A network-level management system to mitigate the global warming potential of road pavements

ABSTRACT This study details a new, network-level optimization tool aimed at supporting transportation agencies in their efforts to reduce the global warming potential of their road pavement infrastructure. Through a two-stage bottom-up algorithm that integrates with a comprehensive cradle-to-grave life cycle assessment, the proposed tool learns optimal management policies for individual pavement sections and uses that information to guide network-level allocation choices. Through a realistic case study based on data made available by a state department of transportation, this study demonstrates that the proposed modelling approach identifies management strategies expected to reduce the global warming potential of a pavement network by up to 4.8% over 20 years relative to a more traditional, reactive management approach. The resulting model presented in this paper can support agencies in achieving ambitious targets to reduce the global warming potential of their paved infrastructure systems.


Introduction
Transportation agencies increasingly rely on pavement management systems (PMS) to cost-effectively maintain their assets.These systems can also be utilized by agencies to mitigate the climate change impacts of their paved infrastructure.An estimated 43% of public roadways in the United States are of poor or mediocre condition, with an estimated backlog of $435 billion required for pavement repairs (ASCE, 2017).A deficient pavement network not only exerts a utility cost to roadway users but also intensifies the transport sector's contribution to global greenhouse gas (GHG) emissions through mechanisms such as rolling resistance (Ziyadi, Ozer, Kang, et al., 2018).A continual challenge facing transportation agencies is the determination of near-optimal maintenance, rehabilitation, and reconstruction (MR&R) policies that account for uncertainties in future conditions (e.g., traffic volume and roadway deterioration).
This study proposes a stochastic, optimization-based tool that can help transportation agencies identify potential reductions in the global warming potential (GWP) of their paved networks.The tool embeds a comprehensive, cradle-to-grave life cycle assessment (LCA) in which (1) optimal policies are learned for individual facilities; and (2) these learned policies are used to inform network-level allocation choices.We refer to this modeling structure as a two-stage bottomup (TSBU) approach throughout this paper, which is consistent with the terminology used in past studies (Medury & Madanat, 2014;Sathaye & Madanat, 2012).To demonstrate the effectiveness of the proposed PMS tool, we apply it to network data generated by one state DOT comprised of 159, 1-mile pavement sections.Our results show that the proposed TSBU technique can identify management strategies expected to reduce the global warming potential of pavement networks by up to 4.8% over 20 years relative to a conventional, reactive management approach.

