Response Of Liquid Storage Tanks Research Articles

Seismic Response Analysis of Rectangular Reinforced Concrete Tank Constructed on Loess Soil

Introduction: Liquid storage tanks are an essential container structure widely used in various industries. In earthquake disasters, liquid storage tanks cause not only direct disasters but also induce secondary severe disasters, such as fires, explosions, nuclear leaks, and human and animal poisoning. The latest research on seismic analysis of structures showed that soils with different stiffness can affect the seismic response characteristics of surface structures, and various irregular topographies can also alter the degree of seismic-induced damage to surface structures. Studying the seismic response of liquid storage tanks can mitigate the risk of earthquake damage to these vital structures. Methods: This study used finite element simulations. Three sizes of liquid storage tanks with different aspect ratios were selected, including the squat, square, and slender tanks. Three conditions were considered for the tanks' liquid: empty, half-filled, and fully filled. Two types of topographies were considered, including flat and step-like slope topography with an inclination angle of 116.6°. Nine natural earthquake records were used for seismic analysis and divided into three categories: high-frequency, medium-frequency, and low-frequency. Established finite element models were validated through comparison with the results of other studies. The dynamic time history analysis was carried out for each finite element model. The tank's base shear forces, the normal stress in the tank wall, the shear stress in the tank bottom, and the maximum displacement of the tank wall were measured and compared. Results: The step-like slope topography and loess soil significantly amplified the seismic response of the liquid storage tank. Moreover, as the liquid height and the tanks’ aspect ratio increased, the seismic damage intensity also increased. The seismic response of the liquid storage tank was generally more sensitive to low-frequency and medium-frequency seismic records. The Eurocode 8’s equation underestimated tanks’ base shear when located on a step-like slope topography. Conclusion: The obtained results demonstrated the significant effect of irregular topography and loess soil on the seismic response of liquid storage tanks. Therefore, it was concluded that they should be considered when liquid storage tanks are designed for seismic actions.

Advantages and design of inerters for isolated storage tanks incorporating soil conditions

Inerter-based isolation systems are effective in providing seismic protection for storage tanks. However, the vibration control-oriented mechanism of inerter-based seismic isolation systems on the seismic response of liquid storage tanks remains unclear, with designs limited to rigid base assumptions. Moreover, the objective existence of the soil-structure interaction (SSI) is overlooked. This study contributes to a discovered advantage of the inerter-based isolation system, including the reduction of input energy and precise control of specific or multiple modes of sloshing heights. Furthermore, an advantageous feature-oriented optimal design for storage tanks with an inerter-based isolation system and with the incorporation of soil conditions is proposed in this study. Initially, an analytical model is developed, considering a storage tank with multi-mode sloshing responses and representing SSIs with frequency-dependent stiffness and damping coefficients. Stochastic response analysis is performed, leading to a novel formulation of multi-mode control and an empirical power equation that quantifies the input energy reduction effect. An advantageous feature-oriented optimal design framework, in which the SSI effect, tank geometric parameters, and inerter-based isolation system parameters are implemented, is established through comprehensive parametric analysis. The results demonstrate that the inerter-based isolation system can be intentionally designed to mitigate specific modes of sloshing height, with the inerter effectively reducing the input power of the entire tank. This study emphasizes the importance of incorporating the SSI effect in the seismic analysis and optimal design of inerter-based tanks. Particularly, the inerter-based isolation system designed assuming a rigid base cannot perform as expected due to the SSI effect, significantly resulting in larger seismic responses and energy dissipation burdens. The developed optimal design method guarantees a target base shear force and sloshing height regarding the considered soil condition.

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

Impact of damping modeling on the seismic response of base-isolated liquid storage tanks

Liquid-filled tanks are important infrastructure for the storage of water, chemicals and fuels, such as oil and liquefied natural gas (LNG). Many such large-scale tanks are located in regions with high seismicity. Therefore, very frequently base isolation technology has to be implemented to reduce the dynamic distress of the superstructure. In structural analysis software base isolators are modeled utilizing special nonlinear isolator elements. Global damping modeling of seismically isolated structures is a crucial issue, since improperly defined damping may worsen significantly the dynamic analysis results, mainly due to the so-called "damping leakage" phenomenon. For this purpose, this work is focused on the impact of damping modeling approach in the dynamic response of liquid storage tanks isolated via single friction pendulum bearings (SFPBs) under strong near-fault ground motions.

