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 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.     

Earthquake response of structures with partial uplift on winkler foundation

The effects of transient foundation uplift on the earthquake response of flexible structures are investigated. The structural idealization chosen in this study is relatively simple but it incorporates the most important features of foundation uplift. In its fixed base condition the structure itself is idealized as a single-degree-of-freedom system attached to a rigid foundation mat which is flexibly supported. The flexibility and damping of the supporting soil are represented by a Winkler foundation with spring-damper elements distributed over the entire width of the foundation. Based on the response spectra presented for several sets of system parameters, the effects of foundation-mat uplift on the maximum response of structures are identified. The influence of earthquake intensity, structural slenderness ratio, ratio of foundation mass to structural mass, foundation flexibility and p-δ effects on the response of uplifting structures is also investigated.     

Tank damage during the may 1983 coalinga earthquake

The magnitude M = 6-5 Coalinga earthquake of 2 May 1983 caused intense ground shaking throughout the epicentral region. Unanchored cylindrical ground supported tanks located at six sites within this oil producing area were damaged; damages included elephant's foot buckling at the base of three moderate sized tanks, joint rupture and top shell buckling in one large old rivetted tank, bottom plate rupture of a relatively new welded tank and damage to the floating roofs of 11 tanks. Also oil spilled over the top of many tanks and secondary damages occurred in pipe connections, ladders, etc. In this paper an estimate is made of the intensity of ground motion at each of the tank sites, based on strong motion records made during the main shock and the strongest aftershock. Then response parameters specified by current codes are correlated with the damages observed at each tank site. Based on this comparison, it is concluded that current U.S. practice under-estimates the sloshing response of tanks with floating roofs and does not adequately address the uplifting mechanism of unanchored ground supported tanks.     

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.     

中国大陆地壳的应变应力场研究

根据全国ＧＰＳ网１９９４年和１９９６年两期测量结果,研究了中国大陆地壳现阶段的水平形变应力场。结果显示,西部青藏块体与新疆块体主压应力场为近南北至北 北东向,而南北地震带以东、长江以及北地区为北东东至近东西向,华南块体上为北 北西至北西向,与滑线场理论模型基本吻合。反映出中国大陆地壳变形的压应力主要来自印度板块与欧亚板块的俯冲碰撞。而太平洋板块与菲律宾板块对欧亚板块的作用力以及地幔向上的作用力总体     

Soil-structure interaction effects on the steady-state response of torsionally coupled buildings

The work presented in this paper investigates the effect of the foundation flexibility on the coupled lateral-torsional response of single-storey buildings excited by translational ground motion. The eccentricity between the centre of mass and the centre of resistance is considered to be the only cause of coupling of the lateral and torsional response of the building. The study is confined to the steady-state response of rigidly supported and flexibly supported torsionally coupled buildings subjected to harmonic free-field ground displacement perpendicular to the direction of the eccentricity. In the case of the flexibly supported building the foundation medium is assumed to be an elastic homogeneous isotropic half-space. The effect of the controlling parameters on lateral-torsional coupling is investigated. It is concluded that for a particular range of values of these parameters (representing most cases of actual buildings) their effect on the coupling of lateral and torsional response is not qualitatively affected by increases in the flexibility of the foundation medium.     

地下储液罐抗爆炸地冲击作用的流固耦合有限元分析

储液罐的抗震性能虽然得到了较为深入的研究,但对其抗爆炸产生的地冲击作用的研究还十分罕见。本文通过建立流固耦合的数值分析模型,研究爆炸地冲击作用下地下立式储液罐的动力特性,包括储液晃动波高、罐壁的应力和应变、底板的提离和浮放储液罐的“象足”变形产生原因及破坏机理等。研究结果表明,储液罐在爆炸地冲击荷载和地震荷载作用下的动力响应有明显区别,地震荷载作用下的储液罐抗震验算方法不适用于爆炸地冲击荷载。     

