A probabilistic approach for earthquake loss estimation

Emergency responses following an earthquake and recovery of damaged structures have major impact on the government budget, thus setting back economic development. In earthquake countries, taking effective measures to reduce earthquake loss becomes important issue. This paper presents a probabilistic model for earthquake loss estimation of a town under earthquake risk. The model enables the decision-makers to make more reliable decisions, before and after an earthquake that strikes the town, by considering probability distribution and variability instead of deterministic approach. Life cycle cost concept is taken into account in the formulation of earthquake loss. Therefore, the model simulates all the benefits and costs, which are prone to variation within Monte Carlo framework. Adapazari, which is extensively damaged city in 1999 earthquake of Turkey, is chosen for the application of Monte Carlo Simulation Model. The model can be used to assess the effects of recovery periods.     

发震断层的永久位移概率评估方法

 基于Cornell地表地震动的概率方法,提出发震断层未来地震引起地表永久位移的概率分析方法,其中断层模型、地震发生模型、震级与破裂面的长度、宽度、地表位移之间关系的参数采用物探结果、震源运动学反演、历史地震资料、现场考察及测年确定。主要技术有2点：(1) 概率分析场点地震动是场点周围断层所有潜在地震的贡献,而场点的地表永久位移仅是该断层的贡献;(2) 场点所在断层发生的所有地震对场点的地震动均有贡献,而场点所在断层发生的少数地震才能对场点永久位移有贡献。应用提出的方法,结合海原断裂地震地质资料和地震活动性资料,给出2种特征地震模型下的不同概率水准的地震地表永久位移。发震断层不同概率水准下的地表永久位移评估为穿越断层的管线和桥梁工程提供基础数据,以便采取合理的抵抗永久地表位移措施,减小地震灾害带来的损失。     

基于概率地震危险性分析的重大工程结构设计地震的研究

本文提出了一种基于概率地震危险性分析 (PSHA)确定重大工程结构设计地震的方法 ,建议设计地震在场地产生的地震动应满足以下条件 :(1)加速度峰值等于PSHA确定的给定超越概率加速度峰值 ;(2 )反应谱值不能超越PSHA确定的一致概率反应谱 ,同时又不小于某一给定下限值。由本方法确定的设计地震是相对合理的 ,工程设计人员容易接受。     

Applying Earthquake Risk Analysis Techniques to Land Use Planning

Recently developed methods of risk analysis are capable of modeling variations in earthquake hazard and its resultant damage to urban development. This type of risk analysis can provide useful information for land use decisions. Our article describes a probabilistic approach to earthquake risk analysis, which begins by estimating and mapping the expected level of ground motion over a study area. Areas subject to the earthquake-induced secondary hazards of landsliding and liquefaction are identified and combined with ground motion to describe the overall hazard. Damage estimates (by type of structure) can be produced for either the existing land use pattern or alternative future scenarios; that information can be used to evaluate alternative land use patterns in terms of their potential for earthquake damage. To illustrate the approach we use a case study application of earthquake risk analysis techniques to an area in San Luis Obispo County, California. We summarize the reactions of several practicing planners to this method of earthquake risk assessment, and we discuss the implications of improved risk analysis techniques for land use planning.     

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.     

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.     

Data-driven probabilistic post-earthquake fire ignition model for a community

Fire following earthquake (FFE), a cascading multi-hazard event, can cause major social and economical losses in a community. In this paper, two existing post-earthquake fire ignition models that are implemented in Geographic Information System (GIS) based platforms, Hazus and MAEViz/Ergo, are reviewed. The two platforms and their FFE modules have been studied for suitability in community resiliency evaluations. Based on the shortcomings in the existing literature, a new post-earthquake fire ignition model is proposed using historical FFE data and a probabilistic formulation. The procedure to create the database for the model using GIS-based tools is explained. The proposed model provides the probability of ignition at both census tract scale and individual buildings, and can be used to identify areas of a community with high risk of fire ignitions after an earthquake. The model also provides a breakdown of ignitions in different building types. Finally, the model is implemented in MAEViz/Ergo to demonstrate its application in a GIS-based software.     

