How long do transport infrastructure last: evidences from Norwegian roads and rail network

How long will transport infrastructure generate benefits for the society (the appraisal period) is an essential assumption in transport appraisals. However, there are considerable differences in the recommended appraisal periods used in cost–benefit analysis between countries. In this paper, we therefore examine how long transport infrastructure was used in the past before it was replaced, closed, or substantially improved. We label this period the ex-post appraisal period. The study considers rail and roads in Norway and analyses how long they were used using the statistical technique survival analysis. The results show that motorways build in the 1960s was used around 40 years before being upgraded, while most of railroad infrastructure have lasted more than 100 years. If these results are applicable for the future use it may indicate that the use of long appraisal periods (more than 50 years) in some countries could be optimistic for roads and rather conservative for railroads.


Introduction
Most of our transport system were built decades ago, some even centuries.Although components of these systems have been replaced, a great deal of this infrastructure still provides benefits for society.However, other infrastructure has been used considerably shorter.One example is bridges that were made obsolete because of technological improvements and had to be replaced because of increased truck loads [15].Another example, is the Roman aqueducts, which are still sturdy despite being long obsolete [2].The time the infrastructure was used could be thought of as the appraisal period that should have been used when calculating the total benefits of the project.We may label this period the ex-post appraisal period.
When appraising new projects, we need to decide how long into the future the project is expected to generate benefits.This period, which corresponds to the (exante) appraisal period, varies between countries [14].The longest appraisal periods are used in countries such as Norway, Sweden, Denmark, and the United Kingdom.It is possible to include benefits of up to 75 years Page 2 of 8 Tveter and Tomasgard European Transport Research Review (2024) 16:30 in Norway, while the default period is 60 years in Sweden, and 50 years in the United Kingdom and Denmark. 1  At the lower end of the spectrum, Australia, New Zealand and the United States have appraisal periods of 25-30 years. 2 Although it might be a regional component for how long transport infrastructure will generate benefits, for example, climate, quality of construction and required maintenance, these differences seem too large to be explained by such differences.A plausible explanation of why the appraisal periods differ could be differences in the components lifetimes.For example, show the review by HEATCO (2005) that the lifetimes of road bridges vary between 30 and 100 years.A third of the countries in the HEATCO review used a lifetime of 100 years, while the remainder were equally distributed between 30 and 60 years.The appraisal periods and lifetimes of HEATCO (2005) shows, however, a very weak correlation. 3Thus, differences in expected lifetimes of components do little to explain the large variation in appraisal periods.
Another approach, which is used in this paper, is to investigate the history and see how long infrastructure have been used in the past.That is examining the expost appraisal period.To our knowledge, no studies have examined the ex-post appraisal period and even the expost service life remains unexplored.Some insight can, however, be found from adjacent literature.One strand of the literature examines the service life of components [1,7,16].The literature shows high levels of variation between components and a substantial cross-country variation, but this evidence is rather different than how long an investment project generates benefits.Another strand of the literature examines the service life of the fixed assets used in national accounts.This literature, recently summarised in Link [17], shows e.g. a service life of motorways between 30 and 60 years.Thus, values not very different from the used appraisal periods across the world.
Examining the appraisal period ex-post, has both advantages and dis-advantages.First, how long the current infrastructure will be used is unknown.This problem of an unknown (unobserved) endpoint, known as censoring in the literature, can be dealt with using the statistical method of survival (duration) analysis.Another issue is that the design of the infrastructure changes over time, such that the past duration of the infrastructure might be different than that of the current infrastructure.In addition, to handle censored data, this method allows for nonlinearity of failure times (see [1,5,7] for applications in various areas [13,19],).A more intrinsic empirical challenge is whether the roads and rails built today differ from past projects.Indeed, today's infrastructure will be of a higher technical standard, and the ability to plan may have improved.Together this might contribute to a longer usage period than before.Nevertheless, unknown factors, such as technical changes, could still appear in the coming years, especially when the planning horizon is several decades.Thus, there are some problems when looking at past projects, but in this case, it is the only data available and certainly better than nothing.
To examine the ex-post appraisal period, we consider railroads and two selected roads in Norway.The railroad infrastructure is analysed using the complete set of railroads built over the last 150 years.It is more challenging to analyse roads because the road system is more complicated and heterogeneous.Moreover, the road network usually changes gradually without clear endpoints.For roads, the analysis is therefore limited to two major trunk roads in the Southern/Eastern part of Norway.

