Dynamic analysis of liquid storage tank under blast using coupled Euler–Lagrange formulation

A growing number of terror attacks all over the world have become a threat to the human civilization. In the last two decades, bomb blasts in crowded business areas, underground railway stations and busy roads have taken numerous lives and destroyed properties in different parts of the world. However, blast response of many important civil infrastructures has still not been well understood due to the complexities in their material behavior, loading and higher nonlinearities. One such example of important civil infrastructure is liquid storage tanks which are undividable parts of any society for storage of water, milk, liquid petroleum, chemicals in industries etc. Blast loading on liquid storage structures may lead to disaster due to water and milk crisis, health hazard owing to the spread of chemicals and fire hazard due to the spread of liquid fuel. Hence, understanding the dynamic behavior of liquid storage structures under blast loading through numerical simulations is of utmost importance. In the present study, three dimensional (3D) finite element (FE) simulations of a steel water storage tank for different tank aspect ratios, percentages of water stored in the tank, tank wall thicknesses, boundary conditions at the bottom of the tank and magnitudes of blast loading have been performed using the FE software Abaqus. The coupled Euler–Lagrange (CEL) formulation in Abaqus has been adopted herein which has the advantage of considering the coupling of structural mechanics and fluid mechanics fundamental equations. The maximum hoop stress and shear stress in the tank wall, the water sloshing heights in tanks and the energy response of the tanks have been studied. It is observed that stresses and liquid sloshing heights in the tank increase with decreasing scaled distance of the explosive material and increasing aspect ratio, i.e. height to radius ratio.     

考虑水体晃动的水塔结构抗震性能分析

传统的水塔结构设计都忽略了水箱中水的晃动作用,把水当成质量块进行处理。本文将水箱中的水体当成一个TLD(调谐液体阻尼器),来考虑水的晃动作用,利用有限元模拟,并结合实例对水塔结构进行抗震分析,结果表明水箱中的水有效地减小了水塔结构的地震反应,对于类似的情况,结构设计时宜予以一定的考虑和分析。     

The effect of earthquake frequency content on the seismic behavior of concrete rectangular liquid tanks using the finite element method incorporating soil-structure interaction

A three-dimensional soil-structure-liquid interaction is numerically simulated using the finite element method in order to analyze the seismic behavior of partially filled concrete rectangular tanks subjected to different ground motions. In this paper, the effect of earthquake frequency content on the seismic behavior of fluid rectangular tank system is investigated using four different seismic motions. A simple model with viscous boundary is used to include deformable foundation effects as a linear elastic medium. This method is capable of considering both impulsive and convective responses of liquid-tank system. Six different soil types defined in the well-recognized seismic codes are considered. The sloshing behavior is simulated using linear free surface boundary condition. Two different finite element models corresponding with flexible shallow and tall tank configurations are studied under the effects of longitudinal, transversal and vertical ground motions. By means of changing the soil properties, comparisons are made on base shear, base moment and sloshing responses under different ground motions. It is concluded that the dynamic behavior of the fluid-tank-soil system is highly sensitive to frequency characteristics of the earthquake record.     

Response modification factor of elevated water tanks with reinforced concrete pedestal

A probabilistic method based on FEMA P695 is employed for validating the response modification factor of reinforced concrete pedestals in elevated water tanks. In the current codes and standards, the response modification factor of elevated water tanks is mainly based on engineering judgement. Ten models of elevated water tanks with different tank sizes and pedestal heights are selected for the investigation. Initially, the prototypes are designed based on the current codes and standards. Next, the finite element models of the prototypes are developed. By performing incremental dynamic analysis, the probability of collapse for each prototype is calculated under different seismic loading conditions and system uncertainties. The results of the study validate and confirm the current response modification factor values and show that the tank size has a significant effect on the nonlinear seismic response behaviour of elevated water tanks. In addition, it is revealed that heavy tank sizes that are designed in accordance with codes and guidelines are more vulnerable under seismic loading compared with light and medium tank sizes.     

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.     

Equivalent mechanical analog for dynamic analysis of pure conical tanks

This study is motivated by the lack of information regarding seismic analysis and design of liquid-filled conical tanks. The main challenge in this type of fluid–structure interaction problem is the estimation of the forces associated with the hydrodynamic pressure resulting from the vibration of the structure. A simplified mechanical analog that can be used to estimate the forces associated with horizontal ground excitation is developed in this study. The proposed mechanical analog takes into account the flexibility of the tank walls and simulates both the impulsive and sloshing components of the hydrodynamic pressure. Parameters of this analog are displayed in chart form as functions of the geometrical parameters of the tanks including the angle of inclination of the tanks’ walls. Finally, an example is provided to illustrate the application of the developed analog for evaluation of the response of liquid-filled conical tanks to horizontal ground excitation.     

