A stochastic model and synthesis for near‐fault impulsive ground motions

The orientations of ground motions are paramount when the pulse‐like motions and their unfavorable seismic responses are considered. This paper addresses the stochastic modeling and synthesizing of near‐fault impulsive ground motions with forward directivity effect taking the orientation of the strongest pulses into account. First, a statistical parametric analysis of velocity time histories in the orientation of the strongest pulse with a specified magnitude and various fault distances is performed. A new stochastic model is established consisting of a velocity pulse model with random parameters and a stochastic approach to synthesize high‐frequency velocity time history. The high‐frequency velocity history is achieved by integrating a stochastic high‐frequency accelerogram, which is generated via the modified K‐T spectrum of residual acceleration histories and then modulated by the specific envelope function. Next, the associated parameters of pulse model, envelope function, and power spectral density are estimated by the least‐square fitting. Some chosen parameters in the stochastic model of near‐fault motions based on correlation analysis are regarded as random variables, which are validated to follow the normal or lognormal distribution. Moreover, the number theoretical method is suggested to select efficiently representative points, for generating artificial near‐fault impulsive ground motions with the feature of the strongest pulse, which can be used to the seismic response and reliability analysis of critical structures conveniently. Finally, the simulated ground motions demonstrate that the synthetic ground motions generated by the proposed stochastic model can represent the impulsive characteristic of near‐fault ground motions. Copyright © 2014 John Wiley & Sons, Ltd.     

Empirical attenuation relationship for Arias Intensity

Arias Intensity is a ground motion parameter that captures the potential destructiveness of an earthquake as the integral of the square of the acceleration–time history. It correlates well with several commonly used demand measures of structural performance, liquefaction, and seismic slope stability. A new empirical relationship is developed to estimate Arias Intensity as a function of magnitude, distance, fault mechanism, and site category based on 1208 recorded ground motion data from 75 earthquakes in active plate‐margins. Its functional form is derived from the point‐source model, and the coefficients are determined through non‐linear regression analyses using a random‐effects model. The results show that for large magnitude earthquakes (M > 7) Arias Intensity was significantly overestimated by previous relationships while it was underestimated for smaller magnitude events (M ? 6). The average horizontal Arias Intensity is not significantly affected by forward rupture directivity in the near‐fault region. The aleatory variability associated with Arias Intensity is larger than that of most other ground motion parameters such as spectral acceleration. However, it may be useful in assessing the potential seismic performance of stiff engineering systems whose response is dominated by the short‐period characteristics of ground motions. Copyright © 2003 John Wiley & Sons, Ltd.     

Simulation of orthogonal horizontal components of near‐fault ground motion for specified earthquake source and site characteristics

A procedure to generate horizontal pairs of synthetic near‐fault ground motion components for specified earthquake source and site characteristics is presented. Some near‐fault ground motions contain a forward directivity pulse; others do not, even when the conditions for such a pulse are favorable. The proposed procedure generates pulse‐like and non‐pulse‐like motions in appropriate proportions. We use our recent stochastic models of pulse‐like and non‐pulse‐like near‐fault ground motions that are formulated in terms of physically meaningful parameters. The parameters of these models are fitted to databases of recorded pulse‐like and non‐pulse‐like motions. Using these empirical “observations,” predictive relations are developed for the model parameters in terms of the earthquake source and site characteristics (type of faulting, earthquake magnitude, depth to top of rupture plane, source‐to‐site distance, site characteristics, and directivity parameters). The correlation coefficients between the model parameters are also estimated. For a given earthquake scenario, the probability of occurrence of a directivity pulse is first computed; pulse‐like and non‐pulse‐like motions are then simulated according to the predicted proportions using the empirical predictive models. The resulting time series are realistic and reproduce important features of recorded near‐fault ground motions, including the natural variability. Moreover, the statistics of their elastic response spectra agree with those of the NGA‐West2 dataset, with the additional feature of distinguishing between pulse‐like and non‐pulse‐like cases and between forward and backward directivity scenarios. The synthetic motions can be used in addition to or in place of recorded motions in performance‐based earthquake engineering, particularly when recorded motions are scarce.     