System loss assessment of bridge networks accounting for multi-hazard interactions

This paper details an integrated method for the multi-hazard risk assessment of road infrastructure systems exposed to potential earthquake and flood events. A harmonisation effort is required to reconcile bridge fragility models and damage scales from different hazard types: this is achieved by the derivation of probabilistic functionality curves, which express the probability of reaching or exceeding a loss level given the seismic intensity measure. Such probabilistic tools are essential for the loss assessment of infrastructure systems, since they directly provide the functionality losses instead of the physical damage states. Multi-hazard interactions at the vulnerability level are ensured by the functionality loss curves, which result from the assembly of hazard-specific fragility curves for local damage mechanisms. At the hazard level, the potential overlap between earthquake and flood events is represented by a time window during which the effects of one hazard type on the infrastructure may still be present: the value of this temporal parameter is based on the repair duration estimates provided by the functionality loss curves. The proposed framework is implemented through Bayesian Networks, thus enabling the propagation of uncertainties and the computation of joint probabilities. The procedure is demonstrated on a bridge example and a hypothetical road network.     

Deep Learning for Accelerated Seismic Reliability Analysis of Transportation Networks

To optimize mitigation, preparedness, response, and recovery procedures for infrastructure systems, it is essential to use accurate and efficient means to evaluate system reliability against probabilistic events. The predominant approach to quantify the impact of natural disasters on infrastructure systems is the Monte Carlo approach, which still suffers from high computational cost, especially when applied to large systems. This article presents a deep learning framework for accelerating seismic reliability analysis, on a transportation network case study. Two distinct deep neural network surrogates are constructed and studied: (1) a classifier surrogate that speeds up the connectivity determination of networks and (2) an end‐to‐end surrogate that replaces modules such as roadway status realization, connectivity determination, and connectivity averaging. Numerical results from k‐terminal connectivity analysis of a California transportation network subject to a probabilistic earthquake event demonstrate the effectiveness of the proposed surrogates in accelerating reliability analysis while achieving accuracies of at least 99%.     

基于增量动力分析的大型地下洞室群性能化地震动力稳定性评估

 基于现有研究成果,将增量动力分析引入大型地下洞室群地震动力稳定性评价领域,形成大型地下洞室群的性能化地震动力稳定性评价方法。首先讨论基于PEER-NGA数据库的强震记录选取方法,根据具体工程的地震地质特性针对性地搜索合适的强震记录,为开展增量动力分析提供最优的输入地震动。然后讨论适用于大型地下洞室群的结构损伤性能参数、地震强度因子的选取,为增量动力分析提供合适的地震强度指标和抗震性能表征。继而立足于现有规范,形成了适用于大型地下洞室群性能化地震动力稳定性评估的2级地震动水平和2级抗震性能水平。最后采用本文的方法及步骤对大岗山水电工程地下洞室群进行地震动力稳定性评估。结果表明,该方法较好地考虑了地震动的随机性,给出洞室群的抗震性能,并可进一步对地震动力稳定性进行概率分析,为大型地下洞室群地震动力灾变失稳提供准则。     

单体建筑抗震韧性评估方法研究与应用

选择已安装观测台阵的某教学楼为例,建立OpenSEES模型,利用振动数据识别结构自振特性标定数值模型,至两者结果吻合良好后,输入10条地震动开展结构弹塑性分析。结果表明楼层层间位移角均在规范限值下,结构抗震性能完好,建筑韧性仅考虑功能损失影响。依据吊顶和填充墙的易损性曲线中2种损伤状态的损失比和发生概率,计算该建筑结构的功能损失R_loss和建筑韧性R_function,结果表明该教学楼在罕遇地震下功能损失超过2/3,建筑韧性仅剩余1/3。计算结果与实际震害中“建筑主体结构完好,吊顶和填充墙等非结构构件破坏严重”结果相符。参考REDi方法对吊顶和填充墙进行功能修复时间评估,依据建筑功能(韧性)与累计恢复时间对应关系,得到建筑的抗震韧性曲线。     

