Time‐variant sustainability assessment of seismically vulnerable bridges subjected to multiple hazards

In the design and assessment of structures, the aspects regarding the future performance are gaining increased attention. A wide range of performance measures is covered by ‘sustainability’ to reflect these aspects. There is the need for well established methods for quantifying the metrics of sustainability. In this paper, a framework for assessing the time‐variant sustainability of bridges associated with multiple hazards considering the effects of structural deterioration is presented. The approach accounts for the effects of flood‐induced scour on seismic fragility. Sustainability is quantified in terms of its social, environmental, and economic metrics. These include the expected downtime and number of fatalities, expected energy waste and carbon dioxide emissions, and the expected loss. The proposed approach is illustrated on a reinforced concrete bridge. The effects of corrosion on reinforcement bars and concrete cover spalling are accounted. The seismic fragility curves at different points in time are obtained through nonlinear finite element analyses. The variation of the metrics of sustainability in time is presented. The effects of flood‐induced scour on both seismic fragility and metrics are also investigated. Copyright © 2013 John Wiley & Sons, Ltd.     

Critical uncertainty parameters influencing seismic performance of bridges using Lasso regression

Recent efforts of regional risk assessment of structures often pose a challenge in dealing with the potentially variable uncertain input parameters. The source of uncertainties can be either epistemic or aleatoric. This article identifies uncertain variables exhibiting strongest influences on the seismic demand of bridge components through various regression techniques such as linear, stepwise, Ridge, Lasso, and elastic net regressions. The statistical results indicate that Lasso regression is the most effective one in predicting the demand model as it has the lowest mean square error and absolute error. As the sensitivity study identifies more than 1 significant variable, a multiparameter fragility model using Lasso regression is suggested in this paper. The proposed fragility methodology is able to identify the relative impact of each uncertain input variable and level of treatment needed for these variables in the estimation of seismic demand models and fragility curves. Thus, the proposed approach helps bridge owners to spend their resources judiciously (e.g., data collection, field investigations, and censoring) in the generation of a more reliable database for regional risk assessment. This proposed approach can be applicable to other structures.     

Spatiotemporal seismic hazard and risk assessment of M9.0 megathrust earthquake sequences of wood‐frame houses in Victoria,British Columbia,Canada

Megathrust earthquake sequences, comprising mainshocks and triggered aftershocks along the subduction interface and in the overriding crust, can impact multiple buildings and infrastructure in a city. The time between the mainshocks and aftershocks usually is too short to retrofit the structures; therefore, moderate‐size aftershocks can cause additional damage. To have a better understanding of the impact of aftershocks on city‐wide seismic risk assessment, a new simulation framework of spatiotemporal seismic hazard and risk assessment of future M9.0 sequences in the Cascadia subduction zone is developed. The simulation framework consists of an epidemic‐type aftershock sequence (ETAS) model, ground‐motion model, and state‐dependent seismic fragility model. The spatiotemporal ETAS model is modified to characterise aftershocks of large and anisotropic M9.0 mainshock ruptures. To account for damage accumulation of wood‐frame houses due to aftershocks in Victoria, British Columbia, Canada, state‐dependent fragility curves are implemented. The new simulation framework can be used for quasi‐real‐time aftershock hazard and risk assessments and city‐wide post‐event risk management.     

Aftershock collapse fragility curves for non‐ductile RC buildings: a scenario‐based assessment

Recent studies have addressed the computation of fragility curves for mainshock (MS)‐damaged buildings. However, aftershock (AS) fragilities are generally conditioned on a range of potential post‐MS damage states that are simulated via static or dynamic analyses performed on an intact building. Moreover, there are very few cases where the behavior of non‐ductile reinforced concrete buildings is analyzed. This paper presents an evaluation of AS collapse fragility conditioned on various return periods of MSs, allowing for the rapid assessment of post‐earthquake safety variations based solely on the intensity of the damaging earthquake event. A refined multi‐degree‐of‐freedom model of a seven‐storey non‐ductile building, which includes brittle failure simulations and the evaluation of a system level collapse, is adopted. Aftershock fragilities are obtained by performing an incremental dynamic analysis for a number of MS–AS ground motion sequences and a variety of MS intensities. The AS fragilities show that the probability of collapse significantly increases for higher return periods for the MS. However, this result is mainly ascribable to collapses occurred during MSs. When collapse cases that occur during a MS are not considered in the assessment of AS collapse probability, a smaller shift in the fragility curves is observed as the MS intensity increases. This result is justified considering the type of model and collapse modes introduced, which strongly depend on the brittle behavior of columns failing in shear or due to axial loads. The analysis of damage that is due to MSs when varying the return period confirms this observation. Copyright © 2017 John Wiley & Sons, Ltd.     

