A brief theory and computing of seismic ground rotations for structural analyses

The seismic ground rotations are important with respect to spatial structural models, which are sensitive to the wave propagation. The rotational ground motion can lead to significant increasing of structural response, instability and unusual damages of buildings. Currently, the seismic analyses often take into account the rocking and torsion motions separately using artificial accelerograms. We present an exact analytical method, proposed by Nazarov [15] for computing of three rotational accelerograms simultaneously from given translational records. The method is based on spectral representation in the form of Fourier amplitude spectra of seismic waves, corresponding to the given three-component translational accelerogram. The composition, directions and properties of seismic waves are previously determined in the form of a generalized wave model of ground motion. It is supposed that seismic ground motion can be composed by superposition of P, SV, SH- and surface waves. As an example, the dynamic response analysis of 25-story building is presented. Here recorded (low-frequency) and artificial (high-frequency) accelerograms were used; each of them includes three translational and three rotational components. In this structural analysis, we have clarified primarily conditions under which rotational ground motion should be taken into account. Next, we have calculated three rotational components of seismic ground motion. Then they were taken as additional seismic loads components for further seismic analysis of the building. Note, soil–structure interaction (SSI) is not considered in this study. For computing, we use the special software for structural analyses and accelerogram processing (FEA Software STARK ES and Odyssey software, Eurosoft Co., Russia). It was developed and is used in engineering practice in the Central Research Institute of Building Constructions (TsNIISK, Moscow, Russia).     

A note on the surface motion of a semi-cylindrical canyon for incident cylindrical SH waves radiated by a finite fault

The plane-wave assumption for incident SH waves can be a good approximation for cylindrical and spherical waves radiated from finite sources, even when the source is as close as twice the size of the inhomogeneity, and when the source and the inhomogeneity are described within the same coordinate system. However, in a more general setting, and when the fault’s radiation pattern must be considered, the plane-wave approximation may not yield satisfactory answers for arbitrary orientation of the fault. Jalali et al. (2015) demonstrated this for a semi-cylindrical, sedimentary valley, and in this study we extend their results to a case in which the semi-circular, sedimentary valley is replaced by a canyon. We describe the effects of incident cylindrical waves on the amplitudes of surface motion in and near the semi-cylindrical canyon when the causative faults are at different distances and have different curvatures and orientations.     

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.     

Earthquake fault‐induced surface rupture—A hybrid strong ground motion simulation technique and discussion for structural design

Unique to the near‐source region of a large earthquake is the occurrence of strong impulsive ground motion and surface faulting referred to as ‘fling‐step’ motion. The objective of this study is to synthesize broad‐band time histories over a wide range of frequencies by characterizing rupture directivity and fling effects from the comprehensive strong motion database of the near‐fault Chi‐Chi event. To aid in the generation of these special types of ground motions, a hybrid modeling technique is introduced based on the stochastic finite‐fault radiation method and an efficient analytical approach to incorporate the observed low‐frequency features in the records close to the ruptured fault. The results show that the overall agreement among the developed hybrid methodology and recorded waveforms and response spectra is quite satisfying. A brief discussion on the design of infrastructures near seismic fault is also included. Copyright © 2011 John Wiley & Sons, Ltd.     

Seismic response of reduced micropolar elastic half-space

This paper explores reduced micropolar theory to simulate ground motion during an earthquake. In this theory, rotational motions are kinematically independent of translational motions. Analytical expressions for ground displacement and rotational motions due to a buried seismic source are presented in this paper. This theory requires two additional material constants which characterise the microstructure of the medium compared with linear elastic theory. Ground motions are simulated for an earthquake of magnitude (M _w) 5.0. The sensitivity of ground motion to these new material constants is reported. It is observed that rotations are sensitive to microstructure of the medium. A comparison with recorded rotations of the M _w 5.2 Izu peninsula, Japan event is also presented in this article.     

