Derivation Of Fragility Curves Research Articles

Utilization of stochastic ground motion simulations for scenario-based performance assessment of geo-structures

Probabilistic seismic performance assessments of engineered structures can be highly sensitive to the seismic input excitation and its variability. In the present study, the scenario-based performance assessment recommended by Federal Emergency Management Agency (FEMA) P-58 guidelines is adopted to estimate seismic fragility of concrete dams for various seismic hazard scenarios. Due to the scarcity of recorded ground motions and thereby their poor representation of uncertainties, stochastic ground motion simulation methods are utilized to obtain the required input excitations. Moreover, to understand the uncertainty in ground motion simulation models, two broadband stochastic simulation models are used to generate input excitations representing six seismic hazard scenarios defined by earthquake magnitude, source-to-site distance, and soil conditions.Optimal intensity measure parameters for each scenario are identified using a systematic procedure that considers criteria such as efficiency, practicality, proficiency, sufficiency, and hazard compatibility. Fragility curves and surfaces are derived using the cloud analysis technique, taking into account various damage measures and limit state functions. The study finds that the derived fragility curves are particularly sensitive to the selection of earthquake scenarios, the choice of records, and the methods used to calculate fragility curves, with less sensitivity observed to different engineering demand parameters. Given this sensitivity, particularly to ground motion selection, the study highlights the necessity of incorporating both model-to-model variability (epistemic uncertainty) and record-to-record variability (aleatory uncertainty), alongside the established material and modeling uncertainties, in the probabilistic seismic assessment.

The Influence of the Aggregate Configuration on the Seismic Assessment of Unreinforced Masonry Buildings in Historic Urban Areas

Unreinforced masonry (URM) buildings in historic urban areas of European countries are generally clustered in an aggregate configuration and are often characterized by façade walls mutually interconnected with adjacent ones. As a result, the seismic performance of buildings in an aggregate configuration can be affected by the mutual interaction between the adjacent units. This interaction, often called the aggregate effect, could significantly influence the level of the seismic vulnerability of URM buildings in aggregate configuration toward in-plane and out-of-plane mechanisms, the latter being the object of the present paper. Traditional methods for assessing the seismic vulnerability of URM buildings neglect the interactions between adjacent buildings, potentially underestimating the actual vulnerability. This study aims to derive fragility curves specific for UMR buildings in aggregate configuration and proposes an innovative methodology that introduces the aggregate effect into an analytical approach, previously developed by the authors for isolated URM buildings. The aggregate effect is modeled by accounting for the friction forces arising among adjacent facades during the development of out-of-plane overturning mechanisms by considering different scenarios, based on how façade walls interact with neighboring structures (e.g., whether they are connected to transverse and/or lateral coplanar ones). The proposed approach is applied to a real case study of an Italian historical center. The obtained results demonstrate that the aggregate effect significantly influences the fragility curves of URM buildings arranged in aggregate configurations. This highlights the importance of considering this effect and the usefulness of the proposed approach for large-scale assessments of seismic vulnerability in historic urban areas, contributing to sustainable disaster risk prevention.

Beta functions adaptation on empirical damage for a fragility model of Italian buildings

In this study, heuristic vulnerability model is presented providing damage distribution as a function of ground motion severity, through the use of given distribution function.Firstly, observational damage distribution are obtained from data collected after the recent earthquakes occurred in Italy and made available by DPC through Da.D.O. platform. The latter collect information on the main characteristics about building position, metrical data (e.g., number of storeys, interstorey height, storey area and construction age), structural types, severity and extension of observed damage on different building components. Moreover, the ground motion characterization was described via the ShakeMap published by the National Institute of Geophysics and Volcanology.Then, the two statistical models mostly used in the literature, i.e. binomial and beta, are used to determine the one most suitable to reproduce the observational damage distributions by means of godness-of-fit test. An introductive section properly examine the pro and cons in their use (number of parameters, flexibility). The observation of mean value and variance couple for more than 2000 damage samples obtained based on the considered database is used to obtain a general relationship which allows to reduce the number of parameters required by beta distribution, preserving its renomate flexibility.This enables the formulation of a novel heuristic vulnerability model for derivation of fragility curves. The model relies on the knoledge of mean damage trend with intensity measure and employs a probability distribution function. In this study, specifically, binomial and beta distributions are utilized. The generality of the method is then customized to suit the characteristics of Italian residential building stock, leveraging the information gathered after the 2009 L'Aquila Earthquake. This database presented an unprecedented opportunity due to the extensive data available on building geometrical and typological characteristics, seismic vulnerability, to the high level of representativeness of samples at municipality level, and to the thorough representation of damage patterns observed on building components.The fragility curves obtained through the presented vulnerability model are compared with those empirically derived from the observational data and are used to fully derive seismic risk scenario after 2009 L'Aquila Earthquake, in terms of economic losses, number of long term unusable buildings, the number of collapse, the number of deaths and severely injuries. The ensuing consequences deriving from the adoption of different fragility curves, i.e. empirical or with beta and binomial vulnerability models are deeply investigated.

