Fragility Analysis Of Structures Research Articles

A direct analytical derivation of the multi-dimensional fragility spaces of structures under nonstationary mainshock-multi-aftershock sequences

Performance-based earthquake engineering (PBEE) is a popular direction in the earthquake community, and at this stage, risk-based PBEE has become mainstream. In the risk-based probabilistic framework, seismic fragility analysis constitutes the most important link, and corresponding research on the mainshock–aftershock sequence has received widespread attention in recent years. Since a mainshock is often accompanied by multiple aftershocks and there is great uncertainty in the vibration characteristics of aftershocks, a seismic fragility analysis of structures under a stochastic mainshock-multi-aftershock sequence is meaningful and necessary. The corresponding questions, such as how to derive the multi-dimensional analytical fragility form under a stochastic mainshock-multi-aftershock sequence and how to correlate multiple intensity measures with multiple demand parameters, still require further investigation. In this paper, a direct analytical derivation of the multi-dimensional seismic fragility spaces of structures under nonstationary stochastic mainshock-multi-aftershock sequences is introduced. The methodology framework, implementation steps, and application examples are also provided in detail. Moreover, two scenarios, the one-mainshock-one-aftershock and one-mainshock-two-aftershocks, are considered, and the obtained multi-dimensional analytical fragility spaces for both scenarios are validated. In general, the matching accuracy of the fragility results for both scenarios is proven to be high, and the direct analytical derivation of the multi-dimensional fragility spaces is validated to be ideally consistent, which further provides a reference for multi-dimensional risk analysis under nonstationary stochastic mainshock-multi-aftershock sequences in future work.

Seismic fragility analysis of structures via an Adaptive Gaussian Mixture Model and its application to resilience assessment

Seismic fragility analysis and seismic resilience assessment are pivotal tasks within the performance-based earthquake engineering framework. The former aims to quantitatively assess the probability of engineering structures sustaining various degrees of damage when subjected to earthquakes of varying intensity levels. In contrast to many traditional seismic fragility methods, this paper introduces a precise and versatile approach grounded in reliability analysis, with the goal of eliminating the restrictive lognormal assumption. Initially, the proposed method involves conducting seismic reliability analysis of structures using the Fractional Exponential Moments-based Maximum Entropy Method (FEM-MEM). This approach efficiently yields failure probabilities. Subsequently, an Adaptive Gaussian Mixture Model (AGMM) is presented for fitting a set of failure probability points, producing comprehensive and continuous seismic fragility curves. Notably, AGMM offers remarkable flexibility in modeling fragility curves, ensuring precise estimations for subsequent resilience assessments. Building upon the results of the fragility analysis, the paper proceeds to assess the seismic resilience of structures. The proposed method’s feasibility and effectiveness are validated through two illustrative numerical examples. The results demonstrate that, in comparison to the conventional lognormal assumption, the proposed method offers superior accuracy and broader applicability for conducting seismic fragility analyses of structures.

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.

Attention mechanism based neural networks for structural post-earthquake damage state prediction and rapid fragility analysis

This paper is devoted to the research on applying the deep learning method to nonlinear structural post-disaster damage state assessment. Transformer and Informer networks with a classification network customized according to the adopted damage assessment framework are proposed for data-driven structural seismic response and damage state modeling. Compared with recurrent neural network and convolution neural network, the networks in this paper can predict the elastoplastic response of nonlinear structures more effectively. In addition, this paper presents a method for rapid structural fragility analysis, which can consider multiple damage assessment indexes at the same time. The performance of the proposed approach is successfully demonstrated through two examples, including a numerical analysis validation and a field sensing validation. The results show that the Transformer network used in this paper is a reliable and computationally efficient approach for predicting the structural seismic response and damage category, and appears great potential in structural health monitoring and rapid assessment on post-disaster structural resilience.

Potential bias of conventional structural seismic fragility for bridge structures under pulse-like ground motions: Bias evaluation and strategy improvement

Previous studies have highlighted the serious biases that may happen in probabilistic structural fragility analysis (PSFA) due to the ignorance of the effect of pulse period under pulse-like excitations. However, the distribution characteristics of the bias associated with structure-pulse damage parameters are less quantitatively investigated. This paper, therefore, focuses on the influence mechanism of the structure-pulse coupled period (defined by pulse period normalized by structural fundamental period) in PSFA and quantitatively describes the bias that occurred in different damage states. Meanwhile, the PSFA of ductile columns conditioned on two different groups of intensity measures are systematically presented and compared based on Artificial Neural Network prediction. Results reveal that the bias of PSFA, with the variation of the normalized period, can be divided into three different stages, including two ranges of normalized period overestimating structural damage probability and one interval indicating the underestimated condition. Additionally, significant biases (larger than 50%) have been frequently observed in the PSFA of structures with different fundamental periods under various damage states. Moreover, the formulas for quickly obtaining the interval that dangerously underestimates structural damage probability and bias modification factor are correspondingly proposed, which can provide a quite useful method and tool for fragility, risk, and resilience analysis of bridge structures in near-field regions.

