Comprehensive Life Cycle Cost Analysis of Pavement Materials 2013

8/18/2019 Comprehensive Life Cycle Cost Analysis of Pavement Materials 2013

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A More Comprehensive Life Cycle Cost Analysis of Pavement Materials Alternatives

byWilliam Colby Dunn

Undergraduate in Materials Science and EngineeringMassachusetts Institute of Technology

Submitted to the Department of Materials Science and Engineeringin Partial Fulfillment of the Requirements for the Degrees of

Bachelors of Science in Materials Science and Engineeringat the

Massachusetts Institute of Technology

June 2013

© 2013 Massachusetts Institute of Technology.All rights reserved.

Signature of author

Department of Materials Science and EngineeringMaterials Systems Laboratory

5/3/2013

Certified by

Joel P. ClarkMaterials Systems Laboratory Faculty Director

Thesis Advisor

Accepted byJeffrey C. Grossman

Undergraduate Committee Chairman

Correspondence: W. Colby Dunn Phone: 617-548-9944 [email protected]


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ACKNOWLEDGMENTS

This research was implemented in tandem with the Materials Systems Laboratory at MIT.

The author is grateful to Omar Swei for his extensive technical input, and to Randolph

Kirchain and Joel Clark for their technical and literary support and mentorship.

Additionally, the author would like to thank MIT for seamless software implementation

and Applied Research Associates, Inc., which helped developed pavement designs used

in the analysis.


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TABLE OF CONTENTS

I. LIST OF FIGURES…………………………………………………………..….5

II.

LIST OF TABLES…………………………………………………………….....6

III. ABSTRACT……………………………………………………...……………….7

IV. INTRODUCTION …………………………………………….…………………8

V. LITERATURE REVIEW …………………………….……………………..…12

a. Literature Review….……..….…...…….……….……….……………….12b. Gap Analysis ….….………………………………………………………15

i. Part 1: Out-of-sample Forecasting ….……………………………15ii. Part 2: Unit-cost Variability Due to Location and Cost…….……16

iii.

Part 3: Case Study Methodology …………………….……..……16

VI. METHODOLOGY ……………………………………………………..………17

a. Part 1: Out-of-sample Forecasting .………………………………………17 i. Section A: Stationary or Non-Stationary Classification

ii. Section B: Forecasting Based on Data Classificationiii. Section C : Accuracy of the Forecast vs. Baseline Case

b. Part 2: Unit-cost Variability Due to Location and Cost………………….21 c. Part 3: Case Study Methodology ……………………………………...…22

i. Section A: Unit Cost Relationshipii. Section B: Uncertainty Characterization without Historical Data

iii.

Section B: Perform and Interpret Simulations

VII. RESULTS & ANALYSIS………………………………………………………24

a. Part 1: Out-of-sample Forecasting……………………………….………24 i. Section A: 40-year Results

ii. Section B: 60-year Resultsb. Part 2: Unit-cost Variability Due to Location and Cost………………….28 c. Part 3: Case Study Methodology ………………………………………...36

VIII. CONCLUSIONS AND FUTURE WORK …………………………………….42

IX.

WORKS CITED…………………………………………………………...……43

!" APPENDICES ……………………………………………………………..……46


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LIST OF FIGURES

1. Figure 1: Two Pavement Designs with Different Net Present Values (NPV) andRisks………………………………………………………...…………………......8

2. Figure 2: The Life-Cycle of a Highway Construction Project….page……………………………………………………………………………....10

3. Figure 3: The Initial and Life-Cycle Costs Associated with HighwayConstruction Projects….…………………………………………………………10

4. Figure 4: The Historical Price Behavior of Dimensioned Stone….……..……...24

5. Figure 5: MAPE vs. Year into the Future (40-year Analysis)…………………..26

6.

Figure 6: MAPE vs. Year into the Future (60-year Analysis)…………………..27

7. Figure 7: Florida linear regression analysis of unit-cost of HMA winningpavement bids with respect to bid volume.………………..……………………..29

8. Figure 8: Aggregate (FL & CO) linear regression analysis of unit-cost of JPCPwinning pavement bids with respect to bid volume.……...….. ……………..…..30

9. Figure 9: Colorado linear regression analysis of unit-cost of HMA winningpavement bids with respect to bid volume……………….……..………………..31

10.

Figure 10: Colorado linear regression analysis of unit-cost of JPCP winningpavement bids with respect to bid volume……………….……..………………..31

11. Figure 11: ARA Pavement Design Specifications………..…………………..…36

12. Figure 12: Initial, discounted rehabilitation, and life-cycle costs of JPCP andHMA pavement designs in Florida and Colorado………..……………….…..…38

13. Figure 13: Florida probabilistic life-cycle cost of urban interstate roadalternatives (gray line represents HMA design, orange represents JPCP design).The dashed lines represent the mean value from the analysis………..……...…..39

14.

