Fragility Curves Research Articles

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.

Development of an Optimization-Based Budget Allocation Model for Seismic Strengthening Based on Seismic Risk Assessment

This study presents a technology used for the prediction of economic losses to facilities in a given area during an earthquake, thereby enabling the efficient application of performance-based maintenance and seismic strengthening. We also propose an algorithm for the establishment of a reinforcement plan that minimizes earthquake-induced economic losses within a constrained budget. The algorithm incorporates fragility functions from prior research and utilizes an optimization technique for budget allocation, leveraging the target damage ratio concept and constrained optimization. Based on the fragility curve, the probability of occurrence for each damage state for a specific PGA value and the damage rate for each damage state are calculated. From these values, the expected damage ratio (EDR) is estimated. An optimization-based budget allocation algorithm is developed to find the elements that would result in the lowest damage rate for a limited cost. To validate the applicability of the model, we created a hypothetical city with a 30 km × 30 km area containing bridges, embankments, and buildings. The estimated pre- and post-reinforcement damage was assessed in two earthquake scenarios, allowing us to test the effectiveness of the optimization-based budget allocation model in reducing damage. These results suggest that the proposed model offers a viable strategy for efficient seismic strengthening within budgetary constraints.

Development of Fragility Curves and Assessment of Mass Irregular Structures with Fixed Base and Base Isolated Under Multiple Earthquakes

ABSTRACT Structures are usually built to withstand the mainshock, aftershocks offer extra difficulties. Aftershocks frequently occur following an earthquake result in multiple earthquakes, therefore they are not isolated events. Due to damage advancement, and stiffness and strength deterioration, a damaged structure might collapse under a multiple earthquakes. Based to a probabilistic perspective, the current study investigates the effect of multiple earthquakes on the likelihood of buildings to collapse. This study’s primary objective is to determine how multiple earthquakes affect fixed- and base-isolated structures. In this context, recorded 14 single and 7 multiple earthquakes with various properties were used to examine and assess three-dimensional reinforced concreteframes with four-storey, having fixed base and isolated base. Dynamic analysis, of the three-dimensional structures are carried out in SAP2000. Fragility curves for fixed base and base isolated structures were produced using the incremental dynamic analysis approach. To find the effect of mass irregularity due to single and multiple earthquakes, mass irregularity is placed at every floor level in each structure. The results are compared in terms of floor displacements, floor accelerations, storey drift, base shear, residual displacement, and probability of collapse for fixed base and base isolated structures. The findings highlight the importance of analyzing the structures subjected to multiple earthquakes. The probability of collapse is reduced for mass irregular structures with base isolation in comparison with fixed base structures, when subjected to multiple earthquakes. The designer’s should select base isolation over the fixed base system when the building’s location may suffer multiple earthquakes more frequently.

Impact of local site conditions on seismic performance of free‐spanning submarine pipelines: Underwater shaking table tests and numerical simulations

AbstractLocal site conditions may pose a significant influence on the seismic responses of submarine pipelines by altering both the offshore motion propagation and soil‐structure interaction (SSI). This paper aims to provide an in‐depth understanding of the influence regularity of local site conditions on the seismic performance of free‐spanning submarine pipelines (FSSPs). For this purpose, a suite of underwater shaking table tests were performed to investigate the seismic responses of FSSP subjected to the offshore spatial motions at three site categories. Response comparison factor () is defined to quantify the structural response discrepancies caused by the seismic inputs at different sites. The test results indicate that responses of the studied model FSSP gradually increase as spatial offshore motions at softer soil sites are employed as inputs; and the values of vary with a maximum magnitude of up to 40%–60% for different response indices when the site soil changes from fine sand to clay. Subsequently, the corresponding numerical simulations are carried out to reproduce the seismic responses of the test model. The experimental and numerical results meet a good agreement, indicating that the developed numerical modeling method can accurately predict the seismic responses of FSSPs. Following this verified modeling method and using the p‐y approach to address the SSI effect, fragility surfaces of the studied FSSP are derived in terms of PGA and site parameter (shear‐wave velocity in the top 30 m of the soil profile) via probabilistic seismic demand analyses. The impact of local site conditions on the seismic performance of the FSSP is quantitatively examined by comparing the fragility curves corresponding to various . Furthermore, a fast seismic damage assessment method is proposed for efficiently evaluating the performance of FSSPs buried in various offshore soil conditions. This approach proves beneficial for designers and decision‐makers, enabling accurate estimation of seismic damage and facilitating the implementation of post‐earthquake maintenance measures for FSSPs.

Regional Seismic Damage Prediction of Buildings Based on Bayesian Network and Community Information Database: A Case Study in Shanghai

ABSTRACT The development of the Community Information Database (CID) provides an opportunity to enhance the accuracy of predicting regional seismic damage. The CID includes fundamental attributes of buildings and daily operation information such as maintenance record, loading variation, and structural defect inspection. However, existing models cannot leverage the daily operational information of the CID to calibrate the real-time seismic performance of regional buildings. In this study, a novel Bayesian network (BN) model is proposed to assess the regional seismic damage of buildings based on information provided by the CID. Buildings in an area in Shanghai, China, are selected to investigate the applicability and accuracy of the proposed model. The investigation indicated that the proposed model can synthesize seismic fragility curves and matrices for various building types and calibrate the prediction based on daily operational information such as structural defect, structural alteration, and property management. If the CID has missing building attributes, the proposed model can also utilize an embedded subnetwork to supply the database. Therefore, the proposed model integrates more comprehensive information than the traditional methods to enhance the accuracy of predicting the regional seismic damage.

Vulnerability of Physical Infrastructure Network Components to Damage from the 2015 Illapel Tsunami, Coquimbo, Chile

AbstractThis study assesses physical infrastructure vulnerability for infrastructure network components exposed during the 2015 Illapel tsunami in Coquimbo, Chile. We analyse road and utility pole vulnerability to damage, based on interpolated and simulated tsunami hazard intensity (flow depth, flow velocity, hydrodynamic force and momentum flux) and network component characteristics. A Random Forest Model and Spearman’s Rank correlation test are applied to analyse variable importance and monotonic relationships, with respect to damage, between tsunami hazards and network component attributes. These models and tests reveal that flow depth correlates higher with damage, relative to flow velocity, hydrodynamic force and momentum flux. Scour (for roads and utility poles) and debris strikes (for utility poles) are strongly correlated with damage. A cumulative link model methodology is used to fit fragility curves. These fragility curves reveal that, in response to flow depth, Coquimbo roads have higher vulnerability than those analysed in previous tsunami event studies, while utility poles demonstrate lower vulnerability than with previous studies. Although we identify tsunami flow depth as the most important hydrodynamic hazard intensity metric, for causing road and utility pole damage, multiple characteristics correlate with damage and should also be considered when classifying infrastructure damage levels.