Seismic Fragility Curves of RC Buildings Subjected to Aging

A large number of existing reinforced concrete (RC) buildings have surpassed their anticipated service life and show signs of degradation due to aging; this degradation is a function of the construction practices adopted in the past as well as environmental conditions. This paper discusses seismic fragility and the risk assessment of RC structures, emphasizing the impact of corrosion due to concrete aging and the associated deterioration mechanisms. The literature on this topic is critically reviewed, and a methodology for studying the seismic fragility of deteriorated RC buildings is proposed. As a case study, a four-story RC building designed according to contemporary code provisions is examined. The investigation encompasses the derivation of fragility curves, considering critical parameters such as the corrosion rate, the initiation time, and the cover depth. The proposed approach enables the evaluation and quantification of the impact of corrosion mechanisms on the seismic performance of buildings.

Utilizing advanced machine learning approaches to assess the seismic fragility of non-engineered masonry structures

Seismic fragility assessment provides a substantial tool for assessing the seismic resilience of these buildings. However, using traditional numerical methods to derive fragility curves poses significant challenges. These methods often overlook the diverse range of buildings found in different regions, as they rely on standardized assumptions and parameters. Consequently, they may not accurately capture the seismic response of various building types. Alternatively, extensive data collection becomes essential to address this knowledge gap by understanding local construction techniques and identifying the relevant parameters. This data is crucial for developing reliable analytical approaches that can accurately derive fragility curves. To overcome these challenges, this research employs four Machine Learning (ML) techniques, namely Support Vector Regression (SVR), Stochastic Gradient Descent (SGD), Random Forest (RF), and Linear Regression (LR), to derive fragility curves for probability of collapse in terms of Peak Ground Acceleration (PGA). To achieve the research objective, a comprehensive input/output dataset consisting of on-site data collected from 646 masonry walls in Malawi is used. Adopted ML models are trained and tested using the entire dataset and then again using only the most highly correlated features. The study includes a comparative analysis of the efficiency and accuracy of each ML approach and the influence of the data used in the analyses. Random Forest (RF) technique emerges as the most efficient ML approach for deriving fragility curves for the surveyed dataset in terms of achieved lowest values for evaluation metrics of the ML methods. This technique scored the lowest Mean Absolute Percentage Error (MAPE) of 16.8 %, and the lowest Root Mean Square Error (RMSE) of 0.0547. These results highlight the potential of ML techniques, particularly RF, in derivation of fragility curves with proper levels of accuracy.

Seismic fragility of circular piers in simply supported RC bridges: A proposal for capacity assessment

Bridges are crucial structures of a roadway system, always exposed to both natural and anthropic hazards. Several approaches have been investigated in the past two decades to evaluate the seismic vulnerability of bridges; the development of fragility curves represents a sound tool to evaluate their performances at a large scale. This study aims at the estimation of seismic fragility curves for a structural element of a very common bridge typology in Italy, that is the single circular cross-section pier of a simply supported Reinforced Concrete (RC) bridge. Two analytical methodologies for deriving fragility curves are applied to a case study model. The first one is the Capacity Spectrum Method (CSM). This method accounts for the non-linearities and the seismic energy dissipation, in fact it is based on a non-linear static analysis and the definition of Damage States (DSs) on the capacity curve of the piers. By contrast, the second one is the Response Spectrum Analysis (RSA), that is a methodology based on a linear method. By using both methods, a parametric study is carried out, varying the bridge’s geometrical and mechanical properties within standard ranges, to evaluate their effect on the seismic vulnerability of the pier. This study refers to four DSs and proposes a multilinear regression model to directly evaluate the pier’s seismic performances based on the geometrical and mechanical properties of the bridge to which it belongs.

