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Article

Rapid Urban-Scale Building Collapse Assessment Based on Nonlinear Dynamic Analysis and Earthquake Observations

by
Mahnoosh Biglari
1,*,
Hiroshi Kawase
2 and
Iman Ashayeri
1
1
Civil Engineering Department, School of Engineering, Razi University, Kermanshah P.O. Box. 6714967346, Iran
2
General Building Research Corporation of Japan, Suita 565-0873, Japan
*
Author to whom correspondence should be addressed.
Buildings 2024, 14(10), 3321; https://doi.org/10.3390/buildings14103321
Submission received: 10 September 2024 / Revised: 17 October 2024 / Accepted: 18 October 2024 / Published: 21 October 2024
(This article belongs to the Special Issue Seismic Resistance and Vulnerability Assessments of Building Structures)
Browse Figures
Figure 1
<p>Concept map for the damage ratio analysis and calibration of the yield shear strength ratio.</p> "> Figure 2
<p>Zoning of the city based on the distribution of synthesized strong motions.</p> "> Figure 3
<p>Seismic parameters extracted from surface ground motion records, (<b>a</b>) peak ground acceleration, PGA, (<b>b</b>) peak ground velocity, PGV, (<b>c</b>) sustained maximum acceleration, and (<b>d</b>) velocity spectrum intensity.</p> "> Figure 3 Cont.
<p>Seismic parameters extracted from surface ground motion records, (<b>a</b>) peak ground acceleration, PGA, (<b>b</b>) peak ground velocity, PGV, (<b>c</b>) sustained maximum acceleration, and (<b>d</b>) velocity spectrum intensity.</p> "> Figure 4
<p>Observed damage ratio (ODR), (<b>a</b>) steel buildings, (<b>b</b>) RC buildings, and (<b>c</b>) masonry buildings.</p> "> Figure 4 Cont.
<p>Observed damage ratio (ODR), (<b>a</b>) steel buildings, (<b>b</b>) RC buildings, and (<b>c</b>) masonry buildings.</p> "> Figure 5
<p>Nonlinear relationships at the basement of standard models.</p> "> Figure 6
<p>Comparison of CDR and ODR with α = 1 (<b>a</b>) steel and RC buildings, and (<b>b</b>) masonry buildings.</p> "> Figure 7
<p>CDRs with α by considering all zones (<b>a</b>) steel buildings α = 0.58, (<b>b</b>) RC buildings α = 0.92, and (<b>c</b>) masonry buildings α = 4.05.</p> "> Figure 7 Cont.
<p>CDRs with α by considering all zones (<b>a</b>) steel buildings α = 0.58, (<b>b</b>) RC buildings α = 0.92, and (<b>c</b>) masonry buildings α = 4.05.</p> "> Figure 8
<p>Comparison of CDR and ODR with α values presented in <a href="#buildings-14-03321-t005" class="html-table">Table 5</a> (<b>a</b>) category I, and (<b>b</b>) category II.</p> "> Figure 9
<p>CDRs considering two categories I and II for zones according to α presented in <a href="#buildings-14-03321-t005" class="html-table">Table 5</a>: (<b>a</b>) steel buildings, (<b>b</b>) RC buildings, and (<b>c</b>) masonry buildings.</p> "> Figure 9 Cont.
<p>CDRs considering two categories I and II for zones according to α presented in <a href="#buildings-14-03321-t005" class="html-table">Table 5</a>: (<b>a</b>) steel buildings, (<b>b</b>) RC buildings, and (<b>c</b>) masonry buildings.</p> "> Figure 10
<p>Comparison between CDRs and ODRs (<b>a</b>) steel buildings, (<b>b</b>) RC buildings, and (<b>c</b>) masonry buildings.</p> ">
Versions Notes

