Urban Seismic Risk Analysis Using Empirical Fragility Curves for Kerend-e-Gharb After Mw 7.3, 2017 Iran Earthquake

This study provides the seismic risk map of the small mountain city of Kerend-e-gharb. This innovative study evaluates the existing methods and formulations with the effects of a devastating earthquake using empirical fragility curves. A seismic vulnerability map is developed at the urban block-scale at a Geographic Information System for a variety of steel, reinforced concrete, confined masonry, unreinforced masonry, and adobe residential buildings. The estimated seismic damages are validated by comparing them with the surveyed building damages in the Sarpol-e-zahab earthquake. Moreover, the damages to the population, including the probability of homelessness, death, severe injuries that need immediate hospital treatment, moderate injuries that require hospital treatment, and light injuries without hospitalization, are assessed. This research also investigated the economic losses and estimation of debris. Finally, the mean damage index map is presented. The mean damage index map is modified due to renovation and retrofitting at higher damage levels, and it is increased at moderate damage levels that have not been structurally improved. The results of this study can be used in seismic crisis management planning in natural hazards to achieve a sustainable city.


Introduction
Seismic risk is the combination of hazard, vulnerability, and value of an element or area affected by an earthquake. This seismic vulnerability is defined as the probability of a particular damage state due to the earthquake event during a specified return period. This can be seen in a Geographic Information System (GIS) framework, which displays the estimated damage from a particular earthquake. Although these definitions only apply to structural features, building damage can result in population and economic loss.
On an urban scale, the goal of seismic risk assessment could be urban macro-management, prioritization of retrofitting vulnerable buildings, and crisis management. This assessment is a scientific tool to reduce urban seismic risk and earthquake crisis management to provide temporary accommodation centers, hospital services, insurance, and debris depots. Statistics and information on residential buildings and essential structures are often crucial in large earthquake-prone cities.
One of the essential tools in seismic risk assessment is fragility curves. Most of the fragility curves have been developed based on the analytical method on the specific type of structure or indirect method from rapid urban assessment data. There are rare cases of seismic risk assessment on an urban scale that have been studied in a city that has previously been devastated by a major earthquake to validate common methods and hypotheses. This was conducted in the current study, which evaluated the seismic risk of Kerend-e-gharb, one of the cities devastated by the 2017 November 12 (Mw 7.3) Sarpol-e-zahab earthquake. The results are managed using a GIS tool.
Among a list of the Sarpol-e-zahab earthquake-affected cities, this city is selected because it is located on rocky land and experienced the maximum acceleration equal to peak design acceleration based on the IRSt2800 (2015) standard. The seismic damages of various types of structures are studied, including steel (ST), reinforced concrete (RC), confined masonry (CM), unreinforced masonry (URM), and adobe (Ad). Empirical fragility curves, developed on the damage data of the 2017 Sarpol-e-zahab earthquake in the large area affected by the earthquake, were the basis for seismic vulnerability, structural and population damage, and economic loss assessment.

The urban area
Kerend-e-gharb is the capital of Dalahu County in Kermanshah Province, Iran (Figure 1a). At the 2016 census, its population was 7,798, in 2,349 families. It has an area of about 2.2 km 2 and an average density of 3,545 inhabitants per km 2 . The new city of Kerend-e-gharb (Figure 1b (Hessami et al., 2003) (yellow lines in Figure 1a), are the earthquake triggers in Kermanshah province. A rupture caused the 2017 Sarpol-e-zahab earthquake (Ashayeri et al., 2019;Ashayeri et al., 2020;Ashayeri et al., 2021) in the MFF.
The Sarpol-e-zahab earthquake caused a peak ground acceleration (PGA) of 283 gals in this city.
The accelerograms of this earthquake were recorded in the KRD station of Iran Strong Motion Network (ISMN, provided by Road, Housing, & Urban Development Research Center). Since this event's peak ground acceleration (PGA) is equal to the one suggested by the IRSt2800 (2015) standard for this city, this case is fit to assess the urban seismic risk.  The pie chart shown in Figure 2b shows the percentage of each of these categories. Recently developed areas in the southeast and the west generally are covered with ST and RC structures. The higher amount of non-engineered buildings, the higher the seismic vulnerability.
The seismic vulnerability of urban blocks is investigated in the next section using fragility curves.