Seismic risk assessment of residential buildings by the Heuristic vulnerability model: influence of fragility curve models and inventory scale

AbstractTypological-observational methods still constitute one of the most commonly applied tools for evaluation of the seismic risk and vulnerability of the existing building stock. Their efficiency is mainly related to the effectiveness of the procedure for deriving fragility curves, and the reliability and completeness of the database that describes the building stock. This paper presents a comparison between the vulnerability and damage distribution assessment provided by fragility curves used in the Macroseismic and Heuristic methods, and a comparison of exposure evaluation methodologies according to two different approaches, namely a compartment- and a building-scale survey. An application to the case study of the residential building stock in the historic center of Alcamo, a town of 45,000 inhabitants in Western Sicily (Italy), shows the major reduction in fragility provided by recalibration of the masonry buildings’ ductility values that characterize the Heuristic method. Moreover, the efficiency of the compartment scale survey approach, based on the CARTIS typological-structural characterization method of ordinary buildings in urban areas, is underlined.

Probabilistic seismic capacity models for circular tunnels at different performance levels

This paper presents a systematic study to develop the probabilistic seismic capacity models for circular tunnel linings. The uncertainties of lining parameters, soil properties, and ground motions are all considered. The Bayesian approach is used to estimate the model parameters based on the capacity samples simulated by a large number of refined dynamical numerical analyses. Finally, probabilistic capacity models are separately constructed for circular tunnels at three performance levels. To demonstrate the properties of the proposed method, the capacity models are used to estimate the capacities and the fragility curves of a typical tunnel. It is concluded that (1) the probabilistic model can quickly estimate the probability distribution of capacity based on existing parameters, with the estimated median value closely approximating the numerical result; (2) the proposed probabilistic capacity models can be used to quickly derive fragility curves for specific tunnels, which facilitates safety evaluation and performance-based seismic design of tunnels.

Fragility analysis of slopes exposed to seismic hazard employing surrogate modeling techniques

AbstractNatural disasters may lead to failure of critical assets part of railway systems. Slope failure often results in major economic consequences. Due to the economic importance that railways systems have, it is pertinent to ensure good performance and long‐term. The objective of the present research is to propose tools that may allow obtaining the failure probability of soil slopes under a seismic event by employing surrogate models to ease the computational cost of considering the uncertainties associated with geotechnical and geometrical properties of a case study located in Portugal. The presented methodology and derived fragility curves, using peak ground acceleration (PGA) as the intensity measure (IM), can be used to assess slope performance under a seismic event for different safety levels, thus providing useful information for prioritizing assets and taking preventive actions to maintain the desired performance of the railway system.

An archetype-based automated procedure to derive global-local seismic fragility of masonry building aggregates: META-FORMA-XL

The paper presents an automated procedure for deriving fragility curves for typological masonry aggregates, named META-FORMA-XL (MEchanical-Typological Approach FOR Masonry Aggregates – X Local). The topic deals with the urban-scale seismic vulnerability analysis, which can provide powerful information for developing risk mitigation plans and implementing strategies for reducing expected losses. However, when masonry buildings in aggregate are analysed, many issues arise, related to the lack of data, the complexity of the structural configurations and the presence of uncertainties. To this scope, the proposed procedure aims to investigate the seismic behaviour of masonry aggregates, based on numerical analyses carried out on ideal representations of the existing building stock, indicated as archetypes, by modelling geometrical and mechanical uncertainties characterizing buildings in the studied area. The archetype buildings are made according to exposure analyses by combining typical inventory collection forms and information derived from freely available databases. By investigating the seismic response of numerical models for a high number of archetype buildings, fragility curves are derived for all limit-states and two main directions, accounting for global and local damage mechanisms. The procedure is tested on low-rise row masonry aggregates in Southern Italy. The output of the procedure is validated on a real case study, for which a near-full information on the geometrical and mechanical features is available, providing a critical comparison in terms of fragility curves. Results highlight several advantages of the proposed approach, such as the possibility of identifying the most likely collapse mechanism for a specific masonry aggregation, the simplicity and the celerity of the analyses despite the large number of archetype models, and the exhaustive consideration of the uncertainties. Finally, the proposed concept can be readily extended to other aggregation forms and structural typologies.