Abstract

:
Rapid damage assessment after an earthquake is crucial for allocating and prioritizing emergency actions. Building damage due to an earthquake depends on the seismic hazard and the building’s strength. While it is now possible to promptly access acceleration data as seismic input through online strong motion networks in urban areas, good models are necessary to evaluate the damage in different zones of the affected area. This study aims to present a rapid method for such an urban-scale building collapse evaluation by conducting a nonlinear dynamic analysis of modeled buildings. Based on the Nagato and Kawase model, this study estimates the yield shear strength of 3-story steel buildings, 3-story reinforced concrete buildings, and 1-story masonry buildings in Sarpol-e-Zahab City after the 2017 Mw7.3 earthquake. The damage ratio is calculated through nonlinear dynamic analyses using estimated records from the main earthquake shock in different city zones. The research found that the seismic yield shear strength of steel and reinforced concrete buildings might be weaker than that of the Iranian seismic code’s standard value. Conversely, masonry-building resistance is stronger than the guidelines assumed. The constructed numerical models can be used for the rapid building damage assessment immediately after a damaging earthquake.

1. Introduction

Seismic risk management involves three phases: pre-seismic, co-seismic, and post-seismic. By following seismic codes and guidelines created by experts, evaluating and reinforcing vulnerable structures before an earthquake, and rapidly assessing the seismic impact for taking practical emergency actions during the event, the catastrophic effects of earthquakes can be reduced. Rapid assessment includes collecting and evaluating real-time ground motions and estimating the extent of seismic damage, casualties, and economic losses caused by the ground motions. This information helps search-and-rescue teams prioritize emergency actions. Furthermore, using damage evaluation functions with the site-specific design earthquake acceleration records can aid in evaluating and reducing seismic risk in urban areas.
One of the methods of seismic damage assessment on the urban scale is using seismic fragility curves (e.g., [1,2,3,4,5,6,7,8,9,10,11,12]). Seismic fragility curves show the likelihood of surpassing a certain damage threshold caused by a specific earthquake intensity or acceleration. These curves can be derived using empirical, analytical, or expert judgment methods for all types of buildings. Empirical fragility curves are created using observed structural damage data from earthquakes. The accuracy of these curves depends on the quality and quantity of the collected data. Whitman et al. [13] proposed the method after the 1971 San Francisco earthquake, using damage probability matrices and fragility curves. Since then, many researchers have refined the method using observed damage data from earthquakes (e.g., [14,15,16,17,18,19]). Analytical methods rely on numerical models of structures to predict the expected damage from ground motion. It is best to calibrate the numerical models with the fundamental frequency response of the actual structure. If that is not possible, validating the analytical fragility curves using natural earthquake damage data is essential. Various approaches have been developed for creating analytical fragility curves, such as displacement-based methods, capacity spectrum methods, and simplified mechanics-based procedures (e.g., [20,21,22,23,24,25,26,27]). Expert judgment-based methods use the knowledge of a group of experts. Verifying this method using observed data is essential. This approach is beneficial when the necessary natural earthquake damage and building inventory data are unavailable. The Applied Technology Council originally developed this method in ATC-13 [28]. Like ATC-13 [28], Italy developed a method for vulnerability assessment and damage estimation based on score assignment through the GNDT II level approach [29]. The potential damage distribution can be determined by analyzing the distribution of earthquake intensity or acceleration in urban areas and considering the building types. However, the fragility curve approach inevitably needs to improve its accuracy due to the scarcity of empirical data and the applicability for different regions other than the damaged area.
Nagato and Kawase [30] introduced an alternative approach to estimating urban scale damage by developing a prediction model for a group of buildings. This model determines the typical building’s tri-linear spring behavior based on the seismic code of the designed buildings as a standard, and the yield shear strength of groups of buildings in the same category is investigated using nonlinear dynamic analysis, then calibrated with observed damage ratios from natural earthquake events. By determining a yield shear strength ratio called α, which is the ratio of existing building yield shear strength to the yield shear strength of the standard building, it is possible to calculate the damage ratio in each zone using nonlinear dynamic analysis for the observed and reproduced ground motions at each zone. This method was used to assess the 3, 6, 9, and 12-story reinforced concrete (RC) buildings in [30], and 3, 4, and 5-story steel buildings in [31] which all were calibrated by the observed damage ratios of the 1995 Hyogo-ken Nanbu (Kobe) earthquake. This method needs to calibrate the yield shear strength ratio for all types of urban buildings. This parameter calibrates for every kind of structure using observed damage data resulting from earthquake events. Following this calibration, the method can quickly identify heavy damage or collapse by conducting dynamic nonlinear analysis of the multi-degrees-of-freedom lump mass model of the structure, utilizing either natural or synthesized earthquake ground motion records. One of the advantages of this method is that, since it is based on dynamic nonlinear analyses, the entire earthquake record motion is used to estimate damage. In contrast, methods based on seismic fragility curves only consider specific seismic parameters extracted from the seismic ground motion in damage assessment.
More recently, Sun et al. [32] reproduced the ground motion records of the 2016 Kumamoto earthquake in different areas of downtown Mashiki in Kumamoto Prefecture. They utilized nonlinear dynamic analysis, to estimate the damage ratio of urban wooden buildings considering the construction age. Subsequently, they compared these estimates with the observed damage ratio distribution and showed that their model could successfully explain the damage ratio distribution in downtown Mashiki. Furthermore, Biglari et al. in [33] employed the α ratio and building parameters from [30] to conduct nonlinear dynamic analyses of main shocks and sequential aftershocks on 3, 6, and 9-story RC buildings in Japan. Their objective was to establish sequential seismic fragility curves.
By following the procedure of these works, we investigated the applicability of the damage prediction scheme specific to Iranian buildings. This study used field surveys and aerial photographs to identify what was heavily damaged or collapsed by the Mw7.3 2017 earthquake in Sarpol-e-Zahab City. The seismic microzonation and ground motion records presented in [34,35] were analyzed to determine the damage ratio for different types of buildings. The analysis involved 3-story steel buildings, 3-story RC buildings, and 1-story masonry buildings, the city’s most popular types of buildings. Adjusting the yield shear strength ratio α can make the calculated damage ratio (CDR) match the observed damage ratio (ODR). As a future application, the proposed models with the determined α value can be used for similar nonlinear dynamic analyses in similar urban areas to assess collapsed or heavily damaged building distribution. After an earthquake, it is crucial to quickly identify the most affected areas and send rescue teams there. The first few hours after an earthquake are crucial for rescuing people trapped under debris. Nowadays, we have online seismographs that can immediately send recorded data to crisis management centers. Assessors can then use the data to quickly analyze the damage to urban buildings and identify those that may have suffered heavy damage or collapse. This method uses a simplified lumped mass model, allowing quick analysis despite its complexity. As a result, this model can be used as a first step in predicting damage after an earthquake. Figure 1 illustrates the research concept map and the methodology flowchart.

