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Seismic Fragility Curves: A Review


In recent literature, one of the ways to investigate the vulnerability of existing buildings is to use fracture curves, which can have many applications before and after earthquakes. These curves are used to assess seismic hazard, prioritize structural rehabilitation, crisis management planning, and multi-risk approaches for different natural hazardous zones to estimate the amount of post-earthquake damage. This paper investigates the practices and methodologies for assessing seismic vulnerability of the existing structures, in areas of moderate to high seismicity. The study involves an extensive collection and review of analytical, empirical, expert-based and hybrid models for assessing fragility curves available in the technical literature and their evaluation according to a set of qualitative criteria in order to select the most appropriate ones for each type of structure. This paper also reveals of the most recent the fragility curves, introduces their advantages and describes the relationship between the intensity of the earth’s earthquake and the probable seismic hazard level to accurately determine the correct choice for specialists and engineers for specific performance level.

1. Introduction

Recent earthquakes have shown that the economic loss and urban resilience are closely relative to the seismic performance of existing structures, designed without considering seismic design or were built by old seismic codes, that showed an unsatisfactory behavior (Kappos and Dimitrakopoulos, 2008; Yamin et al., 2017). Thus, in order to increase the reliance of urban areas by reducing the seismic risk, strategies should be developed. In seismic risk mitigation methods, with regard to the most common types of existing such as bridges, buildings, etc., the quantitative fragility models play the key role. There are different approaches for the construction of fragility models: (a)analytical approaches, (b)empirical approaches, (c) expert opinion based approaches and (d)hybrid approaches. In this paper, all of the mentioned methods have been considered. Due to the importance of the topic, a significant number of studies were developed and published in the last years(Lee and Moon, 2014; Muntasir Billah and Shahria Alam, 2015). Assessing seismic vulnerability of the existing structures, in areas exposed to high seismicity. The study involves an extensive collection and review of analytical, empirical, expert-based and hybrid models for assessing fragility curves available in the recent technical literature and their evaluation according to a set of qualitative criteria in order to select the most appropriate ones for each type of structure. This paper also reveals of the most recent the fragility curves, introduces their advantages and describes the relationship between the intensity of the earth’s earthquake and the probable seismic hazard level to accurately determine the correct choice for specialists and engineers for specific performance levels.

Structure damages can be related to structure displacement or drift. Drift is normally used as parameter to estimate the performance level of a building structure(Hou et al., 2018). Drift can be considered performance-based seismic design (PBSD), which is an approach to earthquake-resistant seismic design. Drift can be described by considering the maximum allowable damage state in identifying the performance level (Hokmabadi, Fatahi and Samali, 2012). It can also be expressed as the maximum desired extent of damage to a structure under a specific earthquake design level.

The drift performance level varies depending on the guidelines that result from intensive research. For example, FEMA-273(FEMA 273, 1997) classifies the performance level into four categories, namely operational phase (OP) with 0.5% drift, immediate occupancy (IO) with 1.0% drift, life safety (LS) with less than 2.5%drift, and collapse prevention (CP)with more than 2.5% drift. The PBSD is incorporated with incremental dynamic analysis (IDA) to determine the structure drift and develop the structure fragility curve. The fragility curve is a log-normal function that expresses the probability of reaching or exceeding a specific damage state. The fragility curve is a highly useful method in predicting the extent of probable damage. It can describe the probability of a structure being damaged beyond a specific state when subjected to different levels of ground shaking (Ibrahim and El-Shami, 2011; Silva et al., 2014a).

The fragility curve was introduced to provide accurate predictions of damage to structures and non-structures. This method is unique because every developed curve depends on ground motions. Numerous researchers have developed fragility curves for different structure types (Bakhshi and Asadi, 2013; Farsangi et al., 2014; Hancilar et al., 2014; Manafpour and Moghaddam, 2014; Moharrami and Amini, 2014; Negulescu et al., 2014; Siqueira et al., 2014).

1.1 HistoricalBackground

Many previous studies, such as those of (Kiremidjian A.S., 1992; Akkar, Sucuoǧlu and Yakut, 2005; Kumitani and Takada, 2009; Frankie, Gencturk and Elnashai, 2012; Bakhshi and Asadi, 2013; Modica and Stafford, 2014; Silva et al., 2014a; Pragalath, DAVIS and SARKAR, 2015; Cutfield, Ryan and Ma, 2016; Joy and Thampsan, 2016) present a brief historical background of  fragility curve. Fragility curves are defined as the probability of reaching or exceeding a specific damage state under earthquake excitation.

The general equation to develop fragility or conditional probability is expressed by (Muntasir Billah and Shahria Alam, 2015)



LS is the limit

state or damage state (DS),

IM is the intensity measure (ground motion), and

Y is the realized condition of ground motion IM.

Various equations were derived from previous research (Table 1). However, all the equations are based on Eq. (1), which is a general equation for generating a fragility curve.

Although most of these studies used different equations to generate their versions of the seismic fragility curves (Table 1), most researchers such as (Serdar Kirçil and Polat, 2006), and (Ibrahim and El-Shami, 2011) used Eq. (2) in their studies. This equation is the simplest one in the group. Yamaguchi and Yamazaki (2000) tested Eq. (2) for different types of structures and found it to be suitable for use in all structural types. This equation is given below:





the standardize normal distribution,

k is the mean of ln x, and

1 is the standard deviation of ln x.