Probabilistic seismic performance assessment of steel moment‐resisting frames considering exposed column‐base plate connections with ductile anchor rods

AbstractThis paper presents a numerical study assessing the seismic performance of steel moment‐resisting frames (SMRFs) designed with ductile exposed column‐base plate (ECBP) connections employing yielding anchor rods. For their potential use as weak bases, the proposed ECBP detail is designed to accommodate plastic deformations in the anchors. The seismic performance of 2‐ and 4‐story archetype SMRFs with ECBPs is investigated to examine the effects of various base‐connection strengths on the frame collapse mechanisms and probabilities. To this aim, the ECBP connections of each frame are designed for a set of three strength levels, ranging from reduced seismic loads to capacity‐designed forces of the adjoining columns. These designs enable the base responses to vary from highly inelastic (i.e., weak‐base design) to elastic (i.e., strong‐base design) when subjected to earthquake‐induced ground shaking. Nonlinear time history analysis (NLTHA) is extensively performed, applying a suite of assembled ground‐motion sequences (i.e., two ground motions in series) to assess the ECBP connection response and the corresponding frame behavior. Fragility analyses accounting for only the first ground motions in each considered sequence (to derive fragility curves), and the entire ground‐motion sequences (to derive fragility surfaces) are also performed to evaluate the probabilities of frame collapse and base connection failure. Finally, key findings regarding the seismic performance of ductile ECBP connections and their effects on the frame collapse are discussed. The limitations of the study are also outlined.

Adaptation of traditional risk-based methodology for slopes to probabilistic-based approach integrating surrogate models

Due to the economic importance that railways systems have in Europe, it is pertinent to ensure good performance and long-term safety. Failure of earth structures (e.g., slopes) often results in major economic consequences, and it is a result of the uncertainties associated with these structures and their failure modes due to a given hazard. Nowadays, different methodologies can be used to assess slopes during operational phases, but often the required information to achieve a reliable assessment may provide the methodologies inapplicable, especially when assessing multiple assets. This research uses methodologies that have been implemented in the industry and adapts them to a probabilistic approach toward risk assessment, supported by the implementation of kriging surrogate model, thus improving its reliability while maintaining the same level of information and computational cost required for its application. A soil cutting located in the Lisbon (Portugal) was selected as case study. Seismic fragility curves are obtained, and a moderate risk level is obtained. The derived fragility curves are based on peak ground acceleration and were developed for different combinations of geometric and geotechnical parameters. The methodology provides useful information for prioritizing assets and taking preventive actions to maintain the desired performance of the railway system.

Seismic vulnerability assessment of Portuguese masonry buildings

According to the 2011 National Housing Census, masonry buildings comprise more than 50% of the Portuguese building stock. This type of construction has demonstrated a poor performance during the destructive events that struck Portugal in the last century (e.g., 1909 M6.3 Benavente, 1969 M7.8 Algarve, 1980 M6.9 Azores). While some efforts have been made towards the vulnerability assessment of individual masonry buildings or the residential building stock at the national scale, this building class has been the target of limited research. In this study, a comprehensive database of material and geometric properties of granite and limestone buildings was used to generate complex 3D numerical models. These models were subjected to nonlinear time history analysis to derive fragility curves considering the record-to-record and building-to-building variability. The structural damage was defined using two novel engineering demand parameters, and the resulting fragility functions were compared against other existing models. These results can be used directly to generate earthquake scenarios at the country scale or in probabilistic seismic risk analysis to identify regions where risk reduction measures should be prioritized.

