Development of fragility curves using high‐dimensional model representation

Fragility curves represent the conditional probability that a structure's response may exceed the performance limit for a given ground motion intensity. Conventional methods for computing building fragilities are either based on statistical extrapolation of detailed analyses on one or two specific buildings or make use of Monte Carlo simulation with these models. However, the Monte Carlo technique usually requires a relatively large number of simulations to obtain a sufficiently reliable estimate of the fragilities, and it is computationally expensive and time consuming to simulate the required thousands of time history analyses. In this paper, high‐dimensional model representation based response surface method together with the Monte Carlo simulation is used to develop the fragility curve, which is then compared with that obtained by using Latin hypercube sampling. It is used to replace the algorithmic performance‐function with an explicit functional relationship, fitting a functional approximation, thereby reducing the number of expensive numerical analyses. After the functional approximation has been made, Monte Carlo simulation is used to obtain the fragility curve of the system. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Framework for the derivation of analytical fragility curves and life cycle cost analysis for non-seismically designed buildings

The quantification of the devastating effects of earthquakes on buildings can be achieved with the use of earthquake risk assessment. The formulation of strategies to minimise this risk is a complex task which relies on data regarding mainly the hazard, vulnerability and remaining life of the building. In this paper, the case study of Limassol municipality is presented. Initially, the building inventory and categorisation is defined followed by the selection of hazard scenarios and the development of analytical vulnerability curves. In the final part, risk assessment is performed leading to the formulation of retrofitting strategies for long term use.     

Methodology for the development of bridge‐specific fragility curves

A new methodology for the development of bridge‐specific fragility curves is proposed with a view to improving the reliability of loss assessment in road networks and prioritising retrofit of the bridge stock. The key features of the proposed methodology are the explicit definition of critical limit state thresholds for individual bridge components, with consideration of the effect of varying geometry, material properties, reinforcement and loading patterns on the component capacity; the methodology also includes the quantification of uncertainty in capacity, demand and damage state definition. Advanced analysis methods and tools (nonlinear static analysis and incremental dynamic response history analysis) are used for bridge component capacity and demand estimation, while reduced sampling techniques are used for uncertainty treatment. Whereas uncertainty in both capacity and demand is estimated from nonlinear analysis of detailed inelastic models, in practical application to bridge stocks, the demand is estimated through a standard response spectrum analysis of a simplified elastic model of the bridge. The simplified methodology can be efficiently applied to a large number of bridges (with different characteristics) within a road network, by means of an ad hoc developed software involving the use of a generic (elastic) bridge model, which derives bridge‐specific fragility curves. Copyright © 2016 John Wiley & Sons, Ltd.     

Earthquake vulnerability of school buildings: Probabilistic structural fragility analyses

The study presents probabilistic structural fragility assessment of public school buildings in Istanbul, which were constructed based on a standardized/typical project. The typical structure is a four-story, reinforced concrete shear wall building with moment resisting frames. Derivation of fragility functions rely on nonlinear dynamic analyses through Monte Carlo simulations. Nonlinear dynamic analyses are initially performed for a fully deterministic structural model based on the blueprints of the typical school building project. Uncertainties are introduced in different analysis cases following a modified version of the algorithm presented in Smyth et al. (2004) [21], which considers the effect of the random distribution of the parameters using a Monte Carlo approach. Aleatory uncertainties concerning material properties (i.e. compressive strength of concrete, yield strength of reinforcing steel and concrete density), geometrical characteristics (i.e. span lengths and story heights) and cross sectional dimensions of beams, columns and shear walls as well as epistemic uncertainty in the direction of ground motion excitation are considered. Statistical distributions for the parameters considered are obtained from in-situ measurements and material sampling tests. Fragility functions are produced in terms of peak ground acceleration and velocity as well as of the elastic spectral displacement at the first vibration period of the building. Mean damage ratios are calculated from the derived fragility functions. They are further compared to mean damage ratios calculated for similar building typologies provided in HAZUS-MH technical manual and in Istanbul building inventory.     

Effect of earthquake ground motions on fragility curves of highway bridge piers based on numerical simulation

Fragility curves express the probability of structural damage due to earthquakes as a function of ground motion indices, e.g., PGA, PGV. Based on the actual damage data of highway bridges from the 1995 Hyogoken‐Nanbu (Kobe) earthquake, a set of empirical fragility curves was constructed. However, the type of structure, structural performance (static and dynamic) and variation of input ground motion were not considered to construct the empirical fragility curves. In this study, an analytical approach was adopted to construct fragility curves for highway bridge piers of specific bridges. A typical bridge structure was considered and its piers were designed according to the seismic design codes in Japan. Using the strong motion records from Japan and the United States, non‐linear dynamic response analyses were performed, and the damage indices for the bridge piers were obtained. Using the damage indices and ground motion indices, fragility curves for the bridge piers were constructed assuming a lognormal distribution. The analytical fragility curves were compared with the empirical ones. The proposed approach may be used in constructing the fragility curves for highway bridge structures. Copyright © 2001 John Wiley & Sons, Ltd.     

