The effects of torsion and motion coupling in site response estimation

Soil amplification characteristics are investigated using data from the Chibaken‐Toho‐Oki earthquake and its aftershocks recorded at Chiba dense array in Japan. The frequency‐dependent amplification function of soil is calculated using uphole‐to‐downhole spectral ratio analysis, considering the horizontal components of shear wave. The identified spectral ratios consistently demonstrate the splitting of peaks in their resonance frequencies and low amplification values in comparison with a 1D model. The torsional behaviour and horizontal ground motion coupling are clarified as the reasons for these phenomena at the site. To prove the hypothesis, the torsional motion is directly evaluated using the data of the horizontal dense array in different depths at the site. The comparison between Fourier spectra of torsional motion and identified transfer functions reveals the peaks at the same frequencies. The wave equation including torsion and horizontal motion coupling is introduced and solved for the layered media by applying wave propagation theory. Using the developed model, the effects of torsional motion with horizontal motion coupling on soil transfer function are numerically examined. Splitting and low amplification at resonance frequencies are confirmed by the results of numerical analysis. Furthermore, the ground motion in two horizontal directions at the site is simulated using site geotechnical specification and optimizing the model parameters. The simulated and recorded motions demonstrate good agreement that is used to validate the hypothesis. In addition, the spectral density of torsional ground motions are compared with the calculated one and found to be well predicted by the model. Finally, the results are used to explain the overestimation of damping in back‐calculation of dynamic soil properties using vertical array data in small strain level. Copyright © 2003 John Wiley & Sons, Ltd.     

采用双向调谐质量阻尼器的大跨度桥梁风振控制仿真分析

传统的调谐质量阻尼器（TMD）设计均仅针对结构某一阶模态单独设置,当用于密频结构减振时会导致附加质量过多。为减小TMD的附加质量,结合大跨度斜拉桥结构的密频与风致耦合振动特点,提出了一种新型的双向共享质量与电涡流阻尼式TMD。具体实现方式是：水平、竖向TMD的刚度构件分别采用悬臂梁与压簧,将水平向TMD整体置于压簧上面,从而构成竖向TMD的质量;导体板固定不动,使安装在TMD质量块的永磁体阵列随质量块竖向或水平方向运动,从而分别产生竖向与水平向的电磁涡流阻尼。研究结果表明：（1）电涡流阻尼可以很好地实现双向TMD装置的共享阻尼,且电涡流阻尼的大小可以很方便地调节;（2）采用双向TMD进行斜拉桥的风致振动控制减振效果良好,可行性强。     

Damping formulation for nonlinear 1D site response analyses

Measurements and observations of ground shaking during large earthquakes have demonstrated the predominant role of site effects in the response of infrastructure during a seismic event. Despite significant efforts to model the hysteretic response and nonlinearity of soils due to medium and large ground motions, the most widely accepted nonlinear site response methods are not able to represent simultaneously the changes of stiffness and energy dissipation (damping) observed in both laboratory tests and during earthquake events. This paper presents two new soil damping formulations implemented in nonlinear one-dimensional site response analysis for small and large strains. The first formulation introduces an approach to construct a frequency-independent viscous damping matrix which reduces the over-damping at high frequencies, and therefore, the filtering at those frequencies. The second formulation introduces a reduction factor that modifies the extended Masing loading/unloading strain–stress relationship to match measured modulus reduction and damping curves simultaneously over a wide range of shear strains. A set of examples are introduced to illustrate the effect of using the two proposed formulations, separately and simultaneously, in nonlinear site response analyses.     

