按中、欧规范设计的钢筋混凝土框架结构抗震性态的对比分析

本文在确认我国GB 50011-2001规范及欧洲EC-EN1998-1规范在设计加速度反应谱取值、对R-μ基本规律的贯彻程度以及框架柱抗弯能力增强措施等方面存在差异的前提下,严格按照中国规范和欧洲规范两个延性等级分别设计0.4g高地震风险区的3个3跨6层钢筋混凝土框架结构算例,进行多条地面运动输入下的非线性动力反应分析并详细对比其在强震下的抗震性能,得出了中国9度0.4g区按一级抗震等级设计的框架结构的抗震性态总体上与同一地震风险区欧洲规范高延性和中等延性两个等级的框架结构相近的初步结论;同时对这两部规范设计规定的差异给抗震性态带来的有利或不利影响分别作了分析评价。     

中美建筑抗震设计规范中工程场地类别的对比和换算关系

本文依据分布于全国的6 824个钻孔数据,按照双参数的不同取值,将GB50011—2010《建筑抗震设计规范》（以下简称中国建抗规）的场地类别进一步划分为更加同质的子类,分析了双参数体系对场地分类结果的影响,建立了每个子类与美国《NEHRP对新建建筑和结构物的推荐地震条款》（National Earthquake Hazards Reduction Program Recommended Provisions for Seismic Regulations for New Buildings and Other Structures,以下简称美国建抗规）的场地类别的对应关系,并对比分析中、美建抗规的场地类别差异,在此基础上建立了中国建抗规与美国建抗规场地类别相互转换的概率表达。研究结果表明:用v_S20近似表示中国场地分类标准的等效剪切波速并不可靠;中国建抗规中Ⅱ类场地和Ⅲ类场地内部不同子类与美国建抗规中场地类别的对应关系截然不同;中国建抗规中覆盖层厚度有效地区分了浅部波速类似而深部波速不同的场地;中国建抗规的Ⅱ类和Ⅲ类场地主体均对应美国建抗规的D类场地,中国Ⅱ类场地略偏对应美国C类场地,中国Ⅲ类场地略偏对应美国E类场地;中国Ⅳ类场地对应美国E类场地,绝大多数美国C类和D类场地均对应中国Ⅱ类场地,说明中国Ⅱ类场地的范围极宽。      

Efficient mode superposition algorithm for seismic analysis of non-linear structures

A step-by-step integration method is proposed to compute within the framework of the conventional mode superposition technique the response of bilinear hysteretic structures subjected to earthquake ground motions. The method is computationally efficient because only a few modes are needed to obtain an accurate estimate of such a response, and because it does not require the use of excessively small time steps to avoid problems of accuracy or stability. It is developed on the basis that the non-linear terms in the equations of motion for non-linear systems may be considered as additional external forces, and the fact that by doing so such equations of motion can be interpreted as the equations of motion of an equivalent linear system, excited by a modified ground motion. These linear equations are then subjected to a conventional modal decomposition and transformed, as with linear systems, into a set of independent differential equations, each representing the system's response in one of its modes of vibration. To increase the efficiency of the method and account properly for the participation of higher modes, these independent equations are solved using the Nigam-Jennings technique in conjunction with the so-called mode acceleration method. The accuracy and efficiency of the method is verified by means of a comparative study with solutions obtained with a conventional direct integration method. In this comparative study, including only a few modes, the proposed method accurately predicts the seismic response of three two-dimensional frame structures, but requiring only, on an average, about 47 per cent less computer time than when the direct integration method is used.     