近断层地震动场预测——以长春市为例

断层带附近地震动场分布的研究,是当前地震工程领域研究的热点问题之一。近断层地震动场的分布对在断层附近进行抗震结构设计时,不仅是提供地震动输入,也是确定建设场地避让范围的重要依据之一。以区域地震构造背景分析、目标断层活动性鉴定、地震危险性评价为基础,结合断层探测结果,利用统计经验关系等最终确定发震断层,并建立相应的震源模型。采用显式有限元和并行计算技术计算目标区域场地的长周期地震动。利用有限断层随机合成的方法,计算高频地震动。将低频和高频地震动合成为目标区域内的宽频带地震动时程。对局部特殊场地条件地区,基于场地调查和勘探的数据,利用等效线性化等方法进行一维土层的非线性反应计算,给出这些特殊场地的宽频带地震动时程。最后,根据地震动时程获得设定地震发生时,目标区域的峰值加速度分布预测图和相应的反应谱。以长春市为例预测了在设定地震发生时,近断层地震动场的分布情况。当长春尖山子—卡伦断层发生6.0级地震时,潜在破坏性地震动的影响范围集中在附近,沿断层走向分布。加速度峰值沿断层垂直变化,主要为90 Gal～140 Gal。只是在长春市南部加速度峰值达到200 Gal。本研究的预测结果具备断层附近地震动的一些最基本的特征,符合当前对断层附近地震动的基本认识。     

Seismological asperities from the point of view of dynamic rupture modeling: the 2007 Mw6.6 Chuetsu-Oki,Japan, earthquake

We study the ground motion simulations based on three finite-source models for the 2007 Mw6.6 Niigata Chuetsu-oki, Japan, earthquake in order to discuss the performance of the input ground motion estimations for the near-field seismic hazard analysis. The three models include a kinematic source inverted from the regional accelerations, a dynamic source on a planar fault with three asperities inferred from the very-near-field ground motion particle motions, and another dynamic source model with conjugate fault segments. The ground motions are calculated for an available 3D geological model using a finite-difference method. For the comparison, we apply a goodness-of-fit score to the ground motion parameters at different stations, including the nearest one that is almost directly above the ruptured fault segments. The dynamic rupture models show good performance. We find that seismologically inferred earthquake asperities on a single fault plane can be expressed with two conjugate segments. The rupture transfer from one segment to another can generate a significant radiation; this could be interpreted as an asperity projected onto a single fault plane. This example illustrates the importance of the fault geometry that has to be taken into account when estimating the very-near-field ground motion.     

CHARACTERISTICS OF TORSIONAL GROUND MOTIONS

Due to the inherent difficulty in directly recording the rotational ground motions, torsional ground motions have to be estimated from the recorded spatially varying translational motions. In this paper, an empirical coherency function, which is based on the recorded motions at the SMART-1 array, is suggested to model the spatial variation of translational motions. Then, the torsional ground motion power spectral density function is derived. It depends on the translational motion power spectral density function and the coherency function. Both the empirical coherency function and the torsional motion power spectral density function are verified by the recorded motions at the SMART-1 array. The response spectra of the torsional motions are also estimated. Discussion on the relations between the torsional motion response spectrum and the corresponding translational motion response spectrum is made. Numerical results presented can be used to estimate the torsional ground motion power spectral density function and response spectrum.     

Ground Motion Modeling for Seismic Hazard Analysis in the Near-source Regime: An Asperity Model

—A new, yet simple, method using the asperity model to estimate ground motion in the near-source regime for probabilistic seismic hazard analyses is proposed in this study. This near-source model differs from conventional empirical attenuation equations. It correlates peak ground motions with the local contributing source in terms of the static stress drop released non-uniformly on the causative fault plane rather than with the whole seismic source in terms of magnitude. Here the model is simplified such that ground motions at a rock or firm soil site near extended vertical strike-slip faults are dominated by direct shear waves. The proposed model is tested by comparing its predictions with strong ground motion observations from the 1979 Imperial Valley and the 1984 Morgan Hill earthquakes. The results have revealed that ground motions in the near-source region can be adequately predicted using the asperity model with appropriate calibration factors. The directivity effect of ground motion in the near-source region is negligible for high-frequency accelerations. The cut-off frequency (?_max?) at a site is an important parameter in the near-source region. Higher values of ?_max yield higher estimates of peak ground accelerations. For high-frequency structures, ?_max should be carefully estimated. In the near- source region both non-uniform and uniform source models can produce non-stationary high-frequency ground motions. Peak motions may not be caused by the nearest sections of the fault (even if the uniform source model is considered).     

