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.     

Simulation of orthogonal horizontal ground motion components for specified earthquake and site characteristics

A method for generating an ensemble of orthogonal horizontal ground motion components with correlated parameters for specified earthquake and site characteristics is presented. The method employs a parameterized stochastic model that is based on a time‐modulated filtered white‐noise process with the filter having time‐varying characteristics. Whereas the input white‐noise excitation describes the stochastic nature of the ground motion, the forms of the modulating function and the filter and their parameters characterize the evolutionary intensity and nonstationary frequency content of the ground motion. The stochastic model is fitted to a database of recorded horizontal ground motion component pairs that are rotated into their principal axes, a set of orthogonal axes along which the components are statistically uncorrelated. Model parameters are identified for each ground motion component in the database. Using these data, predictive equations are developed for the model parameters in terms of earthquake and site characteristics and correlation coefficients between parameters of the two components are estimated. Given a design scenario specified in terms of earthquake and site characteristics, the results of this study allow one to generate realizations of correlated model parameters and use them along with simulated white‐noise processes to generate synthetic pairs of horizontal ground motion components along the principal axes. The proposed simulation method does not require any seed recorded ground motion and is ideal for use in performance‐based earthquake engineering. Copyright © 2011 John Wiley & Sons, Ltd.     

Simulation of synthetic ground motions for specified earthquake and site characteristics

A method for generating a suite of synthetic ground motion time‐histories for specified earthquake and site characteristics defining a design scenario is presented. The method employs a parameterized stochastic model that is based on a modulated, filtered white‐noise process. The model parameters characterize the evolving intensity, predominant frequency, and bandwidth of the acceleration time‐history, and can be identified by matching the statistics of the model to the statistics of a target‐recorded accelerogram. Sample ‘observations’ of the parameters are obtained by fitting the model to a subset of the NGA database for far‐field strong ground motion records on firm ground. Using this sample, predictive equations are developed for the model parameters in terms of the faulting mechanism, earthquake magnitude, source‐to‐site distance, and the site shear‐wave velocity. For any specified set of these earthquake and site characteristics, sets of the model parameters are generated, which are in turn used in the stochastic model to generate the ensemble of synthetic ground motions. The resulting synthetic acceleration as well as corresponding velocity and displacement time‐histories capture the main features of real earthquake ground motions, including the intensity, duration, spectral content, and peak values. Furthermore, the statistics of their resulting elastic response spectra closely agree with both the median and the variability of response spectra of recorded ground motions, as reflected in the existing prediction equations based on the NGA database. The proposed method can be used in seismic design and analysis in conjunction with or instead of recorded ground motions. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Response of nonlinear soil‐MDOF structure systems subjected to distinct frequency‐content components of near‐fault ground motions

This paper is devoted to investigate the effects of near‐fault ground motions on the seismic responses of nonlinear MDOF structures considering soil‐structure interaction (SSI). Attempts are made to take into account the effects of different frequency‐content components of near‐fault records including pulse‐type (PT) and high‐frequency (HF) components via adopting an ensemble of 54 near‐fault ground motions. A deep sensitivity analysis is implemented based on the main parameters of the soil‐structure system. The soil is simulated based on the Cone model concept, and the superstructure is idealized as a nonlinear shear building. The results elucidate that SSI has approximately increasing and mitigating effects on structural responses to the PT and HF components, respectively. Also, a threshold period exists above which the HF component governs the structural responses. As the fundamental period of the structure becomes shorter and structural target ductility reduces, the contribution of the HF component to the structural responses increases, elaborately. Soil flexibility makes the threshold period increase, and the effect of the PT component becomes more significant than the HF one. In the case of soil‐structure system, slenderizing the structure also increases this threshold period and causes the PT component to be dominant. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Strengthening of moment‐resisting frame structures against near‐fault ground motion effects

