关于地震动转动分量的研究

列举了多次地震中的地震动转动现象,概括了国内外对地震动转动分量的产生、传播、合成方法及其对结构的作用等方面的研究成果.还介绍了由地震动平动分量计算转动分量的弹性波动方法,并讨论了其局限性;还介绍了欧洲规范对转动分量的部分规定,指出有必要在结构抗震设计中考虑转动分量的作用.此外,在转动分量的产生、对结构的作用及数值模拟方面还做了一些假设与解释.     

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).     

六分量弹性波场数值模拟与分析

地震波传播过程中,质点的振动不仅包括三个独立的平移部分,还包括三个独立的旋转部分.本文基于一阶速度-应力弹性波方程,采用分裂完全匹配层(SPML)的吸收边界条件,推导了时间导数二阶精度和空间导数高阶精度的交错网格有限差分格式的弹性波速度与应力各分量计算公式,模拟了各向同性介质中均匀模型和层状模型下的六分量波场,并对二维各向同性层状模型下的三个分量地震记录做高分辨率线性拉东变换得到各自的频散能谱.数值模拟分析结果表明:(1)旋转分量的能量要比平动分量弱的多;(2)在平动分量上,面波能量强,频率低,反射P波能量较强,反射S波能量稍弱;在旋转分量上,反射P波能量很弱,S波能量强;(3)与平动分量相比,旋转分量的频散能谱效果更好,能看到基阶和完整的高阶面波,即旋转分量能反映更多的地下介质信息.     

光纤振动传感之一:旋转测量技术及其地震学应用

地震波场可分解为三分量平动和三分量旋转运动.旋转分量包含重要的波场梯度信息,是地震波场重建的关键要素,但过去由于缺乏稳定的高灵敏度旋转测量仪器,它在不同的地震学应用中常被忽略.光纤旋转地震仪是率先打破测量仪器缺乏困境、最先实现商业化的旋转地震仪,也是目前最有发展前景的地震波旋转直接测量设备.光纤旋转地震仪基于Sagnac效应,并依托成熟的光纤陀螺技术实现振动的旋转分量测量.它具有纯光电传感不受平动影响的测量优势;并且能够在高灵敏度和宽频带旋转测量的基础下实现设备的小型化,有利于旋转测量的应用推广.因此,光纤旋转地震仪和传统的地震仪将形成互补,实现旋转和平动六分量(6C)的观测,更好地提取地震波场特征,提高振动监测能力,有效改善震源过程反演、地下结构成像和地震破坏机理研究等应用.本文主要介绍光纤旋转测量的基本原理、旋转地震学的应用及其潜在应用前景.     

Approximate formulas for rotational effects in earthquake engineering

The paper addresses the issue of researching into the engineering characteristics of rotational strong ground motion components and rotational effects in structural response. In this regard, at first, the acceleration response spectra of rotational components are estimated in terms of translational ones. Next, new methods in order to consider the effects of rotational components in seismic design codes are presented by determining the effective structural parameters in the rotational loading of structures due only to the earthquake rotational components. Numerical results show that according to the frequency content of rotational components, the contribution of the rocking components to the seismic excitation of short period structures can never be ignored. During strong earthquakes, these rotational motions may lead to the unexpected overturning or local structural damages for the low-rise multi-story buildings located on soft soil. The arrangement of lateral-load resisting system in the plan, period, and aspect ratio of the system can severely change the seismic loading of wide symmetric buildings under the earthquake torsional component.     

Seismic response of large-span spatial structures under multi-support and multidimensional excitations including rotational components

To achieve rational and precise seismic response predictions of large span spatial structures(LSSSs),the inherent non-uniformity and multidimensionality characteristics of earthquake ground motions should be properly taken into consideration.However,due to the limitations of available earthquake stations to record seismic rotational components,the effects of rocking and torsional earthquake components are commonly neglected in the seismic analyses of LSSSs.In this study,a newly developed method to extract the rocking and torsion components at any point along the area of a deployed dense array from the translational earthquake recordings is applied to obtain the rotational seismic inputs for a LSSS.The numerical model of an actual LSSS,the Dalian International Conference Center(DICC),is developed to study the influences of multi-support and multidimensional excitations on the seismic responses of LSSSs.The numerical results reveal that the non-uniformity and multidimensionality of ground motion input can considerably affect the dynamic response of the DICC.The specific degree of influence on the overall and local structural displacements,deformations and forces are comprehensively investigated and discussed.     

