Sensitivity of Seismic Response and Fragility to Parameter Uncertainty of Single-Layer Reticulated Domes

Quantitatively modeling and propagating all sources of uncertainty stand at the core of seismic fragility assessment of structures. This paper investigates the effects of various sources of uncertainty on seismic responses and seismic fragility estimates of single-layer reticulated domes. Sensitivity analyses are performed to examine the sensitivity of typical seismic responses to uncertainties in structural modeling parameters, and the results suggest that the variability in structural damping, yielding strength, steel ultimate strain, dead load and snow load has significant effects on the seismic responses, and these five parameters should be taken as random variables in the seismic fragility assessment. Based on this, fragility estimates and fragility curves incorporating different levels of uncertainty are obtained on the basis of the results of incremental dynamic analyses on the corresponding set of 40 sample models generated by Latin Hypercube Sampling method. The comparisons of these fragility curves illustrate that, the inclusion of only ground motion uncertainty is inappropriate and inadequate, and the appropriate way is incorporating the variability in the five identified structural modeling parameters as well into the seismic fragility assessment of single-layer reticulated domes.     

Uncertainty in risk of highway bridges assessed for integrated seismic and flood hazards

Probabilistic risk assessment for bridges under natural hazards is of great interest to engineers for the development of risk mitigation strategies and implementation plans. The present study evaluates risk of an existing highway bridge in California, USA, under the integrated impact of regional seismic and flood hazards. A sensitivity study combining tornado diagram and first-order second moment reliability analyses is conducted to screen significant uncertain parameters to which bridge response is mostly sensitive. A rigorous uncertainty analysis, employing random sampling and Monte Carlo simulation techniques, is performed to obtain variations in fragility and risk curves of the bridge. Observed variations in risk curves at various risk levels are quantified through 90% confidence intervals and coefficients of variation (COV) of risk. It is observed that uncertainty in the estimated risk increases due to the presence of flood hazard at the bridge site, although mean risk does not vary with flood hazard level. Research outcome signifies that the variation in risk due to parameter uncertainty and varied flood hazard level should not be ignored to ensure bridge safety under the stated multi-hazard condition.     

Seismic fragility increment functions for deteriorating reinforced concrete bridges

Fragility increment functions are developed to estimate the seismic fragility of reinforced concrete (RC) bridges subject to deterioration due to the onset and progression of corrosion of the reinforcement. For each mode of failure considered, the fragility at time t of a deteriorating bridge is obtained by multiplying the initial fragility of the undeteriorated bridge by a corresponding increment function expressed in terms of the environmental conditions, the original material properties, time, a measure of the seismic demand, and a set of unknown model parameters. The developed increment functions account for the effects on the fragility estimates of the loss of the reinforcement and of the increasing uncertainty over time. As an application, the developed increment functions are used to estimate the seismic fragility of an example RC bridge. The proposed fragility increment functions are useful to estimate the fragility of deteriorating bridges without any extra reliability analysis once the fragility of the undeteriorated bridge is known. In particular, the proposed fragility increment functions can be used to assess the time-variant fragility of bridges for applications such as reliability-based design, life-cycle cost analysis, and risk analysis.     

Seismic fragility estimates for corroding reinforced concrete bridges

Seismic fragility of reinforced concrete (RC) bridges is defined as the conditional probability that the seismic demand exceeds the corresponding capacity, specified for a certain performance level, for given seismic intensity measures. However, the structural properties of RC bridges change over time due to the onset of corrosion in the reinforcing steel. Therefore, seismic fragility of RC bridges changes during a bridge lifetime. This paper proposes a method to estimate the seismic fragility of corroding RC bridges. Structural capacities are defined using probabilistic models for deformation and shear capacities of RC columns. Probabilistic models are also used to estimate the corresponding demands for given seismic intensity measures. The capacity and demand models are then combined with probabilistic models for chloride-induced corrosion and time-dependent corrosion rate to model the dependency on time of the seismic fragility of RC bridges. In particular, the loss of reinforcing steel is modelled as a function of the thickness of the cover concrete for each reinforcing bar in the RC columns. The stiffness degradation in the cover concrete over time due to corrosion-induced cracking is also considered in the fragility estimates. Seismic fragility estimates are then formulated at the column, bent, and bridge levels. The fragility formulations properly incorporate the uncertainties in the capacity and demand models, and the inexactness (or model error) in modelling the material deterioration. The proposed method accounts for the variation of structural capacity and seismic demand over time due to the effects of corrosion in the reinforcing steel. As an application, seismic fragility estimates are developed for a corroding RC bridge with 11 two-column bents over a 100-year period.     