Survival analysis
The ex-post appraisal period can be analysed using a range of methods, with the main distinction being between qualitative and quantitative approaches.A qualitative approach can be used to investigate a few projects and analyse the factors explaining how long they was used.Such a procedure may provide deep insight into these projects, but the generalisability of the results could be limited.A quantitative analysis will provide less in-depth knowledge but is potentially more generalisable.Since the purpose of this study is linked to the appraisal practice, the quantitative approach was chosen.
unclear since infrastructure generally experiences gradual change.
Figure 1 shows three types of observations.First, both the start-and endpoints can be observed.Second, the opening year and a change during the period (hereafter events) can be observed but not the endpoint.Third, only the starting point can be observed.The unobserved points are referred to as censoring in the literature (right censored in this example).Observations of the first two types provide the most knowledge and are preferred.However, the censored cases also provide information.Although we do not know the ex-post appraisal period, we know that the period is at least longer than observed.We needed a sample where at least half of the objects had an observed endpoint/event to estimate the median expost appraisal period.Thus, to calculate the median, we had to at least observe the lower half of the distribution.
We describe the most important statistical relationships in survival reading analysis for completeness. 4We define t as the time after opening.Furthermore, the likeli- hood that the infrastructure will be used longer than T , the survival function S(t) , is defined as This function can also be written as where F (t) is the cumulative density function, the prob- ability that the infrastructure will be replaced (end of life) (1) S(t) = P(T > t). (2) is the density function, and dt is a marginal change in time.
The probability that the infrastructure will not be used longer than at time t , given a duration up to t , the hazard rate, is defined as which, from the definition of conditional probability, can be simplified to 5   The Kaplan-Meier estimator [12] is used in our implementation of survival analysis.This estimator is given by the product of the proportion of observations surviving to a given time where n i is the number of observations that exist at t , while d i are observations that do not exist at t .The method is non-parametric, which means that we do not need to make any assumptions about the shape of the survival function.Regression-based techniques for survival analysis are also available, such as the Cox (3) ( Fig. 1 Observed and unobserved points 4 The exposition is largely based on Greene, W. H. [10].Econometric analysis (5th ed.ed.).Prentice Hall.. 5 First, the numerator is replaced with the conditional probability definition h(t) = lim �t→0 P(t<T <t+�) Second, the denominator is replaced with the conditional probability definition.
regression model [4], but the analysis in this paper was drawn from data sets that were too small for this technique to be appropriate.