Predictive optimal control for seismic analysis of non-linear and hysteretic structures

In this paper, an effective active predictive control algorithm is developed for the vibration control of non-linear hysteretic structural systems subjected to earthquake excitation. The non-linear characteristics of the structural behaviour and the effects of time delay in both the measurements and control action are included throughout the entire analysis (design and validation). This is very important since, in current design practice, structures are assumed to behave non-linearly, and time delays induced by sensors and actuator devices are not avoidable. The proposed algorithm focuses on the instantaneous optimal control approach for the development of a control methodology where the non-linearities are brought into the analysis through a non-linear state vector and a non-linear open-loop term. An autoregressive (AR) model is used to predict the earthquake excitation to be considered in the prediction of the structural response. A performance index that is quadratic in the control force and in the predicted non-linear states, with two additional energy related terms, and that is subjected to a non-linear constraint equation, is minimized at every time step. The effectiveness of the proposed closed-open loop non-linear instantaneous optimal prediction control (CONIOPC) strategy is presented by the results of numerical simulations. Since non-linearity and time-delay effects are incorporated in the mathematical model throughout the derivation of the control methodology, good performance and stability of the controlled structural system are guaranteed. Copyright © 1999 John Wiley & Sons, Ltd.     

不同版本规范设计的底框砌体结构地震易损性对比

历次地震震害表明,底框砌体结构在遭遇大地震时破坏严重。本文比较了《GBJ11-89建筑抗震设计规范》和《GB50011-2001建筑抗震设计规范》中关于该类结构的抗震设计要求。参考某地一个实际底框砌体结构建筑设计资料,分别按上述两版本规范设计了2个具有代表性的底框砌体结构。采用层间剪切模型基于IDA方法对结构进行了地震易损性分析,对比分析结果表明:按两版本规范设计的底框砌体结构的破坏均出现在过渡层;在设防地震作用下,按《89规范》设计的结构达到中等破坏的概率最大,使用功能受到影响,按《01规范》设计的结构达到轻微破坏状态的概率最大,使用功能基本无影响;在罕遇地震作用下,按《01规范》设计的结构发生严重破坏和毁坏的概率比按《89规范》设计的结构明显降低,抗震能力明显提高。本文提供的结果可丰富底框砌体结构地震易损性数据,为区域地震风险评估、震害预测等研究提供更加精细的易损性模型。     

钢框架结构的非线性静力抗震可靠性分析：I有限元反应及其灵敏度

作为一种随机有限元方法，有限元可靠度方法通过有限元反应灵敏度分析将结构可靠度分析的近似解析方法与结构确定性分析的有限元方法结合起来，可以有效地处理结构反应是基本随机变量的隐式函数这一难题，因此成为大型复杂结构可靠度分析的有效工具。采用基于位移的非线性纤维梁柱单元对钢框架结构进行有限元建模，推导了单元与截面的基本方程。针对基于位移的纤维梁柱单元，采用逐级递进方式，分别推导了整体级、单元级、截面级和材料级的有限元反应灵敏度直接微分表达式。研究结果可为采用FORM或SORM等近似解析法进行钢框架结构的非线性静力有限元可靠性分析提供算法支持和编程依据。     

A modal procedure for seismic analysis of non-linear base-isolated multistorey structures

A modal procedure for non-linear analysis of multistorey structures with high-damping base-isolation systems was proposed. Two different isolation devices were considered in the analysis: an high-damping laminated rubber bearing and a lead-rubber bearing. Starting from deformational properties verified by tests, the isolation systems were characterized using three different analytical models (an Elastic Viscous, a Bilinear Hysteretic and a Wen's Model) with parameters depending from maximum lateral strain. After non-linear modelling of isolation and lateral-force-resisting systems, the effects of material non-linearities were considered as pseudo-forces applied to the equivalent linear system (Pseudo-Force Method) and the formally linearized equations of motion were uncoupled by the transformation defined by the complex mode shapes. The modal responses were finally obtained with an extension of Nigam–Jennings technique to non-linear and non-classically damped systems, in conjunction with an iterative technique searching for non-linear contributions satisfying equations of motion and constitutive laws. Since the properties of the isolated structure usually change with maximun lateral strain of isolation bearings, the integration of a new set of governing equations was required for each design-displacement value. The procedure proposed was described in detail and then applied for the determination of modal and total seismic responses in some real cases. At first, a very good agreement between non-linear responses obtained with the proposed mode superposition and with a direct integration method was observed. Then a comparison of results obtained with the three different analytical models of the isolation bearings was carried out. At last, the exact modal response obtained with analytical models depending from the design displacement of the isolation bearings was compared with two different approximated solutions, evaluated using mode shapes and isolation properties, respectively, calculated under simplified hypothesis.© 1998 John Wiley & Sons, Ltd.     

