1 Introduction

Earthquakes are among the most unpredictable, lethal, and destructive natural hazards, particularly in developing countries (Ainuddin and Routray 2012; Wu and Chen 2023; Zhang et al. 2018). According to the United Nations Office for Disaster Risk Reduction reports, earthquakes accounted for 8% of natural hazards (after floods and storms) during 2000–2019. Within this period, earthquakes caused the highest number of human casualties, accounting for 58% of the total, which is equivalent to 721,318 people. The economic loss caused by earthquakes is estimated to be 21% of the total losses attributable to natural hazards, equivalent to $636 billion (after floods and storms) (UNISDR 2019). As a case in point, in the recent earthquake in Turkey and parts of Syria on 6 February 2023, at least 5000 people lost their lives, and thousands were injured (Naddaf 2023). Earthquakes affect cities and their urban infrastructure, leading to serious damage in terms of financial and human capital (Du et al. 2023; Zhang et al. 2018). Evidence shows that earthquake disaster risks are currently increasing in urban areas worldwide. Therefore, dealing with earthquakes is a major global challenge, especially in developing countries (Nazmfar et al. 2019; Zhai et al. 2023).

As the pressure of hazards on the cities increases, global and international institutions and agencies have emphasized the need for enhancing resilience capacities (Amirzadeh et al. 2022; Huang et al. 2021; Roberts et al. 2020). There is a consensus that resilience is a multifaceted concept with different social, economic, cultural, institutional, environmental, and physical dimensions (Bruneau et al. 2003; Godschalk 2003; Meerow et al. 2016; Parizi et al. 2022; Sharifi and Yamagata 2016b; Suárez et al. 2016). The present study is focused on the physical dimension, referring to urban physical resilience as an aspect of urban resilience that relies on the urban built environment and spatial and structural configuration of the city.

A city without resilient structural systems will be extremely vulnerable to disasters such as earthquakes (Du et al. 2023; Godschalk 2003). Although the cultural, social, economic, and institutional urban dimensions are very important for achieving resilience, urban structure and morphology are the first components of an urban system that must withstand pressures and shocks (Abdulkareem and Elkadi 2018). The urban structure plays a vital role in determining the ability and capacity of cities to effectively cope with various events and adapt to changing conditions. During disasters, it is crucial for physical systems to maintain their functionality and sustain critical conditions. If these systems fail, the process of post-disaster recovery will be slow (Godschalk 2003; Parizi et al. 2021; Sefton et al. 2022).. Thus, examining and improving urban physical resilience is of high importance.

The analysis of urban physical resilience depends on the physical features of the place under study (Cutter et al. 2008; Turner et al. 2003; Zhai et al. 2023). Some previous studies have focused on the evaluation of urban physical resilience. For instance, Jones et al. (2010) categorized elements of urban structure into density, housing/building, transport infrastructure, layout, and land use, examining the impact of each on resilience. Allan and Bryant (2010) proposed a model for the evaluation of urban resilience and the role of open spaces in increasing resilience to earthquakes. They focused on the recovery and reconstruction of the components of the urban system, with an emphasis on the role of open spaces. Glavovic et al. (2010) illustrated the potential of land-use planning to reduce natural hazard risks and improve urban resilience by enhancing awareness of the nature of hazards and making hazard avoidance a priority via proactive planning efforts. Villamor et al. (2012) investigated the role of land use and urban physical development programs in the context of the Greendale Fault in New Zealand and provided suggestions for improving urban resilience. In its 2013 report on resilience, the London School of Economics and Political Science defined the physical measures of urban structure in terms of the compactness of the built-up area, the malleability of street configurations, and the tangible effects of physical structures on urban fortitude (Zekry et al. 2020a). In another study, Allan et al. (2013) examined the influence of urban form on the resilience of cities. Their study was carried out based on post-2010 earthquake data in Concepción, Chile, for the recovery and reconstruction phase. The authors concluded that diversity in space and function, connectivity between different spatial elements in the city, redundancy, and efficiency in different urban uses positively affected urban resilience in the recovery and reconstruction phase. León and March (2014) discussed the role of applying urban morphology to promote rapid resilience against tsunamis. The expected floodable areas were identified, followed by the identification of different evacuation zones based on the indicators of urban structure. Zhang and Wang (2016) proposed a new indicator framework based on network reliability and connectivity to assess the resilience of the urban road network. This combines topology, redundancy, traffic pattern, and network performance in the post-earthquake urban recovery and reconstruction phase.

Brand and Nicholson (2016) assessed the self-organization and recovery processes in urban areas following the 2010 and 2011 earthquakes in New Zealand, focusing on how urban public spaces enhance resilience. Shrestha et al. (2018) examined open spaces' role in earthquake resilience and risk perception, analyzing land use, service accessibility, ownership, and the size and density of the surrounding environment. Aydin et al. (2018) developed a graph theory-based method to assess transportation network resilience under seismic hazards, tested in Nepal following the devastating April 25, 2015, earthquake. Sharifi (2019a) and Sharifi (2019c) explored the link between urban structure and resilience across macro, meso, and micro scales, considering factors like city size, development patterns, and landscape connectivity. Sharifi (2019b) further investigated micro-scale urban structure, focusing on street and urban networks through network topology and design indicators. Sharifi et al. (2021) compared the physical resilience of conventional, semi-planned, and planned neighborhoods in Shiraz, Iran, using indicators like urban density, lot size and shape, and street network design. Parizi et al. (2022) proposed a framework for evaluating urban physical resilience, integrating decision-making methods to present 20 physical indicators and 8 resilience characteristics.

