Fragility Curves For Structures Research Articles

Assessing grid hardening strategies to improve power system performance during storms using a hybrid mechanistic-machine learning outage prediction model

Improvements of power system performance during severe weather events are targeted through grid hardening actions, such as strengthening aging infrastructure or performing vegetation management. However, due to the complexity of modeling power system interactions with the environment and the impacts of proposed reinforcements, the benefits of such hardening actions are often unclear. To support hardening assessments, comprehensive models capturing these intricate relationships are necessary. To this end, this study presents a novel application of a hybrid mechanistic-data-driven outage prediction model (OPM) designed to incorporate changes in infrastructure or environmental/vegetation parameters in the prediction of storm outages. The model incorporates physics-based structural fragility curves of the overhead pole-wire system within a machine learning OPM trained on meteorological, topographic, infrastructure, and historic outage data to quantify the benefits of adaptive change in reducing storm-related power outages. A prioritization scheme is formulated to inform improved strategies to strengthen grid resilience under budgetary constraints. As a case study of the distribution system in Connecticut, the model was trained on historical outage data from storms between 2005 and 2020, and a counterfactual analysis is conducted. The results indicate tree removal and pole strengthening are the most cost-effective strategies; for instance, under a $600 million budget, tree removal could have reduced up to 15,000 distribution grid outages over the events analyzed. The developed framework and models can be useful for utility companies, regulatory agencies, and governments to highlight areas of need, inform cost-risk-benefit analyses, and aid in the optimal allocation of funds and resources toward grid hardening.

Field teams coordination for earthquake-damaged distribution system energization

The re-energization of electrical distribution systems in a post-disaster scenario is of grave importance as most modern infrastructure systems rely heavily on the presence of electricity. This paper introduces a method to coordinate the field teams for the optimal energization of an electrical distribution system after an earthquake-induced blackout. The proposed method utilizes a Markov Decision Process (MDP) to create an optimal energization strategy, which aims to minimize the expected time to energize each distribution system component. The travel duration of each team and the possible outcomes of the energization attempts are considered in the state transitions. The failure probabilities of the system components are computed using the fragility curves of structures and the Peak Ground Acceleration (PGA) values which are encoded to the MDP model via transition probabilities. Furthermore, the proposed solution offers several methods to determine the non-optimal actions during the construction of the MDP and eliminate them in order to improve the run-time performance without sacrificing the optimality of the solution.

Development of fragility surfaces for reinforced concrete buildings under mainshock‐aftershock sequences

AbstractA single intensity measure (IM) is commonly used to develop fragility curves for structures subjected to mainshock‐aftershock (MS‐AS) scenarios. This study aims to propose a framework to develop MS‐AS fragility surfaces by characterizing the MS‐AS sequences with two IMs. To do this, the well‐known Park & Ang damage index, which increases monotonically with the ground motion duration, is adopted to represent the accumulative structural damage during sequential excitations. The MS‐AS accumulative damage of structures is thus represented by the combination of the initial damage caused by MS and the incremental damage caused by AS. Based on total probability theorem, the process of assessing MS‐AS fragility is consequently divided into two parts, namely the MS fragility assessment and the AS fragility assessment, respectively, where the cases of dynamic instability are considered. The proposed framework is illustrated using a typical four‐story reinforced concrete frame building. The peak ground velocity values of both MS and AS are taken as the representative IMs for the MS‐AS sequences. The fragility results for MS only and MS‐AS sequences are compared to scrutinize the effects of AS on structural damage. It is found that the MS‐AS sequence can cause significantly larger exceedance probabilities of limit states compared to the MS only. The MS‐AS sequence also leads to a reduction of the MS‐AS fragility median conditioned on a given AS intensity. Such reduction increases with the increase of the AS intensity.

