Modified three‐dimensional seismic assessment method for buildings based on ambient vibration tests: extrapolation to higher shaking levels and measuring the dynamic amplification portion of natural torsion

This paper presents applications of the modified 3D‐SAM approach, a three‐dimensional seismic assessment methodology for buildings directly based on in situ experimental modal tests to calculate global seismic demands and the dynamic amplification portion of natural torsion. Considering that the building modal properties change from weak to strong motion levels, appropriate modification factors are proposed to extend the application of the method to stronger earthquakes. The proposed approach is consistent with the performance‐based seismic assessment approach, which entails the prediction of seismic displacements and drift ratios that are related to the damage condition and therefore the functionality of the building. The modified 3D‐SAM is especially practical for structures that are expected to experience slight to moderate damage levels and in particular for post‐disaster buildings that are expected to remain functional after an earthquake. In the last section of this paper, 16 low to mid‐rise irregular buildings located in Montreal, Canada, and that have been tested under ambient vibrations are analyzed with the method, and the dynamic amplification portion of natural torsion of the dataset is reported and discussed. The proposed methodology is appropriate for large‐scale assessments of existing buildings and is applicable to any seismic region of the world. Copyright © 2016 John Wiley & Sons, Ltd.     

Aftershock collapse vulnerability assessment of reinforced concrete frame structures

In a seismically active region, structures may be subjected to multiple earthquakes, due to mainshock–aftershock phenomena or other sequences, leaving no time for repair or retrofit between the events. This study quantifies the aftershock vulnerability of four modern ductile reinforced concrete (RC) framed buildings in California by conducting incremental dynamic analysis of nonlinear MDOF analytical models. Based on the nonlinear dynamic analysis results, collapse and damage fragility curves are generated for intact and damaged buildings. If the building is not severely damaged in the mainshock, its collapse capacity is unaffected in the aftershock. However, if the building is extensively damaged in the mainshock, there is a significant reduction in its collapse capacity in the aftershock. For example, if an RC frame experiences 4% or more interstory drift in the mainshock, the median capacity to resist aftershock shaking is reduced by about 40%. The study also evaluates the effectiveness of different measures of physical damage observed in the mainshock‐damaged buildings for predicting the reduction in collapse capacity of the damaged building in subsequent aftershocks. These physical damage indicators for the building are chosen such that they quantify the qualitative red tagging (unsafe for occupation) criteria employed in post‐earthquake evaluation of RC frames. The results indicated that damage indicators related to the drift experienced by the damaged building best predicted the reduced aftershock collapse capacities for these ductile structures. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Analysis of the weightiness of site effects on reinforced concrete (RC) building seismic behaviour: The Adra town example (SE Spain)

The damage distribution in Adra town (south‐eastern Spain) during the 1993 and 1994 Adra earthquakes (5.0 magnitude), that reached a maximum intensity degree of VII (European Macroseismic Scale (EMS scale)), was concentrated mainly in the south‐east zone of the town and the most relevant damage occurred in reinforced concrete (RC) buildings with four or five storeys. In order to evaluate the influence of ground condition on RC building behaviour, geological, geomorphological and geophysical surveys were carried out, and a detailed map of ground surface structure was obtained. Short‐period microtremor observations were performed in 160 sites on a 100m × 100m dimension grid and Nakamura's method was applied in order to determine a distribution map of soil predominant periods. Shorter predominant periods (0.1–0.3 s) were found in mountainous and neighbouring zones and larger periods (greater than 0.5 s) in thicker Holocene alluvial fans. A relationship T = (0.049 ± 0.001)N, where T is the natural period of swaying motion and N is the number of storeys, has been empirically obtained by using microtremor measurements at the top of 38 RC buildings (ranging from 2 to 9 storeys). 1‐D simulation of strong motion on different soil conditions and for several typical RC buildings were computed, using the acceleration record in Adra town of the 1993 earthquake. It is noteworthy that all the aforementioned results show the influence of site effects in the degree and distribution of observed building damage. Copyright © 2007 John Wiley & Sons, Ltd.     