竖向地震作用对储液罐地震响应的影响分析

地震作用下大型储液罐的安全问题日益引起重视。基于ANSYS软件建立储罐液体耦合有限元模型,考虑罐底非线性接触效应,以El-Centro南北向和竖直向记录地震波为输入,研究水平激励以及水平和竖向同时激励两种工况下储罐的动力响应。研究结果表明,两种工况下靠近罐底1.2m处均发生了"象足"变形,竖向激励下水平相对位移增加了14%。竖向激励使得罐壁环向应力和轴向压应力均有不同程度的增加。竖向地震激励对液面的竖向晃动影响较小。储液罐底板在地震作用下发生了竖向提离和永久滑移,竖向激励时增长幅度均在10%左右。同时罐体基底剪力在竖向地震作用下也有所增大。储罐抗震设计时应考虑竖向地震分量的影响,研究结论可为立式储罐的抗震设计提供一定的参考和依据。     

Rocking vibrations of a rigid embedded foundation in a poroelastic soil layer

An approximate analytical method is presented for the dynamic response of a rigid cylindrical foundation embedded in a poroelastic soil layer under the excitation of a time-harmonic rocking moment. The soil underlying the foundation base is represented by a single-layered poroelastic soil based on rigid bedrock while the soil along the side of the foundation is modeled as an independent poroelastic stratum composed of a series of infinitesimally thin layers. The accuracy of the present solution is verified by comparisons with existing solutions obtained from other researchers. Numerical results for the rocking dynamic impedance and dynamic response factor are presented to demonstrate the influence of nondimensional frequency of excitation, poroelastic soil layer thickness, depth ratio of the foundation and internal friction of the poroelastic soil.     

Eccentric installation of splice plates for compressive strength improvement of rectangular hollow section braces

Steel hollow section members are often applied as bracing in steel structures. Field-bolted connections of the slotted-in single splice plate and the gusset plate are popular because of their ease of construction. However, eccentricity between the splice and gusset plate axes reduces the compressive strength of the brace. This study proposes compressive strength improvement of rectangular hollow section braces using eccentrically installed splice plates such that the gusset plate axis coincides with the brace axis. To demonstrate the efficacy of the proposed concept, four compressive loading test results are examined in this study. Test results reveal the influences of splice plate eccentric installation on the brace compressive strength, the out-of-plane displacement, and the strain distribution. The proposed concept is effective for the brace with stiffened splice plates for inducing overall buckling with plastic hinges in the gusset plates. Variation of compressive strength is finally discussed based on the discrepancy between the brace axis and the axis of the plates in which the plastic hinges form at the overall buckling mode ends.     

地幔对流对全球岩石圈应力产生与分布的作用

利用动力学模拟方法研究地幔对流对于大尺度岩石圈内部应力场形成的作用. 地幔物质内部的密度横向非均匀及表面板块运动引起地幔流动,并在岩石圈底部产生一个应力场. 该应力场作为面力将造成岩石圈本身变形,从而产生岩石圈内部的应力分布. 模拟计算结果表明,大部分俯冲带及大陆碰撞带区域应力均呈现挤压特征,如环太平洋俯冲带及印度－欧亚碰撞带等;而东太平洋洋脊、大西洋洋脊及东非裂谷处应力状态均表现为拉张;并且绝大多数热点位置处于应力拉张区域,这与目前对全球构造应力状态的理解是一致的. 计算的岩石圈内部最大水平主压应力的方向与观测表现出相当的一致,其结果总体上吻合得较好,然而在局部区域（例如西北太平洋的俯冲带、青藏高原等地区）存在着较大的差异. 研究表明,地幔对流是造成岩石圈内部大尺度应力状态及分布的一个重要因素.     

Simplified analysis of unanchored tanks

Local uplift of the tank wall is perhaps the most important characteristic of the seismic behaviour of unanchored liquid storage tanks made out of steel. Such uplift is necessary, because unanchored tanks rely primarily on the weight of the liquid resting on an uplifted portion of the base plate to balance the overturning moments that occur during strong shaking. A simplified method of analysis for static lateral loads is developed, based on the assumption that the restraining action of the base plate can be modelled with equivalent, non-linear springs. This assumption, together with a Fourier decomposition of the displacements, simplifies the problem to the extent that it can be solved on a personal computer. The solutions are compared with those from experiments and those from current U.S. design analysis methods.     