Applicability of Mass-Spring Models for Seismically Isolated Liquid Storage Tanks

Employing base isolation technique for reduction of seismic response of liquid storage tanks has been proved to be quite effective. The main purpose of this paper is to quantitatively clarify, the contribution of convective and impulsive parts of the contained liquid in seismic behavior of an isolated liquid tank. Moreover, the accuracy of the simplified model which is generally used for the prediction of seismic behavior of conventional tanks is examined for isolated liquid tanks. For these purposes, the seismic response of the isolated cylindrical liquid storage tanks is considered using both the exact finite element model and simplified mass-spring model. The fluid–structure interaction is considered in finite element model. The comparison of the results obtained from two models shows that unlike conventionally constructed tanks, the contribution of convective mass cannot be neglected for seismically isolated tanks. Moreover, the accuracy of the simplified model for evaluating the main design parameters including base shear, global overturning moment, and sloshing height is examined for various tank dimensions and earthquake ground motions. The difference between the base shear and overturning moment results in the FE model and the simplified model of an isolated tank limited to 10%. It approves that the simplified mechanical models can be used with confidence for evaluating the seismic design parameters of various isolated tanks. However, the free surface displacement cannot be accurately predicted by simplified models, especially for medium and broad tanks.

Seismic Performance Evaluation of Liquid Storage Tanks Using Nonlinear Static Procedures

A simplified approach is presented for the seismic performance assessment of liquid storage tanks. The proposed methodology relies on a nonlinear static analysis, in conjunction with suitable “strength ratio-ductility-period” relationships, to derive the associated structural demand for the desired range of seismic intensities. In the absence of available relationships that are deemed fit to represent the nonlinear-elastic response of liquid storage tanks, several incremental dynamic analyses are performed for variable post-yield hardening ratios and periods in order to form a set of data that enables the fitting of the response. Following the identification of common modes of failure such as elephant's foot buckling (EFB), base plate plastic rotation, and sloshing wave damage, the aforementioned relationships are employed to derive the 16%, 50%, and 84% percentiles for each of the respective response parameters. Fragility curves are extracted for the considered failure modes, taking special care to appropriately quantify both the median and the dispersion of capacity and demand. A comparison with the corresponding results of incremental dynamic analysis (IDA) reveals that the pushover approach offers a reasonable agreement for the majority of failure modes and limit states considered.

The effect of composite-elastomer isolation system on the seismic response of liquid-storage tanks: Part I

A typical viable technique to decrease the seismic response of liquid storage tanks is to isolate them at the base. Base-isolation systems are an efficient and feasible solution to reduce the vulnerability of structures in high seismic risk zones. Nevertheless, when liquid storage tanks are under long-period shaking, the base-isolation systems could have different impacts. These kinds of earthquakes can damage the tanks readily. Hence, the seismic behaviour and vibration of cylindrical liquid storage tanks, subjected to earthquakes, is of paramount importance, and it is investigated in this paper. The Finite Element Method is used to evaluate seismic response in addition to the reduction of excessive liquid sloshing in the tank when subjected to the long-period ground motion. The non-linear stress-strain behaviour pertaining to polymers and rubbers is implemented while non-linear contact elements are employed to describe the 3-D surface-to-surface contact. Therefore, Nonlinear Procedures are used to investigate the fluid-structure interactions (FSI) between liquid and the tank wall while there is incompressible liquid. Part I, examines the effect of the flexibility of the isolation system and the tank aspect ratio (height to radius) on the tank wall radial displacements of the tank wall and the liquid sloshing heights. Maximum stress and base shear force for various aspect ratios and different base-isolators, which are subjected to three seismic conditions, will be discussed in Part II. It is shown that the composite-base isolator is much more effective than other isolators due to its high flexibility and strength combined. Moreover, the base isolators may decrease the maximum level pertaining to radial displacement.

Experimental study on the seismic response of liquid storage tanks with Sliding Concave Bearings

It is known that, earthquakes have caused severe damages to a large number of industrial facilities, mainly storage tanks with extremely serious economic and environmental implications. Thus, it is extremely importance to use techniques for reducing the seismic vulnerability of such structures. Seismic base isolation as seismic protection technology is already known and its development continues to grow. The present paper focuses on the seismic performance of broad and slender atmospheric storage steel tanks base isolated by Sliding Concave Bearings (SCB). The performance study carried out through shaking table tests on a vertical cylindrical steel tank model allowed to determine quantitatively the efficiency of the SCB by analyzing two structural parameters: (a) sloshing height and (b) base shear force. Six real ground motions with different characteristics were considered. Results show the effectiveness of SCB in reducing the base shear force values for all studied cases without significantly affecting the sloshing displacements when compared with fixed-base support.

