Bias assessment in Incremental Dynamic Analysis due to record scaling

Incremental Dynamic Analysis (IDA) involves a series of nonlinear response history analyses with a suite of incrementally scaled ground motion records. Although IDA is perhaps the most comprehensive seismic performance assessment method, it receives criticism because several ground motion records are scaled up until the structure collapses. The scaling practice often results to unrealistic multipliers, thus modifying the amplitude of the ground motion and introducing bias on the structural performance estimation. Record scaling is a common practice in earthquake engineering due to the lack of natural records corresponding to large magnitudes and/or small distances from the fault rupture location. In this work we use a large number of ground motion records to compare the predictions of IDA with that of unscaled ground motions and we propose a new methodology in order to quantify the bias introduced in IDA. Apart from natural records, we have conducted broadband ground motion simulations for rupture scenarios of weak, medium and large magnitude events in order to expand our record database. The investigation is performed on a series of inelastic single-degree-of-freedom systems and on two multistory steel moment frame buildings. The results pinpoint both qualitatively and quantitatively, for the full range of limit-states, the bias that IDA introduces on the structural performance estimation.     

On selection and scaling of ground motions for analysis of seismically isolated structures

A broader consensus on the number of ground motions to be used and the method of scaling to be adopted for nonlinear response history analysis (RHA) of structures is yet to be reached. Therefore, in this study, the effects of selection and scaling of ground motions on the response of seismically isolated structures, which are routinely designed using nonlinear RHA, are investigated. For this purpose, isolation systems with a range of properties subjected to bidirectional excitation are considered. Benchmark response of the isolation systems is established using large sets of unscaled ground motions systematically categorized into pulse-like, non-pulse-like, and mixed set of motions. Different subsets of seven to 14 ground motions are selected from these large sets using (a) random selection and (b) selection based on the best match of the shape of the response spectrum of ground motions to the target spectrum. Consequences of weighted scaling (also commonly referred to as amplitude scaling or linear scaling) as well as spectral matching are investigated. The ground motion selection and scaling procedures are evaluated from the viewpoint of their accuracy, efficiency, and consistency in predicting the benchmark response. It is confirmed that seven time histories are sufficient for a reliable prediction of isolation system displacement demands, for all ground motion subsets, selection and scaling procedures, and isolation systems considered. If ground motions are selected based on their best match to the shape of the target response spectrum (which should be preferred over randomly selected motions), weighted scaling should be used if pulse-like motions are considered, either of weighted scaling or spectral matching can be used if non-pulse-like motions are considered, and an average of responses from weighted-scaled and spectrum-matched ground motions should be used for a mixed set of motions. On the other hand, the importance of randomly selected motions in representing inherent variability of response is recognized and it is found that weighted scaling is more appropriate for such motions.     

The effect of amplitude scaling limits on conditional spectrum-based ground motion selection

Amplitude scaling is commonly used to select ground motions matching a target response spectrum. In this paper, the effect of scaling limits on ground motion selection, based on the conditional spectrum framework, is investigated. Target spectra are computed for four probabilistic seismic hazard cases in Western United States, and 16 ground motion suites are selected using different scaling limits (ie, 2, 5, 10, and 15). Comparison of spectral acceleration distributions of the selected ground motion suites demonstrates that the use of a scaling limit of 2 yields a relatively poor representation of the target spectra, because of the small limit leading to an insufficient number of available ground motions. It is also shown that increasing scaling limit results in selected ground motions with generally increased distributions of Arias intensity and significant duration Ds_5-75, implying that scaling limit consideration can significantly influence the cumulative and duration characteristics of selected ground motions. The ground motion suites selected are then used as input for slope displacement and structural dynamic analyses. Comparative results demonstrate that the consideration of scaling limits in ground motion selection has a notable influence on the distribution of the engineering demand parameters calculated (ie, slope displacement and interstory drift ratio). Finally, based on extensive analyses, a scaling limit range of 3 to 5 is recommended for general use when selecting ground motion records from the NGA-West2 database.     