Overview of prior roadway network optimization models
The literature around pavement management systems is diverse in terms of the optimization methods used, the scale and scope of their applications, and the underlying objective functions and constraints.Given that our proposed model seeks to minimize the global warming potential of pavement infrastructure, we only compare past network-level PMS models with a similar overarching goal in Table 1.
Past studies have adopted various techniques to identify opportunities to reduce the global warming potential of pavement infrastructure while balancing fiscal constraints.Zhang, Keoleian, and Lepech (2013) made early headway in this research area, proposing a model where only one of three possible objectives could be minimized: energy consumption, GHG emissions, or cost.Their approach relied on dynamic programming, a technique shared by Lee, Madanat, and Reger (2016) and later used in conjunction with Lagrangian relaxation by Lee and Madanat (2017).The remaining studies have used a diverse range of methods to determine optimal management policies, including genetic algorithms (Gosse, Smith, & Clarens, 2013), Lagrangian duality principles (Reger, Madanat, & Horvath, 2015), greedy randomized adaptive search (Torres-Machi, Pellicer, Yepes, et al., 2017), integer programming (France-Mensah & O'Brien, 2019), and others.
The majority of studies in Table 1 have adopted a two-stage bottom-up approach to develop optimal MR&R policies at the network level (Lee & Madanat, 2017;Lee, Madanat, & Reger, 2016;Reger, Madanat, & Horvath, 2015).The TSBU approach entails first determining optimal and sub-optimal MR&R policies at the project-level for each individual pavement section (i.e., facility).These policies are subsequently evaluated at the network level with the intent to best achieve the systemlevel objective given a budgetary constraint (Medury & Madanat, 2014).A key advantage of solving project and network-level problems separately is that it reduces the size of the solution space.However, a limitation of this technique is that the optimal management policy for individual pavement sections may not be necessarily feasible at the network level due to limited available funding (Torres-Machi, Pellicer, Yepes, et al., 2017).This reality has motived alternative techniques such as genetic algorithms and other methods (e.g., adaptive search) to optimize the management plan for individual facilities while simultaneously taking into consideration network constraints (Gosse, Smith, & Clarens, 2013;Torres-Machi, Pellicer, Yepes, et al., 2017).The main challenge with these approaches is that they increase computational complexity, potentially leading to other modeling simplifications (e.g., limiting the number of available treatments) (Medury & Madanat, 2014).
Eight of the ten studies listed in Table 1 accounted for possible sources of uncertainty and variation.In such instances, the authors generally did so via a sensitivity       analysis.A sensitivity analysis is valuable when constructing LCA and optimization models, as it helps ensure that the results are reliable and robust (Jiang & Wu, 2019).Sensitivity analyses have generally been applied to constraints such as available fiscal resources (France-Mensah & O'Brien, 2019) and acceptable pavement condition such as roughness (Al-Saadi, Wang, Chen, et al., 2020) to understand their effect on systemlevel performance.In select instances, authors have also evaluated the sensitivity of their results due to changes in traffic patterns and delays (Lee & Madanat, 2017).
Across the studies listed in Table 1, the only input that has been modeled as stochastic is pavement deterioration (Lee & Madanat, 2017;Torres-Machi, Pellicer, Yepes, et al., 2017).Nine of the studies examined in Table 1 have accounted for relevant embodied impacts such as materials processing and the transportation, construction, and end-of-life disposal of the pavement.These efforts have generally relied on external LCA tools to characterize embodied impacts (Lee & Madanat, 2017;Zhang, Keoleian, & Lepech, 2013).In addition to embodied impacts, several studies have accounted for roughnessinduced impacts on fuel consumption for users (Lee, Madanat, & Reger, 2016;Reger, Madanat, & Horvath, 2015;Zhang, Keoleian, & Lepech, 2013).Seven of the studies listed in Table 1 have noted pavement roughness as a dominant contributor towards the global warming potential of pavement networks.Less common but still prevalent among the examined studies was the consideration of work-zone congestion during the undertaking of MR&R activities and resulting user impacts (France-Mensah & O'Brien, 2019;Lee & Madanat, 2017).Only one of the examined studies accounted for additional fuel consumption associated with the deflection of the pavement surface, a significant contributor to roadway GHG emissions on high truck traffic roads according to past project-level models (Al-Saadi, Wang, Chen, et al., 2020;Louhghalam, Akbarian, & Ulm, 2017).To the best of our knowledge, no network-level optimization model to date has considered albedo-induced impacts such as radiative forcing (RF) nor environmental impacts associated with lighting paved surfaces (Santero, Masanet, & Horvath, 2011).Having said that, project-level models have shown that pavement albedo can be a significant contributor towards the global warming potential of pavement infrastructure across various roadway classifications (Loijos, Santero, & Ochsendorf, 2013), motivating its inclusion within network-level PMS (AzariJafari, Yahia, & Ben Amor, 2016).
Another trend among the examined studies is the narrow set of agency MR&R interventions considered.Only five of the studies tabulated in Table 1 have considered a reconstruction option and, of the five, none of them included the option for an agency to alter the structural characteristics of the reconstructed roadway.This modeling choice potentially limits the capability of network-level tools to guide decisionmaking for agencies.For example, Shani, Chau, and Swei (2021) recently demonstrated that increasing the structural thickness of individual pavement sections yields improvements in terms of life-cycle cost and global warming potential at the project level, invariant to traffic volume.While this result is compelling, it is uncertain whether such a policy would still produce optimal results when scaled to the network level due to limited annual budgets that are distributed across competing needs.
This study extends the decision-making process proposed by Shani, Chau, and Swei (2021) from a single section to the network level.In doing so, this study assesses whether the outcomes learned by Shani, Chau, and Swei (2021) at the project level (i.e., increasing upfront spending leads to life-cycle cost and global warming potential savings) are valid at the network level.We apply a TSBU trigger-value optimization approach, wherein a recommendation to perform MR&R is based on a specific condition threshold.The optimal trigger value and structural design is learned through the facility-level optimization problem.The proposed optimization methodology seeks to extend past efforts by (1) accounting for a more comprehensive set of pavement life-cycle phases such as radiative forcing, lighting, deflection, and work zone congestion; (2) incorporating a wider selection of MR&R activities; and (3) evaluating the effectiveness of agencies investing more 'up-front' when preserving pavement assets across a roadway network.

