analyses were carried out for two types of storage tanks with different aspect ratios (H/D) of 0.45 and 0.86. FSI model represents detailed 3D fluid-structure interaction model and simplified models are modeled as cantilever mass-spring model, frame type mass-spring model and shell type mass-spring model, considering impulsive and convective components. Seismic analyses were performed with modal analysis followed by time history analysis. Analysis results from all the models were verified by comparing with the results calculated by the code and literature. The results from simplified models show good agreement with the ones from detailed FSI model and calculated results from code and literature, confirming that all three types of simplified models are very valid for conducting failure probability analysis of the cylindrical liquid storage tanks.

A COMPARATIVE ANALYTICAL AND EXPERIMENTAL ANALYSIS OF SLOSHING WAVES IN RECTANGULAR TANK UNDER SEISMIC CONDITION

Many past earthquakes have witnessed failure of liquid storage tanks in various ways. Sloshing action is one of major kinds of them. Hence it becomes essential to detect the pattern of surface wave and use preventive measures. As we know that the mass of water can be thought of as two parts, impulsive at lower depth and convective at upper depth. This analysis work was primarily focused on convective part. In this experimental study, the earthquake induced waves were analyzed with a representing tank model using shake table facility at DTU, Delhi. Further, the wave patterns and seismic parameters were determined analytically, and results were compared. The work gives a fair idea to study the seismic behavior of liquid storage tanks.

MEMBRANE FUNCTION AS INTERIOR WALL TO CONTROL THE DYNAMIC RESPONSE OF TANKS

Sloshing represents a low-frequency fluctuations of the fluid in the half-full tank which if not controlled effectively, could be as one of the most important factors of destruction and reversal of tanks. Thus, study of the behavior of liquid storage tanks and providing new ways to reduce sloshing and to improve seismic response of tanks, due to the high costs of construction, has considerable importance. In this paper, the ability to control sloshing and demand reduction in external solid walls in two parts using two different methods have been investigated. In the first part, analysis are done in ANSYS finite element software and their accuracy are examined. In the second part, possibility of using membrane wall to improve performance of fluid-structure interaction system in tanks, by studying the behavior and performance of a tank with membrane wall in a manner similar to that mentioned in the first part, is studied. In this case, adjustment of fluid dynamics and structure has been done by tuning the tensile force applied to the membrane and the mass of the membrane, and system response has been compared with rigid tank state to evaluate the effects of applying membrane wall.

An efficient computational procedure for the dynamic analysis of liquid storage tanks

Abstract A computationally efficient numerical model is developed in this study for evaluating the dynamic behavior of liquid storage tanks. This model has higher complexity than the Housner model (which corresponds to the simplest and most popular approach for approximating the behavior of rectangular and circular tanks) but still enjoys high computational simplicity to facilitate implementation in practice, while it is applicable to virtually any kind of tank geometry, providing at the same time a high degree of accuracy. In the proposed model, the liquid is assumed to be inviscid, incompressible and irrotational, and its motion is completely characterized by a velocity potential function. Thus, the Continuity and Equilibrium equations characterizing this motion take the form of Laplace and Bernoulli equations, respectively. The Laplace equation is solved through a 2D finite element scheme, and is then combined with the Bernoulli equation through the velocity potential function condensed at the free surface of the liquid. Numerical details for the practical implementation of the proposed scheme are discussed, whereas the approximation is shown to provide results with high accuracy for the dynamic behavior of different type of tanks when compared to the Housner model and a full finite element implementation. As shown in the examples considered the computational efficiency of the proposed model is such that extensive parametric studies can be performed with small numerical effort, which in turn makes the proposed model very attractive not only for analysis purposes but also for the design of liquid storage tanks and other related devices such as tuned liquid dampers.

Behaviour of liquid storage tanks with VCFPS under near-fault ground motions

Earthquake response of slender and broad liquid storage steel tanks isolated with variable curvature friction pendulum systems (VCFPSs) is investigated under near-fault motions. The tanks isolated with VCFPS are idealised with three-degrees-of-freedom associated with convective, impulsive and rigid masses. The frictional forces mobilised at the interface of the VCFPS are assumed to be velocity independent. The governing equations of motion of isolated tank are derived and solved in the incremental form using Newmark's method. For comparative study, the seismic response of liquid storage tanks with the VCFPSs is compared with that of same liquid storage tanks isolated using the friction pendulum systems (FPSs). The seismic response of isolated liquid storage tanks is also compared with that of the non-isolated tanks. Further, a parametric study is carried out to critically examine the behaviour of liquid storage tanks isolated with the VCFPSs. The important parameters considered are the friction coefficient of VCFPS, the fundamental period at the centre of the sliding surface of VCFPS and the tank aspect ratio. It is observed that under near-fault ground motions, the VCFPS is quite effective in controlling the seismic response, viz. the base shear, the sloshing displacement and the impulsive displacement, of liquid storage tanks.

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.

Storage Tanks Under Earthquake Loading

This is a state-of-the-art review of various treatments of earthquake loaded liquid filled shells by the methods of earthquake engineering, fluid dynamics, structural and soil dynamics, as well as the theory of stability and computational mechanics. Different types of tanks and different possibilities of tank failure will be discussed. We will emphasize cylindrical above-ground liquid storage tanks with a vertical axis. But many of the treatments are also valid for other tank configurations. For the calculation of the dynamically activated pressure due to an earthquake a fluid-structure-soil interaction problem must be solved. The review will describe the methods, proposed by different authors, to solve this interaction problem. To study the dynamic behavior of liquid storage tanks, one must distinguish between anchored and unanchored tanks. In the case of an anchored tank, the tank bottom edge is fixed to the foundation. If the tank is unanchored, partial lifting of the tank’s bottom may occur, and a strongly nonlinear problem has to be solved. We will compare the various analytical and numerical models applicable to this problem, in combination with experimental data. An essential aim of this review is to give a summary of methods applicable as tools for an earthquake resistant design, which can be used by an engineer engaged in the construction of liquid storage tanks.

Response of tanks to vertical seismic excitations

AbstractA method for analyzing the earthquake response of elastic, cylindrical liquid storage tanks under vertical excitations is presented. The method is based on superposition of the free axisymmetrical vibrational modes obtained numerically by the finite element method. The validity of these modes has been checked analytically and the formulation of the load vector has been confirmed by a static analysis. Two forms of ground excitations have been used: step functions and recorded seismic components. The radial and axial displacements are computed and the corresponding stresses are presented. Both fixed and partly fixed tanks are considered to evaluate the effect of base fixation on tank behaviour. Finally, tank response under the simultaneous action of both vertical and lateral excitations is calculated to evaluate the relative importance of the vertical component of ground acceleration on the overall seismic behaviour of liquid storage 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.