Structural response for six correlated earthquake components

The paper examines the effect on the structural response of the inevitable correlation which exists between the six earthquake components acting along a set of structural axes. The rotational components are expressed in terms of the spatial derivatives of the translational components. For the calculation of response, modal analysis is employed so that ground response spectra can also be used as seismic input. A methodology is developed to obtain the maximum mean square response which can occur in a structure, irrespective of its orientation with respect to the impinging seismic waves. The application of this methodology for the calculation of design response is advocated, especially for asymmetric structures. For the assumed model of seismic wave motion, the numerical results show a significant contribution to the response from the rotational components. This contribution is, however, expected to be reduced by structural foundation averaging and interaction effects. Further studies with more complete models of seismic wave motions, and their interaction with structural foundations, are thus warranted for a realistic evaluation and characterization of the rotational inputs for design purposes.     

旋转运动在地震学中的应用概述

旋转地震学是研究由天然地震、爆破和周围环境振动引起的地面旋转运动的新兴学科。对于它的研究不仅有助于对质点运动(平移运动、旋转运动和形变)进行完整的描述,而且对广义地球物理学,如强地面运动地震学、地震工程学、地震物理学、地震仪器等的研究也有重要指导意义。本文系统介绍了旋转运动在地震学中4个方面的应用。首先,介绍基于平移运动和旋转运动的共同测量,得出了计算远震瑞利波和勒夫波相速度的理论公式,并以西伯利亚地震为例,得出台站附近的相速度结构;其次,利用环形激光仪仅对地震SH波敏感的特性,分离P波和S波,分辨海洋噪声和面波,确定海洋噪声的反方位角;然后,介绍利用旋转传感器对自由振荡的长周期环形模式的观测;最后,对包含旋转观测量的多参数反演问题的重要性和实用性进行了阐述,并分析了旋转地震学研究现存的问题。     

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.     

Extracting rotational components of earthquake ground motion using data recorded at multiple stations

Rotational components of earthquake ground motion have not been considered for seismic analysis, design and performance assessment because recordings of these components are unavailable. A number of procedures have been proposed to extract rotational components of ground motion from translational time series recorded at multiple, closely spaced recording stations. In this paper, a new procedure that is capable of capturing higher frequency content in rotational time‐series is presented. The frequencies at which numerical errors are introduced in the solution, which are a function of apparent wave velocity and array dimension, are identified. Results are presented for the proposed procedure, the widely accepted geodetic method, and a single‐station procedure developed by the authors, all using data recorded at the Lotung array in Taiwan. Copyright © 2012 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.     

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。     

On the application of fiber optic gyroscopes for detection of seismic rotations

In recent years, the measurement of rotational components of earthquake-induced ground motion became a reality due to high-resolution ring laser gyroscopes. As a consequence of the fact that they exploit the Sagnac effect, these devices are entirely insensitive to translational motion and are able to measure the rotation rate with high linearity and accuracy over a wide frequency band. During the last decade, a substantial number of earthquakes were recorded by the large ring lasers located in Germany, New Zealand, and USA, and the subsequent data analysis demonstrated reliability and consistency of the results with respect to theoretical models. However, most of the observations recorded teleseismic events in the far-field. The substantial mass and the size of these active interferometers make their near-field application difficult. Therefore, the passive counterparts of ring lasers, the fiber optic gyros can be used for seismic applications where the mobility is more important than extreme precision. These sensors provide reasonable accuracy and are small in size, which makes them perfect candidates for strong motion applications. The other advantage of fiber optic gyroscopes is that if the earthquake is local and shallow (like one occurred early this year at Canterbury, New Zealand), the large ring lasers simply do not have the dynamic range??the effect is far too large for these instruments. In this paper, we analyze a typical commercially available tactical grade fiber optic gyroscope (VG-951) with respect to the seismic rotation measurement requirements. The initial test results including translation and upper bounds of seismic rotation sensitivity are presented. The advantages and limitations of tactical grade fiber optic gyroscope as seismic rotation sensor are discussed.     