Methodology
Our optimization approach follows a TSBU technique, where optimal management policies are first learned at the facility level and are subsequently used to guide network-level allocation choices.The facility-level solution builds on the integrated LCA and life-cycle cost analysis (LCCA) model developed by Shani, Chau, and Swei (2021).We begin this section by briefly summarizing the LCA and cost modules adapted from Shani, Chau, and Swei (2021), which are used to estimate the global warming potential and agency cost of different MR&R decisions for an individual section.This discussion is purposely brief given that the modules are detailed in the published literature (Shani, Chau, & Swei, 2021).We subsequently focus our attention towards the facility-level and network-level optimization techniques developed as part of this work, which we apply to a realistic case study to evaluate (1) the fidelity of the optimization technique proposed and (2) changes in its global warming potential across different budgetary levels.The LCA and LCCA models as well as the optimization techniques have been entirely programmed in Python.Doing so has allowed us to not rely on commercial software packages and enabled us to create a framework that is flexible and adaptable to other case studies and contexts.

Overview of project-level LCA and life cycle cost modules
Our probabilistic LCA considers five stages of a pavement's life cycle, as defined by Santero and Horvath (2009).These five stages consist of materials, construction, use, MR&R and end-of-life.The materials, construction, MR&R, and end-of-life impacts reflect the embodied impacts of pavement infrastructure.The quantification of the embodied impact for available treatments is sourced from life-cycle inventory data provided by ecoinvent version 3 (Wernet, Bauer, Steubing, et al., 2016).Characterization factors from the ReCiPe 2016 method are used to quantify the CO 2equivalent impact (i.e., kg CO 2 -e) for each relevant lifecycle process.Both the ecoinvent database and the ReCiPe 2016 method were selected based on their prevalent use in road pavement life-cycle assessments (Grael, Oliveira, Oliveira, et al., 2021;Manosalvas-Paredes, Roberts, Barriera, et al., 2019).Uncertainty around life-cycle inventory data and resulting impacts are assumed to follow a lognormal distribution in accordance with ecoinvent and their pedigree matrix approach (Wernet, Bauer, Steubing, et al., 2016).Similar to Shani, Chau, and Swei (2021), prior to running the full optimization model, the embodied impact for each MR&R treatment is estimated by sampling.100,000 Monte Carlo iterations are used to simulate the quantity and impact for each relevant process.The total global warming potential across the 100,000 samples is subsequently fitted to a log skew normal distribution, which approximates the summation of independent, lognormal random variables (Ben Hcine & Bouallegue, 2014).This step reduces the computational complexity required to run the TSBU optimization model.Information around life-cycle inventory data and their distribution (e.g., underlying variance) for this study are tabulated by Renard, Corbett, and Swei (2021).As the scope of our work emphasizes the management of existing pavement sections, we assume that MR&R treatments do not alter the geometric design of a roadway network.Should the geometric design of existing pavement sections be altered, it would be important to account for the effects of these crosssectional area changes on the environment (Moretti, 2022).
The impact associated with the use stage is classified into four distinct categories: pavement-vehicle interaction (PVI), work-zone congestion, lighting, and radiative forcing (RF).PVI refers to user-induced fuel consumption associated with rolling resistance, which includes pavement roughness, deflection, and texture.Texture is not considered in this study given the lack of available models (Xu, Akbarian, Gregory, et al., 2019).The effects of roughness-induced PVI is modelled through a roughness-speed-impact (RSI) model developed by Ziyadi, Ozer, Kang, et al. (2018).Ziyadi, Ozer, Kang, et al. (2018) provide a series of analytical equations that describe vehicle fuel consumption as a function of, among many factors, the international roughness index (IRI) of a pavement section.Changes in pavement IRI between years is based on a deterioration model developed by Swei, Gregory, and Kirchain (2018), which was calibrated based on data generated as part of Federal Highway Administration's (FHWA) long-term pavement performance (LTPP) program.The LTPP dataset encompasses more than 2,500 pavement sections spread across North America, with pavement ages ranging between 0 and 70 years (Elkins & Ostrom, 2021).The model captures probabilistic changes in pavement IRI due to the non-linear interaction between structural number (SN), average annual daily truck traffic (AADTT), and age for a roadway.This model has been specifically chosen for this study given that it is parsimonious, capturing the effect of available information typically tracked within a PMS (including our case study).Having said that, a shortcoming of this model is its inability to explicitly capture the structural loss experienced by a pavement over its lifetime in defining the future performance of rehabilitation treatments (Abaza, 2018).Excess energy consumed due to pavement deflection is accounted for through the model developed by Louhghalam, Akbarian, and Ulm (2014).Changes in traffic fuel efficiency as well as traffic growth over time are inferred from FHWA data; both factors are assumed to follow a Gaussian distribution based on goodness-of-fit statistics (Renard, Corbett, & Swei, 2021).
Excess fuel consumption for users due to work zonerelated congestion is estimated using a model developed by Zhang, Batterman, and Dion (2011), which is based on field data collected at a site in Ann Arbor, Michigan and is integrated within the Comprehensive Modal Emissions Model (Barth, An, Younglove, et al., 2000).The model identifies the probabilistic uptick in excess passenger car and heavy vehicle fuel consumption due to MR&R-related lane closures.Although the model developed by Zhang, Batterman, and Dion (2011) is based on a single site, we leverage their findings given that they provide a simple, probabilistic understanding of the effect of work-zone congestion on users that can be integrated within our Python-based tool.For both PVI and work-zone congestion, life cycle inventory data made available by ecoinvent, coupled with characterization factors published by Recipe 2016, are used to equate increases in fuel consumption for users into a resulting CO 2 -equivalent impact.
Additional energy demands from street-lamps required to illuminate the roadway for night time travel are captured in this study through the relationships defined in Santero and Horvath (2009).We rely on AASHTO's recommendation of 9 lu per m 2 for asphalt freeways and use a conservative lighting efficiency estimate of 30,000 lu per kW.The global warming potential generated by low albedo surfaces like asphalt pavements are also represented using the models defined in Xu, Swei, Xu, et al. (2020).We only capture RF impacts and ignore the urban-heat island (UHI) effect given that our case study is located in a non-urban environment.
To estimate the probabilistic life-cycle agency expenditures associated with each reconstruction and overlay option, we employ a series of simple, parametric models generated by Shani, Chau, and Swei (2021).These models produce a unit-cost distribution for hot-mixed asphalt, aggregate bases, overlays, and pavement milling as a function of project size to account for economies-of -scale.To capture deviations in real highway construction prices over time, a price index is constructed based on time-series data generated by Wong and Swei (2021).Both the price index and unit-cost distributions are tabulated by Shani, Chau, and Swei (2021) and rely on bid data made available by Oman Systems, Inc.After data processing, their comprehensive bid dataset spans $170 billion worth of paving projects from across the contiguous United States with the exception of the state of New Jersey (Wong & Swei, 2021).

