Life-cycle optimization in the establishment of performance-acceptance parameters for seismic design

A life-cycle formulation is presented for the determination of optimum values of the mechanical properties of a structural system exposed to seismic risk. The resulting values are intended for providing support for the establishment of performance-acceptance criteria and parameters for seismic design. A method is developed for the determination of expected damage functions in terms of simplified reference models of the complex nonlinear systems that are typical of engineering practice. The uncertainties associated with the use of the simplified model to estimate peak dynamic responses of the system of interest are accounted for by means of first-order second-moment probabilistic criteria. An illustrative application of the criteria proposed is presented, together with a discussion about the translation of the results of the optimization studies into engineering criteria and methods expressed in conventional design formats.     

Life-cycle cost optimal design of passive dissipative devices

The cost-effective performance of structures under natural hazards such as earthquakes and hurricanes has long been recognized to be an important topic in the design of civil engineering systems. A realistic comprehensive treatment of such a design requires proper integration of (i) methodologies for treating the uncertainties related to natural hazards and to the structural behavior over the entire life-cycle of the building, (ii) tools for evaluating the performance using socioeconomic criteria, as well as (iii) algorithms appropriate for stochastic analysis and optimization. A systematic probabilistic framework is presented here for detailed estimation and optimization of the life-cycle cost of engineering systems. This framework is a general one but the application of interest here is the design of passive dissipative devices for seismic risk mitigation. A comprehensive methodology is initially presented for earthquake loss estimation; this methodology uses the nonlinear time-history response of the structure under a given excitation to estimate the damage in a detailed, component level. A realistic probabilistic model is then presented for describing the ground motion time history for future earthquake excitations. In this setting, the life-cycle cost is uncertain and can be quantified by its expected value over the space of the uncertain parameters for the structural and excitation models. Because of the complexity of these models, calculation of this expected value is performed using stochastic simulation techniques. This approach, though, involves an unavoidable estimation error and significant computational cost, features which make efficient design optimization challenging. A highly efficient framework, consisting of two stages, is discussed for this stochastic optimization. An illustrative example is presented that shows the efficiency of the proposed methodology; it considers the seismic retrofitting of a four-story non-ductile reinforced-concrete building with viscous dampers.     

Optimal design of hysteretic dampers connecting adjacent structures using multi-objective genetic algorithm and stochastic linearization method

An optimal design method is proposed for nonlinear hysteretic dampers that enhance the seismic performance of two adjacent structures. The proposed method employs nonlinear random vibration analyses by use of a stochastic linearization method in order to efficiently estimate the stochastic responses of coupled buildings without performing numerous nonlinear time-history analyses. The main objectives of the optimal design are not only to reduce the seismic responses but also to minimize the total cost of the damper system. To deal with such conflicting objectives, a multi-objective genetic algorithm is adopted. This approach systematically obtains a set of Pareto optimal solutions that are non-inferior or non-superior to each other. The process for choosing a reasonable design from the optimal surface of Pareto solutions is also discussed. As an example of a nonlinear hysteretic damping device, this study considers passive-type magneto-rheological dampers with fixed input voltages. The optimal voltages and numbers of installed dampers are simultaneously determined. The robustness of the optimal design against uncertain characteristics of ground motions is examined through extensive nonlinear random vibration analyses.     

Finite element model development,validation and probabilistic seismic performance evaluation of Vincent Thomas suspension bridge

Based on recent findings, the main span of the Vincent Thomas suspension bridge crosses directly over the Palos Verdes fault, which has the capacity to produce a devastating earthquake. In spring 2000, the bridge underwent a major retrofit using visco-elastic dampers. This study focuses on seismic vulnerability of the retrofitted bridge. Three-dimensional member-based detailed and panel-based simplified finite element models of the bridge are developed. In order to show the appropriateness of these models, eigenproperties of the bridge are evaluated and compared with the system identification results obtained using ambient vibration data. In addition, a model validation is performed by simulating the dynamic response during the 1994 Northridge earthquake and comparing with the measured response. Finally, considering a set of strong ground motions in the Los Angeles area, nonlinear time history analyses are performed and the ductility demands of critical sections are presented in terms of fragility curves. The study shows that a ground motion with peak ground acceleration of 0.9 g or greater will result in plastic hinge formation at one or more locations with a probability of exceedance of 50%. Also, it is found that the effect of dampers is minimal for low to moderate earthquakes and high for strong earthquakes.     

