Ground Motion Time Histories Research Articles

Parallel Algorithm and Simulation Code for Spatial-Varying Seismic Motion Methods#

The simulation mechanism of seismic ground motion is presented in this paper, and the parallel numerical algorithm is applied as the attempt for the simulation of spatial seismic ground motion time histories on parallel computers, which is consistent with arbitrary response spectra from a specified target. The basic methods of simulation, which involve calculations of auto power spectra, phase difference spectra, cross power spectra, Fourier spectra, and response spectra, etc., are also within the discussions in this paper. According to these analyses, this paper presents a set of integrated methods for nonstationary seismic ground motion simulation with greater capacity of processing multiple spatial points. In additional, Parallel Seismic Ground Motion Simulator, the parallel program for artificial generation of seismic ground motion, has been developed, which is based on Message-Passing Interface and written in Fortran90, and also provides a user-friendly visualized interface based on a commercial finite-element-analysis preprocessor. The new interdisciplinary approach can not only improve scale and efficiency of simulation of the spatial stochastic field but also can provide a useful tool for simulation of seismic input load. Information for improving current seismic design codes is also presented.

Estimation of Strong Ground Motion from the Great 1964 Mw 9.2 Prince William Sound, Alaska, Earthquake

We are generating physically plausible near-field synthetic ground motions for the great 1964 Prince William Sound, Alaska, earthquake compatible with available seismological data, tectonic information, and eyewitness accounts. The first objective of this study is the simulation of the low-frequency (i.e., f <0.03 Hz) strong ground motions on selected locations and on a dense grid of observation points extending over the shallow dipping causative fault of the 1964 Alaska earthquake. In order to accomplish this task, we are utilizing the slip model proposed by Johnson et al. (1996) based on a joint inversion of tsunami waveforms and geodetic data. The calculations are carried out using the discrete wavenumber representation method (Bouchon and Aki, 1977; Bouchon, 1979) and the generalized transmission and reflection coefficient technique (Luco and Apsel, 1983). The second objective of this study is the reconstruction of the strong ground motion time histories and response spectra that the city of Anchorage experienced during the 1964 Alaska earthquake. The low-frequency (i.e., f <0.03 Hz) ground motions are generated using the methodology described previously. The intermediate-frequency (i.e., 0.03< f <0.50 Hz) ground motions are simulated by convolving Green’s functions generated by the discrete wavenumber representation method with far-field radiation pulses of circular cracks (Sato and Hirasawa, 1973; Dong and Papageorgiou, 2002a). The high-frequency (i.e., 0.5< f <8.0 Hz) ground motions are simulated using the stochastic modeling approach. The three independently derived ground-motion components are then properly combined to generate synthetic broadband ground-motion time histories and response spectra for the city of Anchorage due to the 1964 Prince William Sound earthquake. The third objective of this study is the validation of the synthetic strong ground motions for the 1964 Alaska earthquake against observed tectonic deformation, ground-motion estimates inferred from descriptions of structural damage, and eyewitness accounts. In summary, the analysis presented in this study contributes to a better understanding of the seismological aspects of the 1964 Alaska earthquake and provides synthetic time histories and response spectra for engineering applications compatible with all available information (i.e., seismological, tectonic, and eyewitness accounts). It should be noted however that the generated strong ground motions are not necessarily unique, nor do they reflect the entire uncertainty that characterizes the problem under investigation.

Quantifying Nonlinearity Susceptibility via Site-Response Modeling Uncertainty at Three Sites in the Los Angeles Basin

