Near‐fault ground motions,and the response of elastic and inelastic single‐degree‐of‐freedom (SDOF) systems

In order to investigate the response of structures to near‐fault seismic excitations, the ground motion input should be properly characterized and parameterized in terms of simple, yet accurate and reliable, mathematical models whose input parameters have a clear physical interpretation and scale, to the extent possible, with earthquake magnitude. Such a mathematical model for the representation of the coherent (long‐period) ground motion components has been proposed by the authors in a previous study and is being exploited in this article for the investigation of the elastic and inelastic response of the single‐degree‐of‐freedom (SDOF) system to near‐fault seismic excitations. A parametric analysis of the dynamic response of the SDOF system as a function of the input parameters of the mathematical model is performed to gain insight regarding the near‐fault ground motion characteristics that significantly affect the elastic and inelastic structural performance. A parameter of the mathematical representation of near‐fault motions, referred to as ‘pulse duration’ (T_P), emerges as a key parameter of the problem under investigation. Specifically, T_P is employed to normalize the elastic and inelastic response spectra of actual near‐fault strong ground motion records. Such normalization makes feasible the specification of design spectra and reduction factors appropriate for near‐fault ground motions. The ‘pulse duration’ (T_P) is related to an important parameter of the rupture process referred to as ‘rise time’ (τ) which is controlled by the dimension of the sub‐events that compose the mainshock. Copyright © 2004 John Wiley & Sons, Ltd.     

Wavelet‐based characterization of design ground motions

With the recent emergence of wavelet‐based procedures for stochastic analyses of linear and non‐linear structural systems subjected to earthquake ground motions, it has become necessary that seismic ground motion processes are characterized through statistical functionals of wavelet coefficients. While direct characterization in terms of earthquake and site parameters may have to wait for a few more years due to the complexity of the problem, this study attempts such characterization through commonly available Fourier and response spectra for design earthquake motions. Two approaches have been proposed for obtaining the spectrum‐compatible wavelet functionals, one for input Fourier spectrum and another for input response spectrum, such that the total number of input data points are 30–35% of those required for a time‐history analysis. The proposed methods provide for simulating ‘desired non‐stationary characteristics’ consistent with those in a recorded accelerogram. Numerical studies have been performed to illustrate the proposed approaches. Further, the wavelet functionals compatible with a USNRC spectrum in the case of 35 recorded motions of similar strong motion durations have been used to obtain the strength reduction factor spectra for elasto‐plastic oscillators and to show that about ±20% variation may be assumed from mean to 5 and 95% confidence levels due to uncertainty in the non‐stationary characteristics of the ground motion process. Copyright © 2002 John Wiley & Sons, Ltd.     

Seismic response of self‐centring hysteretic SDOF systems

The seismic response of single‐degree‐of‐freedom (SDOF) systems incorporating flag‐shaped hysteretic structural behaviour, with self‐centring capability, is investigated numerically. For a SDOF system with a given initial period and strength level, the flag‐shaped hysteretic behaviour is fully defined by a post‐yielding stiffness parameter and an energy‐dissipation parameter. A comprehensive parametric study was conducted to determine the influence of these parameters on SDOF structural response, in terms of displacement ductility, absolute acceleration and absorbed energy. This parametric study was conducted using an ensemble of 20 historical earthquake records corresponding to ordinary ground motions having a probability of exceedence of 10% in 50 years, in California. The responses of the flag‐shaped hysteretic SDOF systems are compared against the responses of similar bilinear elasto‐plastic hysteretic SDOF systems. In this study the elasto‐plastic hysteretic SDOF systems are assigned parameters representative of steel moment resisting frames (MRFs) with post‐Northridge welded beam‐to‐column connections. In turn, the flag‐shaped hysteretic SDOF systems are representative of steel MRFs with newly proposed post‐tensioned energy‐dissipating connections. Building structures with initial periods ranging from 0.1 to 2.0s and having various strength levels are considered. It is shown that a flag‐shaped hysteretic SDOF system of equal or lesser strength can always be found to match or better the response of an elasto‐plastic hysteretic SDOF system in terms of displacement ductility and without incurring any residual drift from the seismic event. Copyright © 2002 John Wiley & Sons, Ltd.     

