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。     

The effect of seismic uplift on the shell stresses of liquid‐storage tanks

Previous theoretical studies have shown that tank uplift, that is, separation of the tank base from the foundation, generally reduces the base shear and the base moment. However, there is a paucity of experimental investigations concerning the effect of uplift on the tank wall stresses, which is the principal parameter that controls the seismic design of liquid‐storage tanks. This paper reports a series of shake table experiments on a polyvinyl chloride model tank containing water. A comparison of the seismic behaviour of the tank with and without anchorage is described. Stochastically generated ground motions, based on a Japanese design spectrum, and three tank aspect ratios (liquid‐height/radius) are considered. Measurements were made of the stresses at the outer shell of the tank, the tank wall acceleration and the horizontal displacement at the top of the tank. While the top displacement and the tank shell acceleration increased when uplift was allowed, axial compressive stresses decreased by between 35% and 64% with tank uplift. The effect of uplift on the hoop stresses was variable depending on the aspect ratio. A comparison of experimental values with a numerical model is provided. Copyright © 2015 John Wiley & Sons, Ltd.     

立式储罐与地基相互作用地震反应分析

在考虑地基与储罐相互作用的情况下,采用有限元法对储罐住水平地震荷载作用下的反应进行了计算。推导了系统刚度矩阵及质量矩阵的计算过程。通过对四种场地条件下的地震响应分析,得出了储罐各种参数对地震反应的影响。分析表明：不同的地震激励对储罐系统的反应是不同的;地基刚度对系统的动力响应的影响也很大：即地基越“柔”,基底弯矩、罐壁轴向应力越小,但环向应力和底板变形却在增加。     

内罐影响下LNG储罐外罐地震响应分析

为了考虑内罐在不同方向地震动时对LNG(液化天然气)储罐外罐的影响,对有内罐和无内罐情况下LNG储罐外罐进行了地震响应分析。结果表明:有内罐时地震响应比无内罐时小,内罐的存在对LNG储罐抗震有好的影响;竖向地震波对结构振动的影响不能忽视。     

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.     

大型储液罐摩擦摆基底隔震控制分析

针对弹性钢制圆柱储液罐,基于Haroun-Housner模型,将连续流体质量等效为3种集中质量,分别为:对流质量、脉冲质量和刚性质量,与这些集中质量连接的相应刚度取值依赖于储罐壁和流体质量.在水平地震激励下,在储罐底部加摩擦单摆支座,给出了简化的液体 - 储罐-隔震支座的力学分析模型,建立了摩擦摆支座基底隔震体系的振动控制方程,并利用Newmark逐步积分法对控制方程进行了数值求解,研究了摩擦摆支座基底隔震的储液罐地震反应,验证了FPB隔震的有效性.     

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.     

液压阻尼系统（HDS）控制立式钢制储罐地震响应分析

本文采用液压阻尼系统（HDS）控制立式圆柱钢制储罐的地震反应，建立了安装HDS储罐的力学分析模型，并进行了数值计算，从频域对安装HDS后储罐的地震响应进行了分析，研究了HDS的减震效果和HDS和HDS参数对储罐地震反应的影响。     

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.     

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。     

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

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

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

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

Effects of seismic isolation on the seismic response of a California high‐speed rail prototype bridge with soil‐structure and track‐structure interactions