Empirical estimate of fundamental frequencies and damping for Italian buildings

The aim of this work is to estimate the fundamental translational frequencies and relative damping of a large number of existing buildings, performing ambient vibration measurements. The first part of the work is devoted to the comparison of the results obtained with microtremor measurements with those obtained from earthquake recordings using four different techniques: horizontal‐to‐vertical spectral ratio, standard spectral ratio, non‐parametric damping analysis (NonPaDAn) and half bandwidth method. We recorded local earthquakes on a five floors reinforced concrete building with a pair of accelerometers located on the ground and on top floor, and then collected microtremors at the same location of the accelerometers. The agreement between the results obtained with microtremors and earthquakes has encouraged extending ambient noise measurements to a large number of buildings. We analysed the data with the above‐mentioned methods to obtain the two main translational frequencies in orthogonal directions and their relative damping for 80 buildings in the urban areas of Potenza and Senigallia (Italy). The frequencies determined with different techniques are in good agreement. We do not have the same satisfactory results for the estimates of damping: the NonPaDAn provides estimates that are less dispersed and grouped around values that appear to be more realistic. Finally, we have compared the measured frequencies with other experimental results and theoretical models. Our results confirm, as reported by previous authors, that the theoretical period–height relationships overestimate the experimental data. Copyright © 2008 John Wiley & Sons, Ltd.     

Damping modification factors for SDOF systems subjected to near‐fault,far‐fault and artificial earthquakes

Damping modification factors (DMF) are used in modern seismic codes to adjust elastic response spectral values corresponding to 5% of viscous damping to other higher or lower damping levels. This paper presents a simple and effective procedure to estimate DMF for single‐degree‐of‐freedom systems. Empirical expressions are proposed for displacement, velocity and acceleration response spectra, where four types of soil conditions, from hard rock to soft soil are considered. This study also examines, for the first time, the influence of artificial earthquakes on DMF. Furthermore, natural near‐fault and far‐fault seismic ground motions are considered where it is testified that the fault distance has no impact on DMF. Finally, it confirms that, in contrast to the considerations of many seismic codes, DMF are strongly dependent on the period of structural vibration while there are significant problems of using the same modification factor to estimate maximum displacement, velocity and seismic forces. Copyright © 2010 John Wiley & Sons, Ltd.     

抗震结构的阻尼减振效果分析

研究了抗震结构的阻尼减振效果。首先，考虑了单自由度体系在不同频率简谐干扰作用下阻尼比对结构反应的减小效果；然后，考虑了阻尼比对结构地震反应谱的影响，分析了我国现行建筑抗震设计规范反应谱，并讨论了不同阻尼比对水平地震影响系数的修正公式。     

土遗址土动力特性

通过动三轴试验和数值计算,分析甘肃河西地区原状、重塑土遗址土的动模量、阻尼比、抗剪强度和土遗址在破坏地震作用下的动力响应。结果表明：弹性范围内,原状和重塑土遗址土动应力σ_d和动应变ε_d呈非线性关系且符合双曲线模型,动弹性模量E随ε_d的增大而减小,二者初始动弹性模量E₀和剪模比G/G₀差别很小,剪模比曲线基本重合;剪应变γ取值范围相同时,重塑土阻尼比λ随着γ的增大趋势高于原状土;相同实验条件下,原状土遗址土内聚力略高于重塑土。夯实加固法一定程度上恢复了土遗址强度,但当破坏地震来临时,其整体的抗震性能还有待加强     

水平分层土层系统等效阻尼比的简化计算方法

在实际工程场地中,很多土层可视为水平分层,各层土的物理和力学性质存在差异,其中包括土的振动阻尼比。本文讨论水平分层土层系统的等效阻尼比的近似计算方法,基于5个不同的加权函数推导了10种等效阻尼比的计算公式。通过2个算例,分别以等效阻尼比为参数计算水平分层土层的地震反应,并与准确解相比较,分析了不同等效阻尼比近似计算方法的计算精度。数值结果表明,若等效阻尼比计算方法选择不恰当,会导致土层地震反应的计算结果出现较大误差。针对2种不同类型的水平分层土层,建议采用基于三角形分布的加权函数来计算土层系统的等效阻尼比。     

地基土粉砂层动力特性分析试验研究

本文通过对某核电厂取水明渠导流堤地基土粉砂层室内共振柱试验及动三轴液化试验,测定了动剪切模量、阻尼比与动剪应变幅的双曲线关系,分析了粉砂的动力变形特性,探讨了砂土的抗液化强度与液化振次之间的乘幂函数关系,确定了该地基土的抗液化强度指标。为评价导流堤的地震稳定和液化分析提供了相关参数,同时对堤坝工程场地的地震安全性评价和液化评判有良好的借鉴和参考价值。     