Deep structure of the East European platform according to seismic data

The paper presents a review and analysis of new seismic data related to the structure of the mantle beneath the East European platform. Analysis of observations of long-range profiles revealed pronounced differences in the structure of the lower lithosphere beneath the Russian plate and the North Caspian coastal depression. The highest P-velocities found at depths around 100 km are in the range 8.4–8.5 km s^?1. Deep structure of the Baltic shield is different from the structures of both these regions. No evidence of azimuthal anisotropy in the upper mantle was found. A distribution of P-velocity in the upper mantle and in the transition zone consistent with accurate travel-time data was determined. The model involves several zones of small and large positive velocity gradients in the upper mantle, rapid increases of velocity near 400 and 640 km depths and an almost constant positive velocity gradient between the 400 and 640 km discontinuities. The depth of the 640 km discontinuity was determined from observations of waves converted from P to SV in the mantle.     

Efficient non-linear seismic analysis of arch dams

An approximate procedure for seismic analysis of concrete arch dams which is based on the smeared crack method is described. Features include construction sequence modelling, water and foundation interaction, crack formation, opening and closing of joints and cracks, frictional sliding, presence of shear keys, action of internal water pressure, and a reliable solution algorithm. Complete solutions can be obtained in an hour on a fast workstation computer, allowing parameter studies to be run. Results suggest that an arch dam can suffer significant cracking during strong ground shaking and still remain stable. © 1998 John Wiley & Sons, Ltd.     

Modal superposition method for seismic design of non-linear multistorey structures

An approximate procedure is introduced to analyse non-linear multistorey structures within the framework of the conventional response spectrum method. Its derivation is based on the use of non-linear response spectra and an approximate decomposition of the equation of motion for multi-degree-of-freedom non-linear systems. The decomposition is attained by considering the non-linear terms in this equation of motion as additional external forces and, thus, by interpreting it as the equation of motion of linear systems with the initial properties of the non-linear ones when subjected to a modified set of inertia forces. For simplicity, the procedure is herein limited to elastoplastic systems of the shear-beam type. Its accuracy is evaluated by comparing the approximate and step-by-step integration solutions of systems with three and ten degrees of freedom when subjected to three different earthquake ground motions.     

Assessment of the seismic non-linear behavior of ductile wall structures due to synthetic earthquakes

In this paper, different methods for generating synthetic earthquakes are compared in terms of related non-linear seismic response of ductile structures. The objective of the investigation is to formulate recommendations for the use of synthetic earthquakes for reliable seismic analysis. The comparison is focused on the accuracy of the reproduction of the characteristics of the structural non-linear response due to recorded earthquakes. First the investigations are carried out for non-linear single-degree-of-freedom systems. Later, the results are validated for a set of realistic buildings modelled as multi-degree-of-freedom systems. Various options of the classical stationary simulation procedure of SIMQKE and a non-stationary simulation procedure proposed by Sabetta and Pugliese are examined and compared. The adopted methodology uses a set of recorded earthquakes as a reference. Hundred synthetic accelerograms are generated for each examined simulation option with the condition that the related elastic responses are similar to those of the reference set. The non-linear single-degree-of-freedom systems are defined using six recognized hysteretic models and four levels of increasing non-linearity. The non-linear responses computed for the reference set and the studied simulation options are then statistically compared in terms of displacement ductility and energy. The results show that the implementation of the classical stationary procedure always leads to a significant underestimation of the ductility demand and a significant overestimation of the energy demand. By contrast, non-stationary time histories produce much better results. The results with the multi-degree-of-freedom systems are shown to confirm these conclusions.     

