Incorporating Resilience in Infrastructure Prioritization: Application to the Road Transport Sector

Disruption of infrastructure services can cause significant social and economic losses, particularly in the event of a natural disaster. The World Bank Group and the Government of Japan established the Quality Infrastructure Investment Partnership to focus attention on the quality dimensions of infrastructure in developing countries, with a focus on promoting disaster resilience. Moreover, to support infrastructure investment decision making for sustainable and resilient development, the World Bank and Kyoto University have operationalized key resilience concepts at the project level and developed quantitative indicators capturing key aspects of infrastructure resilience related to the road transport sector. These indicators estimate resilience, expressed as functionality loss and recovery time across four dimensions: travel time, economic benefit, provision of life-saving services, and provision of relief goods. The paper applies indicator calculations to three case studies of proposed bypass roads in Japan and provides an example comparison of calculated indicators across the three projects for each resilience dimension. Further piloting of the approach will help refine the indicators, test their relative utility in decision making, and offer a better understanding of the data and analytical demands.


Policy Research Working Paper 8584
Disruption of infrastructure services can cause significant social and economic losses, particularly in the event of a natural disaster. The World Bank Group and the Government of Japan established the Quality Infrastructure Investment Partnership to focus attention on the quality dimensions of infrastructure in developing countries, with a focus on promoting disaster resilience. Moreover, to support infrastructure investment decision making for sustainable and resilient development, the World Bank and Kyoto University have operationalized key resilience concepts at the project level and developed quantitative indicators capturing key aspects of infrastructure resilience related to the road transport sector. These indicators estimate resilience, expressed as functionality loss and recovery time across four dimensions: travel time, economic benefit, provision of life-saving services, and provision of relief goods. The paper applies indicator calculations to three case studies of proposed bypass roads in Japan and provides an example comparison of calculated indicators across the three projects for each resilience dimension. Further piloting of the approach will help refine the indicators, test their relative utility in decision making, and offer a better understanding of the data and analytical demands. This paper is a product of the Infrastructure, PPPs & Guarantees Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/research. The authors may be contacted at dmarcelo@worldbank.org.

Introduction
Modern society depends extensively on physical infrastructure systems, which serve as the foundation for a wide range of human activities. Given the nature of infrastructure as a critical input to trade and industry, economic productivity, public health, human safety, and quality of life, the disruption of infrastructure services can cause catastrophic economic losses and devastating impacts on health and the operability of the regions they serve. Therefore, the World Bank Group and the Government on Japan established the Quality Infrastructure Investment (QII) Partnership with the objective of raising awareness and promoting enhanced attention to the quality dimensions of infrastructure investment projects in developing countries. They identify five aspects that must form the key elements in project design, namely: economic efficiency, safety, environmental and social sustainability, economic and social contribution and resilience against natural disasters.
Due to widespread gaps in infrastructure funding and increasing demands for improved infrastructure services, most countries worldwide face the challenge of having to select from among proposed infrastructure projects to develop and fund those most apt to attain developmental goals. To support project prioritization in infrastructure sectors such as transport, water, and energy, the World Bank Infrastructure, PPPs, and Guarantees Group (IPG) developed the Infrastructure Prioritization Framework (IPF) (Marcelo, et al, 2015). The IPF aggregates underlying project-level indicators into two composite indices, the socioenvironmental index (SEI) and the financial-economic index (FEI), which characterize the expected relative outcomes of proposed projects within a sector.
Although QII principles recognize resilience as a key aspect of infrastructure project design and planning, the composite indicators considered by the IPF have, until now, only assumed an 'ordinary state' of non-disruption, meaning that they do not consider how infrastructure assets maintain operability and/or recover in the face of disaster events. Moreover, the IPF analyses have not yet considered the potential benefits of infrastructure projects regarding their abilities to contribute to overall resilience at the local, regional, or national levels. The aftermath of the 2011 Great East Japan Earthquake that unleashed a tsunami and left some 3 20,000-people dead or missing 1 in Japan, underscores the importance of considering resilience to disaster in infrastructure investment decisions. The disaster heavily affected Sendai, the capital city of Miyagi Prefecture and a regional economic hub. The tsunami completely submerged the city's primary wastewater treatment, while some 500,000 residents lost access to water. Also, the tsunami damaged 325 kilometers of coastal railway assets and flooded about 100 kilometers of the national highway in the Tohoku region, leaving devastated towns in need of assistance without inland transport access. This paper presents a practical approach to bring the concept of infrastructure resilience to the project level, with direct application to transport infrastructure. The proposed approach complements the IPF and offers additional indicators as potential inputs to the framework that can help decision makers discern between projects from a resilience perspective. The paper begins with a discussion of the concept of infrastructure resilience and follows with proposed indicators to measure aspects of resilience in transport at the project level.