Probabilistic seismic response and uncertainty analysis of continuous bridges under near-fault ground motions

Performance-based seismic design can generate predictable structure damage result with given seismic hazard. However, there are multiple sources of uncertainties in the seismic design process that can affect desired performance predictability. This paper mainly focuses on the effects of near-fault pulse-like ground motions and the uncertainties in bridge modeling on the seismic demands of regular continuous highway bridges. By modeling a regular continuous bridge with OpenSees software, a series of nonlinear dynamic time-history analysis of the bridge at three different site conditions under near-fault pulse-like ground motions are carried out. The relationships between different Intensity Measure (IM) parameters and the Engineering Demand Parameter (EDP) are discussed. After selecting the peak ground acceleration as the most correlated IM parameter and the drift ratio of the bridge column as the EDP parameter, a probabilistic seismic demand model is developed for near-fault earthquake ground motions for 3 different site conditions. On this basis, the uncertainty analysis is conducted with the key sources of uncertainty during the finite element modeling. All the results are quantified by the “swing” base on the specific distribution range of each uncertainty parameter both in near-fault and far-fault cases. All the ground motions are selected from PEER database, while the bridge case study is a typical regular highway bridge designed in accordance with the Chinese Guidelines for Seismic Design of Highway Bridges. The results show that PGA is a proper IM parameter for setting up a linear probabilistic seismic demand model; damping ratio, pier diameter and concrete strength are the main uncertainty parameters during bridge modeling, which should be considered both in near-fault and far-fault ground motion cases.     

某双塔斜拉桥抗震性能研究

以某大跨双塔斜拉桥为例,建立了主桥和引桥一体的动力模型,通过反应谱和非线性时程方法,分析了其地震响应,研究表明该桥满足抗震性能目标,纵向设置粘滞阻尼器后能显著的减少纵向地震反应内力。     

Seismic analysis incorporating detailed structure–abutment–foundation interaction for quasi-isolated highway bridges

The Illinois Department of Transportation has adopted an economical and pragmatic methodology for designing earthquake-resistant highway bridges in the Midwestern United States. These so-called quasi-isolated bridges employ low-cost non-seismically designed bearing components as sacrificial structural fuses. During seismic events, fusing actions of these components and subsequent sliding of superstructures on substructures are intended to achieve response characteristics similar to those of conventionally isolated bridges that employ specially designed isolators. This study explores seismic structure-abutment-foundation interaction for quasi-isolated bridges in Illinois, employing a detailed yet efficient non-linear finite-element model for seat-type bridge abutments. The abutment model incorporates many structural components and geotechnical mechanisms that are critical to seismic response of the structure-abutment-foundation (SAF) system. Through non-linear static analyses performed on a complete bridge model, the force-transfer mechanisms, component fusing performance, and potential failure modes of the SAF system were explored. Using earthquake ground motions, non-linear dynamic analyses were conducted to evaluate seismic characteristics of the quasi-isolated bridge, sequences of critical limit state occurrences, and effects of abutment attributes on bridge seismic performance. The influence of abutment model sophistication on simulated bridge response was also highlighted by direct comparison of simulation results obtained from different models.     

Simulation-based robust design of mass dampers for response mitigation of tension leg platforms

A robust stochastic design framework is discussed for design of mass dampers. The focus is on applications for the mitigation of the coupled heave and pitch response of Tension Leg Platforms under stochastic sea excitation. The framework presented fully addresses the complex relationship between the coupled dynamics of the platform, the stochastic excitation and the vibration of the dampers. Model parameters that have some level of uncertainty are probabilistically described. In this probabilistic setting, the system reliability is adopted as the design objective. Stochastic simulation is considered for evaluation of the system model response and the overall reliability performance. This way, all nonlinear characteristics of the structural response and environmental excitation are explicitly incorporated into their respective models. An efficient algorithm is discussed for performing the challenging stochastic design optimization. The ideas are illustrated in an application involving a tension leg platform with closely spaced frequencies for the heave and pitch degrees of freedom.     