Figure 14: Colorado probabilistic life-cycle cost of urban interstate roadalternatives (gray line represents HMA design, orange represents JPCP design).The dashed lines represent the mean value from the analysis………..……….…40

15. Figure 15: 40-year MAPE Analysis with Real dollars, No-change Model…..…49

16. Figure 16: 60-year MAPE Analysis with Real dollars, No-change Model…......50


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LIST OF TABLES

1. Table 1: Florida quantification of unit-cost uncertainty for significant inputparameters. Values in parenthesis represent the standard error of the regression

coefficients………………..……………………….……………………………..33

2. Table 2: Colorado quantification of unit-cost uncertainty for significant inputparameters. Values in parenthesis represent the standard error of the regressioncoefficients….………………..………………..…………………………..……..35

3. Table 3: MEPDG based JPCP and HMA pavement designs for the urbaninterstate and local road case studies.……………………………………………46

4. Table 4: Maintenance schedule for JPCP and HMA pavement designs at MEPDGspecified 90% reliability for the urban interstate and local road case

studies………………..………………..………………………….…….………..47

5. Table 5: Florida Pavement Specifications….………………..…….………...…..48


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ABSTRACT

Life Cycle Cost Analysis (LCCA) is a commonly used tool in analyzing the economic

viability of highway construction investments. The initial and life-cycle materials costs

associated with highway construction involve a high level of uncertainty and therefore

warrant extensive and dynamic cost analysis. These uncertainties derive from extensive

materials usage costs. Despite the advantages of implementing a probabilistic approach to

cost analysis, many state departments of transportation (DOTs) continue to employ a

deterministic model, thereby misjudging, and often altogether neglecting the underlying

uncertainty and risks. The goals of this paper are twofold: first, to validate forecasting as

a viable method to predict future materials’ prices, and second, to explore economies of

scale as a potential driver of uncertainty.

The paper will then apply these results to a case study methodology, looking at a

comparative LCCA of two materials alternative, asphalt vs. concrete pavement designs

for two states: Florida and Colorado. Endeavoring in this light, the author has

characterized uncertainty in a way that will be comprehensible by practitioners. This

research has successfully validated out-of-sample forecasting as a superior method of

forecasting materials prices, characterized uncertainty related to project quantity, and

delivered results using a relatable case study approach.


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INTRODUCTION

Analyzing highway construction projects deterministically is a cursory methodology in

that it oversimplifies input parameters by assigning them a single, static value. These

simplified values effectively mask any uncertainty related to the investment decision on

hand, as shown in Figure 1 (Gransberg 2009). While this approach does provide the user

with a simple selection process, it bases its cost assessment off a limited number of

possible outcomes. Realistically, there are a vast multitude of nuanced scenarios that

could play out; the risk associated with such long-term investments therefore is much

more complicated than a single output. A probabilistic analysis will account for a range

of outcomes, thereby better incorporating the underlying risks associated with a project

(Swei 2013). With a better understanding of the risks associated with different highway

implementations practitioners will be better able to integrate risk-threshold levels into

their highway construction decisions.

Figure 1: Two pavement designs with different net present values (NPV) anddifferent associated risks (error bars). A deterministic approach would effectivelymask the underlying uncertainty here.

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The concept of implementing a probabilistic LCCA is by no means novel. In fact, the

methodology has come strongly recommended by the Federal Highway Administration

(FHWA) since 1998 (Smith and Walls 1998; Temple and William 2004). The

implementers of such models, however, have been hesitant to switch from the traditional

deterministic model for several reasons. The first of which is that the implementation of a

probabilistic model is far more complex and multi-faceted than is its deterministic

counterpart. Secondly, practitioners have been provided little guidance regarding how to

characterize uncertainty regarding input parameters (Tighe 2001).

Life Cycle Cost Analysis (LCCA) is a commonly used analytical investment assessment

tool that accounts for total project costs beginning with the initial building and extending

to the final removal of the venture, as shown in Figure 2 (Lee 2002; Guo 2010). All costs

incurred in-between (e.g. routine maintenance and rehabilitation expenses) are included

(Smith 1998). It is therefore no surprise that projects warrant extensive materials usage,

and the importance of materials in the LCCA, therefore, cannot be stressed enough.

While highway investments extend far into the future (some reaching 50-years), recent

data has shown that practitioners continue to place a disproportionate weighting on initial

costs rather than their life-cycle counterparts (Rangaraju 2008). One explanation for this

phenomenon is that the level of uncertainty is far greater when forecasting costs that

extend far into the future. It is therefore reasonable to abstract that should practitioners be

provided with a framework to better understand potential future cost behavior, they are

likely to weigh life-cycle costs when selecting a paving material (Frangopol 2001).