Seismic risk assessment of a steel building supported on helical pile groups

Designing structures to be the least vulnerable within earthquake-prone areas is a serious challenge for structural engineers. One common and useful tool that structural engineers use to predict the vulnerability of a structure during an earthquake is a fragility curve. However, most structural fragility curves do not take into consideration the contribution of pile foundation systems in the structural vulnerability. Therefore, this study aims to modify existing fragility curves of a six-story fixed-base steel frame hospital building with buckling-restrained braces, to incorporate the effect of helical pile group behavior on the fragility of the structure. To that end, a finite element model of the investigated structure was modified with results from a full-scale shake table test performed on two groups of helical piles embedded in dense sand supporting a superstructure. The primary results show that fixed-base design may not be conservative for all conditions and soil–foundation interaction should be considered when creating fragility curves, especially for a stiff structure on soft soils where a high-intensity earthquake is anticipated.

Multiple failure function based fragility curves for structures equipped with TMD

This paper presents a procedure to develop fragility curves of structures equipped with TMD considering multiple failure functions. The failure criteria considered are maximum inter-story drift ratio as a safety criterion, maximum absolute acceleration as a convenience criterion and TMD stroke length. The relationship between intensity measure and responses of the structure was assumed to follow the power-law model, and a regression analysis was used to estimate its properties. A nonlinear eight-story shear building subjected to near-fault earthquakes was used for the numerical studies. Fragility curves using multiple and single failure functions for an uncontrolled structure and a structure equipped with optimal TMDs were developed. Numerical analysis showed that using multiple failure functions led to increasing the fragility when compared with using the single failure function for both the uncontrolled and controlled structures. However, TMDs slightly reduced the seismic fragility and have the capability to improve the reliability of the structure. Also, it was found that the fragility was significantly influenced by the values of the capacity thresholds of both the acceleration of the structure and TMD stroke length, which should be selected by considering the target performance and application of the structure and control device.

Performance-Based Design through Implementation of FEMA P-58 Methodology in Developing Countries

This paper investigates a simple approach proposed towards performance-based earthquake engineering (PBEE) which has potential applications to the performance-based design (PBD) and performance-based assessment (PBA) fields. The simple method of PBEE encompasses three areas of seismic risk which include seismic hazard, structural analysis, and loss models. The aim of the PBEE process, entitled as FEMA P-58, is to present essential data needed to make a rational decision regarding predicted performance, where various sources of uncertainties are involved. In developing countries, the lack of suitable real ground motions corresponding to site characteristics and seismicity particularly for larger intensities and the scarcity of demands, which makes it hard to identify the seismic capacity of a structure, is the main our motivation of using the FEMA method. In this paper, the method of FEMA P-58 is investigated, in terms of available tools and required data, in such a way that it will be applicable for developing countries which are located in high seismic hazard zones. To achieve this goal, three steel moment-resisting buildings with low and high ductility, and three steel braced-frame buildings are selected as case studies. The mean annual loss is estimated by the available software, Performance Assessment Calculation Tool (PACT). The achieved results, i.e. the loss curves, will provide a simple means by which the engineers can quantify and communicate seismic performance to other stakeholders. In the case study buildings, the braced one has less annual losses in comparison with other investigated cases, and the structure with high ductility can be considered as the next ones. Execution cost of each building should be considered by contractors. Also, seismic fragility curves of structures for various limit states, as well, the corresponding loss models are identified as the most essential data towards application of the investigated PBEE process.

Studying the Effect of Fundamental Structural Period on the Seismic Fragility Curves of Two-Span Integral Concrete Box Girder Bridges

The main step in deriving fragility curves of structures is to develop their probabilistic seismic demand model (PSDM). PSDMs can be expressed as the linear regression of engineering demand parameters and intensity measure suitable pairs in the log-transformed space. However, extracting PSDMs can be costly, computationally challenging, and time-consuming. For these reasons, this study proposes a practical method to estimate the two coefficients of the regression fit line of PSDM based on the fundamental periods of two-span integral concrete box girder bridges. Moreover, the effect of geometrical properties on the fundamental period has been investigated and an equation has been derived for the estimation of the fundamental period. For statistical analyses, 220 bridges are modeled using Latin hyper-cube sampling while 35,200 nonlinear time history analyses are done using OpenSees software to generate PSDMs.

