Seismic Fragility Analysis Research Articles

Efficacy of 3M-PTGL on low-temperature seismic performance of polyurethane elastomeric bearings for bridges

High-capacity casting polyurethane elastomeric (HCPUE) bearing is a new elastomer isolation bearing that features excellent durability, higher vertical capacity, and a simpler production process compared with traditional rubber isolation bearings. However, HCPUE bearing exhibits significant hardening behavior at low temperatures. To expand the application of HCPUE bearings in cold regional structures, this study developed an improved low-temperature resistant 3M-HCPUE bearing by incorporating 3-methyl tetrahydrofuran copolyether glycol (3M-PTGL) in the elastomer formulation. The low-temperature performance improvement of the 3M-HCPUE specimen was verified through characterization and mechanical property tests using six different compounding formulas. HCPUE materials with 15% and 25% 3M-PTGL were selected to prepare improved 3M-HCPUE bearings. The shear hysteretic behavior and ultimate deformation performance of the bearings were tested at different temperatures. Seismic fragility analysis of a three-span box girder bridge with 3M-HCPUE bearings was conducted using different isolation periods and ambient temperatures. The 3M-PTGLimproved 3M-HCPUE bearing exhibited excellent low-temperature performance and effectively alleviated the hardening behavior of the HCPUE bearing at low temperatures. The change rate in the equivalent stiffness for the 3M-HCPUE bearing with 25% 3M-PTGL was °C reduced from 106% to 44% at −20 °C compared with that at 23 °C. The equivalent damping ratio slightly decreased from 25.2% to 19.6%. The improved 3M-HCPUE bearings effectively reduced the failure probability of the pier at low temperatures, but increases the probability of bearing failure.

Efficient seismic fragility analysis method utilizing ground motion clustering and probabilistic machine learning

Machine learning (ML) techniques have been recently adopted in engineering practice to define the relationship between seismic intensity measure (IM) and structural damage measure (DM) based on a limited set of numerical simulations. However, they only offer deterministic prediction, which failing to reflect the aleatoric uncertainty related to input variables (e.g. seismic excitation and structural properties) and the epistemic uncertainty associated with modeling. This paper proposes a probabilistic ML method combined with ground motion clustering for seismic fragility analysis of structures. In the probabilistic ML method, by the natural gradient boosting (NGBoost), the conditional probability distribution can be evaluated for each structural response instead of producing point estimation. In addition, ground motion clustering is based on the time series K-means, which can capture the hidden features and select the representative subset of ground motions. The proposed framework was implemented for seismic fragility analysis of a typical 3-span, 6-storey reinforced concrete (RC) frame system. Analysis results indicated that the point estimation accuracy of the NGBoost was comparable to that based on excellent deterministic ML techniques, e.g. artificial neural network (ANN), random forest (RF), extreme gradient boosting (XGBoost). Moreover, the probabilistic prediction can efficiently provide the conditional probability of exceeding a damaged state in the structure given an IM level, eliminating the need for additional input of uncertainties from structural properties in traditional ML methods. Ultimately, the cluster-based ground motion selection reduced the model uncertainty and improves the prediction accuracy of the probabilistic ML model.

A Quantitative Evaluation Model for the Seismic Resilience of Water Supply Systems Based on Fragility Analysis

A quantitative evaluation model is proposed to assess the seismic resilience of water supply systems. The water supply system is divided into three parts: water sources, aboveground infrastructures, and underground pipeline network, and importance factors for the different parts are quantified. Resilience demand is expressed as the desirable functionality loss and the recovery time of the water supply system after an earthquake. First, seismic fragility models are established for the different components of the water supply system. A water quality index is utilized to represent the impact of earthquakes on the water sources, the seismic performances of aboveground infrastructures are represented by fragility curves, and the repair rate in terms of number of repairs per kilometer is adopted for the pipeline network. Then, the post-earthquake functionality of the water supply system is quantified based on seismic fragility analysis. Changes in the water quality index are used to indicate the functionality losses related to water sources, the functionality losses of aboveground infrastructures are represented by the economic losses derived from component fragility curves, and post-earthquake functionality losses in the underground pipeline network are quantified by hydraulic simulations. The functionalities of the three parts are calculated separately, and then the overall system functionalities are obtained as the sum of the weighted functionalities of the three parts. Finally, a repair strategy is developed and the recovery time is calculated considering the system damage scenarios, system functionality analyses, and resource reserves. The proposed resilience assessment model considers all components of the water supply system, and the results are reliable when the basic information is complete and accurate.

