Tuned liquid dampers simulation for earthquake response control of buildings

This paper is focused on the study of an earthquake protection system, the tuned liquid damper (TLD), which can, if adequately designed, reduce earthquake demands on buildings. This positive effect is accomplished taking into account the oscillation of the free surface of a fluid inside a tank (sloshing). The behaviour of an isolated TLD, subjected to a sinusoidal excitation at its base, with different displacement amplitudes, was studied by finite element analysis. The efficiency of the TLD in improving the seismic response of an existing building, representative of modern architecture buildings in southern European countries was also evaluated based on linear dynamic analyses.     

基底隔震储罐频率特征与减震机理分析研究

研究不同高径比橡胶基底隔震储罐的频率特征,探讨储罐隔震体系3种不同振动频率随支座隔震频率变化规律.分析在不同频谱特性地震波激励下,隔震体系各振型组分对地震响应(基底剪力、支座位移和晃动波高)的影响,以及响应峰值随支座隔震频率和阻尼比的变化特点.研究表明,基底剪力峰值与场地地震波频谱特性密切相关.支座隔震频率不能完全反映减震机理的实质,隔震振型频率是影响基底剪力的重要参数.在软弱场地上隔震储罐的减震效率低,有效隔震频率范围窄.晃动波高峰值是储罐自振特性和地震波频谱特性等多种因素导致的结果,隔震系统设计时需特别考虑晃动波高增大的影响.     

A model of tuned liquid damper for suppressing pitching motions of structures

A tuned liquid damper (TLD), which consists of rigid tanks partially filled by liquid, is a type of passive control device relying upon liquid sloshing forces or moments to change the dynamical properties and to dissipate vibrational energy of a structure. An analytical non-linear model is proposed for a TLD using rectangular tanks filled with shallow liquid under pitching vibration, utilizing a shallow water wave theory. The model includes the linear damping of the sloshing liquid, which is an important parameter in the study of a TLD as it affects the efficiency of the TLD. Shaking table experiments were conducted for verification; good agreement between the analytical simulations and the experimental results was observed in a small excitation amplitude range. The simulations of TLD-structure interaction by using the proposed model show that the TLD can efficiently suppress resonant pitching vibration of a structure. It is also found that the effectiveness of a TLD for suppressing the pitching vibration depends not only on the mass of liquid in the TLD but also on the configuration of the liquid as well as upon the position where the TLD is located. If the configuration of the liquid, i.e. the liquid depth and the TLD tank size, is designed suitably, the TLD can have a large suppressing moment and can be very effective even with a small mass of liquid.     

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.     

An investigation of tuned liquid dampers equipped with damping screens under 2D excitation

This paper reports on the results of a study conducted on tanks partially filled with water, representing tuned liquid dampers (TLD), subjected to both 1D and 2D horizontal excitations. The sloshing response of the water in the tank is characterized by the free surface motion, the resulting base shear force, and evaluation of the energy dissipated by the sloshing water. A 1D non‐linear flow model capable of simulating a TLD equipped with damping screens is employed to model a 2D TLD. Application of this particular model requires the assumption that the response is decoupled and can be treated as the summation of two independent 1D TLDs. Results from the non‐linear flow model are compared with the 2D experimental shake table test results leading to a validation of the decoupled response assumption. This attractive decoupled response property allows square and rectangular tanks to be used as 2D TLDs, which can simultaneously reduce the dynamic response of a structure in two perpendicular modes of vibration. Copyright © 2005 John Wiley & Sons, Ltd.     

An efficient method for estimating the collapse risk of structures in seismic regions

Assessing the probability of collapse is a computationally demanding component of performance‐based earthquake engineering. This paper examines various aspects involved in the computation of the mean annual frequency of collapse (λ_c) and proposes an efficient method for estimating the sidesway collapse risk of structures in seismic regions. By deaggregating the mean annual frequency of collapse, it is shown that the mean annual frequency of collapse is typically dominated by earthquake ground motion intensities corresponding to the lower half of the collapse fragility curve. Uncertainty in the collapse fragility curve and mean annual frequency of collapse as a function of the number of ground motions used in calculations is also quantified, and it is shown that using a small number of ground motions can lead to unreliable estimates of a structure's collapse risk. The proposed method is shown to significantly reduce the computational effort and uncertainty in the estimate. Copyright © 2012 John Wiley & Sons, Ltd.     