Optimal intensity measures for probabilistic seismic demand models of steel moment frames

Selecting an optimal ground motion intensity measure (IM) is a vital step in the earthquake fragility analysis of building structures using probabilistic seismic demand models (PSDMs). This study proposes optimal IMs among 20 considered for seismic fragility analysis of structural steel moment frames in PSDMs. Five steel frames of different heights were selected to propose optimal IMs for steel frames between 2 and 20 stories. The IMs were evaluated using two engineering demand parameters (maximum interstory and roof drifts). Two characteristics of ground motions were investigated (pulse and non-pulse). The results revealed that velocity-related parameters (Housner intensity (HI) and peak ground velocity (PGV)) and spectral pseudo-acceleration at the first natural period (PSa(T1)) tend to be optimal IMs for steel moment frames. For maximum interstory drift, HI is suggested as the optimal IM for steel frames of 2–12 stories for both types of ground motions, while PGV is suggested for steel frames from 12 to 20 stories. Under maximum roof drift, PSa(T1) is the optimal IM for steel frames of all investigated stories subjected to either ground motion type. Peak ground acceleration, which is widely used as a ground motion IM, was observed to be unsuitable for all steel moment frames investigated in this study.

Efficient seismic fragility analysis of structures from dynamic reliability perspective

Seismic fragility analysis of structures quantitatively describes the relationship between the failure probabilities of structures and ground motion Intensity Measures (IMs). Generally, two steps are involved: (1). calculating the failure probabilities of the structure under consideration at a set of IM levels; (2). regressing the IM levels and the corresponding failure probabilities to obtain a bunch of fragility curves. In this paper, a new method is proposed for seismic fragility analysis of structures from a dynamic reliability perspective, where efficiency and accuracy are emphasized. First, the dynamic reliability of structures under fully non-stationary ground motions is presented, where the Fractional Exponential Moments-based Maximum Entropy Method (FEM-MEM) is applied to derive the extreme value distribution with high efficiency. In this method, only a total of 89 samples of fully non-stationary ground motions generated by the spectral representation method and consistent with the design response spectrum that are sufficient in the FEM-MEM for efficient dynamic reliability computations are required. Then, a four-parameter distribution model, which exhibits high flexibility, is used to recover the fragility curves. A two-step strategy is developed for parameter estimation based on four failure probabilities at four different IM levels. In addition, a strategy for selecting a small number of IM levels for all damage states is also suggested, which improves the computational efficiency. Two numerical examples, including a seven-story nonlinear shear frame structure and a five-story three-span frame structure designed according to Chinese codes, are investigated to verify the effectiveness of the proposed method, where the results obtained from the traditional lognormal distribution are also compared.

Seismic fragility analysis of buckling-restrained brace-strengthened reinforced concrete frames using a performance-based plastic design method

An easily-operated performance-based plastic design (PBPD) method for buckling-restrained braced (BRB) reinforced concrete (RC) moment frames is adopted in this research to strengthen existing moment frames by BRBs. The appropriate range of the story base shear ratio p (i.e., the ratio of the base shear resisted by the BRBs to that of the total system) is suggested through a seismic fragility analysis. With an earthquake ground motion set of thirty far-field records, the seismic fragility analysis and risk assessment of an 8-story RC moment frame structure and its strengthened structures with BRBs are reported in this article, in which the fragility curves for different limit states and the corresponding annual exceedance probability are calculated. The applicability of 16 ground motion intensity measures (IMs) in the fragility analysis of the structure before and after strengthening under three damage limit states is further reviewed. As indicated by the fragility analyses, a higher seismic resistance capacity can be obtained for the strengthened structure when the ratio p varies between 0.5 and 0.8. The seismic performance of the structures strengthened using the PBPD method can increase steadily till the advent of the preset target ultimate drift limit, after which the improvement efficiency decreases. The IM Sa,gm(Ti) that considers both effects of softened period and higher mode has a better performance in each limit state of the structure both before and after strengthening.

