Seismic Fragility Analysis Research Articles

Seismic fragility analysis of nuclear containment structure with Bayesian cloud analysis framework

Nuclear containment structure plays a critical role in safe operation of nuclear power plants. Seismic safety of nuclear power plant structures has become a hot issue in nuclear engineering community following Fukushima nuclear accident. Seismic fragility analysis, as a key element in probabilistic safety assessment of nuclear power plants, is widely used in nuclear power plant structures. This study presents an innovative method for seismic fragility analysis of engineering structures. The proposed methodology combines conventional Cloud analysis method and Bayesian framework. The accuracy and efficiency of the proposed methodology were demonstrated by a single-degree-of-freedom system, heavy computational efforts but high accuracy seismic fragility analysis method was adopted for comparison. Seismic fragility analysis of a typical prestressed concrete nuclear containment structure was analyzed using the proposed method. Results indicated that method proposed in this study can improve the accuracy of seismic fragility analysis. Furthermore, with the enhance of performance level, the increasing ratios for median seismic capacity of the nuclear containment structure was decreasing.

Bidirectional seismic fragility analysis of double-deck viaduct frame piers based on stripe-cloud method

To evaluate the influence of bidirectional seismic action on the seismic fragility of double-deck viaduct fram pier (DVFP), this study employs a vector-valued intensity measure (IM) [PGA, Sa (T1, 5 %)], in tandem with the stripe-cloud method. The study compares the median values of Sa and the damage probability difference index (DI) to analyze the fragility of DVFP under both unidirectional and bidirectional seismic actions. Additionally, this research investigates the sensitivity of bidirectional seismic fragility of DVFP to the incidence angles. The results indicate a notable decrease in the median Sa values for DVFP are observed under bidirectional seismic action, with decreases of 28.6 %, 24.3 %, 20.9 %, and 18.8 % corresponding to four damage states, as compared to those under unidirectional seismic action, and the corresponding parameter DIs are measured at 0.122, 0.182, 0.245, and 0.291, respectively. Notably, the most severe damage to DVFP occurs when the bidirectional seismic incidence angle is within the range of 120–135°. At this angle, the median Sa values at four damage states are 85.8 %, 86.1 %, 87.6 %, and 88.6 %, respectively, compared to the angle of 0°. Therefore, neglecting the influence of bidirectional seismic incidence angles may lead to an underestimation of the bidirectional seismic fragility of DVFP.

The site-city interaction effect uncertainty on structural responses and its application to fragility analysis of buildings in Shanghai CBD

Seismic fragility analysis is a crucial tool for assessing the seismic performance of buildings. In areas with dense clusters of tall buildings, the significant site-city interaction (SCI) effect alters wave propagation mechanisms, influencing the seismic fragility of structures. However, a significant increase in computational workload results from the need for detailed modeling of sites and building clusters for the SCI analysis. To address this challenge, this work first investigates the minimum number of earthquake waves required to characterize SCI-induced response changes. The Central Business District of Shanghai is analyzed. A table for the recommended minimum number for a given accuracy requirement and prediction reliability is provided. Moreover, a seismic fragility analysis method considering the SCI effect is proposed for low-rise buildings. The case study indicates that, buildings with similar height will exhibit various fragility changes after considering SCI. For the complete damage state, the mean intensity value of the fragility curve can be 14.4 % smaller than that without SCI. In addition, this approach provides significant computational workload reduction. For the case study, the computational workload of the proposed method is roughly 1/50 of that using traditional IDA method.

Efficient seismic fragility analysis considering uncertainties in structural systems and ground motions

AbstractFragility plays a pivotal role in performance‐based earthquake engineering, which represents the seismic performance of structural systems. To comprehensively understand the structural performance under seismic events, it is necessary to consider uncertainties in the structural model, i.e., epistemic uncertainties. However, considering such uncertainties is challenging due to computational complexity, leading most fragility analyses only to consider the chaotic behavior of ground motions on structural responses, i.e., aleatoric uncertainties. To address this challenge, this study proposes an adaptive algorithm that intertwines with the conventional fragility analysis procedures to consider both aleatoric and epistemic uncertainties. The algorithm introduces Gaussian process‐based metamodels to efficiently consider epistemic uncertainties with a small number of time history analyses. Steel moment‐resisting frame structures and a reinforced concrete building are used to demonstrate the improved efficiency and wide applicability of the proposed method. In each case, the proposed method yields fragility curves consistent with reference solutions but with substantially lower computational effort. Comprehensive discussions are provided regarding ground motion sets, structural types, and definitions of limit‐states to demonstrate the robustness of the proposed approach.

