Machine Learning-Based Seismic Fragility Analysis of Large-Scale Steel Buckling Restrained Brace Frames

Steel frames equipped with buckling restrained braces(BRBs)have been increasingly applied in earthquake-prone areas given their excellent capacity for resisting lateral forces.Therefore,special attention has been paid to the seismic risk assessment(SRA)of such structures,e.g.,seismic fragility analysis.Conventional approaches,e.g.,nonlinear finite element simulation(NFES),are computationally inefficient for SRA analysis particularly for large-scale steel BRB frame structures.In this study,amachine learning(ML)-based seismic fragility analysis framework is established to effectively assess the risk to structures under seismic loading conditions.An optimal artificial neural network model can be trained using calculated damage and intensity measures,a technique which will be used to compute the fragility curves of a steel BRB frame instead of employing NFES.Numerical results show that a highly efficient instantaneous failure probability assessment can be made with the proposed framework for realistic large-scale building structures.

Seismic fragility analysis of clay-pile-pier systems considering the optimization of ground motion intensity measures

The performance of clay-pile-pier system under earthquake shaking was comprehensively examined via three-dimensional finite element analyses,in which the complex stress-strain relationships of a clay and piled pier system were depicted by a hyperbolic-hysteretic and an equivalent elastoplastic model,respectively.One hundred twenty ground motions with varying peak accelerations were considered,along with the variations in bridge superstructure mass and pile flexural rigidity.Comprehensive comparison studies suggested that peak pile-cap acceleration and peak pile-cap velocity are the optimal ground motion intensity measures for seismic responses of the pier and the pile,respectively.Furthermore,based on two optimal ground motion intensity measures and using curvature ductility to quantify different damage states,seismic fragility analyses were performed.The pier generally had no evident damage except when the bridge girder mass was equal to 960 t,which seemed to be comparatively insensitive to the varying pile flexural rigidity.In comparison,the pile was found to be more vulnerable to seismic damage and its failure probabilities tended to clearly reduce with the increment of pile flexural rigidity,while the influence of the bridge girder mass was relatively minor.

Probabilistic fragility analysis:A tool for assessing design rules of RC buildings

In this work, fragility analysis is performed to assess two groups of reinforced concrete structures. The first group of structures is composed of buildings that implement three common design practices; namely, fully infilled, weak ground story and short columns. The three design practices are applied during the design process of a reinforced concrete building. The structures of the second group vary according to the value of the behavioral factors used to define the seismic forces as specified in design procedures. Most seismic design codes belong to the class of prescriptive procedures where if certain constraints are fulfilled, the structure is considered safe. Prescriptive design procedures express the ability of the structure to absorb energy through inelastic deformation using the behavior factor. The basic objective of this work is to assess both groups of structures with reference to the limit-state probability of exceedance. Thus, four limit state fragility curves are developed on the basis of nonlinear static analysis for both groups of structures. Moreover, the 95% confidence intervals of the fragility curves are also calculated, taking into account two types of random variables that influence structural capacity and seismic demand.

Estimation of Aleatory Randomness by S_(a)(T_(1))-Based Intensity Measures in Fragility Analysis of Reinforced Concrete Frame Structures

Based on the multiple stripes analysis method,an investigation of the estimation of aleatory randomness by S_(a)(T_(1))-based intensity measures(IMs)in the fragility analysis is carried out for two typical low-and mediumrise reinforced concrete(RC)frame structures with 4 and 8 stories,respectively.The sensitivity of the aleatory randomness estimated in fragility curves to various S_(a)(T_(1))-based IMs is analyzed at three damage limit states,i.e.,immediate occupancy,life safety,and collapse prevention.In addition,the effect of characterization methods of bidirectional ground motion intensity on the record-to-record variability is investigated.It is found that the damage limit state of the structure has an important influence on the applicability of the ground motion IM.The S_(a)(T_(1))-based IMs,considering the effect of softened period,can maintain lower record-to-record variability in the three limit states,and the S_(a)(T_(1))-based IMs,considering the effect of higher modes,do not show their advantage over S_(a)(T_(1)).Furthermore,the optimal multiplier C and exponentαin the dual-parameter ground motion IM are proposed to obtain a lower record-to-record variability in the fragility analysis of different damage limit state.Finally,the improved dual-parameter ground motion IM is applied in the risk assessment of the 8-story frame structure.

