Fragility Curves Research Articles

Durability fragility curves for service life prediction of concrete with various supplementary cementitious materials subjected to natural carbonation

This study estimates the service life of concretes containing supplementary cementitious materials (SCM) subjected to carbonation from a probabilistic and reliability-based perspective. The aim is to enhance understanding of the risks associated with degradation and to propose an alternative approach for estimating the durability of reinforced concrete (RC) structures. The inclusion of supplementary cementitious materials (SCMs) is crucial for making concrete more sustainable, as these materials can reduce the carbon footprint of concrete production and improve its durability. Using available natural carbonation data from the literature on samples containing SCM, computational codes were developed for reliability analyses via the Monte Carlo Simulation method. The results indicated that all concrete samples exhibited a 100% probability of failure for coverages of 20 mm and 25 mm at an age of 100 years. For a coverage of 30 mm, all samples maintained a failure probability of over 98% within the same period. Notably, concretes incorporating metakaolin showed a substantial reduction in failure probability across all evaluated time periods, indicating superior durability compared to other samples. These findings significantly contribute to a deeper understanding of concrete degradation processes and provide valuable insights for the design and maintenance of RC structures, particularly in the context of using SCM. By adopting a probabilistic approach, the study underscores the importance of considering variability and uncertainties in predicting concrete durability, ultimately aiding in the development of more resilient and long-lasting infrastructure.

A vector‐valued ground motion intensity measure for base‐isolated buildings in far‐field regions

AbstractIn this study, the effects of the spectral acceleration at the superstructure first‐mode period on the isolator displacement are investigated for far‐field ground motions. For this purpose, two different base‐isolated models are subjected to 165 far‐field ground motions. It is demonstrated that considering the spectral acceleration at the superstructure first‐mode period, besides that at the effective period, improves the estimation accuracy of isolator displacement. ASCE 7‐22 modifies the scaling period range to consider the superstructure first mode period and proposes the new period range from the superstructure first‐mode period to the 1.25 times effective period. In the ASCE 7‐22, the same weight factor is used for the whole period range. However, the present study shows that adding the superstructure first‐mode related period range with appropriate weight factor to the effective period‐based scaling range decreases the dispersion of isolator displacement in the nonlinear response history analyses (NRH). Then, to overcome the spectral shape effects on the fragility curves, a vector‐valued intensity measure parameter is obtained by combining spectral acceleration at the effective period and reduced spectral acceleration at the superstructure first‐mode period. The optimum contribution factor for the spectral acceleration at the superstructure first‐mode period is defined as the ratio of the superstructure first‐mode period to the effective period. The article shows that the proposed parameter is efficient and sufficient to be used as an intensity measure for far‐field ground motions. Furthermore, regression analysis results indicate that this vector‐valued intensity measure parameter correlates well with the isolator displacement. Further, the article shows that using the proposed IM parameter in the fragility curves makes the collapse margin ratio of these curves less sensitive to the spectral shape of the selected ground motions.

Seismic response and fragility analysis of railway station typical signal cabinets

The loss of functionality in railway stations due to signal cabinet damage is frequently reported after earthquakes. To maintain the post-earthquake functionality of railway stations, it is essential to study the seismic response and fragility of signal cabinets. This paper divided the structure of railway station signal cabinets into combined cabinets and nine-fold cabinets based on previous investigations. The frequency-shift and train-control cabinets were selected as typical research objects representing these two types. Shaking table tests were conducted to examine their damage characteristics, seismic responses, and failure mechanisms. Based on these tests, finite element models of the two typical cabinets were established and verified, which were then used to analyze cabinet layering and weight distribution in practical applications. Moreover, seismic fragility curves were developed for frequency-shift and train-control cabinets under various damage states, utilizing both test and finite element results. These curves can be applied in seismic performance and functionality assessments of railway stations.