This overview of the literature shows that previous studies have considered few urban structure indicators to evaluate urban resilience, while the urban structural system is a sophisticated combination of different interrelated components. A balanced consideration of all influencing indicators can enable the urban structural system to operate effectively against hazards such as earthquakes. In this article, an attempt has been made to provide a comprehensive list of effective indicators in urban physical resilience along with their connections Besides, previous research has not given a clear answer to the question of how to measure urban physical resilience, indicating the need to provide specific frameworks and methods to measure and quantify the physical dimension. On the other hand, all the frameworks and methods developed to evaluate and map urban resilience have used the city administrative boundaries or census areas as evaluation units. However, there is no adequate information on resilience indicators in different cities. Besides, resilience maps, mainly generated based on aggregated map working units, are influenced by the Modifiable Areal Unit Problem (MAUP). The choice of spatial units may affect how we interpret the study results, leading to spurious inequality between the selected units. Grouping of similar spatial units can even worsen these conditions. Therefore, the validity and accuracy of such maps depend on the choice of spatial unit (Cariolet et al. 2019). Providing a single and standard spatial unit based on the physical characteristics of the study site can address this problem while providing a comprehensive evaluation framework. Therefore, it is possible to introduce a functional and adaptable framework in different geographical scales and spatial zones. In this article, a new spatial unit based on the physical characteristics of any place is presented in the proposed framework.It is also noteworthy that building a resilient system (here, urban morphology and structure) is not a linear process. It is a dynamic and sometimes iterative process influenced by various components across spatial and temporal scales (Sharifi and Yamagata 2016a). However, the review of previous studies shows that the evaluation frameworks have not adequately considered the four phases of resilience (preparation, absorption, recovery, and adaptation). Most research in the field of urban physical resilience has examined the preparation and recovery phases, with few theoretical and practical studies on the absorption and adaptation phases. In this article, all four phases are considered.

Against this background, the objectives of this research are as follows:

  1. 1.

    Providing a better understanding of the concept of urban physical resilience by explaining the underlying indicators of urban structure that can be used to improve evaluation of urban physical resilience across different phases of resilience;

  2. 2.

    Presentation of a spatial unit applicable in different geographical scales and spatial zones; and

  3. 3.

    Investigating changes in the values of urban physical indicators through a case study.

We will develop a framework to measure resilience with a series of flexible methods applicable to different geographical areas and resilience phases. In turn, this will contribute to making the concept of urban physical resilience more measurable and tangible, leading to more practical investigations into future uncertainties.

2 Theoretical foundations

2.1 Resilience and its phases

The concept of resilience is increasingly used in various disciplines. Holling (1973), the ecological theorist, first used the term as an ecological and environmental concept. The theory of resilience was first integrated into urban sciences in the 1990s (Lu and Stead 2013). Ever since, resilience has attracted considerable attention among urban scientists and authorities (Büyüközkan et al. 2022; Chen et al. 2020; Lundberg and Johansson 2015). However, despite many studies on resilience, there is still no single definition for it (Sharifi 2023). ARUP international development (2014) defined urban resilience as “the ability of a community or city to encounter, continue, function, and achieve its goals against hazards in the most complete way possible” (Silva 2014). Habitat (2018) defined urban resilience as “the ability of an urban system to maintain its performance in the face of shocks and hazards while moving consistently toward greater sustainability”. The Rockefeller Foundation defines urban resilience as “the capacity of individuals, communities and systems to survive, adapt, and grow in the face of stress and shocks” (Wardekker et al. 2020). UNISDR has provided a more accepted definition used in urban resilience, which is considered the basis of the present study. According to this definition, resilience is “the capability of a system, community, or society subject to hazards to resist, absorb, accommodate, adapt to, and recover from the impacts of hazards efficiently through the preservation and restoration of its essential basic structures and functions” (Sharifi and Yamagata 2016a). Accordingly, resilience is a combination of preparedness, absorption of disturbances and achievement of balance, recovery, and adaptation capacities. One of the advantages of this definition is in reflecting different resilience phases (Sharifi 2016). Given that adaptation is a dynamic process, these phases are repeated periodically. Each of these phases is defined and explained according to the objectives of this study and based on the definitions of other researchers (Fig. 1) (Arghandeh et al. 2014; Hughes 2015; Sharifi and Yamagata 2016b).

Fig. 1
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Different phases of urban physical resilience and their definitions

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Based on the literature review, the following definition of urban physical resilience can be presented: From an urban structure perspective, resilience is the degree of resistance that different elements and components of the urban structure (which is a complex system with numerous mutual interactions and interrelationships) show against hazards. Urban physical resilience can help cities absorb shocks so that the overall urban functioning is not disrupted, the city can recover quickly, and the urban system's capacity to adapt to changing and severe conditions is improved.

2.2 Spatial unit used to evaluate the urban physical resilience

The elements of urban structure are highly variable in terms of content, level of detail, scale, features, and the type of resources from which they are extracted (Boeing 2018; Cochran and Brunsell 2017; Liu et al. 2022). One of the main issues in the discussion of urban physical resilience is determining the spatial unit and the geographical scale for the investigation and evaluation. Accordingly, it is necessary to have a standard spatial unit based on the physical features of the study site to achieve a comprehensive framework for the assessment of urban physical resilience. For this purpose, this study seeks to divide the city into homogeneous units using the Local Climate Zones (LCZ). We argue that an approach based on LCZs offers a comprehensive model of resilience assessment, where the local and spatial features of the system (here urban structure) can also be utilized. In addition, the indicators used in this physical zoning method are largely compatible with urban physical resilience indicators. Using quantitative and simple methods in this approach helps to moderate the complexity of the problem and the great variety of urban structural indicators. The standardized nature of this method also makes it possible to compare urban physical resilience across different cities. Also, dividing cities into homogeneous zones makes studying urban form indicators and spatial analysis more straightforward because the researcher is provided with an appropriate view of urban structure. This seems to be a very good solution, even for areas with little information about urban structure. Hence, it is possible to perform a comprehensive assessment of resilience using the characteristics of the place instead of a series of constrained and inflexible models and frameworks. This way, the Modifiable Areal Unit Problem (MAUP) is also avoided in resilience mapping.