2. Strong Ground Motions

Comparing the damage ratio calculated by nonlinear dynamic analysis to the observed damage ratio can help calibrate buildings’ yield shear strength ratio. The observed damage ratio following a devastating earthquake is a suitable benchmark for this evaluation.
The 2017 Sarpol-e-Zahab earthquake, Mw7.3, is a valuable source of information for studying the impact on steel, RC, and masonry buildings. This seismic event was caused by the Mountain Front Fault (MFF) running along the Iran-Iraq border with a thrust focal mechanism. Seismic microzonation of Sarpol-e-Zahab City was presented in [35] based on the array and single station microtremor measurements data at 77 locations conducted in [34]. The spatial autocorrelation and ellipticity curve inversion techniques were used to obtain the shear wave velocity profile at the measurement points and the strong motion station [34]. Consequently, the ground-level main shock motion recorded in the strong motion station SPZ (shown with a star symbol in Figure 2) was deconvolved to the bedrock level and then was transferred back to the ground level at every measurement point using the 1D equivalent linear site response analyses [34]. They reported that the PGA of the main shock at softer sites, e.g., AR3, was estimated to be higher than 750 cm/s2, while it was estimated at rock outcropping sites about 450 cm/s2.
Sarpol-e-Zahab was divided into 14 district zones from 35 small Statistical Center of Iran (SCI) districts based on the peak ground acceleration (PGA) in different parts of the city during the earthquake (Figure 2). The naming of the zones was selected similarly to the microtremor survey points in [34]. The observed strong motion station was plotted with a white star, and representative points of ground motion estimation in each zone were plotted with white circles. Figure 3 shows the distribution of seismic parameters extracted from the surface ground motions in different city zones. These ground motions were directly entered as input to the investigated buildings for nonlinear dynamic analysis. Consequently, the impact of the surface layers on each zone has been considered.

