Regional Recovery Modeling and Postdisaster Model Updating: The Case of the 2010 Kraljevo Earthquake in Serbia

In addition to direct losses, such as casualties and repair-and-replacement cost, earthquakes inflict indirect losses, dominated by the downtime, during which buildings cannot safely harbor their intended function. Disruption of housing capacity may lead to negative long-term consequences (Potter et al. 2015), while business interruption may comprise a large amount of total losses (Cremen et al. 2020). Consequently, the primary objective of postearthquake recovery simulation is to estimate the time needed to recover building functionality and get the community back to normal (EERI 2016), while identifying primary factors that hinder recovery.

Building recovery time consists of the delay time, the time between the disaster occurrence and the start of building repair, and the repair time (Comerio and Blecher 2010). Several approaches, often based on the FEMA P-58 framework (FEMA 2018), have been proposed to create high-fidelity models to predict the repair time of individual buildings (Terzić et al. 2021; Molina Hutt et al. 2022). Models that integrate delay time into the building recovery time estimates (e.g., Almufti and Willford 2013) divide the delay time into several impeding factors, whose sequence and duration are often based on expert opinion and data from a limited number of past events. Although such frameworks provide the basis for future research, the expert opinion and empirical estimates used to inform such models focus on the US context. However, the delay time and the repair time largely depend on local regulations and traditions, as evidenced by the application process for public funding after the 2009 L’Aquila earthquake (Di Ludovico et al. 2017a, b). Thus, a recovery modeling framework that explicitly takes into account the local context is required, because the paucity of postdisaster recovery data hinders derivation of comprehensive empirical recovery functions (Fu et al. 2021).

Furthermore, both delay and repair time of a building depend on the state of the entire community, not only the considered building, as functional recovery of buildings involves resources that are shared on a community level (Blagojević and Stojadinović 2022), socioeconomic factors (Nejat et al. 2020; Burton et al. 2022), and performance of infrastructure systems supporting building functions, such as transportation and electricity (You et al. 2021; Blagojević et al. 2022f). Therefore, regional recovery models that can consider the local context and the state of the infrastructure are needed to reliably assess the recovery time of buildings in a community.

Miles et al. (2019) summarized the current trends in regional recovery modeling. Burton et al. (2016) proposed a framework to include building performance into resilience quantification by modeling the steps required to recover to several functionality levels. Costa et al. (2021) modeled housing recovery for a scenario earthquake in Vancouver with an agent-based housing recovery model, including socioeconomic factors. A model that integrates the effect of recovery resource constraints, socioeconomic context, and postdisaster policies on housing recovery is proposed by Sutley and Hamideh (2018). Nasrazadani and Mahsuli (2020) proposed a comprehensive agent-based model for regional recovery simulations and resilience assessment that considers interdependencies among various community systems, from healthcare to civil infrastructure systems. Didier et al. (2018) proposed a framework that characterizes the recovery process by explicitly modeling community postdisaster demand and supply for infrastructure services. The framework has been extended to capture resource and service constraints affecting recovery (Blagojević et al. 2021a; Blagojević and Stojadinović 2022).

Although significant advances in regional recovery modeling have been made in recent years, the application of such models in practice is not widespread. The limited application of regional recovery models is primarily due to challenges in estimating model parameters, variations in recovery and resilience metrics, and the absence of a standardized validation approach for such models. Most regional recovery frameworks are applied to virtual or semivirtual case studies (e.g., Burton et al. 2016; Blagojević and Stojadinović 2022), where numerous model parameters are set for illustration purposes, without guarantee that they will be applicable or available in practical applications. In general, model parameters can be estimated using empirical data, experimental data, or expert opinion. Empirical data related to postdisaster recovery is scarce, incomplete, and sometimes unreliable. Experiments at regional scales are not feasible, while shake-out exercises and similar training activities rely on expert opinion. Thus, postdisaster expert experience and opinion remain as the basis for regional recovery model validation and parameter calibration. Therefore, it is crucial that model parameters are tangible quantities, formulated to be easily understood and estimated by the experts, and potentially generalizable to other disasters, regions, and circumstances. Another aspect of disaster recovery model validation are the utilized recovery and resilience metrics. Available validation studies use different metrics, depending on the available data and the features of the model, making it difficult to generalize and develop a common regional recovery modeling approach. Furthermore, longitudinal postdisaster data collection and processing studies are needed to generate comprehensive data sets for recovery model validation.