Multi-hazard loss analysis of tall buildings under wind and seismic loads

This paper presents a framework for life-cycle loss estimation for non-structural damage in tall buildings under wind and seismic loads. Life-cycle cost analysis is a useful design tool for decision- makers, aimed at predicting monetary losses over the lifetime of a structure, accounting for uncertainties involved in the problem definition. For tall buildings, sensitive to dynamic excitations like earthquake and wind, it can be particularly suitable to base design decisions not only on initial cost and performance but also on future repair expenses. The proposed approach harmonises the procedures for intervention costs evaluation of structures subjected to multiple-hazards, taking into account the peculiar differences of wind and earthquake, in terms of load characterisation, type and evolution of damage. Relative effect of the two hazards on damage to drift- and acceleration-sensitive non-structural elements are examined. The influence of uncertainty in structural damping is also taken into account. It is shown that, although it is commonly believed that the design of a given structure is usually dominated by either winds or earthquakes, when LCC-based design is performed, both winds and earthquakes may be important.     

Probability-based optimal design of friction-based seismic isolation devices

In earthquake engineering the design of seismic isolation devices plays an important role to ensure structural safety and integrity. Such devices on one hand must allow for a sufficiently high level of structural decoupling and energy dissipation in order to reduce structural damage, and on the other hand must provide enough stiffness in order to prevent excessive deformations or residual offsets. This leads to trade-off considerations which can be dealt with through an optimization process. In the present paper, the earthquake excitation is treated as a non-stationary random process. Therefore, the design of the isolation device is based on a suitable probabilistic characterization of the dynamic response, i.e. the first-passage probability of critical response levels. The required first-passage probabilities are computed using a novel efficient Monte Carlo based simulation technique called asymptotic sampling. The design space is covered by using a design of experiment based on Latin Hypercube sampling. Due to the inherent statistical error of Monte-Carlo based analysis it is useful to apply a response surface technique (smoothing) based on the Moving Least Squares method. The design optimization involves conflicting objectives which can be resolved by applying a Pareto-type optimization approach. The main contribution of this paper lies in the connection of high-dimensional Monte-Carlo-based reliability analysis with multi-objective design optimization using a response surface approach and its application to an earthquake engineering problem.     

Bayesian calibration of embankment safety under earthquake loading

This study provides a probabilistic procedure for the back-calculation of factors of safety of embankment slopes during seismic loading. The slope stability is analyzed by the conventional circular arc slip surface method in which the seismic load is introduced in terms of a horizontal body force. The factor of safety of an embankment is inversely estimated using information whether the embankment is still safe or not after the occurrence of an earthquake. In this back-calculation, soil strengths and seismic loads are treated as random variables. This is because, in many actual situations, these two factors are usually uncertain even after the occurrence of an earthquake.The developed procedure is applied to the case records of embankment behavior during the Niigata earthquake of 1964. Six embankments are analyzed. Four of them are damaged embankments while the others are non-damaged. The factors of safety are inversely estimated and they are compared with the state of damage described in the case records.     

A value-based design approach for base-isolated structural systems

The main assumption in seismic design procedures for structural systems is to provide the building with a high level of structural performance, subjected to earthquake loads. Such demand for higher performance needs additional investment on the project. In this work by taking into account the socio-economical aspects of the project, a value-based design approach is used to rationalise the structural design procedure in terms of initial investment. Determination of value design point in this approach is based on providing the optimality criterion from a global perspective. According to the results of this study, while for hospitals located in small cities with no substitute functionality in case of earthquake incident using base isolation for the structural system is quite necessary, for large cities, construction of fixed-base hospitals can still be permitted. The study also shows that, in the countries with higher growth rate, the required structural capacity to deal with earthquake demands in value-based design approach is lower than that required for low growth rate regions.     