Facility-level optimization
The facility-level optimization relies on a trigger-value approach, a widely used method to optimize MR&R treatments for individual sections and networks due to its computational efficiency (Lee, Madanat, & Reger, 2016;Torres-Machi, Osorio-Lird, Chamorro, et al., 2018).The trigger-value approach is employed by practitioners and various state DOTs, including California and Washington, to guide their decision-making process (Jackson, 2008;Reger, Madanat, & Horvath, 2014).
The trigger-value approach involves applying a treatment (e.g., overlay) over the life cycle of a pavement section when its condition exceeds an allowable threshold.In this research, we focus on pavement IRI given that it is an indicator of pavement condition and is ubiquitously used by both state DOTs and smaller municipalities (Ogwang, Madanat, & Horvath, 2019).
As shown in Figure 1, for a given set of initial conditions (e.g., current traffic), the model will select an initial pavement design and trigger value that 'triggers' the application of a pavement overlay.Over the course of 500 Monte Carlo samples, the model will simulate the evolution of various uncertainties such as pavement deterioration, traffic growth, and price inflation until the end of the analysis period.After completion, the model will record the expected life-cycle cost and global warming potential (i.e., kg CO 2 -e) of the selected initial pavement design and trigger value.This process is repeated for a broad set of traffic conditions, pavement condition, pavement designs and trigger values to learn both optimal and sub-optimal policies for the facility (Medury & Madanat, 2014).The implicit relationship between traffic conditions, pavement age, and the structural design of a pavement section is relaxed to explore solutions which may not emerge using a conventional pavement design process and to validate that the model's suggested management strategies are reasonable.
In this study, we record the expected life-cycle cost (LCC) and global warming potential (GWP) for various flexible pavement designs and trigger values across 4 'average' contexts and 5 initial MR&R actions.These tabulated values form a 'look-up' table that guides the network-level optimization.
The 4 'average' contexts are reference roadways based on the average annual daily traffic (AADT) from the network of interest.AADT is used as the defining descriptor between contexts based on the assumption that AADT is highly correlated with average annual daily truck traffic (AADTT), meaning observed increases in passenger vehicles within a context corresponds to a commensurate increase in trucks and other heavy vehicles.This assumption may not necessarily hold across pavement networks, and so it is important that a decision-maker validate this hypothesis when defining their 'average' contexts.For our case study dataset, Pearson's correlation coefficient between AADT and AADTT is 0.85.Each facility is categorized by AADT (and by association AADTT) across the network given that traffic volumes drive the deterioration and use-stage impacts associated with a pavement.Each 'average' context uses the median AADT value of the corresponding quartile (e.g., 12.5, 37.5, 62.5, and 87.5% iles) computed from the existing network.For each 'average' context, the geometric dimensions (e.g., number of lanes, shoulder width) reflect the median values for the relevant sub-sample of the network.
Of the 5 initial MR&R actions considered, the first represents the action to reconstruct at the start of the analysis period, resetting the pavement's age to zero.The remaining initial actions account for 4 alternative scenarios, where the pavement is initially overlaid at 4 different starting ages spanning the range of 10-70 years.The extended pavement age scenarios (e.g., 70 years) are considered to enable the model to evaluate the possibility to rehabilitate, rather than reconstruct, some of the older pavement sections in our case study.The occurrence of this scenario is plausible given a constrained budget or the presence of sections in poorer condition.
For each context and action, we compute the expected LCC and GWP for 17 different flexible pavement designs, which range in terms of their structural number (SN), from as little as 2.6 to as high as 8.6 (i.e., 0.4 increments).The structural number for these pavement designs is dictated by the asphalt concrete layer thickness.All pavement designs within the set of 17 designs share an aggregate base thickness of 6 in (15 cm).For each design, the facility-level model enumerates across 13 different trigger values.Interstates and freeway cases evaluate the life-cycle performance of trigger values between 1.36 m/km to 3.76 m/km (0.2 m/km increments), while lower traffic roadways (e.g., collectors) use trigger values between 1.68 m/km and 4.08 m/km.The higher the trigger value, the less frequent pavement overlays are applied to a facility, reducing agency expenditures but possibly increasing expected GWP due to larger use-phase impacts.
As one may anticipate, it is computationally intractable to enumerate over 17 different designs and 13 different trigger values (i.e., 221 total combinations) across an entire network for an extended analysis period.As a result, the expected outcomes for the 4 'average' contexts and 5 initial actions form the basis of the look-up table to guide facility-level choices for our network-level problem.For each facility across the specified network, the assumed expected LCC and GWP for an available design and trigger value is assumed to follow the 'average' context that is most representative of the facility of interest in terms of its AADT.The combination of structural design and trigger value with the lowest expected GWP is tabulated as the 'optimal' policy for a facility with a similar AADT.This information is subsequently used as part of the networklevel allocation technique.