The effects of near-surface soil stratigraphy on the amplitude and frequency content of ground motion are accounted for in most modern U.S. seismic design codes for building structures as a function of the soil conditions prevailing in the area of interest. Nonetheless, currently employed site-classification criteria do not adequately describe the nonlinearity susceptibility of soil formations, which prohibits the development of standardized procedures for the computationally efficient integration of nonlinear ground response analyses in broadband ground-motion simulations. In turn, the lack of a unified methodology for nonlinear site-response analyses affects both the prediction accuracy of site-specific ground-motion intensity measures and the evaluation of site-amplification factors when broadband simulations are used for the development of hybrid attenuation relations. In this article, we introduce a set of criteria for quantification of the nonlinearity susceptibility of soil profiles based on the site conditions and incident ground-motion characteristics, and we implement them to identify the least complex ground response prediction methodology required for the simulation of nonlinear site effects at three sites in the Los Angeles basin. The criteria are developed on the basis of a comprehensive nonlinear site-response modeling uncertainty analysis, which includes both detailed soil profile descriptions and statistical adequacy of ground-motion time histories. Approximate and incremental nonlinear models are implemented, and the limited site-response observations are initially compared to the ensemble site-response estimates. A suite of synthetic ground motions for rupture scenarios of weak, medium, and large magnitude events (M 3.5–7.5) is next generated, parametric studies are conducted for each fixed magnitude scenario by varying the source-to-site distance, and the variability introduced in ground-motion predictions is quantified for each nonlinear site-response methodology. A frequency index is developed to describe the frequency content of incident ground motion relative to the resonant frequencies of the soil profile, and this index is used in conjunction with the rock-outcrop acceleration peak amplitude (PGA_(RO)) to identify the site conditions and ground-motion characteristics where incremental nonlinear analyses should be employed in lieu of approximate methodologies. We show that the proposed intensity-frequency representation of ground motion may be implemented to describe the nonlinearity susceptibility of soil formations in broadband simulations by accounting both for the magnitude-distance-orientation characteristics of seismic motion and the profile stiffness characteristics. The synthetic ground-motion predictions are next used for the development of site-amplification factors for the alternative site-response methodologies, and the results are compared to published site factors of attenuation relations. For the site conditions investigated, currently established amplification factors compare well with synthetic simulations for class C and D site conditions, while long-period amplification factors are overestimated by a factor of 1.5 at the class E site, where site-specific nonlinear analyses should be employed for levels of PGA_(RO)>0.2g.

Strong motion compatible source geometry

Strong motion array records are analyzed in this paper to identify and map the source zone of four past earthquakes. The source is represented as a sequence of double couples evolving as ramp functions, triggering at different instants, distributed in a region yet to be mapped. The known surface level ground motion time histories are treated as responses to the unknown double couples on the fault surface. The location, orientation, magnitude, and risetime of the double couples are found by minimizing the mean square error between analytical solution and instrumental data. Numerical results are presented for Chi‐Chi, Imperial Valley, San Fernando, and Uttarakashi earthquakes. Results obtained are in good agreement with field investigations and those obtained from conventional finite fault source inversions.

Seismic reliability of a cable-stayed bridge retrofitted with hysteretic devices

This study evaluates the fragility curves of a cable-stayed bridge by an analytical approach based on time history analysis. The presentation of the vulnerability information in the form of fragility curves is a widely practiced approach when several uncertain sources are involved. The ASCE benchmark problem of a cable-stayed bridge is considered as a case study. A passive control technique is adopted and results are compared in term of fragility curves. In order to consider the uncertainties related to the ground motion 24 ground motion time history are considered, corresponding to four different hazard levels, while the uncertainties in the structural characteristics are introduced by defining the different performance thresholds as random variables. The fragility evaluation shows how important a correct estimation of the limit state is for the comparison of different retrofit techniques.

Estimation of Strong Ground Motions in Southwest Western Australia with a Combined Green's Function and Stochastic Approach

As only a very limited number of earthquake strong ground motion records are available in southwest Western Australia (SWWA), it is difficult to derive a reliable and unbiased strong ground motion attenuation model based on these data. To overcome this, in this study a combined approach is used to simulate ground motions. First, the stochastic approach is used to simulate ground motion time histories at various epicentral distances from small earthquake events. Then, the Green's function method, with the stochastically simulated time histories as input, is used to generate large event ground motion time histories. Comparing the Fourier spectra of the simulated motions with the recorded motions of a ML6.2 event in Cadoux in June 1979 and a ML5.5 event in Meckering in January 1990, provides good evidence in support of this method. This approach is then used to simulate a series of ground motion time histories from earthquakes of varying magnitudes and distances. From the regression analyses of these simulated data, the attenuation relations of peak ground acceleration (PGA), peak ground velocity (PGV), and response spectrum of ground motions on rock site in SWWA are derived.

