Simulating the role of transportation infrastructure for community disaster recovery Open Access

Transportation networks are vital for community disaster recovery as they enable the post-disaster flow of the resources and services (R/Ss) needed for emergency relief and reconstruction of damaged community components. Examples of transportation network damage hindering community disaster recovery are the 1995 Kobe earthquake (Chung et al., 1996), 2005 hurricane Katrina (Padgett et al., 2008), 2015 Gorkha earthquake (Aydin et al., 2018) and 2016 Kaikoura earthquake (Davies et al., 2017). Therefore, considering functional recovery of transportation networks in community disaster recovery simulations is important to quantify community disaster resilience properly and investigate the effectiveness of various resilience-improvement measures. As communities are complex systems-of-systems, the underlying structure of tools used for this purpose needs to be broad enough to encompass the different ways in which these systems operate, while providing community disaster resilience metrics for making post-disaster recovery decisions. The ‘resilience – compositional demand/supply’ (Re-CoDeS) framework (Didier et al., 2018a) proposes one such approach, by viewing all components of a community as suppliers and/or users of various resources and services. Disaster resilience metrics are the unmet demands of a community for resources or services that can be integrated over time (Blagojević et al., 2020a) or considered at certain post-disaster time instances (Blagojević et al., 2022a). The proposed approach has been used to quantify the disaster resilience of an electric power (EP) supply system (Didier et al., 2015, 2017a, 2017b), water distribution and cellular communication systems (Didier et al., 2018b), three interdependent infrastructure systems (Blagojević et al., 2020b, 2021a) and housing (Blagojević et al., 2022b). However, none of these studies explicitly considered the R/S constraints that can have an adverse effect on community disaster recovery. This paper shows how the demand–supply approach, the basis of the Re-CoDeS framework, can be applied to simulate various R/S constraints related to community disaster recovery, with an emphasis on the role of transportation infrastructure in enabling community disaster recovery.

The Re-CoDeS framework quantifies the disaster resilience of a system by contrasting its post-disaster evolution of supply, demand and consumption of a R/S over time (Figure 1) (Didier et al., 2018a). A system can be a community, a part of a community, a single civil infrastructure system or any part of a civil infrastructure system. System supply capacity, $Ssys,R/SCt$ and demand $Dsys,R/St$⁠, for a R/S at time t of the resilience assessment interval are obtained as aggregates of supply and demand of all I system components:

where $Di,R/St$ and $Si,R/SCt$ are demand and supply capacity of a component i for R/S at time t, respectively.

The R/Ss need to be transferred among components. Damage to distribution networks, prioritisation, conservation rules or safety measures can disturb or prevent R/S distributions, causing a difference between the supply capacity of the system and the supply available to the components. The system R/S distribution model simulates this phenomenon and enables the computation of a component's consumption that represents the met demand of that component. It can be calculated as the minimal value between the component's demand $Di,R/St$ and the supply that is available to that component $Si,R/Savt$⁠:

By aggregating the consumption of all components, the system consumption for a R/S at time t is defined:

Lack of resilience (LoR) of a system at time step t in relation to a R/S can now be defined as:

and integrated over a considered resilience assessment interval $(t0,tf)$⁠:

iRe-CoDeS is an extension of the Re-CoDeS framework that enables disaster resilience quantification for a system of interdependent systems (Blagojević et al., 2021a). Interdependency among components of interdependent systems is simulated using an iterative demand–supply algorithm. Such an algorithm traverses all the possible ways in which components can affect each other at each time step of community disaster recovery and eliminates the supply capacity of those components whose demand for any R/S is not met at that time step. The interdependency evaluation is repeated at each time step anew, considering the state of all components at that time step.

