Development Of Fragility Curves Research Articles

Relationship between Coastal Hazard Countermeasures and Community Resilience in the Tōhoku Region of Japan Following the 2011 Tsunami

Many coastal communities around the world that are vulnerable to inundation from tsunamis or storm surges are investing significant resources into countermeasures such as seawalls, levees, and breakwaters to limit damage from such events. A potential framework for studying the relationship between coastal hazard countermeasures and their impact on community resilience is proposed in this investigation and is applied to 27 coastal cities in the Tōhoku region of Japan following the 2011 tsunami. Community resilience was quantified using a modified version of the resilience inference measurement (RIM) method in which parameters of intensity, exposure, damage, and recovery were utilized in a k-means clustering analysis to categorize respective cities into four different resilience groups. As a supplemental analysis to the modified RIM method, historical data representing the exposure and damage parameters from the 1896, 1933, and 2011 Tōhoku tsunamis were utilized to establish limit states (LSs) for fragility curves to demonstrate the level of response for a specific damage condition. Three limit states were selected for 2%, 20%, and 40% of dwellings in a city being destroyed for a given tsunami event. An ordinal logistic regression was performed to determine whether there was a relationship between the resilience group of each city and the maximum countermeasure height. No statistically significant correlation was found between the maximum height of a coastal hazard countermeasure and the resilience group of each city, which indicates that investing in such infrastructure does not necessarily impact overall community resilience for an extreme event such as the 2011 Tōhoku tsunami. For this scenario, the probability of damage was assessed by developing fragility curves that demonstrated larger probability of exceedance discrepancies between LSs at lower maximum tsunami runup values. Coastal hazard countermeasures therefore may still be effective in limiting damage and thereby improve community resilience for less extreme tsunami events. The results of this investigation will assist government officials and engineers in selecting coastal resilience policies and strategies to limit future impacts from coastal hazards.

Probabilistic Analysis of RC Buildings Based on Incremental Dynamic Analysis

Earthquake is a natural disaster that can induce immense damage to properties and human lives. Fragility curve, defined as the probability of reaching or exceeding a specific damage state under an earthquake excitation, provides a prediction of damage that may occur during an earthquake. Incremental Dynamic Analysis Curve (IDA curve) developed from Incremental Dynamic analysis can be considered as the initial step of fragility curve development. The present study summarises the development of IDA curve for a RC building considering maximum roof displacement and storey drift as Damage Measure (DM) and peak ground acceleration as Intensity Measure (IM). The fragility curves developed using incremental dynamic analysis provide an overview of the probability of exceedance of damage limits in an existing building when acted upon by different levels of earthquake excitations and the performance level can be improved by incorporating appropriate design changes.

Seismic performance of RC frames with self-centering precast post-tensioned connections considering the effect of infill walls

This paper presents the seismic performance evaluation of self-centering precast post-tensioned concrete (SCPPTC) frames with infill walls. The SCPPTC connection system consists of all-steel bamboo-shaped energy dissipaters (SBED) and prestressed tendons, which provide energy dissipation capacity and self-centering capability, respectively. Using modeling parameters calibrated with experimental tests, nonlinear numerical models of SBED, SCPPTC connection, infill walls, and 2D SCPPTC frames were developed in OpenSees, to compare the performance of the structures with different types of infill wall layouts. Nonlinear static pushover and incremental dynamic analysis (IDA) were performed to study the effect of infill walls on the overall response of SCPPTC frames, in terms of stiffness, strength, maximum interstory drift ratio,θmax, the maximum residual interstory drift ratio, θr,max, and the normalized post-tensioned force. Using the IDA results, the study also developed fragility curves and estimated the collapse margin ratios. The results demonstrated that the shear strength of the SCPPTC frame was improved from 4.19% to 12.2%, and the initial secant stiffness of the SCPPTC frame was augmented from 22.9% to 88.3% with increasing filling rate. The totally infilled SCPPTC frame (SCPPTC-ToI) exhibits a 19.86% lower θmax than that of pilotis-infilled SCPPTC frame (SCPPTC-PiI) under rare earthquakes, and the maximum prestress of SCPPTC-ToI was also 7.14% lower than that of SCPPTC-PiI. With the increase in filling rate, θr,max increased by a maximum of 120.45%. The pronounced soft layer led to the highest failure and collapse probabilities of SCPPTC-PiI among all SCPPTC frames at the same performance level.

