Probabilistic analysis of peak response of MDOF systems with uncertain PSD function

The use of uniform hazard spectra which have the same probability of exceedance at different frequencies has been proposed for the future version of the National Building Code of Canada. Commonly used combination rules to estimate the peak responses of multi‐degree‐of‐freedom (MDOF) systems are the square root of sum of squares rule and the complete quadratic combination rule. However, the probability that the peak response of a MDOF system exceeds the one estimated by using these rules with the peak modal responses from the uniform hazard spectra cannot be inferred directly. The assessment of the probability of exceedance of the peak response of MDOF systems is presented by considering that the uncertainty in seismic excitation due to all potential earthquakes can be lumped in the power spectral density function of the ground acceleration with uncertain model parameters. This probability is evaluated based on the random vibration of linear systems and the first‐order reliability method. It is found that the under‐ or over‐estimations are less than about 5 or 10% if the modal contributions are not within 10–90% of, or not within 20–80% of, the absolute sum of the effective modal peak responses, respectively. Otherwise, severe under‐ or over‐estimation could result. Copyright © 2002 John Wiley & Sons, Ltd.     

Hazard mapping of normalized peak strain in soils during earthquakes: microzonation of a metropolitan area

Seismic hazard maps of the Los Angeles metropolitan area are illustrated for normalized peak strain and for 50 years of exposure. The strain estimates are based on scaling in terms of peak ground velocity. The proportionality factor is the phase velocity with which the wave energy is propagating. A simplified seismicity model is used in which all earthquakes occur on faults represented by buried lines and in one zone of diffused seismicity. Poissonian model of earthquake occurrence is assumed. The same model was used in the 1980's to illustrate a method for microzoning of the same area for response spectral amplitudes. Maps of logarithms of normalized peak strain, cε_max, are presented for probabilities of at least one exceedance p = 0·99, 0·9, 0·5, 0·1 and 0·01. These can be used to construct site specific probability distribution functions of the normalized peak strain, cε_max. Such maps are useful for design of new and for retrofit of existing structures, sensitive to strain and differential ground motions (bridges, tunnels, pipelines, etc.).     

Physical basis of earthquake magnitudes: an extreme value of seismic amplitudes from incoherent fracture of random fault patches

A relation between surface-wave magnitude M_s and fault area S for great earthquakes has been proposed

log S 2M_{s − 11.5 (}M_{s > 7.5)}

A similar formula has been also derived for body-wave magnitude m_b^* redetermined from maximum amplitudes of short-period P-wavetrains

log S ∝ 1.7 m_b^*

These are quite different from a theoretical relation expected on the basis of long-wave approximation. Because wavelengths of seismic waves used for the above magnitudes are very short compared to the size of earthquake sources, these relations represent the short-period nature of the earthquake process. The statistical theory of extreme values has been applied to understand the relations considering that the component waves which constitute the wavetrains for m_b^* and M_s determinations originate from the random fracture of fault heterogeneities.     

A note on distribution of amplitudes of peaks in structural response including uncertainties of the exciting ground motion and of the structural model

This note is an extension of earlier works that presented probability distribution functions for amplitudes of the peaks (the highest, the second highest … the m-th highest) in response of deterministic single degree-of-freedom (SDOF) and multi degree-of-freedom (MDOF) structures to ground motion, with deterministic Fourier spectrum and duration. It shows how these probability distribution functions can be evaluated if the Fourier spectrum and duration of the excitation are random variables specified via distribution functions. Two cases are considered: (l) when the structural model is deterministic, and (2) when the modal frequencies are random variables. The procedure presented here approximates the transfer function of the structural response by Dirac delta functions at the modal frequencies, and is applicable to multi-storey buildings with small modal damping, and with natural frequencies that are not too close. The resulting probability distribution functions are needed in seismic hazard calculations of peak response amplitudes of SDOF and MDOF structures that will not be exceeded with given confidence during the service time of the structure from any earthquake at all known faults within certain distance from the structure.     