The values of R/S supply and demand, and consequently consumption, of a component can change at every time step of the resilience assessment interval. Component properties that directly affect its instantaneous supply capacity $Si,R/SCt$⁠, demand $Di,R/St$ and consumption $Ci,R/St$ values are: damage level, functionality level and repair rate. The damage level of a component is used to quantify the physical damage of a component after a disaster and to track its recovery during the resilience assessment interval. The damage level of a component can span from 0 (no damage) to 1 (complete damage) and its initial post-disaster value can be estimated using vulnerability functions (Blagojević et al., 2020a). The functionality level quantifies how much of the component's functionality is lost due to its damage and recovered as the component is being repaired. The repair rate defines the pace at which a component is being repaired once its repairs start.

Community-level properties defined in the iRe-CoDeS framework are: the time step, total (i.e. system) supply, demand, consumption and LoR (Equations 1–6), and the R/S distribution priorities defined for each R/S separately (Blagojević et al., 2021a).

Two groups of R/Ss are considered in iRe-CoDeS: utilities and transfer services. Components need utilities to operate, while transfer of certain utilities among components is enabled by transfer services, provided by links. Links are components that connect two localities and serve to transfer the utilities among components by supplying transfer services. Examples of links are potable water (PW) pipes, used to transfer PW or EP transmission lines (EPTLs), used to transfer EP. If the transfer of a utility from a supplier (i.e. a component that provides the utility) to a user (i.e. a component that needs the utility to operate) requires a transfer service, the demand for the transfer service used to transfer that utility is assigned to the user component. Therefore, instantaneous component demand values include the amounts of utilities a component needs to operate, and the amounts of transfer services needed to deliver the utilities to the user.

The spatial distribution of components is defined using localities, geographically localised units inside which the transfer of utilities is unconstrained (i.e. transfer services are not required). However, for a utility to flow among components at different localities, links connecting these localities need to be capable of transferring that utility by providing transfer services.

At each time step of the resilience assessment interval, optimal path algorithms are used to identify transfer paths between localities that will be used at that time step, thus maximising the ability of the system to transfer utilities with respect to the available transfer services capacity supplied by the links. A path consists of one or several links. For a utility to be transferred from one component to another, the supply capacity of the optimal path connecting the localities of these components needs to be higher than or equal to the demand of such a utility transfer.

In the presented iRe-CoDeS framework different elements of community disaster recovery, namely accessibility of components for repair and availability of R/Ss needed for component repairs, are considered in the resilience assessment, using the same demand–supply-based algorithms used to simulate the distribution of R/Ss and systems’ interdependencies.

In iRe-CoDeS, demand of a component at a time step of the resilience assessment interval consists of all R/Ss the component needs to operate. By analogy, recovery demand is introduced to represent the amounts of R/Ss needed for component recovery at a time step of community disaster recovery (Figure 2). The recovery demand can include R/Ss such as utilities (e.g. EP is needed for the machinery working on component repair), transfer services (e.g. EP transfer service is needed to transfer EP to machines repairing the damaged component) and a newly introduced group of R/Ss, the repair R/Ss (e.g. workers and materials needed to repair a component). As a component is recovering, the values defined in the recovery demand can change to consider the different R/Ss needed for different stages of component recovery.

The transfer of certain repair R/Ss can be pre-conditioned on the state of the transportation network. This is done by requesting a transportation service (TS), offered by the transportation network, to transfer repair R/Ss between localities. Therefore, if at a time step of resilience assessment interval, a repair R/S needs to be transferred between components in different localities, the TS supply capacity of the optimal path (e.g. usable road width) connecting these two localities is compared to the TS demand of such a R/S transfer. If the capacity is higher than the demand, the repair R/S is transferred to the damaged component, otherwise, the considered repair R/S is not transferred and the recovery demand of the component is not met at that time step, delaying its recovery. It is assumed that such R/S transfer can be executed within a time step of the resilience assessment interval.