Multiple failure criteria-based fragility curves for structures equipped with SATMDs

In this paper, a procedure to develop fragility curves of structures equipped with semi-active tuned mass dampers (SATMDs) considering multiple failure criteria has been presented while accounting for the uncertainties of the input excitation, structure and control device parameters. In this procedure, Latin hypercube sampling (LHS) method has been employed to generate 30 random SATMD-structure systems and nonlinear incremental dynamic analysis (IDA) has been conducted under 20 earthquakes to determine the structural responses, where failure probabilities in each intensity level have been evaluated using Monte Carlo simulation (MCS) method. For numerical analysis, an eight-story nonlinear shear building frame with bilinear hysteresis material behavior has been used. Fragility curves for the structure equipped with optimal SATMDs have been developed considering single and multiple failure criteria for different performance levels and compared with that of uncontrolled structure as well as structure controlled using passive tuned mass damper (TMD). Numerical analysis has shown the capability of SATMDs in significant enhancement of the seismic fragility of the nonlinear structure. Also, considering multiple failure criteria has led to increasing the fragility of the structure. Moreover, it is observed that the influence of the uncertainty of input excitation with respect to the other uncertainties is considerable.

Effects of Near-fault Strong Ground Motions on Probabilistic Structural Seismic-induced Damages

Seismic fragility curves measure induced levels of structural damage against strong ground motions of earthquakes, probabilistically. These curves play an important role in seismic performance assessment, seismic risk analysis and making rational decisions regarding seismic risk management of structures. It has been demonstrated that the calculated fragility curves of structures are changed while the structures are excited by near-field strong ground motions in comparison with far-field ones. The objective of this paper is to evaluate the extents of modification for various performance levels and variety of structural heights. To achieve this goal, Incremental Dynamic Analysis (IDA) method is applied to calculate seismic fragility curves. To investigate the effects of earthquake characteristics, two categories of strong ground motions are assumed through IDA method, i.e. near and far-field sets. To study the extent of modification for various heights of structures, 4 – 6 and 10 stories moment-resisting concrete frames are considered as case studies. Furthermore, to study the importance of involving near-field strong ground motions in seismic performance assessment of structures, the damage levels are considered as the renowned structural performance levels (i.e. Immediate Occupancy, Life Safety, Collapse Prevention and Sidesway Collapse). Achieved results show that the fragility curve of low-rise frame (i.e. 4-story case study) for IO limit state presents more probability of damage applying near-fault sets in comparison with far-fault set. Investigating fragility curves of the other performance levels (i.e. LS, CP and Collapse) and the higher frames, a straightforward conclusion, regarding probability of damage. To achieve the rational results for the higher frames, mean annual frequency of exceedance (MAFE) and probability of exceeding limit states in 50 years are calculated. MAFE is defined as the integration of structural fragility curve over seismic hazard curve. According to the achieved results for 6-story frame, if the structure is excited by near-field strong ground motions the probability of exceedance for LS, CP and collapse limit states in 50 years will be increased up to 11%, 2.4%, 0.7% and 0.4% respectively, comparing with the calculated probabilities while far-field strong ground motions are applied. On the other hand, while the 10-story case study is excited by near-field strong ground motions, the exceedance probability values for mentioned limit states decreases up to 20%, 5%, 4% and 4%, respectively. Consequently, it can be concluded that the lower is the height of the structure, the more will be the increment of probability of damage in the near-field conditions. Furthermore, this increment is much more for IO limit state in comparison with other limit states. These facts can be applied as a precaution for seismic design of low-rise structures, while they are located at the vicinity of active faults.