A hybrid approach for seismic fragility analysis of reinforced concrete structural walls independent of failure pattern

Establishing seismic fragility relationships of reinforced concrete (RC) structural walls plays an important role in the seismic risk and resilience assessment of RC structures. However, RC structural walls have different failure patterns under earthquake excitations, and different analytical models are commonly required to simulate the seismic responses of RC structural walls with different failure patterns. This brings to the difficulty of seismic fragility analysis for a wide variety of RC structural walls due to the failure-pattern-dependence. To overcome this shortcoming, a hybrid approach was developed in this study to establish the seismic fragility relationships of RC structural walls independent of failure patterns by combing experimental data and numerical simulation. The experimental data was collected from past quasi-static tests of RC structural walls having different failure patterns. The Bouc-Wen-Baber Noori (BWBN) model was used to describe the complicated hysteretic behaviors of RC structural walls under different failure patterns, whose model parameters were calibrated using the collected experimental data. Based on the calibrated BWBN models, an equivalent single-degree-of-freedom (ESDOF) system was employed to predict the seismic demand of RC structural walls. Furthermore, the predicted seismic demand of RC structural walls was compared with the seismic capacity that was both identified from the collected experimental data, developing the seismic fragility relationships of RC structural walls independent of failure pattern. For facilitating the application in practice, artificial neural network (ANN) models are finally developed to predict model parameters of the cumulative lognormal distribution for generating the seismic fragility relationships of RC structural walls rapidly. The investigation indicated that the proposed approach provides a promising way to perform the seismic fragility analysis for a wide variety of RC structural walls.

Nonparametric Representation for Seismic Fragility Assessment of Earth Dams with Spatially Variable Soil Properties

Seismic fragility is the conditional failure probability of reaching certain performance states under various intensities of seismic load, which is a significant part of the seismic risk and resilience assessment of structures and infrastructure systems. However, conventional seismic fragility curves are constructed based on the assumption of specific distribution models (i.e., a lognormal distribution), which might lead to a lack of fit and cannot reflect the true structures of data. Therefore, the validity of these assumptions remains questionable. In this study, a nonparametric approach that was based on dynamic reliability theory was employed to calculate the seismic failure probabilities under various intensities of seismic loads and seismic fragility curves were constructed for an earth dam, in which the spatial variability in the soil properties of the earth dam was properly considered by random field (RF) models. In addition, the results from the earth dams with homogeneous, random variables (RV), and RF models were compared to illustrate the effect of spatially variable soil properties on the seismic fragility of earth dams. The numerical results indicated that more comprehensive, reliable, and safe results could be acquired during the seismic fragility analysis of earth dams when the spatially variable dam properties were considered.

Seismic Fragility Analysis of a High-Pier Bridge under Pulse-like Ground Motion, Based on a PCA and K-Means Approach

The objective of this study is to present a novel fragility analysis method that combines principal component analysis (PCA) and the K-means clustering algorithm for a probability assessment of seismic damage in high-pier bridges undergoing pulse-like ground motions. Firstly, the method uses the correlation coefficient and the condition number as judgment indices to eliminate those seismic intensity measures (IMs) with weak correlation and multicollinearity from all 29 of the initial candidate seismic IMs, the optimal combination of IMs that satisfies the requirements for the PCA method is determined. Secondly, the method utilizes PCA to reduce the dimensionality of the optimal combination of IMs to obtain the principal components, after which the K-means algorithm is applied to classify the original group of selected pulse-like ground motions into four classes. Thirdly, a 3D finite element model of the exemplary high-pier bridge is developed via OpenSees, while incremental nonlinear dynamic time-history analyses are conducted to record the maximum cross-section curvatures of high piers under the influence of various categories of ground motions. Finally, based on the analytical procedures used in the increment dynamic analysis (IDA) method, this study develops and compares the fragility curves for the various classes of pulse-like ground motions. The results indicate the necessity of utilizing the PCA and K-means approach for classifying pulse-like ground motions in the seismic fragility analysis of high-pier bridges. This approach also significantly improves the precision and accuracy of damage probability analysis.

Effect of slab stiffness on floor response spectrum and fragility of equipment in nuclear power plant building

The floor response spectrum (FRS) is used to evaluate the seismic demand of equipment installed in nuclear power plants. In the conventional design practice of NPP structure, the FRS is simplified using the lumped-mass stick model (LMSM), assuming the floor slab as a rigid diaphragm. In the present study, to study the variation of seismic response in a floor, the FRSs at different locations were generated by 3-D finite element model, and the response was compared to that of the rigid diaphragm model. The result showed that the FRS significantly varied due to the large opening in a floor, which was not captured by the rigid diaphragm model. Based on the result, seismic fragility analysis was performed for the anchorage of a heat exchanger, to investigate the effect of location-dependent FRS disparity on the high confidence low probability of failure (HCLPF).