Post‐repair effect of column jackets on aftershock fragilities of damaged RC bridges subjected to successive earthquakes

In light of recent earthquakes, structures damaged during an initial seismic event (mainshock) may be more vulnerable to severe damage and collapse during a subsequent event (aftershock). In this paper, a framework for the development of aftershock fragilities is presented; these aftershock fragilities define the likelihood that a bridge damaged during an initial event will exhibit a given damage state following one or more subsequent events. The framework is capable of (i) quantifying the cumulative damage of unrepaired bridges subjected to mainshock–aftershock sequences (effect of multiple earthquakes) and (ii) evaluating the effectiveness of column repair schemes such as steel and fiber‐reinforced‐polymer jackets (post‐repair effect of jackets). To achieve this aim, the numerical model of repaired columns is validated using existing experimental results. A non‐seismically designed bridge is chosen as a case study and is modeled for three numerical bridge models: a damaged (but unrepaired) bridge model, and two bridge models with columns repaired with steel and fiber‐reinforced polymer jackets. A series of back‐to‐back dynamic analyses under successive earthquakes are performed for each level of existing damage. Using simulated results, failure probabilities of components for multiple limit states are computed for each bridge model and then are used to evaluate the relative vulnerability of components associated with cumulative damage and column repair. Copyright © 2016 John Wiley & Sons, Ltd.     

Running safety assessment of trains moving over bridges subjected to moderate earthquakes

A study about the running safety of trains moving over bridges subjected to earthquakes is presented. The study focuses on moderate earthquakes with relatively small return periods and high probability of occurrence. The analyses are performed using a nonlinear train‐bridge interaction method proposed by the authors, being the running safety evaluated with safety criteria existent in the literature. The influence on the train running safety of the seismic intensity levels, train running speed, and track quality is evaluated. Because no significant nonlinearity is likely to be exhibited in the columns for moderate levels of seismicity, the analyses are performed in the elastic domain. However, the reduction in the columns stiffness due to cracking is accounted, and a methodology to compute their effective stiffness is proposed. Copyright © 2015 John Wiley & Sons, Ltd.     

A performance‐based framework for adaptive seismic aftershock risk assessment

Operative seismic aftershock risk forecasting can be particularly useful for rapid decision‐making in the presence of an ongoing sequence. In such a context, limit state first‐excursion probabilities (risk) for the forecasting interval (a day) can represent the potential for progressive state of damage in a structure. This work lays out a performance‐based framework for adaptive aftershock risk assessment in the immediate post‐mainshock environment. A time‐dependent structural performance variable is adopted in order to measure the cumulative damage in a structure. A set of event‐dependent fragility curves as a function of the first‐mode spectral acceleration for a prescribed limit state is calculated by employing back‐to‐back nonlinear dynamic analyses. An epidemic‐type aftershock sequence model is employed for estimating the spatio‐temporal evolution of aftershocks. The event‐dependent fragility curves for a given limit state are then integrated together with the probability distribution of aftershock spectral acceleration based on the epidemic‐type aftershock sequence aftershock hazard. The daily probability of limit state first‐excursion is finally calculated as a weighted combination of the sequence of limit state probabilities conditioned on the number of aftershocks. As a numerical example, daily aftershock risk is calculated for the L'Aquila 2009 aftershock sequence (central Italy). A representative three‐story reinforced concrete frame with infill panels, which has cyclic strength and stiffness degradation, is used in order to evaluate the progressive damage. It is observed that the proposed framework leads to a sound forecasting of limit state first‐excursion in the structure for two limit states of significant damage and near collapse. Copyright © 2014 John Wiley & Sons, Ltd.     