Shaking table tests and seismic performance assessment of a vertical mixed concrete/steel structure with large cantilevers

A series of shaking table tests were carried out on a vertical mixed concrete/steel structure with large cantilevers spanning 12 m. Structural seismic performance in terms of damping ratio, vertical response of the cantilever segment, lateral acceleration and deformation responses, and seismic failure mechanism of the specimen were analyzed through test data. Moreover, a further assessment of the specimen's seismic performance was performed through seismic fragility curves of the upper and lower structures, respectively, resulting from the shaking table test outcomes. It was found that the structure shows satisfactory seismic performance. After being subjected to the input motion with a PGA of 1.8g, cracks in the specimen are mainly observed on the floor of the upper structure, and the natural frequency decreases by 14 % compared to the initial state. And the fragility analysis results demonstrate a lower probability of significant structural damage or collapse. In addition, differences in material and structural form between the upper and lower structures lead to significant variations in seismic performance in the height direction. Deformation and damage occur mainly in the upper steel structure. The failure of the structure is mainly due to the loss of lateral resistance of the upper steel structure. The damage to the cantilever portion of the transfer story occurred in the steel trusses at the lower chord level. The diagonal trusses used for the transition story can provide adequate vertical stiffness and strength. Significant amplification of the cantilever segment on the vertical acceleration response spectrum is observed over the period range of 0–0.2 s.

Exploring seismic fragility and strengthening of masonry built heritage in Lisbon (Portugal) via the Applied Element Method

Although mainland Portugal has been spared from large magnitude earthquakes in recent years, it faces a threat due to the presence of several active fault systems. In such a framework, Portuguese pre-code masonry construction is believed to be the most vulnerable in the existing building stock. Given the lack of information on earthquake damage to this stock, the use of detailed numerical models is a viable strategy to comprehend its seismic behavior. This paper provides an updated fragility characterization of Lisbon pre-code masonry buildings based on their seismic assessment through the Applied Element Method. To limit the computational time, a promising pushover strategy, known as Incremental Ground Acceleration, was adopted. After the characterization of the current fragility, two retrofit layouts based on piers strengthening were modeled and assessed for the building stock whose seismic capacity does not meet expected demand. The aim of the paper is to derive updated fragility curves for the Lisbon region to support risk analysis incorporating the latest hazard studies and to offer insights into potential retrofit interventions.

Seismic vulnerability assessment of urban areas made of adobe buildings through analytical and numerical methods: The case study of the historical center of Cusco (Peru)

This paper aims at giving a contribution to the topic concerning the preservation of valuable adobe buildings, by setting a methodology for assessing their seismic vulnerability at the urban scale by means of analytical and numerical models, accounting for both their in-plane and out-of-plane behaviors. To this purpose, the valuable historical center of Cusco (Peru) is considered as representative case study. The city center of Cusco is an extraordinary example of colonial architecture that preserves essential aspects of its origins, it being representative of a large plethora of historical centers in South America and the Caribbean, where most of the residential buildings are made of adobe masonry.First, archetypes, representative of the whole historical center, are identified in order to get a manageable stock of buildings for which the analyses can be addressed to. The structural capacity of each archetype is then given in terms of capacity curves for both out-of-plane and in-plane mechanisms. Subsequently, these curves are compared with the likely seismic demands to assess the probability of attaining pre-established damage states for different seismic intensities. The obtained probabilities are collected into Damage Probability Matrices (DPMs) and, finally, cumulated to plot the fitting fragility curves.

Seismic correlation coefficient evaluation for the application of separation of variables approach in fragility assessment

Seismic correlation can affect seismic probabilistic risk assessment results when components within the system have similar dynamic characteristics. While the fragility assessment methodology is well established, researches to evaluate and apply seismic correlation in fragility are still in progress. In this study, the seismic correlation coefficient (SCC) was quantitatively analyzed based on fragility assessment methods. In order to evaluate the SCC of several random variables associated with structure response in fragility assessment, a numerical analysis model of the structure was constructed and statistical analysis of the numerical results was performed. The SCC of the floor responses of the structural model considering random variables was evaluated from two perspectives. The first perspective involved applying variables individually or simultaneously when performing probabilistic structural analysis. The second perspective aimed to assess whether simplification of the structural analysis model affects the SCC. For this purpose, SCCs were calculated for each method and applied to a simplified failure sequence model to compare the combined fragility curves. The results of this study demonstrate the applicability of separation of variables method to the evaluation and generalization of the SCC for random variables of the fragility curve.