Experimental research of heat-mass coupling response of liquid storage tanks

In order to study the coupling response process of the liquid tank under the external thermal attack, experiments were carried out on a vertical cylindrical storage tank by electric heating. The response processes of the tank pressure, the medium temperatures, and the wet and dry tank wall temperatures were monitored in the experiments. The coupling responding process between the evolving characters of the medium temperature and the tank wall temperature, as well as the resulting rising features of the tank pressure were analyzed comprehensively. The results indicated that, on the one side the heat transfers process across and through the tank wall were influenced obviously by the thermal-flow fields of the two phase mediums which differ a lot in the thermal physical properties. On the other side, affected by the temperature rise in the wall, the vapor medium became thermal stratified and overheated with respect to the tank pressure, and the flow regime in the liquid medium would transform from causing stratification to promoting de-stratification affected by the wall boiling phenomenon.

Experimental and numerical study of the response of cylindrical steel tanks under seismic excitation

To improve the structural seismic response of liquid storage tanks, in the last 50 years, many researchers have developed different mathematical models, ranging from those based on discrete elements such as simplified two-mass models to those involving fluid–structure interactions by complex formulations. To provide a broad overview on the scope and accuracy of different numerical linear models, in this paper, a comparative study based on the dynamic response assessment of cylindrical ground-supported containers under seismic excitation is conducted. The dynamic response in terms of liquid sloshing height, base shear force and overturning moment is analysed by means of: (a) a simplified mechanical model in which the behaviour of the liquid is represented by a discrete mass-spring system; (b) a complex model based on a Lagrangian fluid finite element approximation and (c) an experimental scaled model whose measured response is considered as benchmark. To obtain robust estimators of the structural response, three different types of cylindrical tanks, including broad and slender tanks, subjected to real ground acceleration time-histories are studied. The results indicate that the finite element model gives good approximation for all response parameters and the simplified mechanical model underestimate the sloshing height and overestimate base shear force and overturning moment.

Evaluation of Soil-Structure Interaction on the Seismic Response of Liquid Storage Tanks under Earthquake Ground Motions

Soil-structure interaction (SSI) could affect the seismic response of structures. Since liquid storage tanks are vital structures and must continue their operation under severe earthquakes, their seismic behavior should be studied. Accordingly, the seismic response of two types of steel liquid storage tanks (namely, broad and slender, with aspect ratios of height to radius equal to 0.6 and 1.85) founded on half-space soil is scrutinized under different earthquake ground motions. For a better comparison, the six considered ground motions are classified, based on their pulse-like characteristics, into two groups, named far and near fault ground motions. To model the liquid storage tanks, the simplified mass-spring model is used and the liquid is modeled as two lumped masses known as sloshing and impulsive, and the interaction of fluid and structure is considered using two coupled springs and dashpots. The SSI effect, also, is considered using a coupled spring and dashpot. Additionally, four types of soils are used to consider a wide variety of soil properties. To this end, after deriving the equations of motion, MATLAB programming is employed to obtain the time history responses. Results show that although the SSI effect leads to a decrease in the impulsive displacement, overturning moment, and normalized base shear, the sloshing (or convective) displacement is not affected by such effects due to its long period.

Experimental and Numerical Simulation Investigation on Dynamic Response of Liquid Storage Tanks under Seismic Excitations

A large-scale earthquake simulation experiment about the unanchored cylindrical steel liquid storage model tanks has been completed. The self-vibration characteristics of the model tanks with liquid inside were investigated based on the experimental data of the acceleration dynamic response. The seismic table test, the analysis methods are designed and conducted, and experimental results of the model tanks were carefully measured. Furthermore, ANSYS finite element software was used to simulate and calculate the low order natural frequency and fundamental frequency of the model tank systems according to the national design standard. The reasons for the existence of consistency and differences between the results obtained from experiments and numerical simulation were discussed.

Numerical Analysis of the Base-Isolated Rectangular Storage Tanks under Bi-directional Seismic Excitation

Liquid storage tanks are critical elements in the water supply scheme and firefighting system in many industrial facilities for storage of water, oil, chemicals and liquefied natural gas. A common effective method to reduce the seismic response of liquid storage tanks is using baseisolation systems. In this research, the finite element method is used to investigate the seismic behavior of rectangular liquid tanks in three-dimensional domains. The continuous liquid mass of the tank was modeled as lumped masses referred as convective mass, impulsive and rigid mass. The rectangular water tank in two cases base isolated and conventional non-isolated system was selected as a case study. The sloshing displacement and base shear response in two mentioned cases subjected to various ground motions under horizontal components X and Y directions were considered and the results were compared. For this purpose the nonlinear time history analyses of the model were performed. As a result, base isolation was found to be effective in reducing the base shear values, without significantly affecting the sloshing displacements.