Network-level optimization
The prior section described the process to estimate the anticipated life-cycle cost and global warming potential for a single facility across a pavement network and the determination of its 'optimal' management policy.This section details how the outcomes at the facility-level are used to inform network-level allocation choices as shown in Figures 2 and 3.It is assumed that, similar to practice, a certain portion of the available budget is allocated to capital outlays (e.g., reconstructions) while another portion is allocated to pavement rehabilitation (e.g., overlays).It is also assumed that the budget from both funds is depleted at the conclusion of each year, meaning any remaining budget from the current year does not carry over to the following year.
The algorithm relies on the 'look-up' table from the 4 'average' contexts as part of the facility-level analysis to guide its decision-making process.At a given timestep, the initial pool of roadway candidates is first filtered by facilities already possessing a SN that is GWP-optimal for their road conditions and whose lifecycle GWP is not reduced by application of an overlay.Facilities that meet this criterion are not considered further.Remaining roadways are further evaluated as potential candidates for MR&R.Roadway sections that exhibit an improvement in expected lifecycle GWP by a reconstruction at the current timestep, as opposed to an overlay, are considered for reconstruction.Roadways with an IRI condition that meets or exceeds its optimal trigger value at the facility-level are considered candidates for overlays.The remaining roadways that have not been selected for either reconstructions or overlays are not considered further.Roadway sections selected for reconstruction are eligible for overlays should funds for capital outlays be insufficient to address all reconstruction candidates.Reconstruction candidates are assigned two benefit-cost ratios to rank the relative urgency of each pavement to receive reconstruction and rehabilitation, respectively.To generate the ratio for reconstructions, the algorithm extracts (for the relevant 'average' context) the expected GWP and LCC for (1) the optimal structural design and its optimal trigger IRI; and (2) the current structural design and its associated optimal trigger IRI, as computed by: E[GWP reconstruction ] and E[LCC reconstruction ] are the expected GWP and LCC associated with reconstructing the facility to its 'optimal' structural number and subsequently overlaying the facility based on the corresponding 'optimal' trigger value; E[GWP overlay ] and E[LCC overlay ] reflect the expected GWP and LCC with maintaining the facility's current structural design and applying an overlay based on a locally optimal trigger IRI.This ratio reflects the expected GWP savings (as E[GWP reconstruction ] must be less than E[GWP overlay ]) when returning the management of the pavement to its preferred reconstruction policy from a locally preferred rehabilitation policy relative to the increase in life-cycle cost to do so (given that E[LCC reconstruction ] is always greater than E[LCC overlay ]).Likewise, the algorithm ranks candidates eligible for as follows: In a similar fashion to Equation 1, expected GWP and LCC are calculated to compare the anticipated outcome of either (1) overlaying the facility and following its optimal trigger value; or (2) delaying (i.e., abstaining) treatment in the current time step.GWP overlay and LCC overlay are calculated the same manner discussed in Equation 1. GWP delay and LCC delay represent the GWP and LCC when maintaining the facility using the trigger value associated with its current condition, which exceeds its optimal value.Equation 2, used in the triaging process for overlay candidates, characterizes GWP savings relative to the increase in LCC to perform an overlay during the current timestep as opposed to delaying treatment.The larger the ratios presented earlier, the greater the GWP savings per dollar spent returning the facility to (1) its preferred design and management policy from its preferred rehabilitation policy (Equation 1); and (2) its preferred rehabilitation policy from the 'no treatment' alternative (Equation 2).Funds are allocated to candidate facilities based on these two ratios in a descending order until the available budgets for both reconstruction and M&R are exhausted.
The application of a reconstruction activity resets the pavement age to zero and its IRI to 1 m/km.Once allocation resources are exhausted for capital outlays, the algorithm turns its attention towards the funding of overlays across the network for candidate facilities in the same, descending order until the budget for overlays is no longer available.The application of a pavement overlay does not affect the age nor SN of a facility but does restore its IRI to a condition of 1 m/km.
Once funds are allocated across the entire network, the model simulates future conditions for each pavement section (e.g., IRI, AADT, fuel efficiency improvements, construction prices, etc.) according to the modules described in earlier sections.This process repeats itself over the entire analysis period.Furthermore, this entire sequence is completed for an additional 1,000 Monte Carlo samples to generate distribution of the total GWP across network over the full analysis period.