内泄下LNG储罐外壁的地震响应分析

针对内罐泄漏条件下LNG储罐混凝土外壁,利用ADINA软件分别建立储罐空罐及满罐LNG储罐有限元模型.在El Fentro地震波作用下,考虑固液耦合作用,对储罐进行地震响应分析.结果表明:通过比较空罐与满罐情况下LNG储罐外壁的地震作用下的位移、加速度曲线,储罐的外壁受罐内LNG储液的影响较大,其位移和加速度在液固耦合...     

A coupled finite element genetic algorithm for optimum design of stiffened liquid-filled steel conical tanks

In the current study an optimum design technique of stiffened liquid-filled steel conical tanks subjected to global and local buckling constraints is developed using a numerical tool that couples a non-linear finite element model developed in-house and a genetic algorithm optimization technique. This numerical tool is an extended version of an earlier one, adapted for the optimum design of unstiffened conical tanks. The design variables considered in the current study are the shell thicknesses, the geometry of the steel vessel as well as the dimensions and number of stiffeners. The developed numerical tool is capable of selecting the set of design variables that leads to optimum safe design. The analysis is conducted twice; first, case of stiffeners free at their bottom edge, which represents the case of retrofitting an existing tank. In the second case the stiffeners are assumed to be anchored to the bottom slab of the tank, which represents the situation of a newly designed tank. Finally, the optimum design of the stiffened tanks is compared to the optimum design of unstiffened tanks computed in a previous study.     

半地下贮液池结构抗震分析方法的修正系数研究

半地下贮液池作为一种特殊的地下结构,在地震作用下可能发生的震害也较为多样.该半地下贮液池结构复杂,有限元模型单元和节点数量多,难以采用时程分析法进行计算;拟静力法计算简单,但不能得出结构在动态的地震波下的最大响应,因此提出一个修正系数用以拟静力法与时程分析法结果的互相转换.本文在建立半地下贮液池实际有限元模型的基础上建...     

Stability of combined imperfect conical tanks under hydrostatic loading

Steel conical vessels with upper cylindrical caps are widely used as liquid containments in elevated water tanks. This type of structure for containing water is referred to as “combined conical tank”. A number of catastrophic failures of combined conical tanks occurred during the past decades in various locations around the globe. Previous studies available in the literature focused on pure conical tanks, where the vessels have no upper cylindrical caps. The current study focuses on characterizing the buckling behaviour of combined conical tanks under the effect of hydrostatic pressure. The study is conducted numerically using a three-dimensional finite element model developed in-house. The effects of geometric imperfection and residual stresses as well as the variation of the geometric and material parameters on the buckling capacity of combined conical tanks are investigated. Finally, a comparison between the buckling capacities of combined and equivalent pure conical tanks is conducted.     

地震作用下储罐参数对其应力影响分析

考虑固液耦合以及储罐与地基的相互作用,运用ADINA有限元软件建立了三种不同体积储罐的有限元数值分析模型,设置不同的储液高度,分析储罐罐壁在水平地震作用下的应力响应,得到了相关结论。     

考虑流固耦合的储液容器地震反应计算

在计算带有自由表面流体晃动问题的三维流体程序中 ,加入了计算弹性结构模型的有限元模块 ,开发出考虑流体和弹性结构的相互作用的三维流固耦合程序 ,应用此程序计算了弹性储液容器在正弦波模拟的地震作用下的动力响应 ,得到了较为合理的结果     

A coupled finite element genetic algorithm technique for optimum design of steel conical tanks

Steel conical tanks having an upper cylindrical section and supported by a reinforced concrete shaft are widely used for water containment in elevated tanks. During the past few decades, a number of conical tanks have failed as a result of buckling of the steel vessel due to inadequate selection of the shell thickness. In the current study a powerful numerical tool that couples a non-linear finite element model and a genetic algorithm optimization technique is developed specifically for the analysis and design of steel conical tanks. The developed numerical tool is capable of selecting the set of design variables which satisfies the structure safety requirements while achieving a minimum structure weight and consequently minimum cost.     

近场地震作用下隔震储罐动力响应参数影响分析

为了研究近场地震作用下,基础隔震参数对储罐地震响应的影响,以1000 m3的储罐为研究对象,通过ADINA建立储罐的有限元模型并输入汶川武都近场地震波,选取不同的隔震参数分析其动力响应,结果表明:基础隔震可以有效降低储罐的基底剪力和罐壁等效应力;随着隔震层阻尼比的增大,储罐罐壁等效应力和基底剪力先增大后减小,隔震层阻尼比取0.1~0.3为宜;随着隔震周期的增大,储罐基底剪力和罐壁等效应力逐渐降低,隔震周期取2~4 s为宜;基础隔震措施不能控制储液的晃动波高。     

Damping enhancement of seismic isolated cylindrical liquid storage tanks using baffles

