立式储液罐地震反应数值分析

本文采用大型有限元程序ANSYS对立式储液罐的地震反应进行了研究,考虑了不同罐体和内部液体的相互作用,采用3个不同容积的储罐,输入不同强度的地震动时程,进行了大量的数值计算,给出了一些结论。     

立式储液罐地震破坏快速评估方法

本文采用大型有限元程序ANSYS对立式储液罐的地震反应进行了非线性数值分析,考虑了罐体和内部液体的相互作用,得到了3个不同容积的储罐,在不同峰值的地震动时程输入下的反应结果。结合地震灾害中立式储罐的地震破坏现象和特点,以及现有的立式储罐地震破坏预测方法,提出了立式储罐的地震破坏快速评估方法。     

Seismic intensity measures for above‐ground liquid storage tanks

A series of scalar and vector intensity measures is examined to determine their suitability within the seismic risk assessment of liquid storage tanks. Using a surrogate modelling approach on a squat tank that is examined under both anchored and unanchored support conditions, incremental dynamic analysis is adopted to generate the distributions of response parameters conditioned on each of the candidate intensity measures. Efficiency and sufficiency metrics are used in order to perform the intensity measure evaluation for individual failure modes, while a comparison in terms of mean annual frequency of exceedance is performed with respect to a damage state that is mutually governed by the impulsive and convective modes of the tank. The results reveal combinations of spectral acceleration ordinates as adequate predictors, among which the average spectral acceleration is singled out as the optimal solution. The sole exception is found for the sloshing‐controlled modes of failure, where mainly the convective period spectral acceleration is deemed adequate to represent the associated response due to their underlying linear relationship. A computationally efficient method in terms of site hazard analysis is finally proposed to serve in place of the vector‐valued intensity measures, providing a good match for the unanchored tank considered and a more conservative one for the corresponding anchored system.     

Seismic risk assessment of liquid storage tanks via a nonlinear surrogate model

A performance‐based earthquake engineering approach is developed for the seismic risk assessment of fixed‐roof atmospheric steel liquid storage tanks. The proposed method is based on a surrogate single‐mass model that consists of elastic beam‐column elements and nonlinear springs. Appropriate component and system‐level damage states are defined, following the identification of commonly observed modes of failure that may occur during an earthquake. Incremental dynamic analysis and simplified cloud are offered as potential approaches to derive the distribution of response parameters given the seismic intensity. A parametric investigation that engages the aforementioned analysis methods is conducted on 3 tanks of varying geometry, considering both anchored and unanchored support conditions. Special attention is paid to the elephant's foot buckling formation, by offering extensive information on its capacity and demand representation within the seismic risk assessment process. Seismic fragility curves are initially extracted for the component‐level damage states, to compare the effect of each analysis approach on the estimated performance. The subsequent generation of system‐level fragility curves reveals the issue of nonsequential damage states, whereby significant damage may abruptly appear without precursory lighter damage states.     

Dynamic fluid effects in liquid-filled flexible cylindrical tanks

The velocity potential of a compressible fluid is found by Galerkin's method. Free surface displacements and a flexible tank wall are assumed. Explicit expressions for the impulsive mass, the impulsive moment and the overturning moment are derived for wave number m = 1. In the case of m ≥ 1 the dynamic effect of the fluid is represented by a fictitious apparent mass in explicit form.     

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.     

Seismic isolation of rigid cylindrical tanks using friction pendulum bearings

Storage tanks are vulnerable to earthquakes, as numerous major earthquakes have demonstrated. The trend of recent revisions to make seismic design criteria for large‐scale industrial storage tanks increasingly stringent has made development of cost‐effective earthquake‐resistant design and retrofit techniques for industrial tanks imperative. This study assesses the feasibility of seismic base isolation for making liquid‐filled storage tanks earthquake resistant. The sliding‐type friction pendulum seismic (FPS) bearings are considered rather than the elastomeric bearings because the dynamic characteristics of an FPS‐isolated tank remain unchanged regardless of the storage level. This work has devised a hybrid structural‐hydrodynamic model and solution algorithm, which would permit simple, accurate and efficient assessment of the seismic response of rigid cylindrical storage tanks in the context of seismic isolation. Extensive numerical simulations confirm the effectiveness of seismic base isolation of rigid cylindrical tanks using FPS bearings. Copyright © 2001 John Wiley & Sons, Ltd.     

Vibration studies and tests of liquid storage tanks

Theoretical and experimental investigations of the dynamic behaviour of ground-supported, deformable, cylindrical liquid storage tanks were conducted. The study was carried out in three phases: (I) a detailed theoretical treatment of the coupled liquid-shell system for tanks rigidly anchored to their foundations; (II) an experimental investigation of the dynamic characteristics of full-scale tanks; and (III) a development of an improved seismic design procedure.     