Benchmarking method
To benchmark the performance of our proposed TSBU solution, we compare it to a 'worst-first' management strategy.This approach reflects a reactive pavement management strategy that has been used historically by many agencies to schedule MR&R activities (Menendez, Siabil, Narciso, et al., 2013).The approach involves assigning the highest urgency to sections the poorest condition (measured in terms of pavement IRI).Inherent in this strategy is a clear preference towards immediate improvements in roadway condition, potentially at the expense of environmental and cost efficiency over the long run (Menendez, Siabil, Narciso, et al., 2013).This management approach will frequently embed decision trees, where a series of conditional statements that reflect distress criteria as well as key contextual factors (e.g., pavement age and traffic volume) help determine the appropriate treatment for a pavement section (Wang & Pyle, 2019).
As formulated in this paper, the worst-first algorithm applies MR&R to each roadway in descending order of IRI until budgets for both capital outlays and M&R are exhausted.Only pavements exhibiting an IRI greater than 1.36 m/km are considered eligible for MR&R in both TSBU and worst-first approaches.Similar to the TSBU algorithm, the total agency budget is portioned between capital outlays and rehabilitation treatments.Facilities whose age exceeds 30 years are first considered for a reconstruction treatment whereas the remaining sections are considered for overlays only.
This process is repeated for 1,000 Monte Carlo simulations to estimate the expected GWP of the worst-first approach.To comment on whether the TSBU approach outperforms the worst-first technique for a given budgetary scenario, we rely on two statistics.First, we compare the expected GWP for both allocation approaches over the 20-year analysis period.Second, in each Monte Carlo simulation we record the difference between the GWP achieved by the TSBU and worst-first approaches over the 20-year analysis period.The frequency that this difference is negative over 1,000 simulations reflects the estimated probability that the TSBU approach will achieve a lower GWP over the analysis period than the worst-first technique (Noshadravan, Wildnauer, Gregory, et al., 2013).As part of this process, we initialize the pseudo-random number generator with the same seed values for the TSBU and worst-first approaches to ensure both algorithms experience similar evolutions in exogenous factors (e.g., traffic growth), avoiding possible statistical bias (Noshadravan, Wildnauer, Gregory, et al., 2013).The effects of the 'worst-first' approach relative to the TSBU algorithm are further discussed in the subsequent sections via a case study.