Parametric investigation of the stability of classical columns under harmonic and earthquake excitations

The seismic response of free‐standing classical columns is analysed numerically through implementation of the distinct element method. Typical sections of two ancient temples are modelled and studied parametrically, in order to identify the main factors affecting the stability and to improve our understanding of the earthquake behaviour of such structures. The models were first subjected to harmonic base motions. The analysis showed that, for frequencies usually encountered in earthquake motions, intact multi‐drum free‐standing columns can withstand large amplitude harmonic excitations without collapse. The dynamic resistance decreases rapidly as the period of the harmonic excitation increases. Imperfections, such as initial tilt of the column or loss of contact area due to edge damage, also reduce the stability of the system significantly. The effects of such imperfections could be additive and the cumulative effect of many imperfections may render deteriorating abandoned monuments vulnerable to earthquakes. The response of more complete sections of the temple, such as two columns coupled with an architrave, did not deviate systematically from that of the single multi‐drum column or indeed of the equivalent single block. Therefore, a much simpler single block analysis can be used to size‐up the seismic threat to the monument. The model of the column of the Temple of Apollo at Bassae was also tested under recorded earthquake motions by scaling‐up the acceleration amplitude progressively until collapse of the column. It was found that the columns are particularly vulnerable to long‐period impulsive earthquake motions. A comparison of the instability thresholds associated with harmonic excitations and earthquake motions throws more light onto the dynamic response: it appears that around three cycles of monochromatic excitation at the predominant period of the expected earthquake motions lead to a gross prediction of the stability of a classical column during an earthquake. Copyright © 2000 John Wiley & Sons, Ltd.     

An improved energy‐based approach for selecting pulse‐like ground motions

This study proposes an improved energy‐based approach for quantitative classification of velocity‐pulse‐like ground motions. The pulse amplitude is determined, in its value and in time location, by the amplitude of the half‐cycle pulse having the largest seismic energy. After conducting statistical analyses, a newly‐determined threshold level for selecting pulse‐like ground motions is derived; and then what followed is a comparison analysis of three pulse‐detecting schemes, one using the wavelet analysis, the other two using the energy concept. It is believed that other than providing a useful way of classifying pulse‐like ground motions for structural demand analysis, knowledge of this work could also benefit the development of the ground motion prediction equations accounting for pulse effects, and further to aid the probabilistic seismic hazard analysis in a near‐fault environment. Copyright © 2016 John Wiley & Sons, Ltd.     

Validation of (not‐historical) large‐event near‐fault ground‐motion simulations for use in civil engineering applications

Ground‐motion simulations generated from physics‐based wave propagation models are gaining increasing interest in the engineering community for their potential to inform the performance‐based design and assessment of infrastructure residing in active seismic areas. A key prerequisite before the ground‐motion simulations can be used with confidence for application in engineering domains is their comprehensive and rigorous investigation and validation. This article provides a four‐step methodology and acceptance criteria to assess the reliability of simulated ground motions of not historical events, which includes (1) the selection of a population of real records consistent with the simulated scenarios, (2) the comparison of the distribution of Intensity Measures (IMs) from the simulated records, real records, and Ground‐Motion Prediction Equations (GMPEs), (3) the comparison of the distribution of simple proxies for building response, and (4) the comparison of the distribution of Engineering Demand Parameters (EDPs) for a realistic model of a structure. Specific focus is laid on near‐field ground motions (<10km) from large earthquakes (M_w7), for which the database of real records for potential use in engineering applications is severely limited. The methodology is demonstrated through comparison of (2490) near‐field synthetic records with 5 Hz resolution generated from the Pitarka et al (2019) kinematic rupture model with a population of (38) pulse‐like near‐field real records from multiple events and, when applicable, with NGA‐W2 GMPEs. The proposed procedure provides an effective method for informing and advancing the science needed to generate realistic ground‐motion simulations, and for building confidence in their use in engineering domains.     