Beyond uncertainties in future costs, investments in highways also warrant extensive


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characterization of initial parameters, such as unit-cost of paving material inputs, which

likely vary as a function of quantity, location, and more as shown in Figure 3. With better

characterization of the impact of these two variables on cost, practitioners will be more

confident in their understanding of the variability associated with a specific pavement

materials selection.

Figure 2: The three main constituents of life-cycle costs in highway constructionprojects. The final removal costs and user costs are excluded.

Figure 3: The initial and life-cycle costs associated with highway constructioninvestments. (Swei 2012)


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The overarching theme of this paper is to provide LCCA practitioners with an improved

structure for understanding uncertainty related to highway costs, particularly uncertainty

related to future materials costs. In this vein, the paper will take a two-pronged approach

in first classifying uncertainty related to future materials prices, and testing whether

forecasting prices decades into the future is a plausible endeavor. The research will then

shift to characterizing the unit-cost of construction inputs associated with highway

construction, exploring how much of the variability can be explained through a likely

relationship which exists between cost and quantity and testing this for multiple

locations. Finally, the author has taken a case study approach in order to test the

implications of the characterized inputs on a probabilistic LCCA for pavement design

alternatives that are considered functionally equivalent. Specifically, an LCCA between

two materials alternatives, asphalt and concrete pavement designs in Florida and

Colorado will be compared. In so doing, drivers of uncertainty will be elucidated in a

way relatable to LCCA practitioners, thereby leading to an improved methodology for

understanding the uncertainty embedded in such long-term investments.


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LITERATURE REVIEW

Economic feasibility is a fundamental concern when assessing any long-term investment

proposition, and highway construction projects are certainly no exception. With historical

LCCA model implementation ranging from thirty to fifty-five years, highways represent

just how important financial viability is to infrastructure projects (Frangopol 2001).

Culminating in what was a revolutionary ordinance in 1995, the Federal Highway

Administration (FHWA) forced all state DOTs to incorporate LCCA models into

highway projects that had estimated costs of over $25mm (National Highway System

Designation Act of 1995). The FHWA further emphasized the importance of sound

highway investment by outlining the shortcomings of a deterministic LCCA (Walls and

Smith 1998). Stressing the relative merits of a probabilistic dynamic model, the FHWA

has established itself as a prominent source of funding for such research.

After the 1995 legislation, teams of researchers set to work developing a more robust

LCCA model to accurately assess the economic performance of highway construction

projects. Specifically, Zimmerman and Peshkin focused their efforts on specifying

optimal maintenance schedules for pavements (Zimmerman and Peshkin 2003).

Embacher and Snyder evaluated the relative economic merits of asphalt (HMA) vs.

concrete (RMC) in low-volume pavement applications (Embacher and Snyder 2001).

Oberlander used factor analysis to make predictions for the cost of construction projects

(Oberlander 2003). The above research endeavors, while having contributed to the

development and implementation of LCCA in the field, are fundamentally flawed, as they

have taken a deterministic approach. In so doing, said research has failed to address the


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uncertainty and risks previously discussed (Swei et al. 2013a). With that said, one

parameter that has traditionally been ignored is the forecasting of future material prices.

Before forecasting prices, however, it is first necessary to verify that statistical methods

exist, which are a superior method of predicting such uncertainties with a relatively high

level of precision.

In order to forecast future cost behavior, one risk that must be considered is how

construction prices will evolve over time. To that extent, research has been geared

towards using statistics in assessing the merits of forecasting future materials prices (i.e.

whether or not historical data is a good predictor of future data). One such methodology,

known as “backcasting”, takes “out-of-sample” data and forecasts said data where the

future price point is known. Multiple studies have implemented these methods. Ashuri

and Lu (2010) created a Construction Cost Index (CCI) that uses an Autoregressive

Integrated Moving Average (ARIMA) model to forecast future costs. The two used a 12-

month out-of-sample forecast in tandem with Mean Square Error (MSE), Mean Absolute

Error, and Mean Absolute Percent Error (MAPE) metrics. Hwang built upon such

research, using Mean Absolute Error (MAE) to access the precision of forecasting

materials prices for a 12-month and 24-month period using the CCI (Hwang 2009;

Hwang 2011). Xu and Moon (2013) used Mean Square Error (MSE) to determine the

validity of their 54-month vector autoregression (VAR) forecasts that established a

relationship between CCI and the Consumer Price Index (CPI). MIT’s Concrete

Sustainability Hub (CSH) have followed a similar methodology as Xu and Moon,

conducting cointegration between multiple time-series to construct a forecasting model


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for asphalt and concretes (Swei 2013b). Moreover, “backcasting” techniques have been

employed, resulting in Mean Average Percent Error (MAPE) values that prove

forecasting future pavement commodity costs (asphalt and concrete constituent materials)

as a valid endeavor to reduce uncertainty (Swei et al. 2013b). In addition to long-term

costs, highway construction projects also warrant extensive risk characterization in short-

term inputs; accordingly, it is crucial to understand the developmental timeline of a

highway.

