Seismic Fragility Curves Research Articles

Seismic response prediction and fragility assessment of high-speed railway bridges using machine learning technology

Nowadays, reliable and accurate prediction of the seismic response of high-speed railway bridges and then rapid assessment of their seismic fragility is crucial for the risk assessment of regional high-speed railway bridges. However, the traditional seismic fragility assessment based on nonlinear time history analysis (NTHA) has a characteristic of high computational cost. Therefore, this study explores different machine learning (ML) methods to develop a reliable rapid seismic fragility assessment framework for high-speed railway bridges. Taking a typical high-speed railway continuous (HRC) bridge as a case, a large number of numerical model and ground motion pairs considering various structural and ground motion features are established. Then, the two types of models including six popular ML methods are investigated, in which Lasso regression, artificial neural network (ANN) and support vector machine (SVM) are single models, and random forest (RF), extreme gradient boosting (XGBoost) and light gradient boosting machine (Light GBM) are ensemble models. A database containing a large number of seismic responses of different components is established through the NTHA to develop prediction models, and the optimal hyperparameters of different ML models are determined by ten-fold cross-validation and grid search. The study results show that the ensemble model can reliably predict the seismic response of the HRC bridge compared with the single model, and the XGBoost model is recommended for seismic fragility assessment. On this basis, the optimal ML model obtained by the performance evaluation is applied to develop seismic fragility curves of the HRC bridge, which are compared with the fragility curves based on NTHA. The results indicate that the XGBoost model can effectively replace the traditional NTHA for rapid seismic fragility assessment of the HRC bridge, which can achieve a sufficient assessment level while saving calculation costs.

Seismic fragility curves for concrete gravity retaining wall

Seismic fragility analysis plays a crucial role in performance-based seismic design (PBSD). The seismic fragility analyses for the concrete gravity retaining walls were performed in this study. Numerical models were developed for two concrete gravity retaining walls using OpenSees, considering two different backfill slope angles (0° and 12°). According to the probabilistic seismic demand models and comprehensive evaluation of intensity measures (IMs), the most suitable IM for concrete gravity retaining walls was determined. An approach for quantifying the limit state performance of concrete gravity retaining walls based on IDA was also proposed, and its reliability was verified based on observed damage during the 2008 Wenchuan earthquake. Seismic fragility curves for concrete gravity retaining walls were established under two backfill slope angles using three IMs. It is demonstrated to what extent a backfill slope angle can influence the damage probability under a specific seismic intensity level.

Seismic fragility analysis of prefabricated self-centering frame structure

The seismic fragility of prefabricated self-centering frame structures composed of self-centering joints is investigated for reference in their seismic design and application. In this paper, a new design of the concrete-filled double steel tubular column-RC beam joint with self-centering capability and friction energy dissipation was proposed. The joint was modeled with ABAQUS and OpenSees, and hysteretic simulation was carried out to verify the reasonableness and accuracy of the OpenSees phenomenological model. Based on the OpenSees platform, a one-bay, six-story prefabricated self-centering frame structure was modeled, and seismic fragility analysis based on the incremental dynamic analysis was performed, in which seismic fragility curves were obtained according to the probabilistic demand analysis model. The results indicated a high coincidence in hysteretic curves between the ABAQUS model and the OpenSees phenomenological model, which showed favorable self-centering and energy dissipation performance of the joint proposed in this paper. Based on FEMA 356, three kinds of performance points were defined, i.e., “Immediate Occupancy” (IO), “Life Safety” (LS), and “Collapse Prevention” (CP). The prefabricated self-centering frame in this paper tended to exceed the IO, where the stiffness and strength of the structure was susceptible to damage. However, the failure probability at the LS performance level remained low, with only 5% and 37% failure probability under moderate and rare earthquakes, respectively. The structure achieved a collapse margin ratio of 4.28, which indicated a high collapse resistance in it.

Seismic fragility assessment of an in-service piled bridge abutment subjected to a liquefaction-induced lateral spreading and mitigation strategy

This study assesses the seismic fragility curves of in-service piled bridge abutments on liquefaction-prone soils and evaluates an optimal countermeasure within the vulnerability framework. Seismic fragility curves, accounting for varying ground motion intensities, assess the seismic risk and describe abutment damage through settlement measurements. The ageing abutment performance is estimated by integrating a corrosion model into fragility curves. The impact of different sheet pile positions on the seismic performance of in-service piled bridge abutments is analysed, and the optimal pile position is discussed. The developed fragility curves provide a rapid and effective risk assessment tool for the seismic performance of in-service abutments and guide liquefaction remedial measures.

