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.     

2021年青海玛多7.4级地震强震动记录及特征分析

2021年5月22日,青海省果洛州玛多县发生7.4级地震,中国强震动观测网络在主震中捕获16组强震动数据。对48条三分向加速度记录进行基线校正、滤波等常规处理,计算相应的地震动参数,发现位于断层破裂前向位置的63DAW台NS向记录的地震动速度波形具有长周期分量丰富的特征。分析6个典型台站的单自由度加速度反应谱,并与我国建筑抗震设计谱比较,分析此次地震的频谱特性。将实际观测到的PGA、PGV和S_a(T=0.1 s、T=1.0 s、T=2.0 s、T=5.0 s)与国内广泛使用的几种地震动预测模型对比,研究此次地震的影响场。通过分析S_a-S_d曲线,探讨此次地震靠近断层区域地面运动大位移与桥梁落梁震害间可能存在的关系。     

Analysis of foreshock sequence of the 1975 Haicheng earthquake of M S 7.3

The “earthquake nucleation” is discussed in this paper. The acceleration is a property of the nucleation phase and is a necessary condition of earthquake instability too. If the acceleration property of this nucleating process is described by the equation dΘ/dt=C/(t _f−t) ⁿ , the process can be summarized briefly that the rate of cumulative seismic release is proportional to the inverse power of the remaining time to failure. Based on this principle, the foreshock sequence of the 1975 Haicheng earthquake withM _S7.3, was analysed backward. It is stated clearly that the time-to-failure and magnitude of the mainshock can be predicted successfully if the coefficientr ² attains to the maximum. In the estimation of mainshock time, the error can generally be less than, or far less than, one-half the remaining time between the time of the last used data point and the mainshock. Contribution No. 95A0024, Institute of Geophysics, SSB, China. This study is the "Eighth-Five" contract project ofSSB.     

The significance of channel recharge rates for estimating debris‐flow magnitude and frequency

The quantification of debris‐flow hazard requires estimates of debris‐flow frequency and magnitude. Several methods have been proposed to determine the probable volume of future debris flows from a given basin, but most have neglected to account for debris recharge rates over time, which may lead to underestimation of debris‐flow volumes in basins with rare debris flows. This paper deals with the determination of debris recharge rates in debris‐flow channels based on knowledge of debris storage and the elapsed time since the last debris flow. Data are obtained from coastal British Columbia and a relation is obtained across a sample of basins with similar terrain and climatic conditions. For Rennell Sound on the west coast of the Queen Charlotte Islands, the power‐law relation for area‐normalized recharge rate, R_t, versus elapsed time, t_e was R_t = 0·23t_e^?0·58 with an explained variance of 75 per cent. A difference in recharge rates may exist between creeks in logged and unlogged forested terrain. The power function for undisturbed terrain was R_t = 0·20t_e^?0·49, while the function for logged areas was R_t = 0·30t_e^?0·77. This result suggests that for the same elapsed time since the last debris flow, clearcut gullies tend to recharge at a slower rate than creeks in old growth forest. This finding requires verification, particularly for longer elapsed times since debris flow, but would have important implications for forest resource management in steep coastal terrain. This study demonstrates that commonly used encounter probability equations are inappropriate for recharge‐limited debris flow channels. Copyright © 2005 John Wiley & Sons, Ltd.     

Attenuation characteristics of peak horizontal acceleration in Northeast and Southwest China

Regional seismic characteristics in northeastern and southwestern China are quite different. Earthquakes are more frequent in SW China than in NE China and intensity attenuates faster in SW China than in NE China. Through regression analyses of data from these two regions we have found the attenuation of peak horizontal accelerations also to be noticeably different. For northeastern China the regression is log₁₀(a) = ?0.474 + 0.613M ? 0.873 log₁₀ (R) ?0.00206R and for southwestern China, the regression is log₁₀ (a) = 0.437 + 0.454M ? 0.739 log₁₀ (R) ?0.00279R where a is acceleration in cm/sec², M is the Chinese surface wave magnitude (Institute of Geophysics, State Seismological Bureau), and R is the distance in kilometres. The formula for northeastern China has distance coefficients similar to those for Central United States as derived by Nuttli and Herrmann¹⁴.     