Evaluation of the structural response under seismic actions using non‐linear static methods

The paper investigates the degree of accuracy achievable when some non‐linear static procedures based on a pushover analysis are used to evaluate the seismic performance. In order to assess the significance of different sources of errors, three types of structural systems are analysed: (i) single‐degree‐of‐freedom (SDOF) systems with different hysteretic behaviour; (ii) shear‐type multi‐degree‐of‐freedom (MDOF) systems with elastic–perfect plastic (EPP) shear force–interstorey drift relationships; (iii) a steel moment‐resisting frame with rigid joints and EPP moment–curvature relationship. In SDOF systems, the source of approximation comes only from the calibration of the demand spectrum, while in MDOF systems some further errors are introduced by the schematization with an equivalent SDOF system. The non‐linear static procedures are compared with rigorous time‐history analyses carried out by considering ten generated earthquake ground motions compatible with the Eurocode 8 elastic spectra. It was found that SDOF systems with longer periods satisfy the equal displacement approximation regardless of the hysteretic model, while hysteresis loops with smaller energy dissipated indicate lower response for shorter periods. This is the opposite of what predicted by the ATC‐40 capacity spectrum method, which underestimates and overestimates, respectively, the actual response of low‐ and high‐ductility systems. Conversely, the inelastic spectrum method proposed by Vidic, Fajfar and Fischinger leads to the most accurate results for all types of structural systems. The analyses carried out on EPP shear‐type frames point out a large concentration of the ductility demand on some storeys. However, such a concentration markedly reduces when some hardening is accounted for. Copyright © 2006 John Wiley & Sons, Ltd.     

Seismic response of linear and non‐linear asymmetric systems with non‐linear fluid viscous dampers

This investigation is concerned with the seismic response of one‐story, one‐way asymmetric linear and non‐linear systems with non‐linear fluid viscous dampers. The seismic responses are computed for a suite of 20 ground motions developed for the SAC studies and the median values examined. Reviewed first is the behaviour of single‐degree‐of‐freedom systems to harmonic and earthquake loading. The presented results for harmonic loading are used to explain a few peculiar trends—such as reduction in deformation and increase in damper force of short‐period systems with increasing damper non‐linearity—for earthquake loading. Subsequently, the seismic responses of linear and non‐linear asymmetric‐plan systems with non‐linear dampers are compared with those having equivalent linear dampers. The presented results are used to investigate the effects of damper non‐linearity and its influence on the effects of plan asymmetry. Finally, the design implications of the presented results are discussed. Copyright © 2005 John Wiley & Sons, Ltd.     

Response of SDOF system to non‐stationary earthquake excitation

Earthquake excitation is often modelled by non‐stationary random process (i.e. uniformly modulated broad‐band excitation) for analysis of structural safety subjected to seismic hazards. In this paper, the non‐stationary response of a single‐degree‐of‐freedom (SDOF) system to non‐stationary earthquake motion is investigated for different shapes of modulating functions. The evolutionary power‐spectral density function (PSDF) of the displacement of the SDOF system is obtained using the time‐varying frequency response function and the PSDF of the earthquake excitation. The close form expressions for time‐varying frequency response function are derived for different shapes of the modulating functions. In order to study the effects of the shape of the modulating function, a comparison of the non‐stationary earthquake response of the SDOF system is also made for different modulating functions having the same energy content. Copyright © 2004 John Wiley & Sons, Ltd.     

Identification of modal parameters of non‐classically damped linear structures under multi‐component earthquake loading

A method for parametric system identification of classically damped linear system in frequency domain is adopted and extended for non‐classically damped linear systems subjected up to six components of earthquake ground motions. This method is able to work in multi‐input/multi‐output (MIMO) case. The response of a two‐degree‐of‐freedom model with non‐classical damping, excited by one‐component earthquake ground motion, is simulated and used to verify the proposed system identification method in the single‐input/multi‐output case. Also, the records of a 10 storey real building during the Northridge earthquake is used to verify the proposed system identification method in the MIMO case. In this case, at first, a single‐input/multi‐output assumption is considered for the system and modal parameters are identified, then other components of earthquake ground motions are added, respectively, and the modal parameters are identified again. This procedure is repeated until all four components of earthquake ground motions which are measured at the base level of the building are included in the identification process. The results of identification of real building show that consideration of non‐classical damping and inclusion of the multi‐components effect of earthquake ground motions can improve the least‐squares match between the finite Fourier transforms of recorded and calculated acceleration responses. Copyright © 2006 John Wiley & Sons, Ltd.     