Near‐fault ground motions with forward directivity are characterized by a large pulse. This pulse‐like motion may cause a highly non‐uniform distribution of story ductility demands for code‐compliant frame structures, with maximum demands that may considerably exceed the level of code expectations. Strengthening techniques for multi‐story frame structures are explored with the objective of reducing maximum drift demands. One option is to modify the code‐based SRSS distribution of story shear strength over the height by strengthening of the lower stories of the frame. The modified distribution reduces the maximum story ductility demand, particularly for weak and flexible structures. However, this strengthening technique is less effective for stiff structures, and is almost ineffective in cases in which the maximum demand occurs in the upper stories, i.e. strong and flexible structures. As an alternative, the benefits of strengthening frames with elastic and inelastic walls are evaluated. The effects of adding walls that are either fixed or hinged at the base are investigated. It is demonstrated that strengthening with hinged walls is very effective in reducing drift demands for structures with a wide range of periods and at various performance levels. Wall inelastic behavior only slightly reduces the benefits of strengthening with hinged walls.Copyright © 2004 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.     

Dominant pulse simulation of near fault ground motions

In this study, a new mathematical model is developed composed of two parts, including harmonic and polynomial expressions for simulating the dominant velocity pulse of near fault ground motions. Based on a proposed velocity function, the corresponding expressions for the ground acceleration and displacement time histories are also derived. The proposed model is then fitted using some selected pulse-like near fault ground motions in the Next Generation Attenuation (NGA) project library. The new model is not only simple in form but also simulates the long-period portion of actual velocity near fault records with a high level of precision. It is shown that the proposed model-based elastic response spectra are compatible with the near fault records in the neighborhood of the prevailing frequency of the pulse. The results indicate that the proposed model adequately simulates the components of the time histories. Finally, the energy of the proposed pulse was compared with the energy of the actual record to confirm the compatibility.     

Simulation of the seismic performance of the Bolu Viaduct subjected to near‐fault ground motions

The seismic performance of the Bolu Viaduct in the Duzce, Turkey, earthquake of November 1999 was studied via a non‐linear, time‐history analysis of a multi‐degree of freedom model. The viaduct had a seismic isolation system consisting of yielding‐steel energy dissipation units and sliding pot bearings. The Duzce earthquake caused a surface rupture across the viaduct, which resulted in excessive superstructure movement and widespread failure of the seismic isolation system. The effect of the rupture was modeled by a static, differential ground displacement in the fault‐parallel direction across the rupture. The ground motions used in the analysis contain common near‐fault features including a directivity pulse in the fault‐normal direction and a fling step in the fault‐parallel direction. The analysis used a finite element package capable of modeling the mechanical behavior of the seismic isolation system and focused on the structural response of a 10‐span module of the viaduct. This analysis showed that the displacement of the superstructure relative to the piers exceeded the capacity of the bearings at an early stage of the earthquake, causing damage to the bearings as well as to the energy dissipation units. The analysis also indicated that shear keys, both longitudinal and transverse, played a critical role in preventing collapse of the deck spans. Published in 2004 by John Wiley & Sons, Ltd.     

Residual slip of sliding blocks induced by near‐fault ground motions

The response of a rigid block supported on a horizontally moving foundation through a dry‐friction contact is investigated to near‐fault ground motions. Such motions can be thought of as consisting of a coherent component (‘pulse’) and an incoherent component, which can be described as a band‐limited ‘random noise’. The equation of motion of this strongly nonlinear system is reduced to a normalized form that reveals important parameters of the problem such as the critical acceleration ratio. The response of the sliding block to a set of uniformly processed near‐fault motions, covering a sufficiently wide range of magnitudes, is evaluated numerically for selected discrete values of the acceleration ratio. For each value of the critical acceleration ratio, the numerically computed residual slips are fitted with a Weibull (Gumbel type III) extreme value probability distribution. This allows the establishment of regression equations that describe accurately design sliding curves corresponding to various levels of non‐exceedance probability. The analysis reveals that the coherent component of motion contributes significantly to the response of the sliding block. Furthermore, the relevant acceleration in specifying the critical acceleration ratio is the (normalized) amplitude, α_{H_pulse}, of the pulse and not the (normalized) amplitude of the incoherent component α_H. Finally, the incoherent component is described quantitatively in terms of the root‐mean‐square acceleration a_RMS, and an attempt is made to understand its influence on the response of the sliding block. Copyright © 2016 John Wiley & Sons, Ltd.     