基于《建筑抗震设计规范》强度包线函数参数取值研究

利用《中国地震动参数区划图》采用的地震动参数衰减关系,以及《中国地震动参数区划图》中地震动峰值加速度和地震动加速度反应谱特征周期反推不同设防烈度和设计地震分组对应的震级和震中距,再根据《建筑抗震设计规范》中各设防水准的峰值加速度确定对应的震级和震中距,进而根据地震动强度包线参数与震级和震中距关系计算地震动强度包线参数的取值,为基于强度包线函数生成人工地震动提供参考,并讨论强度包线参数的取值规律：(1)随着设防烈度的提高,加速度时程曲线上升段持续时间t₁和平稳段持续时间t_s减小,下降段衰减指数c增大;(2)随着地震水准和设计地震分组的提高,加速度时程曲线上升段持续时间t₁和平稳段持续时间t_s增加,下降段衰减指数c减小;(3)在生成人工地震动时,除考虑峰值加速度和设计地震分组影响外,还需要考虑设防烈度影响。     

Effect of peak ground acceleration to velocity ratio on ductility demand of inelastic systems

A statistical analysis is performed to investigate the significance of peak ground acceleration to velocity ratio (a/v) on the displacement ductility demand of simple bilinear hysteretic systems. Three groups of earthquake records representative of low, normal and high<a/v ranges are used as input ground motions. The design yield strength of the inelastic systems is specified from the base shear formula in the 1980 National Building Code of Canada (NBCC 1980) and that in NBCC 1985 respectively. The former case represents the common practice of specifying seismic design base shear based on a peak site acceleration, while in the latter case the base shear is specified based on peak ground velocity and a/v ratio. Mean displacement ductility demands are obtained for the three groups of ground motions; and the corresponding dispersion characteristics are examined. The results show that the ground motion<a/v range has a significant effect on the displacement ductility demand, and it should be accounted for in design strength specification.     

岷县漳县6.6级地震及余震强震动记录特征分析

对2013年7月22日甘肃岷县—漳县地震获取的273条主余震加速度记录进行格式转换、基线校正和滤波等常规处理,分析该地震主震(M_S6.6)和余震(M_S5.6)两次地震记录的幅值、持时以及反应谱特征,发现M_S6.6主震记录的PGA范围在0.728～177.5 gal间,M_S5.6余震记录的PGA范围在0.732～69.3 gal间;将观测数据与霍俊荣和第五代《中国地震动参数区划图》地震动衰减关系进行对比,发现霍俊荣衰减关系更吻合于此次地震的主余震加速度衰减;绘制主余震5%～95%重要持时分布图,并针对主震62MXT反应谱和本地设计谱以及近些年国内主要强震震中反应谱开展比较分析;最后研究土层台、基岩台、相同台站各个震级反应谱的特征。     

Duration of earthquake fault motion in California

Duration of high frequency (5–25 Hz) radiation of energy from earthquake sources in California is consistent with the estimates of fault length and with dislocation velocity estimates of 2–3 km/sec. This duration can be described by an exponential function of magnitude for 2·5 < M < 7·5. It is related to the times it takes the dislocation to spread over the fault width (1/f₂), and the fault length (～ 1/f₁), and to reach its ultimate amplitude (T₀). The results in this paper can be used to estimate the range of amplitudes and the duration of long period pulses of strong ground motion near faults, as these long period pulses can be related to the properties of high-frequency radiation from the source. Such pulses must be considered in the analyses of yielding structures, when the average peak acceleration of the pulse exceeds the yield resistance seismic coefficient of the structure.     

Determination of moment magnitude from acceleration spectrum

The theoretical acceleration spectrum of observation site has been obtained from source acceleration spectrum derived from scaling law, using attenuation modelQ=Q _ν f ^η . A comparison of a set of theoretical acceleration spectra with observation spectra has been made, and we have obtained the attenuation model for observation site and seismic moment magnitude. We obtain thatQ _o=300,η=0.25 for Wuqia area, Xinjing Zizhizhou, and seismic moment magnitudes of 18 greater aftershocks of Wuqia earthquake occurred in 1985. In order to obtain seismic moment magnitued conveniently, three functional tables of acceleration spectra at 1Hz as the distances for variousQ value have been made. The seismic moment magnitude can be quickly measured from acceleration spectrum at 1Hz according to these tables (epicenter has to be known). The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,14, 435–445, 1992.     