Effect of foundation stiffness on the fragility curves of a concrete gravity dam under far-field ground motions

The finite element method is used to model the dam-reservoir-foundation interaction system, with the Latyan dam in Iran as a case study. A comprehensive concrete damage plastic model is employed to simulate the nonlinear behavior of concrete, encompassing its cyclic response, tensile failures, and compressive failure. An acoustic element is incorporated to account for the hydrodynamic effects of the lake reservoir, enabling the modeling of compressive wave propagation within the reservoir. A total of 100 real and scaled accelerograms is used to simulate seismic loading in addition to testing 8 concrete-to-foundation stiffness ratios. Therefore, the fragility curves are acquired for a total of 800 numerical models. The findings reveal that the fragility of the dam-reservoir-foundation interaction system is heavily dependent on the stiffness of the bed. The most favorable results are achieved when the stiffness ratio between the dam and the bed is close to 1, which enhances the seismic safety of the dam. Conversely, either excessively high or low bed stiffness levels are found to decrease the dam's safety. The results suggest that a dam-to-foundation stiffness ratio ranging from 0.75 to 1.5 provides the optimal seismic performance for a concrete gravity dam.

Serviceability fragility assessment of non-seismically designed railway viaducts in Turkey under near-field and far-field earthquakes

While many railway viaducts still in use in Turkish railway networks are located on active fault zones that produced historical destructive earthquakes, they are not seismically designed in accordance to current standards. This study aims to provide a better understanding about the serviceability fragility of such systems by conducting detailed probability-based seismic assessments under near-field and far-field earthquakes. To achieve this, firstly, 3D finite element models of a range of selected viaducts in Turkey were generated based on their original design drawings. The developed FE models were validated by comparing the analytical modal frequencies with the results of in-situ dynamic tests involving a series of acceleration measurements. Nonlinear time history analyses were then carried out under 25 near-field and 25 far-field real three-component ground motion recordings to obtain the seismic response of each selected viaduct. Subsequently, probabilistic seismic demand models were defined using linear regression analysis to determine relationships between engineering demand parameters (EDPs) and ground motion intensity measures (IMs). Peak ground acceleration (PGA), peak ground velocity (PGV) and spectral acceleration at 1.0 s (Sa (1.0)) were used as the IM parameter, while the maximum lateral displacement of the bridge spans for different service velocities defined in the Eurocode was considered as the EDP at serviceability damage state. Finally, analytical fragility curves for all the selected railway viaducts were developed considering maximum damage probability for the IM levels. The results, in general, demonstrate the seismic vulnerability of the existing viaducts in Turkey. It is shown that while at low speed limits the viaducts exposed to far-field ground motions were more vulnerable than those under near-field ground motions, at high speed limits the viaducts subjected to near-field ground motions were more vulnerable. Also, it is seen that reinforced concrete and masonry viaducts are generally more vulnerable to earthquakes than the steel viaducts. The outcomes of this study should prove useful for the seismic risk assessment, loss estimation and rehabilitation of the railway transportation networks in future studies.

Post-earthquake functional state assessment of communication base station using Bayesian network

The reliability and resilience of communication base stations are critical to the post-earthquake performance of the communication system, and consequently influence the communication, rescue, and emergence management after an earthquake. There is a lack of models that can fully evaluate the post-earthquake functional states of base stations with the consideration of the dependencies between different components. This paper proposes a Bayesian network method to evaluate the post-earthquake functionality of communication base stations. The method considers the dependence between the equipment and its hosting building structure, and the impact of power outages. This model produces seismic functional fragility curves for typical base stations that enable both qualitative and quantitative evaluations of base station functionality. The model is validated using seismic damage data from the Ludian Earthquake. It was found that the proposed model can reasonably predict the post-earthquake functional failure of base stations, in good agreement with the observed seismic damage data. The application of this model provides support for the operation and maintenance of communication base stations, and insights for managing seismic risk and resilience of the communication system.