Analytical modelling of near‐source pulse‐like seismic demand for multi‐linear backbone oscillators

Nonlinear static procedures, which relate the seismic demand of a structure to that of an equivalent single‐degree‐of‐freedom oscillator, are well‐established tools in the performance‐based earthquake engineering paradigm. Initially, such procedures made recourse to inelastic spectra derived for simple elastic–plastic bilinear oscillators, but the request for demand estimates that delve deeper into the inelastic range, motivated investigating the seismic demand of oscillators with more complex backbone curves. Meanwhile, near‐source (NS) pulse‐like ground motions have been receiving increased attention, because they can induce a distinctive type of inelastic demand. Pulse‐like NS ground motions are usually the result of rupture directivity, where seismic waves generated at different points along the rupture front arrive at a site at the same time, leading to a double‐sided velocity pulse, which delivers most of the seismic energy. Recent research has led to a methodology for incorporating this NS effect in the implementation of nonlinear static procedures. Both of the previously mentioned lines of research motivate the present study on the ductility demands imposed by pulse‐like NS ground motions on oscillators that feature pinching hysteretic behaviour with trilinear backbone curves. Incremental dynamic analysis is used considering 130 pulse‐like‐identified ground motions. Median, 16% and 84% fractile incremental dynamic analysis curves are calculated and fitted by an analytical model. Least‐squares estimates are obtained for the model parameters, which importantly include pulse period T_p. The resulting equations effectively constitute an R ? μ ? T ? T_p relation for pulse‐like NS motions. Potential applications of this result towards estimation of NS seismic demand are also briefly discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

Stochastic model for simulation of near‐fault ground motions

A parameterized stochastic model of near‐fault ground motion in two orthogonal horizontal directions is developed. The major characteristics of recorded near‐fault ground motions are represented. These include near‐fault effects of directivity and fling step; temporal and spectral non‐stationarity; intensity, duration, and frequency content characteristics; directionality of components; and the natural variability of ground motions. Not all near‐fault ground motions contain a forward directivity pulse, even when the conditions for such a pulse are favorable. The proposed model accounts for both pulse‐like and non‐pulse‐like cases. The model is fitted to recorded near‐fault ground motions by matching important characteristics, thus generating an ‘observed’ set of model parameters for different earthquake source and site characteristics. A method to generate and post‐process synthetic motions for specified model parameters is also presented. Synthetic ground motion time series are generated using fitted parameter values. They are compared with corresponding recorded motions to validate the proposed model and simulation procedure. The use of synthetic motions in addition to or in place of recorded motions is desirable in performance‐based earthquake engineering applications, particularly when recorded motions are scarce or when they are unavailable for a specified design scenario. Copyright © 2016 John Wiley & Sons, Ltd.     

Non‐structure‐specific intensity measure parameters and characteristic period of near‐fault ground motions

This paper focuses on the effects of long‐period pulse of near‐fault ground motions on the structural damage potential. Two sets of near‐fault ground motion records from Chi‐Chi, Taiwan earthquake and Northridge earthquake with and without distinct pulse are selected as the input, and the correlation analysis between 30 non‐structure‐specific intensity measure parameters and maximum inelastic displacements and energy responses (input energy and hysteretic energy) of bilinear single degree of freedom systems are conducted. Based on the frequency characteristic of near‐fault ground motions with remarkable long‐period components, two intensity indices are proposed, namely, the improved effective peak acceleration (IEPA) and improved effective peak velocity (IEPV). In addition a new characteristic period of these ground motions is defined based on IEPA and IEPV. Numerical results illustrate that the intensity measure parameters related to ground acceleration present the best correlation with the seismic responses for rigid systems; the velocity‐related and displacement‐related parameters are better for medium‐frequency systems and flexible systems, respectively. The correlation curves of near‐fault ground motions with velocity pulse differ from those of ground motions without pulse. Moreover, the improved parameters IEPA and IEPV of near‐fault impulsive ground motions enhance the performance of intensity measure of corresponding conventional parameters, i.e. EPA and EPV. The new characteristic period based on IEPA and IEPV can better reflect the frequency content of near‐fault ground motions. Copyright © 2009 John Wiley & Sons, Ltd.     