Applying the Concept of Resilience to Infrastructure Projects
The concept of resilience has been discussed in various academic fields and conceptualized in numerous ways (Cutter et al., 2010). For social sciences, the main interest is the resilience of communities, whereas for engineering fields, the focus is on the resilience and robustness of structures. Organizational resilience, conversely, focuses on the ability of an organization to absorb shocks and to adapt in a changing environment (ISO 22316). In most fields, the concept is recognized to be multifaceted. Bruneau (2003) conceptualizes resilience as the ability of a system to reduce the chances of a shock, to absorb a shock capable of causing abrupt reduction of performance, and to recover quickly after the occurrence of a shock.
In line with these definitions, we present an application of the resilience concept that describes (a) an asset's ability to withstand shocks in such a way that minimizes functionality losses (i.e., robustness or resistance), and (b) the asset's capacity to recover functionality across multiple dimensions following a disaster event (i.e., recoverability). Dealing with the expected 4 functionality of an asset within a transportation system, both pre-and post-shock, inherently considers the asset's connection to a broader network. A network approach to transportation is crucial because transport functionality depends not only on the characteristics of individual assets but also on their contributions to the system's overall functionality and performance.
That said, while an asset's functionality naturally relates to its locus within a system, the focus here is to encompass (a) the ability to minimize loss of asset functionality (within the system) and (b) the ability to recover asset functionality after a disruption. Figure 1 illustrates the "recovering of functionality" process of an asset after a disruption (i.e. natural disaster). In the event of a disaster, an infrastructure asset (e.g., a road or bridge) is susceptible to losing some or all of its functionality. We define the decrease in functionality as loss of functionality ( ). After the disruption, functionality will typically recover, reaching a near-total or total pre-disaster level of performance over time. We term this lapse time for recovery ( ). The recovery time depends on the systems and processes in place, as well as physical attributes of the asset itself. Therefore, the accumulated loss of functionality ( ) will account for the aggregated functionality loss over the recovery time. Mathematically, is equal to the integral of the function over the interval between the disruption and the end of the period. This integral is the area indicated by the shaded area in Figure 1. 2 2 For the sake of simplicity, this illustration assumes that the functionality is recovered in a linear fashion. However, this may not always be the case. In some instances, perhaps the road only opens when full functionality is restored, and, in others, one lane of a many-lane highway may open first, followed gradually by others. Therefore, the ALF's upper bound could take a variety of functional shapes depending on the path of recovery (how much functionality is restored at various stages of repair), such as a straight line (yielding a rectangular ALF area or even a staggered path). The ALF should then be calculated according to the functional shape that emerges from the specific scenario.