Low-LOD fragility curves of structural units in masonry building clusters for territorial risk analysis

The constant yet irregular construction process taking place in historical towns during decades, if not centuries, is based on spontaneous, and often unlawful, aggregation, superposition, and juxtaposition of building units, realized in different times with different construction techniques and materials. This process produces the so-called masonry building clusters, which constitute the fabric of most historical towns in Southern Europe. Though usually well integrated from the functional standpoint, their structural functioning is often hardly interpretable, especially under seismic actions. Since 2008, the Italian technical code, recognizing the complexity of analyzing masonry building clusters, allows subdividing them into distinct structural units and then by performing separate non-linear analyses on each structural unit. The code provides indications on how to identify each structural unit and, once it has been singled out, modeling and analysis can benefit of some simplifications: each floor can be analyzed and verified separately, the axial force variation in the walls can be disregarded, and the global torsional behavior can be neglected. These common-sense simplifications aim at avoiding complex FEM models, which would overexert the simplifications introduced, and encourage the development of more efficient assessment procedures, especially for large scale territorial risk studies, where the required level of detail (LOD) is generally low. Along these lines, this study proposes a procedure formulated in analytical form, which allows developing fragility curves of structural units belonging to masonry building clusters based, both, on gross geometrical data available from typological surveys, and on typical mechanical properties taken from the Italian code. Recognizing that the analysis tool should be commensurate to the knowledge level, the procedure has been implemented in a spreadsheet. This allows producing, with limited computational effort, fragility curves to be used in comprehensive risk assessment studies of historical centers. An application on a masonry building cluster in Umbria, Italy, is presented, which shows that the procedure yields accurate results with concise input data and that the corresponding fragility curves can be obtained with minimal computational effort, which is an extremely useful feature when performing risk analyses of historical city centers.

Seismic Response Estimation and Fragility Curve Development Using an Innovative Response Bound Method

Incremental dynamic analysis (IDA) is one of the widely used methods for structural assessment analysis and fragility curve development, given its unique capabilities in taking into account the aleatory uncertainties of earthquake records and its ability to provide a desirable statistical population of the system response. However, the strong dependence of the results on the number of selected records, the record selection process and scaling procedure, as well as the associated high computational costs are some of the obstacles, which limit the practicality of the IDA method especially in the case of large-scale structures. In the present study, an alternative approach called “Response Bounds” is proposed to estimate the expected range of structural responses under earthquakes with different intensity levels and to develop seismic fragility curves. To reduce computational costs and address the challenges associated with the record selection, a novel scenario-based Endurance Time (ET) analysis method is adopted. The good agreement between the fragility results of 5-, 10-, and 15-storey steel moment-resisting frames obtained by the proposed method and the IDA (less than 9% error) demonstrated the accuracy and reliability of the predicted results. The method could also estimate the mean loss ratio from fragility curves with less than 5% error in all cases. The proposed response-bound method can significantly reduce the computational costs of conventional seismic fragility assessment methods, and therefore can be used as an efficient tool for seismic reliability analysis in practical applications.

Development of Fragility Curves for Reinforced-Concrete Building with Masonry Infilled Wall under Tsunami

A tsunami is a natural disaster that destroys structures and kills many lives in many countries in the world. A risk assessment of the building under a tsunami loading is thus essential to evaluate the damage and minimize potential loss. A crucial tool in risk assessment is the fragility curve. Most building fragility curves for tsunami force were developed using survey building damaged data. This research proposed a method for developing fragility curves under tsunami loading based on the analytical building model data. In the development, the generic building was a one-story reinforced-concrete building with masonry-infilled walls constructed from the structural index, popularly built as residential buildings along the west coast of southern Thailand. Three damage levels were investigated: damage in masonry infill walls, damage in primary structures, and collapses. The masonry infill wall was modeled using multisprings to represent the load-bearing behavior due to tsunami with a hydrodynamic pattern. The fragility curves were developed using the maximum likelihood method and considering the uncertainty due to masonry infill wall type, tsunami flow direction, and tsunami flow velocity. The developed fragility curve agrees well with the empirical tsunami fragility curve of a one-story reinforced-concrete building damage data in Thailand from the 2004 Tsunami. The developed fragility functions could be adopted for assessing tsunami risk assessment and disaster mitigation for similar structures against different tsunami scenarios in the future.

