Empirical equations for the prediction of the equivalent number of cycles of earthquake ground motion

Estimates of the number of cycles of ground motion expected from earthquake scenarios are required for the assessment of liquefaction hazard and the hazard of seismically induced landslides. There are currently very few equations available for the prediction of this parameter despite its importance for several geotechnical applications. In this study, the strong-motion database assembled in the Next Generation of Attenuation (NGA) project is used to derive equations for two different measures of the effective numbers of cycles of ground motion as functions of magnitude, distance, and site classification. There are several different measures of the numbers of cycles in an accelerogram but the definition adopted in this study is that based on rainflow-counting, which is applied with both absolute and relative amplitude thresholds.     

The effective number of cycles of earthquake ground motion

The seismic response of any system that accumulates damage under cyclic loading is dependent not only on the maximum amplitude of the motion but also its duration. This is explicitly recognized in methods for estimating the liquefaction potential of soil deposits. Many researchers have proposed that the effective number of cycles of the ground motion is a more robust indicator of the destructive capacity of the shaking than the duration. However, as is the case with strong‐motion duration, there is no universally accepted approach to determining the effective number of cycles of motion, and the different methods that have been proposed can give widely varying results for a particular accelerogram. Definitions of the effective number of cycles of motion are reviewed, classified and compared. Measurements are found to differ particularly for accelerograms with broad‐banded frequency content, which contain a significant number of non‐zero crossing peaks. The key seismological parameters influencing the number of cycles of motion and associated equations for predicting this quantity for future earthquakes are identified. Correlations between cycle counts and different duration measures are explored and found to be rather poor in the absence of additional parameters. Copyright © 2004 John Wiley & Sons, Ltd.     

砂土震陷分析中多维地震荷载等效循环周数计算

借助有限元数值方法模拟不同砂土试样在多向和单向地震荷载输入条件下的动三轴试验,选取覆盖大震、中震、近场、远场及不同土质条件的155组多向地震输入时程对不同砂土试样分别进行单向和多向加载,建立考虑多向地震荷载作用的等效循环周数计算方法,并研究震级、震中距和砂土特性对等效循环周数比的影响。研究表明,震级和震中距对等效循环周数比影响不明显,砂土特性对等效循环周数比的影响具有主导作用,砂土相对密度为45%、60%、80%和100%时,其对应的等效循环周数比均值分别为1.58、1.75、1.93和2.08,相对密度越大,比值越大,结合该比值,可以较好地应用文中提出方法进行多维地震荷载等效循环周数计算。     

Defining equivalent stationary PSDF to account for nonstationarity of earthquake ground motion

This paper presents three approaches to defining the stationary power spectrum density function (PSDF) of strong ground acceleration, for prediction of structural response corresponding to the strong-motion stationary part of the input excitation. The first approach defines the PSDF in terms of the Fourier amplitude spectrum and a stationary duration of ground acceleration. The PSDF obtained by this approach predicts accurately the response of structures with low to intermediate natural periods. In the second approach, we introduce the concept of stationary duration of response, which is defined as a function of the natural period and damping ratio of the oscillator. Using this approach, it is possible to get accurate estimates of response amplitudes for the broad range of natural periods. However, it is not convenient in practical applications to deal with several stationary durations for a given input excitation. Further, to evaluate these durations it is necessary to specify both the Fourier and the response spectra of ground accelerations; whereas the common engineering practice is to specify the response spectrum only. Therefore, the third approach suggests the use of the response ‘spectrum compatible’ PSDF. The paper presents several improvements in the general methodology used for this purpose. The improvements mainly relate to using more accurate peak factors and to using the transient nature of response. The spectrum compatible PSDFs, as evaluated in the present study, provide realistic specification of strong ground motion for stochastic seismic response analyses of structures.     

Prediction of sunspot number amplitude and solar cycle length for cycles 24 and 25

The prediction of solar activity strength for solar cycles 24 and 25 is made on the basis of extrapolation of sunspot number spectral components. Monthly sunspot number data during the 1850–2007 interval (solar cycles 9–23) are decomposed into several levels and searched for periodicities by iterative regression in each level. For solar cycle 24, the peak is predicted in November 2013 with a sunspot number of 113.3. The cycle is expected to be weak, with a length of 133 mo (months) or 11.1 yr. The sunspot number maximum in cycle 25 is predicted to occur in April 2023 with a sunspot number 132.1 and a solar cycle length of 118 mo or 9.8 yr. Thus, solar cycle 24 is predicted to have an intensity 23% lower than cycle 23, and cycle 25 will be 5% lower than cycle 23.     