. Loss of Functionality
Loss of functionality ( ) accounts for reduced levels of service due to disaster events, most often natural. Since structural robustness helps alleviate or prevent reduced levels of service in the event of a disaster, is a function of both 1) the impact of natural disasters and 2) the structural measures taken to resist or absorb the external forces imposed by these disasters.
Moreover, relates to the ability of an asset or facility to maintain functionality after a disruption by structurally resisting and/or absorbing the external force by design.
indirectly captures the notion of capacity to resist, as it measures the magnitude of the reduction in functionality immediately after a natural disaster. The decrease of functionality is the logical result of the occurrence of a disruption, coupled with the intrinsic capacity of the structure to resist or absorb the physical effects of such an event.
In the case of road transport projects, typical disruptions may include earthquakes, volcanic eruptions, floods, cyclones, storm surges, or landslides caused by intensive rainfall. The design of a structure and the materials used in construction naturally affect its ability to withstand various natural disasters. In the event of a strong earthquake, for example, a road facility can maintain its functionality under most conditions if sufficient structural measures are in place to 6 resist even major earthquakes with the highest seismic intensities. 3 Consequently, an accurate assessment of the requires information on (a) the kinds of disruptions that infrastructure projects are likely to face and (b) the expected functionality levels resulting from these disruptions at various levels of intensity.

Recoverability
Recoverability refers to the ability of an asset to recover its functionality quickly. Recoverability is associated not only with physical factors, but also with social, organizational, resourcerelated, and managerial factors. Recoverability is dependent on the readiness of resources and preparedness of organizations to respond to disaster events. Recovery of functionality requires the availability of human and capital resources (e.g., machinery) as well as organizational plans and processes required to take necessary actions rapidly and effectively.
For example, the recovery of destroyed road facilities requires construction manpower and equipment in addition to established processes and institutional measures, such as agreements between the public and the private sectors to collaborate in an emergency or the establishment of a clear incident management system. A proxy measurement of recoverability is the duration required to reach a target recovery level.

Project-Level versus System-Level Resilience
When evaluating and measuring resilience, it becomes important to clarify the level of analysis.
In other words, the 'resilience of what' matters. To apply the notion of resilience in infrastructure prioritization, it is helpful to distinguish between project-level and system-level resilience.
Assessment of project-level resilience considers the functionality loss in the event of a shock and the ability of an asset to quickly recover from functionality loss. Asset functionality loss is a function of both the structural robustness of the facility and the level of exposure to a disruptive event. Recoverability depends on the availability of resources for reconstruction and the governance of emergency response management.
System-level resilience, on the other hand, refers to the region's or infrastructure network's capacity to absorb and recover from disasters. Infrastructure projects are generally elements 7 of a functional system. This is particularly true for transportation networks. A government, for example, may consider implementing a new road section designated as an emergency transport route instead of a similar project that serves no emergency relief function. Given the nature of road infrastructure assets as network components, the construction of a new road may also enhance resilience by increasing redundancies in the network that allow access to alternative routes and absorb increased traffic in the case of emergency.
The methodology proposed in this paper is intended to estimate project-level resilience and not system-level resilience, though project functionality is inherently dependent on and related to the asset's relationship to other parts of a system. Further, applied to the transport sector, the goal is to use information that is likely to be available in project feasibility studies for proposed road infrastructure or public data sets to estimate the effect of a disruption on various aspects of functionality. Keeping in line with the nature of the Infrastructure Prioritization Framework (IPF), the analysis at this level is also designed to draw on less complex and less analytically-demanding indicators to make the approach more feasible to apply in information-and capacity-constrained environments.