Using experimental data to reduce the single-building sigma of fragility curves: case study of the BRD tower in Bucharest, Romania

The lack of knowledge concerning modelling existing buildings leads to significant variability in fragility curves for single or grouped existing buildings. This study aims to investigate the uncertainties of fragility curves, with special consideration of the single-building sigma. Experimental data and simplified models are applied to the BRD tower in Bucharest, Romania, a RC building with permanent instrumentation. A three-step methodology is applied： （1） adjustment of a linear MDOF model for experimental modal analysis using a Timoshenko beam model and based on Anderson＇s criteria, （2） computation of the structure＇s response to a large set of accelerograms simulated by SIMQKE software, considering twelve ground motion parameters as intensity measurements （IM）, and （3） construction of the fragility curves by comparing numerical interstory drift with the threshold criteria provided by the Hazus methodology for the slight damage state. By introducing experimental data into the model, uncertainty is reduced to 0.02 considering Sd ） as seismic intensity IM and uncertainty related to the model is assessed at 0.03. These values must be compared with the total uncertainty value of around 0.7 provided by the Hazus methodology.     

Assessing the impact of climate variability and human activities on streamflow from the Wuding River basin in China

Located in the Loess Plateau of China, the Wuding River basin (30 261 km²) contributes significantly to the total sediment yield in the Yellow River. To reduce sediment yield from the catchment, large-scale soil conservation measures have been implemented in the last four decades. These included building terraces and sediment-trapping dams and changing land cover by planting trees and improving pastures. It is important to assess the impact of these measures on the hydrology of the catchment and to provide a scientific basis for future soil conservation planning. The non-parametric Mann–Kendall–Sneyers rank test was employed to detect trends and changes in annual streamflow for the period of 1961 to 1997. Two methods were used to assess the impact of climate variability on mean annual streamflow. The first is based on a framework describing the sensitivity of annual streamflow to precipitation and potential evaporation, and the second relies on relationships between annual streamflow and precipitation. The two methods produced consistent results. A significant downward trend was found for annual streamflow, and an abrupt change occurred in 1972. The reduction in annual streamflow between 1972 and 1997 was 42% compared with the baseline period (1961–1971). Flood-season streamflow showed an even greater reduction of 49%. The streamflow regime of the catchment showed a relative reduction of 31% for most percentile flows, except for low flows, which showed a 57% reduction. The soil conservation measures reduced streamflow variability, leading to more uniform streamflow. It was estimated that the soil conservation measures account for 87% of the total reduction in mean annual streamflow in the period of 1972 to 1997, and the reduction due to changes in precipitation and potential evaporation was 13%. Copyright © 2007 John Wiley & Sons, Ltd.     

基于蒙特卡洛方法的地震目录模拟及相符性检验——以汾渭地震带为例

人工地震目录模拟是改进现有地震目录不完备性、弥补大地震记录稀缺,以及完善地震学相关研究的有效途径之一。本文基于地震活动的泊松分布模型、古登堡-里克特震级-频度关系,利用能较逼真描述具有随机性质事物特点及物理实验过程的蒙特卡洛方法,模拟汾渭地震带未来30、50、100年等不同时长的地震目录,并对其进行统计检验。分析表明,模拟地震目录符合设定的地震活动性参数和泊松分布假设特征。依据模拟地震目录,对未来该区域地震趋势进行了分析,以期为地震危险性分析提供参考。     

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.     

Assessment of variability and uncertainties effects on the seismic response of a liquefiable soil profile

The present work deals with the evaluation of the effect of the randomness of both soil parameters and input motion on the seismic response of a sandy soil profile. Special attention is given to estimate the relative contribution of model input parameters on (i) the probability of liquefaction apparition and (ii) the surface seismic response. The Monte Carlo simulations were used for that purpose. This analysis shows that, for the considered case, the choice of the earthquake input signal remains the most subtle parameter in order to define the liquefaction probability. Otherwise, spatial variability of both soil properties and soil model's parameters have a weak impact on the response of the soil profile.     