Despite the scarcity of empirical recovery data, it is important to validate regional recovery models by comparing their predictions to the recovery dynamics observed after a real disaster. This has been done in only a few published studies. Constrained postearthquake recovery resources have been modeled with stochastic queuing models by Alisjahbana and Kiremidjian (2020). The model was used to simulate the housing recovery after the 2018 Lombok, Indonesia, earthquake. Model parameters were calibrated using the housing recovery data from the considered event for a single region, followed by a comparison of the predicted and observed recovery trajectories for the remaining affected regions. Longman and Miles (2019) used the DESaster recovery simulation library to model the recovery of 100 houses damaged by the 2015 Nepal earthquake and compared their predicted state 2 years after the earthquake with the collected recovery data. Nejat et al. (2020) calibrated a spatial logistic regression model using the data collected by interviewing affected single-family households to predict the household recovery decisions in Staten Island, New York, following Hurricane Sandy in 2012. Aghababaei et al. (2020) validated and updated recovery time fragility functions using the data collected in a 5-year longitudinal study of the Joplin, Missouri, community following a 2011 tornado. Similarly, Wang and van de Lindt (2021) validated a regional recovery model against the field data pertaining to 1,874 buildings repaired after the 2011 Joplin, Missouri tornado, considering both the delay times and the repair times conditioned on the building inhabitants’ incomes.

In the early aftermath of a damaging earthquake event, regional recovery predictions may provide valuable, although uncertain, information for planning and execution of various recovery efforts. Considering the continuous inflow of ground-truth impact data is crucial to ensure that decision makers get up-to-date recovery model predictions. Results from the first few days of a safety screening and damage assessment campaign, for instance, provide valuable information on the inflicted damage. Yet, most recovery modeling studies focus on the immediate postevent state, and do not consider inflow of damage information from inspections (e.g., Costa et al. 2021; Nasrazadani and Mahsuli 2020). Very few studies modeled the recovery process by considering dynamically evolving damage data (Tomar et al. 2022).

In this paper, we illustrate how a regional recovery model, based on the bottom-up demand/supply-based iRe-CoDeS framework, is constructed to simulate the recovery of residential buildings following a real event, the 2010 Kraljevo, Serbia, earthquake. We choose the iRe-CoDeS recovery framework due to its ability to account for the local context by including different building-level recovery trajectories and capturing the recovery resource constraints. Apart from recovery resource constraints, the bottom-up demand/supply approach is used to simulate the dynamic interdependencies among infrastructure systems: component interactions depend on the flow of services and resources among components and can change dynamically during the recovery time (Blagojević et al. 2022f). Notably, component interactions are not based on static one-to-one dependency relation defined before the event. Furthermore, the iRe-CoDeS-based regional housing recovery model extends the well-established regional disaster risk assessment methodology and uses tangible quantities that can be reliably estimated through expert opinion as recovery model parameters. The proposed iRe-CoDeS-based residential housing recovery model presented herein has three advantages: first, it can dynamically assess the effect of infrastructure failure on building’s functional recovery (Blagojević et al. 2022f, g) and access to repair (Blagojević et al. 2021a); second, it can be dynamically updated using the incoming stream of building damage inspection data (Bodenmann et al. 2023, 2021); third, the outputs of this iRe-CoDeS-based regional housing recovery model can be used to probabilistically assess community resilience goals (Blagojević et al. 2022c, d) and shape effective resilience-improving measures (Blagojević et al. 2022e; Blagojević and Stojadinović 2022).