Dimensions of Functionality
Infrastructure services attend to a wide array of interconnected purposes: they facilitate trade, allow mobility of people and goods, provide access to services, and support a host of other human activities. The relationships between assets in different infrastructure sectors are complex, and due to sectoral variations with respect to physical structures, locations, and degrees of interconnectivity, natural disasters affect infrastructure assets in different ways. The functionality (and potential loss of functionality) of an infrastructure system is difficult to measure for all sectors within a given region. As such, it is presently more meaningful to make judgments of relative resilience within a sector and for similar types of projects. This paper, therefore, focuses specifically on applying concepts of resilience to road infrastructure projects.
While measurable aspects of functionality may be directly observable in a non-disrupted (normal) state, the magnitude can only be estimated prior to a disruption. Moreover, the magnitude after a disruption is only partially measurable by examining selected aspects of functionality. For road infrastructure, some of the most important elements of functionality include travel time, road utilization, provision of emergency services, and provision of relief 8 goods. The first two interrelated dimensions -travel time and utilization -are aspects related to economic impact, whereas the latter two dimensions -provision of emergency services and relief goods -are life-saving aspects.
When a road network faces a disruption, the loss of functionality manifests itself in many forms of economic loss. Damage may be reflected in increased transaction costs, loss of productivity, destruction of resources and wastage, and other negative economic impacts. Most apparent, however, the loss of functionality relates to increased travel times due to inoperability of affected roads. While reduced connectivity (interconnectedness of various areas) has impacts beyond its relationship with travel time, analyses largely center on the increased travel times between areas affected by a disaster event. Therefore, we focus the consideration of economic impact on the key feature of increased travel time. Moreover, travel time may be used directly as a measure of functionality, or as an input to a traffic demand function.
When a natural disaster strikes, road infrastructure serves another crucial function, namely to facilitate the preservation of human life. In the aftermath of a disaster, road access is prerequisite to effective search and rescue, conveyance of injured and vulnerable citizens to emergency facilities and shelters, and the supply of relief goods, medical services, and other forms of aid. Also, connectivity to resource depots, emergency shelters, and medical facilities is vital to support lifesaving functionality. While the notion of connectivity relates to travel time and other economic impacts, with respect to the preservation of human lives, the question associated with connectivity is whether affected areas are accessible within a window of time required to provide life-saving resources or evacuate the critically ill or injured population.
In addition, road infrastructure must also be structurally robust to prevent road users from harm or death associated with the collapse of road structures. While it is recognized that road assets must be made 'safe to fail' (Ahern, 2011), because the intention of this study is to provide an initial basic methodology to calculate a limited -yet essential -set of resilience indicators, other aspects of resilience such as this will remain areas for future study.
To summarize, then, this approach to analyzing infrastructure resilience focuses on four dimensions of road functionality: travel time , road utilization , access for lifesaving services , and provision of relief . These functions serve as the basis for the set of calculated resilience indicators in road transport described in the following section. 9

Infrastructure Resilience Indicators
This section presents basic infrastructure resilience indicators to support infrastructure investment decision-making. One major concern regarding infrastructure projects is the resilience of constructed facilities, i.e., project-level resistance and robustness that help minimize loss of functionality. When applied to transport, the proposed indicators directly consider resilience at the project level through the concept of accumulated loss of functionality ( ). As shown in the next section, conceptually relates inversely to resilience. In other words, the lower the , the more 'resilient' the project is.