Case study
To characterize the relative performance between the worst-first and TSBU algorithms, both strategies were applied to 159, 1-mile pavement sections of Interstate 95 in Virginia.The pavement section characteristics and traffic conditions originate from data made public through the FHWA's Highway Performance Monitoring System (HPMS) long-term pavement performance database.The condition of the network at the start of the analysis period is excellent, with an average IRI of 1.28 m/km.The average AADT across all pavement sections is 104,078 vehicles, ranging from 36,952 to 230,804 across the full dataset.The entire network is composed of asphalt concrete pavements with initial SN design values ranging from 5.84 to 6.29.The geometry of each section in the network is assumed to be fairly uniform throughout with 3, 12-foot through lanes in each direction.The average left and right shoulder widths are 6.78 ft and 10.03 ft, respectively.Traffic information, structural characteristics, and geometric designs for each of the 159 pavement sections can be found the supplementary information document (Table S1).The analysis period for the network and facilitylevel optimization models is 20 years.This analysis period was selected given that the majority of state (e.g., Virginia) transportation asset management plans are typically developed for a fairly short (i.e., 10 to 20 year) planning horizon (Virginia Department of Transportation, 2019).The facility-and network-level models have been both designed for the same analysis period (i.e., 20 years) to optimize the management of the system for the planning horizon of interest for decisionmakers.

Results and discussion
Figure 4 presents the average GWP across each life-cycle phase over the analysis period for an annual budget of $12 million and for a range of allocations between overlays (i.e., M&R) and reconstructions (i.e., capital outlays).Figure 5 presents the number of reconstruction and overlay treatments the worst-first and TSBU algorithms apply, on average, for each year of the analysis period.Figures 4 also highlights the average frequency each treatment is skipped (i.e., shifted from its preferred timing) due to limited fiscal resources.Skipped treatments are not tracked for worst-first approach, as the technique considers all sections candidates for treatment.The tabulated results (Table S2), as well as the resulting plots (Figure S1-S4) for an annual budget of $8 million and $16 million, respectively, are available in the supplementary information document.
Across the three budgetary levels, the TSBU algorithm outperforms (in terms of expected value) the worst-first technique in all accounts by as little as 0.3% ($8 million annual budget) to as much as 4.8% ($16 million annual budget) under various funding allocations.As can be noted in Table S2, the ability of the TSBU approach to identify a management strategy that achieves a lower GWP than the worst-first approach is statistically significant in 9 of 12 cases at the 1% level and 10 of 12 cases at the 5% level.The difference in the two approaches is statistically significant at the 1% level in all instances for the $12 million and $16 million annual budgets scenarios.
As the annual available budget increases, the TSBU policy generates a lower expected GWP when compared alongside the worst-first approach.For example, by doubling the annual budget in the 20% M&R case from $8 million to $16 million, the savings associated with the TSBU approach grow by 50,786 Mg of CO 2quivalent impact, more than 10 times the savings observed for the $8 million scenario.With an abundance of fiscal resources, the worst-first approach tends to make sub-optimal decisions by applying overlays and reconstructions prematurely.According to Table S2, as the budget increases from $8 million to $16 million, the average number of overlays applied by the worst-first and TSBU approach over the analysis period increase by roughly a similar magnitude (from 65 to 113 and 61 to 119, respectively).Unlike the worstfirst approach however, the TSBU algorithm judiciously refrains from applying reconstructions when the associated embodied impacts outweigh the use-phase GWP savings.This preference is exhibited in Table S2 where the TSBU approach postpones reconstructions in favour of rehabilitation likely in response to the excellent of the pavement network.
In comparing the worst-first and TSBU approaches for an available budget of $12 million in Figure 4, we can note that the presence of embodied impacts as a contributor to lifecycle GWP is at its highest during the early years of the analysis period.This observation stems from the tendency of both approaches to 'renew' the pavement network as early as possible, making an upfront investment to minimize use-phase GWP impacts in later years.
Comparing the TSBU and worst-first policies highlights the importance of M&R in minimizing GWP for a pavement network.As shown, the TSBU algorithm prefers overlays and refrains from applying reconstructions when the associated embodied impacts outweigh the use-phase GWP savings.For transportation agencies, this outcome implies that allocating more fiscal resources towards M&R instead of towards capital reconstruction projects could minimize the GWP of a pavement network.However, at a certain point there is no benefit with more budget.This is shown in Table S2, where expected total GWP is similar for the TSBU policy in the $12 million and $16 million annual budget scenarios for overlay allocations of 40%, 60%, and 80% (1.50 million Mg CO 2 -e).
The previously discussed findings highlight that, across all budgetary levels, the TSBU approach presented in this paper offers agencies a computationally tractable framework to identify strategies to reduce the global warming potential of their existing assets.Inevitably, there are opportunities to further this research in the coming years.Firstly, the TSBU optimization seeks to minimize network GWP by incrementally adjusting all roadway sections within the network to their optimal schedule of rehabilitation and reconstruction treatments.Inherent in this design, the TSBU algorithm skips solutions with timings and pavement designs that may be sub-optimal at the facility-level but are optimal at the network-level.For this reason, future work should consider different optimization to explore and navigate a broader solution space.the TSBU algorithm, use-stage GWP increases annually towards the end of the 20-year analysis period as the application of MR&R becomes more infrequent.This outcome likely stems from the absence of any incentives to administer intensive MR&R activities at this time, as their benefits may extend well beyond the analysis period.To address this issue, future research should explore methods to capture the long-term GWP benefits due to current pavement improvements.Future research into quantifying the future GWP benefits of each MR&R activity will enable pavement management systems such as the TSBU approach to effectively distribute treatments throughout (and beyond) the analysis period.
As a trade-off for network scalability, the TSBU algorithm also imposes straightforward decision rules regarding pavement design and condition to evaluate the viability of performing different MR&R treatments.Future pavement management algorithms may want to consider more complex decision rules to aid in the planning of overlay and reconstruction projects.Furthermore, the choice of pavement MR&R activities has been limited in this study to 1 overlay and 17 reconstruction options.Future solutions may want to consider the environmental and operational effects of a broader set of M&R treatments, including crack sealing, patching, thin and ultrathin overlays, and other available technologies.Moreover, this study is single objective in its nature, only seeking to minimize the global warming potential of a pavement network.Given the variety of performance criteria that pavement engineers must balance, future research should explore the feasibility of adapting this model for multiobjective pavement management.
Finally, it is important to note that the TSBU approach is a parsimonious and modular framework to estimate and optimize the GWP of a pavement network.Its development required the use of existing models, which reflect a specific region, roadway functional classification, or pavement type.The substitution of these models may alter the findings of our case study as well as the results for other network contexts.Consequently, practitioners may choose to substitute these models to improve the representation of their pavements for their particular geographical context.