When assessing the economic viability of highway construction projects, it is important

to account for the substantial cash outflows that span over the highway lifespan. The

outflows can be separated into three distinct phases: the initial costs, use costs, and the

end-of-life costs. The initial costs include materials extraction and production,

transportation, and any costs associated with construction (i.e. equipment and labor).

After the highway is constructed, maintenance costs are incurred throughout the lifespan

of the highway. And, finally, the end-of-life costs (i.e. pavement removal and recycling)

are incurred when the highway is no longer in working condition (Swei et al. 2013a). It is

therefore clear that highway construction is not only a long-term investment venture but

also a multi-faceted project susceptible to uncertainties at phase. Accordingly, it is crucial

to develop as comprehensive an LCCA model as possible to ensure practitioners are not

only aware of the expected costs associated with a project but also cognizant of expected

uncertainties associated with such costs. This research focuses on the cost to the agency,

thereby excluding the user costs, in an attempt to focus the scope of the analysis.


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Due to the increased recognized importance of accounting for uncertainty, researchers

have recently begun to endeavor in extensive research that is geared towards accessing

the uncertainties rooted in the classical deterministic methodology (Swei 2013b).

Specifically, Touran (2003) incorporated uncertainty in bid vs. actual construction costs

by accessing the data from a probabilistic standpoint. Tighe (2001) further contributed by

accessing pertinent inputs and overall construction costs with an emphasis on probability

distributions. Additionally, Osman (2005) employed a Weibull distribution to elucidate

some uncertainty related to pavement performance and maintenance over its life span. In

other words, much attention has been focused on the risks inherent in the input

parameters, with the goal of arriving at a more robust output. This improved model would

better indicate the uncertainty associated with particular highway constructions. In so

doing, the model will provide practitioners with a more robust and holistic perspective,

thereby enabling them to align their investment decisions with their risk thresholds (Swei

et al. 2013c).

GAP ANALYSIS

Part 1: Out-of-sample Forecasting

While a CCI is an invaluable and widely used dataset for forecasting, it is incomplete in

that it is a weighted average index comprised of material, labor, and construction costs.

This consolidation, as stated by Hwang et al., wrongfully assumes that all cost items will

grow at the same rate. (Hwang et al. 2011) It is therefore prudent to delineate each

constituent cost and forecast separately. Moreover, prior research has been limited in that

it has assessed forecasting for a short time period (i.e. 5-years); the novel aspect of this

research is that it will determine the relative merits of forecasting over extended periods


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of time (i.e. 40 years). The research will also explore how much empirical data is needed

in order to forecast with a reasonable level of precision.

Part 2: Unit-cost Variability due to Location and Scale

Location with respect to state will be accessed through analyzing two distinct states. In

other words, this research will see if parameter characterization holds true from state to

state, and if not, by how much they differ. Secondly, establishing a relationship between

unit-cost and quantity for materials used in recent highway construction projects will

assess economies of scale as a potential driver of variability. This data will prove not only

worthwhile for academia but also relatable to practitioners in the field, thereby achieving

the penultimate goal of the research.

Part 3: Case Study Methodology

After validation of forecasting long-term costs and characterization of initial costs, this

paper will deliver the results using a case study methodology. Accordingly, state DOTs

will be able to better understand the implications of variable characterization on a

probabilistic LCCA.


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METHODOLOGY

Part 1: Out-of-sample ForecastingIn order to validate backcasting as a viable means of forecasting, it is crucial to first

establish the historical behavior of the underlying data. In general terms, if the statistical

properties of a data set do not change over time, the data is deemed stationary, and

otherwise is classified as non-stationary. In other words, a joint distribution ( X t 1, X

t n

) is

the same as the joint distribution ( X t 1+r

, X t n+r) for all n and r, thereby depending only on

the distance between t 1 and t n. (Nason et al. 2006). If a time series does not exhibit

stationarity as outlined above, it is deemed non-stationary. After establishing said

behavior, an appropriate forecast can be initiated using empirical data. The model used in

this paper will not be set to the strict standards of stationarity as outlined above, but will

rather adhere to a less rigid criterion, which will be discussed in the coming sections.