System fragility analysis of highway bridge using multi-output Gaussian process regression surrogate model

This study presents a multi-output Gaussian process regression (GPR) surrogate model for seismic-fragility analysis of bridge structural systems. Multi-output GPR can model the correlations among multiple outputs, accuracy and stability are achieved with fewer training data, which reduces the computational cost of fragility analysis. Furthermore, the explainability of the constructed surrogate model is implemented by adopting an automatic relevance-determination (ARD) kernel in the GPR. The estimated hyperparameters can provide the contribution of the uncertainty of each input parameter to the outputs. The fragility analysis using the multi-output GPR surrogate model was verified by applying it to a seismic isolation highway bridge with multiple spans and a curved geometry. The effectiveness of the multi-output GPR was demonstrated by the construction of an accurate and stable surrogate model with 46 inputs and 28 outputs. The relative contributions of the uncertainties to the structural properties and input earthquake loads could also be understood. The fragility curves, at both the component and system levels, were appropriately obtained using a sufficient number of samples in a Monte Carlo calculation. Furthermore, the failure modes were evaluated, identifying which structural components contributed to the system failure. This enabled discussions on structural system failures from the viewpoint of the structural dynamic characteristics of the bridge and earthquake-load properties.

Seismic vulnerability assessment and fragility analysis of tunnels in Oman: Development of risk matrices and functionality guidelines

Past seismic events worldwide inflicted severe damage on tunneling and underground infrastructure projects and resulted in considerable socioeconomic loss. In this study, the seismic vulnerability of tunnels in the Sultanate of Oman is assessed, accounting for tunnel typology and localized site conditions. Seismic Fragility Curves (SFCs) were developed for two seismic zones (Zone 1 and Zone 2) based on the proposed intensity-response relationship, incorporating two different lining properties. Results consistently indicated a 39.56 % decrease in raking ratio for every 15 m/s reduction in shear wave velocity (VSST) across all tunnel models, spanning soft to stiff strata conditions. Employing the fragility functions developed for the Sultanate of Oman, project-specific risk matrices and operational route maps for Al-Sharqiyah Expressway Tunnel-2 (AST2) were formulated, along with an assessment of post-seismic operational accessibility. The insights garnered from this investigation provide fundamental guidance for engineers, designers, and consultants involved in seismic analysis and design of underground structures, encompassing both new constructions and retrofitting endeavors. Furthermore, the data generated herein offers valuable input for governmental stakeholders, facilitating policy formulation and the establishment of national-level design directives concerning tunneling projects within the Sultanate of Oman.

Seismic fragility analysis of three-tower cable-stayed bridges with different connection configurations

Seismic fragility analysis of three-tower cable-stayed bridges with different connection configurations

Seismic Fragility Analysis of Reinforced Concrete Simply Supported Girder Bridges Resting on Double-Column Piers for High Speed Railway

Seismic Fragility Analysis of Reinforced Concrete Simply Supported Girder Bridges Resting on Double-Column Piers for High Speed Railway

Seismic performance assessment and fragility analysis of concrete structures equipped with self-centered hybrid wall systems

ABSTRACT In this study, comprehensive analytical and parametric studies were conducted on seismic performance, collapse and fragility curves of concrete structures equipped with self-centered unbonded post-tensioned hybrid wall system in comparison with conventional structural wall system. For this purpose, analytical models of prototype buildings were developed and to further study the behaviour of hybrid wall, parametric analysis was performed considering four parameters: wall aspect ratio, initial stress of post-tensioned tendons, the total area of PT tendons, the total area of mild bars. The performance of buildings was evaluated under non-linear quasi cyclic and time history method considering two seismic hazard levels, the design-based earthquake level and the risk-targeted maximum credible earthquake level. Hysteresis response, energy dissipation ability and damping ratio, relative self-centering efficiency, residual drift, peak roof drift, column curvature ductility, incremental dynamic analysis data, seismic collapse assessment and fragility curves for collapse and repairable limit states were studied.