不同类型俯冲带地震竖向地震动阻尼修正系数对比研究

俯冲带地区竖向地震动的阻尼修正系数在工程结构抗震设计中起着重要作用。由于俯冲带地区的板块构造复杂,俯冲带地区的地震可划分为浅壳上地幔地震、板内地震和板间地震3种类型。为研究不同类型俯冲带地震的竖向地震动阻尼修正系数间是否具有显著差异而需要分别建立不同的阻尼修正系数模型,采用日本俯冲带地区的地震动数据,通过假设检验和构造差异指标的方式对不同类型地震的竖向加速度和位移反应谱的阻尼修正系数进行两两比较。结果显示:不同地震类型的竖向地震动阻尼修正系数在众多谱周期上存在统计意义和工程实际意义上的显著差异。该研究表明:研究俯冲带地区竖向地震动阻尼修正系数时需要考虑地震类型的影响。     

Free vibration of soils during large earthquakes

Free vibration of soils happens frequently during some large earthquakes, perhaps seeming like a paradox. This happens because the energy released from seismic sources in some cases is not stationary in time, allowing relaxation intervals in between without important seismic wave arrivals in which free soil vibration happens. Two techniques to estimate the natural period of the free vibration from accelerograms are presented: autocorrelograms and Fourier spectra. Both techniques sometimes allow measuring higher mode frequencies of the soil for the three first modes as well as modal damping. Free vibration modal periods satisfy the classic 1D equation S-wave theory. The presence of free vibrations corresponds to shear wave soil energy radiation episodes rather than to energy amplification of incoming stationary seismic shear waves suggested by the dynamic soil amplification. These results explain the discrepancies observed between the theoretical soil dynamic amplification and the accelerographic measurement. Observation of free vibration of soils is not always possible, it depends on the duration of the time windows without important seismic waves arrivals compared to the natural period and damping of the soil.     

Modal analysis of pile‐supported structures during seismic liquefaction

The purpose of this paper is to investigate the effects of liquefaction on modal parameters (frequency and damping) of pile‐supported structures. Four physical models, consisting of two single piles and two 2 × 2 pile groups, were tested in a shaking table where the soil surrounding the pile liquefied because of seismic shaking. The experimental results showed that the natural frequency of pile‐supported structures may decrease considerably owing to the loss of lateral support offered by the soil to the pile. On the other hand, the damping ratio of structure may increase to values in excess of 20%. These findings have important design consequences: (a) for low‐period structures, substantial reduction of spectral acceleration is expected; (b) during and after liquefaction, the response of the system may be dictated by the interactions of multiple loadings, that is, horizontal, axial and overturning moment, which were negligible prior to liquefaction; and (c) with the onset of liquefaction due to increased flexibility of pile‐supported structure, larger spectral displacement may be expected, which in turn may enhance P‐delta effects and consequently amplification of overturning moment. Practical implications for pile design are discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

Seismic response of bridge piers on pile groups for different soil damping models and lumped parameter representations of the foundation

This paper presents a wide parametric study aimed at elucidating the influence, on the computed seismic response of bridge piers, of two related aspects of the model: (1) the adoption of the classical hysteretic or the causal Biot's damping models for the soil and (2) the use of two different lumped parameter models of different complexity and accuracy to approximate the impedances of the pile foundation. A total of 2072 cases, including different superstructures, pile foundations, soil deposits, and seismic input signals, are studied. The results are presented so that the influence of the different parameters involved in the analysis can be assessed. From an engineering point of view, both lumped parameter models provide, in general, sufficiently low errors. The choice of the most adequate model for each case will depend not only on the configuration of the structure and the soil-foundation system but also on the assumed soil damping model, whose influence on the computed seismic responses is relevant in many cases. The nonphysical behaviour provided by the classical hysteretic damping model for the soil at zero frequency generates issues in the process of fitting the impedance functions. It is also found that larger deck displacements are predicted by Biot's model due to the higher damping at low frequencies provided by the classical hysteretic damping model.     