Accumulated Loss of Functionality
Consider a proposal for a road project . Let denote a variable that represents the accumulated loss of functionality for the project associated with each of the four dimensions mentioned above ( =travel time, =road utilization, =life-saving and =relief provision), given the occurrence of natural disaster. In this context, the accumulated loss of functionality for project corresponds to the dotted area in Figure 1. This calculation of the follows the formula below: (1) where measures the loss of functionality for project in dimension , and the time for recovery (time to regain pre-disruption level of functionality). Alternatively, the formula below offers a measurement of project-level resilience conceptualized as the inverse of accumulated loss of functionality: (2) 1.6. Variation in Accumulated Loss of Functionality considers functionality changes before and after a disruption, for example, a land slide or a flood in the case of road transport projects. Policy makers may use this information when comparing infrastructure proposals, giving more priority to projects with lower s. Policy makers may also consider the variation in with and without the proposed infrastructure project. This variation in would represent the project's contribution to the road 10 connection's level of resilience -a metric that can also be useful to inform selection from among a set of proposed projects.
In this form of analysis, let denote the accumulated loss of functionality as in equation 1, but now under two possible states: with project ( ) and without project ( ). From a resilience point of view, the accumulated loss of functionality with project ( ), is expected to be lower than without project ( ), especially if the project specifically aims to improve resilience. The resulting may, however, be equal or even higher than the withoutproject . The difference between the two results (with and without project) provides a measurement of the net contribution of any given project to the reduction on accumulated loss of functionality.
From a resilience point of view, ∆ is expected to be negative, reflecting a reduction in accumulated loss. Depending on the features of the infrastructure project, however, it may be positive or equal to zero. In the best-case scenario, a proposed project generates zero Accumulated Loss of Functionality ( = 0). In this scenario, there would be a 100% reduction in the existing Accumulated Loss of Functionality level. This may be the case, for example, of a road project proposal that, if implemented, guarantees to maintain its level of functionality (e.g. travel time) even after a major disruption (e.g. a magnitude 7 earthquake).
In general, ∆ will be less than zero whenever , since there would be an expected reduction of the existing Accumulated Loss of Functionality level caused by the proposed project. The expected reduction will result from decreases in either or or both. Figure 2 represents a case where, with the project, both and simultaneously decrease. The difference between the areas of the two shaded triangles captures ∆ . if a project improves the current functionality level only in the ordinary state (e.g., road capacity measured in vehicles per day) but maintains the same and expected functionality level following a disruption, then the will increase, since a greater pre-event functionality is expected to be lost (see Figure 3, scenario c). Less intuitively, a project may increase even if it increases the functionality levels (before and after disruption) and reduces the . This is because the loss of functionality considers the difference between levels of functionality before and after disruption. The levels of functionality may increase, while their difference in functionality (pre-and post-disruption) may increase or decrease. 4 To facilitate the comparison of project proposals, s associated with different types of natural disasters are estimated separately. Note that calculations assume that disaster events will, indeed, occur. Further, by calculating baseline functionality levels with-and without-5 While a disaster event could potentially result in a variety of disrupted states with associated probabilities, we choose for the sake of simplicity to model only the s for an observed nondisrupted state ( 0) and an estimated disrupted state ( 1) associated with a potential disaster event . 13 project under hypothesized natural disaster scenarios, calculations also provide the inputs to calculate variations in resulting from the implementation of a project. The last section before the conclusion describes this with examples.
The following sections describe measures to estimate in the economic dimension, more specifically, travel time and utilization, and in the life-saving dimension, including the provision of emergency services and provision of relief goods.

LoF Indicator for Travel Time
In terms of functionality loss for road infrastructure, the simplest way to assess the economic impact resulting from a disaster event is by measuring its effect on travel time between a representative origin-destination pair. Ideally, all roads connected to the proposed link should be evaluated using a network model approach. However, given the data intensity and technical capacity limitations in developing countries, for this analysis, the origin and destination are identified as the primary towns that the link is intended to serve. Transport simulation models can offer estimations for in each case.
For any disaster event , the expected road network resulting from a proposed road project for the travel time dimension ( ) would correspond to (4)

LoF Indicator for Economic Benefit
A more direct measure of economic impact associated with increased travel time is the effect on road utilization (road demand). According to standard transport economics theory, the consumer surplus is a key consideration when assessing the economic benefit of a road network (de Palma, Andre, et al, 2011, World Bank, 2005. Calculation of consumer surplus requires specifying a traffic demand function, i.e., the relationship between travel volumes and generalized costs, including time value of users, travel time, and tariff charges. 14 Traffic demand depends on the generalized cost of transportation, which includes costs to the user such as travel time, safety, vehicle ownership and operation, and taxes, tolls, and other fares (Lee, 2000;Litman, 2017). If the generalized cost of transportation is proportional to travel time, holding other costs constant, transportation volume may be expressed as a function of travel time and vice versa.
We denote as the traffic demand function corresponding to the relationship between volume (e.g., vehicles per day) and travel time when assuming no tariff charges and a uniform time value for users. In addition, for the sake of simplicity, we assume that the function is linear as shown below: where the slope is equal to ⁄ and is a constant.
Disruption of a part of the road network implies increased travel time resulting in the loss of economic benefit. In this specification, the economic loss due to disruption is equal to the difference between the consumer surplus of the ordinary (no disruption) state and that of the disrupted state (see shaded area, Figure 4).

