基于地震易损性解析函数的概率地震风险应用研究

在采用全概率方法的基于性能的地震工程研究中,定量反映地震作用和工程结构中存在的不确定性是研究的关键。利用地震易损性和地震风险的概率解析函数,针对一栋按我国相关规范设计的五层三跨钢筋混凝土框架结构进行了地震易损性分析和风险评估。采用100条实际地震动作为输入以考虑地震动的不确定性,提出了基于控制变换拉丁超立方体抽样技术的随机Pushover方法以考虑结构不确定性对其抗震能力的影响。结果表明：算例结构在50年内发生完全破坏的概率不超过2%,发生严重破坏的概率不超过10%,发生轻微破坏的概率基本不超过63.2%,基本满足我国“小震不坏、中震可修、大震不倒”的三水准要求。     

考虑结构与地震动双重不确定性的混凝土框架建筑地震易损性研究

考虑建筑结构与地震动的双重不确定性对地震易损性分析的影响,采用人工合成地震波及拉丁超立方体抽样来考虑地震动与结构的不确定性,形成了300个"结构-地震动"的随机样本,借助于Open SEES有限元平台对混凝土平面框架结构分别进行概率地震需求分析与概率能力分析,绘制混凝土框架建筑物的地震易损性曲线,并分别讨论结构高宽比及轴压比对混凝土框架结构抗震性能的影响。研究表明:地震动与结构的双重不确定性对地震易损性评估的结果影响显著,结构的地震易损性性能受轴压比影响较为明显,所提及的方法对于地震易损性分析具有很好的应用前景。     

考虑结构不确定性的地震倒塌易损性分析

传统的地震倒塌易损性分析中通常只考虑地震动不确定性的影响。在结构临近倒塌时,通常处于高度非线性状态,会出现结构不确定性与地震动不确定性的耦合放大现象。针对这一问题,将平均值一次二阶矩方法（MVFOSM）与逐步增量动力分析（IDA）相结合,提出了一种可以考虑结构不确定性的基于MVFOSM的随机IDA方法。以五层三跨钢筋混凝土框架结构为例,采用基于MVFOSM的随机IDA方法对其进行了地震倒塌易损性分析,并利用“龙卷风图”方法对结构抗地震倒塌能力的灵敏度进行了分析。研究表明：结构不确定性的存在使得结构抗地震倒塌能力的对数标准差增加了70%,因此有必要在地震倒塌易损性分析中考虑结构不确定性的影响。     

砖石古塔的地震风险评估

为了建立砖石古塔在地震作用下的风险评估体系,基于砖石古塔抗震性能和震害调查,选取易损性评判指标,绘制其易损性曲线,然后将砖石古塔建筑的易损性分析与场地的地震危险性分析相结合,考虑结构的破坏概率和地震损失,建立砖石古塔建筑的地震风险评估数学模型,量化砖石古塔的地震风险。以小雁塔为例运用该方法对其进行概率风险分析,确定小雁塔的风险值。     

考虑多重不确定性的我国多层#br# 冷成型钢结构地震风险评估

准确评估建筑结构的地震风险是实现其性能化抗震设计的重要组成部分。冷成型钢结构体系作为绿色和工业化建筑的典型代表,却鲜有针对于我国的地震风险评估研究。文章旨在分析和评估多层冷成型钢结构抗震分析所涉及的多重不确定性因素,进而定量评估该类结构在我国的地震风险。文章设计1栋八度抗震设防的6层冷成型钢结构,基于经过振动台验证的简化数值分析方法建立结构的简化数值模型,定量求解结构的多重不确定性因素和在使用周期内(50年)的地震风险。研究结果表明：由于我国一些地区的地震危险性形状系数较大,在考虑多重不确定性后,结构的破坏概率显著提高,50年使用周期内倒塌概率的增幅达到10倍以上;算例结构在50年使用周期内基本满足“小震不坏、中震可修、大震不倒”的抗震设防要求,对于个别特殊区域应适当控制结构发生轻微破坏的概率。此外,文章建议应全面考虑多重不确定对冷成型钢结构地震风险的影响,对不确定性参数的取值和地震风险的计算方法可提供借鉴。     