ER2-Earthquake: Interactive web-application for urban seismic risk assessment

An interactive user-friendly web-based application for urban seismic risk assessment referred to as rapid risk evaluator (ER2) is presented. It combines three major input components: seismic hazard, exposed buildings and respective vulnerabilities. Intended primarily for application by the larger public-safety community, ER2 intuitively guides non-expert users with step-by-step prompts and on-screen instructions through otherwise complex risk scenarios. Open-source software is used to offer the application free of all financial cost for users. The analyses are based on parameters of the well-known FEMA's Hazus method. To accelerate the computation and rapidly obtain estimates of the negative impacts, ER2 employs pre-populated inventory and vulnerability databases. The standard displacement-based structural fragility curves and iterative nonlinear static analyses are replaced with fragility curves determined as direct functions of the shaking intensity. Comparison of damage probability results, economic and social losses concur with Hazus estimates for individual buildings and for aggregated inventory at urban scale. An example of seismic risk assessment for Quebec City, Canada, is shown to illustrate the effectiveness of ER2.

Fragility curves for mixed concrete/steel frames subjected to seismic excitation

Use of appropriate fragility curves for structures is an essential and basic tool for earthquake loss estimation. Fragility curves for frames made only of concrete or only of steel members are already available in the literature. In this paper, fragility curves for plane mixed concrete/steel moment resisting framed structures are developed. Parametric numerical results for these mixed structures are presented and discussed.

Wind-load fragility analysis of monopole towers by Layered Stochastic-Approximation-Monte-Carlo method

This paper describes a novel numerical algorithm for the simulation of the along-wind dynamic response of a prototype of slender towers under turbulent winds, using a Layered Stochastic Approximation Monte Carlo algorithm (LSAMC). The proposed algorithm is applied to derive the statistics of the dynamic response in the presence of uncertainties in the structural properties and in the wind loading. Standard “brute force” Monte-Carlo methods are also used for validating the LSAMC results. The proposed methodology efficiently estimates structural fragility curves under extreme wind loads. The methodology enables a significant speedup in the computing time compared to standard Monte Carlo sampling. Furthermore, it is demonstrated that accuracy in the estimation of structural fragility curves is superior to ordinary reliability methods (e.g. “First-order reliability methods” or FORM).

A unified framework for performance-based wind engineering of tall buildings in hurricane-prone regions based on lifetime intervention-cost estimation

Accurate evaluation of structural performance is necessary in modern tall building design. In wind engineering, the current approach employed by researchers is the Monte-Carlo sampling method. Structural failure probability is calculated by combining structural fragility curves with the random variability of wind speed and direction, depending on local wind climate. In the hurricane-prone regions of the USA, wind climate and its effects on building response require accurate assessment of wind-induced structural performance.This paper proposes a simulation framework for tall buildings that combines fragility analysis with local wind climate information to evaluate structural vulnerability. Hurricane wind climate information directly considers maximum wind speed, wind direction along with their correlation at hurricane landfall. Consequently, structural fragility surfaces will be generated, conditional on these two variables. This result will be used to examine lifetime intervention cost accumulation, associated with nonstructural damage on the building façade, and to determine an “optimal” wind-direction-dependent building orientation.

A simplified procedure to estimate peak drift demands for mid-rise steel and R/C frames under narrow-band motions in terms of the spectral-shape-based intensity measure INp

In this study, a simplified procedure to predict the maximum inter-story drift demands of mid-rise framed buildings in terms of a spectral-shape-based ground motion intensity measure is proposed. For this aim, the maximum inter-story drift of steel and reinforced concrete (R/C) frames with 4, 6, 8 and 10 stories subjected to several narrow-band ground motions is estimated as a function of the spectral acceleration at first mode of vibration of the structure Sa(T1), which is commonly used in earthquake engineering and seismology, and with the recently developed parameter related to the structural response known as INp. It is observed that the spectral-shape-based intensity measure INp is the parameter best related with the structural response of the selected frames under narrow-band motions. Therefore, a new approach is used to propose equations to compute maximum inter-story drift demands and seismic uncertainty of mid-rise frames as a function of INp. The equations can be used for the rapid seismic assessment and to obtain structural fragility curves of the steel and R/C frame models. The fragility curves obtained with the simplified approach are compared to those obtained with traditional procedure to compute structural fragility. It is observed that the proposed equations provide good accuracy to calculate fragility curves of steel and R/C structures under narrow-band earthquake ground motions in terms of the spectral-shape-based intensity measure INp.