Influence of lateral-load-resisting system on the earthquake response of structures—a system identification study

Analysis and comparison of the dynamic responses of three well instrumented (with accelerographs) high-rise buildings shaken during the 1984 Morgan Hill earthquake are presented. The buildings examined in the present work are (i) the Town Park Towers Apartment building, a 10-storey, concrete shear wall building; (ii) the Great Western Savings and Loan building, a 10-storey building with concrete frames and shear walls; and (iii) the Santa Clara County Office building, a 13-storey, moment-resistant steel frame building. The structures are located within 2 km of each other and, as may be confirmed by visual inspection of the recorded seismograms, experienced similar ground motions. One-dimensional and three-dimensional linear structural models are fitted to the observations using the modal minimization method' for structural identification, in order to determine optimal estimates of the parameters of the dominant modes of the buildings. The time-varying character of these parameters over the duration of the response is also investigated. Comparison of the recorded earthquake response of the structures reveals that the type of lateral-load-resisting system has an important effect on the dynamic behaviour of the structures because it controls the spacing of the characteristic modes on the frequency axis. The Santa Clara County Office building has closely spaced natural frequencies and exhibits strong torsional response and modal coupling. Its dynamic behaviour is contrasted with that of the Great Western Savings and Loan building which has well separated natural frequencies and exhibits small torsional response and no modal coupling. Strong modal coupling causes a beating-type phenomenon and makes earthquake response of structures different from that envisioned by codes.     

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.     

The effect of near-fault directivity on building seismic collapse risk

Forward directivity may cause large velocity pulses in ground motion time histories that are damaging to buildings at sites close to faults, potentially increasing seismic collapse risk. This study quantifies the effects of forward directivity on collapse risk through incremental dynamic analysis of building simulation models that are capable of capturing the key aspects of strength and stiffness degradation associated with structural collapse. The paper also describes a method for incorporating the effects of near-fault directivity in probabilistic assessment of seismic collapse risk. The analysis is based on a suite of RC frame models that represent both past and present building code provisions, subjected to a database of near-fault, pulse-like ground motions with varying pulse periods. Results show that the predicted collapse capacity is strongly influenced by variations in pulse period and building ductility; pulse periods that are longer than the first-mode elastic building period tend to be the most damaging. A detailed assessment of seismic collapse risk shows that the predicted probability of collapse in 50 years for modern concrete buildings at a representative near-fault site is approximately 6%, which is significantly higher than the 1% probability in the far-field region targeted by current seismic design maps in the US. Copyright © 2012 John Wiley & Sons, Ltd.     

Aftershock collapse fragility curves for non‐ductile RC buildings: a scenario‐based assessment

Recent studies have addressed the computation of fragility curves for mainshock (MS)‐damaged buildings. However, aftershock (AS) fragilities are generally conditioned on a range of potential post‐MS damage states that are simulated via static or dynamic analyses performed on an intact building. Moreover, there are very few cases where the behavior of non‐ductile reinforced concrete buildings is analyzed. This paper presents an evaluation of AS collapse fragility conditioned on various return periods of MSs, allowing for the rapid assessment of post‐earthquake safety variations based solely on the intensity of the damaging earthquake event. A refined multi‐degree‐of‐freedom model of a seven‐storey non‐ductile building, which includes brittle failure simulations and the evaluation of a system level collapse, is adopted. Aftershock fragilities are obtained by performing an incremental dynamic analysis for a number of MS–AS ground motion sequences and a variety of MS intensities. The AS fragilities show that the probability of collapse significantly increases for higher return periods for the MS. However, this result is mainly ascribable to collapses occurred during MSs. When collapse cases that occur during a MS are not considered in the assessment of AS collapse probability, a smaller shift in the fragility curves is observed as the MS intensity increases. This result is justified considering the type of model and collapse modes introduced, which strongly depend on the brittle behavior of columns failing in shear or due to axial loads. The analysis of damage that is due to MSs when varying the return period confirms this observation. Copyright © 2017 John Wiley & Sons, Ltd.     