钢框架结构的非线性静力抗震可靠性分析Ⅱ:可靠度指标及其灵敏度

将有限元反应及其灵敏度分析与结构可靠度分析的近似解析方法结合起来,可以进行具有隐式功能函数的大型复杂结构的可靠性分析。在基于位移的非线性纤维梁柱单元及其灵敏度直接微分表达式的基础上,通过力学变换、概率变换和反应灵敏度,将结构可靠度计算方法FORM和SORM与有限元方法有机地集成在一起。依据现行抗震设计规范,建立了钢框架结构典型构件承载能力和结构层间变形能力的抗震极限状态方程,利用地震作用的等效随机静力模型,采用非线性有限元静力可靠度方法,对一实际工程结构的抗震可靠度及其灵敏度进行了概率分析和评价,结果表明：尽管在大震作用下该结构的层间弹塑性变形可靠度较高,但是构件极限承载能力的可靠度指标较低,仍然存在失效的可能性。因此,仅验算“小震”作用下结构的承载能力可靠度和“大震”作用下结构的变形能力可靠度是不够的,还需要验算在“中震”和“大震”作用下结构的极限承载能力可靠度。     

钢框架结构的非线性静力抗震可靠性分析 II:可靠度指标及其灵敏度

将有限元反应及其灵敏度分析与结构可靠度分析的近似解析方法结合起来,可以进行具有隐式功能函数的大型复杂结构的可靠性分析。在基于位移的非线性纤维梁柱单元及其灵敏度直接微分表达式的基础上,通过力学变换、概率变换和反应灵敏度,将结构可靠度计算方法FORM和SORM与有限元方法有机地集成在一起。依据现行抗震设计规范,建立了钢框架结构典型构件承载能力和结构层间变形能力的抗震极限状态方程,利用地震作用的等效随机静力模型,采用非线性有限元静力可靠度方法,对一实际工程结构的抗震可靠度及其灵敏度进行了概率分析和评价,结果表明:尽管在大震作用下该结构的层间弹塑性变形可靠度较高,但是构件极限承载能力的可靠度指标较低,仍然存在失效的可能性。因此,仅验算"小震"作用下结构的承载能力可靠度和"大震"作用下结构的变形能力可靠度是不够的,还需要验算在"中震"和"大震"作用下结构的极限承载能力可靠度。     

Comparison between seismic vulnerability models and experimental dynamic properties of existing buildings in France

Elastic fundamental frequency is a key-parameter of simplified seismic design and vulnerability assessment methods. Empirical relationships exist in codes to estimate this frequency but they miss experimental data to validate them accounting for national feature of building design and, above all, corresponding uncertainties. Even if resonance frequency extracted from ambient vibrations may be larger than the elastic frequency (at yield) generally used in earthquake engineering, ambient vibration recordings may provide a large set of data for statistical analysis of periods versus building characteristics relationships. We recorded ambient vibrations and estimated the fundamental frequency of about 60 buildings of various types (RC and masonry) in Grenoble City (France). These data complete the set existing yet, made of 26 RC-buildings of Grenoble (Farsi and Bard 2004) and 28 buildings in Nice (France) (Dunand 2005). Statistical analysis of these experimental data was performed for fundamental frequencies of RC shear wall structures and the results are compared with existing relationships. Only building height or number of stories has a statistical relevancy to estimate the resonance frequency but the variability associated to the proposed relationships is large. Moreover, we compared the elastic part of capacity curves of RC and masonry buildings used in the European Risk-UE method for vulnerability assessment with the experimental frequencies. The variability is also large and the curves may not be consistent with French existing buildings.     