The effectiveness of trenches in reducing seismic motion

The effect of placing barriers in the travel path of P, SV and SH seismic waves has been studied using time-domain solutions of plane-strain finite element programs for two-dimensional crustal models. The wavefields considered propagate parallel to the free surface of an elastic medium consisting of a single layer over a halfspace. Barriers take the form of open-air trenches. Effects of damping are assessed by considering representative viscoelastic conditions. Computations are presented as the ratio of spectral energy observed at a point with the barrier system in place in the model to the spectral energy observed at the same point without the barrier system in the model. These spectral ratios are dependent upon the direction of wave propagation. The calculations brought to light the marked role of surficial layering and attenuation properties of the surface rocks or soils on the effectiveness of seismic trench barriers. Barrier models without these features cannot in general reliably predict seismic wavefields at the surface. In the range of cases studied, trench depth d rather than width is the most sensitive parameter. When the ratio d/λ, the ratio of trench depth to the wavelength of shear waves, is greater than about 0·6, power spectral ratios of 0·06 and less are found for SH waves and the vertical component of SV motion for frequencies of 4–6 Hz. By contrast, for frequencies less than 3–4 Hz, power spectral ratios from unity to about two and greater are observed, indicating amplification for the horizontal component of wave motion. Spectral ratios calculated at some locations in front of the barrier system show over two-fold amplification. Spectral ratios also change significantly with the relative location of the free surface observation point.     

小应变硬化模型(HSS)在Rayleigh波作用下场地响应分析中的应用

为研究冲击荷载或地震作用下产生的,以Rayleigh波为主的面波对浅层地表土体动力响应特征以及数值模拟中土层阻尼的设置方法,以厦门地区浅层的素填土及粉质黏土为研究对象,采用有限元动力分析,土体本构采用小应变硬化模型(HSS),利用模型本身的滞回环特性,输入变化的小应变参数,考察HSS模型的小应变参数对场地动力响应的影响,并与土体采用摩尔-库伦模型结合Rayleigh阻尼("MC+Rayleigh阻尼")的计算结果进行对比。研究表明:当采用带有滞回环的HSS模型时,波速随初始剪切模量Gref0的增大而增大,但振幅减小,残余变形量也有所减小;小应变参数γ0.7对波的影响较小;HSS模型能够给出残余变形量,而"MC+Rayleigh阻尼"由于本构模型为理想弹塑性模型,在卸载重加载条件下表现为纯弹性行为,无法反映出卸载重加载过程中塑性应变的积累及其累积阻尼效应;但HSS模型还不能够全面反映循环加载作用下塑性体积应变的累积,因此在考虑滞回阻尼的基础上,仍然建议借助Rayleigh阻尼来更加全面地模拟土体的实际阻尼特性。     

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.     

Wave energy in surface layers for energy-based damage evaluation

Seismic wave energy in surface layers is calculated based on vertical array records at four sites during the 1995 Hyogo-ken Nambu earthquake by assuming vertical propagation of SH waves. The upward energy generally tends to decrease as it goes up from the base layer to the ground surface particularly in soft soil sites. Theoretical study on 1D multi-layers model to investigate the basic energy flow mechanism indicates that the energy at the ground surface can be smaller on softer soils due to high soil damping during strong shaking even if resonance effect is considered. A simple calculation for a shear-vibrating structure resting on foundation ground shows that induced strain in the structure is directly related to the energy or the energy flux of surface layers. Hence, a general perception that soft soil sites tend to suffer heavier damage than stiff sites should be explained not by greater incident energy but by other reasons such as degree of resonance. Furthermore, it is recommended that not only acceleration or velocity but also S-wave velocity should be specified at a layer where a design seismic motion is given, so that the seismic wave energy can clearly be quantified in seismic design practice.     

