土层时域分析中黏滞阻尼形式的比较

时域分析中采用粘滞阻尼反映小应变条件下土的阻尼特性,瑞雷阻尼则是常用的黏滞阻尼形式。本文基于有限差分方法,构建一组数值计算模型,以实际地震记录作为输入,以不同的土层条件作为分析对象,采用加速度、位移和反应谱指标评价了瑞雷阻尼形式对土层地震反应的影响,并将不同阻尼形式下的计算结果与响嘡台阵真实记录进行了对比分析。计算结果表明:阻尼形式对加速度反应和反应谱的影响显著,对位移反应影响有限,但位移幅值沿土层高度的变化规律较复杂;不同阻尼形式时反应谱短周期段的谱值差别明显,而对反应谱长周期段谱值影响有限;高频地震动激励,深软土层中不同阻尼形式的计算结果离散性大;在确定阻尼形式时要综和考虑土层特征和地震动频谱特性,只考虑土层卓越频率的阻尼形式会低估土层地震反应。对于长周期地震动输入,本文建议目标频率取土层第3阶频率,对于高频地震动,目标频率可取为反应谱峰值对应频率。     

土-结构相互作用效应对结构基底地震动影响的试验研究

利用土与结构动力相互作用振动台模型试验数据,通过各种试验工况下土层表面与基础表面加速度反应的比较,深入探讨了土与结构动力相互作用效应对高层建筑结构基底地震动的影响。从输入地震动频谱特性、输入地震动强度水平和上部结构动力特性3个方面详细分析了与SSI效应对高层建筑基底震动影响程度有关的一些因素。结果表明：SSI效应对高层建筑基底地震动的影响与输入地震波的动力特性有很大关系。在地震动的频谱成分方面,SSI效应对高层建筑基底地震动的影响主要体现为土层表面和基础表面在与输入地震动卓越频率相近处的频谱成分有较大差异;SSI效应对高层建筑基底地震动的影响程度随着输入加速度峰值水平的增加而减小;在某一特定地震波作用下,当上部结构的振动频率与地震地面运动的卓越频率相近时,SSI效应对高层建筑基底地震动的影响较为强烈。     

深厚场地地震响应中阻尼矩阵形式的影响分析

深厚覆盖土层地震响应时域分析中阻尼矩阵形式的选取十分重要。本文基于滞后阻尼比和振型阻尼比构造了6种不同的比例阻尼矩阵形式,研究其对深覆盖土层地震响应的影响。以上海某一实际深厚覆盖土层为算例,分别以人工合成基岩地震波、汶川地震时上海佘山记录的基岩地震波为输入,得到6种阻尼矩阵形式下不同深度处的土层地震响应,并以频域解为基准解进行比较。研究结果表明,阻尼矩阵形式对加速度结果的影响程度比位移结果要大,运用同一种阻尼矩阵形式所得结果误差和输入地震波频谱特性有关。地震波自身的频谱特征对阻尼矩阵形式的选取有一定影响,建议综合考虑地震波的频谱特征和场地土层特性来构建合适的阻尼矩阵以获得合理的结果。     

基于场地效应的地震动特性研究

为了研究强地震作用下,场地类别对于地震动幅频特性的影响,本文统计了3 579条日本地震动的时程,并针对场地类别的不同,分别从基岩和土层的峰值加速度幅值特性角度,以及从标准化反应谱和平均加速度反应谱等频谱特性的角度研究其幅频衰减特性,最后给出了各类场地峰值加速度衰减曲线。结果表明,土层对于地震动幅值和频谱的放大作用会随着场地类别的变软而增加,并且场地越软,远场的长周期特性越明显。利用平均加速度反应谱可以有效地反映频谱中的长周期成分。     

