Empirical relationships between natural vibration period and height of buildings in Singapore

Singapore is a classic case of a modern metropolis with low hazard but high exposure to the seismicity in Sumatra. Because of land shortage, more than 80% of the population lives in high‐rise residential buildings. As part of the efforts to assess the seismic performance of buildings in Singapore subjected to long‐distance Sumatran earthquakes, relationships between the natural vibration period and height of high‐rise public residential buildings in Singapore are derived empirically by conducting ambient vibration tests on 116 buildings. The measured buildings have a height ranging from 4 to 30 stories. The aspect ratio of buildings in plan is found to be insignificant in affecting the natural vibration period of the first mode of the buildings. The period‐height relationships are derived using regression analysis considering the site properties of a building. It is concluded that the vibration periods estimated from the proposed period‐height relationship for buildings located at soft‐soil site are about 40% longer than the vibration periods estimated for buildings located at firm‐soil site. Measurements are also conducted to study the influence of buildings on the measured frequency of the surrounding soil. For this purpose, two buildings with 25 and 30 stories located at firm‐soil site and soft‐soil site, respectively, are selected. It is found that the distance of building influence on the measured frequency of the surrounding soil may reach up to one building height for a firm‐soil site and two building heights for a soft‐soil site. Additional data of natural vibration periods of 19 instrumented residential buildings, which have height ranging from 9 to 30 stories, were obtained from the building response recorded during the September 30, 2009 Sumatran earthquake event. The natural vibration periods of these buildings are compared with those estimated using the proposed period‐height relationships, and the absolute differences are found to be less than 12%. Copyright © 2013 John Wiley & Sons, Ltd.     

基于地脉动和地铁振动的钢筋混凝土建筑结构响应分析

在北京城区的一栋钢筋混凝土建筑(Reinforced Concrete building,简称RC)中,进行历时两天的地脉动和地铁振动观测.介绍了利用地脉动和地铁振动信号研究RC建筑结构响应的观测方法、仪器设备、数据采集和数据处理方法.对观测数据进行两种分析:(1)对连续的地脉动背景噪声,采用H/V谱比法;(2)对经过...     

Changes in dynamic characteristics of Lorca RC buildings from pre- and post-earthquake ambient vibration data

This paper estimates fundamental translational period and damping ratio parameters and examines the changes in dynamic characteristics of a set of low-to-medium rise buildings in Lorca town (SE of Spain) affected by the May 11th, 2011 earthquake. These building parameters have been calculated analysing structural dynamic response from ambient vibration measurements recorded at top RC buildings pre- and post earthquake, using the Fast Fourier Transform and the Randomdec technique. The empirical expression relating period \((T)\) and number of floor \((N)\) here obtained analysing ambient noise recorded on 59 healthy buildings before the earthquake is \(T= (0.054\pm 0.002)\, N\) , very similar to others empirical period–height relationships obtained for RC structures in the European built environment but quite different from code provisions. Measurements performed in 34 damaged buildings show a period elongation after the quake according to \(T^{*} =(0.075\pm 0.002)\,N\) expression. Moreover, we found a rise of the fundamental period with the EMS’s grade of damage of buildings. In contrast to natural frequency, damping ratio \((\xi )\) do not shows a significant variation with earthquake damage degree and the product \(\xi \, T\) remains near constant.     

地震安全性评价和高层建筑的地震动输入

本文根据现行的中国地震烈度区划图中烈度的含义,指出在使用现行“建筑抗震设计规范”时存在的一些问题和与《中华人民共和国防震减灾法》的不协调之处。根据多年参加工程场地地震安全性评价的经验,总结了目前进行地震安全性评价过程中存在的一些问题。文中建议：针对高层建筑进行新的场地分类方法的研究;对高层建筑工程场地作地震安全性评价时,可根据高度的不同,适当简化安全性评价过程。     

Cursory seismic drift assessment for buildings in moderate seismicity regions

This paper outlines a methodology to assess the seismic drift of reinforced concrete buildings with limited structural and geotechnical information. Based on the latest and the most advanced research on predicting potential near-field and far field earthquakes affecting Hong Kong, the engineering response spectra for both rock and soil sites are derived. A new step-by-step procedure for displacement-based seismic hazard assessment of building structures is proposed to determine the maximum inter-storey drift demand for reinforced concrete buildings. The primary information required for this assessment is only the depth of the soft soil above bedrock and the height of the building. This procedure is further extended to assess the maximum chord rotation angle demand for the coupling beam of coupled shear wall or frame wall structures, which may be very critical when subjected to earthquake forces. An example is provided to illustrate calibration of the assessment procedure by using actual engineering structural models.     