Seismic performance assessment of nylon lines for protecting museum collections

While earthquakes pose a threat to both museum buildings and collections, the latter can be especially vulnerable. Seismic damage to museum collections can be minimized by securing objects with nylon lines, a widely used strategy in museums. However, this measure is usually adopted on the basis of the subjective interpretations by museum staff rather than scientific assessments of its efficacy, resulting in a lack of standardization. This paper aims to address this issue by proposing an appropriate assessment method on the basis of seismic risk analysis of museum collections. Specifically, the study first introduces a seismic fragility analysis method for the collection-showcase-museum system, which is a comprehensive method for evaluating the effectiveness of nylon lines in enhancing seismic performance. The seismic performance of the nylon lines can then be assessed through a seismic risk calculation of the museum collection. To demonstrate the effectiveness of the proposed method, a case study is conducted. Via numerical analysis, the study examined the impact of nylon line diameter, quantity, and tying angle on their seismic capacity. Moreover, this approach is used for an existing precious artifact in a Chinese museum to provide a practical reference for other museum collections. The findings of this study highlight the practical and scientific nature of the proposed method, indicating that larger diameter nylon lines significantly improve seismic performance. Additionally, collections secured with four nylon lines are more secure than those secured by fewer lines. The nylon lines with smaller tying angle may increases the probability of seismic damage to collections during strong earthquakes.

Multivariable probabilistic seismic demand models for parametric fragility prediction of isolated bridges portfolios under pulse-like GMs

The wide application of friction isolation bearings has led to a rapid increase in the number of frictional isolated bridges. Therefore, the traditional method of seismic fragility analysis based on nonlinear time-history analysis (NLTHA) may not suitable for bridge portfolios. For this purpose, this study developed a multivariable probabilistic seismic demand model (MV-PSDM) for friction isolation bearings conditioned on the earthquake parameters (peak pulse velocity, pulse period), bearing parameters (effective radius) and pier parameters (bending stiffness, pier numbers, pier height), in which a novel formula is adopted to calculate the seismic demand and the dispersion is also estimated. This MV-PSDM can be applied to investigate the influence of various parameters (earthquake parameters, friction bearing parameters, pier parameters) on the seismic demand, sensitivity and the vulnerable range of the bearing. Finally, an efficient parametric fragility prediction method for friction isolation bearing is proposed based on the MV-PSDM, and the flow chart is also provided. In this method, only earthquake parameters, bearing parameters and pier parameters are required to obtain the seismic fragility of friction isolation bearings, which avoids the FE modeling and NLTHA.

Fuzzy logic approach for seismic fragility analysis of RC frames with applications to earthquake-induced damage and construction quality

This study presents a fuzzy logic model which is able to consider various uncertainties for predicting the seismic fragility curves of the structure. The fuzzy models are generated based on a database (generated by the Latin Hypercube Sampling technique) which includes structure’s modeling parameters as input variables. Also, the output section of the database comprises the structure’s fragility parameters at three different limit states. Several classification decision tree-based Mamdani fuzzy logic models are constructed by converting the above-mentioned numerical database to qualitative labels. The appropriate number of membership functions and also pruning levels of the related decision tree are detected by automatically introducing the classification tree-based rules to the fuzzy model and performing about two million fuzzy analyses while evaluating the associated error versus the number of rules. On the basis of 200 structural models, a set of interpretable Mamdani fuzzy models are generated to predict the fragility curve parameters at different seismic performance levels. These fuzzy models can effortlessly perform further assessments such as sensitivity analysis and seismic performance assessment while considering the impact of earthquake damage and construction quality.

Time-dependent multi-hazard seismic vulnerability and risk assessment of deteriorating reinforced concrete bridges considering climate change

Climate change inevitably affects the deterioration of reinforced concrete (RC) bridges exposed to harsh chloride environments. This deterioration reduces the resistance of RC bridges to natural hazards, including earthquakes and floods. This paper proposes an improved framework for time-dependent multi-hazard seismic vulnerability and risk assessment of a deteriorating RC bridge considering climate change. The framework addresses (a) the corrosion initiation and propagation processes affected by climate change, (b) time-dependent corrosion rate, (c) seismic fragility analysis of a deteriorating RC bridge using a three-dimensional finite-element model, and (d) the integration of deterioration due to corrosion, climate change, and earthquake and flood-induced scour hazards into time-dependent seismic vulnerability and risk assessment. This paper provides extensive comparisons to demonstrate the effects of corrosion propagation based on uniform and pitting corrosion models, climate change, intensity of ground motion of earthquakes, and flood-induced scour on seismic vulnerability and risk. For illustration, an existing multi-span RC girder bridge is investigated. The results show that pitting corrosion under climate change with flood-induced scour significantly increases the seismic vulnerability and risk of deteriorating RC bridges.