Conclusion
Pavement management systems have emerged as an effective tool to guide network-level decisions for transportation agencies.Given that the transport sector contributes significantly towards greenhouse gas emissions, there is a tremendous opportunity to leverage pavement management systems to minimize the environmental impact of paved infrastructure.This paper has described a new tool aimed at helping agencies identify management strategies to reduce the global warming potential of their pavement networks.The results of our case study demonstrate that, across different budgetary constraints, the proposed TSBU algorithm can identify reductions in the expected global warming potential of pavement systems by up to 4.8% over 20 years relative to a more reactive management strategy.Our conclusions also emphasize the importance of rehabilitation activities in reducing the GWP of pavements and their potential advantages relative to reconstructions in this regard.Allocating a greater percentage of overall pavement management budgets towards overlay activities rather than reconstructions has been demonstrated to be a promising strategy to reduce the GWP of a pavement network.These findings, as well as the tool developed as part of this research, can assist agencies in enhancing the sustainability of our built environment.

Figure 1 .
Figure 1.Overview of facility-level analysis of available pavement design and trigger-value policies.

Figure 2 .
Figure 2. Detailed overview of the TSBU candidate facility selection algorithm.

Figure 3 .
Figure 3. Detailed overview of the TSBU ranking and allocation approach.

Figure 4 .
Figure 4. Total global warming potential for TSBU and worst-first allocation approaches over 20-year analysis period for $12 million annual budget, with varying overlay allocation percentages.

Figure 5 .
Figure 5. Average count of MR&R activities for TSBU and worst-first allocation approaches over 20-year analysis period for $12 million annual budget, with varying overlay allocation percentages.

Table 1 .
Summary of past network-level optimization papers aimed at minimizing the global warming potential of pavements.