Development of Performance-Based Fragility Curves of Coastal Bridges Subjected to Extreme Wave-Induced Loads

A number of coastal bridges faced significant damage due to recent natural hazards, inducing extreme waves. The fragility function is the basic step for assessing the resilience of a structure, thereby allowing the designers to alleviate post-event structural disasters and develop improved design methods for new structures. The majority of the focus of fragility functions developed in literature are concentrated on superstructure components and wave load on bridge decks. This paper presents a simplified methodology for the definition of damage states of the substructure component (pier drift) due to wave loads acting on piers as well as the bridge deck. The hazard intensity parameters representing the extreme wave loads chosen for this study are wave period, wave height, and still water depth. The Latin hypercube sampling technique is applied to consider the uncertainties in the intensity parameters as well as the material properties for the finite-element bridge models. Results indicate that the wave period is the most dominant factor affecting the wave-load intensity. The deck-level loading caused a higher probability of failure compared with the pier-level wave loading scenario. In both loading scenarios considered, the elastomeric bearing and shear keys are found to be one of the most vulnerable components in the system-level fragility curves developed. The system-fragility curves generated in this paper can be used to assess the resiliency of coastal bridges subjected to extreme wave-induced loads. The findings of this paper will also add to the risk mitigation and reliability assessment of coastal structures under multi-hazard conditions.

Fragility curve development of highway bridges using probabilistic evaluation (case study: Tehran City)

Seismic fragility analysis of bridges can be used to identify the probability of different damage states of bridges under earthquake hazards. This study aims to generate the fragility curve of highway bridges in Tehran, Iran, where these curves are not provided yet. To derive new fragility curves, the fragility curve of highway bridges from studies all around the world has been classified into different categories, based on their structural designs, bridge materials, country, and their analytical methods. A decision-tree analysis has been used to determine new fragility curves. The accuracy of these new curves was then assessed using a case study bridge and incremental dynamic analysis. The assessment analysis indicates that newly developed fragility curves for Tehran city have reasonable accuracy. The average difference between the derived fragility curve by the curves determined using Incremental Dynamic Analysis was acceptable. These new fragility curves helped to identify bridges throughout the Tehran city highways with higher seismic vulnerability. These can also be used for risk assessment and reducing seismic risk studies and future urban planning.

Seismic Fragility Assessment of Inner Peripheries of Italy through Digital Crowd-Sourcing Technologies

The structural and seismic fragility assessment of minor historical centers of the Inner Peripheries of Italy is a key phase of the preservation process of the historical and cultural features of a portion of the Italian building stock, whose reuse is crucial for the reversal of shrinking trends and the stimulation of population growth. In this framework, the opportunities offered by digital crowd-sourcing technologies with respect to performing probabilistic structural safety assessment at a large scale are investigated herein. The objective of this research was to exploit data and information available on the web such that the key building features of an area of interest are collected through virtual inspections, historical databases, maps, urban plans, etc. Thus, homogeneous clusters of buildings identified in the area of interest are catalogued and associated with specific building classes (chosen among those available in the literature), and the buildings’ levels of seismic fragility are determined through the development of fragility curves. The research outcomes show that the proposed approach provides a satisfactory initial screening of the seismic fragility level of an area, thus allowing for the identification of priority zones that require further investigations or structural interventions to mitigate seismic risk.