A component is repaired by reducing its damage level by its repair rate at each time step of the resilience assessment interval at which its repair demand is met, where the repair demand represents the R/Ss needed for component repair. In this study, the recovery demand of a component is set to be identical to its repair demand during the entire resilience assessment interval. However, as the recovery of a component generally consists of the repair time and the time between the occurrence of a disaster and the initiation of repair (i.e. delay time), defined by various impeding factors (Almufti and Willford, 2013), the recovery demand of a component can also be used to simulate the R/S constraints related to the progress in overcoming the component's impeding factors. This extension is not presented in the current paper. When a component is fully repaired (i.e. the damage level reaches zero), the entire repair demand, and consequently the recovery demand, is set to zero.

The iRe-CoDeS recovery modelling framework is used to simulate the recovery and quantify the disaster resilience of a virtual community following a virtual disaster. An object-oriented implementation of the proposed framework in Python is used in this study. The community consists of 20 localities, 33 components in localities, two bridges, 27 potable water pipes (PWPs), cooling water pipes (CWPs), EPTLs, road segments (denoted ‘Roads’ with initial capital letter) and 3600 inhabitants (Figure 3).

Detailed information on the functionality of the civil infrastructure systems considered can be found in Blagojević et al. (2021a). New components introduced in this paper are: Roads that provide the TS; and the emergency response centre (ERC), which supplies the community with workers, machinery, materials and back-up power generators. The topology of Roads and EPTLs is shown in Figure 3. The time step of the iRe-CoDeS resilience assessment is 1 day. However, time step size can be modified based on the purpose of the analysis and the temporal characteristics of the infrastructure systems considered.

A virtual disaster is assumed to have caused complete damage of Roads, EPTLs and bridges marked red in Figure 3. Therefore, an initial damage level of 1 (i.e. 100%), representing the maximal damage level value, is assigned to these components, while all other components are assumed to have suffered no damage (i.e. their initial damage level is zero). Roads, EPTLs and bridges are assumed to be operational once their damage level is reduced to zero following repairs (i.e. they are fully repaired). The resilience assessment is assumed to finish when the damage levels of all components are zero (i.e. all components are fully repaired, and the community is at its pre-disaster state of damage).

In this case study, it is assumed that a component that has suffered complete damage (i.e. has a damage level of 1) can be repaired if ten workers, one machinery unit and two units of material are made available to the component at a time step of community disaster recovery. The transfer of these R/Ss from the ERC, the supplier of workers, machinery and materials, to the damaged component is assumed to require TS, provided by Roads, thus accounting for the component's accessibility for repair.

As components’ repair is defined by decreasing their damage level by the component's repair rate at every time step at which a component's repair demand can be met, the shortest repair time of a component is equal to the ratio of the initial damage level and the repair rate. For example, complete repair of a component with an initial damage level of 0.4 and a repair rate of 0.01 will take 40 time steps, assuming that its repair demand is met at each time step. The repair rate of Roads and EPTLs is set to 0.05 and the repair rate of bridges is 0.01 (Table 1). More advanced component repair simulations can also be implemented (ATC, 2018; Terzić et al., 2016). Furthermore, repair rates can be defined using the existing literature on post-disaster community recovery and defined as probability distributions to account for the uncertainty related to repairs (Blagojević et al., 2020a; Didier et al., 2015). Impeding factors are not considered in this study.

The pre-disaster supply and demand values of all components in localities can be found in Tables 2 and 3. Further information on the supply and demand characteristics of the virtual community can be found in (Blagojević et al., 2021a). The ERC supplies the community with 400 workers/day, 40 units of machinery/day, 5000 units of material and 5 MWh/day of EP. Furthermore, when operational (i.e. fully repaired) Roads and EPTLs can transfer any amount of R/Ss in both directions, as their transfer service supply capacity is assumed to be infinite in this study.

The ability of Roads and EPTLs located on a bridge (e.g. Roads and EPTLs from locality 201 to 301 and locality 301 to 302) to transfer R/Ss depends on the operationality of the bridge carrying the links. This relation is simulated by viewing the bridge as a supplier of carrier services (CSs). The demand and recovery demand of links located on a bridge includes CSs. Therefore, the recovery and operability of links located on a bridge is conditioned on the ability of the bridge to provide CSs to these links. This means that the repair of damaged links located on a bridge can start only once the bridge can provide the CSs. It is assumed that a bridge provides an infinite supply of CS once operational (i.e. fully repaired).