Ground motion scaling methods for different site conditions and structure characteristics

Non‐linear dynamic time‐history analyses conducted as part of a performance‐based seismic design approach often require that the ground motion records are scaled to a specified level of seismic intensity. Recent research has demonstrated that certain ground motion scaling methods can introduce a large scatter in the estimated seismic demands. The resulting demand estimates may be biased, leading to designs with significant uncertainty and unknown margins of safety, unless a relatively large ensemble of ground motion records is used. This paper investigates the effectiveness of seven ground motion scaling methods in reducing the scatter in estimated peak lateral displacement demands. Non‐linear single‐degree‐of‐freedom systems and non‐linear multi‐degree‐of‐freedom systems are considered with different site conditions (site soil profile and epicentral distance) and structural characteristics (yield strength, period, and hysteretic behavior). It is shown that scaling methods that work well for ground motions representative of stiff soil and far‐field conditions lose their effectiveness for soft soil and near‐field conditions for a wide range of structural characteristics. Copyright © 2003 John Wiley & Sons, Ltd.     

Numbers of scaled and matched accelerograms required for inelastic dynamic analyses

Selecting, scaling and matching accelerograms are critically important to engineering design and assessment, enabling structural response to be determined with greater confidence and through fewer analyses than if unscaled accelerograms are employed. This paper considers the response of an 8‐storey multiple‐degree‐of‐freedom reinforced concrete structure to accelerograms selected, linearly scaled or spectrally matched using five different techniques. The first method consists of selecting real records on the basis of seismological characteristics, while the remaining methods make an initial selection on the basis of magnitude and spectral shape before (1) scaling to the target spectral acceleration at the initial period; (2) scaling to the target spectrum over a range of periods; (3) using wavelet adjustments to match the target spectrum and (4) using wavelet adjustments to match multiple target spectra for multiple damping ratios. The analyses indicate that the number of records required to obtain a stable estimate of the response decreases drastically as one moves through these methods. The exact number varies among damage measures and is related to the predictability of the damage measure. For measures such as peak roof and inter‐storey drift, member end rotation and the Park and Ang damage index, as few as one or two records are required to estimate the response to within ±5% (for a 64% confidence level) if matching to multiple damping ratios is conducted. Bias checks are made using predictive equations of the expected response derived from the results of 1656 nonlinear time‐domain analyses of the structure under the action of unscaled accelerograms. Copyright © 2008 John Wiley & Sons, Ltd.     

Ductility‐dependent intensity measure that accounts for ground‐motion spectral shape and duration

The calculated nonlinear structural responses of a building can vary greatly, even if recorded ground motions are scaled to the same spectral acceleration at a building's fundamental period. To reduce the variation in structural response at a particular ground‐motion intensity, this paper proposes an intensity measure (IM_comb) that accounts for the combined effects of spectral acceleration, ground‐motion duration, and response spectrum shape. The intensity measure includes a new measure of spectral shape that integrates the spectrum over a period range that depends on the structure's ductility. The new IM is efficient, sufficient, scalable, transparent, and versatile. These features make it suitable for evaluating the intensities of measured and simulated ground motions. The efficiency and sufficiency of the new IM is demonstrated for the following: (i) elastic‐perfectly plastic single‐degree‐of‐freedom (SDOF) oscillators with a variety of ductility demands and periods; (ii) ductile and brittle deteriorating SDOF systems with a variety of periods; and (iii) collapse analysis for 30 previously designed frames. The efficiency is attributable to the inclusion of duration and to the ductility dependence of the spectral shape measure. For each of these systems, the transparency of the intensity measure made it possible to identify the sensitivity of structural response to the various characteristics of the ground motion. Spectral shape affected all structures, but in particular, ductile structures. Duration only affected structures with cyclic deterioration. Copyright © 2015 John Wiley & Sons, Ltd.     

Tall building performance‐based seismic design using SCEC broadband platform site‐specific ground motion simulations