吉林台水电站坝址人造地震动研究

为满足水库抗震设计的震要,合成了５０年超越概率５％和１００年超越概率２％的基岩加速度时程曲线,考虑到吉林吉台电站所处的特殊地震环境和场地条件,分析其地震危险性认为：５０年超越概率５％的地震动为远震影响;１００年超越概率２％的地震动为近震影响,目前使用的基岩加带度反应谱衰关于关系的来源资料多少丢失一些高频成分,可能低估高频成分的地震动对基岩场地的影响,为此根据大震,远震的特征周期Ｔｇ较大这一规律,把两个概率水平的加速度反应谱的特征周期Ｔｇ都定为０．３ｓ,并增加基岩反应谱高频成分控制,从而把基岩地震加速度反应谱处理成相应的规准谱,在此基础上通过拟合规准谱合成的基岩地震动时程曲线,较好地满足坝址的设防要求。     

鄂尔多斯周缘地区中强震发生前地震矩加速释放时空特征

为研究鄂尔多斯周缘地区中强地震发生前地震矩加速释放时空特征,选取去丛集后的地震目录,基于地震矩释放程度m值,对1981年以来鄂尔多斯周缘地区10例MS≥5.5中强地震进行二维时空扫描,提取与地震矩加速释放特征相关的时空尺度作为矩释放程度时空扫描模型参数,以3个月为扫描步长,对震前12个月m值及累积Benioff应变释放进行拟合计算。结果显示,震前破裂成核点附近存在显著的AMR现象,7次震例存在累积Benioff应变加速释放特征,说明鄂尔多斯周缘地区MS≥5.5地震发生前AMR现象存在一定普遍性,应用矩加速时空扫描方法具有一定优势,但仍需结合其他方法进行综合分析。     

Site effect on vulnerability of high-rise shear wall buildings under near and far field earthquakes

Worldwide experience repeatedly shows that damages in structures caused by earthquakes are highly dependent on site condition and epicentral distance. In this paper, a 21-storey shear wall-structure built in the 1960s in Hong Kong is selected as an example to investigate these two effects. Under various design earthquake intensities and for various site conditions, the fragility curves or damage probability matrix of such building is quantified in terms of the ductility factor, which is estimated from the ratio of storey yield shear to the inter-storey seismic shear. For high-rise buildings, a higher probability of damage is obtained for a softer site condition, and damage is more severe for far field earthquakes than for near field earthquakes. For earthquake intensity of VIII, the probability of complete collapse (P) increases from 1 to 24% for near field earthquakes and from 1 to 41% for far field earthquakes if the building is moved form a rock site to a site consisting a 80 m thick soft clay. For intensity IX, P increases from 6 to 69% for near field earthquake and from 14 to 79% for far field earthquake if the building is again moved form rock site to soft soil site. Therefore, site effect is very important and not to be neglected. Similar site and epicentral effects should also be expected for other types of high-rise structures.     

Effect of structural characteristics distribution on strength demand and ductility reduction factor of MDOF systems considering soil-structure interaction

It is known that structural stiffness and strength distributions have an important role in the seismic response of buildings.The effect of using different code-specified lateral load patterns on the seismic performance of fixed-base buildings has been investigated by researchers during the past two decades.However,no investigation has yet been carried out for the case of soil-structure systems.In the present study,through intensive parametric analyses of 21,600 linear and nonlinear MDOF systems and considering five different shear strength and stiffness distribution patterns,including three code-specified patterns as well as uniform and concentric patterns subjected to a group of earthquakes recorded on alluvium and soft soils,the effect of structural characteristics distribution on the strength demand and ductility reduction factor of MDOF fixed-base and soil-structure systems are parametrically investigated.The results of this study show that depending on the level of inelasticity,soil flexibility and number of degrees-of-freedoms(DOFs),structural characteristics distribution can significantly affect the strength demand and ductility reduction factor of MDOF systems.It is also found that at high levels of inelasticity,the ductility reduction factor of low-rise MDOF soil-structure systems could be significantly less than that of fixed-base structures and the reduction is less pronounced as the number of stories increases.     