地震危险性分析中的不确定性因素及其数学处理

在地震危险性分析中，存在许多不确定性因素，包括随机性，模糊性，未确知性。但引起地震危险性分析结果不确定的主要因素是未确知性，如对地震机理认识不清，历史地震资料不充分，考虑因素不全面等等，未确知性是一种“弱”不确定性，可以用主观概率，主观隶属度等描述随机性和模糊性的手段来描述，减少和避免未确知性的根本出路在于更深入地研究地震发生机制，考虑尽可能多的因素和搜集尽可能充分的地震地质资料。     

考虑倒塌概率修正的钢筋混凝土框架结构地震易损性分析

为研究倒塌概率对非倒塌极限状态的影响,提出了考虑倒塌概率修正的结构地震易损性分析方法。基于全概率定理,将结构极限状态划分为倒塌状态和非倒塌状态两类,若结构发生倒塌则认为结构发生非倒塌极限状态破坏的概率为100%。考虑倒塌概率修正的地震易损性分析方法包含直接方法和间接方法,其中,直接方法是直接对传统地震易损性函数进行修正,而间接方法仅修正地震易损性函数中的概率地震需求参数。以4榀不同高度不同设防烈度的钢筋混凝土平面框架结构作为研究对象,选择100条实际地震动记录作为输入,分别采用直接方法和间接方法开展考虑倒塌概率修正的地震易损性分析。结果表明：倒塌概率对轻微破坏和中等破坏极限状态的影响较小,而对严重破坏极限状态的影响较大;在地震动强度较小时,两种方法对地震易损性的修正结果相差较小;随着地震动强度的提高,两种方法对地震易损性修正结果的差距逐渐增大。     

基于变形的土石坝地震易损性分析

地震易损性分析是地震风险分析的重要组成部分,可以预测结构在遭受不同等级地震荷载作用下发生各级破损的概率。土石坝在地震作用下易发生不同程度的破坏,对其进行易损性分析可以为土石坝地震风险分析及评价提供有效途径。考虑土石坝材料参数及地震动输入不确定性因素的影响,提出了基于变形的土石坝地震易损性分析方法。采用正交设计法选取材料参数样本组合,分别施加不同地震峰值加速度进行地震反应分析,基于坝顶相对沉陷破损评价指标,给出了大坝的易损性曲线。以云鹏心墙土石坝为例进行了地震易损性分析,得到大坝不同震损等级的风险概率,对土石坝地震风险评估和抗震设计优化、维修加固决策等具有重要意义和应用价值。     

基于性能的方钢管混凝土框架结构地震易损性分析

钢-混凝土组合结构由于兼有钢结构和混凝土结构的优点,近年来得到了迅速发展和广泛应用,目前已成为我国高层建筑领域内应用较多的一种结构形式。虽然在地震区越来越多地采用这种新型的结构,但迄今为止还没有发现对钢-混凝土组合结构的地震易损性进行过研究的文献。因此给出一种基于性能的结构整体地震易损性分析方法,该方法既考虑了结构本身的不确定性,又考虑了地震动输入的不确定性。并定义了结构整体和楼层的四个极限破坏状态,从而提出了基于结构极限破坏状态确定结构抗震性能水平限值的方法。最后采用该方法对两个不同类型的方钢管混凝土框架结构进行基于性能的地震易损性分析,得到结构的易损性曲线,对结构的易损性能进行评估和分析,并比较了两个结构的易损性能。     