Data sources
Constructing the observations is challenging in our expost analysis.Some challenges are: What is the criterion for an event or endpoint?For example, do an expansion of a two-lane road to a four-lane road define an endpoint?We encountered similar challenges relating to rail infrastructure in the context of extending single-track lines with double tracks.Other technological changes included the expansion of the track width, electrification and automatic train control (ATC).Are these significant enough such that the old project has come to an end?Luckily, some situations are more straightforward when railroads are closed and physically removed.
To tackle this challenge, we consider two types of events: closures and upgrades (see Table 1).A closure occurs when the infrastructure has been removed, blocked or its purpose changed.Upgrades include various changes to the infrastructure after opening.Changes in use might be that the classification of a road is changed from a motorway to a pedestrian road or cycle path, or a national motorway is changed to a municipal road.Another change of use could include railway lines that still exist but are no longer used for regular passenger transport, for example, lines used for tourist tours.
It is a somewhat philosophical question to ask how large the changes need to be before we should declare the appraisal period as ended.The difficulty in our analysis is whether the events in the "upgrade" categories should be large enough changes for us to declare that the appraisal period ends, and a new infrastructure replaces the existing one.We take here a practical point of view and declare the upgrade with a substantial investment cost as a proxy for a new infrastructure.In this case a lane expansion of the roads entails a change of the road line due to a new road with much higher speed limit and a requirement of a lower gradient.In most cases the widening also means new tunnels and bridges.A new double track is also view as a proxy that the existing line has an ended appraisal period.Although the existing single track is still useful, it would have been substantially less costly to build the original infrastructure with double tracks in the first place, due to scale economies.
Ideally, our datasets should have included the whole network, with observations of events that matched the level of appraisals.For the first data set, the railway network, the number of lines was manageable, and it was possible to match the criterion.The network was much more complex for roads, and changes were often more gradual.Therefore, an exploratory approach was taken for the roads, and we considered the roads for which we had obtained a good overview.
The second dataset comprised the E18, a road from the Swedish border to the city of Kristiansand (see the yellow line in Fig. 2 ), a distance of approximately 410 km and a travel time in low-traffic periods of 4.5 h.In this case, we looked at the opening year for parts of the road by applying the Norwegian Public Roads Administration's roadmap (https:// vegka rt.atlas.vegve sen.no/).Previous changes and opening years regarding this road were collected from the road history books [22,24] and overviews from Wikipedia.Finally, these sources were crossvalidated using digitised articles, reports and books from the National Library's digitalised database. 6he third dataset contained parts of the E6 (the blue line in Fig. 2), with a distance of approximately 202 km and a travel time in low-traffic periods of 2.5 h.In this case, we considered the links from Svinesund (the Swedish border) up to the Hedmark county border in the north and the opening of two-lane and four-lane roads.This information was collected from Wiik [23], with some of the information regarding the completion of the opening year of the two-lane roads coming from other sources such as the project overview from the public road administration, newspaper articles, Wikipedia, and other encyclopaedias.

Descriptive statistics of opening year and events
Table 2 shows descriptive statistics for the opening years of the three datasets.The rail data include 177 observations, with 1909 as the average opening year.The data from the E18 include 33 road stretches, opening in the year 1966.Finally, the data from the E6 include 42 stretches, with an opening year of 1969.
Table 3 displays the number of events in the datasets.The rail data show that a third of the lines have been closed since opening.The extent of upgrade events is more significant: (i) 50% of the lines have implemented remote controls or electrification; (ii) 40% have implemented ATC; (iii) 10% have been extended with double tracks.Noteworthy, these events only Table 1 Types of events in the survival analysis a Representing end of appraisal period (end of use of existing project)

Infrastructure Closed Upgrade
Road NA Lane expansion a , new road line a Rail Closed a , removed a , change in use a Double tracks a , electrification, automatic train control (ATC), Remote steering of trains refer to infrastructure changes after the opening year; therefore, lines opened with ATC are not defined as an event.Moreover, there is an overlap between each of these changes, for example, for several lines, both ATC and remote controls were implemented after the opening year The road-related data (the E6 and E18) only include changes in the infrastructure (upgrade).Next, these road stretches were split into 29 and 42 sections.The average length of each section is 14 km for the E18 and   5 km for the E6.For the E18, 88 percent of the sections were changed, while all sections on the E6 were widened from two-to four-lane roads.In many cases, the whole line of the road was changed, for example, through the building of new tunnels and bridges.However, we do not differentiate between these factors in our analysis.