Accounting for site effect in probabilistic assessment of seismic hazard for Romania and Bucharest: a case of deep seismicity in Vrancea zone

The paper presents recent achievements in evaluations of site-dependent seismic hazard in Romania and the capital city of Bucharest caused by the Vrancea focal zone (SE-Carpathians). The zone is characterized by a high rate of occurrence of large earthquakes in a narrow focal volume at depths 60–170 km. The database that was used for the hazard evaluation includes parameters of seismicity, ground-motion source scaling and attenuation models (Fourier amplitude spectra), and site-dependent spectral amplification functions. Ground-motion characteristics were evaluated on the basis of several hundred records from more than 120 small magnitude (M 3.5–5) earthquakes occurred in 1996–2001 and a few tens of acceleration records obtained during four large (M 7.4, 7.2, 6.9 and 6.3) earthquakes. The data provide a basis for probabilistic seismic hazard assessment in terms of peak ground acceleration, peak spectral acceleration and MSK intensity using Fourier amplitude spectra for various exceedance probabilities or average return periods. It has been shown that the influence of geological factors plays very important role in distribution of earthquake ground-motion parameters along the territory of Romania.     

中国东北和朝鲜半岛地区地壳Lg波宽频带衰减模型

利用1996年10月至2016年10月间发生在中国东北、朝鲜半岛和日本南部的113个壳内地震在602个宽频带地震台站观测到的波形资料,建立Lg波衰减成像数据集.根据22,551条垂直分量波形,计算Lg波振幅谱,提取单台、双台和双事件数据,采用区域Q值、震源函数和台基响应联合反演方法,建立中国东北和朝鲜半岛地区0.05~10.0 Hz的宽频带衰减模型.模型显示火山岩山脉地区如大兴安岭和长白山具有弱衰减特征,沉积盆地衰减相对较强,海水覆盖区域如渤海、黄海和日本海等衰减最强.日本海具有较薄的海洋地壳,对地壳Lg波传播有阻挡作用.通过较大地震事件的跨海记录调查Lg波的传播,强衰减特征最为显著.

     

岩石加速破裂行为的物理自相似律

掌握岩石变形破坏过程中体积膨胀点至峰值强度点之间加速破裂行为的演化规律,是实现地质灾害物理预测的关键.本文考虑裂纹张开和闭合两种情况,基于断裂力学建立了三轴应力作用下裂纹扩展临界尺度与等效应力的关系.对微元体破坏概率,分别采用以等效应力表达的Weibull分布函数和裂纹尺度分形函数,通过对比导出了形状参数m与裂纹分布分维D_f关系的表达式.一个有趣的发现是,岩石峰值强度点与体积膨胀点应变比仅与m或D_f有关.对岩石蠕变或准蠕变破坏,合理的m值范围为[1.0,4.0],在此范围内应变比近似为常数1.48,该常数是描述不同尺度岩石加速破裂规律的物理自相似常数.实例分析表明,基于岩石加速破裂规律构建的多锁固段脆性破裂理论,其适用性广,尤其在崩滑和大地震预测领域,具有良好应用前景.此外,本文给出了b值与m值定量关系,以解释b值的物理意义,并探讨将其用于地震预测的可行性.     

Simulation of digital earthquake accelerograms using the inverse discrete Fourier transform

Acceleration time histories of horizontal earthquake ground motion are obtained by inverting the discrete Fourier transform, which is defined by modelling the probability distribution of the Fourier phase differences conditional on the Fourier amplitude. The Fourier amplitude spectrum is modelled as a scaled, lognormal probability density function. Three parameters are necessary to define the Fourier amplitude spectrum. They are the total energy of the accelerogram, the central frequency, and the spectral bandwidth. The Fourier phase differences are simulated conditional on the Fourier amplitudes. The amplitudes are classified into three categories: small, intermediate and large. For each amplitude category, a beta distribution or a combination of a beta distribution and a uniform distribution are defined for the phase differences. Seven parameters are needed to completely define the phase difference distributions: two for each of the three beta distributions, and the weight of the uniform distribution for phase differences corresponding to small Fourier amplitudes. Approximately 300 uniformly processed horizontal ground motion records from recent California earthquakes are used to develop prediction formulas for the model parameters, as well as to validate the simulation model. The moment magnitude of the earthquakes ranges from 5.8 to 7.3. The source to site distance for all the records is less than 100 km. Copyright © 2002 John Wiley & Sons, Ltd.     