Comparison of seismic fragility analysis methods for arch dams

This study focuses on the seismic fragility analysis of arch dams.The multiple stripe analysis(MSA),cloud analysis(CLA),and incremental dynamic analysis(IDA)methods are compared.A comprehensive dam-reservoir-foundation rock system,which considers the opening of contraction joints,the nonlinearity of dam concrete and foundation rock,the radiation damping effect of semi-unbounded foundation,and the compressibility of reservoir water,is used as a numerical example.225,80,and 15 earthquake records are selected for MSA,CLA,and IDA,respectively.The results show that MSA provides satisfactory fragility analysis,while both CLA and IDA have assumptions that may lead to deviations.Therefore,MSA is the most reliable method among the three methods and is recommended for the fragility analysis of arch dams.It is also shown that the choice of demand level affects the reliability of fragility curves and the effect of the material uncertainty on the fragility of the dam is not significant.

Seismic fragility analysis of bridges by relevance vector machine based demand prediction model

A relevance vector machine(RVM)based demand prediction model is explored for efficient seismic fragility analysis(SFA)of a bridge structure.The proposed RVM model integrates both record-to-record variations of ground motions and uncertainties of parameters characterizing the bridge model.For efficient fragility computation,ground motion intensity is included as an added dimension to the demand prediction model.To incorporate different sources of uncertainty,random realizations of different structural parameters are generated using Latin hypercube sampling technique.Mean fragility,along with its dispersions,is estimated based on the log-normal fragility model for different critical components of a bridge.The effectiveness of the proposed RVM model-based SFA of a bridge structure is elucidated numerically by comparing it with fragility results obtained by the commonly used SFA approaches,while considering the most accurate direct Monte Carlo simulation-based fragility estimates as the benchmark.The proposed RVM model provides a more accurate estimate of fragility than conventional approaches,with significantly less computational effort.In addition,the proposed model provides a measure of uncertainty in fragility estimates by constructing confidence intervals for the fragility curves.

Nonparametric probabilistic seismic demand model and fragility analysis of subway stations using deep learning techniques

A novel and computationally efficient method for developing a nonparametric probabilistic seismic demand model(PSDM)is pro-posed to conduct the fragility analysis of subway stations accurately and efficiently.The probability density evolution method(PDEM)is used to calculate the evolutionary probability density function of demand measure(DM)without resort to any assumptions of the dis-tribution pattern of DM.To reduce the computational cost of a large amount of nonlinear time history analyses(NLTHAs)in the PDEM,the one-dimensional convolutional neural network(1D-CNN)is used as a surrogate model to predict the time history of struc-tural seismic responses in a data-driven fashion.The proposed nonparametric PSDM is adopted to conduct the fragility analysis of a two-story and three-span subway station,and the results are compared with those from two existing parametric PSDMs,i.e.,two-parameter lognormal distribution model and probabilistic neural network(PNN)-based PSDM.The results show that the PDEM-based PSDM has the best performance in describing the probability distribution of seismic responses of underground structures.Differ-ent from the fragility curves,the time-dependent fragility surface of the subway station shows how the exceedance probability of damage state changes over time.It can be used to estimate the escape time and thus the number of casualties in an earthquake,which are impor-tant indexes when conducting the resilience-based seismic evaluation.

Development of seismic fragility curves for low-rise masonry infilled reinforced concrete buildings by a coefficient-based method

This study presents a seismic fragility analysis and ultimate spectral displacement assessment of regular low-rise masonry infilled （MI） reinforced concrete （RC） buildings using a coefficient-based method. The coefficient-based method does not require a complicated finite element analysis; instead, it is a simplifed procedure for assessing the spectral acceleration and displacement of buildings subjected to earthquakes. A regression analysis was first performed to obtain the best-fitting equations for the inter-story drift ratio （IDR） and period shift factor of low-rise MI RC buildings in response to the peak ground acceleration of earthquakes using published results obtained from shaking table tests. Both spectral acceleration- and spectral displacement-based fragility curves under various damage states （in terms of IDR） were then constructed using the coefficient-based method. Finally, the spectral displacements of low-rise MI RC buildings at the ultimate （or near- collapse） state obtained from this paper and the literature were compared. The simulation results indicate that the fragility curves obtained from this study and other previous work correspond well. Furthermore, most of the spectral displacements of low-rise MI RC buildings at the ultimate state from the literature fall within the bounded spectral displacements predicted by the coefficient-based method.

