Identification of structural and soil properties from vibration tests of the Hualien containment model

Measurements of the response of the ¼‐scale reinforced concrete Hualien (Taiwan) containment model obtained during forced vibration tests are used to identify some of the characteristics of the superstructure and the soil. In particular, attempts are made to determine the fixed‐base modal frequencies, modal damping ratios, modal masses and participation factors associated with translation and rocking of the base. The shell superstructure appears to be softer than could have been predicted on the basis of the given geometry and of test data for the properties of concrete. Estimates of the shear‐wave velocity and damping ratio in the top layer of soil are obtained by matching the observed and theoretical system frequency and peak amplitude of the response at the top of the structure. The resulting models for the superstructure and the soil lead to theoretical results for the displacement and rotations at the base and top of the structure which closely match the observed response. Copyright © 2004 John Wiley & Sons, Ltd.     

分层土-基础-高层框架结构相互作用体系振动台模型试验研究

本文设计实现了分层土－基础－高层框架结构相互作用体系的振动台模型试验，再现了地震动激励下上部结构和基础的震害现象和砂质粉土的液化现象。通过试验，研究了相互作用体系地震动反应的主要规律：由于动力相互作用的影响，软土地基中相互作用体系的频率小于不考虑结构－地基相互作用的结构频率，而阻尼比则大于结构材料阻尼比；体系的振型曲线与刚性地基上结构的振型曲线明显不同，基础处存在平动和转动。土层传递振动的放大或减振作用与土层性质、激励大小等因素有关，砂土层一般起放大作用，砂质粉土层一般起减振隔振作用；由于土体的隔震作用，上部结构接受的振动能量较小，各层反应均较小。上部结构顶层加速度反应组成取决于基础转动刚度、平动刚度和上部结构刚度的相对大小。     

Roles of soil-structure interaction and damping in base-isolated structures built on numerous soil layers overlying a half-space

This study examines the roles of soil-structure interaction (SSI), higher modes, and damping in a base-isolated structure built on multiple layers of soil overlying a half space. Closed-form solutions for the entire system, including a superstructure, seismic isolator, and numerous soil layers overlying a half-space, were obtained. The formulations obtained in this study simply in terms of well-known frequencies and mechanical impedance ratios can explicitly interpret the dynamic behavior of a base-isolated structure interacting with multiple soil layers overlying a half-space. The key factors influencing the performance of the isolation system are the damping ratio of the isolator and the ratio of the natural frequency of the fixed-base structure to that of the isolated structure by assuming that the superstructure moves as a rigid body. This study reveals that higher damping in the base isolator is unfavorable to higher mode responses that usually dominate the responses of the superstructure and that the damping mechanism plays an important role in transmitting energy in addition to absorbing energy. It is also concluded that it is possible to design a soft soil layer as an isolation system for isolating vibration energy.     

土-箱形基石础-框架结构相互作用的顶部小幅激振试验研究

设计并完成了野外大比例(1:2)土-箱形基础-框架结构相互作用系统顶部小幅激振试验.通过改变上部结构质量和基础侧限埋深,激振试验得到了同一基础不同上部结构质量与同一上部结构不同基础侧限埋深等5种工况下相互作用对系统自振频率及箱形基础阻抗函数的影响.由试验结果分析可知,当上部结构质量增加时,上部结构与土体间的相对刚度降低,相互作用对系统自振频率的影响减弱;同时由于上部结构和基础间惯性相互作用的影响,基础阻抗函数随上部结构质量的增加而增加.随着基础侧限埋深的减小,基础刚度降低,相互作用体现得更加明显.与理论结果相比,无侧限埋深基础的平动和转动基础阻抗值和理论值吻合较好.由于基础侧边回填土剪切模量小于基础底部土体剪切模量,所以同理论值相比试验得到的基础侧限埋深对基础阻抗影响系数相对较小.     

An analytical model of a deformable cantilever structure rocking on a rigid surface: experimental validation

This paper describes an experimental program to examine the dynamic response of deformable cantilevers rocking on a rigid surface. The primary goal of the tests is to verify and validate a dynamic rocking model that describes the behavior of these structures. The benchmark response data was obtained from shaking‐table tests on deformable rocking specimens with different natural vibration frequencies and different aspect ratios excited by analytical pulses and recorded ground motions. The responses computed using the model are found to be in good agreement with the benchmark test results. Widely used impact, restitution and damping assumptions are revisited based on the experiment results and the analytical model findings. Copyright © 2015 John Wiley & Sons, Ltd.     