Cloud Capacity Spectrum Method: Accounting for record-to-record variability in fragility analysis using nonlinear static procedures

This paper investigates a number of computational issues related to the use of nonlinear static procedures in fragility analysis of structures. Such approaches can be used to complement nonlinear dynamic procedures, reducing the computational and modelling effort. Specifically, this study assesses the performance of the Capacity Spectrum Method (CSM) with real (i.e. recorded) ground motions (as opposed to code-based conventional spectra) to explicitly account for record-to-record variability in fragility analysis. The study focuses on single-degree-of-freedom systems, providing a basis for future multi-degree-of-freedom system applications. A case-study database of 2160 inelastic oscillators is defined through parametric backbones with different elastic periods, (yield) base shear coefficients, values of the ductility capacity, hardening ratios, residual strength values and hysteresis rules. These case studies are analysed using 100 real ground motions. An efficient algorithm to perform the CSM with real spectra is proposed, combined with a cloud-based approach (Cloud-CSM) to derive fragility relationships. Simple criteria to solve the issue of multiple CSM solutions (i.e. two or more points on the backbone satisfying the CSM procedure) are proposed and tested. It is demonstrated that the performance point selection can be carried out based on a particularly efficient intensity measure detected via optimal intensity measure analysis. The effectiveness of the proposed Cloud-CSM in fragility analysis is discussed through extensive comparisons with nonlinear time-history analyses, the code-based N2 method, and a simple method involving an intensity measure as a direct proxy for the performance displacement. The Cloud-CSM provides errors lower than ±20% in predicting the median of the fragility curves in most of the analysed cases and outperforms the other considered methodologies in calculating the fragility dispersion.

A dual response surface-based efficient fragility analysis approach of offshore structures under random wave load

This paper presents an efficient fragility analysis approach for offshore structures subjected to random wave load considering parameter uncertainty. Fragility analysis of structures under random dynamic load is generally accomplished by the direct Monte Carlo simulation (MCS), which requires extensive computational time. Hence, in the present study, a new cumulative distribution function matching-based fragility analysis approach is proposed in the framework of dual response surface method to reduce this computational burden. The proposed approach does not require MCS during failure probability computations once the two response surfaces of mean and standard deviation of response are obtained. Thereby, a substantial amount of computational time is saved. The proposed approach is generic in nature and can be applied to any offshore structure, with different probability distributions of system parameters and higher uncertainty levels, as well. The record-to-record variation of random wave force time-histories (that occurs even for the same set up of hazard parameters) can be easily considered by the proposed approach. The accuracy of the proposed approach is maintained by applying the moving least-squares method, in place of the conventional least-squares method, which is often reported to be a source of error. Two illustrative examples (one simple benchmark problem and another practical steel offshore platform structure) are presented to demonstrate the efficiency of the proposed fragility analysis approach. The results indicate that the present moving least-squares method yields more accurate solutions than the conventional least-squares method. Also, the computational efficiency by the proposed approach over the usual MCS-based approach can be clearly envisaged from the numerical studies.

Expected seismic performance of gravity dams using machine learning techniques

Methods for the seismic analysis of dams have improved extensively in the last several decades. Advanced numerical models have become more feasible and constitute the basis of improved procedures for design and assessment. A probabilistic framework is required to manage the various sources of uncertainty that may impact system performance and fragility analysis is a promising approach for depicting conditional probabilities of limit state exceedance under such uncertainties. However, the effect of model parameter variation on the seismic fragility analysis of structures with complex numerical models, such as dams, is frequently overlooked due to the costly and time-consuming revaluation of the numerical model. To improve the seismic assessment of such structures by jointly reducing the computational burden, this study proposes the implementation of a polynomial response surface metamodel to emulate the response of the system. The latter will be computationally and visually validated and used to predict the continuous relative maximum base sliding of the dam in order to build fragility functions and show the effect of modelling parameter variation. The resulting fragility functions are used to assess the seismic performance of the dam and formulate recommendations with respect to the model parameters. To establish admissible ranges of the model parameters in line with the current guidelines for seismic safety, load cases corresponding to return periods for the dam classification are used to attain target performance limit states.

Effect of ground motion characteristics on seismic fragility of subway station

Seismic fragility analysis of structure is fundamental in performance-based seismic design. The ground motion record set used in the analysis may have a characteristic effect on the fragility curves of a subway station structure. In this paper, fragility data have been developed by conducting the incremental dynamic analysis of subway station structure subjected to far-field record set (FFRS), near-field record set (NFRS), and near-filed record set with a pulse (NFRS + P). The dynamic analysis was conducted employing 2-D finite element models that account for soil nonlinearity and structural plastic damage. The vulnerability curves were derived utilizing the inter-story drift ratio as the damage measure (DM) and the peaks of ground acceleration as the intensity measure (IM). The results show that the second story was more prone to damage than the first story. The fragility curves derived from the data of the second story exhibited widely varying features for three ground motion record sets. The subway station sustained higher damage conditional probability when subjected to NFRS compared to NFRS + P and FFRS ground motions. The difference in the free field response under the three ground motion records sets directly correlates to the difference in the structural seismic vulnerability analysis. These results add to the rapidly expanding field of subway station performance-based seismic design.