MCS-ML based line vulnerability for infrastructural resilience assessment with multi-wind speed cyclonic zones

The resilience of critical infrastructure is paramount for power systems prone to cyclonic activities characterized by varying wind speeds. This study conducts a thorough examination of the impact of cyclone lasting for a week on transmission lines for each passing day. Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) is applied to extract hourly wind speed data for the cyclone. Sequential Monte Carlo Simulation (SMCS) is used to model the day-wise hourly transmission line fragility and determination of line vulnerabilities across high, medium, and low wind speed zones. Fragility curves are developed to depict the correlation between wind speeds and line failure probabilities in each zone. The line outage scenarios are generated based on the critical wind speeds and collapse wind speeds for each zone. Line Vulnerability Index (LVI) is proposed to determine the vulnerability and the resilience status of the transmission lines. Machine Learning (ML) based models, FFNN (Feed Forward Neural Network) and RFC (Random Forest Classifier), are proposed for assessment of infrastructure resilience by vulnerability ranking of the lines. Hourly wind speed and hourly line failure probability are the inputs to train the ML models and, LVI and ranking are predicted for the IEEE 30-bus system.

Methodology to determine the embedment depth of bridge piers considering the duration of rainfall events

Nowadays, there are many bridges that show damage or collapse due to scour, which produces serious consequences in direct and indirect costs. Although there are several studies that analyze scour in bridges, many of them consider that rainfall events are of unlimited duration, without evolution over time, which produces a conservative estimate. This work shows a methodology to develop fragility curves in bridges due to scour, evaluating the scour depth from its construction to the service life of the structure. The methodology used characterizes hydrological hazard, by evaluating the parameters: number of events, arrival time, and intensity and duration, as random series of Poisson processes. Additionally, the depth and average velocity of the flow are determined at the bridge site. With this information, scour depth values are obtained. Considering the overturning of the pier, the loss of support of the deck and the resistance of the pier as damage states, for each one the probability of failure during the useful life of the bridge is obtained. At the end of the work, some recommendations are included for defining the depth at which the pile should be placed to avoid scour.

Assessing the seismic sensitivity of bridge structures by developing fragility curves with ANN and LSTM integration

Assessing the seismic sensitivity of bridge structures by developing fragility curves with ANN and LSTM integration

IDA-Based Seismic Fragility Analysis of a Concrete-Filled Square Tubular Frame

Based on the incremental dynamic analysis (IDA) method, this paper conducts seismic fragility analysis of a CFST plane frame, a CFST spatial frame under 1D (one-dimensional) ground motions, and a CFST spatial frame under 2D (two-dimensional) ground motions, with different attacking angles. Firstly, nine-story, three-span CFST frame structures (including the plane frame and spatial frame) were modeled in OpenSees, based on the accurate simulation of the hysteresis performance of the test CFST frames. Then, twenty-five groups of ground motions were employed to analyze the seismic response. Lastly, the IDA curve clusters, probabilistic demand models, and seismic fragility curves of frame structures were researched, respectively. The analytical results showed that the exceeding probability of the spatial frame under 2D ground motions was successively greater than that under 1D ground motions, and greater than the plane frame, and the maximum difference at each performance level was up to 6% and 16%, respectively. The fragility analysis result of the spatial frame was sensitive to the attacking angle of ground motion, and the exceeding probability of the 135°, 150°, and 165° fragility curves was larger than that of the 0° (original attacking angle) fragility curve at each performance level. The research results provide a reference for seismic fragility analysis of CFST frame structures employing the IDA method.