Dynamic buckling and seismic fragility of anchored steel tanks by the added mass method

Buckling plays a fundamental role in the design of steel tanks because of the small thicknesses of the walls of this class of structures. The first part of the paper presents a review of this phenomenon for liquid‐containing circular cylindrical steel tanks that are fully anchored at the base, considering the different buckling modes and especially the secondary buckling occurring in the top part of the tank. A case study based on a cylindrical tank is then introduced in order to investigate various aspects of dynamic buckling. The finite element model of the case study tank is set‐up using the added mass method for fluid modelling. The influence of pre‐stress states caused by hydrostatic pressure and self‐weight on the natural periods of the structure is first studied and it is found that this influence is very small as far as the global behaviour of the tanks is considered, while it is important for local, shell‐type, vibration modes. In the following, the efficiency and sufficiency of different ground motion intensity measures is analysed by means of cloud analysis with a set of 40 recorded accelerograms. In particular, the peak ground displacement has been found being the most efficient and sufficient intensity measure so far as the maximum relative displacement of the tank walls is concerned. Finally, incremental nonlinear time‐history analyses are performed considering the case study structure under recorded earthquake ground motions in order to identify the critical buckling loads and to derive fragility curves for the buckling limit state. Copyright © 2013 John Wiley & Sons, Ltd.     

Finite element analysis and fragility curves for the evaluation of restoration mortars behavior regarding the earthquake protection of historic structures

The target of this study is the evaluation of repair mortar contribution to the dynamic behavior of Kaisariani Monastery in Athens, by using the tools of finite element analysis and fragility curves. Three types of mortars (concrete) are designed in order to simulate the Hagia Sophia historic mortar, by using different binding material: lime/metakaolin, hydraulic lime, lime/cement. In the developed model the mechanical characteristics of the designed mortars are used. In addition, fragility curves were developed and their results indicated that for the current situation of Kaisariani Monastery and for peak ground acceleration (PGA) value ≥0.24 g, the probability of occurrence of serious damage is 59%. For PGA=0.36 g an overall failure happened. For PGA=0.40 and by using restoration mortar up to 15% of the total bed joint the failure percentage reduces in the range of 12–30%. Better protection is reported for lime/cement mix design followed by hydraulic lime and lime/metakaolin.     

Estimating the effects of spatial variability of infiltration on the output of a distributed runoff and soil erosion model using Monte Carlo methods

Monte Carlo procedures were used to evaluate the effects of spatial variations in the values of the infiltration parameter on the results of the ANSWERS distributed runoff and erosion model. Simulation results obtained were compared with measured values. Field infiltration measurements indicated spatial correlation at much smaller distances than the size of an element. Therefore, at first only the error of the mean had to be taken into consideration for block infiltration rates. Consequently, not only single hydrographs were produced, but also error bands. Secondly, nine other hypothetical spatial correlation structures were also evaluated using Monte Carlo methods. in particular at low nugget variances, increasing spatial correlation of infiltration resulted in increasing coefficients of variation in model outputs. In general, rainstorms with low rainfall intensities were more difficult to simulate accurately than extreme events with high rainfall intensities. This is explained by the greater influence of the infiltration uncertainties at low rainfall intensities.     

Aftershock risk assessment and the decision to open traffic on bridges

Critical issues in emergency management after a seismic event are assessing the functionality of the main infrastructures (hospitals, road network, etc.) and deciding on their usability just after the mainshock. The use of a pure analytical tool to assess the aftershock risk of a structure can be contrasted with the limited time available to make a decision about the usability of a structure. For this reason, this paper presents a method for evaluating post‐earthquake bridge practicability based on a rational combination of information derived from numerical analyses and in situ inspections. In particular, we propose an effective tool to speed up the decision‐making process involved in evaluating the seismic risk of mainshock‐damaged bridges in the context of aftershocks. The risk is calculated by combining the aftershock hazard using the Omori law and the fragility curves of the structure, which are calculated using the regression analysis of a sample of results obtained with data randomly generated by the Latin Hypercube Sampling technique and updated based on the results of in situ inspection. Different decision criteria regarding the practicability of bridges are discussed, and a new criterion is proposed. This tool was applied to an old highway RC viaduct. There are two main findings, including the high sensitivity to Bayesian updating (especially when the damage predicted by numerical analysis does not match the real damage) and the criteria used to decide when re‐open bridges to traffic. Copyright © 2013 John Wiley & Sons, Ltd.     