Determination of horizontal and vertical design spectra based on ground motion records at Lali tunnel,Iran

Most acceleration diagrams show high levels of unpredictability, as a result, it is the best to avoid using diagrams of earthquake acceleration spectra, even if the diagrams recorded at the site in question. In order to design earthquake resistant structures, we, instead, suggest constructing a design spectrum using a set of spectra that have common characteristics to the recorded acceleration diagrams at a particular site and smoothing the associated data. In this study, we conducted a time history analysis and determined a design spectrum for the region near the Lali tunnel in Southwestern Iran. We selected 13 specific ground motion records from the rock site to construct the design spectrum. To process the data, we first applied a base-line correction and then calculated the signal-to-noise ratio (R_SN) for each record. Next, we calculated the Fourier amplitude spectra of the acceleration pertaining to the signal window (1), and the Fourier amplitude spectra of the associated noise (2). After dividing each spectra by the square root of the selected window interval, they were divided by each other (1 divided by 2), in order to obtain the R_SN ratio (filtering was also applied). In addition, all data were normalized to the peak ground acceleration (PGA). Next, the normalized vertical and horizontal responses and mean response spectrum (50%) and the mean plus-one standard deviation (84%) were calculated for all the selected ground motion records at 5% damping. Finally, the mean design spectrum and the mean plus-one standard deviation were plotted for the spectrums. The equation of the mean and the above-mean design spectrum at the Lali tunnel site are also provided, along with our observed conclusions.     

Artificial ground motion compatible with specified peak velocity and target spectrum

In this paper, a method, which synthesizes the artificial ground motion compatible with the specified peak velocity as well as the target acceleration response spectrum, was proposed. In this method, firstly, an initial acceleration time history α8^（0） （t）, which satisfies the prescribed peak ground acceleration, the target spectral acceleration ST（ω, ζ）,and the specified intensity envelope, is generated by the traditional method that generates the requency domain; secondly,α8^（0） （t）is further modulated by superimposing narrow-band time histories upon it in the time domain to make its peak velocity, approach the target peak ground velocity, and at the same time to improve its fitting precision to the target spectrum. Numerical examples show that this algorithm boasts high calculation precisions.     

Seismic fragility of traction elevators

Second‐generation performance‐based earthquake engineering (PBEE‐2) requires a library of component fragility functions to estimate probabilistic damage to a wide variety of building components. The present work draws on a large body of (mostly) post‐earthquake reconnaissance and (some) post‐earthquake survey observations of traction elevators to create fragility functions useful in PBEE‐2. Two surveys provide detailed observations of 115 representative elevators at 12 hospitals shaken in the 1989 Loma Prieta and 1994 Northridge earthquakes and selected without regard to or foreknowledge of damage. Of these, 55 failed and 60 did not. Approximately half were installed after an important code change of 1972, so one can distinguish the performance of pre‐1973 and post‐1973 elevator construction. They experienced a range of strong motion: 22 with peak ground acceleration (PGA) < 0.25 g, 93 with 0.25 g < PGA < 0.85 g. The hospitals had elevator failure rates as low as 0% and as high as 100%. A third survey describes damage qualitatively for six sites with PGA ≤ 0.25 and per‐site failure rates of 0% to perhaps 30%. Fragility functions are offered where the damage state is the loss of functionality of the elevator. The elevators in these surveys exhibit a median capacity of PGA ≈ 0.35 g with a logarithmic standard deviation of 0.40. Capacity is modestly sensitive to whether the elevator was installed before or after 1973. Using building‐specific intensity measures such as S_a(T₁) does not improve the fragility functions. Copyright © 2015 John Wiley & Sons, Ltd.     