Development of a tunable friction pendulum system for semi‐active control of building structures under earthquake ground motions

The Friction Pendulum System (FPS) isolator is commonly used as a base isolation system in buildings. In this paper, a new tunable FPS (TFPS) isolator is proposed and developed to act as a semi‐active control system by combining the traditional FPS and semi‐active control concept. Theoretical analysis and physical tests were carried out to investigate the behavior of the proposed TFPS isolator. The experimental and theoretical results were in good agreement, both suggesting that the friction force of the TFPS isolator can be tuned to achieve seismic isolation of the structure. A series of numerical simulations of a base‐isolated structure equipped with the proposed TFPS isolator and subjected to earthquake ground motions were also conducted. In the analyses, the linear quadratic regulator (LQR) method was adopted to control the friction force of the proposed TFPS, and the applicability and effectiveness of the TFPS in controlling the structure's seismic responses were investigated. The simulation results showed that the TFPS can reduce the displacement of the isolation layer without significantly increasing the floor acceleration and inter‐story displacement of the superstructure, confirming that the TFPS can effectively control a base‐isolated structure under earthquake ground motions.     

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.     

Investigation of the dynamic behaviour of a storage tank with different foundation types focusing on the soil‐foundation‐structure interactions using centrifuge model tests

This paper proposes a dynamic centrifuge model test method for the accurate simulation of the behaviours of a liquid storage tank with different types of foundations during earthquakes. The method can be used to determine the actual stress conditions of a prototype storage‐tank structure. It was used in the present study to investigate the soil‐foundation‐structure interactions of a simplified storage tank under two different earthquake motions, which were simulated using a shaking table installed in a centrifuge basket. Three different types of foundations were considered, namely, a shallow foundation, a slab on the surface of the ground connected to piles and a slab with disconnected piles. The test results were organised to compare the ground surface and foundation motions, the slab of foundation and top of structure motions and the horizontal and vertical motions of the slab, respectively. These were used to establish the complex dynamic behaviours of tank models with different foundations. The effects of soil–foundation–structure interaction with three foundation conditions and two different earthquake motions are focused and some important factors, that should be considered for future designs are also discussed in this research. Copyright © 2017 John Wiley & Sons, Ltd.     

Damped resonant appendages to increase inherent damping in buildings

It is demonstrated that the addition of a tuned mass-spring-dashpot system with a relatively small mass and a high damping ratio can be an effective way to increase the inherent damping characteristics of buildings and reduce, thus, their response to earthquake excitations. The demonstration is based on a theoretical formulation and on numerical and experimental studies that confirm this formulation. In the theoretical formulation, it is shown first that, if certain conditions are satisfied, the damping ratios in two of the modes of the system that is formed by a building and an appendage in resonance are approximately equal to the average of the corresponding damping ratios of the building and the appendage. Based on this finding, it is then shown that an attached appendage with a high damping ratio and tuned to the fundamental frequency of a building may increase the damping ratio in the fundamental mode of the building to a value close to half the damping ratio of the appendage. In the numerical study, the response of a ten-storey shear building is analysed under two different earthquake ground motions with and without the proposed resonant appendages. Appendages with damping ratios of 20 and 30 per cent are considered. In this study, it is found that under one of the ground motions the maximum displacement of the building's roof is reduced 30 per cent with the appendage with 20 per cent damping and 39 per cent with the one with 30 per cent damping. Similarly, with these two appendages the building's base shear is reduced 31 and 41 per cent, respectively. In the experimental study, a wooden three-storey structural model is tested in a shaking table with and without an appendage designed and constructed to have a damping ratio of 53-5 per cent. The test is conducted under random and sinusoidal base excitations. In the shaking table test under random excitation, the attached appendage reduces the response of the model 38-6 per cent, while in that under sinusoidal vibration 45-2 per cent.     

Theoretical and experimental studies on rectangular liquid dampers under arbitrary excitations

This paper presents a study on the behaviour of rectangular liquid dampers under a horizontal excitation of arbitrary time history. The theoretical model to predict motion of a shallow liquid in a rectangular tank is adapted from a previous researchers' model which was developed for sinusoidal excitations. The model includes an energy dissipation term arising from liquid viscosity. In the present consideration of arbitrary excitations, the energy dissipation term is derived in a straightforward way, without resorting to the equivalent linearization method or assumption of harmonic response as used by earlier researchers. The up-crossing rate of wave height is used in furnishing the Reynolds number required for the evaluation of shear stress in the boundary layer. Since there was no known precedent study involving arbitrary excitations, experiments have been performed accordingly to verify the model. Generally, the theoretical model furnishes results which are found to be in close agreement with the experimental ones. The results also illustrate the strong dependency of liquid motion upon the natural frequency of the damper, amplitude and frequency content of the excitation spectrum. The model is then applied to study the effectiveness of tuned liquid dampers in vibration control of a single-degree-of-freedom structure subjected to earthquake excitations. Significant suppression of structural vibration can be achieved using tuned liquid dampers.     