一种深厚覆盖层场地地震动参数的确定方法

基于欧美规范确定了坐落在深厚覆盖层上KH抽水蓄能电站上、下库场地基本运行和最大设计地震动峰值加速度、反应谱和时程等动参数。首先依据场地区域地震烈度区划图、特征周期区划图和依据场地地质地震条件选取的5条种子实测地震动确定场地基岩输入加速度时程、峰值加速度和设计反应谱,进而基于各土层地质参数和一维弹性波传播模拟程序确定覆盖层表面的平均峰值加速度、平均反应谱和5条地震动时程,对所得到的平均反应谱和峰值加速度进行光滑处理后确定可用于各建筑物结构抗震设计的地震动参数,包括覆盖层表面水平向动力响应加速度时程、峰值加速度和设计反应谱。该方法可较好地保留输入地震动的真实动力特性,如持时、相位和频率等,为我国规范中建议的确定场地地震动参数的方法提供有益的补充。     

北京地区中硬场地对地震动加速度反应谱的放大效应研究

当前,合理确定地震动峰值加速度与反应谱特征周期是工程场地地震动参数确定工作的主要内容。本文以北京地区典型中硬场地为研究对象,分析场地条件对不同周期地震动反应谱值的影响。首先,计算不同震级、震中距条件下的基岩地震动加速度反应谱,合成基岩输入地震动时程;再利用110个工程场地的钻孔资料进行土层地震反应计算,分析中硬场地条件对不同输入环境下的地震动加速度反应谱值的放大效应。结果表明,中硬场地对高、中频震动放大效应明显,尤其是对0.2-0.5s周期段地震动加速度反应谱值的放大倍数大多在1.3以上;场地覆盖层厚度变化对不同频段地震动加速度反应谱值的放大倍数所产生的影响是不同的,与场地自振周期的相关性很强;在不同的地震动输入环境下,中硬场地对不同频段地震动加速度反应谱的影响是不同的,这一结论对实际的抗震设防工作具有一定参考价值。     

古田地震水口水电站重力坝强震观测记录的谱结构特征

通过对水口水电站重力坝强震反应台站在古田地震中获取的强震反应观测资料进行信噪比、反应谱和功率谱分析,得到如下结论:①大坝在0.7～15 Hz频率段的振动特性较为可信;②坝基和自由场输入地震动富于高频,峰值加速度反应谱存在较大差异;③坝基输入地震动存在差异性,建议今后此类大坝抗震设计时考虑多点地震动输入;④单个卓越频率携带的能量对反应谱影响不大,反应谱是和输入地震动总能量相关的;⑤坝体刚度较大,此次地震中还处于线弹性状态。初步了解了强震记录的地震动特性和大坝结构的抗震性能,对认识水库地震近场地震动特性和重力坝地震反应有一定的参考意义。     

场地条件对地震动参数影响的关键问题

场地条件对地震动的影响很大,在地震动幅值（如峰值加速度）和频谱特性（如反应谱特征周期）的变化上均有体现,而我国现行抗震设计规范没有考虑不同场地条件下地震动峰值加速度和加速度反应谱平台值的变化。本文介绍了我国现行抗震设计规范中场地类别的划分方法、场地对地震动参数值的规定和存在的问题。详细分析了土层结构、覆盖层厚度等场地条件对地震动峰值加速度和反应谱的影响,以及已经取得的研究成果。最后,就场地分类、影响地震动参数的场地条件、地震动参数随场地条件调整的方法等,提出了有待进一步研究的问题。     

太原地区土动剪切模量和阻尼比几种值的合理性比较

场地地震动参数的确定是工程场地地震安全性评价的主要目标之一,其结果可作为工程场地上的建筑工程抗震设防的资料和依据.场地地震动参数是描述地震发生时场地上地震动特性的量,它主要包括场地地表加速度峰值和加速度反应谱.当有土层存在需考虑近地表局部场地条件对地震动的影响时,常采用一维波动模型来计算土层地震反应.     