After initiating the forecast, the model will then be evaluated on the basis of accuracy

using MAPE against a baseline model that assumes future real prices that are in line with

inflation (Gneiting 2010; Baumeister 2012). Finally, the accuracy of said forecasts will

be compared on the basis of the time extent of the data set. In other words, the author will

assess the accuracy of the model for different sizes of the dataset, which will lead to a

better understanding of how much historical data is sufficient to produce superior results.

Section A: Time-Series Classification – Stationary or Non-Stationary

There are various tests that serve to characterize the historical behavior of a data set,

including the Augmented Dickey-Fuller (ADF) and the Phillip-Perron (PP) test.

(Leybourne 1999) Although the former are more common, the implementation is quite

time consuming, in particular for this research given that 40 different samples will be


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analyzed for the time-series. As such, this research employs a “threshold” test that

utilizes the univariate ARIMA (p, d, q)1 model, seen in equation 1:

!! ! ! !!

!

!!!

!! !! ! !!! ! ! ! !! ! ! !!

!

!!!

!!

(1)

!!: price in year t

!!: error term in year t

!!: autoregressive coefficient

!!: moving average coefficientC : constant drift term

L: lag operator

If an ARIMA (1, 0, 0) model is used, it equates to the following, as shown in equation 2:

!! ! !!!!! ! ! ! !! (2)

Interestingly, the simplified, first-order auto-regressive process, ARIMA (1,0,0), as shown

in equation 2 bears a resemblance to the Ornstein-Uhlenbeck mean-reverting process,

shown in discretized form in equation 3:

!! ! !! ! !!!! ! !" ! !! (3)

K : speed of mean reversion C : mean reversion value

!!: “white noise” error term

The first step is to determine the value of the autoregressive coefficient, ! in equation 2.

It is important to note that ! corresponds to 1-K , seen in equation 3, where K is the rate of

1 p: number of autoregressive termsd : number of non-seasonal differencesq: number of moving average terms


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mean reversion. The inverse of K symbolizes the time it takes for reversion to occur in a

data set; therefore, the higher the value of !, the lower the value of K , and the longer it

takes for reversion. Thus, this research uses a threshold test, in which the data is deemed

to exhibit autocorrelation and is classified as non-stationary if ! is greater than or equal

to 0.95 (Selke et al. (1999). It is also worth noting that the error term will be disregarded

in this analysis, as this research is only concerned with the precision of the forecast, and

so a confidence interval is not pertinent to the scope of this research. Additionally, the

0.95 threshold, which implies a process takes 20 years to revert back to its mean, is in

line with previous research that has found commodities’ can take up to a decade to show

reversion (Pindyck 1999).

Parameters are estimated using Stata and JMP 10, two statistical software packages (Stata

2012; JMP 2012). Excel will also be used extensively to prepare data for result analysis.

Section B: Forecasting Based on Data Classification

After characterizing the behavior of the time-series’ empirical data, the forecast will then

be implemented. If a sample set is classified as “stationary”, the ARIMA (1,0,0) (i.e.

Ornstein Uhlenbeck mean-reverting) model will be used, as was previously shown in

equation 3. If, however, the data are classified as “non-stationary”, this research will use

an ARIMA (1,1,0) model will be used. The ARIMA (1,1,0) is a first-order autoregressive

model that includes one order of non-seasonal differencing and a constant term, as shown

in equation 4.


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!! ! !!!!!!!! !!! ! ! !! (4)

Section C: Accuracy of the Forecast vs. Baseline Case

After collating the results, the future prices will be compared to the baseline case using

MAPE, as defined in equation 5 and, as previously discussed, is one of the more

prevalent “scale-independent” measures of precision (Ahlburg 1992; Armstrong 2001;

Hyndman 2006; Rayer 2008; Swanson 2011)

!"#$ ! !""#!

!"#$%&!

!"#$%&'#$ !"#$%&

!

!!!

(5)

n: number of years

The baseline case used is the “no change” model that assumes prices grow with inflation.

Thus, the forecasting model will be compared to the baseline case (i.e. inflation rate

model) to determine the relative merits of projecting future materials prices. Finally, this

research will vary the sample size of the data set that is used in each forecast, thereby

analyzing how much data is sufficient for forecasts that are more accurate than the

baseline case. Specifically, two simulations will be run, in which one trial uses at least

40-years of empirical data is used to estimate parameters, representing the amount of

available asphalt data, while the other uses at least 60-years of data to forecast future

prices and determine the precision as a function of the extent of the data set. A “well”

performing model will have MAPE values of approximately 10%. (Fan 2010)


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Part 2: Unit-cost Variability due to Location and Scale

Basic economic theory implies that as the quantity associated with a project increases, the

corresponding unit cost will decrease. It is therefore prudent to apply this to the highway

construction data using publically-available bid data provided by state DOTs. Total costs

provided by the DOTs typically encompass both labor and materials into a single number.