Scaling of ductility and damage‐based strength reduction factors for horizontal motions

The conventional approach of obtaining the inelastic response spectra for the aseismic design of structures involves the reduction of elastic spectra via response modification factors. A response modification factor is usually taken as a product of (i) strength factor, R_S, (ii) ductility factor, R_μ, and (iii) redundancy factor, R_R. Ductility factor, also known as strength reduction factor (SRF), is considered to primarily depend on the initial time period of the single‐degree‐of‐freedom (SDOF) oscillator and the displacement ductility demand ratio for the ground motion. This study proposes a preliminary scaling model for estimating the SRFs of horizontal ground motions in terms of earthquake magnitude, strong motion duration and predominant period of the ground motion, geological site conditions, and ductility demand ratio, with a given level of confidence. The earlier models have not considered the simultaneous dependence of the SRFs on various governing parameters. Since the ductility demand ratio is not a complete measure of the cumulative damage in the structure during the earthquake‐induced vibrations, the existing definition of the SRF is sought to be modified with the introduction of damage‐based SRF (in place of ductility‐based SRF). A parallel scaling model has been proposed for estimating the damage‐based SRFs. This model considers damage and ductility supply ratio as parameters instead of ductility demand ratio. Through a parametric study on ductility‐based SRFs, it has been shown that the hitherto assumed insensitivity of earthquake magnitude and strong motion duration may not be always justified and that the initial time period of the oscillator plays an important role in the dependence of SRF on these parameters. Further, the damage‐based SRFs are found to show similar parametric dependence as observed in the case of the ductility‐based SRFs. Copyright © 2000 John Wiley & Sons, Ltd.     

Direct estimation of the seismic demand and capacity of oscillators with multi‐linear static pushovers through IDA

SPO2IDA is introduced, a software tool that is capable of recreating the seismic behaviour of oscillators with complex quadrilinear backbones. It provides a direct connection between the static pushover (SPO) curve and the results of incremental dynamic analysis (IDA), a computer‐intensive procedure that offers thorough demand and capacity prediction capability by using a series of nonlinear dynamic analyses under a suitably scaled suite of ground motion records. To achieve this, the seismic behaviour of numerous single‐degree‐of‐freedom (SDOF) systems is investigated through IDA. The oscillators have a wide range of periods and feature pinching hysteresis with backbones ranging from simple bilinear to complex quadrilinear with an elastic, a hardening and a negative‐stiffness segment plus a final residual plateau that terminates with a drop to zero strength. An efficient method is introduced to treat the backbone shape by summarizing the analysis results into the 16, 50 and 84% fractile IDA curves, reducing them to a few shape parameters and finding simpler backbones that reproduce the IDA curves of complex ones. Thus, vast economies are realized while important intuition is gained on the role of the backbone shape to the seismic performance. The final product is SPO2IDA, an accurate, spreadsheet‐level tool for performance‐based earthquake engineering that can rapidly estimate demands and limit‐state capacities, strength reduction R‐factors and inelastic displacement ratios for any SDOF system with such a quadrilinear SPO curve. Copyright © 2006 John Wiley & Sons, Ltd.     

Non‐iterative equivalent linearization of inelastic SDOF systems for earthquakes in Japan and California

The seismic performance of existing structures can be assessed based on nonlinear static procedures, such as the Capacity Spectrum Method. This method essentially approximates peak responses of an inelastic single‐degree‐of‐freedom (SDOF) system using peak responses of an equivalent linear SDOF model. In this study, the equivalent linear models of inelastic SDOF systems are developed based on the constant strength approach, which does not require iteration for assessing the seismic performance of existing structures. To investigate the effects of earthquake type and seismic region on the equivalent linear models, four ground‐motion data sets—Japanese crustal/interface/inslab records and California crustal records—are compiled and used for nonlinear dynamic analysis. The analysis results indicate that: (1) the optimal equivalent linear model parameters (i.e. equivalent vibration period ratio and damping ratio) decrease with the natural vibration period, whereas they increase with the strength reduction factor; (2) the impacts of earthquake type and seismic region on the equivalent linear model parameters are not significant except for short vibration periods; and (3) the degradation and pinching effects affect the equivalent linear model parameters. We develop prediction equations for the optimal equivalent linear model parameters based on nonlinear least‐squares fitting, which improve and extend the current nonlinear static procedure for existing structures with degradation and pinching behavior. Copyright © 2010 John Wiley & Sons, Ltd.     

