Seismic fragility and reliability of structures isolated by friction pendulum devices: seismic reliability‐based design (SRBD)

The paper deals with the seismic reliability of elastic structural systems equipped with friction pendulum isolators (friction pendulum system). The behavior of these systems is analyzed by employing a two‐degree‐of‐freedom model accounting for the superstructure flexibility, whereas the friction pendulum system device behavior is described by adopting a widespread model that considers the variation of the friction coefficient with the velocity. With reference to medium soil condition, the uncertainty in the seismic inputs is taken into account by considering a set of artificial records, obtained through Monte Carlo simulations within the power spectral density method, with different frequency contents and characteristics depending on the soil dynamic parameters and scaled to increasing intensity levels. The sliding friction coefficient at large velocity is also considered as random variable modeled through a uniform probability density function. Incremental dynamic analyses are developed in order to evaluate the probabilities exceeding different limit states related to both r.c. superstructure and isolation level defining the seismic fragility curves through an extensive parametric study carried out for different structural system properties. Finally, considering the seismic hazard curves related to a site near L'Aquila (Italy), the seismic reliability of the r.c. superstructure systems is evaluated, and seismic reliability‐based design abacuses are derived with the aim to define the radius in plan of the friction pendulum devices in function of the structural properties and reliability level expected. Copyright © 2016 John Wiley & Sons, Ltd.     

地震易损性分析方法研究综述

结构的地震易损性分析对于预测结构的抗震性能、进行结构的抗震设计、加固和维修决策具有重要的应用价值。本文将对近几十年来地震易损性评估方法领域内的重大发展做全面综述,并对易损性分析方法的类别和优缺点及其应用作了总结和讨论。     

油浸式高压变压器地震易损性分析

油浸式变压器是由多种材料组成的复杂结构。本文对油浸式高压变压器建立了较为精确的有限元模型，考虑了各组件之间相互作用的影响。对该设备进行了动力性能和地震响应分析以及易损性分析。分析结果表明，大型高压变压器在地震中的首要破坏模式为瓷套破坏，其地震响应的离散度较高。易损性分析得到设备的地震易损性曲线，可直接应用于电力系统的抗震分析。     

抗震结构最优设防水平决策与全寿命优化设计的简化易损性分析方法

地震破坏状态概率分析是抗震结构最优设防水平决策与全寿命优化设计的关键问题之一,作者们曾根据"三水准"设防原则和地震烈度的危险性分析结果提出了二种实用分析方法.本文建立了结构破坏状态概率分析的地震易损性理论基础,提出了极限状态地震易损性和破坏状态地震易损性的概念.从地震易损性理论的角度,对二种地震破坏状态概率简化分析方法进行了深入分析,指出第1种方法是一种考虑结构宏观抗震能力不确定性的半理论半经验易损性分析方法,而第2种方法则是一种不考虑结构宏观抗震能力不确定性的简化易损性分析方法,根据地震破坏状态概率的计算结果对二种方法进行了对比分析,并提出了相关的建议.     

基于增量动力分析方法的砌体结构地震易损性分析

砌体结构是一种脆性结构,变形能力和承载力均较低,因取材方便、施工简单和造价低等优势在中国被广泛应用。为了评估砌体结构的抗震性能,本文基于增量动力分析（Incremental Dynamic Analysis,IDA）方法研究了多层砌体结构的地震易损性,分析了影响砌体结构地震易损性的主要因素以及群体多层砌体结构地震易损性。研究结果表明:在相同场地条件情况下,砌体结构的房屋层数、砌筑砂浆强度、设防烈度和墙体面积率对结构的地震易损性影响较明显;当结构层高在2.8~3.3 m之间时,层高对结构地震易损性的影响不大。抗震设防砌体结构抗震能力比不设防结构有明显提高,说明构造柱和圈梁等构造措施能显著提高砌体结构的抗倒塌能力,这与目前的基本认识相同,也证明了增量动力分析方法的有效性。     

摩擦耗能框架体系动力分析

采用粘性屈服模型来模拟摩擦耗能器的力－速度关系。建立了带有摩擦耗能器体系的动力分析8方法，采用增量型Rosenbrock二阶三阶半隐式Runge-Kutta法求解动力方程，得到了带有摩擦耗能器单层框架在正弦波激励下反应的解析解，并据此验证粘性屈服模型及求解动力方程算法的正确性，分析了摩擦耗能器的起滑力和支撑刚度对耗能减振效果的影响。     