Spectral and fragility evaluations of retrofitted structures through strength reduction and enhanced damping

A retrofit procedure for existing buildings called the ＂weakening and damping technique＂ （WED） is presented in this paper. Weakening of structures can limit the maximum response accelerations during severe ground motions, but leads to an increase in the displacements or inter-story drifts. Added damping by using viscous dampers, on the other hand, reduces the inter-story drifts and has no significant effect on total accelerations, when structures behave inelastically. The weakening and damping technique addresses the two main causes for both structural and nonstructural damage in structures. The weakening retrofit is particularly suitable for structures that have overstressed components and weak brittle components. In this paper, the advantages of the WeD are verified by nonlinear dynamic analysis and simplified spectral approach that has been modified to fit structures with additional damping devices. A hospital structure located in the San Fernando Valley in California is selected as a case study. The results from both analyses show that the retrofit solution is feasible to reduce both structural acceleration and displacement. A sensitivity analysis is also carried out to evaluate the effectiveness of the retrofitting method using different combinations of performance thresholds in accelerations and displacements through fragility analysis.

Performance-based passive control analysis of adjacent structures:Optimization of Maxwell dampers

The performance-based passive control analysis of the Maxwell dampers between one 10-story and one 6-story adjacent RC frames is conducted in this work.Not only the optimal parameters but also the optimal arrangements of the Maxwell dampers are proposed based on the optimal target of making the total exceeding probability of the adjacent structures to be minimal.The applicability of the analytical expressions of the Maxwell damper damping parameters under different seismic performance targets are firstly examined and then the preferable damping parameters of the Maxwell dampers are proposed through the extensive parametric studies.Furthermore,the optimal arranging positions and optimal arranging numbers of the Maxwell dampers between the adjacent buildings are derived based on a large number of seismic fragility analyses,as well.The general arranging laws of the Maxwell dampers between the adjacent buildings are generated based on the discussion of the theoretical method through the simplified plane model.The optimal parameters and optimal arrangement of the Maxwell dampers presented make both the adjacent structures have preferable controlled effects under each seismic performance target which can satisfy the requirements of multi-performance seismic resistance of the modern seismic codes.

Seismic fragility assessment of low-rise stone masonry buildings

Many historic buildings in old urban centers in Eastern Canada are made of stone masonry reputed to be highly vulnerable to seismic loads.Seismic risk assessment of stone masonry buildings is therefore the first step in the risk mitigation process to provide adequate planning for retrofit and preservation of historical urban centers.This paper focuses on development of analytical displacement-based fragility curves reflecting the characteristics of existing stone masonry buildings in Eastern Canada.The old historic center of Quebec City has been selected as a typical study area.The standard fragility analysis combines the inelastic spectral displacement,a structure-dependent earthquake intensity measure,and the building damage state correlated to the induced building displacement.The proposed procedure consists of a three-step development process：（1） mechanics-based capacity model,（2） displacement-based damage model and（3） seismic demand model.The damage estimation for a uniform hazard scenario of 2% in 50 years probability of exceedance indicates that slight to moderate damage is the most probable damage experienced by these stone masonry buildings.Comparison is also made with fragility curves implicit in the seismic risk assessment tools Hazus and ELER.Hazus shows the highest probability of the occurrence of no to slight damage,whereas the highest probability of extensive and complete damage is predicted with ELER.This comparison shows the importance of the development of fragility curves specific to the generic construction characteristics in the study area and emphasizes the need for critical use of regional risk assessment tools and generated results.