3. Observed Damage Ratio

The observed damage ratio (ODR) in each zone is calculated by dividing the number of heavily damaged or collapsed buildings of each type by the total number of buildings of that type. The data on the total number of buildings of each type was reported by the Statistical Center of Iran (SCI), which collected the population and housing census statistics data in 2016. All the available data is integrated into a geographic information system (GIS), represented in this study by QGIS [36].
Following the 2017 Sarpol-e-Zahab earthquake, a survey assessed the damage to buildings in each city zone. The data collected included various levels of damage to steel, RC, masonry, and adobe buildings. Moreover, Google Earth aerial photos were visually examined before and after the earthquake to ensure that all heavily damaged and collapsed cases were considered. The results were compared with damage assessment from high-resolution Worldview-2 images and semi-automated object-based image analysis from [37].
The data from 3-story steel and RC buildings and 1-story masonry buildings, which were most common in Sarpol-e-Zahab city, were used. Doubtful data were excluded from the analysis. The concentric and eccentric bracing system is the most commonly used seismic-resistant system for steel buildings, while the moment frame is the most common for RC buildings. According to a local survey, more than 80% of steel and RC buildings in the city affected by the 2017 Sarpol-e-Zahab earthquake were constructed between 2005 and 2014 and are expected to adhere to the building code of [38]. Furthermore, as Sarpol-e-Zahab is located on the border of Iraq, where buildings were reconstructed after being destroyed in the first Gulf War (1980 to 1988), most of the masonry buildings are less than 25 years old.
The quality of urban construction in Iran, particularly in small cities, is not well-controlled due to the lack of strict supervision and the use of non-standard materials, despite the compulsion to comply with building codes. The quality of construction largely depends on the owner’s financial ability, which is influenced by the price of the land in each zone. Therefore, it is crucial to consider this factor when calibrating the yield shear strength of buildings. To this end, data on land value in different city zones were collected from the official documents of civil transactions before the earthquake. The studied zones were then classified into two categories: I and II. Category I includes zones with a price per square meter higher than $350, while Category II contains a price per square meter less than $350. However, the AR4 zone is an exception. The AR4 zone is a small area with only a few buildings. These buildings were constructed using high-quality materials and funded by the government to provide housing for low-income individuals. The construction was supervised to ensure compliance with national building regulations and seismic codes. Hence, due to the high construction quality in the AR4 zone, it was reclassified from Category II to Category I. Generally, to utilize this methodology, it is essential to divide the city into zones. Decision-makers can use expert judgment to consider the construction quality in different areas of the urban region based on the characteristics of each category. Table 1 presents the division of city zones based on categories I and II. Table 2 shows the number of heavily damaged or collapsed cases in each zone and the observed damaged ratio (ODR).
Figure 4a–c illustrate the observed deterioration ratio (ODR) distribution in Sarpol-e-Zahab city for steel, RC, and masonry buildings, respectively. ODR will be utilized as the basis for yield shear strength estimation in each zone.

4. Calculated Damage Ratio

In this methodology, the yield shear strength parameters of a standard building designed based on the seismic code to estimate the damage of a standard building caused by a seismic shock on the urban scale extend by a log-normal distribution to cover the city’s construction diversity in 11 other cases (12 in total). For each two-component record and each building, 12 nonlinear dynamic analyses were performed to calculate the damage ratio of that building. The following sections will introduce the parameters of the buildings and explain the calculated damage ratio (CDR) determination mechanism.