LCZ is a method for classifying urban form, texture, and structure. It divides cities into 17 classes (10 built and 7 natural land cover types) (Fig. 2). These classes are homogeneous areas created using features such as surface cover, structure, and constituent materials that span hundreds of meters to several kilometers on a horizontal scale (Stewart and Oke 2012). The various methods, indicators, and even data sources available for the LCZ implementation have made it popular and practical for many cities. This method is based on an interdisciplinary plan to describe urban morphology, and its primary objective is to study the urban heat islands (UHI) (Liu et al. 2022; Zhao et al. 2019). Researchers have used several case studies from cities around the world to evaluate the feasibility of LCZ maps. For example, several studies have been conducted on cities and metropolitan areas around the world with publicly available software and data to generate a global database called the World Urban Database and Access Portal Tools (WUDAPT) (Ferreira and Duarte 2019). This initiative and database aim to collect and publish information about the form and function of cities worldwide. LCZ maps can be used for a wide range of applications, including climate data management, heat island studies, assessment of greenhouse gas emissions, air pollution modeling, comprehensive comparison of urban structure, resilience-based spatial and urban planning, risk mitigation, population assessment, examination of urban spatiotemporal changes and the consequences of climate change and hazards, and monitoring and evaluating decision-makings concerning sustainable development and urban resilience (Bechtel et al. 2016; Fernandes et al. 2023; O'Malley and Kikumoto 2022; Oliveira et al. 2020; Qiu et al. 2018; Středová et al. 2021; Wang et al. 2018; Zhao et al. 2019).

Fig. 2
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Types of classes and zones in the LCZ method along with a definition for each one (Stewart and Oke 2012)

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3 Methodology

This study contains two main steps (Fig. 3). The first step is based on Parizi et al. (2022) and includes:

  1. I.

    Determining effective urban form indicators in each phase of resilience through a review of literature, interviews with experts, and Factor Analysis (FA) method;

  2. II.

    Determining the interrelationships between indicators using Interpretive Structural Modeling (ISM);

  3. III.

    Placing indicators in a framework and determining their weights using the ANP method.

Fig. 3
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The proposed research steps

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The second step includes:

  1. I.

    Adjusting the weight of the indicators using optimization techniques and statistical methods to reduce the potential bias effects of expert opinions.

  2. II.

    Preparing LCZ map and determining LCZ zones of the study area;

  3. III.

    Implementing the framework developed from the previous step in LCZ zones;

  4. IV.

    Determining the urban physical resilience for each zone and in different phases; and

  5. V.

    Performing sensitivity analysis to investigate the effects of changes in the values of indicators on the performance of the proposed method to evaluate urban physical resilience.

These steps will be further explained in the remainder of this section.

3.1 Adjustment of Indicators’ weight

The ANP model used to calculate the weight of the indicators is an expert-based model. Since expert-based methods could lead to biased results, it is possible to achieve higher accuracy by combining the results of this method with statistical and computational methods. Statistical methods allow the assignment of precision measures, including bias, variance, confidence intervals, prediction error, etc., to sample estimates. Also, these methods show the uncertainty or lack of information about the elements of a system.Therefore, this study has used statistical and optimization techniques for weight adjustment to reduce the bias effects of the experts’opinions in the framework, as concluded by Parizi et al. (2022). The steps taken are as follows:

Step 1 Bootsrapping

Bootstrapping is a computational non-parametric method that falls under open sampling techniques in statistics. This method can estimate the error correction models and test hypotheses. It is also applicable in calculating the estimators' variance when the probability distribution function of the estimators is uncertain or complex (Mooney et al. 1993). Using bootstrapping, we determined the confidence interval for the wight of each indicator from the weighted matrix in the ANP model. Thus, if \(I\) represents the total number of indicators, which is equal to 20 in this study, the confidence interval for each indicator weight is defined as an interval \([{L}_{i}, {U}_{i}]\) and \(\{\text{1,2},\dots .I\}\). In the bootstrapping algorithm, the sample space is selected from the weighted matrix.

3.2 Step 2. Computation of Entropy

Entropy indicates the degree of chaos, uncertainty, or lack of information about the elements of a system. The higher entropy of a variable leads to more information from its definitive observation. Entropy theory is used for various resilience assessments, including engineering, society, economics, etc. (Tamvakis and Xenidis 2013). We used the Shannon entropy to calculate the entropy value and evaluate the reliability and feasibility of the indicators’ weight obtained from the ANP model.

Step 3 Solving an optimization problem

This step solves an optimization problem using the results of steps 1 and 2 as follows:

$$\text{min }E . {W}_{S}$$
$$\sum_{i=1}^{I}{w}_{i}=1$$
$${L}_{i} \le {W}_{i} \le {U}_{i}\quad i=\text{1,2},\dots ., I$$
$${W}_{i} \ge \varepsilon \quad i=\text{1,2},\dots , I$$

\({W}_{s}\): The final weight of the indicators obtained from the ANP model.

\(E\): Entropy obtained from Step 2.

\({U}_{i} \, and \, {L}_{i}\): Confidence intervals obtained from Step 1.

\(\varepsilon\): A small value > 0 to ensure that the weights are larger than zero.

The result of this step is the optimized weights of the indicators.