배율조정 및 스펙트럼 맞춤 입력지반운동 모델에 대한 비선형 단자유도 시스템의 파손확률

비선형 구조계의 확률론적 지진해석 방법 중 대표적인 것은 지진 재해도 수준에 해당하는 입력지반운동 모델을 사용한 시간이력을 수행하여 그 응답의 확률분포를 예측하는 것이다. 이 연구에서는 널리 사용되고 있는 두 가지 입력지반운동 모델에 따른 구조계 응답의 분포특성 및 파손확률의 차이와 그 원인을 분석한다 입력지반운동 모델로는 실제 지진기록을 배율 조정하여 사용하는 배율조정 입력지반운동과 설계 응답스펙트럼에 상응하는 인공 지진기록을 사용하는 스펙트럼 맞춤 입력지반운동 두 가지를 고려한다. 동일한 지진재해도 수준을 고려한 해석결과 설계 응답스펙트럼에 상응하는 인공 지진기록을 사용한 입력지반운동 모델은 실제 지진기록을 배율 조정한 입력지반운동 모델보다 평균적으로 응답을 크게 평가하였고 이로 인해 파손확률 또한 더 큰 것으로 나타났다 이러한 경향은 연약한 지반에서 더욱 현저한 것으로 나타났다. 이러한 입력지반운동 모델에 따른 파손확률의 차이는 스펙트럼 맞춤 입력지반운동의 목표로 사용된 도로교 설계기준의 설계 응답스펙트럼이 실제 지진기록의 응답스펙트럼보다 장주기로 갈수록 응답을 크게 평가하도록 보수적으로 만들어졌기 때문인 것으로 나타났다. In probabilistic seismic analysis of nonlinear structural system, dynamic analysis is performed to obtain the distribution of the response estimate using input ground motion time histories which correspond to a given seismic hazard level. This study investigates the differences in the distribution of the responses and the failure probability according to input ground motion models. Two types of input ground motion models are considered: real earthquake records scaled to specified intensity level and artificial input ground motion fitted to design response spectrum. Simulation results fir a nonlinear SDOF system demonstrate that the spectrum matched input ground motion produces larger failure probability than those of scaled input ground motion due to biased responses. Such tendency is more remarkable in the site of soft soil conditions. Analysis results show that such difference of failure probability is due to the conservative estimation of design response spectrum in the range of long period of ground motion.

An earthquake scenario for the microzonation of Sofia and the vulnerability of structures designed by use of the Eurocodes

The study of the site effects and the microzonation of a part of the metropolitan Sofia, based on the modelling of seismic ground motion along three cross-sections are performed. Realistic synthetic strong motion waveforms are computed for scenario earthquakes ( M=7) applying a hybrid modelling method, based on the modal summation technique and finite differences scheme. The synthesized ground motion time histories are source and site specific. The site amplification is determined in terms of response spectra ratio (RSR). A suite of time histories and quantities of earthquake engineering interest are provided. The results of this study constitute a “database” that describes the ground shaking of the urban area. A case study of experiment-based assessment of vulnerability of a cast-in-situ single storey, industrial, reinforced concrete frame, designed according to Eurocodes 2 and 8 is presented. The main characteristics of damage index and storey drift are discussed for the purposes of microzonation.

Seismic Vulnerability and Mitigation during Construction of Cable-Stayed Bridges

The implications of earthquake loading during balanced cantilever construction of a cable-stayed bridge are examined. Finite-element models of a cable-stayed bridge were developed and multiple ground motion time history records were used to study the seismic response at the base of the towers for six stages of balanced cantilever construction. Probabilistic seismic hazard relationships were used to relate ground motions to bridge responses. The results show that there can be a high probability of having seismic responses (forces/moments) in a partially completed bridge that exceed, often by a substantial margin, the 10%/50-year design level (0.21% per annum) for the full bridge. The maximum probability of exceedance per annum was found to be 20%. This occurs because during balanced-cantilever construction the structure is in a particularly precarious and vulnerable state. The efficacy of a seismic mitigation strategy based on the use of tie-down cables intended for aerodynamic stability during construction was investigated. This strategy was successful in reducing some of the seismic vulnerabilities so that probabilities of exceedance during construction dropped to below 1% per annum. Although applied to only one cable-stayed bridge, the same approach can be used for construction-stage vulnerability analysis of other long-span bridges.

Nonstationary Stochastic Simulation of Strong Ground Motion Time Histories Including Natural Variability: Application to the K-Net Japanese Database

Physical models that can be used to obtain realistic accelerograms usually require a thorough knowledge of the source, path, and site effects. In addition, the computational resources needed might be expensive. Thus, empirical models still represent a good alternative for simulating strong ground motion. In this work, we modify and improve the model developed by Sabetta and Pugliese (1996). This new method models the time-domain accelerogram based on the assumption that the phase is random and that the time envelope can be represented by the so-called average instantaneous power. This is, in turn, described as a lognormal distribution for P and S waves combined with an algebro-exponential function representing the envelope of coda waves. In addition, the frequency content of the signal is nonstationary and follows a modified ω -square model. The method depends on four common indicators in earthquake engineering: peak ground acceleration, strong-motion duration, Arias intensity, and central frequency. These indicators are empirically connected to a given database by means of ground-motion prediction equations. In this study we calibrate the model using Japanese data recorded by the K-net array, which has high-quality digital accelerograms and station-site conditions characterized by geotechnical measurements. In addition, this technique permits the inclusion of the uncertainty of the model parameters to take into account the ground-motion natural variability in the stochastic generation of the time histories. The main goal of this work is to provide the earthquake engineering community with a flexible tool to generate realistic accelerograms for dynamic studies.