Multi‐angle,multi‐damage fragility curves for seismic assessment of bridges

The scope of this study is to investigate the effect of the direction of seismic excitation on the fragility of an already constructed, 99‐m‐long, three‐span highway overpass. First, the investigation is performed at a component level, quantifying the sensitivity of local damage modes of individual bridge components (namely, piers, bearings, abutments, and footings) to the direction of earthquake excitation. The global vulnerability at the system level is then assessed for a given angle of incidence of the earthquake ground motion to provide a single‐angle, multi‐damage probabilistic estimate of the bridge overall performance. A multi‐angle, multi‐damage, vulnerability assessment methodology is then followed, assuming uniform distribution for the angle of incidence of seismic waves with respect to the bridge axis. The above three levels of investigation highlight that the directivity of ground motion excitation may have a significant impact on the fragility of the individual bridge components, which shall not be a priori neglected. Most importantly, depending on the assumptions made for the component to the system level transition, this local sensitivity is often suppressed. It may be therefore necessary, based on the ultimate purpose of the vulnerability or the life cycle analysis, to obtain a comprehensive insight on the multiple damage potential of all individual structural and foundation components under multi‐angle excitation, to quantify the statistical correlation among the distinct damage modes and to identify the components that are both most critical and sensitive to the direction of ground motion and carefully define their limit states which control the predicted bridge fragility. Copyright © 2015 John Wiley & Sons, Ltd.     

Evaluation of simplified methods of analysis for structures with triple friction pendulum isolators

Triple friction pendulum isolators, that exhibit behavior with amplitude‐dependent strength and instantaneous stiffness, represent a new development in seismic isolation. The application of simplified methods of analysis for this type of seismically isolated structures requires development of tools of simplified analysis and demonstration of their accuracy. This paper describes these tools and presents validation studies based on a large number of nonlinear response history analysis results. It is shown that simplified methods of analysis systematically provide good and often conservative estimates of isolator displacement demands and good estimates of isolator peak velocities. Copyright © 2009 John Wiley & Sons, Ltd.     

基于增量动力法的剪力墙结构地震易损性分析

地震易损性分析是评估结构地震灾害损失的关键。应用PKPM软件设计了不同设防烈度的6个16层剪力墙结构。应用增量动力法求得各结构在不同罕遇烈度地震作用下的最大层间位移角,回归分析给出了最大层间位移角与地震作用加速度峰值的关系式。以最大层间位移角为整体性能指标,进行结构地震易损性分析,给出了结构地震失效概率关于地震作用加速度峰值的计算公式。计算得到了不同设防烈度剪力墙结构在罕遇地震作用下的震害矩阵,为评估框架-剪力墙结构的地震灾害损失,提供了基础数据。     

摩擦隔震结构中不同摩擦力模型在地震作用下结构响应分析

本文选用两种摩擦力模型来分析隔震结构的地震响应，运用newmark方法推导了隔震结构采用库仑摩擦力模型在地震作用下结构响应的计算公式。并编程计算了实例，进行了综合分析，得出质量比、摩擦系数对隔震效果的影响；并给出在其他结构参数相对稳定的条件下，滑移面摩擦系数的取值范围。     

基于改进云图法的结构概率地震需求分析

概率地震需求分析是美国太平洋地震工程研究中心(Pacific Earthquake Engineering ResearchCenter,PEER)提出的新一代"性能化地震工程(Performance-Based Earthquake Engineering,PBEE)"理论框架的重要一环。传统的概率地震需求分析方法称为"云图法",这种方法针对确定性结构进行一系列地震动作用下的非线性动力分析,从而得到地震动强度参数与结构地震需求的"云图"。然而,传统的云图法只能考虑地震动的不确定性,而无法考虑结构的不确定性。为此,结合拉丁超立方体抽样技术,提出一种能综合考虑地震动不确定性和结构不确定性的改进云图法,并将传统的概率地震需求分析内容拓展为概率地震需求模型、概率地震需求易损性分析、概率地震需求危险性分析三个层次。以一榀五层三跨钢筋混凝土框架结构为例,分别采用传统云图法和改进云图法对其进行概率地震需求分析,得到了该结构的概率地震需求模型、地震需求易损性曲线和地震需求危险性曲线。分析结果表明:提出的方法可以有效地考虑地震动与结构的不确定性,避免不考虑结构的不确定性而低估结构的地震风险性。     