The role of climate change and corrosion modeling strategy in dynamic response of pile-supported wharves

This paper explores the fragility of pile-supported wharves to environmental hazards, notably climate change and corrosion, and underscores the critical need to understand the interplay between these factors when assessing structural safety. The research advocates for comprehensive methodologies that encompass climate change effects, aging, and time-dependent deterioration in evaluating the seismic fragility functions of pile-supported wharves. An examination of aging and seismic effects is performed on a representative pile-supported wharf at designated time intervals. This study highlights the pronounced impacts of climate change and corrosion on the structural integrity of concrete and steel in marine environments. Specifically, it considers effects such as sea level rise, increased temperatures, and heightened relative humidity on pile-supported wharves. Additionally, three corrosion pitting configurations in prestressed strands with and without climate change considerations are analyzed to determine their influence on the strength and ductility of materials, limit states, and ultimately, on the fragility curves. The findings indicate that climate change significantly exacerbates the corrosion of materials in pile-supported wharves, and increases failure probability. The relative increase in corrosion rate after 50 years due to climate change is found to be 94%.

Seismic Fragility Assessment of Equipment in Nuclear Power Plant Structures Considering Nonlinear Hysteretic Behavior of Squat Walls

Accurate seismic risk assessment of structures necessitates precise fragility analysis. This study focuses on the seismic fragility assessment of equipment in nuclear power plant structures, particularly emphasizing the influence of nonlinear hysteretic behavior exhibited by squat walls. By developing and comparing linear and nonlinear models of reactor containment and auxiliary buildings within a nuclear power plant, this research elucidates the significant impact of nonlinear behaviors on the seismic response and subsequent fragility curves of associated equipment and systems. Utilizing a lumped-mass stick model, the study efficiently captures the characteristics of squat shear walls, facilitating the calculation of floor response spectra and fragility for nuclear facility structures. The impacts of pinching and degradation, inherent characteristics of a squat wall’s hysteresis under cyclic loading, were identified as significant. These include the shift and change in amplitude of the floor response’s peak, along with amplification in high-frequency domains. Fragility assessments, informed by seismic response analysis, indicate significant variations in fragility curve parameters based on equipment location and frequency. The findings question the effectiveness of traditional response factor methods and general regression techniques in accurately addressing the complex probabilistic seismic demands of equipment, thus highlighting the importance of using direct analysis for calculating fragility in situations with significant nonlinearity.

Collapse fragility analysis of historical masonry buildings considering in-plane and out-of-plane response of masonry walls.

This paper explores the seismic fragility assessment of historical masonry buildings in the context of performance-based earthquake engineering, using multiple-record incremental dynamic analyses (MR-IDA). The methodology is applied to two case studies, the first being a stiff monumental structure, and the second a tall and slender masonry building. Both case studies are modelled in the OpenSees software using three-dimensional macroelements that account for the in-plane (IP) and out-of-plane (OOP) response of masonry walls. Simultaneously, the numerical models account for the influence of non-linear connections in floor-to-wall interfaces and wall-to-wall interlocking. The record-to-record variability induced by the random nature of the ground motion is addressed through earthquake selection consistent with the variability of European hazard. Ground motion records are normalised at a uniform level of seismic intensity to be sequentially increased for the computation of IDA curves. Once IDA curves and fragility functions are derived, the failure results are thoroughly discussed. The fragility functions accounting for the uncertainties arising from the record-to-record variability are contrasted against the results of the seismic assessments affected by multiple sources of uncertainty in material and modelling parameters from a previous study. Finally, the fragility curves derived from the methodology presented herein are directly compared with fragility functions from probabilistic seismic demand analysis (PSDA). Overall, IDA-based fragility functions are found to provide more conservative predictions than the ones obtained from the cloud-based approach using unscaled records.