Figure 4. Road Demand Function
Therefore, associated with a proposed project in terms of lost consumer surplus (using decreased utilization as a proxy of economic loss), for any given disruption , corresponds to: This approach may be appropriate if data on utilization are available or possible to estimate, as it gives a better indication of the economic losses associated with decreased road use.  The calculation requires making assumptions of future, yet uncertain scenarios. One way to incorporate uncertainty is by defining the probabilities for each disruption scenario. In practice, however, obtaining reliable probabilistic distributions is complicated or costly to determine. Moreover, the calculations presented here do not require them. For the purposes of project comparison, the and calculations assume that each modeled disaster scenario will occur and compare their relative resilience in those hypothetical scenarios. This approach is consistent with construction practice, as required levels of structural robustness are typically specified and incorporated into design code. 17 For these reasons, we propose a deterministic approach that does not directly incorporate probabilities of disaster scenarios in the calculations of potential losses and rather assumes disaster scenarios as if they effectively occurred. If known, however, probabilities of such disaster scenarios may guide the assumptions under this approach. Moreover, if available, these probabilities may provide inputs to calculate an indexed via a weighted average.

Conceptualization of Economic Dimension LoF
The framework can also be applied to the upgrading or improvement of an existing road section. The example in Figure 6 presents the case of a structural robustness upgrade for an existing road section. The logic is basically the same. Now suppose there are two links between cities A and B called Route and Route . Route passes through an area free of earthquake risks, whereas Route does not. A project to structurally reinforce Route is under investigation. Assume three disaster scenarios: (1) the occurrence of a level-5 earthquake ( 1), (2) the occurrence of a level-6 earthquake (  2) and (3) the occurrence of a level-7 earthquake ( 3). Route can withstand an earthquake of SI less than 6, but not one of SI 6 or 7. If Route is upgraded with project , it could withstand an earthquake of SI less than 7 but not one of SI 7.

LoF Indicator for Provision of Emergency Services
With respect to emergency services and S&R, roads must provide quick access to major hospitals. Standard emergency practice assumes higher rates of mortality if emergency care is not offered within the "golden hour" following mass trauma (Lerner & Moscati, 2001). While for S&R is defined as follows: where is the population with access to major hospitals within 30 minutes under the ordinary state (with no disruption) and is the population with emergency access under a specified disaster scenario , for each project .
The contribution to resilience of a project from a life-saving standpoint can be captured by the difference in for the with-and without-project cases.

LoF Indicator for the Dimension of Relief Goods
The functionality of a road network in terms of human safety and lifesaving also includes the delivery of relief goods. With regards to the delivery of relief goods, accessibility is the key issue of functionality, as relief goods will not reach villages and municipalities isolated by the impacts of natural disasters. While is a difference calculation for other aspects of functionality (i.e., the difference between the ordinary and disrupted states), for the functionality of delivery of relief goods is simply defined as the isolated population under the disrupted state, since there is no (zero) isolation under the ordinary state. This calculation, therefore, is as follows: where is the population living in towns and villages that will become isolated under a specified hazard scenario with the project status for each project . Again, the contribution to resilience of a project, with respect to access for provision of relief goods, can be captured by utilizing the difference in for the with-and without-project cases and the time for recovery.

Indicator of TfR
Time for Recovery ( ) depends on the degree of damage as well as the level of emergency preparedness, including the existence of an emergency management plan and the preemptive establishment of cooperative agreements for road clearance works and reconstruction between road administrators and contractors. Let denote the estimated time for recovery for a disrupted road network ( 1) after a natural disaster for each proposed project with implementation status .
To determine , it also becomes necessary to establish the point in time at which recovery can be considered 'complete'. Reconstruction of roads to fully restore pre-event service levels may require extensive time and resources. Therefore, in the emergency period, road administrators often make disrupted roads available by provisional methods of construction that restore service, but not to full pre-event standards. This state of 'temporary recovery' is the state to which applies. 20 The recovery time estimation requires assessing the state of existing assets, evaluating possible damages, and estimating the construction works capacity and availability of financial and human resources. In addition, damage assessments and other estimations can be used to calculate the workforce needed in the event of a disaster. Furthermore, the gap between the workforce needed to recover functionality and actual available personnel provides essential inputs to estimate the time for recovery. If damage assessments are not available or not possible to estimate, proxies using historical data may provide an estimate of the likely resource demands and time required for recovery. Any of these cases will require empirical data obtained through expert interviews and by examining the input requirements for recovery in similar historical cases. City is a regional base in the North Tajima region wherein a first-aid station hospital, Toyooka Hospital, is located.
Some residents in the flooded area are isolated and lose access to the first-aid station hospital. Moreover, the increase in travel time between the two cities due to necessary detouring is not negligible. The proposed bypass route passes through a mountainous area with some tunnels and, hence, is not exposed to flood risk.  Regarding the indicator for saving lives, the population of the coverage area is assumed to be that of Tajima Area, which Toyooka Hospital covers as the primary first-aid station. By using a route search system such as Google, the area accessible to Toyooka Hospital within 30 minutes can be estimated for the ordinary and disrupted cases. The population of that area can be determined by local demographics; therefore, the ratio of population who can access Toyooka