Influential fluid–structure interaction modelling parameters on the response of bridges vulnerable to coastal storms

Analysis of coastal bridges under hurricane-induced wave and surge loads is essential for safety and performance assessment of water crossing bridge inventories. A reliable numerical model that can be employed to study the behaviour of bridges in hurricane events is beneficial because it reduces the cost and effort required for experimental models. Furthermore, it is important to identify modelling parameters that have a significant effect on the simulated response in order to guide uncertainty treatment for future bridge reliability studies. To address these needs, a high fidelity numerical model for simulation of coastal bridges is utilised that takes into account the fluid–structure interaction and includes contact surfaces that permit deck shifting and unseating during surge and wave passage. After validation of the model with experimental test data, it is implemented to examine the response of a typical water crossing bridge in the Houston area, revealing the values of wave and surge loads and also the potential of deck unseating under extreme wave and surge conditions. A sensitivity study is conducted to determine the uncertain structural modelling parameters that significantly affect the bridge response when subjected to surge and wave. Concrete strength and density, coefficient of friction between super- and substructure and soil shear strength are found to influence the bridge response and should be considered in probabilistic analyses and reliability assessments of coastal bridges.     

Closed-form seismic fragility estimates,sensitivity analysis and importance measures for reinforced concrete columns in two-column bents

Closed-form seismic fragility estimates are developed for reinforced concrete (RC) columns in bridges with two-column bents. Deformation and shear modes of failure are considered. The closed-form solutions incorporate the important uncertainties associated with both structural properties and ground motion characteristics. Probabilistic capacity and demand models for RC columns in two-column bents are used for the fragility formulation. Sensitivity and importance measures are computed for the parameters and random variables, respectively, included in the limit state function expressed in terms of probabilistic capacity and demand models. The sensitivity measures suggest that the vulnerability of RC columns in two-column bents can be effectively improved by using high strength reinforcement for the column confinement, reducing the spacing between confining reinforcement, and limiting the use of high strength concrete. The importance measures suggest that the random errors in the probabilistic capacity and demand models represent the principal sources of uncertainty. Thus, an approximate closed-form solution for a fragility estimation of a RC column can be developed by considering only the uncertainty in the random errors of the capacity and demand models. Only a marginal difference exists between the closed-form fragility estimates and the corresponding predictive fragility estimates that include all uncertainties.     

基于地震易损性解析函数的概率地震风险理论研究

基于不确定性传递,推导了考虑本质不确定性的地震易损性函数和考虑知识不确定性的地震易损性函数的解析表达式,并给出了其参数确定方法。证明了基于位移的函数与基于地震动强度的函数之间存在一致性。推导了考虑知识不确定性的地震易损性点估计函数的置信度水平。利用地震风险等于地震危险性与地震易损性的卷积,采用幂指数形式的地震危险性函数,进一步将已获得的地震易损性解析函数拓展得到概率地震风险函数的解析形式。利用得到的地震易损性与风险的解析函数,可简化地震易损性和风险评估的过程,方便对不同结构体系进行概率地震安全评估。     

矮墩大跨连续梁体系桥纵向减隔震设计

以上海大治河桥为实例,分析了矮墩、大跨连续梁体系桥的结构动力特性与地震易损性一般规律。重点探讨了矮墩、大跨连续梁体系桥的纵向地震响应规律与合理抗震设计,并指出了该类桥梁不适宜按延性抗震进行设计。按结构纵向约束要求,提出了采用E型软钢阻尼器组的减隔震设计方案,并给出了具体的设计参数。从非减隔震设计与减隔震设计方案的结构抗震性能对比分析结果可以看出,减隔震设计体系可以有效缓解纵向固定墩支座、墩身以及基础地震惯性力大、构件能力匹配关系难以满足能力保护设计的特点,是矮墩、大跨连续梁体系桥纵向抗震体系的理想解决方案。     

Probabilistic seismic demand analysis of a slender RC shear wall considering soil-structure interaction effects

Reinforced concrete shear walls are often used to resist the lateral loads imposed by earthquakes. Accurate evaluation of the seismic demands on shear walls requires adequate considerations of the nonlinear behavior of structural and foundation elements, the interaction between them, and the uncertainty and variability associated with earthquake ground motions. This paper presents a comprehensive probabilistic seismic demand analysis of a typical mid-rise slender shear wall in western US with a flexible foundation and evaluates the significance of soil-structure interaction (SSI) effects on their damage probability. Utilizing realistic numerical models for the shear wall and its foundation, the nonlinear time history analyses were conducted with a large number of recorded ground motions. Response quantities such as maximum inter-story drift ratio, base shear, foundation displacement and rotation are monitored and related to the intensity measure of ground motions (i.e. the inelastic spectral displacement S_di) for the cases with and without considering the SSI effects. Subsequently, the fragility functions of the shear wall are derived and the impact of SSI effects is investigated. It is found that the SSI generally reduces the damage probability of the shear wall, especially when soil nonlinearity is taken into account. The sensitivity of various seismic demands to soil parameters is also discussed. Under strong ground shakings, SSI effects on the maximum inter-story drift are most sensitive to the friction angle of the soil. It is suggested that the damages in foundation and surrounding soil should also be considered in order to systematically evaluate the SSI effects on damage probability of shear wall buildings.     