2007年宁洱MS6.4地震的地面运动预测

根据普洱、 西双版纳地区6个地震观测台站在2008——2009年获取的5级以上的地震资料, 利用接收函数和面波衰减系数, 反演得到了研究区域的S波速度结构和Qβ结构. 基于该结构模型, 采用随机振动理论方法, 预测了2007年宁洱MS6.4地震发生后, 在震中距为10——300 km范围内引起的地面运动, 并借助获取的强震观测记录检验、 评价了该预测结果. 同时, 将地面运动预测结果与利用回归衰减公式计算得到的结果进行对比, 进而讨论该地震动预测方法在地面运动预测中的可行性． 结果表明, 该预测结果与实测结果吻合．      

Prediction of ground motion in the Osaka sedimentary basin associated with the hypothetical Nankai earthquake

We studied the long-period ground motions in the Osaka sedimentary basin, Japan, which contains a 1- to 3-km thickness of sediments and is the site of many buildings or construction structures with long-natural period. We simulated the broadband ground motions likely to be produced by the hypothetical Nankai earthquake: the earthquake expected to give rise to the most severe long-period ground motion within the basin. For the simulation, we constructed multiscale heterogeneous source models based on the Central Disaster Management Council of Japan (CDMC) source model and adopted a hybrid computation method in which long-period motion and short-period motion are computed using a 3-D finite difference method and the stochastic Green’s function method, respectively. In computing long-period motions, we used a 3-D structure model of the crust and the Osaka sedimentary basin. The ground motions are estimated to have peak velocities of 50–90 cm/s, prolonged durations exceeding 300 s, and long predominant periods of 5–10 s in the area with great thickness of sediments. The predominant periods are in agreement with an approximate evaluation by 4 H/V _s where H and V _s are the thickness of the sediment and the average S wave velocity, respectively.     

Prediction of the median IDA curve by employing a limited number of ground motion records

A methodology has been proposed which can be used to reduce the number of ground motion records needed for the reliable prediction of the median seismic response of structures by means of incremental dynamic analysis (IDA). This methodology is presently limited to predictions of the median IDA curve only. The reduction in the number of ground motion records needed to predict the median IDA curve is achieved by introducing a precedence list of ground motion records. The determination of such a list is an optimization problem, which is solved in the paper by means of (1) a genetic algorithm and (2) a proposed simple procedure. The seismic response of a simple, computationally non‐demanding structural model has been used as input data for the optimization problem. The presented example is a three‐storey‐reinforced concrete building, subjected to two sets of ground motion records, one a free‐field set and the other a near‐field set. It is shown that the median IDA curves can be predicted with acceptable accuracy by employing only four ground motion records instead of the 24 or 30 records, which are the total number of ground motion records for the free‐field and near‐field sets, respectively. Copyright © 2007 John Wiley & Sons, Ltd.     

地震动加速度过程的小波模拟

本文应用基数B－样条小波模拟地震动加速度过程，将小波分析引入地震动加速度过程的研究，实现了地震动加速度的模拟，并可给出其解析表达式，便于设计地震动的调整及地震反应的求解。     

Simulation of risk-consistent earthquake motion

A method to combine probabilistic seismic hazard analysis and stochastic earthquake motion models is presented. A set of parameters characterizing stochastic earthquake motion models is determined on a consistent probabilistic basis. The method proposed herein consists of two steps. First, the ground motion intensity is determined in the context of the conventional hazard curve technique. Next, other ground motion parameters such as duration, predominant frequency and spectral shape parameters are determined as conditional means corresponding to the annual probability of exceedance for the ground motion intensity. Some example applications are presented.     

Stochastic earthquake source model for ground motion simulation

In the analysis and design of important structures with relatively long life spans, there is a need to generate strong motion data for possible large events. The source of an earthquake is characterized by the spatial distribution of slip on the fault plane. For future events, this is unknown. In this paper, a stochastic earthquake source model is developed to address this issue. Here, 1D and 2D stochastic models for slip distribution developed by Lavallée et al.(2006) are used. The random field associated with the slip distribution is heavy-tailed stable distribution which can be used for large events. Using 236 past rupture models, the spectral scaling parameter and the four stable or Levy's parameters against empirical relationship for known quantities like magnitude or fault length are developed. The model is validated with data from 411 stations of 1999 Chi-Chi earthquake. The simulated response spectrum showed good agreement to actual data. Further the proposed model is used to generate ground motion for the 1993 Killari Earthquake where strong motion data is not available. The simulated mean peak ground velocity was in turn related to the intensity(MSK) and compared against values in the literature.     