Seismic fragility of base-isolated water storage tanks under non-stationary earthquakes

Seismic fragility curves for fixed-base and base-isolated liquid storage tanks are developed under non-stationary earthquakes, and their seismic performance are compared. The correlation between different earthquake intensity measure (IM) parameters and peak response quantities of the base-isolated liquid storage tanks are investigated. The failure criteria are chosen based on (1) the elastic buckling strength of the tank wall, which is defined in terms of critical base shear and critical overturning moment, and (2) in terms of the critical isolation displacement. The uncertainty involved is considered in the earthquake characteristics. Non-stationary earthquake ground motions are generated using Monte Carlo (MC) simulation. Influence of the isolator characteristic parameters and modeling approaches on the seismic fragility of the base-isolated liquid storage tanks is also investigated. Peak ground acceleration is found to be the well correlated IM parameter with the peak response quantities of the base-isolated liquid storage tanks. Substantial decrease in the seismic fragility of the base-isolated liquid storage tanks is observed as compared to the fixed-base tanks. Significant influence of the isolator characteristic parameters on the seismic fragility of the base-isolated liquid storage tanks are reported in the present study.     

Seismic response analysis of adjacent liquid‐storage tanks

A refined substructure technique in the frequency domain is developed, which permits consideration of the interaction effects among adjacent containers through the supporting deformable soil medium. The tank‐liquid systems are represented by means of mechanical models, whereas discrete springs and dashpots stand for the soil beneath the foundations. The proposed model is employed to assess the responses of adjacent circular, cylindrical tanks for harmonic and seismic excitations over wide range of tank proportions and soil conditions. The influence of the number, spatial arrangement of the containers and their distance on the overall system's behavior is addressed. The results indicate that the cross‐interaction effects can substantially alter the impulsive components of response of each individual element in a tank farm. The degree of this impact is primarily controlled by the tank proportions and the proximity of the predominant natural frequencies of the shell‐liquid‐soil systems and the input seismic motion. The group effects should be not a priori disregarded, unless the tanks are founded on shallow soil deposit overlying very stiff material or bedrock. Copyright © 2016 John Wiley & Sons, Ltd.     

储液池的抗震问题探讨

应用流体固体动力耦合统一分析模型的有限元法，进行了储液池的抗震分析。分别探讨了储液池内液体的液面大幅波动、池壁刚度变化、池的深宽比等对地震响应的影响。研究结果表明：储液池壁刚度是比较敏感的物理量，弹性比刚性池壁与液体相互作用的非线性行为强，池壁所受流体的作用力大；液面波的影响也有同样规律，刚性池壁情况下考虑面波与否影响不太大，但弹性池壁却有较大影响；另外宽池比窄池的响应强。     

Analysis of unanchored liquid storage tanks under lateral loads

Many liquid storage tanks consist of a steel cylindrical shell, which is welded to a base plate, but not fixed to the foundation. When such an unanchored tank is subjected to lateral loads due to earthquake induced hydrodynamic pressures in the liquid, the tank wall tends to uplift locally, pulling the base plate up with it. The contact problem of the partially uplifted base plate and its interaction with the the cylindrical shell is solved in this paper using the finite difference energy method, and a Fourier decomposition of the displacements in the circumferential direction. Non-linearities due to contact, finite displacements and yield of the steel are included in the analysis. However, the equations for the shell are linearized. This uncouples the equations for the Fourier displacement coefficients in the cylindrical shell, and enables the degrees of freedom for the shell to be eliminated by static condensation at very little computational cost. Comparing the analytical results to (for the most part existing) experimental results, produces good agreement in some cases and not so good in others. A number of effects that could give rise to such differences are discussed. In most cases they represent experimental conditions that are not known or modelled in the analysis. The analysis results are also compared to those from a simplified analysis in which the hold-down action of the base plate is modelled by means of nonlinear Winkler springs.     

Seismic analysis of base-isolated liquid storage tanks using the BE–FE–BE coupling technique

A three-dimensional soil–structure–liquid interaction problem is numerically simulated in order to analyze the dynamic behavior of a base-isolated liquid storage tank subjected to seismic ground motion. A dynamic analysis of a liquid storage tank is carried out using a hybrid formulation, which combines the finite shell elements for structures and the boundary elements for liquid and soil. The system is composed of three parts: the liquid–structure interaction part, the soil–foundation interaction part, and the base-isolation part. In the liquid–structure interaction part, the tank structure is modeled using the finite elements and the liquid is modeled using the internal boundary elements, which satisfy the free surface boundary condition. In the soil–foundation interaction part, the foundation is modeled using the finite elements and the half-space soil media are modeled using the external boundary elements, which satisfy the radiation condition in the infinite domain. Finally, above two parts are connected with the base-isolation system to solve the system's behavior. Numerical examples are presented to demonstrate the accuracy of the developed method, and an earthquake response analysis is carried out to demonstrate the applicability of the developed technique. The properties of a real LNG tank located in the west coast of Korea are used. The effects of the ground and the base-isolation system on the behavior of the tank are analyzed.     