Seismic rotational displacement of gravity walls by pseudo-dynamic method: Passive case

Prediction of the seismic rotational displacements of retaining wall under passive condition is an important aspect of design in earthquake prone region. In this paper, the pseudo-dynamic method is used to compute the rotational displacements of rigid retaining wall supporting cohesionless backfill under seismic loading for the passive earth pressure condition. The proposed method considers time, phase difference and effect of amplification in shear and primary waves propagating through both the backfill and the retaining wall. The influence of ground motion characteristics on rotational displacement of the wall is evaluated. Also the effects of variation of parameters like wall friction angle, soil friction angle, amplification factor, shear wave velocity, primary wave velocity, period of lateral shaking, horizontal and vertical seismic accelerations on the rotational displacements are studied. The rotational displacement of the wall increases substantially with increase in amplification of both shear and primary waves, time of input motion, period of lateral shaking and decreases with increase in soil friction angle, wall friction angle. The rotational displacements of the wall also increase when the effect of wall inertia is taken into account. Results are provided in graphical form.     

On planar seismic wavefront modeling for estimating rotational ground motions: Case of 2-D SH line-source

At large hypocentral distances, it is convenient to approximate the curved transient seismic wavefronts as planar to estimate rotational ground motions from the single-station recordings of translational ground motions. In this paper, we investigate whether and when this approximation, referred to as the ‘plane-wave’ approximation, can be considered adequate close to the source. For this, we consider a simplistic source model comprising a two-dimensional, kinematic shear dislocation SH line-source buried in a homogenous, elastic half-space and assume this to be an equivalent representation of a finite-sized fault. The ‘plane-wave’ rotational motion is then synthesized from the exact translational motion solution to the assumed model and compared with the exact rotational motion solution for this model. The comparison between the two sets of rotational amplitudes in frequency domain suggests that the plane-wave approximation may be adequate, when the wavelengths of the seismic waves are much smaller than the source depth. When this is not true, the plane-wave approximation is seen to underestimate the Fourier amplitudes close to the source by several orders, particularly when the fault planes are vertically oriented. A similar comparison in the time domain indicates that a severe underestimation may also occur when the source rise time is longer than the shear-wave arrival time at the epicenter. Significant discrepancies are also observed between the waveforms of the exact and plane-wave rotational motions.     

Seismic response of bridge pier on rigid caisson foundation in soil stratum

An analytical method to study the seismic response of a bridge pier supported on a rigid caisson foundation embedded in a deep soil stratum underlain by a homogeneous half space is developed. The method reproduces the kinematic and inertial responses, using translational and rotational distributed Winkler springs and dashpots to simulate the soil-caisson interaction. Closed-form solutions are given in the frequency domain for vertical harmonic S-wave excitation. Comparison with results from finite element （FE） analysis and other available solutions demonstrates the reliability of the model. Results from parametric studies are given for the kinematic and inertial responses. The modification of the fundamental period and damping ratio of the bridge due to soil-structure interaction is graphically illustrated.     

Analysis of a group of seismic events using rotational components

Analysis of a group of seismic events which took place in central Italy and have been recorded at the l’Aquila Observatory reveals proportionality between the maximum seismic signal (the displacement velocity) and the maximum amplitudes of rotational components. To compare the seismic events in the aspect of energy emitted as rotational motions, the rotation indices are used; these indices help us also to differentiate between the results obtained for different frequency spectra. In the adopted higher frequency range, 2.6–43 Hz, the relation between maximum displacement velocities and the rotation indices is roughly reciprocal, while for the lower frequencies, 0.3–3 Hz, there is no clear relationship. The share of rotation motions in the whole seismic energy emitted from the source varies during the seismic event. Research on the rotational components hidden in the seismic field gives a new insight into the processes in the source.