场地类型对反应谱平台值的影响

文中在总结一些学者研究基础上,利用土层地震反应分析的一维等效线性化波动方法,以建筑抗震设计规范规定的反应谱为目标谱,合成不同加速度峰值和特征周期加速度时程曲线共28条,将其作为土层地震反应分析的输入地震动,选取和构造了四种场地类型的225个土层剖面,计算了不同土层剖面在不同地震动输入下的设计反应谱的平台值.基于统计分析...     

比例阻尼矩阵构建方法对高重力坝地震反应的影响

通过二维数值计算,讨论合理建立阻尼矩阵对高重力坝时域内进行地震反应计算的重要性。首先,以4个不同坝高的混凝土重力坝为计算对象,将三种地震波作为水平输入,解得6种不同的阻尼矩阵形式下坝体的地震反应。然后以频域内解为标准,研究各种阻尼矩阵的合理性。研究结果表明：坝高超过250 m高的重力坝在时域内进行的地震反应计算是长周期系统的动力分析问题,应重视阻尼矩阵的建模方式,不宜采用单频率参数的质量比例阻尼矩阵和刚度比例阻尼矩阵,应采用双频率参数的Rayleigh阻尼矩阵,在确定2个频率参数时除采用坝体基频外还应考虑激振地震波的频谱特性以获得合理的坝体地震反应计算结果。     

基于等效线性化方法的一维土层地震反应通用计算程序对比

基于等效线性化的一维土层地震反应计算是目前国内外普遍采用的方法,国外的SHAKE91、DEEPSOIL和我国的LSSRLI-1即是根据这一方法编制的通用计算程序。本文采用这3个程序进行了不同地震波、不同输入地震动幅值下不同场地类型的土层地震反应计算,并对三者的结果进行了全面的比较分析。结果表明:①SHAKE91和DEEPSOIL程序的计算结果完全相同;②当土层最大剪应变均采用时域计算时,LSSRLI-1程序的计算结果与SHAKE91和DEEPSOIL程序基本相同,但有微小差别,其原因是:在基于等效剪应变通过离散形式的剪切模量和阻尼比随等效剪应变变化的关系曲线确定等效剪切模量和阻尼比时,DEEPSOIL和SHAKE91采用的插值方法与LSSRLI-1不同;③当LSSRLI-1程序采用频域经验关系计算土层最大剪应变时,特别是在强地震动输入下得到的土层地表加速度峰值和加速度反应谱与另外两个程序的计算结果有差别,且土层最大剪应变随着输入加速度的增大出现较大的差别。因此,本文建议:当采用LSSRLI-1程序计算土层地震响应时,应使用程序中的时域解方法代替以往默认的频域经验关系方法。     

Time‐domain viscoelastic analysis of earth structures

In this paper two causal models that approximate the nearly frequency‐independent cyclic behaviour of soils are analysed in detail. The study was motivated by the need to conduct time‐domain viscoelastic analysis on soil structures without adopting the ad hoc assumption of Rayleigh damping. First, the causal hysteretic model is introduced in which its imaginary part is frequency independent the same way that is the imaginary part of the popular non‐causal constant hysteretic model. The adoption of an imaginary part that is frequency independent even at the zero‐frequency limit, in conjunction with the condition that the proposed model should be causal, yields a real part that is frequency dependent and singular at zero frequency. The paper shows that the causal hysteretic model, although pathological at the static limit, is the mathematical connection between the non‐causal constant hysteretic model and the physically realizable Biot model. The mathematical structure of the two causal models is examined and it is shown that the causal hysteretic model is precisely the high‐frequency limit of the Biot model. Although both models have a closed‐form time‐domain representation, only the Biot model is suitable for a time‐domain viscoelastic analysis with commercially available computer software. The paper demonstrates that the simplest, causal and physically realizable linear hysteretic model that can approximate the cyclic behaviour of soil is the Biot model. The proposed study elucidates how the dynamic analysis of soil structures can be conducted rigorously in terms of the viscoelastic properties of the soil material and not with the ad hoc Rayleigh damping approach which occasionally has been criticized that tends to overdamp the higher vibration modes. The study concludes that under pulse‐type motions the Rayleigh damping approximation tends to overestimate displacements because of the inappropriate viscous type of dissipation that is imposed. Under longer motions that induce several cycles, the concept of equivalent viscous damping is more appropriate and the Rayleigh damping approximation results to a response that is comparable to the response computed with a rigorous time‐domain viscoelastic finite element analysis. Copyright © 2000 John Wiley & Sons, Ltd.     