Investigation of ground rotational motions caused by direct and scattered P-waves from the 4 March 2008 TAIGER explosion experiment

High-frequency rotational motions of P-waves and coda waves were analysed using rotation rate sensors and strong motion array data from the 4 March 2008 TAiwan Integrated GEodynamics Research (TAIGER) explosion experiment in northeastern Taiwan. Theoretical and observational investigations focussed on the effects of this experiment on the free surface. The main goal of this study was to explore possible applications of combined measurements of artificial explosion-derived translational and rotational motions. Also investigated was the consistent ground rotation observed directly by rotation rate sensors and derived using translational seismic arrays. Common near-source high-frequency rotational motion observations and array-recorded translational motions from one shallow borehole explosion are analysed in this study. Using a half-space assumption of plane P-wave propagation across the recording site, we conclude that: (1) rotational motions induced by direct P-waves interacting with a free surface in theory can be used to estimate wave radial direction, velocity and anisotropic properties; (2) rotational motions derived from scattering are predominant among the observed rotations during the TAIGER explosion experiments and allow us to image the heterogeneous structure of the medium at the investigated site; and (3) rotation sensor measurements undertaken during TAIGER explosion experiments may be affected by cross-axis sensitivities, which need to be considered when using the data obtained during these experiments.     

旋转地震合成及其在大跨度悬索桥中的应用

为探究旋转地震动在大跨度悬索桥中的应用,首先,从线弹性理论和功率谱角度基于随机振动理论提出了6维地震动加速度功率谱模型;其次,基于MATLAB编制旋转地震动人工地震合成程序,从反应谱角度对合成地震动进行了正确性验证和拟合精度迭代调整;最后,分析了旋转地震动与地震动入射角对桥梁结构地震响应的影响。研究表明：人工合成的地震动平动分量反应谱与实测地震动的平动分量反应谱吻合度较高;六维地震动的主梁跨中竖向位移越是三维平动地震动的3倍,而主缆轴力峰值接近2.25E+05kN,约是三维平动地震动的1.3倍;旋转地震动和地震动入射角将会加大桥梁结构的位移响应和内力响应,且会减小塔底截面和桩最不利截面的安全性。     

Ground motion selection for simulation‐based seismic hazard and structural reliability assessment

This paper examines four methods by which ground motions can be selected for dynamic seismic response analyses of engineered systems when the underlying seismic hazard is quantified via ground motion simulation rather than empirical ground motion prediction equations. Even with simulation‐based seismic hazard, a ground motion selection process is still required in order to extract a small number of time series from the much larger set developed as part of the hazard calculation. Four specific methods are presented for ground motion selection from simulation‐based seismic hazard analyses, and pros and cons of each are discussed via a simple and reproducible illustrative example. One of the four methods (method 1 ‘direct analysis’) provides a ‘benchmark’ result (i.e., using all simulated ground motions), enabling the consistency of the other three more efficient selection methods to be addressed. Method 2 (‘stratified sampling’) is a relatively simple way to achieve a significant reduction in the number of ground motions required through selecting subsets of ground motions binned based on an intensity measure, IM. Method 3 (‘simple multiple stripes’) has the benefit of being consistent with conventional seismic assessment practice using as‐recorded ground motions, but both methods 2 and 3 are strongly dependent on the efficiency of the conditioning IM to predict the seismic responses of interest. Method 4 (‘generalized conditional intensity measure‐based selection’) is consistent with ‘advanced’ selection methods used for as‐recorded ground motions and selects subsets of ground motions based on multiple IMs, thus overcoming this limitation in methods 2 and 3. Copyright © 2015 John Wiley & Sons, Ltd.     

On the characteristics of ground motion rotational components using Chiba dense array data

An effort is made to examine the properties of rotational (torsional and rocking) ground motions using Chiba dense array data. The Chiba array system, located 30 km east of Tokyo, Japan, is composed of 15 boreholes with separation distances varying from 5 to 320 m. This provides a unique opportunity to examine the characteristics of rotational components. For this purpose, 17 events are considered and rotational ground motions are evaluated using spatial derivatives of translational ones. The effects of seismological parameters and separation distances between stations on properties of rotational motions are examined, showing a sudden increase in rotational motions for the earthquakes with large magnitude or PGA and decrease of these motions with increasing separation distance. While the duration of torsional motion is found to be larger than translational ones, there is no significant difference between durations of rocking and vertical motions. The effects of separation distance and earthquake magnitude on rotational response spectra are also investigated. The normalized rotational response spectra are found to be strongly affected by separation distance. The spectral ratios of rotational and translational motions are not linearly proportional to period as suggested by the previous studies. Finally, the torsional motion is predicted from translation ones for different separation distances at the site. The comparison of the predicted and the calculated torsional motions reveals a weak estimation in close separation distances (<30m) and satisfactory predictions in other cases. Copyright © 2007 John Wiley & Sons, Ltd.     