Velocity structure of the upper mantle of the East European platform according to seismic noise data

Cross-correlation functions of noise are constructed on 119 interstation paths from seismic noise records at stations of Eastern Europe. Dispersion curves of the group velocity of Rayleigh waves obtained from the cross-correlation functions are used for constructing the three-dimensional distribution of the velocity of transverse waves on the East European platform and in adjacent regions by methods of surface-wave tomography. The mean velocity in the crust is minimum in the region of the Caspian depression and Black Sea basin (<3.3 km/s) and maximum in the Baltic shield area (>3.7 km/s). The upper mantle beneath the Baltic and Ukrainian shields is characterized by increased velocity and the absence of the asthenospheric layer. Reduced velocities are noted in the upper mantle of the Black Sea basin. A low-velocity anomaly in the shape of a vertical column is revealed at depths of 200–300 km in the central part of the Dnieper-Donets aulacogen, which confirms the existence of a paleorift in this region.     

Assessment of European seismic design procedures for steel framed structures

This paper assesses the fundamental approaches and main procedures adopted in the seismic design of steel frames, with emphasis on the provisions of Eurocode 8. The study covers moment-resisting as well as concentrically-braced frame configurations. Code requirements in terms of design concepts, behaviour factors, ductility considerations and capacity design verifications, are examined. The rationality and clarity of the design principles employed in Eurocode 8, especially those related to the explicit definitions of dissipative and non dissipative zones and associated capacity design criteria, are highlighted. Various requirements that differ notably from the provisions of other seismic codes are also pointed out. More importantly, several issues that can lead to unintentional departure from performance objectives or to impractical solutions, as a consequence of inherent assumptions or possible misinterpretations, are identified and a number of clarifications and modifications suggested. In particular, it is shown that the implications of stability and drift requirements as well as some capacity design checks in moment frames, together with the treatment of post-buckling response and the distribution of inelastic demand in braced frames, are areas that merit careful consideration within the design process.     

On the evaluation of seismic response of structures by nonlinear static methods

In the most recent seismic codes, the assessment of the seismic response of structures may be carried out by comparing the displacement capacity, provided by nonlinear static analysis, with the displacement demand. In many cases the code approach is based on the N2 method proposed by Fajfar, which evaluates the displacement demand by defining, as an intermediate step, a single degree‐of‐freedom (SDOF) system equivalent to the examined structure. Other codes suggest simpler approaches, which do not require equivalent SDOF systems, but they give slightly different estimation of the seismic displacement demand. The paper points out the differences between the methods and suggests an operative approach that provides the same accuracy as the N2 method without requiring the evaluation of an equivalent SDOF system. A wide parametric investigation allows an accurate comparison of the different methods and demonstrates the effectiveness of the proposed operative approach. Copyright © 2009 John Wiley & Sons, Ltd.     

The role of the stochastic equivalent linearization method in the analysis of the non-linear seismic response of building structures

The stochastic equivalent linearization method has been significantly improved during the last two decades, leading to rather efficient and accurate estimates of the first- and second-order statistical moments of the random response process, even when the non-stationarity of the excitation and the hysteretic degrading non-linearities of the structural system are taken into account. The purpose of this paper, apart from presenting a short survey of the most relevant methods developed in this area, indicating their main restrictions, is to call attention to the remarkable possibilities of the equivalent linearization technique as the most powerful approximate method to deal with the seismic response analysis of MDOF non-linear building structures, deserving to be considered by the engineering codes in the near future as an appropriate formulation for that purpose. To illustrate the real interest of this method, several applications concerning a simple shear-building structural model are presented, considering columns with non-linear restoring forces, either bilinear elastic or hysteretic, and the results obtained by some computer programs developed on the basis of the equivalent linearization technique are compared with the estimates achieved by digital simulation in order to check the level of accuracy. Moreover, these results are also used to evaluate limit violation (failure) probabilities, based on the vulnerability function concept.