Fragility curves for reinforced concrete (RC)/steel vertical hybrid frame structure under mainshock–aftershock sequences

ABSTRACT A reinforced concrete (RC)/steel vertical hybrid frame structure usually consists of a lower concrete structure and an upper steel structure connected in series. This study aims to derive fragility curves for RC/steel vertical hybrid frame structures under mainshock–aftershock sequences. For this purpose, a double incremental dynamic analysis (D-IDA) approach is performed to derive fragility curves for a five-story RC/steel vertical hybrid frame (a three‐story RC frame at the bottom + a two‐story steel frame at the top) under 14 real mainshock– aftershock earthquake ground motions. The fragility curves obtained for RC/steel frame are also compared with fragility curves for a five‐story purely RC frame. Also, residual capacity diagrams are provided for RC/steel and purely RC frames based on the D-IDA results. The results show that RC/steel frame structure has larger collapse capacity than that of the purely RC frame structure, and can diminish collapse probability by 33% compared to purely RC frame structure.

Seismic fragility analysis of low-rise unreinforced masonry buildings subjected to near- and far-field ground motions

Unreinforced masonry (URM) is considered one of the most cost-effective structural typologies for low-rise buildings in seismic regions. Near-field (NF) ground motions are sometimes characterized by high-velocity pulses that are typically more destructive than far-field (FF) seismic events. Therefore, a seismic fragility analysis of low-rise URM building typologies subjected to NF and FF seismic events was performed. Four URM walls were chosen, and nonlinear models of the walls were developed based on the double-modified, multiple vertical line element model (DM-MVLEM). The zero-moment coefficient was used to determine the effective uncracked section length of a pier. This parameter must be calculated for each pier of a perforated URM wall to derive the maximum shear strength of the piers used in a nonlinear model development process. A simplified analytical method was proposed to obtain the zero-moment coefficient factor of piers by performing linear static analysis on nine perforated walls and regression analyses of the results. Subsequently, nonlinear pushover analysis was performed to derive the capacity curves, and the damage limit states were defined for each model according to the Eurocode 8 standard. Subsequently, incremental dynamic analysis (IDA) was performed for each case study by applying FF and NF ground motions. Finally, fragility curves were developed based on the IDA results for each damage limit state. The susceptibilities of one- and two-story URM walls subjected to FF and NF seismic events were investigated by examining the derived fragility curves.

Bridge seismic fragility model based on support vector machine and relevance vector machine

In the area of bridge seismic fragility studies, the fragility curve is commonly defined as a log-normal cumulative distribution function, and its parameters are usually estimated through two methods. However, the fragility curves derived by one of these two methods may intersect, whereas the other imposes significant restrictions on the shape of the curves. The purpose of this study is to derive fragility curves by utilizing machine learning tools (in particular, tools that are based on multi-classification probabilistic prediction), to address the limitations that are present in existing methodologies. To be more precise, support vector machine for classification (SVC) and relevance vector machine for classification (RVC) are utilized to construct fragility curves, while two other classic methodologies are chosen for comparison and validation. The four approaches were tested on a dataset acquired using numerical analysis, and their performance was measured using Brier-Score and Log-Loss. The results show that both SVC and RVC not only overcome the limitations and outperform the classical method, but also show robustness to arbitrarily partitioned training sets, whereas the classical method sometimes performs poorly.

Empirical predictive model for seismic damage and economic losses of Italian school building heritage

Schools should be safe places where children and young people are hosted during their training years to develop their abilities and skills and to receive an education that makes them prepared to become the future of the nations where they live. Even though these aspects are of paramount importance and widespread recognized, the same importance does not seem to be equally ensured to school facilities. Educational institutes, indeed, are often old and realized without recent safety Standards, becoming consequently non-resilient, nor robust structures towards multiple natural hazards. This aspect concerns lots of countries worldwide, without making distinction among their richness level.In this paper empirical models for the prediction of damage and retrofit costs expected after earthquakes are presented. These probabilistic models relate seismic intensity to expected damage and economic losses, through the definition of continuous indexes, and are based on data collected after a recent earthquake occurred in Central Italy. Empirical data, required to define the probabilistic models, have been obtained by combining information coming from shaking maps, provided by the National Institute for Geophysics and Volcanology (INGV), information on the building properties (e.g. locations, dimensions, construction typology), provided by the Ministry of Education, and data about the damage suffered by constructions and funding for retrofit actions including damage repairing and seismic upgrading, provided by the Reconstruction Office. Proposed models provide the opportunity to directly derive fragility curves, to make it possible the use of the research outcomes in risk frameworks based on a discrete description of the damages and losses.Model parameters have been calibrated for the considered set of available data, but the methodology is general and can be also applied to different contexts, given data are available. Finally, the proposed models have been used to simulate the post-earthquake damage and losses scenario following a seismic event. A proposal for the analyses of probabilistic outputs have been developed to provide information useful to decision making purpose.