Indicator Data
Hospital within 30 minutes can be estimated.
Residents in the flooded-area are isolated and, therefore, are unable to access the first-aid station hospital. The new bypass would be free from flood risk, but the existing road section is not. Regarding Time for Recovery, , the record of road clearance work of the Great Eastern Japan Earthquake shows it took an average of 0.1 km per hour.
For the existing road section in the case study, since clearance work can occur from the two edges of the road, the time for recovery is estimated to be 6/0.2=30 hours 24 or 1.25 days. 6 This would be affected if the bypass is built because it would allow for clearance work to start from two additional edges (as seen in Figure 8), making the necessary time to complete the road clearance work equal to 6/0.4 = 15 hours or 0.625 days. The new bypass is not vulnerable to flood risk and so, there is no associated .

Numerical Calculation of Indicators
As described in section 3.3.1, economic loss associated with utilization is calculated as follows: Therefore, the contribution to resilience associated with the variation to ALF for lifesaving is: serves. This road section is exposed to the high possibility of a tsunami caused by the Nankai Trough Earthquake which is expected to occur in the next few decades. The proposed bypass runs outside the tsunami-prone area, and, therefore, works as the alternative route during disruption of the existing national highway. Most residents live along the existing national highway and would lose access to the major hospital if the road is obstructed. Therefore, even with the bypass, the population suffering due to the tsunami would remain the same. However, the critical impact of the bypass would be on the recovery time since it allows for additional points to start road clearance work.
Indicator Data Table 2  Kamitonda and Kushimoto is assumed to be the design traffic volume in the ordinary state, whereas the volume in the disrupted state is assumed to be zero, based on expert opinion.
The expected time for recovery in the case of a disruption of the existing route is 255 hours (10.625 days), based on the road clearance plan for a tsunami disaster prepared by MLIT.

Case 3. Construction of Bypass Road in Landslide-Prone and Heavy Snow Area
The third case project is the construction of a bypass road intended to avoid a landslide-prone area. National Highway No. 9 is a major route along the north shore of western Honshu, the main island of Japan. The particular road section of interest is located in an area where largescale landslides can occur. In addition, this road section includes a pass vulnerable to snowy weather. The risk considered in this analysis is only that of landslides, since the impact is 30 expected to be heavier as compared to a snowstorm in terms of recovery time required. The national highway is the major corridor in this area, though a detour route is still available. The proposed bypass tunnel would run through the landslide-prone area and allow for this road section to remain free from the risk of landslides.

338.55
Likewise, for the dimension of saving lives and for the dimension of providing relief goods can be calculated as follows: because the ratio of population who can access the major hospital is same in the ordinary and disrupted state, ∆ 0. And finally, because the flood scenario does not cause any isolation of villages, ∆ 0.