This paper starts with an overview of the iRe-CoDeS-based regional housing recovery model. Then, a method to improve estimates of regional housing recovery using early inspection data is introduced. Finally, the proposed framework for recovery prediction is applied in a case study based on the 2010 Kraljevo earthquake, a 5.4 magnitude event that caused damage to about 16,000 buildings, resulted in two fatalities, and required about 2 years of recovery efforts. The 2010 Kraljevo case study shows how parameters of an iRe-CoDeS regional housing recovery model can be obtained by consulting experts and using scarce empirical data. Furthermore, recovery predictions obtained from the iRe-CoDeS model are compared to the postevent data in an effort to validate the model and identify its main shortcomings. Importantly, the iRe-CoDeS regional housing recovery model can be integrated with methods that use early-arriving damage inspection data to update the damage predictions on the regional level, showing how such immediate and continuous postevent updating can be used to reduce the uncertainty in recovery time predictions.

To model regional recovery, this study employs a bottom-up simulation workflow that is based on three main components: exposure information, the estimation of physical damage, and finally, the recovery simulation. These components are explained below, with a particular focus on recovery simulation.

The bottom-up prediction of earthquake-induced damage and the subsequent recovery process requires high-resolution exposure information. Such information is compiled from multiple sources and, in many cases, additionally relies on predictive models to estimate building attributes that are not directly available in existing databases (Pittore et al. 2018; Crowley et al. 2020; Diana et al. 2019). Physical damage to buildings and infrastructure systems’ components is then quantified using sequential, collectively exhaustive, and mutually exclusive damage states, ranging from no damage to complete damage, and estimated via a well-established simulation workflow. First, conditional on the earthquake rupture characteristics, ground-motion intensity measures (IMs) at the building or component locations are sampled from their joint multivariate log-normal distribution (Jayaram and Baker 2008). Then, conditional on the sampled IM, damage states are drawn from a categorical distribution, where the individual probabilities are derived from fragility functions (Crowley et al. 2021b).

Once the damage of buildings and infrastructure systems’ components, labelled together as components, considered in the regional recovery analysis is estimated, the recovery of each component is simulated as a sequence of recovery activities, related to delay and repair times (Blagojević and Stojadinović 2022). Such a sequence is conditioned on the component’s characteristics (e.g., occupancy type, ownership structure) and its initial postdisaster damage. Each recovery activity is characterized by its preceding activities that need to be completed before the activity can start, resource demand, representing the resources required to perform the activity, and duration, the amount of time needed to finish the activity once it starts.

In the iRe-CoDeS framework, interactions among components are simulated at each time step of the recovery simulation as a flow of various resources among components. Such an approach is used to capture recovery resource constraints (Blagojević and Stojadinović 2022), dynamic component interdependencies and cascading effects (Blagojević et al. 2022f), access to repair (Blagojević et al. 2021a), the effect of infrastructure systems on building’s functional recovery (Blagojević et al. 2022g), and estimate the components’ resource consumption to assess system’s ability to meet its resilience goals (Blagojević et al. 2022c). To capture the listed aspects of regional recovery, each component is characterized by its supply, operation demand, and recovery demand. Resource supply at a certain time step represents the amount of resources that the component is providing to other components and depends on component’s state of damage and its operation demand fulfillment at that time step. The component’s recovery demand consists of all resources that a component needs for its recovery activities to progress at a certain time step of the recovery simulation. In the same manner in which the component’s supply is conditioned on component’s operation demand fulfillment, the progress of recovery activities is conditioned on the recovery demand fulfillment.

The steps to define an iRe-CoDeS regional recovery model are outlined in an earlier report (Blagojević et al. 2022f) and summarized here. To construct an iRe-CoDeS recovery model, the spatial limits of the considered region need to be first defined, followed by the selection of systems (e.g., infrastructure systems and/or housing) and the resources to be considered in the analysis. Then, components of each system are characterized by their predisaster supply and operation demand, and a set of functions that describe how their physical damage and interdependencies affect their postdisaster supply and operation demand. Finally, component recovery models are adopted to simulate the increase in their functionality over the recovery period.