地震大小的度量

本文首先对地震大小度量的研究历程作了简要回顾。在此基础上着重指出以下几点: ① 近几十年广泛使用的M_L、m_b(m_B)、M_S震级标度,作为对地震大小的度量,不仅都存在着“以偏概全”和“震级饱和”的问题,而且由于未充分顾及地震波衰减的区域差异,尤其台站场地对地震动放大作用的差异,因此都只是对地震大小的不精确的度量。 ② 地震矩M₀不仅物理含义明确,而且克服了M_L、m_b(m_B)、M_S震级标度所存在的各种问题,是最适合科学度量地震大小的物理量。为了继续延用“震级”这一术语,Kanamori定义了矩震级标度M_W,虽然其假定的前提条件仍有待研究,但也是对地震相对大小的较合理的度量。 ③ 为更加科学地度量地震的大小,必须充分利用现代区域数字地震台网产出的大量波形数据,加强地震波衰减特征、场地效应和震源参数测定及有关定标关系的研究,在完善M_L、m_b(m_B)、M_S震级测定方法的基础上,重点改进、完善M_W标度,逐渐推进以M_W作为统一度量地震相对大小的物理量,为地震科学研究和地震预测研究奠定更加坚实的基础。     

Earthquake hazard in Marmara Region, Turkey

Earthquake hazard in the Marmara Region, Turkey has been investigated using time-independent probabilistic (simple Poissonian) and time-dependent probabilistic (renewal) models. The study culminated in hazard maps of the Marmara Region depicting peak ground acceleration (PGA) and spectral accelerations (SA)'s at 0.2 and 1 s periods corresponding to 10 and 2% probabilities of exceedance in 50 yrs. The historical seismicity, the tectonic models and the known slip rates along the faults constitute the main data used in the assignment. Based on recent findings it has been possible to provide a fault segmentation model for the Marmara Sea. For the main Marmara Fault this model essentially identifies fault segments for different structural, tectonic and geometrical features and historical earthquake occurrences. The damage distribution and pattern of the historical earthquakes have been carefully correlated with this fault segmentation model. The inter-event time period between characteristic earthquakes in these segments is consistently estimated by dividing the seismic slip estimated from the earthquake catalog by the GPS-derived slip rate of 22±3 mm/yr. The remaining segments in the eastern and southern Marmara region are also identified using recent geological, geophysical studies and historical earthquakes. The model assumes that seismic energy along the segments is released by characteristic earthquakes. For the probabilistic studies characteristic earthquake based recurrence relationships are used. Assuming normal distribution of inter-arrival times of characteristic earthquakes, the ‘mean recurrence time’, ‘covariance’ and the ‘time since last earthquake’ are developed for each segment. For the renewal model, the conditional probability for each fault segment is calculated from the mean recurrence interval of the characteristic earthquake, the elapsed time since the last major earthquake and the exposure period. The probabilities are conditional since they change as a function of the time elapsed since the last earthquake. For the background earthquake activity, a spatially smoothed seismicity is determined for each cell of a grid composed of cells of size 0.005°×0.005°. The ground motions are determined for soft rock (NEHRP B/C boundary) conditions. Western US-based attenuation relationships are utilized, since they show a good correlation with the attenuation characteristics of ground motion in the Marmara region. The possibility, that an event ruptures several fault segments (i.e. cascading), is also taken into account and investigated by two possible models of cascading. Differences between Poissonian and renewal models, and also the effect of cascading have been discussed with the help of PGA ratio maps.     

Use of Seismotectonic Information for the Seismic Hazard Analysis for Surat City, Gujarat, India: Deterministic and Probabilistic Approach