Effect of the angle of seismic incidence on the fragility curves of bridges

This study examines the effect of the angle of seismic incidence θ on the fragility curves of bridges. Although currently, fragility curves of bridges are usually expressed only as a function of intensity measure of ground motion (IM) such as peak ground acceleration, peak ground velocity, or S_a(ω₁), in this study they are expressed as a function of IM with θ as a parameter. Lognormal distribution function is used for this purpose with fragility parameters, median c_m and standard deviation ζ to be estimated for each value of θ chosen from 0 < θ < 360°. A nonlinear 3D finite element dynamic analysis is performed, and key response values are calculated as demand on the bridge under a set of acceleration time histories with different IM values representing the seismic hazard in Los Angeles area. This method is applied to typical straight reinforced concrete bridges located in California. The results are validated with existing empirical damage data from the 1994 Northridge earthquake. Even though the sample bridges are regular and symmetric with respect to the longitudinal axis, the results indicate that the weakest direction is neither longitudinal nor transverse. Therefore, if the angle of seismic incidence is not considered, the damageability of a bridge can be underestimated depending on the incidence angle of seismic wave. Because a regional highway transportation network is composed of hundreds or even thousands of bridges, its vulnerability can also be underestimated. Hence, it is prudent to use fragility curves taking the incident angle of seismic waves into consideration as developed here when the seismic performance of a highway network is to be analyzed. Copyright © 2012 John Wiley & Sons, Ltd.     

Development of seismic fragility curves for low-rise masonry infilled reinforced concrete buildings by a coefficient-based method

This study presents a seismic fragility analysis and ultimate spectral displacement assessment of regular low-rise masonry infilled (MI) reinforced concrete (RC) buildings using a coefficient-based method. The coefficient-based method does not require a complicated finite element analysis; instead, it is a simplified procedure for assessing the spectral acceleration and displacement of buildings subjected to earthquakes. A regression analysis was first performed to obtain the best-fitting equations for the inter-story drift ratio (IDR) and period shift factor of low-rise MI RC buildings in response to the peak ground acceleration of earthquakes using published results obtained from shaking table tests. Both spectral acceleration-and spectral displacement-based fragility curves under various damage states (in terms of IDR) were then constructed using the coefficient-based method. Finally, the spectral displacements of low-rise MI RC buildings at the ultimate (or near-collapse) state obtained from this paper and the literature were compared. The simulation results indicate that the fragility curves obtained from this study and other previous work correspond well. Furthermore, most of the spectral displacements of low-rise MI RC buildings at the ultimate state from the literature fall within the bounded spectral displacements predicted by the coefficient-based method.     

摩擦摆基础隔震结构双向地震反应分析

采用双向耦合力学模型模拟摩擦摆支座的双向耦合效应,对摩擦摆基础隔震结构进行了单向和双向地震反应对比分忻,分析表明在双向地震作用下结构各层的加速度反应较小,隔震层的层间位移较大,而上部结构的层间位移较小,并且在双向地震作用下,支座的最大位移明显大于单向地震作用时的支座最大位移,因而应考虑双向地震作用对摩擦摆基础隔震结构地震反应和隔震支座性能的影响。     

Shake table testing on restoring capability of double concave friction pendulum seismic isolation systems

After an earthquake, non‐negligible residual displacements may affect the serviceability of a base isolated structure, if the isolation system does not possess a good restoring capability. The permanent offset does not affect the performance unless the design is problematic for utilities, also considering possible concerns related to the maintenance of the devices. Starting from experimental and analytical results of previous studies, the restoring capability of Double Concave Friction Pendulum bearings is investigated in this paper. A simplified design suggestion for the estimation of maximum expected residual displacements for currently used friction pendulum systems is then validated. The study is based on controlled‐displacement and seismic input experiments, both performed under unidirectional motion. Several shaking table tests have been carried out on a three‐dimensional isolated specimen structure. The same sequence of seismic inputs was applied considering three different conditions of sliding surfaces corresponding to low, medium and high friction. The accumulation of residual displacements is also investigated by means of nonlinear dynamic analysis. Copyright © 2017 John Wiley & Sons, Ltd.     