A novel lifetime cost-benefit analysis method for seismic retrofitting of low-rise reinforced concrete buildings

This article presents a novel simplified method for assessing seismic damage to low-rise reinforced concrete (RC) buildings by using the hazard curve of response spectral acceleration. Moreover, the occurrence of an earthquake is assumed to follow a Poisson process when analysing the occurrence probability of a specified damage state in the remaining service life and expected losses induced by seismic damage. Then, a novel procedure for estimating lifetime costs and benefits of seismic retrofitting is proposed. In the case study, 16 practical design projects for seismic retrofitting of RC school buildings in Taipei are subjected to lifetime cost-benefit analysis using the proposed method. It can be found that not only lifetime cost-benefit ratios but also the financial return period for each dollar invested seismic retrofitting can be identified conveniently. Additionally, they are useful information for making decisions about whether to retrofit a building or not.     

估计不同服役期结构的抗震设防水准的简单方法

对现行建筑抗震设计规范中三个设防水准的概率含义进行了讨论。指出除基本烈度地震以外 ,另外两个水准的概率含义是不明确的 ,只能从平均意义上去理解。根据规范中考虑的三个概率水准的设防烈度之间的平均相互关系 ,建议了一种可以用于估计不同服役期结构抗震设防烈度的简便方法。这样确定的设防烈度虽然不能很好反映当地的实际情况 ,但是可以反映设防烈度随服役期限变化的一般趋势 ,故可作为确定一般工程设防烈度的参考。此外 ,还讨论了建立与三水准设防相对应的基本加速度和设计反应谱放大倍数     

Probabilistic assessment of earthquake insurance rates for important structures: Application to Gumusova–Gerede motorway

A probabilistic model is presented for the assessment of the earthquake insurance rates for important engineering structures, for which the seismic losses could be quite significant. The proposed model is used to estimate the earthquake insurance premiums for the structures taking place in the Bolu Mountain Crossing in the Gumusova–Gerede motorway Section, Turkey. The model requires two types of studies, namely: seismic hazard analysis and estimation of potential damage to structures based on damage probability matrices (DPM). The computations are carried out according to the proposed model by using the seismic hazard results and the best estimate DPM’s developed in the study and the annual pure risk premiums are obtained for the different components of the motorway system by making a distinction between sections completed and sections under construction.     

生命线系统对城市地震灾害损失评价研究

在城市地震中,生命线系统功能的保证对震后人民生活和抗震救灾起着至关重要的作用。因此,确定生命线系统的抗震能力是城市防震减灾中的一个重要问题。本文建立了评价城市生命线系统抗震能力的评估模型:首先在目前的研究成果和震害经验的基础上建立指标体系的具体内容;然后根据生命线系统在地震中的破坏特点,确定了生命线系统的指标权数:最后提出了如何考虑生命线系统对城市地震灾害损失影响的评价方法。     

Analysis of lifetime losses of low-rise reinforced concrete buildings attacked by corrosion and earthquakes using a novel method

In the estimation of the losses caused by an earthquake for a reinforced concrete (RC) building, the effect of corrosion of the reinforcing steel incurred by environmental conditions, e.g. carbonation and chloride ions, is seldom mentioned because of the corrosion with uncertainty and time dependence. However, because the structural capacity of a corroded RC building declines over time, one must apply an appropriate method that estimates the structural capacity of an RC building in a corrosive environment. Therefore, this work integrated degradation factors into the structural properties of a corroded RC building. Additionally, by considering life-cycle earthquake events, lifetime losses resulting from earthquakes and corrosion can be derived. This work can help both owners and investors to identify lifetime losses of RC buildings due to seismic structural damage, including the corrosion effect, within a specified service life. Although the case study only addresses a selection of the most appropriate concrete cover depth for an RC building corroded by chloride ions, the proposed procedure can be utilised when making decisions about whether to prevent building deterioration based on economic considerations.