Out‐of‐plane seismic behaviour of rocking masonry walls

The evaluation of the out‐of‐plane behaviour of unreinforced walls is one of the most debated topics in the seismic assessment of existing masonry buildings. The discontinuous nature of masonry and its interaction with the remainder of the building make the dynamic modelling of out‐of‐plane response troublesome. In this paper, the results of a shaking table laboratory campaign on a tuff masonry, natural scale, U‐shaped assemblage (façade adjacent to transverse walls) are presented. The tests, excited by scaled natural accelerograms, replicate the behaviour of external walls in existing masonry buildings, from the beginning of rocking motion to overturning. Two approaches have been developed for modelling the out‐of‐plane seismic behaviour: the discrete element method and an SDOF analytic model. Both approaches are shown to be capable of reproducing the experimental behaviour in terms of maximum rotation and time history dynamic response. Finally, test results and numerical time history simulations have been compared with the Italian seismic code assessment procedures. Copyright © 2011 John Wiley & Sons, Ltd.     

Inelastic response of RC frame buildings with seismic isolation

A comprehensive parametric study on the inelastic seismic response of seismically isolated RC frame buildings, designed for gravity loads only, is presented. Four building prototypes, with 23 m × 10 m floor plan dimensions and number of storeys ranging from 2 to 8, are considered. All the buildings present internal resistant frames in one direction only, identified as the strong direction of the building. In the orthogonal weak direction, the buildings present outer resistant frames only, with infilled masonry panels. This structural configuration is typical of many existing RC buildings, realized in Italy and other European countries in the 60s and 70s. The parametric study is based on the results of extensive nonlinear response‐time history analyses of 2‐DOF systems, using a set of seven artificial and natural seismic ground motions. In the parametric study, buildings with strength ratio (F_y/W) ranging from 0.03 to 0.15 and post‐yield stiffness ratio ranging from 0% to 6% are examined. Three different types of isolation systems are considered, that is, high damping rubber bearings, lead rubber bearings and friction pendulum bearings. The isolation systems have been designed accepting the occurrence of plastic hinges in the superstructure during the design earthquake. The nonlinear response‐time history analyses results show that structures with seismic isolation experience fewer inelastic cycles compared with fixed‐base structures. As a consequence, although limited plastic deformations can be accepted, the collapse limit state of seismically isolated structures should be based on the lateral capacity of the superstructure without significant reliance on its inherent hysteretic damping or ductility capacity. Copyright © 2012 John Wiley & Sons, Ltd.     

基于泸定6.8级地震某二层混凝土框架结构损伤分析

2022年9月5日四川甘孜州泸定县发生6.8级地震,相关台站记录到水平向地震动峰值加速度达到891cm/s²,竖直向地震动峰值加速度为175cm/s²,地震造成严重人员伤亡和建筑物倒塌。为进一步了解本次地震对建筑物破坏作用,采用大型通用有限元软件SAUSG2022,对震中某二层钢筋混凝土框架结构进行弹塑性动力时程分析。结果表明,在泸定地震动作用下,该建筑物损伤严重,有倒塌风险,损伤部位与损伤程度与现场情况基本相符。而采用隔震技术后,分析结果表明在泸定地震动作用下建筑物损伤轻微。     

Effects of infill walls and floor diaphragms on the dynamic characteristics of a narrow‐rectangle building

Most buildings in Singapore are lightly reinforced concrete structures, which are mainly designed for gravity loading only, because Singapore is an island country located in a low‐to‐moderate seismic region. The dynamic properties of a typical high‐rise residential building with a long, narrow rectangular floor plan are studied using both experimental and numerical methods. The effects of the brick infill walls and the flexible diaphragms on the dynamic characteristics of the building are discussed in detail. The results from the ambient vibration tests are correlated with the numerical results of three different finite element models with different levels of sophistication. They include a bare frame model, a frame model with brick infill walls, and a frame model with both brick infill walls and flexible diaphragms. The dynamic properties of the third model match very well with the measured results in terms of both the natural frequencies and the mode shapes. The correlation results demonstrate the respective effects of the brick infill walls and the flexible diaphragms on the dynamic characteristics of the narrow‐rectangle building structure. Copyright © 2006 John Wiley & Sons, Ltd.     