Investigation of MRS and SMA Dampers Effects on Bridge Seismic Resistance Employing Analytical Models

This study dealt with investigating the seismic performance of the smart and shape memory alloy (SMA) and magnets plus rubber-spring (MRS) dampers and their effects on the seismic resistance of multiple-span simply supported bridges. The rubber springs in the MRS dampers were pre-compressed. For this aim, a set of experimental works was performed together with developing nonlinear analytical models to investigate dynamic responses of the bridges subjected to earthquakes. Fragility analysis and probabilistic assessment were conducted to assess the seismic performance for the overall bridge system. Fragility curves were then generated for each model and were compared with those of as-built. Results showed dampers could increase the seismic capacity of bridges. Furthermore, from system fragility curves, use of damper models reduced the seismic vulnerability in comparison to the as-built bridge model. Although the SMA damper showed the best seismic performance, the MRS damper was the most appropriate one for the bridge in that the combination of magnetic friction and pre-compressed rubber springs was cheaper than the shape memory alloy, and had the similar capability of the damper.     

基于半桥试验的双塔斜拉桥纵向地震响应研究

克服振动台进行小比例大跨度斜拉桥模型试验的局限性,以一座主跨为680m的对称大跨双塔斜拉桥为原型,设计缩尺比为1∶40的混凝土斜拉桥的半桥模型。采用振动台试验方法,研究纵向一致地震激励下半桥模型替代对称双塔斜拉桥的可行性。首先,基于动力学基本理论,提出双塔斜拉桥简化为等效半桥模型的边界条件,并通过两种模型的动力特性对比验证所提出的等效边界的合理性。其次,设计纵向地震作用下对称边界的实现方式,开展不同结构体系的半桥模型在纵向地震作用下的振动台试验;并进一步对比探讨纵向黏滞阻尼器对斜拉桥地震响应的控制效果。研究结果表明：不同PGA的地震动纵向一致作用下,等效半桥模型与全桥模型的地震响应规律基本相同;黏滞阻尼器对半漂浮体系斜拉桥的梁端和塔 梁的位移响应的有较好的减震效果。     

Comprehensive nonlinear seismic performance assessment of MR damper controlled systems using virtual real‐time hybrid simulation

Magnetorheological (MR) dampers have gained significant attention in seismic mitigation of structural systems due to their distinguished characteristics such as inherent stability and minimum power requirements. Their performance in control of nonlinear structural response, however, has not been widely investigated. This paper provides comprehensive nonlinear seismic performance assessment of a three‐story benchmark structure equipped with a large‐scale MR damper using virtual real‐time hybrid simulation to efficiently capture the nonlinear behavior of the damper. The framework is first verified by means of available experimental results of an actual RTHS on the same structural system. A set of 12 earthquake ground motions, each one scaled to have 12 different intensities are then utilized to perform nonlinear dynamic analyses. An energy‐based adaptive passive‐on control strategy is proposed, and its performance is compared with passive‐on, passive‐off, and uncontrolled response of the structure in terms of interstory drifts shown by fragility curves, residual drifts, MR damper control force, and the ability to maintain a uniform interstory drift along the height of the structure.     

Modeling considerations in seismic assessment of RC bridges using state-of-practice structural analysis software tools

The increasing awareness of the general society toward the seismic safety of structures has led to more restrictive performance requirements hence, many times, to the need of using new and more accurate methods of analysis of structures. Among these, nonlinear static procedures are becoming, evermore, the preferred choice of the majority of design codes, as an alternative to complete nonlinear time-history analysis for seismic design and assessment of structures. The many available software tools should therefore be evaluated and well understood, in order to be easily and soundly employed by the practitioners. The study presented herein intends to contribute to this need by providing further insight with respect to the use of commonly employed structural analysis software tools in nonlinear analysis of bridge structures. A comparison between different nonlinear modeling assumptions is presented, together with the comparison with real experimental results. Furthermore, alternative adaptive pushover procedures are proposed and applied to a case study bridge, based on a generic plastic hinge model. The adopted structural analysis program proved to be accurate, yielding reliable estimates, both in terms of local plastic hinge behavior and global structural behavior.     