Decoupling approximation to the evaluation of earthquake-induced plastic slip in earth dams

Newmark's sliding block analysis for evaluating earthquake-induced permanent displacements of earth dams and slopes did not consider the effects of elastic dynamic response. Makdisi and Seed extended the analysis to include such effects, using the simpfying assumption that the computation of dynamic response and plastic slip can be decoupled. This paper examines the error introduced by this assumption, using three idealized lumped-mass models for a dam. Both sinusoidal and synthetic earthquake motions are employed. When the predominant frequency of the input motion lies in the proximity of the fundamental frequency of the dam, the slip based upon the decoupling assumption exceeds the exact value. This error decreases as the threshold acceleration required to initiate slip and the damping in the soil increase. For practical application, the error should seldom exceed 20 per cent.     

关于土层地震反应分析中阻尼矩阵建模方式的讨论

阻尼矩阵的选择对土层时域内地震反应计算的准确性有重要意义。本文构造了质量比例阻尼、刚度比例阻尼、Rayleigh阻尼、Caughey阻尼和Clough阻尼矩阵,研究各阻尼对土层地震反应分析精度的影响。以苏通大桥5号桥塔基础处的工程场地为例,分别以人工合成基岩波,Northridge波、Parkfield波和汶川波为输入,得到不同阻尼模型下土层的地震反应,结果表明Clough阻尼在计算精度和误差稳定性上要优于其他阻尼模型,针对Clough阻尼的不足之处提出了改进方法,算例表明改进后的Clough阻尼能在保证计算精度的前提下减少计算机的存储量和计算量。     

Significance of ground motion time step in one dimensional site response analysis

The discrete nature of the numerical methods utilized in 1D site response analysis and calculation of the response spectra (e.g., frequency domain, Duhamel integral, and Newmark β methods) introduces time-step dependence in the resulting solution. Using an input ground motion with too large of a time-step leads to under-prediction of high-frequency characteristics of the system response due to limitations in the numerical solution of single and multiple degree of freedom systems. In order to reduce potential errors, using a sampling rate at least ten times greater than the maximum considered frequency is recommended. The preferred alternative is selection of input ground motions with a sufficiently small time step to avoid introducing numerical errors. However, where such motions are not available, then the time step of the ground motion can be reduced through interpolation. This paper demonstrates that the use of Fourier transform zero-padded interpolation is the preferred approach to obtain a ground motion with an adequate time step for the calculation of the elastic acceleration response spectra, and to analyze site response using either frequency or time domain methods.     

Centrifuge modeling of seismic response of layered soft clay

Centrifuge modeling is a valuable tool used to study the response of geotechnical structures to infrequent or extreme events such as earthquakes. A series of centrifuge model tests was conducted at 80g using an electro-hydraulic earthquake simulator mounted on the C-CORE geotechnical centrifuge to study the dynamic response of soft soils and seismic soil–structure interaction (SSI). The acceleration records at different locations within the soil bed and at its surface along with the settlement records at the surface were used to analyze the soft soil seismic response. In addition, the records of acceleration at the surface of a foundation model partially embedded in the soil were used to investigate the seismic SSI. Centrifuge data was used to evaluate the variation of shear modulus and damping ratio with shear strain amplitude and confining pressure, and to assess their effects on site response. Site response analysis using the measured shear wave velocity, estimated modulus reduction and damping ratio as input parameters produced good agreement with the measured site response. A spectral analysis of the results showed that the stiffness of the soil deposits had a significant effect on the characteristics of the input motions and the overall behavior of the structure. The peak surface acceleration measured in the centrifuge was significantly amplified, especially for low amplitude base acceleration. The amplification of the earthquake shaking as well as the frequency of the response spectra decreased with increasing earthquake intensity. The results clearly demonstrate that the layering system has to be considered, and not just the average shear wave velocity, when evaluating the local site effects.     