Probabilistic evaluation of soil–foundation–structure interaction effects on seismic structural response

Complex seismic behaviour of soil–foundation–structure (SFS) systems together with uncertainties in system parameters and variability in earthquake ground motions result in a significant debate over the effects of soil–foundation–structure interaction (SFSI) on structural response. The aim of this study is to evaluate the influence of foundation flexibility on the structural seismic response by considering the variability in the system and uncertainties in the ground motion characteristics through comprehensive numerical simulations. An established rheological soil‐shallow foundation–structure model with equivalent linear soil behaviour and nonlinear behaviour of the superstructure has been used. A large number of models incorporating wide range of soil, foundation and structural parameters were generated using a robust Monte‐Carlo simulation. In total, 4.08 million time‐history analyses were performed over the adopted models using an ensemble of 40 earthquake ground motions as seismic input. The results of the analyses are used to rigorously quantify the effects of foundation flexibility on the structural distortion and total displacement of the superstructure through comparisons between the responses of SFS models and corresponding fixed‐base (FB) models. The effects of predominant period of the FB system, linear vs nonlinear modelling of the superstructure, type of nonlinear model used and key system parameters are quantified in terms of different probability levels for SFSI effects to cause an increase in the structural response and the level of amplification of the response in such cases. The results clearly illustrate the risk of underestimating the structural response associated with simplified approaches in which SFSI and nonlinear effects are ignored. Copyright © 2010 John Wiley & Sons, Ltd.     

Effect of peak ground velocity on deformation demands for SDOF systems

The effect of peak ground velocity (PGV) on single‐degree‐of‐freedom (SDOF) deformation demands and for certain ground‐motion features is described by using a total of 60 soil site records with source‐to‐site distances less than 23 km and moment magnitudes between 5.5 and 7.6. The observations based on these records indicate that PGV correlates well with the earthquake magnitude and provides useful information about the ground‐motion frequency content and strong‐motion duration that can play a role on the seismic demand of structures. The statistical results computed from non‐linear response history analyses of different hysteretic models highlight that PGV correlates better with the deformation demands with respect to other ground motion intensity measures. The choice of PGV as ground motion intensity decreases the dispersion due to record‐to‐record variability of SDOF deformation demands, particularly in the short period range. The central tendencies of deformation demands are sensitive to PGV and they may vary considerably as a function of the hysteretic model and structural period. The results provided in this study suggest a consideration of PGV as a stable candidate for ground motion intensity measure in simplified seismic assessment methods that are used to estimate structural performance for earthquake hazard analysis. Copyright © 2005 John Wiley & Sons, Ltd.     

Identification of critical ground motions for seismic performance assessment of structures

A method is established to identify critical earthquake ground motions that are to be used in physical testing or subsequent advanced computational studies to enable seismic performance to be assessed. The ground motion identification procedure consists of: choosing a suitable suite of ground motions and an appropriate intensity measure; selecting a computational tool and modelling the structure accordingly; performing Incremental Dynamic Analysis on a non‐linear model of the structure; interpreting these results into 50th (median) and 90th percentile performance bounds; and identifying the critical ground motions that are close to these defining probabilistic curves at ground motion intensities corresponding to the design basis earthquake and the maximum considered earthquake. An illustrative example of the procedure is given for a reinforced concrete highway bridge pier designed to New Zealand specifications. Pseudodynamic tests and finite element based time history analyses are performed on the pier using three earthquake ground motions identified as: (i) a Design Basis Earthquake (10% probability in 50 years) with 90 percent confidence of non‐exceedance; (ii) a Maximum Considered Event (2% probability in 50 years) representing a median response; and (iii) a Maximum Considered Event representing 90 percent confidence of non‐exceedance. Copyright © 2006 John Wiley & Sons, Ltd.     