Comparative seismic analysis of frames with shape memory alloy slip friction dampers

This study investigated the seismic performance of 6-, 9-, and 12-story concentrically braced steel frames utilizing shape memory alloy slip friction dampers (SMASFDFs). For comparison purposes, identical frames equipped with self-centering braces (SCBFs) and buckling-restrained braces (BRBFs) were also designed and analyzed. The seismic performance of considered frames was evaluated through nonlinear static and nonlinear time history analysis (NLTHA) under three seismic hazard levels, i.e., frequently occurred earthquakes (FOE), design basis earthquakes (DBE), and maximum considered earthquakes (MCE). Incremental dynamic analysis (IDA) was conducted to examine the seismic responses, including peak interstory drift ratios (PID), peak floor accelerations (PFA), and residual interstory drift ratios (RID), of the designed frames under varying levels of seismic intensity. Fragility curves considering single and multiple seismic responses were obtained based on the IDA results. The results show that the SMASFDFs have comparable deformation control capacity as the BRBFs while exhibiting zero RID and more uniform deformation distribution over the building height. Moreover, in most circumstances, the joint failure probability is lowest for the SMASFDFs when considering multiple seismic responses. From a seismic design perspective, current results suggest that the SMASFDFs can be designed with the same strength reduction factor (R) if the PID is especially concerned.

Comprehensive evaluation of seismic fragility in base isolated buildings enhanced with supplemental dampers considering pounding phenomenon

Base isolation is a proven technology effective in minimizing earthquake-induced damage to both the structural and non-structural elements (especially freestanding contents) of buildings. Nevertheless, it has been shown that allowing the flexible isolation layer to endure substantial demand displacements might subject the isolated structure to failure. This vulnerability arises from potential superstructure yielding due to increased deformations and reduced stiffness, such as those occurring through pounding against a moat wall during intense earthquakes. One alternative to controlling these large deformations is to use supplementary dampers at the isolation plane of the building, creating a hybrid base isolation system (HIS), which adds damping to the isolation system. In this research, the seismic performance of base isolated structures with lead-rubber bearing (LRB) are studied in conjunction with linear viscous dampers (LVD). Due to this aim, a base-isolated steel frame with 2 story X-type braces and a surrounding moat wall is modeled with two various configurations: LRB, and LRB with LVD. Fragility curves are developed for an ensemble of near-field (NF) pulse-like ground motions and for the maximum inter-story drift ratio (MIDR) as an engineering demand parameter (EDP). The incremental dynamic analysis (IDA) is conducted to calculate the damage probability of the structure by assuming different threshold values for damage states. It was found that adding viscous dampers to the isolation system balanced the behavior of the structure under near field pulse-type records; resulting in reduced isolation displacement while its adverse effects are insignificant and can be ignored. Moreover, the median spectral acceleration, namely the spectral acceleration associated to a probability of exceedance (POE) equal to 50 %, at the specific limit state, in the hybrid base isolation system is higher compared to the conventional one.

Seismic fragility estimation through real-time hybrid simulation and surrogate-based multi-fidelity Monte Carlo predictor

The intricate dynamic responses of structures, particularly when confronted with uncertainty, poses significant challenges in constructing reliable analytical models, thus resulting in unreliable fragility assessment. This study presents an approach that integrates data-driven techniques with real-time hybrid simulation (RTHS) to achieve reliable fragility analysis. RTHS data and imprecise surrogate models are fused using a multi-fidelity Monte Carlo predictor (MFMC), yielding unbiased estimations for parameters of fragility curve. The MFMC predictor can be considered as an optimized forecasting tool that harnesses the computational efficiency of low-fidelity simulations and the precision of high-fidelity experiments. RTHS is utilized for obtaining high-fidelity experimental data, part of which is leveraged to establish low-fidelity surrogate models, ultimately enabling multi-fidelity analysis through direct data-to-data analysis. A two-story steel moment-resisting frame equipped with self-centering viscous dampers is used as a proof-of-concept to demonstrate the proposed method. Structural and ground motion uncertainties are incorporated to reflect practical engineering environment. The low-fidelity Kriging models were built using portion of high-fidelity RTHS data. Simulation and experimental investigations were conducted to evaluate the effectiveness and efficiency of the proposed approach. The results suggest that the proposed method provides a promising tool for accurately evaluating seismic fragility, particularly when simulation-based methods are not feasible.