Shake table tests for the seismic fragility evaluation of hospital rooms

Health care facilities may undergo severe and widespread damage that impairs the functionality of the system when it is stricken by an earthquake. Such detrimental response is emphasized either for the hospital buildings designed primarily for gravity loads or without employing base isolation/supplemental damping systems. Moreover, these buildings need to warrant operability especially in the aftermath of moderate‐to‐severe earthquake ground motions. The provisions implemented in the new seismic codes allow obtaining adequate seismic performance for the hospital structural components; nevertheless, they do not provide definite yet reliable rules to design and protect the building contents. To date, very few experimental tests have been carried out on hospital buildings equipped with nonstructural components as well as building contents. The present paper is aimed at establishing the limit states for a typical health care room and deriving empirical fragility curves by considering a systemic approach. Toward this aim, a full scale three‐dimensional model of an examination (out patients consultation) room is constructed and tested dynamically by using the shaking table facility of the University of Naples, Italy. The sample room contains a number of typical medical components, which are either directly connected to the panel boards of the perimeter walls or behave as simple freestanding elements. The outcomes of the comprehensive shaking table tests carried out on the examination room have been utilized to derive fragility curves based on a systemic approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Predictive control of seismic structures with semi‐active friction dampers

In this paper a predictive control method especially suitable for the control of semi‐active friction dampers is proposed. By keeping the adjustable slip force of a semi‐active friction damper slightly lower than the critical friction force, the method allows the damper to remain in its slip state throughout an earthquake of arbitrary intensity, so the energy dissipation capacity of the damper can be improved. The proposed method is formulated in a discrete‐time domain and cast in the form of direct output feedback for easy control implementation. The control algorithm is able to produce a continuous and smooth slip force for a friction damper and thus avoid exerting the high‐frequency structural response that usually exists in structures with conventional friction dampers. Using a numerical study, the control performance of a multiple degrees of freedom (DOF) structural system equipped with passive friction dampers and semi‐active dampers controlled by the proposed method are compared. The numerical case shows that by merely using a single semi‐active friction damper and a few sensors, the proposed method is able to achieve better acceleration reduction than the case using multiple passive dampers. Copyright © 2004 John Wiley & Sons, Ltd.     

Protection of seismic structures using semi‐active friction TMD

Although the design and applications of linear tuned mass damper (TMD) systems are well developed, nonlinear TMD systems are still in the developing stage. Energy dissipation via friction mechanisms is an effective means for mitigating the vibration of seismic structures. A friction‐type TMD, i.e. a nonlinear TMD, has the advantages of energy dissipation via a friction mechanism without requiring additional damping devices. However, a passive‐friction TMD (PF‐TMD) has such disadvantages as a fixed and pre‐determined slip load and may lose its tuning and energy dissipation abilities when it is in the stick state. A novel semi‐active‐friction TMD (SAF‐TMD) is used to overcome these disadvantages. The proposed SAF‐TMD has the following features. (1) The frictional force of the SAF‐TMD can be regulated in accordance with system responses. (2) The frictional force can be amplified via a braking mechanism. (3) A large TMD stroke can be utilized to enhance control performance. A non‐sticking friction control law, which can keep the SAF‐TMD activated throughout an earthquake with an arbitrary intensity, was applied. The performance of the PF‐TMD and SAF‐TMD systems in protecting seismic structures was investigated numerically. The results demonstrate that the SAF‐TMD performs better than the PF‐TMD and can prevent a residual stroke that may occur in a PF‐TMD system. Copyright © 2009 John Wiley & Sons, Ltd.     

支座摩擦系数对摩擦摆基础隔震结构地震反应的影响

对不同地震烈度作用下的摩擦摆基础隔震结构进行了地震反应分析,分析了支座摩擦系数对支座位移、楼层加速度和楼层剪力的影响。结果表明随着摩擦摆支座摩擦系数的增大,支座位移逐渐减小,而结构的加速度和楼层剪力逐渐增大;随着地震作用强度的提高,摩擦系数对支座位移的影响逐渐增大,而摩擦系数对结构加速度和楼层剪力的影响逐渐减小。     

摩擦摆基础隔震结构多维地震反应分析

对摩擦摆基础隔震结构进行了单向、双向和三向地震反应对比分析,表明考虑双向水平地震动时摩擦摆基础隔震结构的支座位移增大,而结构的加速度和楼层剪力减小,其中对支座位移和结构加速度影响较大;考虑竖向地震动时摩擦摆基础隔震结构的支座位移略有减小,而结构的加速度和楼层剪力增大,其中对结构加速度影响较大.因而,在进行摩擦摆基础隔震结构地震反应分析时,应考虑多维地震动的影响.