A maximum entropy-driven support vector classification model for seismic collapse fragility curves estimation of reinforced concrete frame structures

A novel method called maximum entropy-driven support vector classification (MED-SVC) for estimating the seismic collapse fragility curves of reinforced concrete (RC) frames is proposed in this paper. In comparison to kernel-based learning (KBL) methods, a subset selection process based on the maximum Renyi entropy criterion is embedded into the proposed MED-SVC, which can actively select an informative small-scale subset from a large-scale training dataset. The selected subset can accurately reflect the data distribution of the large-scale training dataset, which can be further used to explicitly establish a high-dimensional feature variable. Due to this, the computational complexity of training the proposed MED-SVC model only depends on the dimension of the feature variable, which can effectively solve the problem related to the low efficacy of training the KBL model in the context of a large-scale training dataset. Meanwhile, the proposed MED-SVC model can also reduce the negative effect of randomness in the subset selection process on predictive performance. The robustness, accuracy, and efficiency of the proposed MED-SVC model are thoroughly validated by comparison with random sampling driven SVC (RSD-SVC), KBL methods, random forest, neural network, and naive bayes based on 33,000 damage data of RC frames under earthquakes. Then, the proposed MED-SVC model is applied to estimate the seismic collapse fragility curve of an RC frame structure outside the aforementioned dataset. The results show that the proposed MED-SVC model can generate seismic collapse fragility curves that agree well with those produced by the finite element method (FEM) and performs more robustly than RSD-SVC.

Performance-based assessment of the novel prefabricated CFST bridge pier by numerical approach

This study aims to profoundly investigate the seismic performance and application prospect of the typical continuous beam bridge with the novel prefabricated concrete-filled steel tubular (CFST) piers, with advantages in simple on-site assembly, convenient transportation of prefabricated components, good seismic performance, and low construction cost. According to two prototype continuous beam bridges respectively equipped with low and tall typical reinforced concrete (RC) piers, 7 bridge cases with prefabricated CFST piers featuring various configurations of the tie beams are designed. Three-dimensional numerical models of these bridge cases are established and verified with the previous experimental studies, and numerical simulations of all the bridge cases are conducted to assess and compare the seismic responses and fragility curves. The results show that the bridges with prefabricated CFST piers exhibit a reduction in top pier transversal displacement and maximum curvature along the pier height, which are 43 % and 138 % lower than those of the prototype RC piers, respectively. Besides, the bridges with prefabricated CFST piers generally present lower probabilities of being damaged compared to those of the prototype bridges with RC piers.

Two-Scale Probabilistic Seismic Fragility Assessment for a Prestressed Concrete-Steel Hybrid Wind Turbine Tower with Incremental Dynamic and Multiple Stripe Analysis

ABSTRACT To evaluate the seismic performance of a prestressed concrete-steel hybrid (PCSH) wind turbine tower, the seismic fragility curves based on incremental dynamic analysis (IDA) and multiple stripe analysis (MSA) on a two-scale model are presented and compared. The peak ground acceleration (PGA) and peak lateral drift on the top of the tower are adopted as the intensity measure (IM) and engineering demand parameter (EDP) of analysis, respectively. Finally, the seismic performance of the PCSH tower subjected to seismic action at different soil is investigated. The fragility curves obtained by IDA and MSA methods are compared.