基于性能的输电塔地震易损性分析

本文以某高压输电塔为研究对象,同时考虑了结构本身的随机性和地震作用的随机性,采用了非线性屈曲分析及动力响应分析对结构的抗震性能、地震反应进行了分析。在基于性能的分析框架下,通过蒙特卡罗数值模拟获得了输电塔的抗震能力曲线,并分析了其统计特性,计算得到结构的地震易损性曲线,为输电塔的抗震防灾规划提供风险评估的数据基础。     

液化地基中群桩基础地震响应分析

可液化地基中桩基础地震响应分析一直是岩土工程抗震研究的热点和难点。针对这一问题,采用砂土液化大变形统一本构模型来描述可液化地基土体的应力应变关系,建立了一个3×5的群桩三维计算模型,采用三维弹塑性有限元动力时程分析,将地基、群桩基础和上部结构作为一个系统研究群桩基础的地震动响应规律,重点关注桩与土的运动相互作用以及水平方向的弯矩在地震荷载作用下的分配情况。结果表明可液化地基中桩基础的弯矩受桩与土运动相互作用影响显著;不同桩的弯矩最大值不同,角桩最大,边桩次之,中心桩最小;弯矩最大值出现的位置不相同,角桩和边桩弯矩最大值出现在上部非液化层与液化层界面处,中心桩弯矩最大值出现在桩头处。     

Performance-based seismic fragility analysis of retaining walls based on the probability density evolution method

Seismic fragility analysis is an efficient way to study the seismic behaviour and performance of structures under the excitation of earthquakes of varying intensity, and an essential part of the seismic risk assessment of structures. A recently developed dynamic reliability methodology, the probability density evolution method (PDEM), is proposed for the dynamic reliability and seismic fragility analysis of a retaining wall. The PDEM can obtain an instantaneous probability density function of the seismic responses and easily acquire the seismic reliability of the structural system. An important advantage of the PDEM is its high efficiency relative to that of the Monte Carlo simulation method, which is often used in the reliability and fragility analysis of structures. The present study uses a typical gravity retaining wall to illustrate stochastic seismic responses and fragility curves that can be obtained by the PDEM. The combined uncertainties of the seismic force and soil properties are explicitly and systematically modelled by stochastic ground motions and random variables respectively. The performance of the retaining wall is analysed for different acceptable levels of backfill settlement. Additionally, seismic fragility curves are constructed without assuming the distribution of the seismic response.     

Practical seismic fragility estimation of Japanese railway embankments using three seismic intensity measures

This study proposes a practical fragility estimation equation for Japanese standard models of railway embankments using the peak ground acceleration, peak ground velocity, and Arias intensity. The analytical models were implemented as unreinforced and geosynthetic-reinforced embankment models. A sensitivity analysis of the seismic fragility estimation of the embankment models was conducted on various embankment heights, average values of friction angles in the backfill soil, and tensile strengths of the primary reinforcement. Consequently, a unique formula for the fragility function in the presence of different seismic intensities was successfully presented. The parameters of the fragility function were successfully estimated using commonly used design parameters, such as the embankment height, average value of the friction angle of the backfill soil, and average value of the tensile strength. Additionally, another sensitivity analysis using different seismic databases was conducted to explore the effect of the seismic database on the fragility curve estimation of railway embankments. As a result, using different seismic databases, different fragility curves were obtained. These results highlight the importance of checking the sensitivity of the seismic database when developing the fragility curve.     

连续梁桥减、隔震体系的优化设计

本文根据连续梁桥减、隔震体系设计的特点,建立了桥梁减、隔震体系优化设计公式,实现了应用结构最优化设计理论设计桥梁减、隔震支座动力控制参数,使得桥梁墩、台所受到的地震水平力最小的同时满足小震作用下桥梁结构保持弹性;强震作用下减、隔震支座发生弹塑性变形耗散地震能量的减、隔震设计思想.通过编制的桥梁减、隔震体系优化设计程序,对连续梁桥减、隔震体系优化设计进行了算例分析,得出了一些有用的结论.     