Railroad lines
The datasets presented in Sect. 2 were used to create Kaplan-Meier survival functions corresponding to a cumulative survival rate.Our primary interest in the median period of use corresponded with the point where the survival function crosses the P50 line (0.50 on the y-axis), representing the median life.This intersection provides an estimate of the ex-post appraisal period.When the line crosses the P50 line, more than half of the objects have fallen out of the dataset.Figure 3 displays the survival functions of railroads.Panel A shows the survival functions before an upgrade was done, while Panel B shows the survival functions in terms of closure of the lines.From the survival function in Panel A, we observe an average survival of 100 years for the changes in ATC, remote control and electricity.There are some difference between the lines at the start, but they vanished in the last part of the period.For the implementation of doubles tracks, too few changes occurred, even after 150 years, to say anything meaningful about the typical time before the change.Although most of these changes should be considered as to small to represent an end of the appraisal period, all these changes use the existing infrastructure and improve it, it has takes well above 50 years for any of them to be implemented.This shows that the initial project was used for a long time before any additional investments was made.
Panel B shows that it takes many years for lines to be closed.Even after 75 years, only a few of the routes had been closed; after 150 years, more than half were still in operation.The level of analysis in Panel B is arguably closest to the one used in the appraisals.

Roads
The following two datasets look at how long motorways have generated benefits before a substantial reinvestment.We examine how long the stretches of the E18 (Panel A) and E18 (Panel B) lasted before being replaced.Both the number of observations and events are displayed below each figure.The survival function shows that the median road lasted around 40 years in both cases, before being replaced.When we look at the original motorway, we see that most changes began after 20 years and declined at different speeds until most roads were replaced after 60 years Fig. 4.

Conclusion
This study has examined the ex-post appraisal period of transport infrastructure by looking at how long infrastructure was in use before upgraded or replaced.The analysis is relevant to changes in the service life and appraisal period over the last decade, which have significantly increased the estimated benefits in cost-benefit analysis [11].
To examine the ex-post appraisal period, we have examined how long roads and rail infrastructure built in Norway have been used.In terms of the road infrastructure, the analysis dealt with motorway changes since 1960.For railways, we looked back to the latter half of the nineteenth century when the first lines were built.We employed survival analysis as the methodological approach of the paper.This method enables a study of how long infrastructure is typically used even though much of the infrastructure around us still exists and, thus, has an unknown (residual) period.
The study's main findings are that railway lines have been used for many years, and an appraisal period of 75 years was a conservative estimate in the past.Roads have had a significantly shorter period before being changed.The motorways from Eastern and Western Norway, have typically lasted around 40 years before being replaced.
Even if the results differ and do not give a complete picture of long infrastructure have been used in the past, they can contribute to the discussion of the (ex-ante) appraisal period.First, our ex-post analyses showed a substantial variation in service life.If historical infrastructure were to have a lifespan of 75 years, this would mean that infrastructure built just before the Second World War would be beneficial up to 2014.Nevertheless, how much did we know in the late 1930s about the need for transport infrastructure in the 1990s?The changes ahead may be similar, and we should not rule them out in the same way as in the previous decades.One to deal with such uncertainty is to use a conservative appraisal period.Another approach is to allow the appraisal period to vary to a greater degree between projects, for example, by performing an analysis that aims to identify the project's risk of becoming obsolete due to changes in technology or other factors.
As far as we know, this study of the ex-post appraisal period.Although we looked at three datasets, the analysis has only scratched the surface of how long transport infrastructure have been used in the past.The following topics can help increase knowledge about the service life of infrastructure.
• Analysis from other countries.
• An analysis of the whole Norwegian transport network, including European and national roads.Such an analysis would provide a complete picture and eliminate several of the uncertainties in our study.• Qualitative analyses with in-depth analyses of selected projects.• A study focusing on operating and maintenance costs, reliability and inconvenience costs or estimates of reinvestment/midlife update towards the end of life.
Hopefully, this can increase our knowledge of history, putting us in an even better position to shape and predict the future.

Table 2
Descriptive statistics opening year

Table 3
Overview of events: Frequency and per cent