土-箱形基础-框架结构相互作用的顶部小幅激振试验研究

设计并完成了野外大比例(1∶2)土-箱形基础-框架结构相互作用系统顶部小幅激振试验。通过改变上部结构质量和基础侧限埋深,激振试验得到了同一基础不同上部结构质量与同一上部结构不同基础侧限埋深等5种工况下相互作用对系统自振频率及箱形基础阻抗函数的影响。由试验结果分析可知,当上部结构质量增加时,上部结构与土体间的相对刚度降低,相互作用对系统自振频率的影响减弱;同时由于上部结构和基础间惯性相互作用的影响,基础阻抗函数随上部结构质量的增加而增加。随着基础侧限埋深的减小,基础刚度降低,相互作用体现得更加明显。与理论结果相比,无侧限埋深基础的平动和转动基础阻抗值和理论值吻合较好。由于基础侧边回填土剪切模量小于基础底部土体剪切模量,所以同理论值相比试验得到的基础侧限埋深对基础阻抗影响系数相对较小。     

Full-scale experimental modal analysis of an arch dam: The first experience in Iran

Forced vibration field tests and finite-element studies were conducted on the Shahid Rajaee concrete arch dam in Northern Iran to determine the dynamic properties of the dam–reservoir–foundation system. The first forced vibration tests on the dam were performed with two different types of exciter units, with a limited maximum force, bolted on the dam crest for alternative in-phase and out-of-phase sequencing. Because of an insufficient number of recording sensors, two arrangements of sensors were used to cover sufficient points on the dam crest and one gallery during tests. Two kinds of vibration tests, on–off and frequency sweeping, were carried out on the dam. The primary natural frequencies of the coupled system for both symmetric and anti-symmetric vibration modes were approximated during on–off tests in two types of sequencing of exciters, in phase and out-of-phase, with a maximum frequency of 14 Hz. The principal forced vibration tests were performed at precise resonant frequencies based on the results of the on–off tests in which sweeping around the approximated frequencies at 0.1 Hz increments was performed. Baseline correction and suitable bandpass filtering were applied to the test records and then signal processing was carried out to compute the auto power, cross power and coherence spectra. Nine middle modes of vibration of the coupled system and corresponding damping ratios were estimated. The empirical results are compared against the results from calibrated finite-element modeling of the system using former ambient vibration tests, considering the dam–reservoir–foundation interaction effects. Good agreement is obtained between experimental and numerical results for eight middle modes of the dam–reservoir–foundation system.     

Non-classical damping in dynamic analysis of base-isolated structures with internal equipment

It has been shown that the use of base isolation not only attenuates the response of a primary structural system but also reduces the response of a secondary system mounted on or within the main structure. The isolation system, superstructure and equipment may be made of different materials with significantly different energy dissipation characteristics such that the damping matrix for the combined system is non-classical and can only be approximately expressed by modal damping ratios if the classical mode method is used for analysis. The object of this paper is to evaluate the accuracy of this procedure in approximating the responses of base-isolated structures and internal equipment. The complex mode method can provide exact solutions to problems with non-classical damping and is used here to find the exact response of the isolation-superstructure-equipment system. The entire system is assumed to be linear elastic with viscous damping and the superstructure is assumed to be proportionally damped so that the deformation of the superstructure can be expressed in terms of its classical modes. Recognizing that the ratio of the equipment mass to the structural mass and the ratio of the stiffness of the isolation system to the superstructural stiffness are both small, perturbation methods are used to find the response. This study shows that the response of base-isolated structures can be determined by the classical mode method to some degree of accuracy, but the higher frequency content is distorted. The equipment response derived by the classical mode method is much smaller than the exact solution so that the complex mode method should be applied to find equipment response.     

Seismic response of heavily damped base isolation systems

The development of an efficient energy-dissipating mechanism that works in conjunction with laminated elastomeric bearings in order to reduce the lateral deformation of the isolation system has always been a goal of base isolation research. Theoretically, this deformation will be reduced to the minimum if damping augmentation of the isolation system can reach a critical value. However, augmenting the isolation damping may cause some unwanted side effects. The purpose of this paper is to study the influence of isolation damping on the seismic response of heavily damped base-isolated buildings. The base isolation system is assumed to be linearly viscoelastic and is analysed using the complex mode method. Solutions derived by using perturbation techniques for a two-degree-of-freedom system and the computer simulation for a multiple-degree-of-freedom system reveal that augmenting the isolation damping can reduce efficiently the deformation of the isolation system, but at the price of increasing the high-frequency vibration in the superstructure. When the damping ratio of the isolation system is beyond some level, increasing the isolation damping will enlarge the extreme values of the base and superstructural accelerations. It is also found that approximate solutions derived from the use of classical damping and classical modes of vibration in the seismic analysis of heavily damped base isolation systems can be substantially in error.     