Description and analysis of building damage due to Pyrgos, Greece earthquake

On March 1993 an earthquake of magnitude M_s = 5·5 shook Pyrgos, a town in Western Peloponnissos, one of the most seismic prone areas in Greece. The damage induced to modern reinforced concrete buildings was rather light in contrast to the damage induced to historic and traditional buildings of adobe, stone or brick masonry which was severe. In order to study the causes of structural damage, detailed data are collected from a rather large statistical sample of 1023 masonry buildings and 22 reinforced concrete framed buildings with visible damage. For each building the number of storeys, the material of construction, as well as the type and the degree of damage are recorded. In addition, consideration is given to the site of the building within the town and the corresponding soil conditions. For reinforced concrete buildings, damage occured mostly in areas with relatively high estimated spectral accelerations and fundamental soil periods of vibration close to those of the buildings. Nevertheless, further analysis is required to explain the selective damage of a very small number of buildings. For masonry houses, the effect of soil conditions is more systematic. Moreover, the effects of the number of storeys as well as the age and material of construction appear to be dominant.     

Seismic loss estimation of non‐ductile reinforced concrete buildings

Non‐ductile reinforced concrete buildings represent a prevalent construction type found in many parts of the world. Due to the seismic vulnerability of such buildings, in areas of high seismic activity non‐ductile reinforced concrete buildings pose a significant threat to the safety of the occupants and damage to such structures can result in large financial losses. This paper introduces advanced analytical models that can be used to simulate the nonlinear dynamic response of these structural systems, including collapse. The state‐of‐the‐art loss simulation procedure developed for new buildings is extended to estimate the expected losses of existing non‐ductile concrete buildings considering their vulnerability to collapse. Three criteria for collapse, namely first component failure, side‐sway collapse, and gravity‐load collapse, are considered in determining the probability of collapse and the assessment of financial losses. A detailed example is presented using a seven‐story non‐ductile reinforced concrete frame building located in the Los Angeles, California. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Determination of the seismic performance factors for post‐tensioned rocking timber wall systems

Post‐tensioned technologies for concrete seismic resistant buildings were first developed in the 1990s during the PREcast Seismic Structural Systems program. Among different solutions, the hybrid system proved to be the most resilient solution providing a combination of re‐centering and energy dissipative contributions respectively by using post‐tensioned tendons and mild steel reinforcement. The system, while providing significant strength and energy dissipation, reduces structural element damage and limits post‐earthquake residual displacements. More recently, the technology was extended to laminated veneer lumber (LVL) structural members, and extensive experimental and numerical work was carried out and allowed the development of reliable analytical and numerical models as well as design guidelines. On the basis of the experimental and numerical outcomes, this paper presents the evaluation of the seismic performance factors for post‐tensioned rocking LVL walls using the FEMA P‐695 procedure. Several archetype buildings were designed considering different parameters such as the building and story height, the type of seismic resistant system, the magnitude of gravity loads and the seismic design category. Lumped plasticity models were developed for each index archetype to simulate the behavioral aspects and collapse mechanisms. Non‐linear quasi‐static analyses were carried out to evaluate the system over‐strength factor; moreover, non‐linear time history analyses were performed using the incremental dynamic analysis concept to assess the collapse of each building. From the results of quasi‐static and dynamic analyses the response modification factor, R, system over‐strength factor, Ω₀, and deflection amplification factor, C_d, values of, respectively, 7, 3.5 and 7.5 are recommended. Copyright © 2016 John Wiley & Sons, Ltd.     

Improved performance‐based seismic assessment of buildings by utilizing Bayesian statistics

This paper addresses two important issues of concern to practicing engineers and researchers alike in application of performance‐based seismic assessment (PBSA) methodology on buildings: (i) the number of ground motion records required to exercise PBSA—current practice (FEMA P‐58‐1) requires eleven or more pairs of motions for this purpose, and (ii) the time and effort associated with performing the number of nonlinear response history analyses required to exercise PBSA. We present a method for exercising of PBSA that employs classical linear modal analysis to develop a first estimate (i.e., a priori) of probability distribution of loss, followed by utilizing Bayesian statistics to update this estimate using estimates of loss obtained by utilizing a small number of nonlinear response history analyses of a detailed model of the building (i.e., posterior). The proposed technique is used to assess the distribution of monetary loss of two case studies, a 4‐story reinforced concrete moment‐resisting frame building and a 20‐story steel moment‐resisting frame building, both located in Los Angeles, for a ground motion hazard with 10% probability of exceedance in 50 years. The efficiency of the proposed PBSA method is demonstrated by showing the similarity between the distribution of monetary loss at each story of case study buildings obtained from the traditional/sophisticated PBSA methodology and the proposed PBSA method in this study. Copyright © 2015 John Wiley & Sons, Ltd.     