4.1. Structural Parameters and Nonlinear Dynamic Analysis

Nagato and Kawase code [30] is used for nonlinear dynamic analysis. This code uses the Newmark beta method with β = 0.25 and a time interval of 0.005 s. Nagato and Kawase’s [30] code is based on the lumped mass model of multi-degrees-of-freedom structures. Therefore, the code does not directly model the plan and details of the structural elements. The effect of these details was applied to the structural parameters. It was introduced with the nonlinear spring’s characteristic of degrading trilinear hysteresis type (D-tri type). The detailed rules of D-tri type hysteresis were presented in [12]. These parameters were obtained by analyzing the standard structure designed according to the seismic codes. The D-tri curves were derived from the nonlinear static analysis of buildings using nonlinear elements introduced in [39] for columns, beams, connecting springs, and braces in steel and RC buildings. Based on field observations and statistics, three representative building models have been selected for Sarpol-e-Zahab city. The chosen buildings are a 3-story steel building with a braced frame, a 3-story RC building with a moment-resisting frame, and a 1-story unconfined masonry building. The Statistical Center of Iran (SCI) data indicates that structures with an area of about 100 m2 are the most common in this city. Following Iran’s construction standards, buildings of various types with a 100 m2 area were designed. As per reference [39], nonlinear behavior was incorporated into each structural element, and the representative structures were analyzed using a nonlinear static method to propose nonlinear properties of the structure.
The results indicate that the characteristics of the degrading tri-linear hysteresis type (D-tri) spring introduced in references [40,41] can be used to model the nonlinear behavior. However, the standard models and their analyses are not presented in this text due to space constraints. Multi-mass models with nonlinear shear springs between two adjacent stories were employed in the simulations, as seen in works [30,31,42]. Figure 5 illustrates the standard model’s nonlinear factors, depicting D-tri-type relationships between the story drift angle and base shear ratio. Besides, Table 3 displays the parameters of the standard building models.

4.2. Yield Shear Strength Estimation

The parameters listed in Table 3 for steel and RC buildings are based on standard buildings following Iranian building codes. It is worth noting that according to the Iranian seismic code [38], masonry buildings are considered highly vulnerable, and new masonry structures are not permitted. The structural parameters and specifications outlined in Iranian guidelines are used here. It is important to note that variations in materials, design quality, supervision, and execution across different urban areas can lead to nonstandardized building yield shear strength. Shibata [43] used damage statistics from the 1978 Miyagi-Ken Oki earthquake to consider this variation for low-rise buildings, employing a log-normal distribution. Based on this assumption, 12 different yield shear strengths have been considered, with six levels weaker and five levels more robust than the standard, with an existence ratio determined by a log-normal distribution with a mean of 0.095 and a standard deviation of 0.423, as detailed in Table 4. Nagato and Kawase [30] found that 12 representative factors have the best accuracy and calculation time convergence.
Nonlinear dynamic analysis is performed in each zone, using the yield shear strength distribution from Table 4, to determine the calculated damage ratios for the North-South and East-West components of acceleration records. The damage criteria and the yield shear strength distribution should be determined in advance for response analysis. According to [38], if the maximum story drift angle exceeds 1/40 radians, steel, and RC buildings are considered heavily damaged or collapsed. For masonry buildings, the threshold of 1/50 radians is assumed. The damage ratio is then calculated by dividing the sum of the existing ratios for buildings with a drift angle larger than the defined limit by the total number of 12 investigated states. Finally, the obtained CDR for each zone is compared with its corresponding ODR value. In nonlinear dynamic analysis, seismic effects are considered by reproducing acceleration waveform records in each zone from the deconvolved ground-level main shock motion recorded in the strong motion station.
Figure 6 compares the total CDR and ODR with α = 1. The comparison reveals that the CDR of steel and RC buildings is smaller than the ODR, indicating that the existing steel and RC buildings in the city are weaker than the standard. On the other hand, in masonry buildings, the CDR is greater than the ODR, suggesting that masonry buildings exhibit more resistant behavior than initially assumed. Therefore, to replicate the observed damage, the yield shear strength of steel and RC buildings should be lower than the standard value, and the yield shear strength of masonry buildings should be higher than the standard value.
Nagato and Kawase [30] proposed using the yield shear strength ratio of α, a multiplicative factor, as the actual yield shear strength ratio relative to the standard yield shear strength to modify the yield shear strength relative to the standard yield shear strength. The best results can be obtained by conducting the grid-search analysis with different α values and comparing the results of CDRs with ODRs until the CDRs match the ODRs. The optimal α for steel, RC, and masonry buildings is estimated as 0.58, 0.92, and 4.05, respectively. Figure 7a–c depict the CDRs for steel, RC, and masonry buildings with the optimal α, respectively. A comparison of the CDRs presented in Figure 7 with the results of ODRs presented in Figure 4 reveals that the obtained CDRs do not align well with the distribution of observed damages, even though the average levels of CDRs are consistent with those of ODRs.
Furthermore, comparing the seismic record parameters provided in Figure 3 with the ODRs shown in Figure 4 reveals that unexpected damages have occurred despite weaker seismic record parameters in zones where the land has a lower value. This discrepancy can be attributed to differences in material quality and implementation supervision. Nonstandard materials are often utilized to reduce costs, and building codes may be more easily overlooked. In such scenarios, the primary concern shifts away from ensuring safety. By collecting the statistics on the base price of land in different city zones before the earthquake, the urban zones were divided into two categories, I and II. Table 2 outlines the division of zones into categories I and II.
After conducting separate analyses for each category, two α values were introduced for each type of building. Table 5 reports the α values for each type of building. The α value for steel and RC buildings is less than 1, while it is greater than 1 for masonry buildings. The lower α in Category II zones signifies that the buildings in these zones are comparatively weaker than those in Category I. The CDRs from the best α values for each building type in each category is presented in Table 5 match the ODRs quite well, as shown in Figure 8. Figure 9a–c present the CDRs using these new α values for steel, RC, and masonry buildings, respectively.