Influence of dynamic soil–structure interaction on the nonlinear response and seismic reliability of multistorey systems

AbstractA set of reinforced concrete structures with gravitational loads and mechanical properties (strength and stiffness) representative of systems designed for earthquake resistance in accordance with current criteria and methods is selected to study the influence of dynamic soil–structure interaction on seismic response, ductility demands and reliability levels. The buildings are considered located at soft soil sites in the Valley of Mexico and subjected to ground motion time histories simulated in accordance with characteristic parameters of the maximum probable earthquake likely to occur during the system's expected life. For the near‐resonance condition the effects of soil–structure interaction on the ductility demands depend mainly on radiation damping. According to the geometry of the structures studied this damping is strongly correlated with the aspect ratio, obtained by dividing the building height by its width. In this way, for structures with aspect ratio greater than 1.4 the storey and global ductility demands increase with respect to those obtained with the same structures but on rigid base, while for structures with aspect ratio less than 1.4 the ductility demands decrease with respect to those for the structures on rigid base. For the cases when the fundamental period of the structure has values very different from the dominant ground period, soil–structure interaction leads in all cases to a reduction of the ductility demands, independently of the aspect ratio. The reliability index β is obtained as a function of the base shear ratio and of the seismic intensity acting on the nonlinear systems subjected to the simulated motions. The resulting reliability functions are very similar for systems on rigid or on flexible foundation, provided that in the latter case the base rotation and the lateral displacement are removed from the total response of the system. Copyright © 2006 John Wiley &amp; Sons, Ltd.

안정대륙권역의 중규모지진에 의한 근단층지반운동의 모델링

이 논문에서는 안정대륙권역(Stable Continental Regions, SCRs)에서의 중규모 지진에 의한 근단층지반운동(Near Fault Ground Motion, NFGM) 모델을 처음으로 제시한다. 근단층지반운동은 큰 진폭의 장주기 속도 펄스를 갖는 특징을 가지고 있다. 이 속도 펄스를 모델링하기 위해서는 그 주기와 진폭을 지진의 규모와 단층거리의 함수로 표현할 수 있어야 한다. 그런데 안정대륙권역에서는 관측 자료가 빈약하여 지진데이터로부터 이 관계식을 직접 유도하는 것은 어렵기 때문에 이 연구에서는 간접적인 접근법을 채택하였다. 속도 펄스의 주기와 진폭은 단층파열의 상승시간과 파열속도의 함수임이 알려져 있고 활성구조권역(Active Tectonic Regions, ATRs)에 속하는 미국 서부지역에서는 실험적 공식이 확립되어 있다. 안정대륙권역에서의 상승시간과 단층파열속도의 지진규모에 대한 함수관계는 WUS와 CEUS에서의 자료를 비교하여 도출하였다. 이 관계식들로부터 안정대륙권역에서의 NFGM의 속도 펄스의 주기와 진폭을 지진규모 및 단층 거리에 대한 관계식으로 유도하였다. 안정대륙권역에서의 NFGM의 가속도 시간이력은 추계학적으로 생성된 원역지진지반가속도에 새로운 관계식에 의한 속도 펄스를 중첩하여 얻어진다. 적용 예제로서 탄소성 단자유도 시스템의 근단층지반운동에 대한 응답을 분석하였다. This paper proposes a method for modeling new fault ground motion due to moderate size earthquakes in Stable Continental Regions (SCRs) for the first time. The near fault ground motion is characterized by a single long period velocity pulse of large amplitude. In order to model the velocity pulse, its period and peak amplitude need be determined in terms of earthquake magnitude and distance from the causative fault. Because there have been observed very few new fault ground motions, it is difficult to derive the model directly from the recorded data in SCRs. Instead an indirect approach is adopted in this work. The two parameters, the period and peak amplitude of the velocity pulse, are known to be functions of the rise time and the slip velocity. For Western United States (WUS) that belongs active tectonic regions, there art empirical formulas for these functions. The relations of rise time and slip velocity on the magnitude in SCRs are derived by comparing related data between Western United States and Central-Eastern United States that belongs to SCRs. From these relations, the functions of these pulse parameters for NFGM in SCRs can be expressed in terms of earthquake magnitude and distance. A time history of near fault ground motion of moderate magnitude earthquake in stable continental regions is synthesized by superposing the velocity pulse on the for field ground motion that is generated by stochastic method. As an demonstrative application, the response of a single degree of freedom elasto-plastic system is studied.