Ground motion characteristics of the Chi‐Chi earthquake of 21 September 1999

The purpose of this paper is to investigate the ground motion characteristics of the Chi‐Chi earthquake (21 September 1999) as well as the interpretation of structural damage due to this earthquake. Over 300 strong motion records were collected from the strong motion network of Taiwan for this earthquake. A lot of near‐field ground motion data were collected. They provide valuable information on the study of ground motion characteristics of pulse‐like near‐field ground motions as well as fault displacement. This study includes: attenuation of ground motion both in PGA and spectral amplitude, principal direction, elastic and inelastic response analysis of a SDOF system subjected to near‐field ground motion collected from this event. The distribution of spectral acceleration and spectral velocity along the Chelungpu fault is discussed. Based on the mode decomposition method the intrinsic mode function of ground acceleration of this earthquake is examined. A long‐period wave with large amplitude was observed in most of the near‐source ground acceleration. The seismic demand from the recorded near‐field ground motion is also investigated with an evaluation of seismic design criteria of Taiwan Building Code. Copyright © 2000 John Wiley & Sons, Ltd.     

近断层地震动破裂向前方向性与滑冲效应对隔震建筑结构抗震性能的影响

选择台湾集集地震和美国北岭地震的近断层地震动记录作为输入,考察了近断层地震动破裂向前方向性与滑冲效应引起的两种不同速度脉冲运动对单自由度体系和长周期橡胶支座隔震建筑结构抗震性能的影响.反应谱分析表明,破裂向前方向性与滑冲效应对工程结构地震响应的影响是随结构周期变化的.在中短周期段,含破裂向前方向性效应地震动的谱加速度值大于含滑冲效应地震动的谱加速度值;而在长周期段,含滑冲效应地震动的谱加速度大于含破裂向前方向性效应的谱加速度值.并且,与无脉冲地震动作用相比,含破裂向前方向性与滑冲效应脉冲的近断层地震动作用下隔震建筑的地震响应显著增大.滑冲效应引起的速度脉冲使隔震建筑底部的层间变形和楼层剪力明显增大,这意味着滑冲效应脉冲比向前方向性效应脉冲对长周期建筑结构的破坏更具危害性.     

Earthquake response analysis of the Hualien soil–structure interaction system based on updated soil properties using forced vibration test data

This paper presents results of the earthquake response analysis on a large‐scale seismic test (LSST) structure which was built at Hualien in Taiwan for an international cooperative research project. The analysis is carried out using a computer program which has been developed based on axisymmetric finite element method incorporating dynamic infinite elements for far‐field soil region and a substructured wave input technique. The non‐linear behaviour of the soil medium is taken into account using an iterative equivalent linearization procedure. Two sets of the soil and structural properties, namely the unified and the FVT‐correlated models, are utilized as the initial linear values. The unified model was provided by a group of experts in charge of the geotechnical experiments, and the correlated model was obtained through a system identification procedure using the forced vibration test (FVT) results by the present authors. Three components of ground accelerations are artificially generated through an averaging process of the Fourier amplitude spectra of the ground accelerations measured near the test structure, and they are used as the control input motions for the earthquake analysis. It has been found that the earthquake responses predicted using the generated control motions and with the FVT‐correlated model as the initial linear properties in the equivalent linearization procedure compare very well with the observed responses. Copyright © 2001 John Wiley & Sons, Ltd.     