5. Comparison of Observed and Calculated Damage Ratio Distribution

The comparisons between ODRs presented in Figure 4a–c and their corresponding CDRs from Figure 9a–c are shown in Figure 10a–c for steel, RC, and masonry buildings on each city block, respectively.
The comparisons in Figure 10a–c show that the obtained α provides an acceptable damage estimate for most city zones. The lower ODR in most areas can be attributed to inaccuracy in detecting collapse cases. The FM9 and TM04 regions exhibit the most variation between CDR and ODR. This variation is due to poorly constructed buildings in both zones, categorized as II. They were situated on loose alluvial ground near the river, making them highly vulnerable. These zones are small and have few buildings. The few buildings lead to the uniformity of the yield shear strength of the investigated structures. Consequently, the assumption of a normal distribution of yield shear strength is invalid. Therefore, when using this method, it is crucial to have an adequate number of buildings in each zone to benefit from the normal distribution of yield shear strength accurately.
An analysis of Figure 10c for masonry buildings reveals the most significant difference in the FM9 and AR3 zones. In these zones, the CDR is dramatically higher than the ODR, possibly due to the effects of the alluvial near the river, which demonstrates high acceleration, leading to increased CDRs. However, the survey indicates that the damage is insignificant because only a few masonry buildings are in these zones, and the exposure asset is minor. The lower CDRs of masonry and RC than ODRs in the FM27 zone suggest that despite being in Category I, the yield shear strength of structures in the southeastern part of this zone is less than the standard.
The accuracy and precision of observational data surpass all estimation and calculation methods. However, surveying many buildings in urban areas in the critical days following an earthquake is challenging. Besides, calculation methods can be used to predict damage before an earthquake in the absence of observational data. Overall, the selected α has effectively estimated the damage in different city zones to an acceptable extent for rapid assessment methods and evaluating the yield shear strength of buildings on an urban scale with adequate accuracy.