Lateral response of pile foundations in liquefiable soils

Liquefaction has been a main cause of damage to civil engineering structures in seismically active areas.The effects of damage of liquefaction on deep foundations are very destructive. Seismic behavior of pile foundations is widely discussed by many researchers for safer and more economic design purposes. This paper presents a pseudo-static method for analysis of piles in liquefiable soil under seismic loads. A freefield site response analysis using three-dimensional(3D) numerical modeling was performed to determine kinematic loads from lateral ground displacements and inertial loads from vibration of the superstructure. The effects of various parameters, such as soil layering, kinematic and inertial forces,boundary condition of pile head and ground slope, on pile response were studied. By comparing the numerical results with the centrifuge test results, it can be concluded that the use of the p-y curves with various degradation factors in liquefiable sand gives reasonable results.     

砂桩加固液化砂土振动台试验中的孔隙水压力

以砂桩加固液化砂土的振动台试验为基础,通过测试加固与未加固模型土、同一桩距不同桩长下加固液化砂土的孔隙水压力,试验得出,未加固模型土埋深较浅的土层易液化,液化持续的时间较长,并随着深度的增加,液化程度有减小的趋势.     

土层的概率模型及其在桩基分析中的应用

本文讨论土层概率模拟的一些概念,特别介绍随机场的理论及一些新发展。该理论考虑土性的变异及由抽样所做成的误差。本文亦提出一种分析粘性土中桩基承载力的概率分析方法,并透过算例作具体说明。     

Fragility of skewed bridges under orthogonal seismic ground motions

The paper evaluates seismic fragility characteristics of skewed bridges under simultaneous action of orthogonal ground motion components. The effect of skew angle on bridge seismic fragility characteristics is investigated through nonlinear time-history analyses of Painter Street Overpass, a 38.5° skewed bridge located in Rio Dell, CA, and six representative bridges with skew angles varying between 0° and 50°. Ground motion incident angle is varied from 0° to 180° to investigate the effect of the direction of ground motion incidence on bridge seismic performance. Bridge seismic response is used to generate fragility curves and contours plots that quantify the sensitivity of bridge fragility characteristics on skew angle and incident angle. For any value of incident angle, bridge seismic vulnerability increases with an increase in skew angle; however, no such general trend is found to describe the effect of incident angle on bridge fragility characteristics. Results show that the variation of maximum rotation of bridge columns for an earthquake does not follow any particular trend with the change in skew angle and incident angle. Analysis-based fragility curves are further compared with empirical fragility curves generated using real-life seismic damage data of skewed bridges and a reasonable agreement is observed between these two.     

Reliability index for offshore piles subjected to bending

A first order second moment formulation is developed for analyzing the reliability of individual cross sections of piles driven on soft soils and subjected to random lateral static loads. The soil properties are expressed in terms of random p–y curves for a set of non-linear Winkler springs. The stiffness of the pile is taken as deterministic, but uncertainty about bending strength is accounted for. An algorithm is proposed and applied for determining probabilistic second moment estimates of internal forces and lateral displacements of a pile, taking into account both non-linear behavior and uncertainty about the parameters of the p–y curves. The cases studied include hypothetical piles driven on identical soft clays, and the loads correspond to the design conditions representative of several locations throughout the world. Very wide variations are found for the reliability index β of piles designed in accordance with ordinarily accepted regulations.     

Seismic performances of dyke on liquefiable soils

Various field investigations of earthquake disaster cases have confirmed that earthquake-induced liquefaction is a main factor causing significant damage to dyke, research on seismic performances of dyke is thus of great importance. In this paper, seismic responses of dyke on liquefiable soils were investigated by means of dynamic centrifuge model tests and three-dimensional (3D) effective stress analysis method which is based on a multiple shear mechanism model and a liquefaction front. For the prototype scale centrifuge tests, sine wave input motions with peak accelerations 0.806 m/s², 1.790 m/s² and 3.133 m/s² of varied amplitudes were adopted to study the seismic performances of dyke on the saturated soil layer foundation with relative density of approximately 30%. Then, corresponding numerical simulations were conducted to investigate the distribution and variations of deformation, acceleration, excess pore-water pressure (EPWP), and behaviors of shear dilatancy in the dyke and the liquefiable soil foundation. Moreover, detailed discussions and comparisons between numerical simulations and centrifuge tests were also presented. It is concluded that the computed results have a good agreement with the measured results by centrifuge tests. The physical and numerical models both indicate that the dyke hosted on liquefiable soils subjected to earthquake motions has exhibited larger settlement and lateral spread: the stronger the motion is, the larger the dyke deformation is. Compared to soils in the deep ground under the dyke and the free field, the EPWP ratio is much smaller in the shallow liquefiable soil beneath the dyke in spite of large deformation produced. For the same overburden depth soil from free site and the liquefiable foundation beneath dyke, the characteristics of effective stress path and stress–strain relations are different. All these results may be of theoretical and practical significance for seismic design of the dyke on liquefiable soils.