Incorporation of machine learning into multiple stripe seismic fragility analysis of reinforced concrete wall structures

This study proposes a novel procedure that incorporates machine learning (ML) into the multiple stripe analysis (MSA) approach to efficiently produce seismic fragility curves for reinforced concrete (R/C) shear walls in building frame systems. The proposed procedure aims to mitigate computational challenges associated with the original MSA approach. In this context, ML models were developed for predicting the failure probability of R/C walls subjected to ground motions based on a specified threshold of maximum interstory drift ratio (MIDR). Specifically, the result of each numerical analysis, taken as the output variable of the ML models, was classified as either “B” (Below) or “E” (Exceeding) to indicate whether the MIDR of R/C walls was below or exceeding the specified threshold. This binary categorization was then used to calculate the failure probability points, which are necessary to derive fragility curves per the MSA approach. Data for training and testing the ML models were generated from nonlinear time history analyses of 46 distinct R/C walls subjected to 1000 ground motions. The R/C walls varied in height from four to 40 stories, and the ground motions included far-field, near-field pulse, and near-field no-pulse types. Four well-established ML methods, including random forest (RF), extreme gradient boosting, light gradient boosting machine, and categorical boosting, were considered. The performances of the ML models were compared using a confusion matrix. Based on this comparison, the RF model was selected and incorporated into the proposed procedure. Subsequently, the proposed approach was demonstrated to create the seismic fragility function of a new R/C wall structure. This study highlights the potential of ML applications in optimization problems within the earthquake engineering domain.

Seismic fragility analysis of long-span rigid-frame bridge on mountainous soft clay site

In order to assess the damage condition of bridge components for a large-span rigid bridge in a soft clay site in a mountainous area in China southwest, a finite element model of a large-span rigid bridge is established based on the OpenSees software, and the joint probability density distribution function of the ground motion strength and seismic demand and the marginal distribution function of the ground motion are introduced into the kernel density function. As a basis to get the method of calculating the fragility of the bridge members, and the method is verified for its feasibility, on this basis, the damage condition of the bridge components are analyzed, and finally the damage condition of the bridge system are analyzed by the first-order bounds method and the improved PCM method (IPCM). The results showed that: (1) Kernel density method (KDE) can effectively calculate the damage probability of each component, for example, under ground motions with PGA equal to 0.2 g, the probability of slight damage of the 1# pier is 29%, that of the intermediate consolidation pier (2# pier ~ 4# pier) is about 90%; the probability of slight damage of the 1# bearing is 48%, and that of the 2# bearing is 87%. (2) Reasonable value of the expansion joints can effectively reduce the probability of main beam collision. In this investigation, the value is taken as 0.18 m ~ 0.24 m. (3) The bridge system is more likely to be damaged than a single component in the system, and the damage probability of a single component cannot be used as a criterion for the bridge system in the actual working condition. Comparing the first-order boundary law with the IPCM method, the IPCM method has higher accuracy.

Seismic behavior and design of concrete-filled steel tubular frame-RC core tube structures

In the design of frame-core tube structures, the method for adjusting the frame bearing capacity and stiffness to ensure the structure as a dual system is a critical issue. This study investigates the effects of frame shear distribution ratio, frame bearing capacity, and column pattern on the seismic performance of concrete-filled steel tubular frame to reinforced concrete core tube structures (CFRCTs). Time-history and seismic fragility analyses on eight representative models are performed and the distribution pattern of inter-story drift ratios, structural damage modes, and collapse safety margins are compared. The study results show that CFRCTs possess superior seismic performance (with a collapse margin ratio > 9.3) compared to the structures with reinforced concrete columns and the collapse margin ratio continuously increases from 9.3 to 11.2 with increasing frame stiffness. Enhancing the frame bearing capacity mitigates the frame damage, while improving slightly on structure’s collapse resistance (< 0.1 %). Without adjusting the frame for the second fortification line, damage to the column is not serious and the frame can still effectively withstand the increased shear force transmitted from the core tube during an extremely severe earthquake. The frame experiences more shear force and damage as the frame shear distribution ratio increases; while the core tube damage is effectively alleviated. Due to the redistribution of internal forces, the distribution pattern of inter-story drift ratios under the collapse state is markedly distinct from that under the elastic stage and severe earthquakes. Based on the analysis, design suggestions considering both collapse resistance and economic efficiency are proposed for CFRCTs.