近场强地震动数值模拟的简化计算方法

近场强地震动除受场地条件的影响外,还受到震源破裂面上子源的空间分布特点、子源破裂先后顺序的强烈控制,基于数值格林函数法的近场强地震动数值模拟方法可以综合考虑震源、传播途径及局部场地条件的影响,对计算过程进行合理简化,分2步完成地震动模拟:第1步,在介质均匀区采用矩张量的解析解计算所有子源在盖层底面的位移,形成下一步有限元计算的输入场;第2步,在盖层介质不均匀区,结合局部人工透射边界技术,采用时、空解耦的波动显式有限元方法计算地表强地震动。在有限断层模型中,采用具有9个力偶的等效地震矩张量表达断层产状、滑动方向等的影响,采用Brune模型定义各子源的滑动时间函数,描述滑动的时、空不均匀分布特征,从而细化震源模型。通过对Northridge地震中4个基岩台站地表地震动的模拟结果和强震记录,验证了此简化计算方法的可行性     

Recipe for Predicting Strong Ground Motion from Crustal Earthquake Scenarios

We developed a recipe for predicting strong ground motions based on a characterization of the source model for future crustal earthquakes. From recent developments of waveform inversion of strong motion data used to estimate the rupture process, we have inferred that strong ground motion is primarily related to the slip heterogeneity inside the source rather than average slip in the entire rupture area. Asperities are characterized as regions that have large slip relative to the average slip on the rupture area. The asperity areas, as well as the total rupture area, scale with seismic moment. We determined that the areas of strong motion generation approximately coincide with the asperity areas. Based on the scaling relationships, the deductive source model for the prediction of strong ground motions is characterized by three kinds of parameters: outer, inner, and extra fault parameters. The outer fault parameters are defined as entire rupture area and total seismic moment. The inner fault parameters are defined as slip heterogeneity inside the source, area of asperities, and stress drop on each asperity based on the multiple-asperity model. The pattern of rupture nucleation and termination are the extra fault parameters that are related to geomorphology of active faults. We have examined the validity of the earthquake sources constructed by our recipe by comparing simulated and observed ground motions from recent inland crustal earthquakes, such as the 1995 Kobe and 2005 Fukuoka earthquakes.     

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.     

近断层速度脉冲地震动的三维有限差分模拟

根据台湾西部地质地貌特征和1999年集集M_W7.6地震的研究成果,建立三维速度结构模型和震源模型,并采用三维有限差分法对双冬断层可能产生的近断层脉冲型地震动进行数值模拟。结果表明,方向性效应引起的双向速度脉冲集中在垂直于断层滑动分量的方向上,而滑冲效应引起的单向速度脉冲则集中在平行于断层滑动分量的方向上。受方向性效应和上盘效应的共同调制,近断层脉冲型地震动反映出不对称带状分布的特征,速度脉冲主要分布在距离断层面约10 km的范围内。凹凸体的特性影响着地震动的时空分布,由地震波场显示南投和台中处于强地震动危险区。近场脉冲型地震动的研究对分析速度脉冲形成机理以及地震危险性有一定的参考意义。     

断层走向对刚构桥地震反应的影响

我国西部部分连续刚构桥临近地震断层建设,在抗震分析时通常会忽略断层走向与桥梁纵桥向夹角对其地震反应的影响。利用Midas Civil软件建立4座墩高不同的大跨度连续刚构桥模型,选取10组近断层强震记录进行时程分析,研究断层走向对刚构桥地震反应(位移和弯矩反应)的影响。结果显示：在水平双向近断层地震动输入下,桥梁主墩及主梁纵桥向地震反应在断层走向与纵桥向夹角为75°～135°范围内最大,而横桥向最大地震反应则发生在夹角为0°～30°或120°～180°范围;在三向近断层地震动输入下,与仅考虑水平双向地震动输入下的桥梁地震反应相比,竖向地震动对主梁竖向弯矩响应的影响较大,特别是主墩和主梁的交界处,增大比例可达2倍及以上。就文章选取的4座桥梁算例,不考虑断层走向和桥梁纵桥向的夹角则存在低估桥梁地震反应的可能,低估误差在15%～40%左右。