Damage Potential of the 1999 Athens, Greece, Accelerograms

Athens experienced a devastating earthquake on September 7, 1999, centred about 10km beneath the outskirts of the city, with peak accelerations in the meizoseismal area estimated above 0.5 g. While the magnitude of the earthquake was moderate (M_S=5.9), damage and loss of life were extensive, numbering over 143 fatalities, 90 collapsed buildings, and over 100,000 rendered homeless. The most severe losses took place within 8 km of the fault, and peak rock accelerations in excess of 0.35 g were recorded 12 km from fault in downtown Athens. Local geologic effects played an important role, as demonstrated by concentrations of building damage on pockets of soft soil and near river canyons in the northwest part of the city. The earthquake was the first to severely damage Athens in over 2500 years. This study examines the engineering characteristics of 12 triaxial strong motion accelerograms recorded during the main shock. Properties investigated include peak ground acceleration and velocity, bracketed duration, Housner intensity, and response spectra. Spectral values at different orientations in the horizontal plane (“planar spectra”) are computed to infer the interaction of source directivity effects and building period, on damage potential. The role of rupture directivity close to the fault is investigated by means of idealized triangular pulses. Inelastic effects are examined using ductility spectra and sliding block analyses. Evidence is presented that low-rise structures in the area may have higher strength and longer natural period than those anticipated by building codes. The implications of the damage potential calculations for earthquake hazard assessment in Eastern North America and Northern Europe are also addressed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Probabilistic seismic hazard assessment of Switzerland: best estimates and uncertainties

We present the results of a new genera tion of probabilistic seismic hazard assessment for Switzerland. This study replaces the previous intensity-based generation of national hazard maps of 1978. Based on a revised moment-magnitude earthquake catalog for Switzerland and the surrounding regions, covering the period 1300–2003, sets of recurrence parameters (a and b values, M _max ) are estimated. Information on active faulting in Switzerland is too sparse to be used as source model. We develop instead two models of areal sources. The first oriented towards capturing historical and instrumental seismicity, the second guided largely by tectonic principles and express ing the alterative view that seismicity is less stationary and thus future activity may occur in previously quiet regions. To estimate three alterna tive a and b value sets and their relative weighting, we introduce a novel approach based on the modified Akaike information criterion, which allows us to decide when the data in a zone deserves to be fitted with a zone-specific b value. From these input parameters, we simulate synthetic earthquake catalogs of one-million-year duration down to magnitude 4.0, which also reflect the difference in depth distribution between the Alpine Foreland and the Alps. Using a specific predictive spectral ground motion model for Switzerland, we estimate expected ground motions in units of the 5% damped acceleration response spectrum at frequencies of 0.5–10 Hz for all of Switzerland, referenced to rock sites with an estimated shear wave velocity of 1,500 m/s² in the upper 30 m. The highest hazard is found in the Wallis, in the Basel region, in Graubünden and along the Alpine front, with maximum spectral accelerations at 5 Hz frequency reaching 150 cm/s² for a return period of 475 years and 720 cm/s² for 10,000 years. Electronic supplementary material The online version of this article (doi: ) contains supplementary material, which is available to authorized users.     

Rapid on-site peak ground acceleration estimation based on support vector regression and P-wave features in Taiwan

This study extracted some P-wave features from the first few seconds of vertical ground acceleration of a single station. These features include the predominant period, peak acceleration amplitude, peak velocity amplitude, peak displacement amplitude, cumulative absolute velocity and integral of the squared velocity. The support vector regression was employed to establish a regression model which can predict the peak ground acceleration according to these features. Some representative earthquake records of the Taiwan Strong Motion Instrumentation Program from 1992 to 2006 were used to train and validate the support vector regression model. Then the constructed model was tested using the whole earthquake records of the same period as well as the 2010 Kaohsiung earthquake with 6.4 M_L. The effects on the performance of the regression models using different P-wave features and different length of time window to extract these features are studied. The results illustrated that, if the first 3 s of the vertical ground acceleration was used, the standard deviation of the predicted peak ground acceleration error of the whole tested 15-years earthquake records is 20.89 gal.The length of time window could be shortened, e.g. 1 s, and the prediction error is slightly sacrificed, in order to prolong the lead-time before destructive S-waves reaches.     