Seismic fragility assessment of storage tanks considering different sources of uncertainty

Liquid storage tanks are critical facilities in petroleum depots that must remain intact and functional following an earthquake. The seismic fragility function is a useful tool for quantifying structural vulnerability. This study accordingly explored the effects of different uncertainties on the seismic fragility of a case study floating-roof storage tank by applying an appropriate approach to seismic fragility analysis. First, an orthogonal sensitivity analysis was performed using a finite element model to determine the random model variables most affecting the seismic responses of the storage tank. Considering the different sources of uncertainty, seismic fragility was subsequently evaluated by combining a cloud analysis with model sampling. Then, the seismic fragility curves of the storage tank system were developed by studying the correlations among multiple failure modes. The results indicate that the computational requirements of the present method were significantly less demanding than those of direct Monte Carlo simulation. Geometric uncertainty was found to exert the greatest impact on the seismic responses. The maximum difference among the fragility function parameters for different sources of uncertainty was 28.9%. The damage assessment of the tank system was shown to be more reasonable when considering the correlations among multiple failure modes. This analysis technique can accordingly provide practical guidance for the seismic design of vertical floating-roof storage tanks.

Seismic fragility analysis of nuclear containment structure under chloride-induced reinforcing steel corrosion conditions

Chloride-induced corrosion of reinforcing steel is one of the critical degradation factors influence the life cycle performance of the containment structure. Therefore, it is of great significance to study the safety performance of containment structure under chloride-induced reinforcing steel corrosion condition. This study presents fragility evaluation of the containment structure under chloride-induced reinforcing steel corrosion condition. Nonlinear time history analysis of the containment structure under different reinforcing steel corrosion conditions is carried out considering various uncertainties including uncertainty in material strength, record to record uncertainty and uncertainty in corrosion parameters. Roof drift under different ground motion intensity levels and seismic fragility of the containment structure corresponding to different performance level with typical service life are analyzed. Results reveal that with the increase of the service life of the containment structure, the increasing rate for roof drift of the containment structure decreases, while the variability of roof drift of the containment structure changes slightly. Service life of the containment structure has different impacts on the fragility of the containment structure corresponding to different performance levels. With the increase of service life, the increasing rate for failure probability of containment structure increases.

Seismic fragility analysis of bridge-isolator-foundation-soil systems in subfreezing temperatures

Several cold regions around the world are in seismic active zones. Seasonal freezing can significantly affect the seismic performance of complex bridge-isolator-foundation-soil systems by inducing brittle failure and premature collapse due to a combination of load reversals and cold temperature behavior of the bridge material. In cold conditions, constitutive material of bridge components, namely, concrete, steel reinforcement, rubber, and supporting soil undergo substantial stiffening which afflicts the ductility capacity of bridges. This study investigates the seismic performance of four bridge cases, namely, isolated bridge supported by pile groups, monolithic bridge supported by pile groups, isolated fixed-base bridge, and monolithic fixed-base bridge at room and subfreezing temperatures to unmask the effectiveness of using Fiber Reinforced Elastomeric Isolator (FREI) as a retrofit measure and to evaluate the performance of bridges at temperatures ranging from room (i.e. 20 °C) to −37 °C. To this end, an analysis matrix is developed based on the climatic condition of the bridge site along with the code provisions. A seismic fragility analysis is carried out in the context of Incremental Dynamic Analysis (IDA) using a set of synthetic ground motion records for longitudinal and transverse directions of the bridge, independently. It is shown that while the seismic isolation system can effectively mitigate the probability of damage to the bridge at room temperatures, isolated bridges demonstrated an acceptable behavior at subfreezing temperatures.