Seismic fragility analysis of human perception in high‐rise buildings subjected to far‐field long‐period earthquake ground motions: A case study for Shanghai tower

AbstractHuman perception in high‐rise buildings during far‐field long‐period earthquake ground motions often induces psychological discomfort, including fear and anxiety. A comprehensive understanding on human perception of seismic events is vital for city planning and emergency management, facilitating effective evacuation plans and minimizing stampede risks. This study addresses a gap by employing the seismic fragility analysis method to delineate how human perception in high‐rise buildings is affected during far‐field long‐period ground motions. The methodology involves several key steps. First, the far‐field long‐period earthquake ground motion was identified by detecting the later‐arriving surface waves, and a series of records were selected from the next generation attenuation (NGA) West‐2 ground motion database of the Pacific Earthquake Engineering Research center. Then, a high‐rise building in Shanghai, China was modeled using ETABS 20. Through the linear‐elastic time history analysis, the structural seismic response at each floor was computed. Furthermore, human perception thresholds to vibration were introduced to assess the degree of human perception at each floor, illustrating the difference of human perception to seismic tremor at different floors. Finally, a novel earthquake intensity measure (IM), namely average response spectrum intensity (ARSI) within the vibration period ranging from 0.1 s to 10 s was introduced to generate seismic fragility curves for human perception. According to the investigation, it was found that the corner frequency and the associated energy ratio are useful indicators to identify the far‐field long‐period earthquake ground motions. The ARSI is an effective parameter to assess human perception to seismic tremor compared to the spectral acceleration at a given fundamental period. The generated seismic fragility analysis can provide a complete and thorough understanding on the probability of people that should be evacuated under different earthquake intensity levels. The probability of human perception at different floors varies along the building height, demonstrating the difficulty to make crowd evacuation plan in practice. This insight is vital for understanding and mitigating seismic concerns in high‐rise buildings, particularly in low‐to‐moderate seismicity regions.

Confinement effects within the seismic design of reinforced concrete frames: reliability assessment and comparison

The current Italian code “NTC2018” and Eurocode “EC8” provide specific design requirements in terms of flexural overstrength factors for reinforced concrete (RC) buildings in seismic areas. This study proposes to improve the design methodology by including explicitly the confinement effects within the seismic design of a new regular RC frame due to their influence on the capacity design principles (at structural and member level). Specifically, the seismic performance of a RC frame designed according to codes is compared, in reliability terms, with the one of the same frame designed including the concrete confinement effects. Moreover, a comparison between three constitutive models for confined concrete is performed. Selecting L’Aquila (Italy) as reference site, the two design methodologies combined with the three confinement models are numerically implemented. Scaling 30 non-frequent natural ground motions to increasing seismic intensity measures, according to the site seismic hazard, non-linear incremental dynamic analyses (IDAs) have been developed. Assuming the interstory drift indices as engineering demand parameters, the peak responses have been fitted through log-normal distributions to define IDA curves. Subsequently, appropriate limit state thresholds have been adopted to define the seismic fragility curves. Finally, through the convolution integral and Poisson model, the seismic reliability curves have been derived showing the importance of the proposed design methodology. In fact, for the frame under investigation, the seismic performance strongly improves in terms of ductility respecting all the reliability objective levels if the confinement effects are explicitly considered in the seismic design. Furthermore, the different confinement models provide similar results when the proposed seismic design is adopted, implying a reduction of the model uncertainty.

Development of seismic fragility curves for hospital buildings using empirical damage observations

Fragility curves are widely recognized as an essential tool for assessing and projecting asset damage, vulnerability, and seismic risk. The technical literature provides different fragility curves for residential buildings that exhibit unique characteristics for different categories of buildings, however, comparatively fewer curves are available for hospital buildings. The specific design criteria for hospital buildings necessitate specialized fragility curves for them. In the current study, a set of empirical fragility curves for hospitals have been developed utilizing the data of 341 damaged hospital buildings in previous earthquakes. The peak ground acceleration of the occurred earthquake events in the location of the considered hospitals is utilized as earthquake intensity measure. Fragility curves are developed for the three categories of low-rise concrete moment frame, medium-rise concrete moment frame, and masonry hospital buildings. Due to the lack of appropriate available data, the fragility curves of masonry hospitals are developed by merging the collected data with the fragility curves acquired from the existing literature. The creation of fragility curves for non-structural components of hospitals is another contribution of this study. Finally, a comparison of the fragility curves derived in the current study with those documented in existing research papers is provided.