Parameter identification of framed structures using an improved finite element model‐updating method—Part II: application to experimental data

In this study, we determine an updated finite element model of a reinforced concrete building—which was damaged from shaking during 1994 Northridge earthquake—using forced‐vibration test data and a novel model‐updating technique. Developed and verified in the companion paper (viz. BVLSrc, Earthquake Eng. Struct. Dyn. 2006; this issue), this iterative technique incorporates novel sensitivity‐based relative constraints to avoid ill conditioning that results from spatial incompleteness of measured data. We used frequency response functions and natural frequencies as input for the model‐updating problem. These data were extracted from measurements obtained during a white‐noise excitation applied at the roof of the building using a linear inertial shaker. Flexural stiffness values of properly grouped structural members, modal damping ratios, and translational and rotational mass values were chosen as the updating parameters, so that the converged results had direct physical interpretations, and thus, comparisons with common parameters used in seismic design and evaluation of buildings could be made. We investigated the veracity of the updated finite element model by comparing the predicted and measured dynamic responses under a second, and different type of forced (sine‐sweep) vibration, test. These results indicate that the updated model replicates the dynamic behaviour of the building reasonably well. Furthermore, the updated stiffness factors appear to be well correlated with the observed building damage patterns (i.e. their location and severity). Copyright © 2006 John Wiley & Sons, Ltd.     

Seismic damage estimation for low- and mid-rise buildings in japan

While much effort has been spent on analysis of individual structures, building class seismic damage estimators, of value in disaster planning, code-writing, city planning, national hazards policy formulation, etc., have been little investigated. Based largely on data from Sendai City, Japan in the 12 June, 1978 Miyagiken-oki earthquake (M_L = 7.4), estimators of seismic damage for low- and mid-rise buildings in urban Japan have been determined. For low-rise buildings, based on damage to over 60,000 buildings, damage ratios for onset of damage and collapse and for cost of damage are found to correlate best with response spectra at 0.75 s. Using published test data and average building properties, a seismic damage model explains the low-rise building behaviour and permits examination of the effect of structural changes on the estimated damage. For mid-rise buildings, damage states (0: none, 4: total) are determined as a function of maximum storey displacement, based on published natural period determinations (pre- and post-earthquake) for 189 mid-rise buildings in Sendai. The effects of structural changes on expected damage can also be estimated. With these two building class damage estimators, a large part of future seismic damage to urban Japan can be estimated, as well as the effects of various mitigation measures.     

Use of collision shear walls to minimize seismic separation and to protect adjacent buildings from collapse due to earthquake‐induced pounding

The use of collision shear walls (bumper‐type), acting transversely to the side subject to pounding, as a measure to minimize damage of reinforced concrete buildings in contact, is investigated using 5‐story building models. The buildings were designed according to the Greek anti‐seismic and reinforced concrete design codes. Owing to story height differences potential pounding in case of an earthquake will occur between floor slabs, a case specifically chosen because this is when pounding can turn out to be catastrophic. The investigation is carried out using nonlinear dynamic analyses for a real earthquake motion and also a simplified solution for a triangular dynamic force of short duration, comparable to the forces caused by pounding. For such analyses, nonlinear, prismatic beam–column elements are used and the effects of pounding are expressed in terms of changes in rotational ductility factors of the building elements. The local effects of pounding on the collision shear walls are investigated using a detailed nonlinear finite element model of the shear walls and results are expressed in terms of induced stresses. It is found that pounding will cause instantaneous acceleration pulses in the colliding buildings and will somewhat increase ductility demands in the members of the top floor, but all within tolerable limits. At the same time the collision walls will suffer repairable local damage at the points of contact, but will effectively protect both buildings from collapse, which could occur if columns were in the place of the walls. Copyright © 2008 John Wiley & Sons, Ltd.