Probabilistic Seismic Sensitivity Analyses of High-Speed Railway Extradosed Cable-Stayed Bridges

It is known that the extradosed cable-stayed bridge, a hybrid bridge, possesses the virtues of both classic cable-stayed bridges and girder bridges in mechanical behaviors. In this paper, the sensitivity of seismic fragility demand parameters (SFDP) of a high-speed railway extradosed cable-stayed bridge is studied systematically along with the consideration of structural parameter uncertainty. Based on the probability distribution and correlation of random parameters, the Latin hypercube sampling method is adopted herein. The dynamic 3D finite element model of the employed bridge is established by using powerful and attractive OpenSEES nonlinear software. A nonlinear incremental dynamic analysis is performed to consider the randomness of structural parameters using sampling analysis. Some important conclusions are drawn indicating that the structural design parameter uncertainty predominantly has influence on the SFDP for fragility analysis of bridge structures. The design parameters of extradosed cable-stayed bridges are categorized and identified as primary, secondary and insensitive parameters. The high sensitivity parameters of extradosed cable-stayed bridges for fragility analysis include friction coefficient of bearing, concrete bulk density, damping ratio, peak compressive strength of confined concrete, component size and peak strain of confined concrete. Additionally, the strength and strain of unconfined concrete cannot be ignored. Furthermore, the uncertainty of structural design parameters fails to be responsible for the cable force responses due to larger girder stiffness. The structural design parameter uncertainty has a significant influence on the responses of extradosed cable-stayed bridges for seismic fragility analysis.

Seismic performance analysis and evaluation of tall structures using grille‐type steel plate composite shear walls

SummaryGrille‐type steel plate composite (GSPC) shear wall is an innovative wall system consisting of concrete cores, steel faceplates, steel tie plates, and steel channels with more advantages than conventional reinforced concrete (RC) walls, including better ductility, higher bearing capacity, and easy‐modular characteristics. This paper mainly discusses the seismic performance and damage resistance of GSPC walls to the entire structure from the aspect of the structural level. Three nonlinear numerical models of high‐rise structures with different structural heights and types were established by PERFORM‐3D software to study the influence of GSPC walls on the change in structural internal forces and deformations compared with RC walls. One of these structures was selected to conduct the seismic fragility analysis based on the incremental dynamic analysis and to assess the structure's seismic performance with GSPC walls. Finally, the seismic damage prediction method was used to evaluate the damage levels of the GSPC wall structure. Results indicate that the structures with GSPC walls suffer more significant seismic forces than those with RC walls, although they experience lesser structural deformations. Moreover, GSPC walls can effectively improve the structure's collapse and seismic damage resistance.

Seismic fragility analysis of suspended cable trays in civil buildings

The cable tray is a kind of non-structural component used to distribute the electric cable, which plays a vital role in maintaining the function of the building. Post-earthquake investigations proved that the collapse of the cable tray led to the loss of human life and business continuity. This study aims to understand the seismic fragility of typical suspended cable trays in civil buildings through full-scale shaking table tests and numerical simulation. Based on the shaking table test results, the damage states of the cable tray are defined. The finite element model for cable tray is established and verified by test results. The seismic fragility analysis of the cable tray is carried out by the incremental dynamic analysis method. The peak floor acceleration and the spectral acceleration are taken as intensity measures of seismic motions. The calculation results show that the peak floor acceleration is more suitable to be an intensity measure for the seismic fragility analysis of the cable tray. Seismic fragility curves of two typical types of cable trays are generated.

地震動予測変数別のリスク解析による地震リスク評価の精度向上の試み

Seismic risk analysis consists of seismic hazard analysis and fragility analysis using single index of ground motion intensity. Though the intensity of the index is identical, the responses of buildings may be different due to the difference in earthquake characteristics. Using the single index brings the large error in risk analysis, though it is more convenient than using plural indices or conducting multi-event analysis. This paper proposed the risk analysis method using the ground motion prediction parameter dependent seismic hazard analysis and fragility analysis. The efficiency of the method was proved by the trial application using model site and buildings.

Progressive failure and seismic fragility analysis for transmission towers considering buckling effect

Transmission towers are essential components supporting the operation of the power grid. Accurately predicting their ultimate bearing capacity and progressive failure improve the performance design of electrical power systems. This paper proposes a progressive failure method for transmission towers considering the buckling and post-buckling behaviors of steel angles. To simulate the nonlinear hysteretic behaviors of steel angles, a phenomenological hysteretic model (PHM) is introduced and embed into the ABAQUS software by calling a user-defined subroutine VUMAT. The accuracy and reliability of the PHM are verified through a full-scale test of a transmission tower. The comparison results demonstrate that the PHM can accurately reproduce the displacement and strain responses of the transmission tower and the ultimate bearing capacity, with a maximum error of <15%. The buckling failure of leg members is the main factor for the collapse of the transmission tower. The study also investigates the progressive failure process of the transmission tower under strong earthquakes and estimates the collapse fragility and seismic losses. The results reveal that early failures of steel angles may alter the local force transmission path of the tower and eventually lead to its collapse. This research provides suggestions for the structural optimization and design decision-making of transmission towers.

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

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