Effect of the spectral shape of ground motion records on the collapse fragility assessment of degrading SDOF systems

The main purpose of this paper is to study the collapse capacity of single degree of freedom(SDOF)systems and to produce fragility curves as well as collapse capacity spectra while considering a broad range of structural parameters,including system degradation,the P-Δeffect,ductility capacity and the post-capping stiffness ratio.The modified Ibarra-Krawinkler deterioration model was used to consider hysteretic behavior.A comprehensive study was conducted to extract the collapse capacity spectrum of SDOF systems with a wide range of periods,varying from 0.05 to 4 s,to cover short,intermediate and long periods.Incremental dynamic analysis(IDA)was performed for SDOF systems to identify the condition in which the collapse capacity of the system is determined.The IDAs were performed using different sets of seismic ground motions.The ground motion records were categorized into different sets based on three spectral shape parameters,including the epsilon,SaRatio and N_(p).The collapse fragility curves of SDOF systems with different periods were extracted to illustrate the collapse capacity at different probability levels.The results show that structural degradation and ductility as well as the spectral shape parameters significantly affect the collapse capacity of SDOF systems.On the other hand,the post-capping stiffness ratio and small levels of the P-Δeffect do not remarkably change collapse capacity.Also,the collapse capacity of SDOF systems is more sensitive to the records categorized based on SaRatio and N_(p)than those classified based on epsilon.

Assessing the seismic behavior of steel moment frames equipped by elliptical brace through incremental dynamic analysis(IDA)

Incremental dynamic analysis and nonlinear static pushover analysis are carried out on a performance-based design to determine the seismic demands and capacities of an elliptic braced moment resisting frame(ELBRF).The objective is to assess ductility,overstrength and response modification factors in a modern steel-braced structural system based on incremental dynamic analysis.This integrated system is connected to a beam and column with an appropriate length while providing enough architectural space to allow for an opening without having the common problems associated with architectural spaces in braced systems.Several different classes of buildings are considered on soil type II.Linear dynamic analysis,nonlinear static pushover analysis and incremental nonlinear dynamic analysis related to 12 records from past earthquakes are carried out using OpenSees software.The factors of ductility,overstrength and response modification are calculated for this system.The values of 9.5 and 6.5 are found and suggested only for the response modification factor for ELBRF systems in allowable stress and ultimate limit state methods,respectively.The fragility curves are plotted for the first time for this type of bracing,which contributes to the assessment of building seismic damage.

Seismic performance of non-structural components and contents in buildings: an overview of NZ research

This paper summarizes the research on non-structural elements and building contents being conducted at University of Canterbury in New Zealand. Since the 2010-2011 series of Canterbury earthquakes, in which damage to non-structural components and contents contributed heavily to downtime and overall financial loss, attention to seismic performance and design of non-structural components and contents in buildings has increased exponentially in NZ. This has resulted in an increased allocation of resources to research leading to development of more resilient non-structural systems in buildings that would incur substantially less damage and cause little downtime during earthquakes. In the last few years, NZ researchers have made important developments in understanding and improving the seismic performance of secondary building elements such as partitions, facades, ceilings and contents.

Collapse fragility assessment of steel roof framings with force limiting devices under transient wind loading

Steel structural frame is a popular structural form to cover large-span roof space and under high winds.Either part of the roof enclosure or the entire roof structure can be lifted off a building,particularly for low sloped roofs subject to wind-induced suction force.Collapse of roof could cause severe economic loss and poses safety risk to residents in the building.The buckling of members in a steel roof frame structure,which may lead to progressive collapse,may be dynamic in nature.This paper presents a fragility analysis of the collapse of steel roof frame structures under combined static and transient wind loading.Uncertainties associated with wind load change rate and member imperfections are taken into account in this study.A numerical example based on a Steel Joist Institute(SJI)K series joist was used to demonstrate the use of force limiting devices for collapse risk mitigation.For the presented fragility assessment of steel roof collapse,a Monte Carlo method combined with response surface approach was adopted,which greatly reduces the computation time and makes the Monte Carlo simulation feasible for probabilistic collapse analysis of steel roof frame structures.