Step 4 Computation of the adjusted weights

A combination of subjective weights (obtained from the ANP model) and objective weights (obtained from the optimization and statistical techniques (previous step) is considered to calculate the final adjusted weight as follows:

$${W}_{A }=\left\langle \frac{{W}_{i}^{O}* {W}_{i}^{s}}{\sum_{i=1}^{I}({W}_{i}^{O}* {W}_{i}^{s})} \right\rangle , i=\text{1,2},\dots , I$$

Such a technique makes a difference in disposing of the negative impacts of subjective judgments within the experts’ scoring. It also puts subjective and objective weights together to achieve integrated weights.

3.3 Preparation of LCZ map of the study area and determination of LCZ classes

3.3.1 Study area and data collection

The study area is defined as a polygon using Google Earth. The selected scope should be larger than the study area to ensure that the entire area has been covered. The file is saved in the kmz format after determining the study area. Since satellite images of the study are required, Landsat 8 satellite images, preferably from different seasons, are downloaded from the USGS website.

3.3.2 Determining training area

At this step, five experts with sufficient knowledge of the physical structure of the study area were asked to identify at least one class sample for each LCZ class using Google Earth. The criteria presented in Table 1 are considered to determine the training areas.

Table 1 Important criteria for determining training areas
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3.3.3 Preparation of input files in SAGA GIS software

At this stage, downloaded satellite images and the.kmz file of the study and training areas are entered into the SAGA GIS software, followed by applying the necessary import settings, such as pixel size, image system, merging, etc.

3.3.4 LCZ classification map for the study area

The final map is prepared at this stage using SAGA GIS software and the outputs in the previous stages. This software uses the Random Forest algorithm for classification. The output, which is the LCZ map, can be saved as both.kmz and.shp files according to the settings made. Another output is the classification accuracy of the prepared map. It is also possible to open the.kmz file in the Google Earth environment and control the created zones under the current situation to evaluate the accuracy of the zones and the LCZ map.

Sensitivity Analysis is used to investigate the behavior of systems and the effect of input variables on the output responses of the system. Sensitivity analysis was conducted in the current study to find out how the resilience of each zone changes or improves through changes in the values of indicators.

4 Study area

Iran is an earthquake-prone country on the Alpine-Himalayan orogenic belt (Kamranzad et al. 2020). More than 90% of the country's cities are on or near earthquake faults. An earthquake is a powerful and often happening natural event that can cause severe damage to Iranian cities. According to statistics released by the United Nations in 2020, 94% of the deaths that occur annually due to natural disasters in Iran are related to earthquakes, and the rest are because of floods (Meshkini et al. 2021). Tehran, the capital of Iran, is at high seismic risk because it is surrounded by several active faults. It is located on the southern slopes of the Central Alborz Mountains, with an area of approximately 730 square kilometers. The city is geographically located at 51°8′ to 51°37′ east longitude and 35°34′ to 35°50′ north latitude (Firuzi et al. 2019). Tehran is the capital and the largest city in Iran. It has extensive economic, communication, political, service, and cultural functions on a regional, national, and international scale. Therefore, examining the status of resilience in Tehran is one of the important issues faced by planners, managers, and city officials. Research on earthquake resilience in Tehran goes back to about a decade. However, there are still relatively limited studies in this field (Meshkini et al. 2021). District 4 of Tehran is one of the largest districts in the northeast of the city. Mosha and North Tehran Faults are this district's most famous and important seismically active faults. The proximity of the district to these faults and major activity centers (green and military spaces), high population density, and the relatively old infrastructure in the district reveal the need to address the issue of urban physical resilience in this area (Fig. 4).

Fig. 4
figure 4

Location of the study area

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5 Results

5.1 Identification of indicators in the resilience phases

The indicators used in this study are adopted from Parizi et al. (2022). These 20 indicators related to urban physical resilience are updated based on the methods and requirements of this study.The importance of urban form indicators in each phase was determined according to previous studies and expert opinions. Results are shown in Table 2.

Table 2 Urban physical indicators s and their weights
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According to the results of Table 2, the Robustness of Building (ROB) was the most important urban form indicator in ensuring cities can handle earthquakes. Buildings are one of the most important urban components, and their robustness can be a major barrier against earthquake hazards. The results of the implementation of the ANP model also show the significance of this indicator. The next indicator is Building Density (BD); high density may increase casualties and damage during an earthquake, making it troublesome to supply help. Aspect Ratio (AR) is the next important indicator. As the amount of blockage may increase (greater height of the building compared to the narrow width of the street), the likelihood of the streets getting blocked during an earthquake increases.

5.2 Adjustment of the weight of Indicators

The ANP model utilized to calculate the weight of the indicators is expert-based. Therefore, this study has used statistical and optimization techniques for weight adjustment to reduce the bias effects of the experts’ opinions in the framework and the resulting weights while also achieving higher precision. The steps taken are as follows:

Step 1 Bootsrapping

The output of this step is the confidence intervals shown in Table 3.

Table 3 Feasible interval
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Step 2 Computation of Entropy

Table 4 shows the results of Shannon entropy implementation.

Table 4 Entropy values
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Step 3 Solving an optimization problem

The result of this step is the optimized weights of the indicators.

Step 4 Calculating the adjusted weights

Figure 5 indicates the weights obtained from the ANP model and the adjusted weights of the indicators.

Fig. 5
figure 5

Initial and adjusted weights of indicators

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As shown in Fig. 5, there were slight changes in the weight of the indicators and the order of their importance in evaluating urban physical resilience after statistical and optimization techniques were applied to the weight of the indicators. Robustness of Building (ROB) is the most critical indicator, followed by street width (SW). In the weights obtained from ANP, the second place belongs to building density (BD), transferred to the third place after weight adjustment. In the adjusted weights, aspect ratio (AR) has relegated to the fourth rank in importance. Figure 5 shows the rest of the weights.

5.3 LCZ zones’ map of the study area

As stated earlier, in order to achieve a comprehensive framework for evaluating urban physical resilience, it seems necessary to have a spatial unit based on the physical characteristics of the study area.