The scarcity of strong ground motion records presents a challenge for making reliable performance assessments of tall buildings whose seismic design is controlled by large‐magnitude and close‐distance earthquakes. This challenge can be addressed using broadband ground‐motion simulation methods to generate records with site‐specific characteristics of large‐magnitude events. In this paper, simulated site‐specific earthquake seismograms, developed through a related project that was organized through the Southern California Earthquake Center (SCEC) Ground Motion Simulation Validation (GMSV) Technical Activity Group, are used for nonlinear response history analyses of two archetype tall buildings for sites in San Francisco, Los Angeles, and San Bernardino. The SCEC GMSV team created the seismograms using the Broadband Platform (BBP) simulations for five site‐specific earthquake scenarios. The two buildings are evaluated using nonlinear dynamic analyses under comparable record suites selected from the simulated BBP catalog and recorded motions from the NGA‐West database. The collapse risks and structural response demands (maximum story drift ratio, peak floor acceleration, and maximum story shear) under the BBP and NGA suites are compared. In general, this study finds that use of the BBP simulations resolves concerns about estimation biases in structural response analysis which are caused by ground motion scaling, unrealistic spectral shapes, and overconservative spectral variations. While there are remaining concerns that strong coherence in some kinematic fault rupture models may lead to an overestimation of velocity pulse effects in the BBP simulations, the simulations are shown to generally yield realistic pulse‐like features of near‐fault ground motion records.     

A procedure on ground motion selection and scaling for nonlinear response of simple structural systems

This study presents a ground-motion selection and scaling methodology that preserves the basic seismological features of the scaled records with reduced scatter in the nonlinear structural response. The methodology modifies each strong-motion recording with known fundamental seismological parameters using the estimations of ground-motion prediction equations for a given target hazard level. It provides robust estimations on target building response through scaled ground motions and calculates the dispersion about this target. This alternative procedure is not only useful for record scaling and selection but, upon its further refinement, can also be advantageous for the probabilistic methods that assess the engineering demand parameters for a given target hazard level. Case studies that compare the performance of the proposed procedure with some other record selection and scaling methods suggest its usefulness for building performance assessment and loss models. Copyright © 2012 John Wiley & Sons, Ltd.     

Inelastic displacement ratios for evaluation of structures built on soft soil sites

This paper summarizes the results of a comprehensive statistical study aimed at evaluating peak lateral inelastic displacement demands of structures with known lateral strength and stiffness built on soft soil site conditions. For that purpose, empirical information on inelastic displacement ratios which are defined as the ratio of peak lateral inelastic displacement demands to peak elastic displacement demands are investigated. Inelastic displacement ratios were computed from the response of single‐degree‐of‐freedom systems having 6 levels of relative lateral strength when subjected to 118 earthquake ground motions recorded on bay‐mud sites of the San Francisco Bay Area and on soft soil sites located in the former lake‐bed zone of Mexico City. Mean inelastic displacement ratios and their corresponding scatter are presented for both ground motion ensembles. The influence of period of vibration normalized by the predominant period of the ground motion, the level of lateral strength, earthquake magnitude, and distance to the source are evaluated and discussed. In addition, the effects of post‐yield stiffness and of stiffness and strength degradation on inelastic displacement ratios are also investigated. It is concluded that magnitude and distance to the source have negligible effects on constant‐strength inelastic displacement ratios. Results also indicate that weak and stiffness‐degrading structures in the short spectral region could experience inelastic displacement demands larger than those corresponding to non‐degrading structures. Finally, a simplified equation obtained using regression analyses aimed at estimating mean inelastic displacement ratios is proposed for assisting structural engineers in performance‐based assessment of structures built on soft soil sites. Copyright © 2006 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.     

基于分解方法的脉冲型地震动非弹性反应谱分析

本文旨在分析脉冲型地震动中不同频率的地震动分量对于原始地震动幅值及其非弹性反应谱的影响.首先以近期12次大地震的53条典型脉冲型地震动为数据基础,基于多尺度分解方法获取脉冲型地震动中的高频分量和低频分量.为与传统方法对比,本文获取了能够表征地震动脉冲特性的卓越分量及滤除卓越分量的剩余分量.然后对比分析原始地震动和4种地震动分量的幅值特征和非弹性反应谱的特性,以讨论地震动分量对原始地震动幅值参数及其非弹性反应谱的影响.最后结合简谐地震动模型和地震动分量的性质,讨论脉冲型地震动非弹性反应谱诸多特征的产生原因.分析发现,低频分量不仅是控制脉冲型地震动速度和位移幅值的主要因素,其对原始地震动的加速度幅值也具有不可忽略的影响.低频分量也是导致脉冲型地震动非弹性位移比谱偏大以及强度折减系数谱偏小的直接原因,从而造成结构在脉冲型地震动作用下需要具有更大的非弹性位移以及更高的强度需求.     