Seismic fragility analysis of structures based on Bayesian linear regression demand models

Bayesian linear regression (BLR) based demand prediction models are proposed for efficient seismic fragility analysis (SFA) of structures utilizing limited numbers of nonlinear time history analyses results. In doing so, two different BLR models i.e. one based on the classical Bayesian least squares regression and another based on the sparse Bayesian learning using Relevance Vector Machine are explored. The proposed models integrate both the record-to-record variation of seismic motions and uncertainties due to structural model parameters. The magnitude of uncertainty involved in the fragility estimate is represented by providing a confidence bound of the fragility curve. The effectiveness of the proposed BLR models are compared with the commonly used cloud method and the maximum likelihood estimates methods of SFA by considering a nonlinear single-degree-of-freedom system and a five-storey reinforced concrete building frame. It is observed that both the BLR models can estimate fragility with improved accuracy compared to those common analytical SFA approaches considering direct Monte Carlo simulation based fragility results as the benchmark.

Damage risk assessment of a high-rise building against multihazard of earthquake and strong wind with recorded data

The high-rise buildings designed with a long lifetime may be exposed to one or more extreme hazards. Traditionally, specifications separately treated the multiple extreme hazards according to the controlling load case. Thus, the ability of high-rise buildings designed by the current codes to face the combined threats of earthquake and wind is rather vague. This paper presents a multihazard-based framework to assess the damage risk of a high-rise building subjected to earthquake and wind hazards separately and concurrently, which can be broken into three parts: the modeling of hazards, the structural fragility analysis and the damage probability computation. Firstly, based on the earthquake and wind data from 1971 to 2017 recorded in the Dali region of China, the hazard curves of single earthquake and wind, and the copula-based surface of bi-hazards are well established. Secondly, the multihazard-based fragility analysis of a high-rise building in Dali Prefecture is performed with the consideration of various load conditions. Lastly, upon completing the hazard models and fragility analyses, quantifications of the damage probabilities for the separate and concurrent hazards are determined directly. Numerical results indicate that the damage probability and contributions of each hazard circumstance are sensitive to damage severity. Furthermore, the damage probability induced by the bi-hazards dominates the total probability under most damage states conflicted with the common assumptions presented in the available researches. The comprehensive application highlights the necessity of examining the responses of high-rise buildings subjected to multihazard. The potential of the presented framework is of great help for decision-making.

Gaussian mixture–based equivalent linearization method (GM‐ELM) for fragility analysis of structures under nonstationary excitations

SummaryGaussian mixture–based equivalent linearization method (GM‐ELM) is a recently developed stochastic dynamic analysis approach which approximates the random response of a nonlinear structure by collective responses of equivalent linear oscillators. The Gaussian mixture model is employed to achieve an equivalence in terms of the probability density function (PDF) through the superposition of the response PDFs of the equivalent linear system. This new concept of linearization helps achieve a high level of estimation accuracy for nonlinear responses, but has revealed some limitations: (1) dependency of the equivalent linear systems on ground motion intensity and (2) requirements for stationary condition. To overcome these technical challenges and promote applications of GM‐ELM to earthquake engineering practice, an efficient GM‐ELM‐based fragility analysis method is proposed for nonstationary excitations. To this end, this paper develops the concept of universal equivalent linear system that can estimate the stochastic responses for a range of seismic intensities through an intensity‐augmented version of GM‐ELM. Moreover, the GM‐ELM framework is extended to identify equivalent linear oscillators that could capture the temporal average behavior of nonstationary responses. The proposed extensions generalize expressions and philosophies of the existing response combination formulations of GM‐ELM to facilitate efficient fragility analysis for nonstationary excitations. The proposed methods are demonstrated by numerical examples using realistic ground motions, including design code–conforming nonstationary ground motions.

Kriging Metamodeling-Based Monte Carlo Simulation for Improved Seismic Fragility Analysis of Structures

ABSTRACT The polynomial response surface method (RSM) is mostly adopted to overcome computational challenge of Monte Carlo Simulation (MCS)-based seismic fragility analysis (SFA) of structure. However, such SFA approach is primarily based on dual RSM involving lognormal assumption which lacks desired accuracy. The present study explores the advantage of adaptive nature of Kriging approach for improved SFA by random selection of metamodel to implicitly consider record to record variations of earthquakes. Without additional computational burden, the approach avoids a prior distribution assumption unlike dual RSM. The effectiveness of the approach over the usual polynomial RSM for SFA is elucidated numerically.