Influence of frequency characteristics of seismic ground motion on the fragility of an RC frame structure

Ground-motion frequency characteristics have a significant impact on structural damage. A quantitative description of the impact of ground-motion spectral features on structures is an urgent topic that requires solutions. In this study, the ratio of peak displacement to peak acceleration (R d2a ) is used as a representative index of the ground-motion spectral characteristics. The seismic records collected from the Kik-net strong-motion array in Japan are grouped according to their R d2a values. By adopting the incremental dynamic analysis method, the seismic fragility curves of a six-story RC frame structure loaded by inputting seismic records with different R d2a values are calculated using the OpenSees platform. The influence of R d2a values on the structural fragility is analyzed. Ground-motion records of liquefied sites are collected, and the peak ratios of seismic records at the liquefied sites are analyzed to reveal the differences in the fragility of the six-story RC structures at liquefied and non-liquefied sites. The results of this study are expected to serve as a reference for the evaluation of structural fragility and to understand the effect of ground-motion frequency characteristics on the fragility of RC frame structures.

Selection of optimal intensity measures for seismic performance evaluation of underground utility tunnel and internal pipeline system

Seismic intensity measures (IMs), which are closely related to both earthquake hazards and structural responses, play a critical role in the performance-based earthquake engineering (PBEE) framework. This paper aims to investigate and define the most representative IMs for probabilistic seismic demand model (PSDM) for the longitudinal utility tunnel and internal pipeline system. Similar to the requirements by the Chinese Code for seismic design of urban rail transit structures, the utility tunnel in this study is assumed being buried in four typical engineering site classes for the analyses. Soil-tunnel-pipeline interactions are simulated using a double-beam system resting on a nonlinear foundation. Soil-tunnel interaction, tunnel-pipeline interaction and joint connections are modeled as nonlinear springs with different mechanical properties. A series of 17 pairs of outcrop ground-motion records and 27 commonly used IMs are selected in the analyses. Engineering demand parameter (EDP) is defined based on the maximum joint opening and the maximum strain of the utility tunnel and internal pipeline, respectively. The selected IMs for predicting the seismic responses of tunnel-pipeline systems are tested using different criteria, i.e., correction, efficiency, practicality, and proficiency. The final decision-making procedure employs a fuzzy multi-criteria decision method. The numerical results indicate that: (1) The velocity-related IMs are the most representative IMs based on the four criteria for structures buried in four sites of different conditions; (2) The optimal seismic IMs vary with different criteria, site classes and structure types. According to the fuzzy multi-criteria decision approach, optimal IMs for the tunnel-pipeline system are PGV, PGV, EPV and HI for site classes I – IV, respectively. The proposed optimal IMs can be utilized to construct seismic fragility curves of utility tunnel, internal pipeline and tunnel-pipeline systems in four different site classes.

Seismic capacity models for earth dams and their use in developing fragility curves

This article develops seismic capacity models for earth dams and demonstrates how the proposed seismic capacity models may be used to develop seismic fragility curves that predict the probability of damage as a function of ground shaking intensity. Developing earth dam fragility curves requires two major components: (1) a seismic capacity model that predicts the probability of a damage state given the relative settlement (RS) and (2) an engineering demand model that predicts the RS as a function of ground motion intensity. While seismic demand models for earth dams have been studied by various researchers, there is a scarcity of seismic capacity models. This article focuses first on developing seismic capacity relationships using a dataset of earthquake case histories of dam performance. Different from previously developed relationships, only the damage description for each dam is used when assigning the damage state, which results in statistical variability in the capacity relationship between the damage state and RS. The fragility curve development is demonstrated by combining the seismic capacity relationships with a seismic demand model for RS derived from nonlinear, dynamic finite element analyses for a 20-m generic dam geometry subjected to a suite of earthquake motions from the NGA-West2 database.

Study on seismic fragility of prefabricated columns connected by grouted sleeves based on IDA method

PurposePrefabricated columns connected by grouted sleeves are increasingly used in practical projects. However, seismic fragility analyses of such structures are rarely conducted. Seismic fragility analysis has an important role in seismic hazard evaluation. In this paper, the seismic fragility of sleeve connected prefabricated column is analyzed.Design/methodology/approachA model for predicting the seismic demand on sleeve connected prefabricated columns has been created by incorporating engineering demand parameters (EDP) and probabilities of seismic failure. The incremental dynamics analysis (IDA) curve clusters of this type of column were obtained using finite element analysis. The seismic fragility curve is obtained by regression of Exponential and Logical Function Model.FindingsThe IDA curve cluster gradually increased the dispersion after a peak ground acceleration (PGA) of 0.3 g was reached. For both columns, the relative displacement of the top of the column significantly changed after reaching 50 mm. The seismic fragility of the prefabricated column with the sleeve placed in the cap (SPCA) was inadequate.Originality/valueThe sleeve was placed in the column to overcome the seismic fragility of prefabricated columns effectively. In practical engineering, it is advisable to utilize these columns in regions susceptible to earthquakes and characterized by high seismic intensity levels in order to mitigate the risk of structural damage resulting from ground motion.