The parameters required to define the recovery model of a building or a component are the recovery activities sequence and the duration and resource demands for each recovery activity. Such information can be found in the literature (FEMA 2018, 2020; Terzić et al. 2021), but the sources are region-specific. For regions where no systematic data collection was done, the recovery activities sequence, duration, and resource demands can be obtained through expert elicitation and/or empirical data. While recovery activities sequences are usually defined based on the adopted recovery plans or the experience from past events, most recovery models do not explicitly consider the effect of regional resource constraints (e.g., Almufti and Willford 2013). In such models, the estimated duration of recovery activities includes both the time that the building waits to obtain a resource, the waiting time, and the actual duration of the activity (the time needed to perform the activity once the resources it needs are provided). The waiting time is context-specific and depends on the regional supply and demand for recovery resources, access to repair, and building’s priority for resource allocation. Such a complex variable is difficult to reliably assess only through expert opinion. To alleviate this issue in iRe-CoDeS, the waiting time of a recovery activity is explicitly captured by simulating the flow of recovery resources among damaged buildings and conditioning their recovery on their recovery demand fulfillment. Thus, in iRe-CoDeS, the experts need to estimate the actual duration of an activity, which, according to our experience, the experts can estimate with less uncertainty. Furthermore, this estimate is transferable to similar regions. To simulate the waiting time, the information on regional supply, buildings’ resource demand, and resource allocation priority is needed. A building’s resource demand can be reliably estimated using expert opinion (e.g., how many engineers are needed to inspect a building or how many workers are needed for repairs), while a building’s resource allocation priority depends on the selected resource allocation strategy, and is an input to the regional recovery model. The regional supply of recovery resources can also be estimated using expert opinion, the data on the regional workforce availability, or data from recent events in the considered region. Therefore, in iRe-CoDeS an effort is made to define the recovery model parameters as tangible quantities that can be reliably estimated or defined based on the adopted recovery plans and are transferable to other regions, while allowing disaster management decisions to be incorporated as model inputs.

In the immediate aftermath of an earthquake, regional recovery predictions rely on model-based estimates of earthquake-induced damage. The precision and accuracy of such damage estimates depend on the density of the seismic network used to constrain the uncertainty in the geographic distribution of ground-motion IMs, the available exposure information, and on how well the fragility functions reflect the seismic behavior of the local building stock, among other inputs. Recently, Bodenmann et al. (2023) proposed to use Gaussian process (GP) models for a dynamic updating of regional damage estimates using observed damage data from early inspections.

The proposed method leverages building inspection data to update the initially specified fragility functions and to constrain the uncertainties of the ground-motion IM geographical distribution. Namely, the random field of logarithmic ground-motion IMs is expressed as a function with a GP prior (Rasmussen and Williams 2006), whose mean and covariance functions are specified using ground-motion and spatial correlation models. Then, variational inference is used to compute updated fragility functions, as well as an approximate posterior distribution of the ground-motion IM conditional on the observed damage data from building inspection. Finally, the posterior predictive distribution of the ground-motion IM is computed for the locations of buildings that have not yet been inspected. Generating correlated samples from that distribution, in combination with the updated fragility functions, leads to improved regional damage estimates (Bodenmann et al. 2023).

On November 3, 2010, at 1:56AM local time, a 5.4 magnitude earthquake struck the municipality of Kraljevo, Serbia (Antonijević et al. 2013). The epicenter was located close to the center of the city of Kraljevo, which, in 2010, housed more than half of the 120,000 people living in the entire region. The earthquake claimed 2 casualties and 180 injuries. Around 16,000 houses and 8,500 multifamily dwelling units were damaged (UN 2011; RTS 2011).

Immediately after the earthquake, local civil engineers and architects started a rapid damage inspection with the goal to assess the life safety of buildings (Marinković et al. 2018). Supported by the academic staff from Serbian universities, official building damage assessment documents were developed and the damage estimation process was initiated about 10 days following the event. The damage estimation reports specified the building damage category, which served as the basis for subsequent recovery decisions and actions (Marinković et al. 2018; Manić and Bulajić 2012). Specifically, building damage was classified into six categories conditioned on the damage state of structural and nonstructural building components and the extent of the required repair activities: buildings in the first three categories (K1,2,3) experienced primarily nonstructural damage that did not require major repairs; buildings in categories K4 and K5 needed structural repairs; finally, buildings in category K6 required demolition and replacement. For the purpose of this study, this custom-developed damage scale (K1 to K6) was reduced to four damage categories (DS1 to DS4), following Stojadinović et al. (2021) and Blagojević et al. (2021b): K1 and K2 are combined into DS1, K3 is mapped to DS2, K4 and K5 are lumped into DS3, and K6 is mapped to DS4.