Seismic fragility curves for structures using non-parametric representations

Fragility curves are commonly used in civil engineering to assess the vulnerability of structures to earthquakes. The probability of failure associated with a prescribed criterion (e.g. the maximal inter-storey drift of a building exceeding a certain threshold) is represented as a function of the intensity of the earthquake ground motion (e.g. peak ground acceleration or spectral acceleration). The classical approach relies on assuming a lognormal shape of the fragility curves; it is thus parametric. In this paper, we introduce two non-parametric approaches to establish the fragility curves without employing the above assumption, namely binned Monte Carlo simulation and kernel density estimation. As an illustration, we compute the fragility curves for a three-storey steel frame using a large number of synthetic ground motions. The curves obtained with the non-parametric approaches are compared with respective curves based on the lognormal assumption. A similar comparison is presented for a case when a limited number of recorded ground motions is available. It is found that the accuracy of the lognormal curves depends on the ground motion intensity measure, the failure criterion and most importantly, on the employed method for estimating the parameters of the lognormal shape.

Reliability over time of wind turbines steel towers subjected to fatigue

A probabilistic approach that combines structural demand hazard analysis with cumulative damage assessment is presented and applied to a steel tower of a wind turbine. The study presents the step by step procedure to compare the reliability over time of the structure subjected to fatigue, assuming: a) a binomial Weibull annual wind speed, and b) a traditional Weibull probability distribution function (PDF). The probabilistic analysis involves the calculation of force time simulated histories, fatigue analysis at the steel tower base, wind hazard curves and structural fragility curves. Differences in the structural reliability over time depending on the wind speed PDF assumed are found, and recommendations about selecting a real PDF are given.

Exploring hurricane wind speed along US Atlantic coast in warming climate and effects on predictions of structural damage and intervention costs

This paper proposes a methodology for the rational assessment of lifetime costs on tall buildings due to hurricane-induced damage along the US Atlantic coastline accounting for plausible future warming climate scenarios. The hurricane simulation is based on Vickery’s empirical model. Initially, regression errors in Vickery’s model are discussed; some adjustments are proposed to enable hurricane simulation in future climates. After verification of the hurricane model’s ability to simulate the results of the United States historical hurricane database, simulation of hurricane activity in future climates is examined. The warming climate scenarios are reproduced from the results of the community earth system model, maintained by the National Center for Atmospheric Research (NCAR). Three different future climate scenarios, RCP2.6, RCP4.5 and RCP8.5, are considered. The influence of warming climate on two quantities, relevant to wind engineering, is examined: hurricane frequency and hurricane intensity. It is found that, in a warming climate environment, the hurricane frequency and hurricane intensity may vary depending on the RCP scenario. Therefore, the probability distribution of the wind speed in hurricane-prone areas of the United States, both coastal and interior areas, will also be influenced by the RCPs.The numerical methodology for computing wind speed probability distribution in a future warming climate, influenced by the various RCP scenarios, is subsequently coupled with an existing approach for structural performance analysis against wind hazards to predict the indirect effect of future warming climate on the structural intervention costs (i.e. repair costs), induced by the damaging winds. A 180-m tall benchmark building, located in Miami (Florida, USA), is used as one example of application in conjunction with a series of structural fragility curves, derived from a recent study for the same structure. The evaluation of lifetime intervention costs is later expanded to demonstrate the ability of the proposed methodology to predict hurricane wind damage, if the location of the structure is moved to several other cities along the Atlantic coast of the United States.