Behavior of moment‐resisting frame structures subjected to near‐fault ground motions

Near‐fault ground motions impose large demands on structures compared to ‘ordinary’ ground motions. Recordings suggest that near‐fault ground motions with ‘forward’ directivity are characterized by a large pulse, which is mostly orientated perpendicular to the fault. This study is intended to provide quantitative knowledge on important response characteristics of elastic and inelastic frame structures subjected to near‐fault ground motions. Generic frame models are used to represent MDOF structures. Near‐fault ground motions are represented by equivalent pulses, which have a comparable effect on structural response, but whose characteristics are defined by a small number of parameters. The results demonstrate that structures with a period longer than the pulse period respond very differently from structures with a shorter period. For the former, early yielding occurs in higher stories but the high ductility demands migrate to the bottom stories as the ground motion becomes more severe. For the latter, the maximum demand always occurs in the bottom stories. Preliminary regression equations are proposed that relate the parameters of the equivalent pulse to magnitude and distance. The equivalent pulse concept is used to estimate the base shear strength required to limit story ductility demands to specific target values. Copyright © 2004 John Wiley & Sons, Ltd.     

Inelastic displacement demand of bridge columns considering shear–flexure interaction

Reinforced concrete bridge columns exhibit complex hysteretic behavior owing to combined action of shear, bending moment, and axial force under multi‐directional seismic shakings. The inelastic displacement of columns can be increased by shear–flexure interaction (SFI). This paper develops a simple yet reliable demand model for estimating the inelastic displacement and ductility based on the nonlinear time history analyses of 24 full‐size columns subject to a suite of near‐fault ground motions. A coupled hysteretic model is used to simulate the shear‐flexure interactive (SFI) behavior of columns and the accumulated material damage during loading reversals, including pinching, strength deterioration, and stiffness softening. Guided by rigorous dimensional analysis, the inelastic displacement responses of bridge columns are presented in dimensionless form showing remarkable order. A dimensionless nonlinearity index is derived taking into account of the column strength, ground motion amplitude, and softening or hardening post‐yield behavior. Strong correlation is revealed between the normalized inelastic displacement and the dimensionless structure‐to‐pulse frequency, the dimensionless nonlinearity index as well as the aspect ratio. Two regressive equations for displacement and ductility demands are proposed and validated against the simulation results. The SFI effects are discussed and included explicitly through the aspect ratio in the proposed model. This study offers a new way to realistically predict the inelastic displacement of columns directly from structural and ground motion characteristics. Copyright © 2010 John Wiley & Sons, Ltd.     

Seismic response analysis of multidrum classical columns

This paper presents a numerical investigation on the seismic response of multidrum classical columns. The motivation for this study originates from the need to understand: (a) the level of ground shaking that classical multidrum columns can survive, and (b) the possible advantages or disadvantages of retrofitting multidrum columns with metallic shear links that replace the wooden poles that were installed in ancient times. The numerical study presented in this paper is conducted with the commercially available software Working Model 2D?, which can capture with fidelity the sliding, rocking, and slide‐rocking response of rigid‐body assemblies. This paper validates the software Working Model by comparing selected computed responses with scarce analytical solutions and the results from in‐house numerical codes initially developed at the University of California, Berkeley, to study the seismic response of electrical transformers and heavy laboratory equipment. The study reveals that relative sliding between drums happens even when the g‐value of the ground acceleration is less than the coefficient of friction, µ, of the sliding interfaces and concludes that: (a) typical multidrum classical columns can survive the ground shaking from strong ground motions recorded near the causative faults of earthquakes with magnitudes M_w=6.0–7.4; (b) in most cases multidrum classical columns free to dislocate at the drum interfaces exhibit more controlled seismic response than the monolithic columns with same size and slenderness; (c) the shear strength of the wooden poles has a marginal effect on the sliding response of the drums; and (d) stiff metallic shear links in‐between column drums may have an undesirable role on the seismic stability of classical columns and should be avoided. Copyright © 2005 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.     