Energy-based modelling of in-plane fragility curves for the 2D ultimate capacity of Italian masonry buildings

The high seismic hazard of the Italian territory and the vulnerability of its historic masonry heritage require the development of fragility curves that must be increasingly reliable and robustly correlated to exposure. To date, national-scale seismic risk analyses mainly use empirical curves derived from the statistical analysis of damage induced by past events. These curves have shown good reliability, but they correlate only with a few typological-structural characteristics of the building, such as the number of floors, the vertical structure typology or the construction period. The present research paper aims to overcome this limitation with a hybrid approach that provides a better exposure characterisation. Specifically, the proposed strategy integrates the SAVE and Piecewise Rigid Displacement (PRD) methods. SAVE is an empirical approach based on the damage assessment due to past seismic events used to identify a seismic behaviour of a structure, while the PRD method is a numerical approach that solves the boundary value problem for normal, rigid, no-tension material. It can model different structural typologies, and as a result, it also provides the value of the horizontal static multiplier that drives the masonry construction to collapse. An extended numerical campaign is carried out considering a sample of 750 masonry buildings distributed throughout the Italian territory and extracted from the PLINIVS typological database. Looking at each construction, first, a PRD analysis is conducted to define its seismic capacity, paying special attention to modelling construction details. After that, the SAVE method is used to classify the construction in a specific seismic vulnerability class, i.e., from A to C, with decreasing vulnerability. All the buildings belonging to the same class are then collected, and three fragility curves representative of the collapse state (one for each vulnerability class) are derived and validated against empirical and analytical ones commonly adopted in the Literature. The integrated methodology shows a good agreement between simulations and observations, confirming the viability of the proposed hybrid methodology for the large-scale assessment of masonry buildings, providing an effective strategy to plan mitigation and rehabilitation interventions.

Comparison of seismic fragility of RC moment-resisting frame structures designed according to Chinese and Indian code

Seismic fragility analysis is a method used to evaluate the vulnerability experienced by structures when subjected to earthquakes. In this study, the seismic performance of 18 reinforced concrete moment-resisting frame structures designed according to Chinese code and Indian code is analyzed. A parametric study is conducted by varying the height of the building and the type of soil on which the building is constructed. Nonlinear time history analyses are conducted to develop fragility curves for four different damage levels: fully operational, operational, repairable, and collapse prevention. Linear regression analysis is conducted to correlate the engineering demand parameter (maximum inter-story drift) and the intensity of an earthquake (peak ground acceleration). The results show that the structures designed according to the Indian code experience higher story drift than those designed according to Chinese code, making them more vulnerable to the same earthquake intensity.

Machine Learning-based Seismic Fragility Curves for RC Bridge Piers

A significant part of ongoing studies in the field of earthquake engineering is directed toward the seismic risk assessment of buildings and infrastructures at a territorial scale. This task is usually accomplished by grouping the structures into homogenous classes in terms of typology, for which seismic fragility curves are then obtained for different limit states via numerical simulations or from the statistical analysis of observational data when available. Particularly, the development of typological fragility curves for bridges under earthquake is useful for assessing the reliability and resilience of transportation networks in seismic areas and can be also effective decision-making support. Within this framework, the proposed study establishes a machine learning-based paradigm for the closed-form prediction of the main statistical parameters required to obtain relevant seismic fragility curves for reinforced concrete bridge piers. Initially, a huge training dataset has been obtained by Monte Carlo simulations and displacement-based bridge pier assessments by assuming data representative of the Italian highway transportation network. Next, symbolic nonlinear regression formulae for estimating the main statistical parameters of seismic fragility curves have been generated. With the aid of those formulae, the effort of calculating the seismic fragility curves is greatly reduced since the corresponding main statistical parameters can be directly calculated from a set of commonly available attributes. Therefore, the proposed study provides a helpful tool for the rapid preliminary assessment of damage and risk level of existing highway transportation networks exposed to seismic hazards.