A review of adverse effects of damping in seismic isolation

In this paper the question of possible adverse effects of damping in seismic isolation because of higher mode response is investigated by means of simple models with a few degrees of freedom (DOF). In particular the second mode response of a 2 DOF system is examined in detail for both viscous and hysteretic (e.g. friction or elastoplastic) damping devices. Qualitative and approximate quantitative estimates are obtained by neglecting the influence of the modal coupling terms, due to viscous damping or friction forces, on the first mode response. It is shown that additional viscous damping has a diminishing effect on base displacement, storey shear force and floor spectra values in the vicinity of the first mode resonance. However, a significant amplification of the floor spectra values near the higher mode frequencies may occur. In accordance with the results of previous works, compared with the viscous damping case, hysteretic damping amplifies moderately the first storey shear force and significantly the upper storeys shear force. It also results, in a much more pronounced amplification of the floor spectral values than viscous damping, in the vicinity of the higher eigenfrequencies. However, the higher modes' response is milder if a realistic velocity dependence of the friction coefficient is taken into account. Copyright © 2007 John Wiley & Sons, Ltd.     

A practical method for utilization of commercial cyclic testing apparatuses for computation of site response in central Adapazari

We suggest a practical method for estimating strain–modulus–damping relationships for utilization in equivalent-linear site response analyses, so that the necessity for more sophisticated sampling and testing procedures can be justified. The method employs the commercial cyclic testing apparatuses, which have limitations in low-strain ranges, and the in-situ seismic tests. The shear modulus at about 1% cyclic shear strain amplitude and the shear-wave velocity measured in-situ is used for building a hyperbolic relationship between shear stress and shear strain. An extension of Masing׳s rule and the constraint on hysteretic damping at 1% cyclic shear strain amplitude leads to a strain–damping relationship. By putting a particular emphasis on the soils of Adapazarı, a city famous for the concentrated damage on alluvium basin during the 1999 Kocaeli (Mw7.4) earthquake, we demonstrated the usefulness of the method, and concluded that the shear-modulus reduction and damping characteristics of Adapazarı soils can yield to site amplification factors greater than those predicted by strain–modulus–damping relationships presented in literature, and can more efficiently explain the concentration of damage on the alluvium basin. Through the comparisons of spectral amplification factors computed by equivalent-linear site response analyses, we justified the necessity to run a more sophisticated testing program on determination of cyclic stress–strain behavior of Adapazarı soils, and consequently to consider transient nonlinear site-response analyses in order to reduce the possible bias in calculation of spectral amplification factors.     

Effects of Impedance Contrast and Soil Thickness on Basin-Transduced Rayleigh Waves and Associated Differential Ground Motion

This paper presents the effects of impedance contrast (IC) across the basin edge, velocity contrast between the basin and underlying bedrock, Poisson’s ratio and soil thickness on the characteristics of basin-transduced Rayleigh (BTR) waves and associated differential ground motion (DGM). Analysis of simulated results for a two-dimensional (2D) basin revealed complex mode transformation of Rayleigh waves after entering the basin. Excellent correlation of frequencies corresponding to different spectral ratio peaks in ellipticity curves of BTR waves and spectral amplification peaks was obtained. However, such correlation was not observed between values of peaks in ellipticity curves and spectral amplification at the corresponding frequencies. An increase of spectral amplification with IC was obtained. The largest spectral amplification was more than twice the IC in the horizontal component and more than the IC in the vertical component in the case of large and same impedance contrast for P- and S-waves. It was concluded that the frequency corresponding to the largest spectral amplification was greater than the fundamental frequency of soil by around 14% and 44% in the vertical and horizontal components, respectively. Spectral amplification of the vertical component was negligible when soil thickness was less than around 15–20 times the S-wave wavelength in the basin. The largest values of peak ground displacement (PGD) and peak differential ground motion (PDGM) were obtained very near the basin edge, and their values with offset from the edge were strongly dependent on the IC across the basin edge, Poisson’s ratio, velocity contrast between the basin and underlying bedrock (dispersion), damping and soil thickness. The obtained value of PDGM for a span of 50 m in the horizontal and vertical components due to the BTR wave was of the order of 0.75 × 10^?3 and 1.32 × 10^?3 for unit amplitude (1.0 cm) in the horizontal component of the Rayleigh wave at rock very near the basin edge.