近断层地震作用下设备-结构耦合隔震体系动力响应分析

建立设备-结构耦合隔震体系模型,选取近断层脉冲型和非脉冲型地震波各50条,计算耦合隔震体系的动力响应。分析表明,近断层脉冲型地震动对耦合隔震体系的影响大于非脉冲型地震动,且对主体结构的影响大于对设备的影响;近断层脉冲型地震作用下的隔震层位移、层间位移、楼层加速度、设备加速度和设备位移的平均响应分别达到非脉冲型地震作用的2.25倍、2.17倍、2.24倍、1.17倍和1.20倍。进行设备-结构耦合隔震体系设计时,需考虑近断层地震动脉冲作用的影响,同时需注意引起主体结构和设备最大响应的地震动不一定相同。     

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.     

Establishing absorbed energy spectra—an attenuation approach

For energy‐based seismic design, energy demand in the form of absorbed energy spectra was established by an attenuation relationship. The absorbed energy is proposed for evaluating the energy demand in an inelastic system because the absorbed energy is directly related to the pseudo‐velocity in the elastic case. Based on a total of 273 ground motion records from 15 significant earthquakes in California, an attenuation relationship of the absorbed energy was established from a two‐stage non‐linear regression analysis. This relationship was established for a given earthquake magnitude, source‐to‐site distance, site class, and ductility factor. A similar expression for the normalized absorbed energy was also developed. This study showed that the absorbed energy for near‐field ground motions can be significantly larger than that predicted by the attenuation relationship for normal ground motions. Copyright © 2000 John Wiley & Sons, Ltd.     

Shaking table testing of multidrum columns and portals

A common type of ancient monuments around the Mediterranean is the ancient Greek temple. Unfortunately, very few remain intact; most of them surviving in the form of free‐standing multidrum columns. Composed of stones resting on top of each other without any connection, such columns are considered vulnerable to earthquakes. The paper presents an experimental study of such structures, aiming to explore their seismic vulnerability and derive insights on the key factors affecting their response. Reduced scale models of a single multidrum column and of a portal were tested at the shaking table of the National Technical University of Athens Laboratory of Soil Mechanics. The models, constructed of marble just as the originals, were excited by idealized Ricker pulses and real seismic records. Single columns exhibit a remarkable earthquake resistance. Subjected to the strongest motions ever recorded in Greece, where many such monuments are situated, the columns hardly suffered any permanent deformation. Collapse is probable only for extremely harsh directivity‐affected seismic motions. Portals proved even more robust, surviving extreme seismic excitations. Their superior performance is related to the beneficial role of the epistyle, which adds energy dissipation and restoring force to the system. Their performance is very sensitive to minor changes in geometry or input motion. The complexity increases exponentially with the number of drums, being directly associated with the number of drum‐to‐drum interfaces and the increased probability of interface imperfections. In contrast to PGA, the maximum spectral displacement SD_max and the length scale L_p have turned out to be effective intensity measures. Copyright © 2014 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.     

三维竖向断层场地对地面运动的影响

实际工程场地中的断层通常具有三维尺寸,应进行三维分析。本文考虑均匀弹性半空间内存在不同长度、深度的三维断层,由下向上垂直入射一个脉冲波,主要采用三维时域显式有限元结合透射人工边界的方法及相应编写的三维显示有限元波动程序DSI3,计算断层附近地震地面运动的时程反应,研究含有三维断层场地地面运动的一些特点,并与自由场反应对比,以说明三维竖向断层对地震波传播的特点和对断层附近地面运动的影响。     

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.