The fragility curves are established to provide a prediction of potential damage during an earthquake. These curves represent the seismic risk assessment and are used as an indicator to identify the physical damage in the strongest mainshock. Apart from the mainshock, probability aftershock must also be investigated to decide whether or when to permit re-occupancy of a building. The fragility function is also directly used to reduce damage cost and loss of life during a seismic event. Therefore, fragility curves can be used as a decision-making tool for both pre- and post-earthquake situations. Moreover, these curves may help develop future local code provisions.

Two main components in the probabilistic seismic risk assessment have been identified. These components include information about ground motion hazard on the location of structure and fragility knowledge with respect to the intensity of the ground motion.(Polese et al., 2013) stated four important factors available for a large database, which include the number of stories, age of construction, regularity (in plan, elevation, and in-fill), and position of building in the block. (Silva et al., 2014a) proposed vulnerability curves using the HAZUS tool (HAZUS, 1999) for risk assessment. The curves were created specifically for buildings in the US.

2.1       Structural Types

Fragility curves were discussed based on two types of structures, namely, steel, and reinforced concrete. Most studies covered steel and reinforced  concrete structures. Many studies developed fragility curves for infrastructures, including those of (Shinozuka et al., 2000; Alessandri, Giannini and Paolacci, 2011; Siqueira et al., 2014; Muntasir Billah and Shahria Alam, 2015). However, the fragility curves for buildings are categorized into three types. These types are low-, mid-, and high-rise buildings based on the number of stories (Table 2).

The important factors of vulnerability, which are also available for large data- bases, include a number of stories, age of construction, regularity in plan and elevation, infill regularity, and building position in the block(Polese et al., 2013) . Thus, classifying buildings is one of the significant factors that must be considered in developing fragility curve. Differences in materials, height, and number of bays also result in different shapes of vulnerability curves. Researchers from different

Table 2 Classification of Building by Number of Stories

Presented by Building Classification
Low-rise Mid-rise High-rise
Number of stories
Singhal and Kiremidjian (1996), Akkar et al. (2005), Uma et al. (2011) 1–3 4–7 8 and up
Modica and Stafford (2014), Silva et al. (2014a) 1–3 4–6 7 and up
Hancilar et al. (2014) 1–4 5–8 9 and up
Hosseinpour and Abdelnaby (2017) 3 7 12

countries have developed their respective versions of the curve. Table 3 shows the synopsis of fragility analysis performed by several researchers.

2.2       Earthquake Records

Ground motion records play the main role in establishing fragility curves. Selecting an appropriate ground motion and scaling the ground motions are very important in generating this curve. If the ground motion is randomly scaled up to a specific spectral acceleration, Sa, at a period, T, over conservative structural response may occur (Baker, Lin and Haselton, 2014).

A few parameters must be considered in selecting ground motion, including event magnitude, peak ground acceleration (PGA), distance between epicenter/ source and affected area, and soil type (Nazri and Alexander, 2012). In addition, ground motion characteristics must be considered to obtain accurate prediction and to minimize the dispersion of the analytical behavior of buildings. Ground motion characteristics that must be considered include, ground motion intensity, spectral shape, duration, frequency content, near-fault, amplitude, and number of cycles (Ibrahim and El-Shami, 2011; Ruiz-García and Negrete-Manriquez, 2011; Song, Li and van de Lindt, 2014).

The selected ground motion must come from previously recorded earthquake events. Ground motion can be selected from certain websites, such as Pacific Earthquake Engineering Research (PEER) NGA database website, Consortium of Organization for Strong Motion Observation System, or K-NET. (Silva et al., 2014a) list other websites where ground motion records can be obtained, including the European Strong Motion database, the French Accelerometric Network, and the Swiss Earthquake Database.

The suitable number of ground motions depends on the application and structural response prediction. Two types of ground motions are considered as fore- shocks: near-field site and far-field site. Researchers discuss a few important factors in selecting ground motion. For far-field site, the important factors include spectral shape over the period range of interest, magnitude, site-to-source distance, and hazard curve at a period, T. Meanwhile, for near-field site, the factors to be

considered include spectral shape and the possible presence of velocity pulses. Table 2.4 presents an overview of recommendations for selecting and scaling ground motion (Whittaker et al., 2012).

Apart from obtaining data from the aforementioned databases, ground motion records can also be generated based on the equation. For example, (Sudret, Mai and Konakli, 2014) generated ground motion records from several equations. The procedure to simulate synthetic ground motion is briefly explained because stimulating synthetic ground motion usually takes too long. In their study, they concluded there are three temporal parameters, three spectral parameters, and a standard Gaussian random vector of size that must be considered to generate a seismic model. Compared with synthetic ground motion, real accelerograms are more widely used as ground motion records and then scaled to cover the range of ground motion level that might occur (Ay and Akkar, 2014).

(Jones and Reasenberg, 1996) reported that earthquakes occur in clusters, that is, when one earthquake strikes, another earthquake will occur in the nearby locations. According to (Uhrhammer, 1986), events that only occur in a zone approximately parallel to the fault rupture or surround the main events are considered foreshocks or aftershocks. In an earthquake event, the magnitude can be classified into three terms, namely, foreshock, mainshock, and aftershock. The largest magnitude is called mainshock, whereas the earthquakes that occur before and after the main- shock are called foreshock and aftershock, respectively. However, mainshocks are often redefined as foreshock if a subsequent earthquake in a cluster has a larger magnitude.



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