Seismic assessment of unanchored steel storage tanks by endurance time method

Liquid storage tanks are essential structures that are often located in residential and industrial areas; thus an assessment of their seismic performance is an important engineering issue. In this paper, the seismic response of unanchored steel liquid storage tanks is investigated using the endurance time (ET) dynamic analysis procedure and compared to responses obtained for anchored tanks under actual ground motions and intensifying ET records. In most cases, the results from ground motions are properly obtained with negligible differences using ET records. It is observed that uplifting of the tank base, which is closely related to the tank aspect ratio, has the greatest significance in the responses of the tank and can be predicted with reasonable accuracy by using currently available ET records.     

Soil-structure interaction effects for laterally excited liquid storage tanks

A comprehensive study is made of the effects of soil-structure interaction on the response of liquid containing, upright, circular cylindrical tanks subjected to a horizontal component of ground shaking. A simple, physically motivated method of analysis is employed which elucidates the effects and relative importance of the principal actions involved. Both the impulsive and convective actions of the liquid are examined. The interrelationship of the tank responses to horizontal and rocking actions of the foundation is established, and the well known mechanical model for laterally excited, rigid tanks supported on a non-deformable medium is generalized to permit consideration of the effects of tank and ground flexibilities and base rocking. Critical responses are evaluated for harmonic and seismic excitations over wide ranges of tank proportions and soil stiffnesses, and the results are presented in a form convenient for use in practical applications. In addition to a precise method of analysis, an approximate, hand-computation method is presented with which the effects of the primary parameters may be evaluated readily. The soil-structure interaction effects in the latter approach are provided for by modifying the natural frequency and damping of the tank-liquid system and evaluating its response to the prescribed free-field ground motion considering the tank to be rigidly supported at the base. The requisite modifications may be determined from information presented herein. It is shown that soil-structure interaction may reduce significantly the impulsive components of response but that it has a negligible effect on the convective components.     

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.     

Seismic design of yielding structures on flexible foundations

This paper introduces a simple method to consider the effects of inertial soil–structure interaction (SSI) on the seismic demands of a yielding single‐degree‐of‐freedom structure. This involves idealizing the yielding soil–structure system as an effective substitute oscillator having a modified period, damping ratio, and ductility. A parametric study is conducted to obtain the ratio between the displacement ductility demand of a flexible‐base system and that of the corresponding fixed‐base system. It is shown that while additional foundation damping can reduce the overall response, the effects of SSI may also increase the ductility demand of some structures, mostly being ductile and having large structural aspect ratio, up to 15%. Finally, a design procedure is provided for incorporation of the SSI effects on structural response. Copyright © 2015 John Wiley & Sons, Ltd.     

Dynamic response of vertically excited liquid storage tanks considering liquid-soil interaction

The paper presents a dynamic response analysis of vertically excited liquid storage tanks including both liquid-tank and liquid-soil interaction. The system considered is a thin-walled, elastic cylindrical shell entirely filled with an incompressible and inviscid fluid, resting on a flexible foundation over an elastic halfspace with frequency dependent stiffness and damping parameters. The problem is treated analytically by the generalized-coordinate approach and then solved numerically using the complex frequency response analysis. For one special tank, natural frequencies and equivalent damping ratios are evaluated and compared with those corresponding to a rigid ground. The maximum dynamic pressure is calculated using the response spectra of the 1976 Friuli earthquake. A parameter study is carried out to show the great influence of variable soil stiffness upon the damping ratio of the shell-liquid-soil system.     

中美欧储罐抗震规范中地震作用的比较研究

对比分析了中国、美国和欧州国家储罐抗震设计规范在抗震设防基准、设防目标、设计参数、储罐简化模型、设计反应谱和地震力降低系数等方面的不同特点,比较各规范设计地震作用的大小.研究表明:我国鉴定标准、美国API650和欧洲EC-8的抗震设防水准基本相当,而欧洲EC-8的抗震设防目标偏低.对于中等类型场地上的低自振周期储罐,我国鉴定标准设计地震作用与美国API650相当,但低于欧洲EC-8设计值,鉴定标准的晃动波高大于欧洲EC-8.另外以我国常用系列浮顶罐和大型浮顶罐为研究对象,比较储罐频率、液体等效质量、晃动波高等参数的不同.研究得到一些结论和建议,对修订我国储罐抗震设计规范有借鉴意义.     

Sloshing behaviours of rectangular and cylindrical liquid tanks subjected to harmonic and seismic excitations

A numerical and experimental study on the sloshing behaviours of cylindrical and rectangular liquid tanks is addressed. A three‐dimensional boundary element method for space with the second‐order Taylor series expansion in time is established to simulate the sloshing phenomenon and its related physical quantities inside a liquid tank subjected to horizontal harmonic oscillations or recorded earthquake excitations. The small‐scale model experiments are carried out to verify some results of numerical methods in this study. The comparisons between numerical and experimental results show that the numerical method is reliable for both kinds of ground excitations. Finally, the water wave and the base shear force of a rectangular tank due to harmonic excitation are also presented at different frequencies. A huge cylindrical water tank subjected to a recorded earthquake excitation is used for application and discussion. Copyright © 2007 John Wiley & Sons, Ltd.