Seismic risk assessment considering cumulative damage due to aftershocks

Calculating the limit state (LS) exceedance probability for a structure considering the main seismic event and the triggered aftershocks (AS) is complicated both by the time‐dependent rate of aftershock occurrence and also by the cumulative damage caused by the sequence of events. Taking advantage of a methodology developed previously by the authors for post‐mainshock (MS) risk assessment, the LS probability due to a sequence of mainshock and the triggered aftershocks is calculated for a given aftershock forecasting time window. The proposed formulation takes into account both the time‐dependent rate of aftershock occurrence and also the damage accumulation due to the triggered aftershocks. It is demonstrated that an existing reinforced concrete moment‐resisting frame with infills subjected to the main event and the triggered sequence exceeds the near‐collapse LS. On the other hand, the structure does not reach the onset of near‐collapse LS when the effect of triggered aftershocks is not considered. It is shown, based on simplifying assumptions, that the derived formulation yields asymptotically to the same Poisson‐type functional form used when the cumulative damage is not being considered. This leads to a range of approximate solutions by substituting the fragilities calculated for intact, MS‐damaged, and MS‐plus‐one‐AS‐damaged structures in the asymptotic simplified formulation. The latter two approximate solutions provide good agreement with the derived formulation. Even when the fragility of intact structure is employed, the approximate solution (considering only the time‐dependent rate of aftershock occurrence) leads to higher risk estimates compared with those obtained based on only the mainshock. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

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.     

Influence of frequency‐dependent soil–structure interaction on the fragility of R/C bridges

Bridge performance under earthquake loading can be significantly influenced by the interaction between the structure and the supporting soil. Even though the frequency dependence of the interaction mentioned in this study has long been documented, the simplifying assumption that the dynamic stiffness is dominated by the mean or predominant excitation frequency is still commonly made, primarily as a result of the associated numerical difficulties when the analysis has to be performed in the time domain. This study makes use of the advanced lumped parameter models recently developed 1 in order to quantify the impact of the assumption on the predicted fragility of bridges mentioned in this study. This is achieved by comparing the predicted vulnerability for the case of a reference, well studied, actual bridge using both conventional, frequency‐independent, Kelvin–Voigt models and the aforementioned lumped parameter formulation. Analysis results demonstrate that the more refined consideration of frequency dependence of soil–structure interaction at the piers and the abutments of a bridge not only leads to different probabilities of failure for given intensity measures but also leads to different hierarchy and distribution of damage within the structure for the same set of earthquake ground motions even if the overall probability of exceeding a given damage state is the same. The paper concludes with the comparative assessment of the effect for different soil conditions, foundation configurations, and ground motion characteristics mentioned in this study along with the relevant analysis and design recommendations. Copyright © 2016 John Wiley & Sons, Ltd.     

On the vulnerability assessment of monumental buildings

In all European countries the will to conserve the building heritage is very strong. Unfortunately, large areas in Europe are characterised by a high level of seismic hazard and the vulnerability of ancient masonry structures is often relevant. The large number of monumental buildings in urban areas requires facing the problem with a methodology that can be applied at territorial scale, with simplified models which need little easily obtainable, data. Within the Risk-UE project, a new methodology has been stated for the seismic vulnerability assessment of monumental buildings, which considers two different approaches: a macroseismic model, to be used with macroseismic intensity hazard maps, and a mechanical based model, to be applied when the hazard is provided in terms of peak ground accelerations and spectral values. Both models can be used with data of different reliability and depth. This paper illustrates the theoretical basis and defines the parameters of the two models. An application to an important church is presented.     