Utility R/Ss are distributed using the method presented in Blagojević et al. (2021a), while the transfer services are distributed using the following simple optimal path algorithm: at each time step of the resilience assessment interval, a path with the maximal transfer service supply capacity is chosen from a set of pre-defined potential paths consisting of different links connecting two localities, and is considered as optimal in that time step (Table 4). One optimal path is defined for each locality pair separately and each transfer service considered has its own set of optimal paths connecting localities determined anew at each time step. The transfer service supply capacity of a path is assumed to be the minimal transfer service supply capacity of all links in a path. The transfer service supply capacity of all links remains constant in a time step. More complex optimal path algorithms, such as that of Bertsekas (1993), can also be implemented.

Following the virtual disaster, virtual community components (Figure 3) are repaired at their repair rate at each time step when their recovery demand is met. Figure 4 presents a Gantt chart of community recovery, where the time steps during which damaged components are not being repaired are blank, during which they are being repaired are marked red, while time steps during which these components are operational (i.e. are fully repaired and are supplying the community with R/Ss) are marked green. Numbers next to component abbreviation or name represent the localities these components connect. Community supply capacity for workers, machinery and materials is enough to meet the repair demand of all damaged components immediately after the disaster, as illustrated in Figure 5 in the case of workers. However, despite a large enough supply capacity of workers, machinery and materials, the repair of several components is delayed due to their inaccessibility.

The repair of Roads, EPTLs and bridges that were accessible after the disaster starts immediately. Accessible components are those that could be accessed from localities 201, 203, 205, 206 and 207, as the Roads from ERC – the supplier of workers, machinery and materials – to these localities remained operational after the virtual disaster. Once the Roads leading from these localities to localities 303, 305, 306 and 307 are repaired and start providing TS, workers, machinery and materials could be transferred to the remaining EPTLs and Roads, whose repair could then start, in this case approximately 20 days after the disaster. The repair of the Road and the EPTL connecting localities 201 and 301 had to wait for 100 days after the disaster, until the bridge carrying these two components and connecting the two localities was repaired. Similarly, the repair of the Road and EPTL located on the bridge connecting localities 301 and 302, was delayed until that bridge was repaired.

The negative effect of the transportation network damage on community disaster recovery can also be seen on Figure 5, which illustrates the post-disaster supply, demand and consumption of workers. In the immediate aftermath of the disaster, there is a demand for 240 workers. Despite having 400 workers/day available, only 90 can be assigned to damaged components, since the remaining 150 required workers cannot access the remaining damaged components due to Road and bridge damage (it was assumed that no more than ten workers can repair a damaged component at the same time). After 20 days, several components are repaired and the total demand for workers thus decreases. In the same time, the consumption of workers increases to 110 workers/day, since more components are now accessible to repair. Once workers finish repairing a component, they return to the ERC and are made available to the remaining damaged components. Only after 140 days is the demand for workers equal to the consumption, since all remaining damaged component are accessible for repair.