P波入射时含圆柱形空腔板弹性波散射与动应力集中

采用波函数展开法给出了板的横截面处孔洞在平面P波入射下动应力集中问题的解。本文使用大圆弧假定法来满足板中的自由表面的边界条件。数值结果表明,上表面和孔洞间的距离与下表面和孔洞间的距离都对结果有影响。如果孔洞半径相对板的厚度很小,解近似等于孔洞全空间解。所给出的解是半解析解。因此能被用来验证诸如BEM,FEM,FDM等数值法。     

Dynamic response of non-linear building-foundation systems

An analysis is made of the steady-state response of a bilinear hysteretic structure supported on the surface of a viscoelastic half-space. The method of equivalent linearization is used to solve the equations of motion, and simplified approximate formulas are obtained for the fundamental resonant frequency of the system and for an effective critical damping ratio. Numerical results indicate that for non-linear hysteretic structures compliance of the soil foundation may lead to larger displacements than would occur if the base were rigid. This behaviour differs from that generally observed for linear systems, for which the effect of soil-structure interaction is to reduce the rigid-base response.     

Complex response analysis of shells of revolution including uniform base translation and rocking

A complex response algorithm for the dynamic analysis of axisymmetric thin shells supported on an interactive foundation is developed. The substructure deletion method is employed through the utilization of a dynamic boundary system at the contact area between the superstructure and the substructure. A new mathematical formulation in conjunction with the shell behaviour is developed to deal with rigid body motions due to the negation of the fixed base assumption. Four foundation conditions, that is, a fixed base, two pile foundation cases and a flexible base, are to examine the effect of base flexibility on the seismic response of cooling towers. Also, excellent comparative results between the frequency domain solution and a time domain solution are obtained.     

非线性弹性地基上圆形薄板三次超谐共振

本文研究非线性地基上圆形薄板受简谐激励的次谐波共振问题。按照弹性力学理论建立非线性地基上圆形薄板受简谐激励的动力学方程。利用Galerk in方法将其转化为非线性振动方程。应用非线性振动的多尺度法求得系统满足3次超谐共振条件的一次近似解,并进行数值计算。分析阻尼、地基系数、调谐值、激励等参数对共振响应曲线的影响。     

Dynamic response of flexible rectangular foundations on an elastic half-space

An approximate method for the analysis of the dynamic interaction between a flexible rectangular foundation and the soil with consideration of the out-of-plane deformation of the foundation is presented. The procedure is based on an extension of the subdivision method developed by Wong and Luco for rigid foundations. Numerical results describing the influence of the flexibility of the foundation on the vertical and rocking impedance functions and on the contact stresses between the foundation and the soil are presented. The possibility of representing a flexible foundation by an equivalent rigid foundation having the same force-displacement relationships is also discussed. The results obtained indicate that at low frequencies, the dynamic stiffness coefficients for flexible foundations are lower than those for a rigid foundation of the same area. At higher frequencies the opposite behaviour is observed. The radiation damping coefficients for flexible foundations are significantly lower than those for a rigid foundation of the same area.     

Analysis of wave propagation in a plate resting on a Winkler foundation with a sample application to vibration control

A variational statement in the field of complex numbers and its semi-analytical solution are presented to study the wave propagation in plates resting on a Winkler foundation. The method and its computer program are verified by comparison with the available results for a freely supported plate and performing a time domain analysis for a plate-Winkler foundation system. A variety of wave propagation phenomena is observed, and useful information can be extracted from the results. The foundation is found to act as a low frequency band-stop filter for flexural modes, and a stiffer foundation leads to wider widths of these stop bands. As a sample application, a barrier design for controlling flexural motions in the system is proposed. The effectiveness of the design is also demonstrated.     

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.