Probability analysis of seismic pounding of adjacent buildings

The need to investigate the level of seismic pounding risk of buildings is apparent in future building code calibrations. In order to provide further insight into the pounding risk of adjacent buildings, this study develops a numerical simulation approach to estimate the seismic pounding risk of adjacent buildings separated by a minimum code‐specified separation distance during a certain period of time. It has been demonstrated that the period ratio of adjacent buildings is an important parameter that affects the pounding risk of adjacent buildings. However, there is no specific consideration for the period ratio in the related seismic pounding provisions of the 1997 Uniform Building Code. Results also reveal that, for two adjacent buildings, the probability distribution of required distance to avoid seismic pounding fits very well with the type I extreme value distribution. Copyright © 2001 John Wiley & Sons, Ltd.     

Assessment of the frequency domain decomposition technique by forced‐vibration tests of a full‐scale structure

Dynamic characteristics of buildings are of utmost importance in earthquake engineering. The vibration periods are required to determine design loads, and damping is necessary in time‐history analysis. These parameters are generally obtained through forced‐vibration tests (FVTs) or after a seismic event in the case of permanently instrumented structures. However, for large civil engineering structures, FVTs are often too costly or practically difficult, and ambient or output‐only methods are used. This paper describes a comparison between ambient and FVTs carried out on a two‐story building. Results from both testing methods are compared and discussed in order to assess the vibration properties estimates obtained with the frequency domain decomposition technique. Copyright © 2007 John Wiley & Sons, Ltd.     

昆明高(超高)层建筑环境振动特性实测与统计分析

对昆明16栋典型钢筋混凝土高层建筑物的振动特征(包括建筑物的固有频率、振型和阻尼比)进行观测与分析,对地震响应数值模拟研究,获取实测高层建筑物第一至第三振型及结构,计算第一至第二振型自振周期结果,采用数学线性回归方法,模拟得到昆明高(超高)层建筑结构实测第一至三振型和计算第一至第二振型周期公式,为类似建筑结构的设计提供经验和依据。     

Empirical estimate of fundamental frequencies and damping for Italian buildings

The aim of this work is to estimate the fundamental translational frequencies and relative damping of a large number of existing buildings, performing ambient vibration measurements. The first part of the work is devoted to the comparison of the results obtained with microtremor measurements with those obtained from earthquake recordings using four different techniques: horizontal‐to‐vertical spectral ratio, standard spectral ratio, non‐parametric damping analysis (NonPaDAn) and half bandwidth method. We recorded local earthquakes on a five floors reinforced concrete building with a pair of accelerometers located on the ground and on top floor, and then collected microtremors at the same location of the accelerometers. The agreement between the results obtained with microtremors and earthquakes has encouraged extending ambient noise measurements to a large number of buildings. We analysed the data with the above‐mentioned methods to obtain the two main translational frequencies in orthogonal directions and their relative damping for 80 buildings in the urban areas of Potenza and Senigallia (Italy). The frequencies determined with different techniques are in good agreement. We do not have the same satisfactory results for the estimates of damping: the NonPaDAn provides estimates that are less dispersed and grouped around values that appear to be more realistic. Finally, we have compared the measured frequencies with other experimental results and theoretical models. Our results confirm, as reported by previous authors, that the theoretical period–height relationships overestimate the experimental data. Copyright © 2008 John Wiley & Sons, Ltd.     

Availability of seismic vulnerability index (Kg) in the assessment of building damage in Van,Eastern Turkey

The seismic vulnerability index(Kg) is a parameter that depends on the dynamic properties of soil. With this parameter, it is possible to evaluate the vulnerability of a point-based site under strong ground motion. Since it is related to the natural vibration period and amplification factor, the parameter can be calculated for both soil and structure. In this study, HVSR microtremor measurements are recorded at more than 200 points in the Van region to generate a seismic vulnerability index map. After generating the map, it is determined that the hazard potential and seismic vulnerability index is high at the sites close to Van Lake and at the densely populated city center. Damage information of the buildings investigated after the 2011 Van earthquakes(Mw = 7.1) are placed on the seismic vulnerability index map and it is realized that there may be a correlation between the damage and the seismic vulnerability index. There is a high correlation, approximately 80 percent, between the damage rate map based on the damaged building data and the K_g values. In addition, vulnerability indexes of buildings are calculated and the effect of local soil conditions and building properties on the damage levels are determined. From the results of this study and the site observations after the 2011 Van earthquakes, it is found that structural damage is not only structure-dependent but is also related to the dynamic behavior of soil layers and local soil conditions.     