Development of attenuation relation for the near fault ground motion from the characteristic earthquake

A composite source model has been used to simulate a broadband strong ground motion with an associated fault rupture process. A scenario earthquake fault model has been used to generate 1 000 earthquake events with a magni-tude of Mw8.0. The simulated results show that, for the characteristic event with a strike-slip faulting, the character istics of near fault ground motion is strongly dependent on the rupture directivity. If the distance between the sites and fault was given, the ground motion in the forward direction (Site A) is much larger than that in the backward direction (Site C) and that close to the fault (Site B). The SH waves radiated from the fault, which corresponds to the fault-normal component plays a key role in the ground motion amplification. Corresponding to the sites A, B, and C, the statistical analysis shows that the ratio of their aPG is 2.15:1.5:1 and their standard deviations are about 0.12, 0.11, and 0.13, respectively. If these results are applied in the current probabilistic seismic hazard analysis (PSHA), then, for the lower annual frequency of exceedance of peak ground acceleration, the predicted aPG from the hazard curve could reduce by 30% or more compared with the current PSHA model used in the developing of seismic hazard map in the USA. Therefore, with a consideration of near fault ground motion caused by the rupture directivity, the regression model used in the development of the regional attenuation relation should be modified accordingly.     

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.     

Stochastic procedure for the simulation of synthetic main shock‐aftershock ground motion sequences

According to the current seismic codes, structures are designed to resist the first damaging earthquake during their service life. However, after a strong main shock, a structure may still face damaging aftershocks. The main shock‐aftershock sequence may result in major damage and eventually the collapse of a structure. Current studies on seismic hazard mainly focus on the modeling and simulation of main shocks. This paper proposes a 3‐step procedure to generate main shock‐aftershock sequences of pairs of horizontal components of a ground motion at a site of interest. The first step generates ground motions for the main shock using either a source‐based or site‐based model. The second step generates sequences of aftershocks' magnitudes, locations, and times of occurrence using either a fault‐based or seismicity‐based model. The third step simulates pairs of ground motion components using a new empirical model proposed in this paper. We develop prediction equations for the controlling parameters of a ground motion model, where the predictors are the site condition and the aftershock characteristics from the second step. The coefficients in the prediction equations and the correlation between the model parameters (of the 2 horizontal components of 1 record and of several records in 1 sequence) are estimated using a database of aftershock accelerograms. A backward stepwise deletion method is used to simplify the initial candidate prediction equations and avoid overfitting the data. The procedure, based on easily identifiable engineering parameters, is a useful tool to incorporate effects of aftershocks into seismic analysis and design.     

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.     

Effects of near‐fault ground motions on the nonlinear dynamic response of base‐isolated r.c. framed buildings

Near‐fault ground motions are characterized by long‐period horizontal pulses and high values of the ratio between the peak value of the vertical acceleration, PGA_V, and the analogous value of the horizontal acceleration, PGA_H, which can become critical for base‐isolated (BI) structures. The objective of the present work is to check the effectiveness of the base isolation of framed buildings when using High‐Damping‐Rubber Bearings (HDRBs), taking into consideration the combined effects of the horizontal and vertical components of near‐fault ground motions. To this end, a numerical investigation is carried out with reference to BI reinforced concrete buildings designed according to the European seismic code (Eurocode 8). The design of the test structures is carried out in a high‐risk region considering (besides the gravity loads) the horizontal seismic loads acting alone or in combination with the vertical ones and assuming different values of the ratio between the vertical and horizontal stiffnesses of the HDRBs. The nonlinear seismic analysis is performed using a step‐by‐step procedure based on a two‐parameter implicit integration scheme and an initial‐stress‐like iterative procedure. At each step of the analysis, plastic conditions are checked at the potential critical sections of the girders (i.e. end sections of the sub‐elements in which a girder is discretized) and columns (i.e. end sections), where a bilinear moment–curvature law is adopted; the effect of the axial load on the ultimate bending moment (M‐N interaction) of the columns is also taken into account. The response of an HDRB is simulated by a model with variable stiffness properties in the horizontal and vertical directions, depending on the axial force and lateral deformation, and linear viscous damping. Copyright © 2011 John Wiley & Sons, Ltd.     