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.

Seismic fragility analysis and reliability evaluation for ancient stone pagoda using distinct element method

This study presents an application of performance-based assessment to establish fragility functions and evaluate the seismic reliability of an ancient stone pagoda in Korea. The pagoda was constructed of stone elements which were stacked over each other in layers without bonding material. To account for the discrete nature of this kind of structural configuration, the distinct element method is used to perform the incremental dynamic analysis to develop fragility functions. Three performance levels are specified on the capacity curve which is established based on non-linear pushover analysis. The randomness in seismic demand generation was considered when exciting the pagoda by a set of 23 input ground motion records, which were scaled into different intensity levels. The seismic response of the pagoda under different ground motions at several peak ground acceleration levels shows that the predominant frequency of the excitation is closely related to the behavior of this kind of structure. Ground motions with lower predominant frequency values induce stronger distortion to the pagoda than the ones with higher predominant frequency. The fragility functions estimated by maximum likelihood method show that earthquakes with peak ground motion of 0.469 g have a 50% probability of causing a collapse on the pagoda in the most conservative assessment. The probability of the pagoda collapsing within 50 years is 1.65% for the most earthquake-vulnerable site among the sites considered in the study.

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.

Investigating the effect of earthquake incident angle on seismic response and fragility analysis of irregular RC buildings with nonparallel systems

Investigating the effect of earthquake incident angle on seismic response and fragility analysis of irregular RC buildings with nonparallel systems

Dynamic reliability and seismic fragility analysis for high concrete-faced rockfill dam slopes subjected to stochastic earthquake and parameter excitation via PDEM

The randomness of material parameters and earthquake excitation greatly impacts the seismic stability of high concrete-faced rockfill dam (CFRD) slopes. However, no research has comprehensively analyzed the impacts of stochastic earthquake excitations, random parameters and their coupled effects on seismic stability of CFRD slopes and selected a multi-indicator evaluation criterion to carry out performance-based safety assessment. This paper develops a novel and comprehensive framework for evaluating the seismic stability of CFRD slopes based on the generalized probability density evolution method (GPDEM) with high efficiency and accuracy. The effects of three kinds of randomness on seismic stability of CFRD slopes were comprehensively compared and analyzed on the basis of multi-indices (safety factor (FS), cumulative slip displacement and cumulative time with FS < 1.0). Firstly, the nonlinear shear strength parameters of 40 high CFRDs were statistically collected to obtain the statistical characteristics of rockfill material strength parameters of actual CFRD projects. Secondly, three kinds of random samples were generated using generalized F-discrepancy (GF-discrepancy) method and Spectral expression-Random function (SERF) method. Then, the GPDEM was introduced to combine with three indices to perform the stochastic analysis and reliability evaluation. Finally, the fragility analysis of the CFRD slope was conducted. The results reveal that FS is more sensitive to the ground motions randomness, while cumulative slip displacement and cumulative time with FS < 1.0 are more sensitive to the material parameters randomness. The seismic safety evaluation of CFRD slopes based on multiple indices with full consideration of coupled randomness effects is necessary.

Seismic performance assessment of a base-isolated hospital building subjected to February 6, 2023, Kahramanmaraş, Türkiye earthquakes (Mw 7.7 Pazarcık and Mw 7.6 Elbistan) and seismic fragility analysis considering different construction stages