In this paper, by using the LCZ method, an attempt was made to divide and zone the study area into homogeneous units. According to the steps of preparing the LCZ map of the study area, explained in the methodology section, creating training zones is one of the steps of preparing this map. Figure 6 shows an example of training areas created on Google Earth software and in the study area. The style and color considered for each of these training areas are according to the existing standards and expresse by WUDAPT.

Fig. 6
figure 6

Training areas in the study area

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At that point, concurring to the procedure mentioned in the methodology section, the LCZ map of the study area was prepared. This map is in the raster format. In this paper, in order to make a better view and understanding of this map as well as the spatial units, this map was converted into the vector format using analytical functions in ArcGIS software. Figure 7 shows the different LCZ classes of the studied area.

Fig. 7
figure 7

LCZ map of the study area

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Next, Fig. 8 shows the accuracy of this classification and the resulting map. Overall accuracy is equal to 0.77.

Fig. 8
figure 8

Overall accuracy values for each class of LCZ map

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5.4 Determining the urban physical resilience in the selected study areas

Some of the zones were selected as study sample spatial units. Figure 9 shows these sample zones. These zones been selected from among the built classes because the urban physical resilience is mainly focused on the built parts of the city. Also, in addition to the main classes of LCZ, some sample areas are a combination of the main classes. Tehran's District 4, including its urban structures, developed and expanded over time without initial planning. In some parts of the district, old structures have been renovated and improved over time. This creates a mix of textures and urban styles. We tried to select zones from all classes of the built-type LCZs as well as their most prominent and important combinations so that the various physical tissues in the study area can be evaluated. A total of 22 zones were considered in the study area.

Fig. 9
figure 9

LCZs zones determined in the study area

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Next, we measured the urban physical indicators in each zone. Different sources, including a detailed plan of District 4, existing maps of Tehran Municipality, maps of Tehran Crisis Management Organization, etc., were used to examine the status of urban form indicators in each zone. These maps were then scrutinized and updated using land surveys and Google Earth and Open Street Map (OSM) data. Table 5 shows the values of the indicators in each LCZ.

Table 5 The values of indicators in LCZs zones
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Using the GIS tools, the resilience maps were initially prepared for each phase of the resilience. According to Table 2, which shows the effective indicators of each phase, the analytical functions available in the software determine the weight and significance of each indicator for urban physical resilience and indicator overlapping (IO). Then, the final map of urban physical resilience was prepared as a combination of maps in four phases (Fig. 10).

Fig. 10
figure 10

Physical resilience map in the study area

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According to the map of urban physical resilience, most of the zones in the study area had a moderate level of physical resilience.

5.5 Sensitivity analysis

Sensitivity Analysis (SA) is essential for examining systems' behavior and determining the effect of input variables on system output responses (Salas and Yepes 2020). The main purpose of sensitivity analysis is to evaluate the effect of a variable on the output of the overall model by manipulating the variables. When we are faced with uncertainty, this analysis of one or more parameters is essential. We conducted SA to explore how changes or enhancements in the values of indicators can impact the resilience of each zone. Urban form indicators were divided into different classes according to their values. The current status of each indicator in each zone was specified. Four scenarios were considered for sensitivity analysis, including −50% or 2-rank decrease, −25% or 1-rank decrease, +25% or 1-rank increase, and +50% or 2-rank increase in the values/class of indicators. For each scenario, the resilience of each zone was measured. Figure 11 shows the changes in the values of urban form indicators and the degree of urban physical resilience in each scenario.

Fig. 11
figure 11figure 11

The results of ssensitivity analysis

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6 Discussion

Urban physical resilience is determined by the performance of urban form indicators that reflect characteristics of an integrated set of land plots and urban blocks, road networks, and open green spaces. These indicators play a crucial role in shaping the urban structure and functioning during different stages, including preparedness, response, and long-term recovery immediately after and years post-earthquake occurrence. The current paper sought to highlight the significance and weight of influential indicators on urban physical resilience using a hybrid ISM-ANP model, statistical analyses, and optimization models. The study also focused on eliminating biases in expert judgments and opinions to attain more reliable results.

6.1 Importance of the indicators

Based on the results, urban physical resilience was primarily influenced by the robustness of the building, which was the most influential factor. The other important indicators were the width of streets, the density of buildings, aspect ratio, granulation of parcels, centrality, accessibility, and connectivity, respectively. Distribution of uses, accessibility of some land uses, including medical centers and fire stations, suitability of land uses, accessibility of open and green spaces, location status of hazardous uses, including gas stations, and urban form network ranked the next. Finally, the next levels of importance were occupied by land use diversity, distribution of open and green spaces, street length, the density of the built environment around open spaces, the size of open and green spaces, and slope ratio.

Buildings are the main components of the built environment, whose damage or collapse in an earthquake interferes with the overall function of the city and considerably affects earthquake-related casualties, leading to inefficient urban functioning, particularly during recovery and adaptation, due to high human causalities, blockage of street networks, etc. Nonetheless, cities can become more physically resilient, especially in the preparedness and absorption phases, by adequate resistance of buildings to earthquakes.

Building density is among the predominant indicators of urban resilience. Earthquake-related damage and casualties resulting from high building density can hamper the prompt delivery of emergency services in the absorption phase. Nevertheless, building robustness, especially along the main street networks, enhances the adaption against earthquakes, even in highly dense areas. For instance, considerable building robustness in LCZ1 has led to good resilience under high-density conditions.

Another major factor influencing urban resilience is the aspect ratio, which indicates the proportional relationship between building height and street network width. The likelihood of street network blockage will increase with an increasing aspect ratio, leading to substantial challenges in the preparedness and absorption phases. In such conditions, evacuation operations and relief services are delivered inadequately due to street network blockage by building debris, delaying the recovery and self-organization stages of crisis management. Reducing the degree of enclosure, especially in places where the robustness of buildings is low, helps adapt the urban physical against risks.