Ground motion scaling methods for linear‐elastic structures: an integrated experimental and analytical investigation

The task of selecting and scaling an appropriate set of ground motion records is one of the most important challenges facing practitioners in conducting dynamic response history analyses for seismic design and risk assessment. This paper describes an integrated experimental and analytical evaluation of selected ground motion scaling methods for linear‐elastic building frame structures. The experimental study is based on the shake table testing of small‐scale frame models with four different fundamental periods under ground motion sets that have been scaled using different methods. The test results are then analytically extended to a wider range of structural properties to assess the effectiveness of the scaling methods in reducing the dispersion and increasing the accuracy in the seismic displacement demands of linear‐elastic structures, also considering biased selection of ground motion subsets. For scaling methods that are based on a design estimate of the fundamental period of the structure, effects of possible errors in the estimated period are investigated. The results show that a significant reduction in the effectiveness of these scaling methods can occur if the fundamental period is not estimated with reasonable certainty. Copyright © 2012 John Wiley & Sons, Ltd.     

Modal pushover‐based scaling of earthquake records for nonlinear analysis of single‐story unsymmetric‐plan buildings

The modal pushover‐based scaling (MPS) procedure, currently restricted to symmetric‐plan buildings, is extended herein to unsymmetric‐plan buildings. The accuracy of the extended MPS procedure was evaluated for a large set of three‐degree‐of‐freedom unsymmetric‐plan structures with variable stiffness and strength. The structures were subjected to nonlinear response history analysis considering sets of seven records scaled according to the MPS procedure. Structural responses were compared against the benchmark values, defined as the median values of the engineering demand parameters due to 30 unscaled records. This evaluation of the MPS procedure has led to the following conclusions: (i) the MPS procedure provided accurate estimates of median engineering demand parameter values and reduced record‐to‐record variability of the responses; and (2) the MPS procedure is found to be much superior compared to the ASCE/SEI 7‐10 scaling procedure for three‐dimensional analysis of unsymmetric‐plan buildings. Copyright © 2013 John Wiley & Sons, Ltd.     

Influence of deterioration modelling on the seismic response of steel moment frames designed to Eurocode 8

This paper assesses the influence of cyclic and in‐cycle degradation on seismic drift demands in moment‐resisting steel frames (MRF) designed to Eurocode 8. The structural characteristics, ground motion frequency content, and level of inelasticity are the primary parameters considered. A set of single‐degree‐of‐freedom (SDOF) systems, subjected to varying levels of inelastic demands, is initially investigated followed by an extensive study on multi‐storey frames. The latter comprises a large number of incremental dynamic analyses (IDA) on 12 frames modelled with or without consideration of degradation effects. A suite of 56 far‐field ground motion records, appropriately scaled to simulate 4 levels of inelastic demand, is employed for the IDA. Characteristic results from a detailed parametric investigation show that maximum response in terms of global and inter‐storey drifts is notably affected by degradation phenomena, in addition to the earthquake frequency content and the scaled inelastic demands. Consistently, both SDOF and frame systems with fundamental periods shorter than the mean period of ground motion can experience higher lateral strength demands and seismic drifts than those of non‐degrading counterparts in the same period range. Also, degrading multi‐storey frames can exhibit distinctly different plastic mechanisms with concentration of drifts at lower levels. Importantly, degrading systems might reach a “near‐collapse” limit state at ductility demand levels comparable to or lower than the assumed design behaviour factor, a result with direct consequences on optimised design situations where over‐strength would be minimal. Finally, the implications of the findings with respect to design‐level limit states are discussed.     

Validation of the SCEC Broadband Platform simulations for tall building risk assessments considering spectral shape and duration of the ground motion