With the launch of the high‐speed train project in California, the seismic risk is a crucial concern to the stakeholders. To investigate the seismic behavior of future California High‐Speed Rail (CHSR) bridge structures, a 3D nonlinear finite‐element model of a CHSR prototype bridge is developed. Soil‐structure and track‐structure interactions are accounted for in this comprehensive numerical model used to simulate the seismic response of the bridge and track system. This paper focuses on examining potential benefits and possible drawbacks of the a priori promising application of seismic isolation in CHSR bridges. Nonlinear time history analyses are performed for this prototype bridge subjected to two bidirectional horizontal historical earthquake ground motions each scaled to two different seismic hazard levels. The effect of seismic isolation on the seismic performance of the bridge is investigated through a detailed comparison of the seismic response of the bridge with and without seismic isolation. It is found that seismic isolation significantly reduces the deck acceleration and the force demand in the bridge substructure (i.e., piers and foundations), especially for high‐intensity earthquakes. However, seismic isolation increases the deck displacement (relative to the pile cap) and the stresses in the rails. These findings imply that seismic isolation can be promisingly applied to CHSR bridges with due consideration of balancing its beneficial and detrimental effects through using appropriate isolators design. The optimum seismic isolator properties can be sought by solving a performance‐based optimum seismic design problem using the nonlinear finite‐element model presented herein. Copyright © 2016 John Wiley & Sons, Ltd.     

Modelling non‐linear ground response of non‐liquefiable soils

A non‐linear finite element (FE) model is presented to account for soil column effects on strong ground motion. A three‐dimensional bounding surface plasticity model with a vanishing elastic region, appropriate for non‐liquefiable soils, is formulated to accommodate the effects of plastic deformation right at the onset of loading. The elasto‐plastic constitutive model is cast within the framework of a FE soil column model, and is used to re‐analyse the downhole motion recorded by an array at a Large‐Scale Seismic Test (LSST) site in Lotung, Taiwan, during the earthquake of 20 May 1986; as well as the ground motion recorded at Gilroy 2 reference site during the Loma Prieta earthquake of 17 October 1989. Results of the analysis show maximum permanent shearing strains experienced by the soil column in the order of 0.15 per cent for the Lotung event and 0.8 per cent for the Loma Prieta earthquake, which correspond to modulus reduction factors of about 30 and 10 per cent respectively, implying strong non‐linear response of the soil deposit at the two sites. Copyright © 2000 John Wiley & Sons, Ltd.     

悬垂管道跨越结构地震反应分析

管道悬垂是一种简单且应用广泛的管线跨越方式,水流冲刷等地质灾害也会造成埋地管线部分悬空。本文充分考虑了管-土相互作用和支座非线性因素的影响,采用非线性增量有限元方法对悬垂管道跨越结构在地震作用下的反应进行了分析。     

Seismic response analysis of reinforced concrete frames using inelasticity‐separated fiber beam‐column model

Evaluating the inelastic seismic response of structures accurately is of great importance in earthquake engineering and generally requires refined simulation, which is a time‐consuming process. Because the material nonlinearity generally occurs in a small part of the whole structure, many researches focus on taking advantage of this characteristic to improve the computational efficiency and the inelasticity‐separated finite element method (IS‐FEM) proposed recently provide a generic finite element formulation for solving this kind of problems efficiently. Although the fiber beam‐column element is widely used for the simulation of reinforced concrete (RC) framed structures, the inelastic deformation is often detected in a large part of the numerical model under earthquake excitation so that it is hard to achieve high efficient computation when applying the IS‐FEM to the inelastic response analysis of RC fiber models directly. In this paper, a new numerical scheme for seismic response analysis of RC framed structures model by fiber beam‐column element is proposed based on the IS‐FEM. To implement the RC fiber model for use in IS‐FEM and improve the computational performance of proposed scheme, a method of identifying the local domains with severe section inelasticity level is proposed and a modified Kent‐Park concrete material model is developed. Because the Woodbury formula is adopted as the solver, the global stiffness matrix can keep unchanged throughout the analysis and the main computational effort is only invested on a small matrix representing local inelastic behavior. The numerical examples demonstrate the validity and efficiency of the proposed scheme.     