Granulation of parcels is one of the important and, at the same time, controversial indicators in the urban environment, whose effects on urban physical resilience against earthquakes have been subject to numerous and occasionally contradictory reports. According to some researchers (Bruwier et al. 2018; Sharifi 2019a; Sharifi et al. 2021), fine-grained lots increase the effectiveness of urban resilience against earthquakes by ensuring more interconnectedness and ease of access. In addition to a wide range of uses and activities facilitating absorption and preparedness, smaller lots provide higher flexibility and enhance adaptation and self-organization. On the other hand, increasing the size of lots for specific purposes, including residential uses, will increase the density of buildings while reducing the diversity of uses and imposing spatial restrictions on urban green and open spaces. Other disadvantages of larger lots, adversely affecting various phases of urban physical resilience, include decreased interconnectedness, ease of access, and permeability because of the expansion of these lots along street network edges. Larger lots are also less adjustable to changing conditions, which will diminish urban functionality throughout various operations, such as aggregation or separation. However, some researchers claim that disruption in the practical operation of open spaces for evacuation, shelter, etc. is a serious outcome of dividing the larger into smaller lots, making them more vulnerable to earthquakes (Salat 2017; Silva et al. 2017). Meanwhile, the positive contribution of smaller lots to higher levels of urban physical resilience was confirmed in the present research using the results of sensitivity analysis carried out in various zones.

Direct and indirect impacts of various resilience phases on land use and other relevant parameters, including diversity, adaptation, and distribution, have also been reported. Although non-mixed land uses develop across cities, different facilities and services can be provided near the buildings in urban areas benefiting from adequate diverse and proportionate land uses. Such a proportional distribution of services facilitates reaction against natural disasters, including earthquakes, and enhances performance throughout the preparedness,absorption, and adaptation phases. However, some studies have implicitly referred to the positive contribution of diversity and mixed land use to reinforcing social interactions and capital in neighborhoods, significantly affecting absorption and adaptation capacities (Downes et al. 2016; Irajifar et al. 2016). Proper distribution according to the land use adaptability of single buildings and urban spaces with their nearby structures plays a critical role in dealing with problematic land uses within residential and medical spaces and contributes effectively to the absorption and adaptation stages. Thus, higher levels of incompatibility due to the presence of industries, explosives, combustibles, etc., will make urban neighborhoods more vulnerable. On the other hand, unoccupied lots, green spaces, farms, parks, cemeteries, parking lots, etc., lead to higher compatibility, facilitate relief provision, and reduce the likelihood of damage during a disaster. Appropriate land use distribution also ensures prompt accessibility of the most critical land uses during a crisis, subsequently enhancing absorption as an essential component of urban physical resilience. Besides, the potential post-earthquake cascading multi-hazard risks, such as fires, are alleviated or prevented through the appropriate distribution of uses, speeding up the recovery and self-organization phases and consequently adaption phase.

Furthermore, health centers and fire stations are among the land uses that require particular attention because of facilitating relief services during adverse events such as earthquakes. Buildings providing such services should be sufficiently robust to ensure continuous post-earthquake service provision. The distance of such spaces should be adequately and fairly organized to speed up rescue and relief services, enhancing urban structure absorption, adaptation, and recovery abilities while comforting the victims.. Besides, lower relief rates may significantly decrease preparedness and absorption capacities in the case of inadequately accessible fire stations for residential uses. All these, along with potential cascading and sequential hazards, will have adverse impacts on the preparedness, absorption, and recovery phases of urban disaster management.

Urban physical resilience to earthquakes can also increase through appropriate street networks as an essential component of urban structure.. Street width is a crucial contributor to urban resilience because wider networks decrease the possibility of a street blockage and increase the likelihood of evacuation and relief services, ultimately enhancing preparedness, absorption and adaption capacities. Moreover, wider street networks provide more adaptability and recovery because they enable modifications in geometries and infrastructures, along with a mixture of various transportation modes, including special bus and bicycle paths, sidewalks, etc. Accessibility and connectivity, as two essential indicators ensuring access to suitable and safe open spaces for evacuation during disasters…. In addition to the above, the recovery and self-organization stages of urban physical resilience are also facilitated due to higher levels of urban context permeability resulting from accessibility. Centrality reflects the respective significance of nodes/links within a communication network. The blockage of high-centrality nodes/links considerably disrupts accessibility to crisis-stricken areas and has severe impacts on the adsorption capacity of urban structures. Improper distribution of the centrality values, such as surrounding a high-centrality node/link with low-centrality ones, exacerbates these unsatisfactory conditions, In such a situation, the adaptability of the urban physical is greatly reduced Various modes of networking, comprising connectivity, centrality, and different lengths of communication links, contribute significantly to absorption, adaptation, and organization capacities and have been examined by some researchers, including Sharifi (2019b).

Some other substantial and influential factors in various stages of urban physical resilience include size, distribution, and accessibility of open and green spaces, which contribute to urban resilience against earthquakes in several ways. First of all, open and green spaces facilitate the preparedness phase by providing a place for evacuation and shelters, temporarily providing shelters for residents throughout the absorption phase until they safely return to their homes. Throughout the preparedness phase, open and green spaces can adjust the density, establish safer environments, and separate various vulnerabilities. They can also act as alternatives to disrupted street networks, facilitating the absorption phase while providing the necessary resources to reinforce the recovery phase, including a space to improve, restore, and reconstruct buildings in the self-organization phase. Finally, rescue teams can be established in such spaces to provide relief and urban services, facilitating urban physical resilience's absorption and adaptation phases. Yousuf Reja (2012) emphasized the significance of open and green spaces surrounding buildings in terms of collective connectivity and assistance during crises and as post-disaster shelters, In this way, the adaptation phase is strengthened Allan et al. (2013) conducted a study in Concepción, indicating how open and green spaces contributed effectively as temporary shelters in the vicinity of disaster-stricken neighborhoods and buildings. Thus, small communities are formed in neighborhoods, allowing residents to establish emotional connections with each other following disasters such as earthquakes, speeding up the process of recovery. In addition, the proximity of residents to their homes and neighborhoods enables them to take care of their property. In addition to all the above, open and green spaces may have different sizes and distributions, providing a wide range of rescue and restoration alternatives and chances.