Seismic assessment of damaged piloti‐type RC building subjected to successive earthquakes

Building structures damaged by a seismic event may be exposed to the risk of aftershocks or another event within a certain period. In this paper, the seismic assessment of damaged piloti‐type RC buildings was carried out to evaluate probabilistic retrofitting effects under successive earthquakes. First, a framework to evaluate the effectiveness of retrofitting was proposed, and then the proposed methodology was demonstrated with a structure retrofitted with buckling‐restrained braces (BRBs). For consideration of realistic successive earthquakes, past records measured at the same station were combined. Within the framework, a series of nonlinear time history analyses were performed for an as‐is model subjected to single earthquake, a damaged model subjected to successive earthquakes, and a damaged model retrofitted with BRBs subjected to successive earthquakes. In addition, fragility analysis was systematically applied in the framework for evaluation of effectiveness of the retrofitting strategy. The proposed framework was capable of quantifying the influence of successive earthquakes and evaluating the effectiveness of BRB retrofitting by considering the severity of the first earthquake damage and the hysteresis behavior of the retrofit element. Copyright © 2014 John Wiley & Sons, Ltd.     

Application of open tools and datasets to probabilistic modeling of road traffic disruptions due to earthquake damage

The disruption of a transportation network can have a high social and economic impact on the welfare of a society, as it can significantly affect the daily routines of a community. Although many studies have focused on the estimation of physical risk in the components that compose these networks, only a limited number have analyzed their interconnections and impact in the traffic flow. The present study analyzes how earthquake damage can disrupt the road network in an urban environment, and how this will influence the ability of the population to travel. Traffic due to daily commutes is modeled for different layouts of the network, corresponding to possible disruptions caused by earthquake damage. The duration and length of each trip were calculated both for the undamaged network conditions and for the disrupted network. The increase in the median duration and length of each trip allows estimating the economic loss for each event due to drivers' delay. By combining the probability of a specific road being blocked with its number of users, the average number of affected vehicles was estimated, and the most critical segments identified. The methodology was applied to a case study concerning the road network of the area around the Italian city of Messina in Sicily. The results were calculated for both a repetition of the well-known historical event of 1908 and a set of simulated earthquakes consistent with the national probabilistic seismic hazard model of Italy.     

Seismic vulnerability assessment to slight damage based on experimental modal parameters

The aim of this paper is to adjust behaviour models for each class of structure for vulnerability assessment by using ambient vibration. A simple model based on frequencies, mode shapes and damping, taken from ambient vibrations, allows computation of the response of the structures and comparison of inter‐storey drifts with the limits found in the literature for the slight damage grade, considered here as the limit of elastic behaviour. Two complete methodologies for building fragility curves are proposed: (1) using a multi‐degree of freedom system including higher modes and full seismic ground‐motion and (2) using a single‐degree of freedom model considering the fundamental mode f₀ of the structure and ground‐motion displacement response spectra S_D(f₀). These two methods were applied to the city of Grenoble, where 60 buildings were studied. Fragility curves for slight damage were derived for the various masonry and reinforced concrete classes of buildings. A site‐specific earthquake scenario, taking into account local site conditions, was considered, corresponding to an M_L = 5.5 earthquake at a distance of 15 km. The results show the benefits of using experimental models to reduce variability of the slight damage fragility curve. Moreover, by introducing the experimental modal model of the buildings, it is possible to improve seismic risk assessment at an overall scale (the city) or a local scale (the building) for the first damage grade (slight damage). This level of damage, of great interest for moderate seismic‐prone regions, may contribute to the seismic loss assessment. Copyright © 2011 John Wiley & Sons, Ltd.     

Developing an Event Tree for probabilistic hazard and risk assessment at Vesuvius

Probabilistic characterizations of possible future eruptive scenarios at Vesuvius volcano are elaborated and organized within a risk-based framework. In the EXPLORIS project, a wide variety of topics relating to this basic problem have been pursued: updates of historical data, reinterpretation of previous geological field data and the collection of new fieldwork results, the development of novel numerical modelling codes and of risk assessment techniques have all been completed. To achieve coherence, many diverse strands of evidence had to be unified within a formalised structure, and linked together by expert knowledge. For this purpose, a Vesuvius ‘Event Tree’ (ET) was created to summarise in a numerical-graphical form, at different levels of detail, all the relative likelihoods relating to the genesis and style of eruption, development and nature of volcanic hazards, and the probabilities of occurrence of different volcanic risks in the next eruption crisis. The Event Tree formulation provides a logical pathway connecting generic probabilistic hazard assessment to quantitative risk evaluation. In order to achieve a complete parameterization for this all-inclusive approach, exhaustive hazard and risk models were needed, quantified with comprehensive uncertainty distributions for all factors involved, rather than simple ‘best-estimate’ or nominal values. Thus, a structured expert elicitation procedure was implemented to complement more traditional data analysis and interpretative approaches. The structure of the Vesuvius Event Tree is presented, and some of the data analysis findings and elicitation outcomes that have provided initial indicative probability distributions to be associated with each of its branches are summarized. The Event Tree extends from initiating volcanic eruption events and hazards right through to human impact and infrastructure consequences, with the complete tree and its parameterisation forming a quantitative synoptic framework for comprehensive hazard evaluation and mapping of risk impacts. The organization of the Event Tree allows easy updating, as and when new information becomes available.     