Earthquake simulation technologies are advancing to the stage of enabling realistic simulations of past earthquakes as well as characterizations of more extreme events, thus holding promise of yielding novel insights and data for earthquake engineering. With the goal of developing confidence in the engineering applications of simulated ground motions, this paper focuses on validation of simulations for response history analysis through comparative assessments of building performance obtained using sets of recorded and simulated motions. Simulated ground motions of past earthquakes, obtained through a larger validation study of the Southern California Earthquake Center Broadband Platform, are used for the case study. Two tall buildings, a 20‐story concrete frame and a 42‐story concrete core wall building, are analyzed under comparable sets of simulated and recorded motions at increasing levels of ground motion intensity, up to structural collapse, to check for statistically significant differences between the responses to simulated and recorded motions. Spectral shape and significant duration are explicitly considered when selecting ground motions. Considered demands include story drift ratios, floor accelerations, and collapse response. These comparisons not only yield similar results in most cases but also reveal instances where certain simulated ground motions can result in biased responses. The source of bias is traced to differences in correlations of spectral values in some of the stochastic ground motion simulations. When the differences in correlations are removed, simulated and recorded motions yield comparable results. This study highlights the utility of physics‐based simulations, and particularly the Southern California Earthquake Center Broadband Platform as a useful tool for engineering applications.     

Kinematic soil-structure interaction effects on maximum inelastic displacement demands of SDOF systems

This paper presents a statistical study of the kinematic soil-foundation-structure interaction effects on the maximum inelastic deformation demands of structures. Discussed here is the inelastic displacement ratio defined as the maximum inelastic displacement demands of structures subjected to foundation input motions divide by those of structures subjected to free-field ground motions. The displacement ratio is computed for a wide period range of elasto-plastic single-degree-of-freedom (SDOF) systems with various levels of lateral strength ratios and with different sizes of foundations. Seventy-two earthquake ground motions recorded on firm soil with average shear wave velocities between 180 m/s and 360 m/s are adopted. The effects of period of vibration, level of lateral yielding strength and dimension of foundations are investigated. The results show that kinematic interaction will reduce the maximum inelastic displacement demands of structures, especially for systems with short periods of vibration, and the larger the foundation size the smaller the maximum inelastic displacement becomes. In addition, the inelastic displacement ratio is nearly not affected by the strength ratio of structures for systems with periods of vibration greater than about 0.3 s and with strength ratios smaller than about 3.0. Expressions obtained from nonlinear regression analyses are also proposed for estimating the effects of kinematic soil-foundation-structure interaction from the maximum deformation demand of the inelastic system subjected to free-field ground motions.     

Structural performance assessment under near‐source pulse‐like ground motions using advanced ground motion intensity measures

This paper demonstrates the effectiveness of utilizing advanced ground motion intensity measures (IMs) to evaluate the seismic performance of a structure subject to near‐source ground motions. Ordinary records are, in addition, utilized to demonstrate the robustness of the advanced IM with respect to record selection and scaling. To perform nonlinear dynamic analyses (NDAs), ground motions need to be selected; as a result, choosing records that are not representative of the site hazard can alter the seismic performance of structures. The median collapse capacity (in terms of IM), for example, can be systematically dictated by including a few aggressive or benign pulse‐like records into the record set used for analyses. In this paper, the elastic‐based IM such as the pseudo‐spectral acceleration (S_a) or a vector of S_a and epsilon has been demonstrated to be deficient to assess the structural responses subject to pulse‐like motions. Using advanced IMs can be, however, more accurate in terms of probabilistic response prediction. Scaling earthquake records using advanced IMs (e.g. inelastic spectral displacement, S_di, and IM _1I&2E; the latter is for the significant higher‐mode contribution structures) subject to ordinary and/or pulse‐like records is efficient, sufficient, and robust relative to record selection and scaling. As a result, detailed record selection is not necessary, and records with virtually any magnitude, distance, epsilon and pulse period can be selected for NDAs. Copyright © 2008 John Wiley & Sons, Ltd.     

Correlations between Energy and Displacement Demands for Performance-Based Seismic Engineering