Comparing Project Resilience
The calculations in the above cases can be used to compare the projects' variations in accumulated loss of functionality (   Table 4 suggests that the second project will make the greatest contributions to reducing loss in the event of an extreme event. This is because, first, even though all three projects reduce functionality losses in terms of utilization by 100%, the bypass in Case 2 would impact a greater amount of traffic volume. Second, while the functionality loss for saving lives is reduced only by 50% in Case 2 as compared to 74% in Case 1, again, the absolute number of people whose access to lifesaving services is preserved is greater. Similarly, for the last dimension, even though the percentage loss is the same between the first two cases, the absolute number of people saved from potential isolation is greater in the second. In other words, the Case 2 project makes the greatest contribution to resilience among the three proposed bypass projects in absolute terms. 33

Sensitivity Analysis
In this section, we test the results of the analysis by varying some of the underlying assumptions to ensure that results are not highly sensitive to minor variations. To do so, the saving lives indicators were re-estimated. The assumption underpinning the calculations changed, from the percentage of the population that can access a major hospital within 30 minutes (as in the original calculation), to the percentage that can access emergency care within 60 minutes. Comparing the results in Tables 4 and 5, we find that there is a negligible variation in the results even when the time assumption is doubled. This suggests that the results of the analysis are sufficiently robust for project comparison.

Discussion and Conclusion
The proposed indicators offer a starting point for calculating and applying resilience indicators to support project selection. Moreover, the World Bank's Infrastructure Prioritization Framework (IPF) can use the resilience measurements presented in this paper in two ways.
First, if the data to calculate the proposed resilience estimates are available or acquirable at the project level, they can be directly inputted into the IPF as additional criteria in the socialenvironmental index (SEI). In most countries, however, the required data are likely to be sparse.
In that case, the aim should be to measure infrastructure resilience for only those projects that emerge as "high priority" from the prioritization analysis and use resilience indicators as complementary information to support final project selection, but not as a part of the SEI.
While this approach is not intended to 'solve' problems of resilience or determine sector-wide or regional strategies for mitigating disaster, the proposed indicators introduce considerations of resilience that can guide infrastructure investment decisions. Moreover, the indicators offer two potential approaches to consider resilience with respect to infrastructure investments. On the one hand, the proposed transport asset's expected Accumulated Loss of Functionality ( ) may be considered in isolation to better understand the 'resilience' of road projects. In this case, the question at hand is how much functionality various proposed projects will lose in the event of a disaster. On the other hand, if projects are pursued specifically to improve a region's overall resilience, a more important metric would be an variation (∆ALF) that measures a project's impact on the overall road system.
The proposed indicators also address four interrelated dimensions of resilience: travel time, utilization, provision of emergency services, and provision of relief goods and services. What measures are included in resilience calculations and what approach to measurement is taken ( or ∆ALF) will depend on the policy goals associated with the proposed projects, as well as the information available to inform considerations of functionality and resilience.
Piloting application of these approaches in real-life contexts will help further develop the indicators themselves and improve their application to infrastructure decision-making. Also, piloting these indicators will lead to a better understanding of the different approaches' and dimensions' relative usefulness for decision-making. Also, the results should be subject to 35 expert review and compared to alternative (possibly qualitative) approaches to assessing the relative 'resilience' of proposed projects. In addition, since there are likely to be uncertainties related to data used for estimating functionality as well as the assumptions employed, it is essential to test the results with a range of specifications during the piloting of this work. This would not only test the sensitivity of the results but also their robustness.
Piloting should also aim to develop guidance for applying the ∆ALF indicator where investments follow the specific policy goal of improving system or regional resilience. Further guidance should be developed to understand the prevalence of and develop approaches to deal with the special cases described in section 1.6, wherein projects may improve functionality in the ordinary state but make relatively lower or no improvements to post-hazard functionality.
In these situations, there may be calculated increases to due to the relatively higher losses of functionality due to overall gains in functionality. A potential option to deal with this, which should be tested in piloting, is to compare estimated post-hazard functionality with a proposed project to the estimated post-hazard functionality without the project.
Further, piloting will also lead to a better understanding of the informational and analytical demands associated with estimating loss of functionality and time for recovery. Since these resilience indicators are intended to support infrastructure decision-making under various informational conditions, it is important that the input data required to calculate resilience indicators be reasonably accessible. Piloting should focus on improving approaches to estimating time for recovery.