Experimental and theoretical simulations of seismic poundings between two adjacent structures

Shaking table tests have been carried out to investigate the pounding phenomenon between two steel towers of different natural frequencies and damping ratios, subject to different combinations of stand‐off distance and seismic excitations. Both harmonic waves and ground motions of the 1940 El Centro earthquake are used as input. Subjected to sinusoidal excitations, poundings between the two towers could appear as either periodic or chaotic. For periodic poundings, impact normally occurs once within each excitation cycle or within every other excitation cycle. A type of periodic group poundings was also observed for the first time (i.e. a group of non‐periodic poundings repeating themselves periodically). Chaotic motions develop when the difference of the natural frequency of the two towers become larger. Under sinusoidal excitations, the maximum relative impact velocity always develops at an excitation frequency between the natural frequencies of the two towers. Both analytical and numerical predictions of the relative impact velocity, the maximum stand‐off distance, and the excitation frequency range for pounding occurrences were made and found to be comparable with the experimental observations in most of the cases. The stand‐off distance attains a maximum when the excitation frequency is close to that of the more flexible tower. Pounding appears to amplify the response of the stiffer structure but suppress that of the more flexible structure; and this agrees qualitatively with previous shaking table tests and theoretical studies. Copyright © 2003 John Wiley & Sons, Ltd.     

考虑桩土作用的储罐模拟地震振动台试验

为研究考虑桩土相互作用的储液罐的动力响应及长周期地震波对储液晃动、储罐提离的影响,根据量纲分析法设计了桩-土-储罐模型进行了振动台试验。试验中采用4条基岩波、4条地表波进行振动台试验。试验显示基岩波与地表波输入时,体系变化规律基本一致,其结果表明:土体地表加速度被放大,且输入加速度峰值增加,地表加速度放大倍数减小;一般地震波时,随着输入加速度峰值的增加,储液晃动波高大致呈线性增加。长周期地震波下则为非线性增加,且晃动波较大。此外,液体产生的晃动波高与储罐类型相关。细高型储罐产生的波高稍大;储罐提离高度随着输入加速度峰值的增加呈非线性增长。长周期地震波激励下,储罐提离高度小于一般地震波时的提离高度。细高型储罐在长短周期地震波激励下,提离高度较为接近,而一般储罐在两种地震波激励下,提离高度相差较大。细高型储罐提离高度大于一般储罐的提离高度。建议在储罐设计时考虑长周期地震波的影响。     

Response‐only modal identification of structures using strong motion data

Dynamic characteristics of structures — viz. natural frequencies, damping ratios, and mode shapes — are central to earthquake‐resistant design. These values identified from field measurements are useful for model validation and health‐monitoring. Most system identification methods require input excitations motions to be measured and the structural response; however, the true input motions are seldom recordable. For example, when soil–structure interaction effects are non‐negligible, neither the free‐field motions nor the recorded responses of the foundations may be assumed as ‘input’. Even in the absence of soil–structure interaction, in many instances, the foundation responses are not recorded (or are recorded with a low signal‐to‐noise ratio). Unfortunately, existing output‐only methods are limited to free vibration data, or weak stationary ambient excitations. However, it is well‐known that the dynamic characteristics of most civil structures are amplitude‐dependent; thus, parameters identified from low‐amplitude responses do not match well with those from strong excitations, which arguably are more pertinent to seismic design. In this study, we present a new identification method through which a structure's dynamic characteristics can be extracted using only seismic response (output) signals. In this method, first, the response signals’ spatial time‐frequency distributions are used for blindly identifying the classical mode shapes and the modal coordinate signals. Second, cross‐relations among the modal coordinates are employed to determine the system's natural frequencies and damping ratios on the premise of linear behavior for the system. We use simulated (but realistic) data to verify the method, and also apply it to a real‐life data set to demonstrate its utility. Copyright © 2012 John Wiley & Sons, Ltd.     