Seismic vulnerability assessment
Seismic fragility curves represent the probability of damage in specific ground motion. Fragility curves are defined as the probability of exceeding a certain damage level or state, Dk (k = 0, 1, 2, 3, 4, 5, or k=0, 1, 2, 3, 4). They are influenced by the parameter of the specific distribution function (i.e., beta distribution, binomial distribution, or standard normal distribution). These fragility curves allow estimating the damage probability for the specific structural typology. The European Macroseismic Scale (EMS-98) (Grünthal, 1998) with five damage states is used in this study.
These states of damages are defined by Grünthal (1998) Biglari et al. (2021), for confined masonry and unreinforced masonry structures were designed by Biglari and Formisano (2020), and for adobe structures were given by Omidvar et al. (2012).
The vulnerability index is a normalized score between 0 and 1 that presents the seismic building behavior. The closer the index is to 1, the more seismic vulnerable the structure is. Meanwhile, the closer the index is to zero, the less seismic vulnerable the structure is. Table 1 shows the vulnerability indices (Vi) for different structural typologies. As shown in Equation 1 (found in Milutinovic and Trendafiloski (2003)), the discrete probability of damage state k, P(Dk), are derived from the difference of cumulative probabilities PD(k).  Omidvar et al. (2012) As an overview, Figure 4 shows the number of buildings suffering each level of damage. This indicates that most of the buildings of this city in the face of PGA=283 gals suffer slight (D1) damage state to moderate (D2) damage states. These calculations were performed on a block scale.  Here eight different typology buildings from (Kalantari et al., 2019) have been selected for validation of the results. Figure 6 shows the location of target buildings. Damage caused by the Sarpol-e-zahab earthquake in these buildings has been collected and compared to the predictive damage derived from fragility curves. Table 2 presents the typologies of the target buildings along with the observed damage grade and the most probable damage grade determined from Figure 5.
It shows that there is a good agreement between the fragility curves analysis results and the earthquake experienced. The photo of the building shown in Figure 6 belongs to case No. 2. This building is a five-story steel structure, which in one direction has braced frames and in a perpendicular direction has moment-resisting frames. There is no structural damage on the building due to the earthquake, and only slight non-structural damage happened. Facade stones (highlighted by yellow circles in Figure 6) have collapsed due to a lack of screwing to the back wall (damage state D1). Another example in the southeastern region of the city is a six-story steel building (No. 4). This building in one direction has braced frames and in a perpendicular direction has moment-resisting frames. There is no structural damage due to the peak acceleration of 283 gals, but slight non-structural damage has been seen on it (damage state D1). Building No. 5 is one story confined masonry structure that neither structural nor non-structural damages have at the peak acceleration of 283 gals (damage state D0). Buildings No. 6 and No. 7 are similar in typology, but Building No. 7 has more weaknesses in ceilings and walls. There is no structural damage, but slight non-structural damage happened by a recorded earthquake (damage state D1). Finally, building No. 8 is an example of an adobe structure that, surprisingly, did not have any structural and non-structural damage after this earthquake (damage state D0).  It is possible to define the structural collapse probability and unusable structure probability at the block scale in the GIS map. In Italy, Bramerini et al. (1995) proposed two expressions, illustrated in Equations 2 and 3, for estimating collapsed and unusable buildings, respectively.
The homeless probability can be used for a post-earthquake emergency plan based on the people's social culture. This can help determine the number of temporary shelters needed to house the homeless people, the location of temporary accommodations, and the store of the basic facilities (e.g., drinking water, dry and canned food, heating appliances, clothes, and blankets). Often, after an earthquake, homeless people tend to live as close to their former damaged home to protect the remnants of their home appliances.

Figure 8 Homeless probabilities per block
On the other hand, to evaluate the probability of deaths and injuries to the population caused by an earthquake, the casualty model presented by Coburn et al. (1992) is applied at blocks. The casualty model of Coburn et al. (1992) was presented based on the collected worldwide database of 1100 earthquakes that caused life loss.
In this model, the number of casualties (Ks) depend on the number of collapsed buildings (D5) and is directly proportional to parameters such as; Equation 5 presents the casualty model given by Coburn et al. (1992):  Coburn et al. (1992). Finally, the M5 factor is the same proposed by Coburn et al. (1992) for a community capable of organizing rescue activities. severely injured, moderately injured, and lightly injured people. The results show that the highest probability of dead and unsavable people is in the northeastern and central parts of the city. In these areas, in addition to recommending the retrofitting of buildings, the construction of medical centers and rescue stations can also aid with on-time rescue and risk reduction. Figure 9 Distribution of the probability of a) dead and unsavable people, b) severely injuries, c) moderately injuries, and d) lightly injuries per block.
The post-earthquake number of dead, verify the prediction made. The earthquake at Sarpol-ezahab caused no casualties in this city. On the other hand, the probability of death in this city is less than 1.4%.