The effect of baffles in reducing earthquake responses of seismically isolated cylindrical liquid storage tanks is investigated in this study. Seismic isolation is a well-known approach to reduce the earthquake effects on structures by lengthening their fundamental natural periods at the expense of larger displacements in the structural system. To reduce such effects in a system a higher damping ratio is required. In moving liquid containers, baffles play an important role in damping the liquid motion. Thus to study the effects of using baffles in seismically isolated tanks, in the first instance the velocity contours in a cylindrical tank are analysed to determine the most effective shape of baffle. Next, the damping coefficients are analytically determined for horizontal ring shape and vertical blade shape baffles. To estimate the sloshing height level and the damping ratio, a methodology, based on Tank Body Spectra, is developed in which the higher sloshing amplitude and the relative fluid velocity with respect to baffles in base isolated tanks are taken into consideration. A computer program is developed to put all these together and investigate the effect of baffles for different tank dimensions under the effect of four different earthquakes. The results show that the average damping ratio of sloshing mode due to ring baffle increases with a decrease in liquid height and highest damping may be achieved for height to radius ratios of between 1.0 and 1.5. In addition, for reasonable ring baffle dimensions, an average reduction of 6% in base displacement of base isolated tanks and an average reduction of more than 30% in the sloshing height of base isolated and fixed base tanks may be achieved. To study the effect of baffles on the distribution of hydrodynamic and tank body forces with height, a simple dynamic model is proposed. The results of analyses using this model indicate a constant reduction in sloshing forces and different reductions in moment and shear forces for different heights. This happens because contribution of the sloshing force to the total hydrodynamic force varies with height.     

Simplified procedure for design of liquid-storage combined conical tanks

Steel vessels in the form of combined conical-cylindrical shells are commonly used for liquid storage in elevated water tanks. A number of such tanks collapsed in different places around the globe due to instability of the steel shells. An essential cause of those collapses is the lack of adequate design procedures for such structures. In this study, a simplified design approach is developed to ensure safety of hydrostatically loaded combined steel conical tanks against buckling. The study is conducted numerically using a non-linear finite element model that accounts for the effects of large deformations and geometric imperfections on the stability of combined conical tanks. The finite element results together with a non-linear regression analysis are used to develop magnification functions that relate the overall shell stresses to the membrane stresses which can be evaluated analytically. Numerical examples are presented to explain application of the suggested design approach.     

大型储罐自振特性分析

为了给大型储罐地震动力响应进一步分析提供数据,建立了大型储罐有限元简化模型,考虑了罐体的固液耦合作用,对储罐系统的自振特性进行了分析,结果表明,有限元结果与规范计算结果误差很小,计算结果可靠。     

Dynamic characteristics of combined conical-cylindrical shells

The truncated conical shape having a superimposed top cylindrical cap is widely used as a containment vessel for elevated water tanks. The evaluation of the wind and seismic responses of these tanks requires the knowledge of the dynamic characteristics of the vessels. This study reports the results of the first experimental and numerical investigation conducted to assess the dynamic behaviour of combined conical vessels. Shake table testing is conducted on a small-scale combined conical shell model. The tested specimen is then simulated numerically in a three-dimensional finite element analysis. The numerical model is validated through comparison with experimental results. An extensive parametric study is then conducted using the validated numerical model in order to determine the dynamic characteristics of full-scale combined conical vessels. Equations and charts describing the natural frequencies, the mode shapes and the generalized and effective masses of the vessels are obtained from this parametric study.     

Generalized SDOF system for seismic analysis of concrete rectangular liquid storage tanks

This paper presents a simplified method using the generalized single degree of freedom (SDOF) system for seismic analysis and design of concrete rectangular liquid storage tanks. In most of the current design codes and standards for concrete liquid storage tanks, the response of liquid and tank structures is determined using rigid boundary conditions for the determination of hydrodynamic pressures. Also, the lumped mass approach is used for dynamic analysis. However, it has been shown that the flexibility of a tank wall increases the hydrodynamic pressures as compared to the rigid wall assumption. On the other hand, the consistent mass approach reduces the response of liquid containing structures as compared to the lumped mass approach. In the proposed method, the consistent mass approach and the effect of flexibility of a tank wall on hydrodynamic pressures are considered. The prescribed vibration shape functions representing the first five mode shapes for the cantilever wall boundary condition are studied. The application of the proposed shape functions and their validity are examined using two different case studies including a tall and a shallow tank. The results are then compared with those using the finite element method from a previous investigation and ACI 350.3 commonly used in current practice. The results indicate that the proposed method is fairly accurate which can be used in the structural design of liquid containing structures. It is also concluded that the effect of the second mode should also be considered in the dynamic analysis of liquid containing structures.     

Challenges in the computation of lower-bound buckling loads for tanks under wind pressures

This paper reports on the implementation of a lower-bound approach for the buckling of imperfection-sensitive shells using general purpose finite element codes. The stability of cylindrical steel tanks under wind pressure is evaluated for two tank configurations: conical roof tanks and open top tanks. For both tank configurations, several geometric relations are considered in order to find the variation of the knock-down factor as the geometry changes. The reduced energy method is implemented to compute a lower-bound for critical wind pressures and the results are compared with the static non-linear analysis carried out on the same models. An alternative way to implement the reduced energy method is presented to improve the results obtained with the proposed methodology.