Sloshing analysis of rectangular tanks with a submerged structure by using small-amplitude water wave theory

A new sloshing analysis method for rectangular tank systems with a submerged structure are proposed by using the velocity potential and the linear water wave theory. The velocity potential functions are obtained by decomposing the surface wave into a wall-induced wave, reflected and transmitted waves, and a scattered wave. A simplified method using a response spectrum for zero damping is also proposed. The results of the simplified method are in good agreement with those of the analytical method. The sloshing response of the fluid-structure system is found to be very sensitive to the characteristics of the ground motion and the configuration of the system. Under typical earthquakes, the submerged structure shows a tendency to decrease sloshing amplitude, hydrodynamic pressure, and base shear, while it shows a tendency to increase the overturning moment. For the ground excitation dominated by low-frequency contents, the sloshing response increases significantly and the contribution of the higher sloshing modes increases. Copyright © 1999 John Wiley & Sons, Ltd.     

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.     

水平地震激励下储罐液体晃动与提离分析

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在水平地震荷载作用下的液面晃动及储罐提离反应进行了分析。结果表明:罐内液体的晃动是长周期运动,其周期受地震动影响。无论是小体积罐还是大体积罐,在一定的地震烈度下均可以发生提离,而且储罐发生提离的时刻大多数是在地震动的峰值过后的一段时间内。大体积的储罐的提离明显小于小体积的罐。底板提离区域为月牙形。     

A seismological overview of long-period ground motion

Long-period ground motion has become an increasingly important consideration because of the recent rapid increase in the number of large-scale structures, such as high-rise buildings and oil storage tanks. Large subduction-zone earthquakes and moderate to large crustal earthquakes can generate far-source long-period ground motions in distant sedimentary basins with the help of path effects. Near-fault long-period ground motions are generated, for the most part, by the source effects of forward rupture directivity. Far-source long-period ground motions consist primarily of surface waves with longer durations than near-fault long-period ground motions. They were first recognized in the seismograms of the 1968 Tokachi-oki and 1966 Parkfield earthquakes, and their identification has been applied to the 1964 Niigata earthquake and earlier earthquakes. Even if there is no seismogram, we can identify far-source long-period ground motions through the investigation of tank damage by liquid sloshing.     

Parametric analysis of liquid storage tanks base isolated by curved surface sliding bearings

Curved surface sliding bearings, which are usually called as friction pendulum system (FPS) are commonly used for base isolation of liquid storage tanks since the period of the isolation system is independent of the storage level. However the restoring force and the damping at the isolation system are functions of axial load which changes during an earthquake excitation. This change might be in appreciable amounts especially for the tanks with high aspect ratios. The present paper focuses on earthquake performances of both broad and slender tanks base isolated by FPS bearings. The effects of overturning moment and vertical acceleration on axial load variation at the bearings are considered. The efficiency of the isolation system is investigated by analyzing the effects of various parameters such as; (i) isolation period, (ii) tank aspect ratio and (iii) coefficient of friction. The Haroun and Housner's three-degrees-of-freedom lumped mass model was used to solve the governing equations of motion in which convective, impulsive and rigid masses were included. A number of selected ground motions were considered and the results were compared to those of non-isolated cases.As a result, base isolation was found to be effective in reducing the base shear values for both broad and slender tanks without significantly affecting the sloshing displacements of the broad ones. The efficiency was even more pronounced for slender tanks subjected to near fault ground motions for isolation periods above 3 s. This specific value of isolation period also eliminated possible design problems arising from under-estimation of base shear values (up to 40%) due to ignoring the effects of axial load variation in lower isolation periods. Overturning effects should not be ignored especially for tanks with high aspect ratios (S) and being subjected to near fault ground motion.     

The effects of repeated earthquake ground motions on the non‐linear response of SDOF systems

In many parts of the world, the repetition of medium–strong intensity earthquake ground motions at brief intervals of time has been observed. The new design philosophies for buildings in seismic areas are based on multi‐level design approaches, which take into account more than a single damageability limit state. According to these approaches, a sequence of seismic actions may produce important consequences on the structural safety. In this paper, the effects of repeated earthquake ground motions on the response of single‐degree‐of‐freedom systems (SDOF) with non‐linear behaviour are analysed. A comparison is performed with the effect of a single seismic event on the originally non‐damaged system for different hysteretic models in terms of pseudo‐acceleration response spectra, behaviour factor q and damage parameters. The elastic–perfect plastic system is the most vulnerable one under repeated earthquake ground motions and is characterized by a strong reduction of the q‐factor. A moment resisting steel frame is analysed as well, showing a reduction of the q‐factor under repeated earthquake ground motions even larger than that of an equivalent SDOF system. Copyright © 2002 John Wiley & Sons, Ltd.