确定结构基底等效输入地震动的简化方法

本文用理论和实例计算分析了土与结构间的动力相互作用。根据基底等效输入的地震动相对入射地震动的传递函数特点研究出了一种等效输入的方法，该方法比较好地反映了场地和结构的动力特性对基底等效输入的影响。为利用刚性基底假设理论来分析土-结构动力相互作用提供了一种方法。     

地震动强度对场地地震反应的影响

通过对场地地震反应的研究发现,地震动强度不同,同样的场地对地震动的影响也不同,得到的反应谱形状也不同。目前我国抗震设计规范中不同烈度下的设计反应谱形状完全一致,没有考虑地震动强弱对相同场地反应谱形状的影响。     

Site-dependent models of earthquake ground motion

Random vibration analyses of structural systems subjected to seismic loading are dependent upon the characterization of earthquake ground motion as a stochastic process. The response of structural systems to earthquakes is dependent strongly on the local geological conditions, which should be incorporated into seismological models of ground motion. In the study presented herein, three previously developed ground-motion models are adapted to incorporate site-dependent characteristics. Records obtained from two recording stations in California are used as a basis for the ground-motion models. Single-degree-of-freedom (SDOF) oscillators are subjected to ensembles of accelerograms generated from these models, and both elastic and inelastic response are considered. Response statistics are compared to those generated by the analysis of structural response to ensembles of recorded motion from the two sites. The important features of the ground motion for effective reproduction of response statistics are identified, and observations are made on the sensitivity of specific response parameters to site-dependent characteristics of the ground motion.     

Dynamic equivalent soil characteristics identification using earthquake records

Techniques for soil property estimation can be categorized into two main groups, in-situ and laboratory methods. Previous investigations indicated that strong ground motions record provides a very useful tool to estimating the in-situ characteristics of soil. The main objective of the present work is to utilize the particle swarm optimization algorithm(PSOA) integrated with linear site response method to obtain the equivalent soil profile characteristics from the available surface and bedrock earthquake motion records. To demonstrate the numerical efficiency and the validity of this approach, the procedure is validated against an available case. Then this procedure is utilized to identify the soil properties profiles of the site by using strong ground motions data recorded during the Bam earthquake of December 26, 2003. The magnitude and PGA of Bam earthquake were MW 6.6 and 0.8 g respectively.     

地震动加速度过程的四阶基数B—样条小波模拟

应用四阶基数B-样条小波来模拟地震动加速度过程，将小波分析引入了地震动加速度过程的研究。     

对若干地震动包线函数的比较分析

对已经提出的四种经常使用的包线函数模型进行了评价,认为对于评价单峰点包线函数,除了要求形式简单以外,其优劣可以用函数对峰点位置和高峰隆起程度的控制能力作为标准。借助结构动力试验中阻尼比的确定方法,提出用平稳度指数来评价单峰点包线函数平缓程度。据此对四种包线函数的平稳度进行了分析,还对某些包线函数提出了一些改进。通过分析指出如果把“金井清谱”和“Penzien谱”等模型,看作是时间域中包线,这两个模型的调节能力都很强,而且比较方便,其中“Penzien谱”模型可以用来表示具有两个峰点的包线。文中的比较分析结果可以用于地震动包线函数选择和模拟。     

大震速报所选台数与新疆地震编目结果的对比

在最短的时间内,准确的报出地震三要素,是速报工作的关键.经过对所选的速报地震进行分析定位后,发现在速报中,所选台数是至关重要的,在以包围震中为原则的前提下,一般网内与网缘地震所选台数在7个台,网外地震所选台数在7～9个台,这样的速报结果与新疆地震目录结果最为接近.     

Estimating the number of blasts in the Dushanbe-Vakhsh earthquake catalog

The daily periodicity in four regions of the Dushanbe–Vakhsh area is analyzed. The study considers representative, nonrepresentative, and intermediate-energy earthquakes. Analysis of the specific features of the shape of the diurnal variation on workdays and weekends make it possible (1) to reliably conclude that the anomalous daily variation on workdays in medium-energy earthquake samplings is of technogenic origin and (2) suggest similarities in samplings of the weakest and strongest earthquakes. Apparently, the catalog includes a large number of industrial blasts. The number of blasts in earthquake samplings of various epochs and energies is estimated.     

改进的 Clough-Penzien地震地面运动模型

简要介绍了Kanai-Tajimi模型、Clough-Penzien模型和改进的Kanai-Tajimi模型。基于Clough-Penzien和改进的Kanai-Tajimi模型，提出了改进的Clough-Penzien模型。利用拉普拉斯变换。导出了改进的Clough-Penzien模型。比较了Kanal-Tajimi模型、Clough-Penzien模型和改进的Kanai-Tajimi模型和改进的Clough-Penzien模型的统计特性。