Probabilistic hurricane risk analysis of coastal bridges incorporating extreme wave statistics

Coastal bridges sustained severe damage during hurricanes Ike, Katrina, and Ivan. Reducing the impact of future hurricane events to coastal bridges requires conducting a comprehensive risk analysis. A comprehensive risk analysis of bridges enables owners to assign limited resources to the most critical bridges in the inventory through a risk-informed decision making process. This study presents a computationally efficient methodology for structural fragility analysis and risk assessment of simply supported coastal bridges vulnerable to hurricane hazard. Various sources of uncertainty associated with hurricane hazard and bridge response are identified, and thereby establishing probability distributions. The novelty of the proposed method includes the consideration of uncertainties in extreme wave heights and wave period by means of a wave spectral density distribution in the calculation of wave forces. The proposed hurricane risk analysis method was successfully applied to coastal bridges located in the state of Georgia (U.S.A). The application presents the derivation of probabilistic models of demand, capacity and hazard; and highlights the potential of the proposed framework for identification and ranking of the most vulnerable bridges.

Performance-based seismic fragility analysis of retaining walls based on the probability density evolution method

Seismic fragility analysis is an efficient way to study the seismic behaviour and performance of structures under the excitation of earthquakes of varying intensity, and an essential part of the seismic risk assessment of structures. A recently developed dynamic reliability methodology, the probability density evolution method (PDEM), is proposed for the dynamic reliability and seismic fragility analysis of a retaining wall. The PDEM can obtain an instantaneous probability density function of the seismic responses and easily acquire the seismic reliability of the structural system. An important advantage of the PDEM is its high efficiency relative to that of the Monte Carlo simulation method, which is often used in the reliability and fragility analysis of structures. The present study uses a typical gravity retaining wall to illustrate stochastic seismic responses and fragility curves that can be obtained by the PDEM. The combined uncertainties of the seismic force and soil properties are explicitly and systematically modelled by stochastic ground motions and random variables respectively. The performance of the retaining wall is analysed for different acceptable levels of backfill settlement. Additionally, seismic fragility curves are constructed without assuming the distribution of the seismic response.

Examination of experimental variability in HFFB testing of a tall building under multi-directional winds

Examination of wind loading uncertainty is necessary for structural fragility analysis of tall buildings in the context of performance-based wind engineering. One of the sources of uncertainly is represented by random experimental error, which may occur during a standard test in wind tunnel, such as the high frequency force balance (HFFB) test. Few examples of systematic experimental error analysis are available. This study examines a series of experiments on a model of a standard benchmark building under simulated turbulent flow. HFFB experiments were conducted in the Northeastern University's small-scale wind tunnel. Three model equations are proposed to represent the power spectral density (PSD) functions of the above three forces in the frequency domain.Furthermore, effects of experimental errors are incorporated by allowing the parameters in each function to vary randomly. Variability is evaluated by considering the second-order statistical moments of the parameters (standard deviations and correlations). At last, this paper introduces a data-driven Monte-Carlo approach to reconstruct the generalized PSD of the wind loading through model equations. Experimental variability is accounted for by exploiting information on the probability distributions of the model parameters. Verification of the reconstructed PSD functions against experiments suggests that the Monte-Carlo approach can effectively generate synthetic PSD curves.

Simulation based improved seismic fragility analysis of structures

The Monte Carlo Simulation (MCS) based seismic fragility analysis (SFA) approach allows defining more realistic relationship between failure probability and seismic intensity. However, the approach requires simulating large number of non-linear dynamic analyses of structure for reliable estimate of fragility. It makes the approach computationally challenging. The response surface method (RSM) based metamodeling approach which replaces computationally involve complex mechanical model of a structure is found to be a viable alternative in this regard. An adaptive moving least squares method (MLSM) based RSM in the MCS framework is explored in the present study for efficient SFA of existing structures. In doing so, the repetition of seismic intensity for complete generation of fragility curve is avoided by including this as one of the predictors in the response estimate model. The proposed procedure is elucidated by considering a non-linear SDOF system and an existing reinforced concrete frame considered to be located in the Guwahati City of the Northeast region of India. The fragility results are obtained by the usual least squares based and the proposed MLSM based RSM and compared with that of obtained by the direct MCS technique to study the effectiveness of the proposed approach.