The construction period of large structures such as hospitals can be prolonged due to complex construction processes. The behavior of frictional pendulum systems (FPSs) is strongly influenced by the seismic weight of the superstructure and the corresponding coefficient of friction. Therefore, the effects of the isolator behavior, which varies throughout the construction stages (CSs), on structural responses should be evaluated. Existing literature lacks adequate investigation into the behavior of isolated structures subjected to earthquakes during CSs. To address this gap, this paper investigates the structural performance of a base-isolated hospital building equipped with FPSs that experienced residual displacements during the February 6, 2023, Kahramanmaraş, Türkiye earthquakes (Mw 7.7 Pazarcık and Mw 7.6 Elbistan). At the time of the earthquakes, the building was still under construction (65–70 % complete). In addition to the hospital building under consideration, there were three more hospital buildings equipped with FPSs under construction during the 2023 Kahramanmaraş-Türkiye earthquakes in Türkiye. The seismic behavior and residual displacements of the structure during this CS were evaluated and numeric results were validated with real data measured in the field. Moreover, fragility analyses were performed for different CSs of the hospital building to reveal the probabilities of damage for base-isolated buildings exposed to earthquakes at various CSs. For fragility assessment, damage states (slight, moderate, extensive, collapse) were defined and four damage measures were chosen. Thus, the extent to which construction stages affected which types of damage was determined. A total of 1296 nonlinear time-history analysis were conducted to obtain fragility curves for all CSs and damage measures considering lower bound, nominal, and upper bound values of isolators. Selected isolated hospital building showed vulnerability in maximum top floor acceleration (MTFA) and maximum isolator displacement (MID) damage measures, but resilience in maximum roof drift ratio (MRDR) and maximum inter-story drift ratio (MIDR) damage measures. For the design basis earthquake (DBE) level, the probability of reaching the extensive damage state was 5.25 % for the MID, 11.39 % for MTFA, and 0 % for MIDR and MRDR. Similarly, for the maximum considered earthquake (MCE) level, these values were determined as 34.09 % for MID, 43.42 % for MTFA, and 0 % for MIDR and MRDR. The analysis revealed that while the probability of damage to the base isolation system was not related to CSs, residual displacements increased as construction progressed. Collapse thresholds for MIDR and MRDR demand exceptionally severe seismic events. As construction progresses, probabilities of exceeding damage states increase for MIDR and MRDR, indicating heightened vulnerability.

Probabilistic curvature limit states of corroded circular RC bridge columns: Data-driven models and application to lifetime seismic fragility analyses

Reinforcement corrosion has been recognized as an influential factor in the seismic fragility, both demand and capacity models, of aging reinforced concrete (RC) bridges. For capacity models, accurate and applied prediction tools accounting for aging effects are yet to be well established. Current practices usually perform numerical analyses to obtain time-variant capacity models, which are time-consuming particularly when multi-source structural and environmental uncertainties are considered and sometimes even suffer computational non-convergence. To address these issues, this study leverages a rigorously optimized artificial neural network architecture to develop data-driven models for rapid estimates of probabilistic curvature capacity of corroded circular RC bridge columns with flexural failure modes. An extensive database of multi-level curvature limit states (i.e. slight, moderate, severe, and complete) is created through experimentally validated moment–curvature analyses. A new threshold for the moderate limit state is defined based on the strain of core concrete, rather than cover concrete, to account for the potential full erosion of the cover with drastic corrosion. The data-driven probabilistic capacity models are applied to aid the lifetime seismic fragility assessment of a typical highway bridge, where the spectral acceleration at 1.0 s (Sa-10), peak ground velocity (PGV), and Housner intensity (HI) are found consistently, for the first time, as optimal intensity measures for probabilistic demand modeling of RC columns with different extents of aging effects. For the ease of application, the database and code for the data-driven probabilistic capacity models are accessible at https://bit.ly/3uAa8EY .

Seismic testing and fragility analysis considering material strength uncertainty of 1100 kV GFRP composite power transformer bushing

Nowadays glass-fibre reinforced polymer (GFRP) composite insulators are widely employed in electrical equipment in substations. However, there is a scarcity of reports on seismic qualification of transformer bushings that adopt GFRP insulators. Thereby, this case implements shaking table tests on a 1100 kV GFRP composite power transformer bushing. The study analyses the acceleration responses and dynamic amplification effects, as well as the strain responses. The combined stresses at the vulnerable positions are computed to authenticate the seismic performance. Using a simulation model, the seismic fragility of the transformer bushing considering the material strength uncertainty is assessed and discussed. The results indicate that the GFRP composite bushing meets the requirements of the relevant code and its seismic performance is qualified under an artificial ground motion with PGAs of 0.6 g and 0.8 g. For a given factor of safety of 1.67, the bushing can sustain 0.4 g earthquakes with a failure probability near 0 and 0.8 g earthquakes with a failure probability<50 %. Controlling coefficient of variation of the GFRP material strengths is beneficial to decreasing seismic fragility of the transformer bushing within a specific PGA range. Weibull and Normal distributions for fitting the strength distributions of the GFRP materials have different impacts on the seismic fragility of the bushing, which should be given more attention in seismic design.