This case study focuses on the recovery of the residential buildings, which was organized by the municipal government. The supporting infrastructure (i.e., electric power, water, and communication systems) was not severely affected in this earthquake event and was not considered in this regional recovery model. The postearthquake habitability of the damaged buildings was addressed first: all DS4 buildings and a small percentage of DS3 buildings were evacuated. No multifamily residential buildings were identified as unsafe. Following inspections, recovery activities for damaged residential buildings continued, with the recovery activity sequence depending on the damage category and the ownership structure (single-family versus multifamily buildings). Repair financing procedures were established after the earthquake and were also conditioned on building’s damage category and ownership structure. Repair financing procedures for single-family buildings that experienced only nonstructural damage evolved over the first couple of months after the earthquake until the payment of a fixed amount, conditioned on building damage, was adopted. Owners of single-family buildings that experienced structural damage were first provided with the funds for repair design, which also resulted in a bill of quantities used as the basis for the second payment intended to fund the repair work. The local government prioritized and led the replacement of completely damaged (DS4) single-family buildings as well as the repair work for damaged multifamily buildings, fully funded by the state government. Owners of DS4 single-family buildings received prefabricated houses that were installed on the foundations built on the land they own. Erection of these prefabricated houses was often done before the demolition of the damaged houses, as some owners prevented the demolition teams from accessing their premises. Marinković et al. (2018) concluded that the delays due to financing prolonged the recovery process by a couple of months. An important recovery impeding factor was the winter weather: although the earthquake occurred in November 2010, the majority of recovery activities started only in spring 2011. These included mostly nonurgent nonstructural repairs, while structural repairs of buildings with impaired safety were performed as soon as possible.

Components of the regional housing recovery model and simulation for the 2010 Kraljevo earthquake are explained next. We start with exposure modeling and a brief description of the regional building stock. Then, we present the damage estimation model and the method used to update the postearthquake damage estimates using early-arriving damage inspection data. We continue with a detailed description of the regional housing recovery model and the data used for its validation. This section concludes with a comparison of the damage estimate and recovery model results to the observed data.

Making disaster resilience planning and implementation actionable from the engineering standpoint necessitates tools to model and analyze the disaster damage and postdisaster recovery process. While seismic risk modeling and analysis is well established in engineering research and practice, frameworks to model and quantify postdisaster recovery are in the nascent development stage. An important step toward the use of such frameworks for decision making consists in illustrating their practical applicability, building trust in the recovery predictions through validation studies, and identifying their main shortcomings.

In this study, we applied the iRe-CoDeS framework to simulate the regional housing recovery following the 2010 Kraljevo, Serbia, earthquake. The aim was to show how such a framework for regional recovery modeling can be applied in a realistic context by profiting from existing data and expert opinion. Furthermore, we show how the outputs of the recovery model can be updated using early damage inspection data to reduce uncertainty and increase the accuracy of recovery predictions. Importantly, we used the data collected after the 2010 Kraljevo earthquake to model the postearthquake housing recovery and validate the simulation outcomes against the reported data.