Adaptive knowledge-based seismic risk assessment of existing reinforced concrete buildings using the SLaMA method

This paper presents and discusses the ongoing developments towards the definition of a multi-knowledge level seismic assessment procedure for large-scale seismic risk applications. The procedure involves the analytical-mechanical SLaMA (Simple Lateral Mechanism Analysis) method and allows for an adaptive and updatable assessment of the seismic performance of buildings accounting for different data acquisition (knowledge) levels. By coupling this approach with vulnerability assessment survey forms, a range/domain of expected capacity curves of a structure can be obtained and used to evaluate the seismic safety and the expected economic losses according to the state-of-the-art procedures in literature. Moreover, the results of the analytical assessment method can be used to develop fragility curves through simplified spectrum-based procedures. Combining the results of the fragility analysis with the hazard analysis, the seismic risk of a structure can be assessed in terms of Mean Annual Frequency (MAF) of collapse, as well as in terms of Expected Annual Losses (EAL). The proposed SLaMA-based approach is illustrated for an existing reinforced concrete building. Results confirm the effectiveness of the methodology for seismic-risk assessment studies at large scale, thus overcoming the issue related to limited building information, yet allowing for a continuous update of the “digital twin” model as further data/information becomes available.

Seismic Fragility Assessment of Irregular High Rise Buildings using Incremental Dynamic Analysis

The construction of high rise buildings is common in city areas. These buildings may be irregular because of aesthetics or other requirements. As Nepal lies in a seismically active region these irregular high rise buildings may not perform well during earthquakes. Two existing irregular high rise buildings are taken as case study buildings that had pre-existing torsion. Shear walls are added to the building at the required location to minimize torsion in the buildings. The objective of the study is to determine the performance of building with and without torsional irregularity. The seismic performance of all the buildings is carried out by taking seven pairs of ground motions using nonlinear time history analysis. These ground motions are scaled to the required intensity to develop incremental dynamic analysis (IDA) curve. These IDA curves are used to develop fragility curves to access the performance in the buildings. The result from the analysis showed that performance in one building improved by 35% and in another by 70% at the peak ground acceleration (PGA) of 0.35g.

Development of fragility curves for seismic vulnerability assessment: The case of Philippine General Hospital spine building

Development of fragility curves for seismic vulnerability assessment: The case of Philippine General Hospital spine building

Seismic Fragility Analysis of an Existing Bridge Pier

The main objective of this paper is to develop the fragility curves for an existing bridge having circular pier by static nonlinear analysis (Pushover Analysis). In this study, a cantilever circular bridge pier which is located in Assam, a highly seismic zone in India is considered for development of seismic fragility curve. Capacity of the bridge has been determined by Pushover analysis of bridge pier and demand parameter of the bridge were obtained by using ATC 40 Capacity Spectrum method and IS 1893:2016 (Part 1) along with IRC 6:2017. Civil Software SAP 2000 version 20 is used to analyze the bridge pier. The fragility curves of the pier have been constructed assuming a lognormal distribution. The evaluation results presented here describes the probabilistic seismic failure of the bridge pier and its capacity to meet the desired performance level.

An unsupervised machine learning based ground motion selection method for computationally efficient estimation of seismic fragility

AbstractIn the context of performance‐based earthquake engineering (PBEE), response‐history analysis is currently considered an analytical tool for developing fragility curves. Typically, this involves subjecting a structural system to a large number of ground motion records (GMRs) representing seismic hazards at a site of interest and may be a time‐consuming task. To address this computational challenge, this study proposes a method for selecting a representative subset of GMRs that enables the reproduction of the fragility curve of the general GMR set. In this method, dimension reduction techniques are used to preferentially extract the principal features of earthquake intensity measures, which are applied to construct the feature space. Then, the divisive hierarchical clustering technique is applied to the feature space to obtain a subset of GMRs from the general set until the fragility curve converges. The performance of the proposed method is successfully demonstrated through various numerical examples that include a wide class of single‐degree‐of‐freedom systems and two steel‐frame buildings. The results confirm that the seismic hazard at a given site represented by a general GMR set can be covered in structural fragility estimation using a representative subset of GMRs selected based on the proposed method. The proposed method could contribute to significantly reducing the computational costs for structural fragility estimation without compromising the accuracy.