Effects of pulse period of near‐field ground motions on the seismic demands of soil–MDOF structure systems using mathematical pulse models

In this paper, the effects of pulse period associated with near‐field ground motions on the seismic demands of soil–MDOF structure systems are investigated by using mathematical pulse models. Three non‐dimensional parameters are employed as the crucial parameters, which govern the responses of soil–structure systems: (1) non‐dimensional frequency as the structure‐to‐soil stiffness ratio; (2) aspect ratio of the superstructure; and (3) structural target ductility ratio. The soil beneath the superstructure is simulated on the basis of the Cone model concept. The superstructure is modeled as a nonlinear shear building. Interstory drift ratio is selected as the main engineering demand parameter for soil–structure systems. It is demonstrated that the contribution of higher modes to the response of soil–structure system depends on the pulse‐to‐interacting system period ratio instead of pulse‐to‐fixed‐base structure period ratio. Furthermore, results of the MDOF superstructures demonstrate that increasing structural target ductility ratio results in the first‐mode domination for both fixed‐base structure and soil–structure system. Additionally, increasing non‐dimensional frequency and aspect ratio of the superstructure respectively decrease and increase the structural responses. Moreover, comparison of the equivalent soil–SDOF structure system and the soil–MDOF structure system elucidates that higher‐mode effects are more significant, when soil–structure interaction is taken into account. In general, the effects of fling step and forward directivity pulses on activating higher modes of the superstructure are more sever in soil–structure systems, and in addition, the influences of forward directivity pulses are more considerable than fling step ones. Copyright © 2013 John Wiley & Sons, Ltd.     

Case studies of damage to 19‐storey irregular steel moment‐frame buildings under near‐source ground motion

This paper describes the three‐dimensional nonlinear analysis of six 19‐storey steel moment‐frame buildings, designed per the 1997 Uniform Building Code, under strong ground motion records from near‐source earthquakes with magnitudes in the range of 6.7–7.3. Three of these buildings possess a reentrant corner irregularity, while the remaining three possess a torsional plan irregularity. The records create drift demands of the order of 0.05 and plastic rotation demands of the order of 4–5% of a radian in the buildings with reentrant corners. These values point to performance at or near ‘Collapse Prevention’. Twisting in the torsionally sensitive buildings causes the plastic rotations on the moment frame on one face of the building (4–5% of a radian) to be as high as twice of that on the opposite face (2–3% of a radian). The asymmetric yield pattern implies a lower redundancy in the lateral force‐resisting system as the failure of the heavily loaded frame could result in a total loss of resistance to torsion. Copyright © 2006 John Wiley & Sons, Ltd.     

Near‐source seismic demand and pulse‐like records: A discussion for L'Aquila earthquake

Rupture directivity effects in ground motion are known since many years to both seismologists and earthquake engineers, i.e. in sites that are in a particular geometrical configuration with respect to the rupture, the velocity fault‐normal signals may show a large pulse which occurs at the beginning of the record and contains the most of energy. The results are waveforms different from ordinary ground motions recorded in the far field or in geometrical conditions not favorable with respect to directivity. Current attenuation laws are not able to capture such effect well, if at all, and current probabilistic seismic hazard analysis is not able to predict the resulting peculiar spectral shape. Moreover, it is believed that structures with dynamic behavior in a range of periods related to the pulse period may be subjected to underestimated seismic demand. In the paper this is investigated and increments in both elastic and inelastic seismic actions are quantified using a large dataset of records, from the next generation attenuation project (NGA), in which a fraction is comprised of velocity pulses identified in other studies. These analyses employ recently developed tools and procedures to assess directivity effects and to quantify the associated threat in terms of seismic action on structures. Subsequently, the same tools are used in one of the first attempts to identify near‐source effects in the data recorded during a normal faulting earthquake, the mainshock of the recent Abruzzo (central Italy) sequence, leading to conclude that pulse‐like effects are likely to have occurred in the event, that is (1) observation of pulse‐like records in some near‐source stations is in fair agreement with existing predictive models, (2) the increment in seismic demand shown by pulse‐like ground motion components complies with the results of the analysis of the NGA data, and (3) seismic demand in non‐impulsive recordings is generally similar to what expected for ordinary records. The results may be useful as a benchmark for inclusion of near‐source effect in design values of seismic action and structural risk analysis. Copyright © 2010 John Wiley & Sons, Ltd.