Multistage seismic damage constitutive model and parameter calibration of reinforced concrete columns

The road traffic network contains a large number of bridges,and calculating bridge damage using refined models demands significant time and resources.Therefore,developing a rapid evaluation method for the seismic capacity of regular bridges has become a crucial scientific challenge.This study presents an approach in which the ductile column is represented by a single degree-of-freedom model with elastic-plastic constitutive characteristics.Utilizing an uncoupled multivariate power function model and a plastic hinge model,a multidimensional power function model for section hierarchical curvature is constructed.Subsequently,the seismic multistage damage constitutive model(SMSD-CM)of member hierarchy is deduced and calibrated through theoretical methods.This model efficiently derives the trilinear constitutive model of components by inputting several crucial parameters.The SMSD-CM accurately simulates the hysteretic curve and displacement time-history under actual seismic conditions and aligns well with pushover analysis results from tests.The efficiency,ease of operation,and accuracy make the model suitable for rapid evaluation of the seismic capacity of regular bridges within the road traffic network.

Fragility assessment of wood sheathing panels and roof-to-wall connections subjected to wind loading

The performance of the wood-frame buildings after tornadoes has shown that the majority of the wind damage resulted from building envelope failure most typically due to the loss of the roof.To assess the performance and the reliability of low-rise wood-frame residential buildings with a focus on the roofs,fragility analysis can be used to estimate the probability of failure of a roof when constructed with specified nails and sheathing sizes.Thus,this paper examines the fragility of specific types of nails,roof-to-wall(RW)connection details,and sheathing sizes based on the damaged roofs that were previously assessed in the Dunrobin area in Ottawa(Ontario)that was hit with an Enhanced Fujita(EF3)tornado on September 21,2018.The presented fragility analysis considers four scenarios,including different sheathing and nail sizes.Dead loads,wind loads,and resistance on the sheathing panels were compiled and analyzed to determine the failure of the examined roofs.The eight fragility models suggest that the safest roof sheathing(RS)is the 1.22 m×1.22 m sheathing panel with 8 d nails,and the safest RW connections is achieved by using H2.5 hurricane clips.

Integrated framework for seismic fragility assessment of cable-stayed bridges using deep learning neural networks

The increasing intensity of strong earthquakes has a large impact on the seismic safety of bridges worldwide.As the key component in the transportation network,the cable-stayed bridge should cope with the increasing future hazards to improve seismic safety.Seismic fragility analysis can assist the resilience assessment under different levels of seismic intensity.However,such an analysis is computationally intensive,especially when considering various random factors.The present paper implemented the deep learning neural networks that are integrated into the performance-based earthquake engineering framework to predict fragility functions and associated resilience index of cable-stayed bridges under seismic hazards to improve the computational efficiency while having sufficient accuracy.In the proposed framework,the Latin hypercube sampling was improved with additional uniformity to enhance the training process of the neural network.The well-trained neural network was then applied in a probabilistic simulation process to derive different component fragilities of the cable-stayed bridge.The estimated fragility functions were combined with the Monte Carlo simulations to predict system resilience.The proposed integrated framework in this study was demonstrated on an existing single-pylon cable-stayed bridge in China.Results reveal that this integrated framework yields accurate predictions of fragility functions for the cable-stayed bridge and has reasonable accuracy compared with the conventional methods.

Multi-hazard socio-physical resilience assessment of hurricane-induced hazards on coastal communities

Hurricane-induced hazards can result in significant damage to the built environment cascading into major impacts to the households,social institutions,and local economy.Although quantifying physical impacts of hurricane-induced hazards is essential for risk analysis,it is necessary but not sufficient for community resilience planning.While there have been several studies on hurricane risk and recovery assessment at the building-and community-level,few studies have focused on the nexus of coupled physical and social disruptions,particularly when char-acterizing recovery in the face of coastal multi-hazards.Therefore,this study presents an integrated approach to quantify the socio-physical disruption following hurricane-induced multi-hazards(e.g.,wind,storm surge,wave)by considering the physical damage and functionality of the built environment along with the population dynamics over time.Specifically,high-resolution fragility models of buildings,and power and transportation infrastructures capture the combined impacts of hurricane loading on the built environment.Beyond simulat-ing recovery by tracking infrastructure network performance metrics,such as access to essential facilities,this coupled socio-physical approach affords projection of post-hazard population dislocation and temporal evolution of housing and household recovery constrained by the building and infrastructure recovery.The results reveal the relative importance of multi-hazard consideration in the damage and recovery assessment of communities,along with the role of interdependent socio-physical system modeling when evaluating metrics such as housing recovery or the need for emergency shelter.Furthermore,the methodology presented here provides a foundation for resilience-informed decisions for coastal communities.