跨倾滑正断层桥梁地震响应数值模拟

为揭示跨倾滑正断层桥梁的地震响应规律，以海文大桥跨断层引桥为研究对象，根据地震震级和断层参数间的关系构建了铺前-清澜断层的物理模型，并基于空间随机场模型生成该断层滑动的空间非均匀分布；采用基于断层破裂物理过程的地震动混合模拟方法生成断层两侧可能发生的最大永久位移地震动；同时，采用OpenSees建立了全桥三维动力有限元模型，分析了永久位移地震动频带、桥梁与断层相对位置、竖向地震动及减隔震方法对该桥地震响应的影响规律。研究结果表明：所采用的地震动模拟方法可以合理考虑断层断裂的复杂性，生成地震动的反应谱在短周期段和设计反应谱吻合良好，在长周期段具有显著的滑冲效应特征，可有效模拟断层两侧的永久位移地震动;在跨断层桥梁地震响应分析方面，断层错位和高频带地震动对跨断层桥梁地震响应均有较大的贡献，跨断层桥梁地震响应分析须采用具有永久位移的宽频带地震动作为地震动输入，仅采用高频带地震动或者采用断层错位进行静力分析均会低估桥墩的地震响应；而位于断层同侧的桥梁主要受高频地震动的影响，跨断层桥梁的地震响应远大于断层同侧桥梁的响应；不考虑竖向地震动会低估跨倾滑断层桥梁纵桥向的地震响应，且跨径越小竖向地震动的影响越大，在进行跨倾滑断层桥梁抗震设计时，应选取较大跨径的简支梁桥来减轻竖向地震动的影响。同时，合理的限位拉索设计可利用桥墩的抗震能力明显改善跨断层桥梁的支座变形，减小因断层错位引起的桥梁损伤。     

Application of cumulative prospect theory: Implied seismic design preference

Optimal seismic design level can be prescribed based on the minimization of the expected lifecycle cost or the expected utility theory. Recently, behavioral economists and cognitive psychologists have developed the popular cumulative prospect theory (CPT) to describe observed decision making behavior. In this study, an attempt is made in applying the CPT to reveal the implied seismic design preference by decision makers of bounded rationality. An approach incorporating the CPT, seismic risk assessment, and lifecycle cost analysis is used to investigate the sensitivity of the implied seismic design preferences to risk attitudes and possible people’s overreaction and unawareness in facing low probability high consequence risk. The impact of model parameters of the adopted value and weighting functions on the design preference is assessed through numerical examples. In general, the implied seismic design preference does not coincide with that dictated by minimizing the expected lifecycle cost, and the intervals of the implied preferences for sets of admissible combinations of model parameters of the value and weighting functions are relatively wide and depend on the adopted reference point.     

非线性粘滞阻尼器在框架结构抗震加固设计中的应用

本文介绍了非线性粘弹性阻尼器的性能特点及消能减震原理。并以实际抗震加固工程为例对粘滞阻尼器、屈曲约束支撑及传统加固方法的特点进行了对比,并对粘滞阻尼器的设计流程及方法进行了阐述和探讨。     

自锚式悬索桥磁流变阻尼器减震控制研究

为了减小自锚式悬索桥的地震响应,基于桥梁结构地震动力方程及磁流变阻尼器力学模型,建立桥梁结构—磁流变阻尼器减震系统并将其程序化,对某主跨350 m的独塔自锚式悬索桥进行减震控制研究,讨论了磁流变阻尼器输入电流、数目及安装位置对减震效果的影响。研究结果表明:采用磁流变阻尼器能够有效地减小自锚式悬索桥的纵向地震响应;随安装在塔梁之间顺桥向的磁流变阻尼器输入电流的增大及数目的增加,塔顶和主梁的纵向位移逐渐减小,结构的内力响应也得到有效控制;将全部磁流变阻尼器安装在塔梁之间顺桥向时减震效果最佳。     