It is therefore difficult to further separate the data based on cost specification;

nevertheless, it will likely prove valuable to establish what is likely to be a relationship

between unit price for materials-intensive construction activities and the quantity of those

activities. Specifically, the log-transformation of the average unit-cost will be plotted as a

function of the log-transformation of the bid volume associated with the project.

Statistical significance will then be gauged by the reported p-value of the dependent

variable through the use of a univariate regression analysis. In statistical analysis, the p-

value represents the probability of observing an extreme statistic in a data set, with the

assumption that the null hypothesis is warranted. In other words, for the scope of this

research, any statistical anomalies (i.e. outside of the 5% threshold) will be deemed

statistically insignificant.

Construction projects that are deemed statistically significant in respect to unit-cost vs.

quantity will then be used to project initial costs. It is important to note, however, that

this model does not effectively incorporate seasonality, location, and other more

qualitative drivers that may affect unit cost. These factors will instead be modeled using

the standard error of the univariate regression in the Monte Carlo simulations. In the case


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that the relationship is not statistically significant, a chi-square best-fit log-normal

distribution will be fitted to the data.

Part 3: Case Study MethodologySection A: Monte Carlo Simulations

A Monte Carlo simulation will be used to build a probabilistic distribution that

incorporates the characterized uncertainty while maintaining the structural integrity of the

model. It is thus of paramount importance that the model incorporates inter-variable

correlations and dependencies. For example, if concrete prices were being compared

between two projects, we would assume that the growth rate is constant between the two

alternatives. Along that vein, we assume the distance between concrete processing plants

are the same, and thus transportation costs associated with using concrete are constant

between projects. By accurately considering these relationships in the data, the model

will be able to select reasonable values that are representative of what one would expect

in the real world. There are many ways to interpret the results from the aforementioned

Monte Carlo simulation. The more common method of visualization in most fields is a

probability distribution function (PDF), but this research will use a cumulative

distribution function (CDF), as is standard in cost analysis.

This research has incorporated additional sources of uncertainty, such as pavement

deterioration and maintenance, inputs that lack historical data, and future materials prices.

Specifically, in terms of future maintenance schedules, the recently developed

Mechanistic Empirical Pavement Design Guide (MEPDG) combines pavement design

parameters (e.g. pavement type, thickness, etc.) with contextual conditions (e.g. climate,


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traffic flows, etc.) into a predicted level of pavement performance (15). This design guide

uses models validated from the Long-Term Pavement Performance (LTPP) program (21).

This performance is measured through distress levels that incorporate top-down and

bottom-up cracking. Furthermore, variables that lack historical data, such as layer

thickness, have been quantified by using a pedigree matrix approach, a method used by

the life cycle assessment (LCA) community.

Section B: Case Study

The aforementioned results will then be collated and applied to two urban interstate case

studies located in Florida and Colorado. The case studies will be analyzing the relative

economic merits of concrete vs. asphalt pavement designs using the recently developed

Mechanistic-Empirical Pavement Design Guide (MEPDG) software, the new state of the

art pavement design tool.


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RESULTS AND ANALYSIS

The results and subsequent analysis can be separated into this paper’s three inexorably

linked pieces: out-of-sample forecasts, unit-cost relationship, and the case study

methodology. These three sections will discuss and analyze explanatory drivers of

uncertainty in the highway selection process and validate the probabilistic model as a

more comprehensive and prudent implementation of LCCA.

Part 1: Out-of-sample ForecastingData for dimensioned stone has been collected through publically available databases at

the United States Geological Service (USGS), as shown in Figure 4. Dimensioned stone

was selected as part of this analysis since it is a common input for construction activities

and because there is sufficient data that extends as far back as 1900, making it possible to

backcast (Kelly 2012).

Figure 4: Dimensioned Stone historical price behavior.

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Out-of-sample forecasting has been conducted using at least 40-years of empirical data

using the previously discussed ARIMA (1,0,0) for stationary time-series, ARIMA (1,1,0)

for non-stationary time-series, as well as a real-dollars, no-change model. The MAPE of

each model was used to gauge precision. Out-of sample forecasts have been constructed

between 1945 and 1986, with the minimum amount of data used being 40 years (for the

1945 forecast) and the maximum being 80 years (for the 1985 forecast). In each forecast,

the precision of the forecast is measured for up to 40 years, if possible. Of course, it is

impossible to track an out-of-sample forecast made after 1970 for 40 years, and so the

sample size of the MAPE reduces for further years out. The selection of 40-years as a

bottom threshold is because there are only 40-years of empirical data for asphalt. Having

said this, the calculated MAPE is conducted using the forecast errors made between 1966

and 1986, in order to understand if increasing the sample size improves the relative

performance of the forecasting model.