Dynamic experimental investigation on the uplift response of liquid storage tanks under seismic excitations with different characteristics

A series of seismic table tests about the large steel cylindrical liquid storage tank models with floating roof were taken in this study. Horizontal and vertical direction seismic excitations were input respectively to the experimental structure system under different working conditions to test and analyze the seismic response behavior. The effects of various factors, such as the liquid surface height, the floating roof, the different wave amplitudes and frequencies, as well as their combined effects on the seismic dynamic response were obtained. The absolute displacement and the uplift response behavior law of the test models were obtained under different conditions. It was concluded that not only uplift value but also the absolute displacement of the tank bottom should be considered. And it should be noticed that a critical input frequency exists during the model response changing with frequency. In addition, important factors in experiment were described systematically in this article, for example, the experimental equipment selection, the experimental method, the tank model design, the laser displacement sensors, the data acquisition, the measurement point layout method, seismic excitation input method and so on. A reliable basis could be provided for theoretical analysis, structural design and computer numerical simulation research through this investigation.

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.

On the seismic behavior of cylindrical base-isolated liquid storage tanks excited by long-period ground motions

A common effective method to reduce the seismic response of liquid storage tanks is to isolate them at base using base-isolation systems. It has been observed that in many earthquakes, the foregoing systems significantly affect on the whole system response reduction. However, in exceptional cases of excitation by long-period shaking, the base-isolation systems could have adverse effects. Such earthquakes could cause tank damage due to excessive liquid sloshing. Therefore, the numerical seismic response of liquid storage tanks isolated by bilinear hysteretic bearing elements is investigated under long-period ground motions in this research. For this purpose, finite shell elements for the tank structure and boundary elements for the liquid region are employed. Subsequently, fluid–structure equations of motion are coupled with governing equation of base-isolation system, to represent the whole system behavior. The governing equations of motion of the whole system are solved by an iterative and step-by-step algorithm to evaluate the response of the whole system to the horizontal component of three ground motions. The variations of seismic shear forces, liquid sloshing heights, and tank wall radial displacements are plotted under various system parameters such as the tank geometry aspect ratio (height to radius), and the flexibility of the isolation system, to critically examine the effects of various system parameters on the effectiveness of the base-isolation systems against long-period ground motions. From these analyses, it may be concluded that with the installation of this type of base-isolation system in liquid tanks, the dynamic response of tanks during seismic ground motions can be considerably reduced. Moreover, in the special case of long-period ground motions, the seismic response of base-isolated tanks may be controlled by the isolation system only at particular conditions of slender and broad tanks. For the case of medium tanks, remarkable attentions would be required to be devoted to the design of base-isolation systems expected to experience long-period ground motions.

Generalized SDOF system for dynamic analysis of concrete rectangular liquid storage tanks: effect of tank parameters on response

This paper presents the results of parametric studies on the seismic response of concrete rectangular liquid storage tanks using the generalized single-degree-of-freedom (SDOF) system. The effects of height of liquid and width of tank on the dynamic response of liquid storage tanks are investigated. The liquid level varies from the empty condition to a full tank. Also, instead of the commonly used ratio of width of tank to liquid height, Lx/HL, the ratio of width of tank to full height of the tank wall, Lx/Hw, is used as a characteristic parameter of tanks to study the effect of tank size on the dynamic response. The trends of added mass of liquid, effective height, and natural frequencies for different sizes of tanks are established. The values of the added mass of liquid due to impulsive hydrodynamic pressure and the effective height in the relationship with the ratios Lx/Hw and HL/Hw are determined and can be used in the seismic design of liquid storage tanks. Since the natural frequencies of liquid-containing structures are within a band of frequencies between that of a full tank and that of an empty tank, the recommended frequency to be used in the design of the tank wall is the frequency that causes the maximum dynamic response .