Artificial ground motion compatible with specified ground shaking peaks and target response spectrum

This article describes a hybrid simulation method to generate artificial ground motion time histories that are compatible with specified peak seismic acceleration, velocity and displacement as well as the target response spectrum of absolute acceleration. First, based on traditional methods that match the target spectrum in the frequency domain, an initial acceleration time history was synthesized to satisfy the specified peak acceleration, target spectral acceleration and intensity envelope. Second, by using the inversion formula of the seismic input to a linear single-degree-of-freedom system and by superimposing a series of narrow-band time histories in the time domain, the initial time history is further modified to allow its peak velocity and displacement to approach the targets and improve its matching precision with the target spectrum. Numerical examples are provided to demonstrate that the proposed method achieves good agreement with the target values.

Microvibration control of coupled high tech equipment-building systems in vertical direction

Vertical ground motion induced by a moving train is one of the major sources of environmental loads that affect the normal operation of sensitive equipment installed in a high tech building nearby the railway. This paper investigates the microvibration level of a high tech building subject to nearby train-induced vertical ground motion and its mitigation using a hybrid control platform for sensitive equipment. The hybrid platform is an elastic body mounted on the building floor through a series of passive mounts and controlled by hydraulic actuators with a sub-optimal control algorithm. The finite element model and the governing equations of motion of the coupled platform-building system are established in the absolute coordinate to facilitate the feedback control and performance evaluation of the platform. The time histories of vertical ground motion are generated from the ground motion spectra that are the functions of track, train, and soil parameters. Numerical simulation and parametric studies are conducted on a typical three-story high tech building. The results show that the use of hybrid control platform can effectively reduce vertical microvibration of a batch of high tech equipment to the level satisfying the most stringent microscale velocity requirement specified in the BBN criteria. The hybrid control platform is superior to the passive platform because of its higher performance and robustness.

Prediction of Broadband Ground-Motion Time Histories: Hybrid Low/High- Frequency Method with Correlated Random Source Parameters

We present a new method for calculating broadband time histories of ground motion based on a hybrid low-frequency/high-frequency approach with correlated source parameters. Using a finite-difference method we calculate low- frequency synthetics (< ∼1 Hz) in a 3D velocity structure. We also compute broadband synthetics in a 1D velocity model using a frequency-wavenumber method. The low frequencies from the 3D calculation are combined with the high frequencies from the 1D calculation by using matched filtering at a crossover frequency of 1 Hz. The source description, common to both the 1D and 3D synthetics, is based on correlated random distributions for the slip amplitude, rupture velocity, and rise time on the fault. This source description allows for the specification of source parameters independent of any a priori inversion results. In our broadband modeling we include correlation between slip amplitude, rupture velocity, and rise time, as suggested by dynamic fault modeling. The method of using correlated random source parameters is flexible and can be easily modified to adjust to our changing understanding of earthquake ruptures. A realistic attenuation model is common to both the 3D and 1D calculations that form the low- and high-frequency components of the broadband synthetics. The value of Q is a function of the local shear-wave velocity. To produce more accurate high-frequency amplitudes and durations, the 1D synthetics are corrected with a randomized, frequency-dependent radiation pattern. The 1D synthetics are further corrected for local site and nonlinear soil effects by using a 1D nonlinear propagation code and generic velocity structure appropriate for the site’s National Earthquake Hazards Reduction Program (nehrp) site classification. The entire procedure is validated by comparison with the 1994 Northridge, California, strong ground motion data set. The bias and error found here for response spectral acceleration are similar to the best results that have been published by others for the Northridge rupture.

Selection of the appropriate methodology for the deterministic seismic hazard assessment on the territory of the Republic of Serbia

This paper presents a discussion regarding the most common approaches to the deterministic seismic hazard analysis, as well as their relation with the probabilistic hazard analysis. Different methodologies for estimation of the strong earthquake ground motion at a site of interest on the territory of the Republic of Serbia are also discussed. When generation of the synthetic ground motion time histories on the territory of the Republic of Serbia is concerned, a method developed by Trifunac and his associates is suggested having in mind that this approach uses only those input parameters that can be easily and accurately defined while at the same time being able to model all properties of strong earthquake ground motion that are presently known as well as to consider the probabilistic nature of earthquake occurrence.