Section A: 40-year Results

Figure 5 shows the calculated MAPE values of the data set over time with at least 40-

years of empirical data. It is clear that the no-change performs substantially better for the

first 30-years. After this midpoint, however, the ARIMA (1,0,0) begins to outperform its

counterpart, representing the stationary characteristics of the data set.


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Figure 5: MAPE vs. Years into the Future (at least 40-years of empirical data)

Section B: 60-year ResultsFigure 6 shows a similar analysis but for at least 60-years of empirical data. The two

models are shown again, as outlined in the graphic. It is clear to see a similar trend with

the 40-year data: the real-dollars no change outperform the ARIMA (1,0,0) model at the

onset of forecasting. However, after 20-years (unlike 30-years previously), the ARIMA

(1,0,0) model begins to outperform. Therefore, not only is it more accurate to use more

empirical data, but it also takes less time for to observe reversion in the 60-year data set

than it does in the 40-year data set. This is an interesting observation, as it shows that

with more empirical data, practitioners will be better able to access future price trends of

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materials costs, thereby reducing uncertainty and incorporating their risk threshold into

pavement selection.


Not only do these results show that with more empirical data, more accurate forecasts can

be generated, but these data also validate forecasting as a worthwhile endeavor to

understand future price behavior that extends decades into the future (i.e. a timeline in

line with a highway’s life-cycle). Furthermore, it shows that by applying such models

going forward, practitioners will be able to better quantify the uncertainty related to

materials prices relevant to their projects.

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Part 2: Unit-cost Variability Due to Location and ScaleTables 1 and 2 show the linear regression analysis of construction bid projects for Florida

and Colorado, respectively. Materials used in the projects were broken down into

Concrete, Basestone, Asphalt, and repair costs (i.e. patching, milling, and grinding), in

accordance with outlines set forth in Table 5. The repair and basestone cost show very

little statistical significance, while most other material constituent costs show a

determination coefficient of at least 0.50, implying that 50% of the variation in the data

can be explained by economies of scale. In the Florida data, there were not enough JPCP

data points to create a statistically meaningful regression; therefore, a regression was run

on all JPCP data (Colorado and Florida), as shown in Figure 8. This aggregation will

likely increase uncertainty, but with such a low JPCP construction rate in Florida, the

endeavor is uncertain as it is. It is also worth noting that one of the base stones in the

Colorado data is the only material for which we found a p-value greater than the 0.05

threshold value.

Figures 7-10 show the regression analysis of the unit-price of HMA and JPCP pavement

designs as a function of bid quantity over a 36-month span in Florida and Colorado,

respectively. Figure 7 shows the regression data of winning bids of HMA pavement

designs in Florida. The corresponding equation shows that approximately 65% of the

uncertainty related to HMA pavement development projects can be explained by

economies of scale.


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Figure 7: Florida linear regression analysis of unit-cost of HMA winning pavement bidswith respect to bid volume.

Figure 8 then shows the same result for the aggregate JPCP designs in Florida and

Colorado. This aggregation is a result of Florida not having statistically sufficient data for

analysis, as was previously discussed. As shown in Figure 8, 38% of uncertainty in this

aggregation of JPCP designs can be explained by economies of scale.

LN (unit-cost) = 5.58 - 0.13 * LN (quantity) R" = 0.65

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Figure 8: Florida and Colorado linear regression analysis of unit-cost of JPCP winningpavement bids with respect to bid volume.

Figures 9 and 10 show the same results for HMA and JPCP, respectively for winning bids

in Colorado. As shown in figure 9, approximately 57% of the uncertainty in HMA data

can be explained by economies of scale. Analogously, figure 10 shows that 44% of

uncertainty in JPCP bids can be attributed to cost-quantity relationships.

LN (unit-cost) = 6.20 - 0.12 * LN (quantity) R" = 0.38

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Figure 9: Colorado linear regression analysis of unit-cost of HMA winning pavementbids with respect to bid volume.

Figure 10: Colorado linear regression analysis of unit-cost of JPCP winning pavementbids with respect to bid volume.

LN (unit-cost) = 7.36 - 0.35 * LN (quantity)R" = 0.57

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In both states, regression coefficients are similar, while the determination coefficients

vary dramatically between the HMA and the JPCP selections. This discrepancy

represents the need for probabilistic LCCA models, as it has been proven that an

uncertain cost is not the only factor to consider when assessing highway construction

projects. Moreover, the figures show a clear relationship between cost and quantity,

accounting for at least 44% of the variance in bid prices. Looking at the data from an

inter-state perspective, it can be observed that economies of scale play a more prominent

role in the Colorado data than it does in the Florida data. Tables 1 and 2 have collated the

statistical results for all constituent materials related to winning bid prices for Florida and

Colorado, respectively. As shown, bid data are delineated into concrete and base

materials, asphalt designs, and maintenance expenses relevant to the two designs. Table 1

shows the data and pertinent statistical parameters in the winning bids in Florida. As was

previously discussed, the data lacked a sufficient sample size to analyze JPCP bids, while

the HMA bids mostly show high determination coefficients, owing to the role economies

of scale has in pavement construction projects.