Application of nonlinear fluid–structure interaction methods to seismic analysis of anchored and unanchored tanks

Seismic response of liquid storage tanks is quite different from conventional structures not only due to hydrodynamic effects acting on the tank shell but also owing to many sources of nonlinear behavior mechanisms of tanks such as buckling of the tank shell, large amplitude nonlinear sloshing, nonlinear tank–soil interaction, material yielding, plastic rotation of base plate and successive contact and separation between tank base and soil. For the assessment of earthquake response of such structures, numerical methods are indispensable tools since they offer a concise way of accurately considering all these nonlinearities in the same model. Yet, before using numerical techniques for design purposes for the evaluation of different configurations of the fluid–tank systems when subjected to several earthquake ground motions, they should be validated by experimental results. For this purpose, in this study, a fully nonlinear fluid–structure interaction algorithm of finite element method is employed for the seismic analysis of anchored and unanchored steel liquid storage tanks. An existing experimental study carried out on anchored and unanchored tanks is utilized for the verification of the numerical procedure. In the numerical models, Arbitrary Lagrangian Eulerian (ALE) description of the liquid–structure interface which is described by the mesh nodes at the boundary is employed. Fluid motion is governed by compressible Navier–Stokes equations. Both material and geometric nonlinearities are considered in order to accurately determine stress, strain and strain rate distributions throughout the tank. Successive contact and separation between base plate and foundation along with friction effects are taken into account by contact modeling algorithm. Response parameters of tanks, such as free surface sloshing wave height, pressure time histories, base plate uplifting and shell stresses obtained by numerical simulations are correlated with those of experimentally observed. By means of experimental and numerical results, the principal effects of base uplifting on the seismic response of unanchored cylindrical steel tank are highlighted with comparing that of rigidly restrained tank. Moreover, the provisions given in the current tank seismic design codes for metal cylindrical tanks are discussed and the response parameters of tanks are computed per minimum requirements of these codes. The results are compared with findings of numerical and experimental studies and the comments on the consistency of these results are explained in detail. Strong correlation between the experimental and numerical results is obtained for investigated response parameters although code requirements present deviations from the reference experimental study especially for uplift displacement and free surface wave height.

Seismic Response of Liquid Storage Tanks Incorporating Soil Structure Interaction

A frequency domain method is presented to compute the impulsive seismic response of circular surface mounted steel and concrete liquid storage tanks incorporating soil-structure interaction (SSI) for layered sites. The method introduces the concept of a near field region in close proximity to the mat foundation and a far field at distance. The near field is modeled as a region of nonlinear soil response with strain compatible shear stiffness and viscous material damping. The shear strain in a representative soil element is used as the basis for strain compatibility in the near field. In the far field, radiation damping using low strain soil response is used. Frequency dependent complex dynamic impedance functions are used in a model that incorporates horizontal displacement and rotation of the foundation. The focus of the paper is on the computation of the horizontal shear force and moment on the tank foundation to enable foundation design. Significant SSI effects are shown to occur for tanks sited on soft soil, especially tanks of a tall slender nature. SSI effects take the form of period elongation and energy loss by radiation damping and foundation soil damping. The effects of SSI for tanks are shown to reverse the trend of force and moment reduction under earthquake loading as is usually assumed by designers. The reasons for this important effect in tank design are given in the paper and relate to the very short period of most tanks, hence, period lengthening may result in load increase. A comparison is made with SSI effects evaluated using the code SEI/ASCE 7-02. Period elongation is found to be similar for relatively stiff soils when assessed by the code compared with the results of the dynamic analysis. For soft soils, the agreement is not as good. Code values of system damping are found to agree reasonably well with an assessment based on the dynamic analyses for the range of periods covered by the code. Energy loss by material damping and radiation damping is discussed. It is shown that energy loss may be computed using the complex dynamic impedance function associated with the viscous dashpot in the analytical model. The proportion of energy loss in the translation mode compared to that dissipated in the rotational mode is addressed as a function of the slenderness of the tank. Energy loss increases substantially with the volume of liquid being stored.

Slosh dynamics of liquid-filled containers with submerged components using pressure-based finite element method

Seismic response of liquid storage tank can be strongly influenced by the presence of submerged components. This modification of the dynamic characteristics of the liquid tank systems with internal components can be very useful for improving their seismic behavior. In this paper, a pressure-based finite element technique has been developed to analyze the slosh dynamics of a partially filled rigid container with bottom-mounted submerged components. The fluid is assumed homogeneous, isotropic, inviscid, and to exhibit only limited compressibility. The problem is linearized assuming the frequency of the exciting oscillation not in the immediate neighborhood of the natural slosh frequency, so that the slope of the free surface is small. The linearized problem is spatially discretized using the Galerkin weighted residual method. Earthquake excitations are used as the prescribed boundary condition. The solution is advanced in time using Newmark's constant average acceleration method. The developed code has been used to investigate the effect of a bottom-mounted rectangular component on the slosh dynamics of a liquid-filled rigid container. Numerical results obtained are compared with the existing solutions to validate the code. The parametric study of the tank–fluid system shows the importance of height, width and location of the submerged structural components.