Experimental Seismic Response of High-Voltage Transformer-Bushing Systems

This paper describes the shake table testing of a full-scale high-voltage electrical transformer-bushing system. The main objective of the study was to investigate the amplification between the ground motion and the motion at the base of the bushing under various ground-motion time histories and intensities. Another objective of the testing was to assess the predictions of a three-dimensional finite-element model of the transformer-bushing system. The experimental results obtained indicated that the rocking motion of the bushing and turret, facilitated by the top plate flexibility of the transformer, influenced significantly the dynamic characteristics of the bushing. The finite element model was able to predict absolute accelerations, relative displacements, and stress distributions in the systems with reasonable accuracy considering its complexity.

Analysis of Coupled Lateral-Torsional-Pounding Responses of One-Storey Asymmetric Adjacent Structures Subjected to Bi-Directional Ground Motions Part I: Uniform Ground Motion Input

This paper presents results of a parametric study of seismic induced lateral-torsional-pounding responses of an asymmetric and a symmetric one-storey system subjected to bi-directional ground motion. The properties of the symmetric model are fixed, while the vibration frequency and eccentricity of the asymmetric model vary in the numerical computation. 20 sets of bi-directional horizontal earthquake ground motion time histories are numerically simulated for the analysis. All the simulated motions are compatible individually with the Newmark-Hall design response spectrum with 5% damping and normalized to 0.5g. Ensemble mean peak responses of the two systems to the 20 sets ground motions are estimated. Both linear elastic and nonlinear inelastic behaviours are studied. Effects of torsional stiffness, structural vibration frequency, eccentricities, and initial gap between two structures are investigated. Numerical results are presented in dimensionless form and compared with the code torsional provisions. In this paper, the input ground motion time histories at all the structural supports are assumed to be uniform. An accompany paper of this study is devoted to discuss the effect of the spatially varying ground motion on coupled lateral-torsional-pounding responses of the adjacent structures (Hao and Gong 2005).

Analysis of Coupled Lateral-Torsional-Pounding Responses of One-Storey Asymmetric Adjacent Structures Subjected to Bi-Directional Ground Motions Part II: Spatially Varying Ground Motion Input

This is the second paper presenting numerical results of a parametric study of seismic induced lateral-torsional-pounding responses of an asymmetric and a symmetric one-storey adjacent structure. The accompany paper (Part I) (Gong and Hao 2004) assumed ground motion input at all structural supports as uniform. Torsional responses are generated because of inherent structural eccentricity and eccentric pounding. In reality, seismic ground motion at different structural supports inevitably varies owing to wave propagation. Spatially varying ground motion will induce torsional responses of structures, and generate out-of-phase responses between adjacent structures. Thus it might have a significant effect on coupled lateral-torsional-pounding responses. This paper studies the ground motion spatial variation effect. For comparison purpose, same adjacent structure models and impact element used in Part I of this study are adopted here again. 20 sets of spatially varying ground motion time histories are stochastically simulated. All the time histories are compatible with the Newmark-Hall design response spectrum with 5% damping and normalized to 0.5g. The spatial variation of any two simulated time histories is compatible with an empirical coherency loss function. Coupled lateral-torsional-pounding responses of the two structures to the simulated ground motions are calculated. Discussions on the ground motion spatial variation effects are made.

A Kinematic Source-Time Function Compatible with Earthquake Dynamics

We propose a new source-time function, to be used in kinematic modeling of ground-motion time histories, which is consistent with dynamic propagation of earthquake ruptures and makes feasible the dynamic interpretation of kinematic slip models. This function is derived from a source-time function first proposed by Yoffe (1951), which yields a traction evolution showing a slip-weakening behavior. In order to remove its singularity, we apply a convolution with a triangular function and obtain a regularized source-time function called the regularized Yoffe function. We propose a parameterization of this slip-velocity time function through the final slip, its duration, and the duration of the positive slip acceleration ( Tacc ). Using this analytical function, we examined the relation between kinematic parameters, such as peak slip velocity and slip duration, and dynamic parameters, such as slip-weakening distance and breakdown-stress drop. The obtained scaling relations are consistent with those proposed by Ohnaka and Yamashita (1989) from laboratory experiments. This shows that the proposed source-time function suitably represents dynamic rupture propagation with finite slip-weakening distances.