The development of a scientific framework for performance-based seismic engineering requires, among other steps, the evaluation of ground motion intensity measures at a site and the characterization of their relationship with suitable engineering demand parameters (EDPs) which describe the performance of a structure. In order to be able to predict the damage resulting from earthquake ground motions in a structural system, it is first necessary to properly identify ground motion parameters that are well correlated with structural response and, in turn, with damage. Since structural damage during an earthquake ground motion may be due to excessive deformation or to cumulative cyclic damage, reliable methods for estimating displacement demands on structures are needed. Even though the seismic performance is directly related to the global and local deformations of the structure, energy-based methodologies appear more helpful in concept, as they permit a rational assessment of the energy absorption and dissipation mechanisms that can be effectively accomplished to balance the energy imparted to the structure. Moreover, energy-based parameters are directly related to cycles of response of the structure and, therefore, they can implicitly capture the effect of ground motion duration, which is ignored by conventional spectral parameters. Therefore, the identification of reliable relationships between energy and displacement demands represents a fundamental issue in both the development of more reliable seismic code provisions and the evaluation of seismic vulnerability aimed at the upgrading of existing hazardous facilities. As these two aspects could become consistently integrated within a performance-based seismic design methodology, understanding how input and dissipated energy are correlated with displacement demands emerges as a decisive prerequisite. The aim of the present study is the establishment of functional relationships between input and dissipated energy (that can be considered as parameters representative of the amplitude, frequency content and duration of earthquake ground motions) and displacement-based response measures that are well correlated to structural and non-structural damage. For the purpose of quantifying the EDPs to be related to the energy measures, for comprehensive range of ground motion and structural characteristics, both simplified and more accurate numerical models will be used in this study for the estimation of local and global displacement and energy demands. Parametric linear and nonlinear time-history analyses will be performed on elastic and inelastic SDOF and MDOF systems, in order to assume information on the seismic response of a wide range of current structures. Hysteretic models typical of frame force/displacement behavior will be assumed for the local inelastic cyclic response of the systems. A wide range of vibration periods will be taken into account so as to define displacement, interstory drift and energy spectra for MDOF systems. Various scalar measures related to the deformation demand will be used in this research. These include the spectral displacements, the peak roof drift ratio, and the peak interstory drift ratio. A total of about 900 recorded ground motions covering a broad variety of condition in terms of frequency content, duration and amplitude will be used as input in the dynamic analyses. The records are obtained from 40 earthquakes and grouped as a function of magnitude of the event, source-to-site condition and site soil condition. In addition, in the data-set of records a considerable number of near-fault signals is included, in recognition of the particular significance of pulse-like time histories in causing large seismic demands to the structures.     

Inelastic displacement ratio of near‐source pulse‐like ground motions

Near‐source pulse‐like records resulting from rupture's directivity have been found to depart from so‐called ordinary ground motions in terms of both elastic and inelastic structural seismic demands. In fact, response spectra may be strong if compared with what is expected from common ground motion prediction equations. Moreover, because not all spectral ordinates are affected uniformly, a peculiar spectral shape, with an especially amplified region depending on the pulse period, may follow. Consequently, inelastic seismic demand may show trends different to records not identified as pulse‐like (i.e., ordinary). This latter aspect is addressed in the study reported in this short communication, where a relatively large dataset of identified impulsive near‐source records is used to derive an analytical‐form relationship for the inelastic displacement ratio. It is found that, similar to what was proposed in literature for soft soil sites, a double‐opposite‐bumps form is required to match the empirical data as a function of the structural period over the pulse period ratio. The relationship builds consistently on previous studies on the topic, yet displays different shape with respect to the most common equations for static structural assessment procedures. Copyright © 2012 John Wiley & Sons, Ltd.     

Scaling of response spectrum and duration for aftershocks

Aftershocks have the potential to cause collapse of a structure that has been already damaged by the preceding main shock. Seismic safety of a structure should therefore be ascertained through a damage analysis using the anticipated main shock and few larger-aftershock motions. Simulation of aftershock motions needs characterization of the seismic hazard due to aftershocks, and therefore it will be useful to develop a conditional scaling model that can predict the response spectrum of an anticipated aftershock motion consistent with the design spectrum of the main shock motion anticipated at the same station. In this study an attempt is made to develop a conditional scaling model for the pseudo spectral velocity spectrum via linear regression analysis on the aftershock and main shock recordings for the 1999 Chi–Chi earthquake. It is shown that it may be possible to obtain a simpler and approximate version of the conditional model from an unconditional model. Damage-causing potential of a ground motion also depends on its strong motion duration (SMD) and therefore a conditional scaling model is developed for SMD of the aftershock motion in several narrow frequency-bands. The model is developed for the larger-aftershock motions and it is shown that a reasonable replacement of such a model may be obtainable directly from an unconditional model. Finally, a simple weighted averaging scheme is proposed to obtain the composite SMD from the SMDs for different frequency bands by using the pseudo spectral acceleration spectrum of the motion.