A comparative study of Monte Carlo simple genetic algorithm and noisy genetic algorithm for cost-effective sampling network design under uncertainty

This study evaluates and compares two methodologies, Monte Carlo simple genetic algorithm (MCSGA) and noisy genetic algorithm (NGA), for cost-effective sampling network design in the presence of uncertainties in the hydraulic conductivity (K) field. Both methodologies couple a genetic algorithm (GA) with a numerical flow and transport simulator and a global plume estimator to identify the optimal sampling network for contaminant plume monitoring. The MCSGA approach yields one optimal design each for a large number of realizations generated to represent the uncertain K-field. A composite design is developed on the basis of those potential monitoring wells that are most frequently selected by the individual designs for different K-field realizations. The NGA approach relies on a much smaller sample of K-field realizations and incorporates the average of objective functions associated with all K-field realizations directly into the GA operators, leading to a single optimal design. The efficacy of the MCSGA-based composite design and the NGA-based optimal design is assessed by applying them to 1000 realizations of the K-field and evaluating the relative errors of global mass and higher moments between the plume interpolated from a sampling network and that output by the transport model without any interpolation. For the synthetic application examined in this study, the optimal sampling network obtained using NGA achieves a potential cost savings of 45% while keeping the global mass and higher moment estimation errors comparable to those errors obtained using MCSGA. The results of this study indicate that NGA can be used as a useful surrogate of MCSGA for cost-effective sampling network design under uncertainty. Compared with MCSGA, NGA reduces the optimization runtime by a factor of 6.5.     

中国大陆大地震危险性判定的经验方法与实例研究

对大陆地震危险性判定的经验指标(地震活动图像异常因子)进行了初步归纳，结合当前震情趋势对未来10a大陆地震的危险性作出了初步判定。     

Assessing the impact of interannual variability of precipitation and potential evaporation on evapotranspiration

The impact of interannual variability of precipitation and potential evaporation on the long-term mean annual evapotranspiration as well as on the interannual variability of evapotranspiration is studied using a stochastic soil moisture model within the Budyko framework. Results indicate that given the same long-term mean annual precipitation and potential evaporation, including interannual variability of precipitation and potential evaporation reduces the long-term mean annual evapotranspiration. This reduction effect is mostly prominent when the dryness index (i.e., the ratio of potential evaporation to precipitation) is within the range from 0.5 to 2. The maximum reductions in the evaporation ratio (i.e., the ratio of evapotranspiration to precipitation) can reach 8–10% for a range of coefficient of variation (CV) values for precipitation and potential evaporation. The relations between the maximum reductions and the CV values of precipitation and potential evaporation follow power laws. Hence the larger the interannual variability of precipitation and potential evaporation becomes, the larger the reductions in the evaporation ratio will be. The inclusion of interannual variability of precipitation and potential evaporation also increases the interannual variability of evapotranspiration. It is found that the interannual variability of daily rainfall depth and that of the frequency of daily rainfall events have quantitatively different impacts on the interannual variability of evapotranspiration; and they also interact differently with the interannual variability of potential evaporation. The results presented in this study demonstrate the importance of understanding the role of interannual variability of precipitation and potential evaporation in land surface hydrology under a warming climate.     

东北地区中等地震前地磁空间相关性异常特征初步分析

应用黑龙江、吉林、内蒙古和辽宁等省的地磁总场强度F北京时21点绝对观测值,研究了其空间相关性在东北地区几次中等地震前的变化.结果显示,在这些地震前地磁总场F的空间相关性会出现下降变化,本文初步给出了判定异常的指标.     

On the treatment of uncertainty in seismic vulnerability and portfolio risk assessment

In a related study developed by the authors, building fragility is represented by intensity‐specific distributions of damage exceedance probability of various damage states. The contribution of the latter has been demonstrated in the context of loss estimation of building portfolios, where it is shown that the proposed concept of conditional fragility functions provides the link between seismic intensity and the uncertainty in damage exceedance probabilities. In the present study, this methodology is extended to the definition of building vulnerability, whereby vulnerability functions are characterized by hazard‐consistent distributions of damage ratio per level of primary seismic intensity parameter—Sa(T₁). The latter is further included in a loss assessment framework, in which the impact of variability and spatial correlation of damage ratio in the probabilistic evaluation of seismic loss is accounted for, using test‐bed portfolios of 2, 5, and 8‐story precode reinforced concrete buildings located in the district of Lisbon, Portugal. This methodology is evaluated in comparison with current state‐of‐the‐art methods of vulnerability and loss calculation, highlighting the discrepancies that can arise in loss estimates when the variability and spatial distributions of damage ratio, influenced by ground motion properties other than the considered primary intensity measure, are not taken into account.