Empirical formula for fundamental vibration periods of reinforced concrete buildings in Taiwan

More than 30 buildings around Taiwan have been selected to monitor the floor responses under seismic excitation. The structural array monitoring system in each building controls at most 27 channels of accelerometers distributed in several floors. Those buildings were triggered by many events during the past five years of operation. In each building, the records at the basement can be considered as the ground excitation, and the others at the upper floors are the structural responses. The frequency transfer functions of those buildings can be identified by ARX models, and then the fundamental vibration periods are estimated. The identified fundamental vibration periods using different events are compared in order to ensure the reliability of system identification. An empirical formula in predicting the fundamental vibration period is presented through the regression analysis to the identified fundamental vibration periods of 21 reinforced concrete (RC) moment‐resisting frame (MRF) buildings. It is found that the height of a building plays an important role in predicting the fundamental vibration period, compared with the length, width, and time after completion of the building. It is also found that the RC MRF buildings in Taiwan tend to be stiffer than those in the U.S. Copyright © 2000 John Wiley & Sons, Ltd.     

甘肃省河西地区高层建筑动力特性脉动观测研究

采用脉动观测方法对甘肃省河西地区的武威皇台大厦,张掖电力大厦和张掖国税大厦３栋高层建设的自振特性进行测试。在分析３栋建筑的自振周期、振型和阻尼比时,结合对当地场地特性的分析,指出了河西地区对高层建设有利的场地条件以及今后在该地区修建以建筑时应注意的若干问题。     

Nonlinear dynamic response of r.c. framed structures subjected to near-fault ground motions

The nonlinear dynamic response of reinforced concrete (r.c.) framed buildings subjected to near-fault ground motions is studied to check the effectiveness of current code provisions with reference to study cases. Three-, six- and twelve-storey r.c. plane frames, representative of symmetric framed buildings, are designed according to the European seismic code (EC8), assuming medium and high ductility classes and stratigraphic profiles A (rock) and D (soft soil) in a high-risk seismic region. The nonlinear seismic analysis is performed using a step-by-step procedure; a bilinear model idealizes the behaviour of the r.c. frame members. Artificially generated motions (matching EC8 response spectra for subsoil classes A and D) and horizontal motions (recorded on rock- and soft soil-site at near-fault areas) are considered. The results indicate that near-fault ground motions may require a special consideration in the code, in particular when designing r.c. framed structures placed on a soft soil-site; particular attention should be paid to the design of the frame members of the lower storeys.     

The importance of ambient and forced vibration measurements for the results of seismic performance assessment of buildings obtained by using a simplified non-linear procedure: case study of an old masonry building

The seismic performance assessment of existing masonry buildings involves many uncertainties, whose impact can be reduced to some extent by using non-destructive in-situ tests of such buildings, at least when destructive in-situ tests, which can provide more reliable results, cannot be performed. In this paper the extent of the potential beneficial effects achievable by calibration of a structural model of a building to its experimentally estimated vibration periods has been investigated. This was done by performing measurements of ambient and forced vibrations on an old two-storey masonry building, and by then assessing its seismic performance using a simplified nonlinear method. The results of numerical investigations revealed that the natural vibration periods of such buildings can be reproduced with sufficient accuracy, although it is possible that they will be overestimated or underestimated by analysts by up to around 40 %. This means that the accuracy of the prediction of the intermediate results of the seismic performance assessment of any particular building can be significantly increased by calibration of the structural model. Additionally, the beneficial effects of such calibration were observed even in the case of the final outcome of the nonlinear analysis, which is expressed through the near-collapse limit state capacity in terms of the peak ground acceleration.     

Influence of different sites on seismic base shear of buildings

In this paper, a statistical study based on thirty-two strong rock motions is presented for the dynamic base shear of buildings on three different sites representing stiff soil, deep cohesionless soil and soft clay conditions. A short and squatty building and a tall and slender building are selected. For each building height, frame, wall and shearwall–frame systems are considered. It is found that short and squatty frame systems have the largest base shear. As for buildings on rock, the response of buildings on stiff and deep cohesionless soil conditions depends on the peak horizontal acceleration and peak horizontal velocity of the rock motion. Furthermore, the soil–structure interaction which affects only the stiff structures is found to reduce the dynamic base shear.     

Comparison between seismic vulnerability models and experimental dynamic properties of existing buildings in France

Elastic fundamental frequency is a key-parameter of simplified seismic design and vulnerability assessment methods. Empirical relationships exist in codes to estimate this frequency but they miss experimental data to validate them accounting for national feature of building design and, above all, corresponding uncertainties. Even if resonance frequency extracted from ambient vibrations may be larger than the elastic frequency (at yield) generally used in earthquake engineering, ambient vibration recordings may provide a large set of data for statistical analysis of periods versus building characteristics relationships. We recorded ambient vibrations and estimated the fundamental frequency of about 60 buildings of various types (RC and masonry) in Grenoble City (France). These data complete the set existing yet, made of 26 RC-buildings of Grenoble (Farsi and Bard 2004) and 28 buildings in Nice (France) (Dunand 2005). Statistical analysis of these experimental data was performed for fundamental frequencies of RC shear wall structures and the results are compared with existing relationships. Only building height or number of stories has a statistical relevancy to estimate the resonance frequency but the variability associated to the proposed relationships is large. Moreover, we compared the elastic part of capacity curves of RC and masonry buildings used in the European Risk-UE method for vulnerability assessment with the experimental frequencies. The variability is also large and the curves may not be consistent with French existing buildings.     