6.2 Urban physical resilience in the case study area

The LCZ framework offers a universal methodology to identify standard zones according to the physical characteristics of the study area. This could contribute to addressing challenges related to the development of standard and comprehensive spatial evaluation frameworks. Different resilience classes are defined in these zones. In LCZ1-3 with a compact texture, indicators such as high density of physical structure, presence of large lots, a relatively long distance from fire stations and hospitals, high aspect ratio, a long distance from open and green urban spaces, and high density of built-in environment around them weaken resilience. However, other indicators such as high robustness of buildings, appropriate diversity of land use, adaptation of land uses, a long distance from dangerous uses, appropriate width of street networks, accessibility and proper form of street networks, large open and green spaces, and their adaptable distribution increase resilience. According to the total number of these indicators and the weight of each, the indicators are overlapped in the ArcGIS software. These indicators have generally brought about a moderate degree of resilience in these areas.

In LCZ4-6, indicators such as low density, high suitability of land uses and relatively good distribution of them, the relatively long distance from hazardous land uses, very high robustness of buildings, great length and width of street networks, high connectivity, the large size of open and green spaces, and low density of the built environment around them enhance resilience. Indicators such as low diversity of uses, coarse-grained lots, inadequate access to hospitals and health centers, high aspect ratio, and the relatively high slope weaken urban resilience. Overlapping these indicators have led to relatively high resilience in these zones. In LCZ 7, the very low robustness of buildings, high slope, and high centrality of intersections are the most important indicators leading to the low resilience of this zone. In LCZ 8, indicators such as low density, adaptation of uses, appropriate distance from hazardous areas, well-distributed land uses, small-scale lots, moderately robust buildings, suitable aspect ratio, street network design and centrality have contributed to a good level of resilience. In LCZ 9, low density, high adaptability of land usage, safe distance from hazards, resilient buildings connect with various levels of urban green space and connectivity contribute to higher levels of resilience. Likewise,a combination of different LCZ zones has resulted in varying levels of resilience. Overall, this method can also be very useful for areas that lack data on the urban structure because LCZ zones are formed based on the physical characteristics of the desired site.

This study evaluated District 4 of Tehran, which is one of the largest districts in the city and is located near major faults. In this district, 22 zones were selected for the study after preparing the LCZ map. The selected zones included the main classes of the LCZ map, some of which were a combination of two or three LCZ zones, depending on the urban physical structure. As Fig. 9 shows, urban physical resilience is divided into five classes in these zones. Most of these zones generally have moderate resilience to earthquakes at different phases. Parts of these zones have buildings constructed in new urban development, showing more resilience to earthquakes. These zones have moderate physical resilience due to the high robustness of buildings, the suitable width of street networks and therefore an appropriate aspect ratio, although they have a high density. Wide street networks around the district and in some parts of its internal structure have improved resilience. Zones with low and relatively low resilience are located in zones where the robustness of buildings is low, and the whole structure of the zone has an old and compact texture. Inadequate distribution of fire stations and hospitals throughout the region is a factor of concern during relief efforts. Also, access to open and green spaces is not uniform across the studied zones. Hence, the parts of the district with an older texture have a much lower level of accessibility than other parts, indicating the inappropriate distribution of such spaces in the district.

Sensitivity analysis was performed on the values of framework indicators in the last step of this research. Sensitivity analysis examines the input and output relationships of the framework and investigates the effect of input changes on framework outputs. Sensitivity analysis increases the reliability of the framework by examining other states of the inputs and reducing the uncertainties in the results. Also, sensitivity analysis is considered an optimization process because by changing the input values and determining its effect on the model's output, the best state and input values can be determined to reach the desired solution. Sensitivity analysis is a method to determine the strength and reliability of evaluations by examining the impact of results with changes in methods, models, values of unmeasured variables, or assumptions. These uncertainties in the results increase in events such as earthquakes due to the lack of real post-earthquake data. The urban physical structure is a collection of related interacting elements and features. In other words, all the elements and indicators of urban structure interact to determine urban physical resilience at different phases. Therefore, all the indicators should be in the ideal condition to achieve proper urban physical resilience. Thus, the present study examined the changes in the values of all indicators to find the optimal combination of indicators for each zone. Four scenarios were implemented on different zones with a range of +50 to −50% changes in the values of the indicators to determine physical resilience. For example, LCZ1 had the worst conditions in all four scenarios compared to its present state. Therefore, the values and changes of the indicators in the current situation should be improved and maintained in the planning for this zone. In some zones, such as LCZ2, more resilience is obtained by changing the values of the indicators in all four scenarios. Similarly, it is possible to examine the optimal value of indicators for other zones to achieve the highest level of physical resilience. In general, according to the most effective and important indicators determined from the framework and given the values of the desired indicators for each zone, it is possible to conduct targeted urban planning and spatial decisions to increase urban physical resilience.

7 Conclusion

. Today,, earthquakes are one of the most unpredictable and damaging natural hazards. So far, the approach to managing crises and addressing natural hazards has predominantly focused on coping with immediate challenges and mitigating threats.However, as a very popular concept and paradigm in crisis and risk management, resilience has recently shifted its focus from merely risk management and mitigation to an increase in risk adaptation and urban recovery. Therefore, urban residents, managers, and politicians can act more effectively in the face of unknown and uncertain natural hazards.