Response of base-isolated buildings to random excitations described by the Clough-Penzien spectral model

The stationary response of base-isolated buildings subjected to earthquake excitation is studied. The frequency content of earthquake input is described by the Clough-Penzien spectral model. The response parameters of interest are (1) the root-mean-square (RMS) displacement σ_x of the basement relative to the foundation (i.e. shear deformation of the isolation system) and (2) the ratio (σ_a/σ_a0) of the RMS value of the absolute acceleration at the roof of the isolated structure over the corresponding value when the isolation system is locked. The variation of these response parameters with the effective frequency f₀ of the base-isolated structure is investigated. As input, earthquakes with moment magnitudes M = 7-3 and M = 6-0 are considered. The acceleration spectra corresponding to these two earthquake sizes have pronouncedly different frequency content over the frequency range 0–1-1–0 Hz which is of primary importance for base-isolated structures. An important conclusion that comes from these analyses is that confidence in the effectiveness of a base-isolated system should be based primarily on its capacity to absorb/dissipate energy and less on its influence in shifting the fundamental period of the structure out of the range of dominant earthquake energy.     

云南漾濞6.4级地震强地面运动三要素基本特征分析

2021年5月21日云南漾濞发生6.4级地震,中国数字化强震动观测网络在主震中捕获28组加速度数据。对84条三分向加速度记录进行常规处理,计算出对应的地震动参数,并绘制震中附近水平向PGA和PGV等值线图,结果显示其走向和形态与震后烈度调查结果相近。将实际观测的相对持时进行曲线回归,求得相关系数,并据此计算出T_d(5%～95%)持时对应的震源持续时间在10.22～13.06 s间,与震源破裂过程反演结果基本一致。再通过分析近场6个台站记录的加速度反应谱,并与抗震设计谱比较,总结此次地震的频谱特性,为该区域抗震设防提供参考依据。     

Freestanding block overturning fragilities: Numerical simulation and experimental validation

The overturning fragilities of symmetric and asymmetric freestanding blocks, ranging in height from 0.54 to 3.6 m and with height‐to‐width ratios ranging from 2.1 to 6.6, are determined numerically. A probabilistic formulation regularizes the overturning responses when exposed to earthquake‐like random‐vibration waveforms. The peak amplitude of the forcing excitation (peak ground acceleration or PGA) is parameterized as a function of the block size, block shape, overturning probability, and either the PGA normalized peak ground velocity (PGV/PGA), spectral acceleration at 1 s (S_a(1)/PGA), or spectral acceleration at 2 s (S_a(2)/PGA). These later intensity measures are correlated with the duration of the predominant acceleration pulse. The overturning fragilities are compared with shake table experiments using blocks ranging in height from ～0.2 to 1.2 m and with height‐to‐width ratios ranging from ～2 to 10. Excitations utilized in the shake table experiments include recordings of the 1979 Imperial Valley, 1985 Michoacan, 1999 Duzce, 1999 Chi‐Chi, and 2002 Denali Earthquakes along with synthetic waveforms. The overturning fragilities accurately represent the overturning responses of blocks with simple basal contact conditions. Objects with multiple rocking points, such as precariously balanced rocks, are more fragile than predicted. Nondestructive tilting tests are used to account for blocks with complex basal contact conditions, demonstrating that these blocks overturn similarly to more slender blocks with simple contact conditions. Copyright © 2008 John Wiley & Sons, Ltd.     

Inelastic spectra to predict period elongation of structures under earthquake loading

Period lengthening, exhibited by structures when subjected to strong ground motions, constitutes an implicit proxy of structural inelasticity and associated damage. However, the reliable prediction of the inelastic period is tedious and a multi‐parametric task, which is related to both epistemic and aleatory uncertainty. Along these lines, the objective of this paper is to investigate and quantify the elongated fundamental period of reinforced concrete structures using inelastic response spectra defined on the basis of the period shift ratio (T_in/T_el). Nonlinear oscillators of varying yield strength (expressed by the force reduction factor, R_y), post‐yield stiffness (a_y) and hysteretic laws are examined for a large number of strong motions. Constant‐strength, inelastic spectra in terms of T_in/T_el are calculated to assess the extent of period elongation for various levels of structural inelasticity. Moreover, the influence that structural characteristics (R_y, a_y and degrading level) and strong‐motion parameters (epicentral distance, frequency content and duration) exert on period lengthening are studied. Determined by regression analyses of the data obtained, simplified equations are proposed for period lengthening as a function of R_y and T_el. These equations may be used in the framework of the earthquake record selection and scaling. Copyright © 2015 John Wiley & Sons, Ltd.