6. Concluding Remarks

This study calibrated the damage ratios obtained from dynamic nonlinear analysis using the standard characteristics of 3-story steel and RC buildings and 1-story masonry buildings, with the damage ratios observed after the Mw7.3, 2017 Sarpol-e-Zahab earthquake. This allowed us to estimate the yield shear strength of buildings on an urban scale. The parameters were determined by multiplying the yield shear strength ratio, α, with the standard parameters obtained from the buildings designed according to Iranian building codes. To best match the observed damage ratios with the calculated damage ratios, the city zones are categorized into two categories, I and II, based on the land value, and performed the calibration for each zone separately. Finally, GIS-based maps of damage ratio distribution were generated for ODRs and CDRs and compared for steel, RC, and masonry buildings. The results indicated a good agreement between the observed and calculated damage ratios for each building type and city zone.
It was demonstrated that existing steel and RC buildings are weaker than the standards dictate. Conversely, masonry buildings exhibit greater yield shear strength than what is assumed in the national guidelines. However, the yield shear strength values presented, particularly for masonry buildings, are applicable only under conditions similar to those in Sarpol-e-Zahab City. Using the parameters given for masonry buildings is not recommended for older buildings in historical cities in central Iran.
As for the future application of the model, utilizing building parameters and yield shear strength ratios, α, it is possible to rapidly assess the distribution of damage in the city during earthquake events with similar structural conditions. These structural parameters can also estimate potential damage in upcoming scenarios, aiding in proactive planning. Quantitative prediction of ground motions for future potential events is indispensable for these preventive countermeasures, not only its intensity index like PGA. Another opportunity for the research is to apply the proposed methodology to countries with sufficient observed damage data and strong ground motion records.

Author Contributions

Conceptualization, H.K.; methodology, H.K. and M.B.; software, H.K., M.B. and I.A.; validation, M.B. and H.K.; formal analysis, M.B.; investigation, M.B.; data curation, M.B. and I.A.; writing—original draft preparation, M.B.; writing—review and editing, M.B., H.K. and I.A.; visualization, M.B. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.

Acknowledgments

Permission and instructions from Hiroshi Kawase and Kenichiro Nagato for using the Kawase-Nagato code are greatly appreciated.