考虑结构不确定性的多层框架结构地震易损性分析

文中选取常见的六层钢筋混凝土框架结构作为研究对象,考虑地震动与结构模型的双重不确定性,基于拉丁超立方抽样和正交设计相结合的试验方法针对结构模型建立了27个结构样本,应用OpenSees分别对每个样本开展增量动力分析,分别计算出每个样本在27条地震动的12次调幅作用下的各算例所对应的最大层间位移角。并对最大层间位移角与峰值加速度结果进行回归分析。以结构最大层间位移角作为损伤指标得到结构地震易损性曲线,并对比分析了地震动记录条数与模型不确定性对结构地震易损性的影响。结果表明,文中提出的分析方法能够较好的考虑地震动不确定性与结构自身不确定性,是一种有效的理论易损性求解方法;结构模型自身的不确定性对结构地震易损性结果具有较大的影响,这种影响对结构在大震作用下的抗倒塌能力尤为明显;文中的研究结果可为评估多层框架结构的地震灾害损失提供基础数据。     

Bayesian analysis of uncertainty for structural engineering applications

There has been recent interest in differentiating aleatory and epistemic uncertainties within the structural engineering context. Aleatory uncertainty, which is related to the inherent physical randomness of a system, has substantially different effects on the analysis and design of structures as compared with epistemic uncertainty, which is knowledge based. Bayesian techniques provide powerful tools for integrating, in a rigorous manner, the two types of uncertainties. In a purely probabilistic viewpoint, the uncertainties merge, resulting in widened probability densities. From the viewpoint of design or experimentation, however, the two types of uncertainties have widely different effects. The purpose of this paper is to develop insight into these effects, using Bayesian-based analytical expressions for the aleatory and epistemic uncertainties. The paper goes beyond standard Bayesian conjugate distributions by incorporating the effects of model uncertainty, where the applicability of two or more analytical models are used to describe the structure of interest. The influence of multiple model uncertainties is explored for two problems: the Bayesian updating process as data is acquired, and the design of simple parallel systems.     

Structural fragility and principle of maximum entropy

The concept of structural fragility with application to seismic probabilistic risk assessment is considered. Different formats of structural fragility representation are discussed. The principle of maximum entropy for a fragility distribution is formulated. Using this principle, the appropriate analytical forms of the state-of-knowledge fragility distribution for several important cases are selected. In the case where few fragility data are available, the joint distribution of uncertainty of fragility parameters is developed using the likelihood density function method.     

Probabilistic analysis of uncertainties in seismic hazard assessment

Sources and current methods of analysis of uncertainty from randomness, fuzziness and ignorance or incomplete knowledge in seismic hazard assessment problem are briefly discussed at beginning; understandings of the authors are then presented in the following order. All three types of uncertainty come from incomplete knowledge. Probabilistic method can be applied to all of them, objective probability for random factors and subjective probability for the other two types of uncertain factors. Discrete subjective probability mass functions for incomplete and fuzzy factors can be obtained from logic-tree and membership functions respectively. Fractile curves may be used to show the scattering of any uncertainty factor, but a unified probabilistic treatment may be applied to any combination of all three types of uncertainty.     

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.     

Simplified seismic life cycle cost estimation of a steel jacket offshore platform structure

The purpose of the present paper is to develop a simple methodology for seismic life cycle cost (LCC) estimation for a steel jacket offshore platform structure. This methodology accounts for accuracy of LCC modelling as well as simplicity of application. Accuracy is maintained through incorporating the effect of aleatory and epistemic uncertainties in the LCC estimation framework. Simplicity is achieved by using equivalent single-degree-of-freedom (ESDOF) system instead of the full structure and by eliminating full incremental dynamic analysis and fragility analysis. Instead, an approximate fragility curve and a localised incremental dynamic analysis curve are used along with a probabilistic simple closed-form solution for loss estimation. In the design of model structures, different bracing systems are used for the seismic design of the offshore platform, such as conventional and buckling-restrained braces. The proposed LCC methodology is validated through comparison with the results from a more rigorous method. It is found that even though the proposed methodology results in a slightly different solution compared to the reference method, the method can be used as an efficient tool for preliminary LCC evaluation of structures.     