Seismic performance of buildings with structural and foundation rocking in centrifuge testing

Rocking motion, established in either the superstructure in the form of a 2‐point stepping mechanism (structural rocking) or resulting from rotational motion of the foundation on the soil (foundation rocking), is considered an effective, low‐cost base isolation technique. This paper unifies for the first time the 2 types of rocking motion under a common experimental campaign, so that on the one hand, structural rocking can be examined under the influence of soil and on the other, foundation rocking can be examined under the influence of a linear elastic superstructure. Two building models, designed to rock above or below their foundation level so that they can reproduce structural and foundation rocking respectively, were tested side by side in a centrifuge. The models were placed on a dry sandbed and subjected to a sequence of earthquake motions. The range of rocking amplitude that is required for base isolation was quantified. Overall, it is shown that the relative density of sand does not influence structural rocking, while for foundation rocking, the change from dense to loose sand can affect the time‐frequency response significantly and lead to a more predictable behaviour.     

Comparisons between ambient and forced vibration experiments

The ambient and forced vibration techniques for testing full-scale structures are critically compared. Both methods, based on small level excitation, may be used to determine many mode shapes and frequencies of vibration and the corresponding damping values, with adequate accuracy for most purposes. The two techniques give mutually consistent results. The mode amplitudes determined by ambient and forced vibration tests show systematic departure for high modes and near the top levels of buildings tested. This phenomenon is attributed to the participation of all mode shapes and is a consequence of excitation by a concentrated force near the top of a building and at a frequency differing by only a few per cent from a natural frequency of vibrations. A new way of showing the effect of unwanted modes on the response near resonance of the mode being sought is developed. It is particularly useful for the analysis of steady, forced vibration tests of structures using eccentric mass vibration generators.     

Vibration characteristics of rigid body placed on sand ground

This study aims to investigate experimentally the vibration properties of rigid body placed on sand ground surface. The rigid body models with circular or rectangular base with variable mass, inertial moment and base sizes, were prepared, and the vibration behavior was observed in some series of free vibration tests and forced vibration tests. The observed behavior was analyzed and the vibration mode, vibration period and damping ratio were examined. It was found that the natural vibration period depends not only on the mechanical properties of rigid body and ground, but also on the magnitude of vibration amplitude. This suggested the notable effect of nonlinear strain dependent stiffness of ground material. A physical model with distributed spring–dashpot element was used to model the interactive mechanical behavior between rigid body and ground. The stiffness of the spring–dashpot element was evaluated through the modal analysis of the observed vibration behaviors. The effects of base shape, base size and base pressure on the stiffness of spring–dashpot element are discussed. The spring–dashpot model was verified with the behavior observed in forced vibration tests.     

Dynamic properties analysis of a stay cable-damper system in consideration of design and construction factors

A numerical solution based on the Steffensen stable point iterative method is proposed to resolve the transcendental frequency equation of a stay cable-damper system. The frequency equation, which considers clamped supports and fl exural rigidity of the cable, is intended to investigate the infl uence of the parameters of the cable damper system on its dynamic characteristics. Two factors involved in the design and construction phases, the damping coeffi cient induced by external dampers and the cable tension, are the focus of this study. Their impact on modal frequencies and damping ratios in these two phases of cable-damper systems are investigated by resolving the equation with the proposed solution. It is shown that the damping coeffi cient and cable tension exert more noticeable effects on the modal damping ratios than on the modal frequencies of stay cable-damper systems, and the two factors can serve as design variables in the design phase and as adjustment factors in the construction phase. On the basis of the results, a roadmap for system-level optimal design of stay cable-damper systems that can achieve global optimal vibration suppression for the entire bridge is proposed and discussed.     

System identification for evaluating soil–structure interaction effects in buildings from strong motion recordings

Parametric system identification is used to evaluate seismic soil–structure interaction effects in buildings. The input–output strong motion data pairs needed for evaluations of flexible- and fixed-base fundamental mode parameters are derived. Recordings of lateral free-field, foundation, and roof motions, as well as foundation rocking, are found to be necessary for direct evaluations of modal parameters for both cases of base fixity. For the common situation of missing free-field or base rocking motions, procedures are developed for estimating the modal parameters that cannot be directly evaluated. The accuracy of these estimation procedures for fundamental mode vibration period and damping is verified for eleven sites with complete instrumentation of the structure, foundation, and free-field. © 1998 John Wiley & Sons, Ltd.     