Multi-metric evaluation of the optimal intensity measure for mainshock-aftershock fragility analysis of transmission towers

Identifying the optimal intensity measure (IM) contributes to reducing uncertainties in probabilistic seismic demand models (PSDM) and enhancing confidence of their results. Although many studies have discussed appropriate IMs for mainshocks, relatively less attention is paid to the potential aftershock effect. In particularly, the optimal IMs for developing PSDM of transmission towers subjected to sequential earthquakes has not been well studied previously. Therefore, this paper conducts a multi-metric evaluation to identify the optimal IM in the context of mainshock-aftershock (MSAS) fragility analysis of transmission towers. This evaluation process includes collecting a set of ground motions recorded with varying magnitudes and fault distances to construct MSAS sequences, followed by comprehensive discussions on their seismic characteristics by comparing thirty-six potential IMs candidates. Additionally, a finite element model of a transmission tower is established to numerically investigate different engineering demand parameters (EDP) of the tower under the selected MSAS sequences. The optimal PSDM of the transmission tower is determined by evaluating each couple of IM−EDP on a logarithmic space using multiple evaluation metrics. Through this analysis, the first-mode spectral acceleration Sa(T1,ξ) is identified as the optimal IM as it exhibits excellent correlation, efficiency, practicality and proficiency with the EDPs of the transmission tower, especially with the inter-segment displacement ratio. Consequently, seismic fragility curves of the transmission tower are developed using the optimal IM. The research outcome can contribute to improving the understanding of the probabilistic assessment of transmission towers in the MSAS scenario.

Seismic Damage Probability Assessment of Existing Reinforced Concrete School Buildings in Afghanistan

Existing Reinforced Concrete School buildings with low earthquake resistance may suffer structural failure or severe damage in a catastrophic seismic event. Ascertaining earthquake resistance in existing school buildings is vital to confirming the safety of students, teachers, and all school members. Reinforced concrete (RC) has been used significantly for numerous years as the primary material due to its easy access and low cost-effectiveness in construction. The current research focused on analyzing the existing RC school buildings designed and constructed in various regions of Afghanistan over the last three decades. Seismic fragility curves, which are generated from incremental dynamic analysis (IDA), have been used to evaluate the damage probability of RC school buildings against earthquake ground motions. In this investigation, 34 RC school buildings were selected from an extensive database and subsequently classified as either A-type or B-type based on specific criteria, including design details and construction year. Following this classification, an assessment of the seismic damage probability for these buildings was conducted using probabilistic models based on IDA curves. The results indicate that A-type school buildings with newer construction are less prone to damage compared to B-type school buildings, showing improved resilience. Especially the B-type buildings in seismic Zone-I are found to be highly vulnerable under the maximum considered earthquake scenarios.

Seismic time-dependent resilience assessment of aging highway bridges incorporating the effect of retrofitting

Bridges are one of the most critical components of transportation networks, which are highly vulnerable due to exposure to natural hazards. In addition, multiple degradation mechanisms can considerably affect the functionality of highway bridges during their service life. Therefore, accumulated damage could also arise continuously because of seismic loading and structural deterioration, which consequently can change system resilience over its life-cycle. This study presents a probabilistic methodology to systematically evaluate and develop the time-dependent seismic resilience curves for Reinforced Concrete (RC) bridges under chloride attacks. In this regard, different jacketing materials with varying thicknesses are chosen for retrofitting purposes. In each case, the time-dependent seismic fragility curves (four damage states) for calculating the time-dependent seismic resilience curves are established through Probabilistic Seismic Demand Models (PSDMs) by performing Incremental Dynamic Analysis (IDA). Finally, the time-dependent seismic resilience curves are evaluated based on the time-dependent seismic fragility curves using the restoration function for all the retrofitting strategies by considering the effect of structural deterioration over time. The results indicate that aging, earthquake intensities, and retrofitting strategies undeniably affect the time-variant seismic resilience of bridges, which is helpful for the long-term safety and reliability of bridges.