A comprehensive collapse fragility assessment of moment resisting steel frames considering various sources of uncertainties

Different sources of uncertainties contribute to the collapse and safety assessment of structures. In this paper, impact of construction quality (CQ) is considered in developing analytical collapse fragility curves for moment resisting steel frames. Furthermore, the interaction of this source of uncertainty with epistemic uncertainty inherent in modeling parameters, due to lack of knowledge and inaccuracy of predictor equations, is investigated. Beam strength, column strength, beam ductility, and column ductility meta-variables are defined as modeling parameters which are being suffered by informal uncertainty. Quadratic equations for the mean and the standard deviation of collapse fragility curves are derived by utilizing response surfaces, which are interpolated to analytically-derived values considering realizations for modeling variables and for various levels of construction quality. To the best of the authors’ knowledge, interaction of modeling and CQ uncertainty in analytical collapse fragility curve has not been considered in previous investigations. A fuzzy rule-based method is applied to employ the effects of uncertainty due to CQ. Using Monte Carlo simulation for the modeling variables and the construction quality index, and subsequently computing response surface coefficients via a fuzzy inference system, and finally deriving collapse fragility curve parameters through response surfaces, result in collapse fragility curves of structures. In developing these curves, different sources of uncertainties are involved, ranging from lexical to informal and stochastic types. It is concluded that neglecting the effects of these sources leads to the underestimation of collapse fragility probability. This shows the importance of considering modeling and construction quality uncertainty effects on collapse fragility curves. It is shown that for a sample moment resisting steel frame collapse probability is increased 53% and 60% for 10% and 2% probability of exceedance in 50 years seismic hazard levels, respectively, while interaction of CQ and modeling uncertainties are considered in comparison with neglecting them. Otherwise, if only modeling uncertainty is involved, this increment is evaluated at 42% and 16%, respectively for the aforementioned probabilities of exceedance.

Fragility curves for structures under tsunami loading

Susceptibility to structural damage can be characterized by a fragility curve, which is expressed as a normal or lognormal cumulative distribution of the conditional probabilities of reaching or exceeding a particular damage state, for given values of the demand parameter. Such curves have been produced for a variety of damage states in different categories of buildings exposed to tsunami loading in different parts of the world, with the demand parameter taken as inundation depth. Harmonization was sought across these studies with respect to the median inundation depth. Three categories of single-storey buildings were identified based on construction material, namely reinforced concrete, masonry and timber. The median inundation depths for the complete damage state decreased from reinforced concrete (5.4–7.3 m) through masonry (2.3–2.5 m) to timber (~1.6 m) structures. The fairly narrow ranges above represent a number of different studies and indicate that a common family of curves or “bands” can be arrived at. Such ranges were identified for other partial damage states too. Our genuinely original contribution is a probabilistic model that was developed using a Monte Carlo simulation to produce synthetic fragility functions for masonry and reinforced concrete structures under tsunami loading. The probabilistic model consisted of a geometric model that captured the geometrical and wall-type variations of the building lot, a loading function and a set of failure criteria, all of which required appropriate simplifying assumptions. The resulting synthetic fragility curves matched the fragility curves based on observed tsunami damage for the complete collapse damage state reasonably well.

Fragility functions for code complying RC frames via best correlated IM–EDP pairs

This paper provides an investigation on the correlations between ground motion intensity measures (IMs) and engineering demand parameters (EDPs) through nonlinear dynamic analyses of MDOF systems under real earthquake recordings and then structural fragility curves are derived for the best correlated IM–EDP pairs. For this purpose, a parametric study on reinforced concrete (RC) buildings is carried out. Study buildings comprise 5-, 10-, 15- and 20-story, RC, code-complying, regular, moment-resisting frames designed for different strength reduction factors, e.g. R = 2, 4 and 6. The input ground motion dataset consists of 734 horizontal components of earthquake accelerograms. The best correlations between IMs and EDPs are computed by regression analysis. Sets of fragility curves in terms of maximum inter-story drift ratio, maximum plastic end rotation and maximum floor acceleration are derived based on log-normal distribution assumption. Fragility curves are presented not for a specific damage state such as slight, moderate etc. but for a range of damage thresholds on EDP.