Despite the challenges posed by the available data quality, numerous modeling assumptions, and the current limitations of the iRe-CoDeS framework, the outputs of the recovery model using the reported building damage data and concerning the recovery of DS1, DS2, and DS4 buildings and the regional shelter capacity aligned with the reported data reasonably well: the difference in the observed and simulated median recovery metrics spanned from 5% to 39%. However, the accuracy of recovery models utilizing pre-event building damage estimates obtained using ground-motion models and fragility functions was found to be less accurate. Based on the comparison of the two recovery models, it is evident that improving the damage estimation models should be the first priority to increase the accuracy of future regional recovery simulations. This can be achieved through the development of region-specific damage estimation models. Additionally, we showcased the benefits of using early inspection data to update recovery projections and thus increase their accuracy. Apart from identifying the effect of different building damage estimation models on recovery model outputs, we identified certain limitations of the iRe-CoDeS framework. The simplified assumption that buildings recover as soon as the recovery resources are available was shown not to be correct: weather conditions can also delay the start of repairs, particularly when the damage does not significantly impair building safety and functionality. This delay was not captured in this study but will be considered in future work. Furthermore, we need better methods to estimate community’s ability to supply recovery resources, such as repair workers, and the evolution of this ability over time, as the effect of resource constraints on regional housing recovery needs to be modeled and evaluated better to reduce uncertainty. The uncertainties in damage and recovery model outputs are also affected by the magnitude and severity of the considered event. While this case study tackled a moderate-magnitude event, large-magnitude events are likely to result in higher uncertainties. Such events are less frequent, which implicitly limits the data availability for model development and validation purposes. More severe events may also cause secondary effects, such as landslides and ground rupture, producing cascading effects (e.g., preventing access to repair) further complicating the recovery process, and thus, requiring the consideration of additional recovery activities that introduce extra uncertainty. However, the added iRe-CoDeS capability to dynamically update the damage estimates using a stream of early-arriving damage inspection data was shown to improve the recovery process predictions by reducing the uncertainties associated with pre-event damage and recovery models. Importantly, the dynamic updating capabilities of the iRe-CoDeS framework can be applied to the incoming recovery process data, making the iRe-CoDeS framework suitable for better planning and execution of the postdisaster recovery process.

The iRe-CoDeS bottom-up demand/supply framework was shown to be a good basis for developing regional recovery models capable of simulating a preplanned disaster recovery process of modern communities, given the necessary hazard, exposure, and vulnerability data. The simulations can be used in what-if studies to estimate the duration of the recovery effort in total, as well as the duration of individual recovery activities and the recovery resource demands they impose on the community. The iRe-CoDeS regional recovery models can be refined by integrating advanced building repair/recovery models, allowing a more in-depth consideration of building repair and the required resources. Additionally, integrating the postdisaster performance of interdependent infrastructure systems and their effect on buildings’ functional recovery in future studies will allow for a more comprehensive resilience quantification using the iRe-CoDeS framework. Finally, iRe-CoDeS-based regional recovery models can be improved by conducting similar validation case studies involving higher-magnitude events in different regions, as well as by updating and recalibrating recovery model parameters based on the observed recovery processes and sequences to prepare for the next disaster.

It is clear that recovery data collection efforts, through longitudinal postdisaster data collection projects or similar studies, are needed to establish a validation database for regional recovery models. Such studies will eventually enable recovery models capable of reliably predicting the recovery trajectories of communities after future disasters. It is important to note that constructing a regional recovery model involves discussing various elements of community disaster resilience with the stakeholders and outlining recovery plans prior to future disasters. Thus, the sole process of constructing a regional recovery model is already a step toward community disaster preparedness and contributes to community resilience. Studies, such as the one presented herein, are a necessary first step toward developing reliable regional recovery models. Such studies outline the data collection process, identify the main sources of uncertainty and point to important shortcomings of current recovery models that need to be addressed in the future.

Some or all data, models, or code used during the study were provided by a third party. Direct requests for these materials may be made to the provider as indicated in the Acknowledgments.

The case study presented in this paper would not be possible without the information provided by experts involved in the Kraljevo 2010 earthquake recovery; thus, the authors would like to thank Dragan Milivojević, Aleksandar Avramović, Zdravko Maksimović, Dejan Karapandžić, and Predrag Blagojević. Furthermore, the authors would like to thank the City of Kraljevo for sharing the GIS data. The work presented in this paper was financially supported by the Real-time Earthquake Risk Reduction for a Resilient Europe “RISE” project, financed under the European Union’s Horizon 2020 research and innovation program, under grant agreement No 821115, the ETH Risk Center project “DynaRisk,” financed under grant agreement ETH-11 18-1, and the ETH Chair of Structural Dynamics and Earthquake Engineering.