Seismic demand models for probabilistic risk analysis of near fault vertical ground motion effects on ordinary highway bridges

The influence of vertical ground motions on the seismic response of highway bridges is not very well understood. Recent studies suggest that vertical ground motions can substantially increase force and moment demands on bridge columns and girders and cannot be overlooked in seismic design of bridge structures. For an evaluation of vertical ground motion effects on the response of single‐bent two‐span highway bridges, a systematic study combining the critical engineering demand parameters (EDPs) and ground motion intensity measures (IMs) is required. Results of a parametric study examining a range of highway bridge configurations subjected to selected sets of horizontal and vertical ground motions are used to determine the structural parameters that are significantly amplified by the vertical excitations. The amplification in these parameters is modeled using simple equations that are functions of horizontal and vertical spectral accelerations at the corresponding horizontal and vertical fundamental periods of the bridge. This paper describes the derivation of seismic demand models developed for typical highway overcrossings by incorporating critical EDPs and combined effects of horizontal and vertical ground motion IMs depending on the type of the parameter and the period of the structure. These models may be used individually as risk‐based design tools to determine the probability of exceeding the critical levels of EDP for pre‐determined levels of ground shaking or may be included explicitly in probabilistic seismic risk assessments. Copyright © 2011 John Wiley & Sons, Ltd.     

Performance‐based grouping methods of bridge classes for regional seismic risk assessment: Application of ANOVA,ANCOVA, and non‐parametric approaches

One of the key tasks to enable a regional risk assessment is to group structures with similar seismic performances and generate fragility curves representative of the grouped structures. The grouping has been traditionally performed based primarily on engineering judgment and prior experience. This paper (i) presents an overview of various statistical techniques such as analysis of variance, analysis of covariance, and Kruskal–Wallis test for grouping the bridges of similar performance; (ii) compares the groupings that emerge from the various grouping techniques; and (iii) identifies the method that has more statistical power in creating bridge sub‐classes of distinct structural performance. The grouping is achieved by comparing the structural responses of bridge classes obtained from the non‐linear time history analysis of bridges. The relative merits of these grouping techniques are discussed with the case study of box‐girder bridges in California. Copyright © 2017 John Wiley & Sons, Ltd.     

Earthquake risk assessment of buildings accounting for human evacuation

A primary goal of earthquake engineering is to protect society from the possible negative consequences of future earthquakes. Conventionally, this goal has been achieved indirectly by reducing seismic damage of the built environment through better building codes, or more comprehensibly, by minimizing seismic risk. However, the effect that building damage has on occupants is not explicitly taken into account while designing infrastructure. Consequently, this paper introduces a conceptual framework and numerical algorithm to assess earthquake risk on building occupants during seismic events, considering the evacuation process of the structure. The framework combines probabilistic seismic hazard analysis, inelastic structural response analysis and damage assessment, and couples these results with the response of evacuating agents. The results are cast as probability distributions of variables that measure the overall performance of the system (e.g., evacuation times, number of injured people, and repair costs) for specific time windows. As a testbed, the framework was applied to the response of a reinforced concrete frame building that exemplifies the use of all steps of the methodology. The results suggest that this seismic risk evaluation framework of structural systems that combine the response of a physical model with human agents can be extended to a wide variety of other situations, including the assessment of mitigation actions in communities and people to improve their earthquake resilience. Copyright © 2016 John Wiley & Sons, Ltd.