Optimizing net present values of risk avoidance for mountain railway alignments with seismic performance evaluation

Railway alignment optimization in earthquake-prone mountainous (EPM) regions should quantify and trade off construction investments and seismic risks. Unfortunately, slight attention has been previously devoted to this trade-off. To this end, based on the FEMA-P58 methodology, a net present value (NPV) model of risk avoidance is presented and solved. In the model, alignment alternatives are first segmented into structural groups with different probabilistic seismic fragility curves, which are then used to generate structural repair cost and repair time curves. Afterward, a probabilistic seismic hazard curve is introduced to estimate the expected annual repair cost and time for computing railway direct and indirect seismic losses. Hence, the railway total annual loss caused by seismic activity can be obtained. Next, a benefit–cost analysis is performed to combine construction cost and seismic loss as the risk-cost NPV. To optimize this objective function, a particle swarm algorithm is used as the basic approach. For implementing the probabilistic seismic performance analysis, a Monte Carlo simulation (MCS) is employed as the risk assessment module. Furthermore, due to the computationally intensive nature of MCS, a CPU-based parallelization is embedded into the algorithm to expedite the search. Finally, the proposed model and method are applied to a representative real-world railway case in an EPM region. Their effectiveness is discussed and verified in five experiments, including algorithm convergence analysis, alignment solution comparison, seismic risk interpretation, computational efficiency test, and a specific sensitivity analysis.     

Application of shape memory alloy dampers in the seismic control of cable-stayed bridges

This paper focuses on introducing and investigating the performance of a new passive seismic control device for cable-stayed bridges made with shape memory alloys (SMAs). The superelasticity and damping capability of SMAs is sought in this study to develop a supplementary recentering and energy dissipation device for cable-stayed bridges. Three-dimensional long-span bridge model, including the effect of soil-structure interaction is developed and utilized in the study. SMA dampers are implemented at the bridge’s deck-pier and deck-tower connections. The bridge is subjected to three orthogonal components from two historic ground motion records. The effectiveness of the SMA dampers in controlling the deck displacement and limiting the shear and bending moment demands on the bridge towers is assessed. Furthermore, a study is conducted to determine the sensitivity of the bridge response to the hysteretic properties of the SMA dampers. The analytical results show that SMA dampers can successfully control the seismic behavior of the bridge. However, the effectiveness of the new dampers is significantly influenced by the relative stiffness between the dampers used at the deck-tower and deck-pier connections. The results also show that the variation in the SMAs’ strain hardening during phase transformation has a small effect on the bridge response compared to the variation in the unloading stress during reverse phase transformation.     

反应谱离散性对梁桥概率地震需求预计的影响

以一座三跨非规则钢筋混凝土连续梁桥为例,选择2组实际地震波作为输入地面运动,通过IDA分析探讨地震波反应谱的离散度对于梁桥结构概率地震需求预计的影响,得到以下结论：实际地震波的反应谱离散度与桥梁结构概率地震需求预计的离散度密切相关;针对基于概率理论的PBEE和PBSD,合理的选择实际地震波进行动力分析,可以使地震需求的概率分布更加符合实际情况,提高概率地震需求预计、易损性曲线等计算结果的精确性和计算效率。     

Optimum structural design based on seismic reliability and response distribution

An analytical approach to the optimum structural design parameters is developed on the basis of seismic reliability and inter-story response distribution. An earthquake-like stationary random excitation being assumed, probabilistic earthquake response is estimated as the solution of a simple simultaneous algebraic equation. Based on this probabilistic earthquake response, the optimum parameters are determined by selecting seismic structural reliability and an inter-story response distribution index as objective functions. The validity of this approach is demonstrated by examining the perspective and contour lines of the objective functions regarded as a function of design parameters for elastic structural systems with six degrees of freedom. The possible application of this approach is also presented to the determination of elasto-plastic structural parameters with bi-linear hysteretic characteristics. Other aspects of the approach's validity are also examined from the response distribution viewpoint for the elastic structural system with recorded strong earthquake motions. The influence of the higher modal response and the earthquake's predominant angular frequency on the optimum parameters are also discussed.