基于CPU并行计算的概率地震需求#br# 分析与地震易损性分析

概率地震需求分析体现了不确定性从地震动强度参数到工程需求参数的传递过程,文中介绍并对比概率地震需求分析中云图法、单条带法与多条带法的优缺点。以MATLAB+OpenSEES实时交互方式,提出基于CPU并行计算架构的概率地震需求分析方法,显著提高分析效率。提出并行-云图法、并行-单条带法与并行 多条带法,通过RC框剪结构的概率地震需求分析,开展不同层高RC框剪结构的地震易损性分析。研究表明：云图法的对数标准差普遍大于单条带法与多条带法,过高地估计了结构的抗震性能,而单条带法与多条带法在易损性中位值与对数标准差确定方法上存在差异,单条带法的对数标准差普遍低于多条带法。     

Uncertainty propagation in probabilistic seismic loss estimation

Probabilistic estimation of losses in a building due to earthquake damage is a topic of interest to decision makers and an area of active research. One promising approach to the problem, proposed by the Pacific Earthquake Engineering Research (PEER) Center, involves breaking the analysis into separate components associated with ground motion hazard, structural response, damage to components and repair costs. Each stage of this method has both inherent (aleatory) randomness and (epistemic) model uncertainty, and these two sources of uncertainty must be propagated through the analysis in order to determine the total uncertainty in the resulting loss estimates. In this paper, the PEER framework for seismic loss estimation is reviewed and options for both characterizing and propagating the various sources of uncertainty are proposed. Models for correlations (among, e.g., element repair costs) are proposed that may be useful when empirical data is lacking. Several options are discussed for propagating uncertainty, ranging from flexible but expensive Monte Carlo simulation to closed form solutions requiring specific functional forms for relationships between variables to be assumed. A procedure that falls between these two extremes is proposed, which integrates over the discrete element damage states, and uses the first-order second-oment method to collapse several conditional random variables into a single conditional random variable representing total repair cost given the ground motion intensity. Numerical integration is then used to incorporate the ground motion hazard. Studies attempting to characterize epistemic uncertainty or develop specific elements of the framework are referenced as an aid for users wishing to implement this loss-estimation procedure.     

Seismic risk analysis for reinforced concrete structures with both random and parallelepiped convex variables

This article develops an improved seismic risk assessment formulation exhibiting both random and bounded uncertainties using a probability and parallelepiped convex set mixed model. Limit thresholds for different types of components are described via a probabilistic model. The distribution parameters of limit thresholds are originally treated by employing a multidimensional parallelepiped convex model, in which marginal intervals are utilised to represent scattering levels for the distribution parameters, while relevant angle are employed to express the correlation between uncertain distribution parameters. The structural responses, i.e., engineering demand parameters (EDPs), are considered as correlated random variables and are assumed to follow a multidimensional lognormal distribution. A performance limit state function, which allows considering the relationship between the EDPs and the corresponding limit thresholds, is employed to reflect the coexistence of both random and parallelepiped convex variables. The limit state function is mapped into the standard parameter space via a transformation technique. Then, the improved seismic risk formulation, characterised through a probability and parallelepiped convex mixed variables, can be derived with the combination of the seismic fragility function and the ground motion hazard curve. The main purpose is to illustrate that the performance limit states should be properly modeled as random and parallelepiped convex mixed variables rather than only random or deterministic quantities. A six-story reinforced concrete building designed according to Chinese codes are used to illustrate the proposed approach for constructing hazard curves. The interstory drift and the peak floor acceleration are the selected EDPs, calculated through incremental dynamic analysis. The results demonstrate that the calculated failure probabilities for different limit states in 50?years are found capable of meeting the requirements of Chinese seismic norms after the proposed seismic risk formulation is adopted.     

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.