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.     

考虑SSI效应的立式储罐水平基础隔震研究

立式储罐在地震作用下破坏严重,损失较大.为了降低立式储罐在水平地震激励下的地震响应,考虑土与结构相互作用对储罐地震响应的影响,将立式储罐基础隔震体系简化为3质点5自由度力学模型.依据Hamilton原理建立立式储罐基础隔震体系的控制方程,给出了立式储罐基底剪力、倾覆弯矩、晃动波高和应力的理论表达.选取150000m3储罐,采用wilson-θ法对其进行了地震动响应分析.结果表明:储罐基础隔震体系能够降低储罐的地震响应;为获得理想的地震响应,场地、隔震周期和阻尼比存在优化取值区间;储罐抗震与减震设计要视设计安全需要来决定是否考虑土与结构的相互作用.     

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。     

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.     

模型储罐三维地震反应振动台试验研究

针对立式钢制模型罐,进行了三维地震激励和一维地震激励振动台的动响应试验研究。结果表明:储罐在三维地震动激励下的反应与一维激励相比,加速度反应、罐壁的应变反应、储罐提离反应具有较明显的放大效应。位移反应在不同地震激励下,其放大效应不同,El Centro波激励下各测点三维激励下位移较一维激励下位移放大明显,Taft、天津波激励下各测点三维激励下位移较一维激励下位移有放大也有缩小,幅度均不大。由罐壁测点加速度功率谱分析表明:一维激励其峰值频率区域较为集中,主峰突出,能量主要集中于低频区;在三维地震激励下,频率峰值区域明显拉长,峰值点模糊,频率成份十分丰富,表现出多主峰的特点。     

Seismic design of flexible cylindrical liquid storage tanks

Seismic response of cylindrical storage tanks anchored to rigid base slabs is considered. Finite elements are used for the liquid and tank wall, idealized as a thin shell. For steel tanks of practical dimensions, design charts are presented for natural frequencies, maximum shear and overturning moment on the foundation, and maximum stress resultants in the tank wall. Furthermore, an analytical expression for the superelevation of the free surface is presented.     

Finite element analysis of the seismic response of anchored and unanchored liquid storage tanks

The seismic response of liquid-filled cylindrical storage tanks has been investigated using finite element techniques implemented in the general purpose structural analysis computer code ANSYS. Both added mass concepts and displacement-based fluid finite elements were employed to allow for the effects of the liquid. Simplified response spectrum modal analyses of a tank making use of the axisymmetric harmonic displacement patterns of the principal modes of deformation were found to give accurate predictions of the tank behaviour with a rigidly anchored base. Time history analyses of three-dimensional finite element models of unanchored and flexibly anchored tanks, with gap conditions between the tank base and the supporting floor to allow lift-off of the base, indicated that stresses in the tank and resultant loads on the floor can be much greater than for a rigidly restrained tank. These results demonstrate the importance of carefully considering the restraint conditions when performing seismic design calculations on storage tanks.     

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.     

A simplified seismic analysis of rigid base liquid storage tanks under vertical exicitation with soil-structure interaction

A study is carried out to evaluate dynamic response of an elastic circular cylindrical tank having a rigid base under a vertical excitation taking into consideration the interaction with the foundation soil. At first, the soil is represented by frequency-independent parameters. Two coupled differential equations, governing the motion of the shell and the base, are solved using a step by step integration technique. The hydrodynamic pressures, acting on the shell and on the base, are derived from a velocity potential function which satisfies the Laplace equation and the appropriate boundary conditions. The response of the simplified model of a tank having a rigid base on a stiff foundation soil is compated to that obtained elsewhere to check the accuracy of the present model. Reasonable agreement is found between the maximum wall displacement and the associated stresses with those found by a more elaborate model. The interaction of the tank and the soil reduces the response than that calculated under the assumption of a rigid foundation soil. A parametric study to examine the effects of the height-to-radius ratio of the tank, and the effects of the shear wave velocity of the soil on the response is conducted. Varieties of foundation models are used to assess the sensitivity of the response to the variation in the soil parameters. Finally, a more representative solution for the problem in the frequency domain is obtained where the soil is appropriately modelled by frequency-dependent parameters. The transfer functions of the response of the tank wall and of the relative base motion are evaluated, and a comparison between the frequency-dependent and the frequency-independent solutions is made.     

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.     

Dynamic response of cylindrical structures considering coupled soil-structure interaction under seismic loading

This paper attempts to develop a mathematical model for estimating the seismic response of a cylindrical shaped nuclear reactor building resting in an elastic halfspace considering foundation compliance. Most of the research carried out on this topic has either been carried out by resorting to finite element method (FEM) which makes the computational cost expensive or based on the simplifying assumption of assuming the cylindrical structure as a multi degree lumped mass stick model with soil coupled as boundary springs. In the present paper an analytical model has been developed in which the deformation of the cylindrical body (including its shear deformation characteristics) has been taken into cognizance and then coupling with foundation stiffness a comprehensive solution has been sought based on Galerkin’s weighted residual technique. The results are finally compared with FEM to check the reliability of the same. The results are found to be in good agreement with the detailed finite element analysis.     

Dynamic response of rigid tanks with inhomogeneous liquids

A study of the response to horizontal ground shaking of a rigid cylindrical tank containing an inviscid liquid with a continuous vertical variation in density is presented. In addition to the free vibrational sloshing characteristics of the liquid, the responses examined include the vertical displacements at the free surface, and the impulsive and convective components of the hydrodynamic wall pressures and associated tank forces. The equations of motion for the system are formulated for an arbitrary variation in liquid density but the solutions presented are for a density that increases exponentially from top to bottom. Comprehensive numerical data are included which elucidate the underlying response mechanisms and the effects and relative importance of the various parameters involved. The solution for the continuous density variation considered herein is also compared with a previously reported solution in which the liquid was modelled as a multi-layered, discrete system.     

隔震立式储罐地震反应谱分析

基于反应谱理论,研究了的基底隔震储罐的地震响应问题.将储罐简化为三质点体系力学模型,罐内连续液体质量等效为对流质量、脉冲质量和刚性质量,并引入隔震刚度.与时程分析对比,验证反应谱法的适用性,分析隔震立式储罐的地震响应并研究主要参数对隔震储液罐地震响应的影响,主要考虑的参数有:(1)场地类别;(2)隔震周期;(3)高径比.结果表明:反应谱法计算隔震立式储罐地震响应是偏于安全的;随着场地类别和隔震周期的增大,基底剪力减震率逐渐降低,晃动波高变化不明显,隔震后,液动压力呈线性变化,液动压力随着场地类别和高径比的增大而增大,随着隔震周期的增大而减小;高径比存在一定的优化段,在优化段内,基底剪力减震率较大,隔震效果较好.     

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 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.     

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.     

Effects of soil-structure interaction on seismic response of elevated tanks

Models of two-dimensional x-braced elevated tanks supported on isolated footings are analyzed to investigate the effects of dynamic interaction between the tower and the supporting soil-foundation system. Static, dynamic elastic, and dynamic inelastic responses of towers under horizontal ground motions are evaluated. Effects of soil properties, represented by the shear wave velocity, on joint displacements and on member end actions are studied. In general, soil-tower interaction reduces member end actions except near the base of tower.     

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.