Comprehensive seismic loss model of Tehran, Iran in the case of Mosha fault seismic scenario using stochastic finite-fault method

This paper presents the results of a study caried out to assess probable seismic loss, in term of damage to the residential buildings and the number of fatalities, in the case of Mosha Fault seismic scenario in Tehran, Iran. Accordingly, seismic risk components (including seismic hazard, exposure model and fragility curves) are evaluated. The stochastic finite-fault method with dynamic corner frequency is applied for quantifying ground motion values. The results shows that PGA on the soil surface could range between 0.1 g to 0.45 g. Then, a reliable model of building exposure by analyzing census data from Tehran is compiled. This model included 19 different classes of buildings and is used to evaluate the potential damage to buildings from seismic scenario. The results indicate that the median of damage ratio from 100,000 iterations for the whole of the city is about 6% ± 1.54%. The study found that the central and eastern parts of Tehran are the most vulnerable areas, with an estimated 15,952 residents at risk of losing their lives in this scenario. This is equivalent to 0.2 percent of total population of Tehran. The finding from this study can be used by local authorities to provide appropriate emergency-response and preparedness plans in the case of Mosha Fault seismic scenario.

Reference prior for Bayesian estimation of seismic fragility curves

One of the key elements of probabilistic seismic risk assessment studies is the fragility curve, which represents the conditional probability of failure of a mechanical structure for a given scalar measure derived from seismic ground motion. For many structures of interest, estimating these curves is a daunting task because of the limited amount of data available; data which is only binary in our framework, i.e., only describing the structure as being in a failure or non-failure state. A large number of methods described in the literature tackle this challenging framework through parametric log-normal models. Bayesian approaches, on the other hand, allow model parameters to be learned more efficiently. However, the impact of the choice of the prior distribution on the posterior distribution cannot be readily neglected and, consequently, neither can its impact on any resulting estimation. This paper proposes a comprehensive study of this parametric Bayesian estimation problem for limited and binary data. Using the reference prior theory as a cornerstone, this study develops an objective approach to choosing the prior. This approach leads to the Jeffreys prior, which is derived for this problem for the first time. The posterior distribution is proven to be proper (i.e., it integrates to unity) with the Jeffreys prior but improper with some traditional priors found in the literature. With the Jeffreys prior, the posterior distribution is also shown to vanish at the boundaries of the parameters’ domain, which means that sampling the posterior distribution of the parameters does not result in anomalously small or large values. Therefore, the use of the Jeffreys prior does not result in degenerate fragility curves such as unit-step functions, and leads to more robust credibility intervals. The numerical results obtained from two different case studies—including an industrial example—illustrate the theoretical predictions.

Seismic fragility of vertically irregular gravity column-core tube structure subjected to pulse-like ground motions

The effects of the pulse-like ground motion and structurally vertical irregularity on the seismic fragility of the new gravity column-core tube structural system are investigated. Based on the shaking table test, the finite element parameters are verified. By changing the stiffness ratio of the first story to the second story, the typical vertically irregular gravity column-core tube structure models of 20-, 30- and 40-stories are established. Selecting 10 pulse-like and 10 corresponding non-pulse-like ground motion records, the incremental dynamic analysis and seismic fragility analysis are performed to these structures employing CANNY program. The results show that the maximum inter-story drift ratio (θmax) and the probability of exceeding the limit state (Pf) of each structure under pulse-like cases are significantly greater than those under non-pulse-like cases. From slight damage to approaching collapse state, the difference in seismic fragility curves between pulse-like cases and non-pulse-like cases is gradually amplified. It is suggested that the seismic strength reduction factor of these new type of structures be reduced properly to consider the pulse-like ground motion effect. With the stiffness ratio decreases, θmax and Pf have an increasing trend. However, the increasing quantity is small, which may be due to the effect similar to the isolation in the first story. As a limit value of vertical irregularity in the first story, the stiffness ratio of 1.5 provisioned in the code is conservative. To give consideration to both the safety and the economy, it is recommended to lower the limit value to about 1.2 for the gravity column-core wall structures with stiffness irregularity at the first story.