Estimating non‐linear site response by single period approximation

Site effects characterize the filtering mechanisms within the soil sedimentary layers overlying bedrock. In regions of high seismicity such as California where strong motion records are relatively abundant, site coefficients can be developed by regression of recorded ground shaking parameters. In regions of low‐to‐moderate seismicity or of high seismicity but with a paucity of recorded strong motion data, such empirical models cannot be obtained in the same way. This study describes the theoretical development of a simple, rational manual procedure to calculate site coefficients, based on a single period approximation (SPA), and to construct displacement response spectra (RSD) for soil sites. The proposed simplified model, which takes into account the non‐linear behaviour of soil that is dependent on the level of shaking, impedance contrast at the soil–bedrock interface and the plasticity of soil material, has been verified by comparison with results obtained from non‐linear shear wave analyses and data recorded during the 1994 Northridge earthquake. The proposed model is believed to be a convenient tool for calculating non‐linear site responses and constructing site‐specific response spectra, which has the potential of being incorporated into code provisions. Copyright © 2006 John Wiley & Sons, Ltd.     

浮放储罐三维地震反应有限元分析

针对立式储罐,考虑液固耦合效应、地基与储罐结构的相互作用,采用有限元分析方法,对储罐在三维地震荷载作用下动反应进行了数值分析。分析结果表明：储罐三维地震加速度反应较一维地震加速度反应增加、提离高度明显放大、储罐轴向应力增加、基底剪力与弯矩增大。     

Nonlinear sloshing in a floating‐roofed oil storage tank under long‐period seismic ground motion

A hybrid analytical and FEM is proposed to investigate the nonlinear sloshing in a floating‐roofed oil storage tank under long‐period seismic ground motion. The tank is composed of a rigid cylindrical wall and a flat bottom, whereas the floating roof is treated as an elastic plate undergoing large deflection. The contained liquid is assumed to be inviscid and incompressible, and the flow is assumed to be irrotational. The method of analysis is based on representation of the liquid motion by superposing the analytical modes that satisfy the Laplace equation and the rigid wall and bottom boundary conditions. The FEM is then applied to solve the remaining kinematic and dynamic boundary conditions at the moving liquid surface coupled with the nonlinear equation of motion of the floating roof. This requires only the discretization of the liquid surface and the floating roof into finite elements, thus leading to a computationally efficient and accurate method compared with full numerical analysis. As numerical examples to illustrate the applicability of the proposed method, two oil storage tanks with single‐deck type floating roofs damaged during the 2003 Tokachioki earthquake are studied. It is shown that the nonlinear oscillation modes with the circumferential wave numbers 0, 2 and 3 caused by the finite liquid surface elevation as well as the membrane action due to large deflection of the deck produce excessively large stresses in the pontoon, which may cause the catastrophic failure of pontoon followed by the submergence of the roof. Copyright © 2012 John Wiley & Sons, Ltd.     

Dynamic analysis of flexible rectangular fluid containers subjected to horizontal ground motion

In this paper, an analytical method is proposed to determine the dynamic response of 3‐D rectangular liquid storage tanks with four flexible walls, subjected to horizontal seismic ground motion. Fluid–structure interaction effects on the dynamic responses of partially filled fluid containers, incorporating wall flexibility, are accounted for in evaluating impulsive pressure. The velocity potential in which boundary conditions are satisfied is solved by the method of separation of variables using the principle of superposition. The impulsive pressure distribution is then computed. Solutions based on 3‐D modeling of the rectangular containers are obtained by applying the Rayleigh–Ritz method using the vibration modes of flexible plates with suitable boundary conditions. Trigonometrical functions that satisfy boundary conditions of the storage tank such that the flexibility of the wall is thoroughly considered are used to define the admissible vibration modes. The analysis is then performed in the time domain. Moreover, an analytical procedure is developed for deriving a simple formula that evaluates convective pressure and surface displacements in a similar rigid tank. The variation of dynamic response characteristics with respect to different tank parameters is investigated. A mechanical model, which takes into account the deformability of the tank wall, is developed. The parameters of such a model can be obtained from developed charts, and the maximum seismic loading can be predicted by means of a response spectrum characterizing the design earthquake. Accordingly, a simplified but sufficiently accurate design procedure is developed to improve code formulas for the seismic design of liquid storage tanks. Copyright © 2013 John Wiley & Sons, Ltd.