Development of seismic fragility curves for RC/MR frames using machine learning methods

Development of seismic fragility curves for RC/MR frames using machine learning methods

Effect of Inadequate Lap Splice Length on the Collapse Probability of Concrete wall Buildings in Malaysia

Background: In recent decades, Malaysia has shown a significant increase in the number of constructed high-rise buildings due to rapid urbanization and an increase in its population. However, due to the country's low seismicity, the majority of such tall buildings and infrastructures have not been designed against seismic actions. Therefore, they do not comply with the required seismic detailing and often suffer from inadequate lap splice length. After the 2015 Sabah earthquake that imposed significant damage to public buildings, the seismic vulnerability of buildings in Malaysia received increasing attention. As a result, researchers have tried to quantify the seismic vulnerability of buildings in Malaysia through the development of fragility curves. Objectives: In Malaysia, most developed seismic fragility curves for buildings have not taken into account the effect of inadequate lap splice length. Therefore, this study investigates to what extent an inadequate lap splice length can alter the concrete wall buildings’ probability of collapse. Methods: Two 25-story concrete wall buildings with an identical plan but different parking levels were selected. Fifteen natural far-field earthquake records were used in the incremental dynamic analysis to calculate the inter-story drift demand and capacities. The inelastic response of beams and columns was simulated through the lumped plasticity model, and that of concrete walls and slabs was taken into account through the fiber-based distributed plasticity model. The effect of inadequate lap splice length in columns was simulated in the finite element models using the proposed method in ASCE/SEI 41-17 code. The developed fragility curves were compared with those established by other researchers for the same buildings. Results: It was observed that seismic-induced damage mostly concentrated on the columns of parking levels while the concrete walls remained in the elastic region. The obtained inter-story drift capacities were all less than 2%. Besides, the inter-story drift capacities of interior frames were less than half of exterior frames. The exterior frame of the building with three parking levels exhibited a larger probability of exceeding the CP limit state than the interior frame. A similar observation was made for the building with five parking levels when the PGA was more than 0.25g. Moreover, the probability of exceeding the CP limit state of the exterior frame with three parking levels was significantly more than that of the exterior frame with five parking levels. A similar observation was made for the interior frames when the PGA was larger than 0.2g. Furthermore, the conducted comparison showed that an inadequate lap splice length could increase the concrete wall buildings’ probability of collapse between 38 to 89%. The increase in the collapse probability of the interior frame with five parking levels was almost twice that of the exterior frame. Conclusion: It was concluded that the inadequate lap splice length could significantly reduce columns’ rotational capacity and result in brittle failure mode and limited residual strength. Besides, the inadequate lap splice length of columns reduced the inter-story drift capacity of investigated buildings and significantly increased their probability of collapse. Therefore, it was strongly suggested to include the effect of inadequate lap splice length in the finite element models when conducting seismic vulnerability studies.

Development of Fragility Curves for the Underground PVC Water Distribution Pipes in Quezon City and Damage Estimation under a Magnitude 7.2 Scenario Earthquake

Quezon City is traversed by the West Valley Fault System (WVFS) that has the capability of generating a magnitude 7.2 earthquake known as “The Big One”. It has an extensive water distribution network that is very susceptible to damages that will be caused by the ground shaking component of the M 7.2 earthquake. This study focuses on determining the behavior and estimating the damage of underground polyvinyl chloride (PVC) water pipes due to the M 7.2 earthquake by using appropriate empirical repair rates (RR) and developing fragility curves. The appropriate empirical RR equation was determined by comparing the results of selected PVC RR equations and the simulation using line-element modeling. The PGV ranges from 23.10 cm/s to 64.49 cm/s as determined using the Boore and Atkinson (2008) ground motion prediction equation. Using the results from the empirical and simulations methods, the equation by the American Lifelines Alliance (2001) was determined to be the appropriate empirical RR equation for the study area. The expected average repair rate of PVC is 0.05 repairs/km length of pipe or an estimated 84 total PVC pipe repairs in the city. Three fragility curves were generated showing the relationship of PGV and RR which is an important tool in estimating the underground pipe damages with respect to the M 7.2 earthquake and other future earthquakes of similar properties.