Ductility demands of tall buildings subjected to base rocking induced by Rayleigh waves

Performance-based earthquake engineering requires accurate estimation of structural response associated with different damage states because of strong ground motion. In recent work (Meza-Fajardo and Papageorgiou, 2018, EESD), we demonstrated that a significant contribution to the response of elastic soil-structure systems for high-rise buildings is attributed to base rocking associated with Rayleigh waves. The present paper presents results of a study investigating the effects of Rayleigh waves on the response of soil-structure systems with nonlinear behavior at the level of the superstructure. By introducing a rigid-elastic rotational spring at the base of the building, we take into account the stiffness reduction due to damage to the lateral load-resisting system at its root, and with it, increased displacement demands. Considering different levels of ductility and post-yield stiffness, we investigate the impact of rocking because of Rayleigh waves on maximum and residual interstory drift ratios. Our results indicate that rocking due to surface waves should be an important consideration for design and evaluation of tall buildings, as inelastic action elongates their effective natural period, and consequently, they are more prone to be damaged by resonance and excitation of extended duration because of Rayleigh waves.     

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.     

Appropriate viscous damping for nonlinear time‐history analysis of base‐isolated reinforced concrete buildings

There is no consensus at the present time regarding an appropriate approach to model viscous damping in nonlinear time‐history analysis of base‐isolated buildings because of uncertainties associated with quantification of energy dissipation. Therefore, in this study, the effects of modeling viscous damping on the response of base‐isolated reinforced concrete buildings subjected to earthquake ground motions are investigated. The test results of a reduced‐scale three‐story building previously tested on a shaking table are compared with three‐dimensional finite element simulation results. The study is primarily focused on nonlinear direct‐integration time‐history analysis, where many different approaches of modeling viscous damping, developed within the framework of Rayleigh damping are considered. Nonlinear direct‐integration time‐history analysis results reveal that the damping ratio as well as the approach used to model damping has significant effects on the response, and quite importantly, a damping ratio of 1% is more appropriate in simulating the response than a damping ratio of 5%. It is shown that stiffness‐proportional damping, where the coefficient multiplying the stiffness matrix is calculated from the frequency of the base‐isolated building with the post‐elastic stiffness of the isolation system, provides reasonable estimates of the peak response indicators, in addition to being able to capture the frequency content of the response very well. Furthermore, nonlinear modal time‐history analyses using constant as well as frequency‐dependent modal damping are also performed for comparison purposes. It was found that for nonlinear modal time‐history analysis, frequency‐dependent damping, where zero damping is assigned to the frequencies below the fundamental frequency of the superstructure for a fixed‐base condition and 5% damping is assigned to all other frequencies, is more appropriate, than 5% constant damping. Copyright © 2013 John Wiley & Sons, Ltd.     

Seismic control of rocking structures via external resonators

Tall rigid blocks are prevalent in ancient historical constructions. Such structures are prone to rocking behaviour under strong ground motion, which is recognizably challenging to predict and mitigate. Our study is motivated by the need to provide innovative nonintrusive solutions to attenuate the rocking response of historical buildings and monuments. In this paper, we examine a novel scheme that employs external resonators buried next to the rocking structure as a means to control its seismic response. The strategy capitalizes on the vibration absorbing potential of the structure-soil-resonator interaction. Furthermore, the benefits of combining the resonators with inerters in order to reduce their gravitational mass without hampering their motion-control capabilities are also explored. Advanced numerical analyses of discrete models under coherent acceleration pulses with rocking bodies of different slenderness ratios under various ground motion intensities highlight the significant vibration absorbing qualities of the external resonating system. The influence of key system parameters such as the mass, stiffness, and damping of the resonator and those of the soil-structure-resonator arrangement are studied. Finally, a case study on the evaluation of the response of rocking structures with external resonators under real pulse-like ground-motion records confirms the important reductions in peak seismic rotational demands obtained with the proposed arrangement.     

应县木塔环境振动试验

对于复杂的塔状古建筑物,建立一个合适的简化的数学模型是不易实现的。与强迫振动试验相比,环境振动试验比较简单、方便,所确定出的小振幅水平下的木塔结构动力特性具有足够的精度。本文首先结合应县木塔结构环境振动测试实例对环境振动测试方法作了简要介绍,并采用随机信号数据频域分析方法对测试数据进行了分析,确定木塔结构的自振频率。同时,依据不同测点在固有频率处响应的比及零迟时互相关函数确定木塔结构的振型。最后,本文依据自功率谱和互功率谱采用半功率点法计算各振型的阻尼比。本文分析结果表明,在两水平方向上木塔的振动特性存在些微差异,第一振型阻尼比较第二振型阻尼比大。