瑞利阻尼对砂土场地非线性地震响应的影响分析

在地震荷载作用下,自由场地会产生土体侧向变形和地表响应放大现象。由于土体的高度非线性,计算自由场地地震响应时,不同的阻尼比及剪切模量取值是造成其计算结果与试验结果相差较大的原因之一。目前动力计算常采用瑞利阻尼方法,其系数取值会在一定程度上影响计算结果。选用两模态简化瑞利阻尼系数计算方法,分析土体阻尼比及控制频率的取值对计算结果的影响,对比离心机模型试验,利用开源有限元平台OpenSees,采用适合于土体动力分析的多屈服面本构模型(PDMY),建立剪切梁模型模拟三维自由场地,并分析瑞利阻尼参数对自由场地地震响应和侧向变形计算结果的影响。结果表明,针对相对密度为60%的Nevada干砂,阻尼比为4%、控制频率比为5时,场地响应计算结果与试验结果较为符合。综合分析显示场地非线性响应时域计算时,应特别注意选用的瑞利阻尼参数值。     

Appropriate viscous damping for nonlinear time‐history analysis of base‐isolated reinforced concrete buildings

There is no consensus at the present time regarding an appropriate approach to model viscous damping in nonlinear time‐history analysis of base‐isolated buildings because of uncertainties associated with quantification of energy dissipation. Therefore, in this study, the effects of modeling viscous damping on the response of base‐isolated reinforced concrete buildings subjected to earthquake ground motions are investigated. The test results of a reduced‐scale three‐story building previously tested on a shaking table are compared with three‐dimensional finite element simulation results. The study is primarily focused on nonlinear direct‐integration time‐history analysis, where many different approaches of modeling viscous damping, developed within the framework of Rayleigh damping are considered. Nonlinear direct‐integration time‐history analysis results reveal that the damping ratio as well as the approach used to model damping has significant effects on the response, and quite importantly, a damping ratio of 1% is more appropriate in simulating the response than a damping ratio of 5%. It is shown that stiffness‐proportional damping, where the coefficient multiplying the stiffness matrix is calculated from the frequency of the base‐isolated building with the post‐elastic stiffness of the isolation system, provides reasonable estimates of the peak response indicators, in addition to being able to capture the frequency content of the response very well. Furthermore, nonlinear modal time‐history analyses using constant as well as frequency‐dependent modal damping are also performed for comparison purposes. It was found that for nonlinear modal time‐history analysis, frequency‐dependent damping, where zero damping is assigned to the frequencies below the fundamental frequency of the superstructure for a fixed‐base condition and 5% damping is assigned to all other frequencies, is more appropriate, than 5% constant damping. Copyright © 2013 John Wiley & Sons, Ltd.     

Soil-structure interaction with Rayleigh waves

Presented is a plane-strain method for soil-structure interaction analysis consisting of the superposition of the free field motions and the interaction motions in a generalized seismic environment. The free field is modelled as a horizontally layered viscoelastic medium and the seismic environment may consist of a combination of S, P and Rayleigh waves. The soil-structure system is modelled with viscoelastic finite elements, transmitting boundaries, viscous boundaries and a three-dimensional simulation. Comparative analyses of the same structure are conducted for an input of R waves and for vertically propagating S and P waves in a rock site and sand site. In the rock site the R waves produce higher peak horizontal spectral acceleration up to 25 per cent, and a significant rocking effect at points away from the centre of gravity of the structure. However, the S and P waves show higher peak vertical spectral acceleration by up to 15 per cent at the centre of the structure. Very similar horizontal response, but higher vertical response only at the centre of the structure for S and P waves, is obtained for the sand site.