Inelastic spectra for infilled reinforced concrete frames

In two companion papers a simplified non‐linear analysis procedure for infilled reinforced concrete frames is introduced. In this paper a simple relation between strength reduction factor, ductility and period (R–µ–T relation) is presented. It is intended to be used for the determination of inelastic displacement ratios and of inelastic spectra in conjunction with idealized elastic spectra. The R–µ–T relation was developed from results of an extensive parametric study employing a SDOF mathematical model composed of structural elements representing the frame and infill. The structural parameters, used in the proposed R–µ–T relation, in addition to the parameters used in a usual (e.g. elasto‐plastic) system, are ductility at the beginning of strength degradation, and the reduction of strength after the failure of the infills. Formulae depend also on the corner periods of the elastic spectrum. The proposed equations were validated by comparing results in terms of the reduction factors, inelastic displacement ratios, and inelastic spectra in the acceleration–displacement format, with those obtained by non‐linear dynamic analyses for three sets of recorded and semi‐artificial ground motions. A new approach was used for generating semi‐artificial ground motions compatible with the target spectrum. This approach preserves the basic characteristics of individual ground motions, whereas the mean spectrum of the whole ground motion set fits the target spectrum excellently. In the parametric study, the R–µ–T relation was determined by assuming a constant reduction factor, while the corresponding ductility was calculated for different ground motions. The mean values proved to be noticeably different from the mean values determined based on a constant ductility approach, while the median values determined by the different procedures were between the two means. The approach employed in the study yields a R–µ–T relation which is conservative both for design and performance assessment (compared with a relation based on median values). Copyright © 2004 John Wiley & Sons, Ltd.     

Envelope‐based pushover analysis procedure for the approximate seismic response analysis of buildings

An envelope‐based pushover analysis procedure is presented that assumes that the seismic demand for each response parameter is controlled by a predominant system failure mode that may vary according to the ground motion. To be able to simulate the most important system failure modes, several pushover analyses need to be performed, as in a modal pushover analysis procedure, whereas the total seismic demand is determined by enveloping the results associated with each pushover analysis. The demand for the most common system failure mode resulting from the ‘first‐mode’ pushover analysis is obtained by response history analysis for the equivalent ‘modal‐based’ SDOF model, whereas demand for other failure modes is based on the ‘failure‐based’ SDOF models. This makes the envelope‐based pushover analysis procedure equivalent to the N2 method provided that it involves only ‘first‐mode’ pushover analysis and response history analysis of the corresponding ‘modal‐based’ SDOF model. It is shown that the accuracy of the approximate 16th, 50th and 84th percentile response expressed in terms of IDA curves does not decrease with the height of the building or with the intensity of ground motion. This is because the estimates of the roof displacement and the maximum storey drift due to individual ground motions were predicted with a sufficient degree of accuracy for almost all the ground motions from the analysed sets. Copyright © 2013 John Wiley & Sons, Ltd.     

A ground motion selection procedure for enforcing hazard consistency and estimating seismic demand hazard curves

This paper develops a procedure to select unscaled ground motions for estimating seismic demand hazard curves (SDHCs) in performance‐based earthquake engineering. Currently, SDHCs are estimated from a probabilistic seismic demand analysis, where several ensembles of ground motions are selected and scaled to a user‐specified scalar conditioning intensity measure (IM). In contrast, the procedure developed herein provides a way to select a single ensemble of unscaled ground motions for estimating the SDHC. In the context of unscaled motions, the proposed procedure requires three inputs: (i) database of unscaled ground motions, (ii) I M , the vector of IMs for selecting ground motions, and (iii) sample size, n; in the context of scaled motions, two additional inputs are needed: (i) a maximum acceptable scale factor, SF_max, and (ii) a target fraction of scaled ground motions, γ. Using a recently developed approach for evaluating ground motion selection and modification procedures, the proposed procedure is evaluated for a variety of inputs and is demonstrated to provide accurate estimates of the SDHC when the vector of IMs chosen to select ground motions is sufficient for the response quantity of interest. Copyright © 2015 John Wiley & Sons, Ltd.     

Evaluation of damping reduction factors for estimating elastic response of structures with high damping

The damping reduction factors are used in a few building codes in order to estimate the elastic response spectrum with high damping ratios from its 5%‐damped counterpart. At present, much research regarding this factor has been published. The purpose of this paper is to evaluate the accuracy of five different models of damping reduction factors. In addition, the damping reduction factors adopted in the recent U.S.A. seismic codes are also evaluated. Statistical studies are carried out according to a total of 216 earthquake ground motions recorded on firm sites in California. Considered here are elastic single‐degree‐of‐freedom (SDOF) systems with natural vibrating periods between 0.1 and 6.0 s. Mean ratios and dispersion of approximate to exact maximum elastic displacement demands corresponding to various damping reduction factors are computed as functions of the natural vibrating period and the viscous damping ratio. Copyright © 2005 John Wiley & Sons, Ltd.