The damage of the transportation network also leads to longer recovery times of the electric power supply system (EPSS), as the repair of EPTLs was delayed due to their inaccessibility for repair. Figure 6 presents the post-disaster change in the supply, demand and consumption of EP. Immediately after the disaster, the only source of EP was the ERC's back-up generator that provided 5 MWh/day of EP, since the two electric power plants (EPPs) could not operate even though they did not suffer any damage. Their inoperability was a result of their interdependency with the water supply system (WSS) and cellular communication system (CCS). Damaged EPTLs prevented the transfer of EP from EPPs to components of the WSS and CCS that required EP to operate, causing a feedback loop. As the components of the WSS and CCS could not operate due to the unmet demand for EP, they could not meet the demand of the EPPs for cooling water and communication services, and the EPPs could not produce any EP (Table 3). Once a portion of the EP distribution network was repaired, 20 days after the disaster, the feedback loop was eliminated and the supply capacity of the community for EP jumped to its pre-disaster level. However, even after the pre-disaster supply capacity of the system for EP is restored, there is still unmet demand for EP, since the remaining inoperable part of the EP distribution network (i.e. EPTLs between localities 201, 301, 302, 303, 304, 305, 306 and 307) is preventing the EP produced from reaching certain EP users. This causes a total $LoRsys,EP$ of 5370.4 MWh, increasing the societal cost of the disaster, herein illustrated as the unmet demand of various users for EP. In addition, the framework presented can at the same time quantify the lack of resilience of other interdependent civil infrastructure systems, such as the water supply system, which was also inoperable in the first 20 days after the disaster, as the EP demand of PW suppliers could not be met due to the damage suffered by the EPTLs (Figure 7). Furthermore, a sensitivity analysis of the model presented here can identify components that are the most important for community disaster resilience (Blagojević et al., 2021b, 2022b).

Transportation networks allow the transfer of resources and services in communities after a disaster, enabling emergency relief and reconstruction. Decrease of their post-disaster functionality hinders community disaster recovery. Therefore, community disaster recovery and resilience quantification simulations should consider the effect of the functional recovery of transportation networks on community disaster resilience.

This paper presents the way in which a demand–supply-based community disaster recovery and resilience quantification framework, iRe-CoDeS, can be used to simulate accessibility of damaged components for repair. Resources and services that a component needs to recover are defined as the component's recovery demand. Component recovery progresses at a time step of community disaster recovery simulation only if the component's recovery demand is met. By conditioning the transfer of workers, machinery and materials on the availability of transportation services, as offered by the transportation network, the accessibility of damaged components for repair is accounted for in community post-disaster recovery simulation.

A case study of a virtual community with 3600 inhabitants is used to illustrate the proposed iRe-CoDeS framework. A virtual disaster is assumed to damage a portion of the transportation network, which consists of roads and bridges, and a portion of the EP distribution network, which consists of EPTLs. Damaged roads and bridges cause a delay in the repair of those components that cannot be accessed by workers, machinery and materials. This delay is quantified and illustrated using Gantt charts. Furthermore, the framework presented can simulate the interdependency among various civil infrastructure systems supporting community functionality. To illustrate this, it is shown how the delay of component repair caused by transportation network damage affects the functional recovery of the EP supply system. Lastly, a decrease in the post-disaster functionality of the damage-free water supply system, caused by its interdependency with the EP supply system, is quantified. Thus, the proposed iRe-CoDeS framework is able to capture a more comprehensive societal cost of the virtual disaster, reflected in the unmet demand of users for EP and PW, caused by the disaster-induced damage of the transportation and EP distribution networks. The case study results further imply that damage to the transportation network can reduce the ability of a community to mobilise its repair resources. Therefore, investments in better disaster preparedness, such as purchasing additional machinery or tools, should also consider the expected damage to the transportation network. Such damage may delay or prevent access to a certain number of damaged infrastructure components in other infrastructure systems, reducing the amount of repair resources that can be used at the same time and prolonging the recovery of these systems. However, realistic validation studies need to be conducted to assess or confirm the ability of the iRe-CoDeS framework to capture real-life community disaster recovery dynamics.

$Ci,R/St$

consumption of component i for resource or service (R/S) at time t

$Csys,R/St$

system consumption for R/S at time t

$Di,R/St$

demand of component i for R/S at time t

$Dsys,R/St$

system demand for R/S at time t

$LoRsys,R/St$

system's lack of resilience (LoR) for R/S at time t

$Si,R/SCt$

supply capacity of component i for R/S at time t

$Ssys,R/SCt$

system supply capacity for R/S at time t

t₀

beginning of the resilience assessment interval

t_f

end of the resilience assessment interval