Fundamental periods of vibration of RC buildings in Portugal from in-situ experimental and numerical techniques

Since the early nineteen seventies we have been measuring the in-situ dynamic characteristics of the different structures built in Portugal, essentially based on ambient vibration and using expedite techniques. A data-base containing not only the fundamental dynamic characteristics of those structures but also their most important geometric and constructive properties has been created with the aim of setting correlations between construction typologies and fundamental periods or frequencies, and damping characteristics, and calibrate numerical modelling of those structures. This paper presents the main results for circa 197 reinforced concrete (RC) buildings, obtaining the fundamental period as a linear function of height or number of storeys for different typologies and situations, and showing that numerical models, made for a number of illustrative cases, can reproduce with great accuracy the in-situ measurements. The main parameters having remarkable influence on the overall correlation laws are identified and a measure of uncertainty deduced. Comparisons with published formulae for other regions of the world show that we can group these laws by regions with similar expression within each group but with large variations from group to group. Discussion on how to deal with the elongation of the periods of vibration due to moderate and large amplitude motion, causing changes in the seismic behaviour and on appearance of damage, will also be briefly introduced, keeping in mind current code practices.     

An inventory of buildings in the city of Tunis and an assessment of their vulnerability

Tunis is a densely populated city. Its building stock was constructed without any seismic design code and mostly over soft soils. These facts make a seismic risk assessment of the city necessary. To prepare a large-scale vulnerability assessment of the buildings of Tunis, the following methodology was employed: (1) a collection of data based on a rapid visual screening procedure was gathered using an inventory form. These data were composed of files and information placed at the disposal of the authors by the municipality of Tunis. The data also contained information gathered by surveys carried out by engineering departments and information gathered from building owners. (2) A classification of building typologies was carried out considering construction material, structural system, age, height, function and state of maintenance. A measure of seismic vulnerability was assigned to each typology considering the first two parameters. (3) A large-scale vulnerability assessment using two methods was conducted for buildings for which few data were available. Vulnerability methods inspired by the EMS98 concepts and the Italian GNDT concepts were modified and applied to pilot-scale buildings located in the downtown zone (Habib Bourguiba Avenue) and in the old zone (Medina). The data analysis, through the application of the two methods, suggests that the vulnerability of buildings surveyed in Tunis is significant and risk mitigation efforts are necessary.     

Quantification of fundamental frequency drop for unreinforced masonry buildings from dynamic tests

The knowledge of fundamental frequency and damping ratio of structures is of uppermost importance in earthquake engineering, especially to estimate the seismic demand. However, elastic and plastic frequency drops and damping variations make their estimation complex. This study quantifies and models the relative frequency drop affecting low‐rise modern masonry buildings and discusses the damping variations based on two experimental data sets: Pseudo‐dynamic tests at ELSA laboratory in the frame of the ESECMaSE project and in situ forced vibration tests by EMPA and EPFL. The relative structural frequency drop is shown to depend mainly on shaking amplitude, whereas the damping ratio variations could not be explained by the shaking amplitude only. Therefore, the absolute frequency value depends mostly on the frequency at low amplitude level, the amplitude of shaking and the construction material. The decrease in shape does not vary significantly with increasing damage. Hence, this study makes a link between structural dynamic properties, either under ambient vibrations or under strong motions, for low‐rise modern masonry buildings. A value of 2/3 of the ambient vibration frequency is found to be relevant for the earthquake engineering assessment for this building type. However, the effect of soil–structure interaction that is shown to also affect these parameters has to be taken into account. Therefore, an analytical methodology is proposed to derive first the fixed‐base frequency before using these results. Copyright © 2010 John Wiley & Sons, Ltd.     

设计反应谱长周期区段的研究

本文利用近20年国内外大地震时获得的数字强震仪记录分析强震动的长周期分量特性,给出了不同场地上的平均加速度反应谱及其拟合曲线。结果表明,现行抗震设计规范中设计谱的特征周期和长周期谱值明显偏小。在此基础上提出了长周期设计反应谱的修正建议。文中还根据统计分析提出了不同阻尼比的反应谱修正公式。