Fragility curves for residential unreinforced masonry buildings prone to out-of-plane mechanisms: the case of the historical center of Sora

The earthquake events of the past and recent years highlight as the seismic protection of historical towns is a crucial and current issue in Italy, but also in many other earthquake prone areas of Europe, where severe damages and collapse of buildings have been observed after seismic events. In particular, significant damages have been detected in historic centers of small and medium towns, mainly characterized by unreinforced masonry buildings, highly vulnerable with regard to out-of-plane collapse mechanisms. In this context, the assessment of the seismic vulnerability of unreinforced masonry buildings is a fundamental issue, in that they represent the most widespread construction typology in Italian and European small and medium towns. One of the most effective approaches in predicting potential damages of building typologies, is based on the derivation of fragility curves. An important aspect that affects the construction of fragility curves is the choice of response spectra to define the seismic demand; both Italian code and European guidelines allow the use of natural records, but also propose to employ smoothed spectra, in that the first one is hardly applicable by practitioners. Nevertheless, the employment of the smoothed spectra does not allow for adequate considerations about the influence of record-to-record variability. Downstream of this brief discussion, the paper presents the evaluation of fragility curves for unreinforced masonry buildings typical of the Central Italy, prone to the occurrence of out-of-plane collapse mechanisms, by considering both the spectral-shapes directly derived from the Italian codes and spectra obtained by the selection of natural accelerograms.

Empirically based approaches for the derivation of fragility curves of Italian RC building typologies

In this study, fragility curves for Italian RC building typologies are derived, by taking advantage of post-earthquake damage data gathered after the Irpinia (1980) and L'Aquila (2009) seismic events. The severity of the ground shaking is characterized by extrapolating peak ground acceleration values from updated INGV ShakeMaps and a global level of damage, consistently defined with the EMS-98 and accounting for both structural and non-structural damage observed on preselected building components, is associated with each inspected building. RC buildings are allocated to twenty-four building typologies, accounting for construction age, design level and number of storeys. Statistical processing of observational damage data showed the general tendency of seismic vulnerability to increase with the number of storeys and to reduce with design level and construction age. In some cases, the reliability of the obtained results was however affected by the limited amount of damage data and/or by scarcely populated building typologies. Two alternative empirically based approaches, relying on different data processing techniques and fitting strategies, are hence developed, overcoming issues in empirical fragility assessment driven by data paucity and allowing for a robust seismic fragility model.

Closing the Resilience Gap: A Preliminary Study on Establishing the National Fragility Curve Catalog for Multi-Hazard Assessment in Indonesia

This research paper presents a preliminary study aimed at closing the resilience gap in Indonesia through the establishment of a national fragility curve catalog for multi-hazard assessment. Indonesia is located in a high-risk hazard area, yet it currently lacks a comprehensive fragility curve catalog, which hinders effective risk assessment and mitigation strategies. By developing this database, the study aims to improve the understanding of structural vulnerability and enhance resilience planning across various hazards, such as earthquake, tsunami, wind, and flood. The research methodology involves collecting and analyzing data on the performance of different building types, exposed to multiple hazards. This includes considering various factors such as construction materials, design standards, and geographical characteristics. Statistical techniques and analytical modeling will be utilized to derive fragility curves that depict the probability of exceeding different damage levels or performance states given a specific hazard intensity. The findings of this study will provide valuable insights into the vulnerability of infrastructure and communities in Indonesia, enabling more informed decision-making for disaster risk reduction and resilience planning. The fragility curve database will facilitate quantitative risk assessments, support the development of appropriate building codes and standards, and inform the prioritization of mitigation measures. Ultimately, the establishment of a national fragility curve database will contribute to enhancing Indonesia's resilience to multi-hazard events and improving disaster preparedness at various scales.