This study investigated urban physical resilience since urban structure is the first part of the urban system that must withstand an earthquake. Despite the great growth of research on resilience, urban resilience is still a relatively active field and dimension of resilience studies. A physically resilient city ought to be prepared for unexpected events which include earthquakes, absorb initial shocks, maintain functionality during difficult situations, and provide grounds for changes in line with the improvement of urban structure. In the end, a resilient city requires the ability to restore to its pre-disaster conditions while ensuring urban development along with diffused and flexible changes through the years. This definition of urban physical resilience encompasses four important phases of resilience, including Preparedness, Absorption, Recovery, and Adaptation, and Self-organization. Considering that urban structure is a complicated system, it is necessary to link this definition to several urban form indicators that define urban physical structure to make the idea more clear and sensible and evaluate it through a comprehensive framework. This study defined the physical dimension of urban resilience using 20 indicators related to urban built environments, street networks, and urban open and green spaces. These indicators were determined and scrutinized through previous studies, expert opinions, and statistical methods of factor analysis, followed by determining the effectiveness of each in different resilience phases. These indicators have interactions and interdependencies in the complex urban structure, which should be identified for their placement in an evaluation framework. This study used the ISM method to structure the problem and determine these relationships, followed by determining the weight and importance of each indicator in the evaluation of urban physical resilience. Since ANP is an expert-based method, the study used statistical and optimization methods to adjust and scrutinize the weights of the indicators obtained from this framework. Finally, a hybrid indicator was obtained considering the weights of these indicators and the type of their relationships to evaluate urban resilience at different phases of resilience.

Any evaluation of urban physical resilience will be successful and feasible if it is based on spatial or physical indicators and characteristics of the desired place. Therefore, a spatial unit dependent on the morphological features of the study site was employed to develop and implement this framework in different locations and spatial scales. The LCZ map and LCZ zones are prepared as homogeneous and standard zones based on the physical characteristics of the study site. It is possible to quantify and implement such a framework in different locations. Finally, this framework underwent sensitivity analysis. A city will be resilient when all urban features and components are in an ideal state of growth and improvement. The unbalanced enhancement of various physical characteristics in the course of urban resilience may undermine urban resilience. Therefore, the values of all indicators in different scenarios underwent sensitivity analysis. The use of this method is recommended in multi-criteria spatial decisions and urban planning.

This framework was implemented in District 4 of Tehran. Tehran, as the capital of Iran, is prone to severe and destructive earthquakes due to its special natural and geographical conditions, along with its location in the high seismic hazard zone. The North Tehran Fault and the Mosha Fault are the two most important faults that affect District 4 of Tehran. The implementation of the suggested framework in this area shows a moderate state of urban physical resilience. The main indicators weakening urban physical resilience in designated areas include non-compliance with construction standards, particularly as high densities, inadequate implementation of street networks and accessibilities, higher blockage, heterogeneous development with merely economic approaches and without considering the adaptation of land uses, vulnerable and compact textures with inadequate gradation, lack and inadequate distribution of urban open spaces and green spaces, etc.

In general, developing frameworks for the evaluation of urban physical resilience, preparation of maps, scenario building, and sensitivity analysis can help determine urban strengths and weaknesses against earthquakes. These results can help planners and managers in developing policies to mitigate the risk of crises and determine procedures to deal with weaknesses of the city, ultimately increasing urban physical resilience. It is also possible to completely direct and manage rescue, search, and relief operations in the event of crises while avoiding the waste of the golden rescue time. Besides, the grounds for the improvement of urban structure to more ideal conditions than the pre-earthquake state are also provided.

Some other recommendations that can help urban and spatial planners to increase urban physical resilience are as follows. Considering the importance values obtained for the urban physical resilience indicators, physical robustness should be at the top of measures aimed at increasing the urban physical resilience against earthquakes. This consideration should be taken into account in new urban developments, as well as in the reinforcement of existing structures and buildings by revising laws related to urban construction and urban networks. This measure is particularly important in cities like Tehran, with a large share of old and worn out urban fabric. Considering a reasonable and appropriate building density, especially in areas with a small street width, is very effective in physical resilience. Also, increasing building density and high-rise construction in narrow networks should be avoided. Preventing the increase of confinement is one of the next important indicators. Connecting urban networks with different widths through a structured hierarchy and designing them in such a way as to create high permeability is also essential. This will contribute to having urban networks with proper connections and an integrated and connected structure that can effectively respond to risks such as earthquakes. Having optimal plot sizes should also receive enough attention. Very small lots could increase vulnerability to earthquakes. Therefore, optimized aggregation of fine-grained lots for more suitable land use plans is critical. Further, optimal siting of essential uses and services such as medical facilities and crisis management support centers is critical for enhancing resilience. Such facilities should be located near main and wide urban networks that feature optimal levels of centrality and accessibility to speed up rescue operations and service delivery. Similarly, suitable provision of open and green spaces across the urban network contributes to more effective disaster absorption, response, and recovery.These are some of the important provisions that should be considered in urban and spatial planning, considering the weight and importance of indicators.

One of the limitations of this research was the validation of results. It was impossible to validate the results accurately due to the lack of real post-earthquake data. This study tried to solve this problem using sensitivity analysis, but future studies can use other methods. Other adjustment methods, such as discretized choice models, can also be utilized to achieve more accurate weights of the indicators to be used as the main basis of the evaluation framework. Finally, this study used the LCZ zones to assess urban physical resilience. Future research can use this method to evaluate other aspects of resilience, such as social, cultural, and environmental dimensions.