Conflicts of Interest

Author Hiroshi Kawase was employed by the company General Building Research Corporation of Japan. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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Buildings 14 03321 g001
Figure 1. Concept map for the damage ratio analysis and calibration of the yield shear strength ratio.
Figure 1. Concept map for the damage ratio analysis and calibration of the yield shear strength ratio.
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Figure 2. Zoning of the city based on the distribution of synthesized strong motions.
Figure 2. Zoning of the city based on the distribution of synthesized strong motions.
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Figure 3. Seismic parameters extracted from surface ground motion records, (a) peak ground acceleration, PGA, (b) peak ground velocity, PGV, (c) sustained maximum acceleration, and (d) velocity spectrum intensity.
Figure 3. Seismic parameters extracted from surface ground motion records, (a) peak ground acceleration, PGA, (b) peak ground velocity, PGV, (c) sustained maximum acceleration, and (d) velocity spectrum intensity.
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Figure 4. Observed damage ratio (ODR), (a) steel buildings, (b) RC buildings, and (c) masonry buildings.
Figure 4. Observed damage ratio (ODR), (a) steel buildings, (b) RC buildings, and (c) masonry buildings.
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Figure 5. Nonlinear relationships at the basement of standard models.
Figure 5. Nonlinear relationships at the basement of standard models.
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Figure 6. Comparison of CDR and ODR with α = 1 (a) steel and RC buildings, and (b) masonry buildings.
Figure 6. Comparison of CDR and ODR with α = 1 (a) steel and RC buildings, and (b) masonry buildings.
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Figure 7. CDRs with α by considering all zones (a) steel buildings α = 0.58, (b) RC buildings α = 0.92, and (c) masonry buildings α = 4.05.
Figure 7. CDRs with α by considering all zones (a) steel buildings α = 0.58, (b) RC buildings α = 0.92, and (c) masonry buildings α = 4.05.
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Figure 8. Comparison of CDR and ODR with α values presented in Table 5 (a) category I, and (b) category II.
Figure 8. Comparison of CDR and ODR with α values presented in Table 5 (a) category I, and (b) category II.
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Figure 9. CDRs considering two categories I and II for zones according to α presented in Table 5: (a) steel buildings, (b) RC buildings, and (c) masonry buildings.
Figure 9. CDRs considering two categories I and II for zones according to α presented in Table 5: (a) steel buildings, (b) RC buildings, and (c) masonry buildings.
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Figure 10. Comparison between CDRs and ODRs (a) steel buildings, (b) RC buildings, and (c) masonry buildings.
Figure 10. Comparison between CDRs and ODRs (a) steel buildings, (b) RC buildings, and (c) masonry buildings.
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Table 1. The city zones division based on categories I and II.
Table 1. The city zones division based on categories I and II.
CategoryZone
IAR3, AR4, FM1, FM12, FM15, FM27, FM28, OC, TM06
IIAR2, FM9, FM25, SM01, TM04
Table 2. Building damage statistics.
Table 2. Building damage statistics.
TypeSteel BuildingsRC BuildingsMasonry Buildings
CategoryIIIIIIIII
Total number of collapsed buildings5567111561
Total number of buildings35641481170255736951140
Total observed damage ratio0.00140.0380.0040.0190.0040.053
Table 3. Parameters of standard building models.
Table 3. Parameters of standard building models.
ParameterStorySteel BuildingsRC BuildingsMasonry Buildings
Weight (tf)1130160100
2130160-
390150-
Height (cm)1320320320
2320320-
3320320-
First yield story
drift angle (rad)		10.003580.00320.0002
20.003831
30.003043
First yield base
shear coefficient *		10.6100.520.075
20.726
31.147
Second yield story
drift angle (rad) 		10.00990.00460.0007
20.0106
30.0063
Second yield base
shear coefficient *		10.130.5870.13
20.13
30.13
Second stiffness ratio10.010.0050.001
20.01
30.01
Damping ratio 5%5%5%
Damage criterion 1/401/401/50
* These base shear coefficients are those of the standard model.
Table 4. Relationships between the yield shear strength factor and its existing ratio based on the probability density distribution [30].
Table 4. Relationships between the yield shear strength factor and its existing ratio based on the probability density distribution [30].
Yield Strength/Standard Yield Strength0.300.370.450.550.670.821.001.221.491.822.232.72
Ratio of Existence0.0020.0070.0210.0500.0950.1470.1820.1810.1450.0930.0480.029
Table 5. Estimated yield shear strength ratio, α, separately for category I and II.
Table 5. Estimated yield shear strength ratio, α, separately for category I and II.
Building TypeYield Shear Strength Ratio, α
Category ICategory II
Steel0.760.45
RC0.970.77
Masonry5.002.81
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Biglari, M.; Kawase, H.; Ashayeri, I. Rapid Urban-Scale Building Collapse Assessment Based on Nonlinear Dynamic Analysis and Earthquake Observations. Buildings 2024, 14, 3321. https://doi.org/10.3390/buildings14103321

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Biglari M, Kawase H, Ashayeri I. Rapid Urban-Scale Building Collapse Assessment Based on Nonlinear Dynamic Analysis and Earthquake Observations. Buildings. 2024; 14(10):3321. https://doi.org/10.3390/buildings14103321

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Biglari, Mahnoosh, Hiroshi Kawase, and Iman Ashayeri. 2024. "Rapid Urban-Scale Building Collapse Assessment Based on Nonlinear Dynamic Analysis and Earthquake Observations" Buildings 14, no. 10: 3321. https://doi.org/10.3390/buildings14103321

APA Style

Biglari, M., Kawase, H., & Ashayeri, I. (2024). Rapid Urban-Scale Building Collapse Assessment Based on Nonlinear Dynamic Analysis and Earthquake Observations. Buildings, 14(10), 3321. https://doi.org/10.3390/buildings14103321

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