Surat, the financial capital of Gujarat, India, is a mega city with a population exceeding five millions. The city falls under Zone III of the Seismic Zoning Map of India. After the devastating 2001 Bhuj earthquake of Mw 7.7, much attention is paid towards the seismic microzonation activity in the state of Gujarat. In this work, an attempt has been made to evaluate the seismic hazard for Surat City (21.170?N, 72.830?E) based on the probabilistic and deterministic seismic hazard analysis. After collecting a catalogue of historical earthquakes in a 350?km radius around the city and after analyzing a database statistically, deterministic analysis has been carried out considering known tectonic sources; a further recurrence relationship for the control region is found out. Probabilistic seismic hazard analyses were then carried out for the Surat region considering five seismotectonic sources selected from a deterministic approach. The final results of the present investigations are presented in the form of peak ground acceleration and response spectra at bed rock level considering the local site conditions. Rock level Peak Ground Acceleration (PGA) and spectral acceleration values at 0.01?s and 1.0?s corresponding to 10% and 2% probability of exceedance in 50 years have been calculated. Further Uniform Hazard Response Spectrum (UHRS) at rock level for 5% damping, and 10% and 2% probability of exceedance in 50 years, were also developed for the city considering all site classes. These results can be directly used by engineers as basic inputs in earthquake-resistant design of structures in and around the city.     

震级变异系数与地震序列类型、 性质的统计物理特征和早期判定方法的研究

根据G-R公式和非线性动力学观点, 在分析不同类型地震序列震级分布细结构基础上, 提出用震级变异系数δ_m、 b值和震级熵H(m)、 马尔柯夫链理论值h和信息量维数D₁等统计量, 来综合描述和界定不同类型、 性质的地震序列; 同时对截止震级问题、 b值、 平均震级m、 h和D₁等统计物理含义进行了探讨。 认为δ_m、 b值和H(m)及其与理论指数分布的震级熵H(∞)的差值ΔH(m)相结合将有助于区分前震序列、 前兆性震群和各种不同类型(主-余震型、 震群型、 孤立型)地震序列, 并且可以对这些类型进行早期判断。     

Generalized conceptual modeling of dimensionless overland flow hydrographs

The rising and recession limbs of conceptual dimensionless overland flow hydrographs are calculated for specific values of the rating exponent in the range 1 ≤ m ≤ 3, including a linear reservoir (m = 1); 100% turbulent Chezy friction (m = 3/2); 100% turbulent Manning friction (m = 5/3); 67% turbulent Chezy (or 75% turbulent Manning) (m = 2); and 100% laminar flow (m = 3). These conceptual overland flow hydrographs show finite amounts of diffusion, increasing with decreasing rating exponent, unlike the kinematic wave hydrograph, which is nondiffusive.     

湖南中强地震活动地区Ⅱ类场地放大效应研究

利用工程场地地震安全性评价工作中大量实际钻孔和土工实验资料,建立了实际工程场地模型,在50年超越概率为63%、10%、2%共3种地震动输入下,采用SHAKE91和ELSSRA两种等效线性化方法,研究了湖南省Ⅱ类场地土层的放大效应.计算结果表明:湖南省50年超越概率10%的场地效应放大因子为1.30,若使用<中国地震动参数区划图(GB18306-2001)>认定的1.25系数,将低估湖南中强地震活动地区的场地放大效应.湖南省50年超越概率63%、10%、2%这3个设定水准的场地效应放大因子满足1.10:1.00:0.95的关系.这些结果有益于为湖南省提供更为合理的抗震设防标准.     

华北地区强震活动特点研究

华北地区是我国的政治、经济和文化中心,也是我国地震多发地区之一。华北地区历史地震资料记载时间较早且较为连续,是研究我国强震活动的理想试验场。选取第三、第四活动期M≥6.0地震目录作为基础资料研究华北地区强震活动特点。首先探讨华北地区强震活动与活动地块、边界带的关系,然后从时间和空间上分析华北地区强震活动的轮回性阶段及其期幕活动特点,最后计算未来5年华北地区发生下一次M≥6.0地震的累积概率和条件概率。研究结果表明:①华北地区M≥6.0地震活动主要集中在活动地块的边界带,M≥7.0地震则全部发生在活动地块的边界带上,同时华北地区地震应变释放速率与边界带的构造活动速率呈线性相关;②第四活动期各活跃幕的能量释放均低于第三活动期,因此华北地区未来仍可能发生M≥6.0地震;③第三、第四活动期的主体活动区存在显著差异,且第四活动期的强震活动较第三活动期向东迁移;④在2020年年初发生第四活动期闭幕M≥6.0地震的累积概率为80%左右,而在2022年年底前发生M≥6.0地震的条件概率为50%。本研究可为华北地区地震大形势分析和中长期地震危险性预测提供重要参考。