Economic cost
The construction sector in Iran has a very high inflation rate. Inflation has risen in recent years as a result of economic crises in Iran caused about by sanctions. In general, economic loss is defined as the cost of replacing damaged buildings with ST or RC buildings constructed by the latest earthquake-resistant standards. The cost of constructing a ST or RC building per square meter (excluding land cost) in the years following the Sarpol-e-zahab earthquake (from 2017 to 2021) has been incredibly diverse (for a standard building from about ten million Rials to forty-five million Rials).Two economic cost scenarios are evaluated; the first is the absolute (and subsequently the total) cost in 1000 million Rials, and the second is the relative economic cost. Lantada et al. (2010) (as Equation 6) suggested that the absolute economic cost in 1000 millions of Rials due to the damage of residential building contents should be increased fifty percent to estimate the total cost (TCost).
where CS(k) is the repairing costs due to the damage state k (absolute cost); VC is the cost per unit area; Area(j) is the area of the building j; PS(k,j) is the probability of damage level k on the building j; and RC(k, j) is the percentage of the replacement cost per square meter for damage level k in building j. The values for RC(k,j) are given by ATC-13 (1985) for each damage level and are taken as 0% for no damage (D0), 2% for slight damage (D1+D2), 10% for moderate damage (D3), 50% for severe damage (D4), and 100% for complete damage (D5).
A relative economic cost RCost is calculated by Equation 7.
(7) Figure 10 shows the economic cost for Kerend-e-gharb city in block scale for both relative ( Figure   10a) and absolute total (Figure 10b) expressions. The replacement cost is assumed 22 million Rials per square meter to determine the total cost. As expected, areas with higher seismic vulnerability have a higher economic loss.
where Area(j) is the floor area of building typology j; EDF(i,j) is the expected debris fraction of debris type i due to structural damage for building typology j; P(k,j) is the probability of structural damage level k for building typology j; and DF(i, k, j) is the debris weight fraction of debris type i for building typology j in structural damage level k. Table 4 shows the unit weights of different building materials used in this study adapted from HAZUS (1999). Figure 11 shows the debris amount per block.  Figure 11 Debris per block in tons

Prediction of the mean damage index in the repetition of the design earthquake
The most likely damage state of the building (i.e., mean damage grade, μD) is defined as mean damage index, DIm. DIm is a single parameter used for analyzing and describing the damage distribution which has been adopted to represent the five damage states by Lantada et al. (2010) as described in Equation 9.
where k takes the values 0, 1, 2, 3, 4, and 5 for the damage states, and P(Dk) represents the probability of occurrence for the damage state k. Figure 12a shows the mean damage index per block just after Sarpol-e-zahab 2017 earthquake predicted by empirical fragility curves at design earthquake based on the IRSt2800 (2015) standard. A study of mainshocks and aftershocks effects on the structures that have experienced strong ground motions show that exposure to repeated earthquakes may lead to damage accumulation and progressive collapse. In most cases, previous earthquake effects are ignored when calculating the seismic capacity of existing structures. As a result, the probability of structural damage from many mainshock events or aftershocks after the mainshock is considered.
The performance of structures that have experienced strong ground motions in a very short duration after the mainshock is different from when these ground shakings occurred years after the mainshock. As a result, the buildings' performance four years after the Sarpol-e-zahab earthquake differs from their performance before the severe ground motion and in the immediate aftermath of the mainshock. The performance was increased by renovation and remediating interventions for very heavy and destructed damaged buildings (D4 and D5). The performance remains constant for slight and moderate damage buildings (D1 and D2) (Luco et al., 2011). Hence, the previous fragility curves can be used to estimate the prospective damage. The performance of buildings that experienced the heavy damage level (D3) without any structural interventions decreases.
Therefore, the mean damage index of each block needs to be modified depending on the previous earthquake experience. The mean damage index for D4 and D5 damage states is reduced to D0 since these buildings are renovated and retrofitted. The mean damage index for D1 and D2 remains constant and is calculated by previous empirical fragility curves. If the deformation is permanent and structural capacity is reduced from D2 to D3, the mean damage index for D3 increases by the same amount as the difference between the mean damage index of D3 and the mean damage index of D2. Figure 12b shows the prospective design's mean damage index per block four years following the earthquake by taking into account the city's redevelopment and retrofitting. Although the situation is more vulnerable for D3 damage state buildings with permanent damage caused by the previous earthquake that were never retrofitted, it is expected that the vulnerabilities would reduce in many locations as a result of the rehabilitation and retrofitting interventions. Most of these vulnerable blocks are in the northeastern part of the city. Figure 12 Mean damage index per block: a) 2017 November 12 th earthquake; b) prospective design earthquake

Summary and Conclusions
In this study, the seismic risk of a small mountain city near the western border of Iran, which was affected by the 2017 Sarpol-e-zahab earthquake, was investigated. It includes the seismic vulnerability assessment of buildings at the urban block scale using empirical fragility curves derived from damages under the above-mentioned devastating earthquake. A Geographic Information System (GIS) was utilized to store and display the data. The results have complete agreement with the damage caused by the Sarpol-e-zahab earthquake.
Moreover, the damage to the population, the economic losses, and the debris were assessed.
Finally, the mean damage index for each block in the Sarpol-e-zahab earthquake and the most probable design earthquake in the future were provided. The findings show that the city's northeast is at high seismic risk, requiring special attention to this area before another severe earthquake.
This study presents the vulnerability of the city blocks and the distribution of human casualties for the emergency management, the rescue, and the provision of necessary treatment systems in each area before the earthquake for preparing a sustainable urban plan.