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Table 1: Florida quantification of unit-cost uncertainty for significant input parameters. Values in parenthesis represent the standard error of the regression

coefficients.

Input Units P-Value R 2

Regression Equation

Ln(P)=a*Ln(Q)+b

Best-fit Log-

Normal

Distribution

Concrete and Bases

JPCP Small Sample Size, Aggregate Regression Conducted

Base Group 06Square

Yards


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Table 2 shows similar data for winning bids in Colorado. Again, these data have been

separated into concrete and bases, asphalt designs, and maintenance expenses. Statistical

parameters are shown, and it is worth noting that the final base stone was the only

material that did not fit within the p-value threshold. These final base stone data have

thus been fit to a lognormal distribution, as opposed to the linear regression. It is also

worth noting that the uncertainty in HMA designs attributable to economies of scale

varies much more than does the Florida data, which will prove interesting when accessing

the comparative LCCA from a probabilistic standpoint. Finally, most of the maintenance

data show very little statistical significance.


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Table 2: Colorado quantification of unit-cost uncertainty for significant input parameters. Values in parenthesis represent the standard error of the regression

coefficients.

Input Units P-Value R 2

Regression Equation

Ln(P)=a*Ln(Q)+b

Best-fit Log-

Normal

Distribution

Concrete and Bases

Concrete Cubic

Yards


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Part 3: Case Study MethodologyA third-party associate, namely the Applied Research Associates (ARA), have developed

Hot Mix Asphalt (HMA) and Joint Plain Concrete Pavement (JPCP) designs that

although made with different materials, are “functionally” equivalent (Fig. 11). The goal

of this section is to apply the characterized uncertainty values in realistic pavement

decisions in order to understand how they could potentially impact the likely pavement

selection.

Jointed Plain

ConcretePavement (JPCP)

Hot Mixed Asphalt

(HMA)

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Figure 11: Applied Research Associates (ARA) Pavement Design Specifications

Tables 3 and Table 4 show these designs and their respective maintenance schedules with

a corresponding reliability of 90%. The MEPDG software has been constructed for a

major highways consisting of three lanes of traffic in each direction with an expected

Annual Daily Truck Traffic (AADTT) of 8,000. Finally, the life-cycle costs have been

discounted at a 4% annual rate (consistent with FHWA ordinances) over a maintenance

schedule that extends 50-years into the future.

Deterministic Analysis:

A deterministic model has been implemented to predict the likely pavement selection

under the current state DOT methodology. Historical bid data was collated for Florida

and Colorado for the past 36-months using Oman bid tabs database. Figure 3 presents the

initial, discounted rehabilitation, and discounted life-cycle costs for HMA and JPCP

designs in both Florida and Colorado. The analysis shows that all costs associated with

HMA design selection are lower than their JPCP counterparts. Additionally, the

differences between the initial costs in Florida are statistically insignificant, while all

other costs (Florida and Colorado) vary significantly. As was previously noted, however,

the deterministic analysis lacks sufficient characterization of risk. It is therefore prudent

to endeavor in the same way using a probabilistic model in order to observe the

differences.


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Figure 12: Initial, life cycle, and discounted rehabilitation costs of JPCP andHMA pavement designs in Florida and Colorado

Probabilistic Analysis:

Figures 13 and 14 show the analysis for the same data using a probabilistic model for

Florida and Colorado, respectively. The analysis shows that the expected net present

value (ENPV) of the HMA design is, in fact, more expensive than its JPCP alternative.

Given that rehabilitation costs account for a larger proportion of HMA pavement

investment, a probabilistic LCCA, which considers all reliability levels rather than 90%

as does its deterministic counterpart, could potentially favor the HMA mean values.

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Figure 13 shows the CDF plots for JPCP (gray) and HMA (black) life-cycle costs in

Florida. The symmetry in the plot shows that one’s pavement design selection should not

change as one’s risk threshold changes. Moreover, one can see the mean costs associated

with each pavement design; specifically, the mean cost per mile for JPCP design is

$1.83mm, while its HMA counterpart $2.52mm per mile. Perhaps the budget-conscious

state DOTs would benefit from a risk-threshold analysis, wherein practitioners could

analyze the cost of a project with a level of certainty. For instance, an LCCA practitioner

could use these data to say with 95% certainty that the highest JPCP life-cycle cost per

mile would be $2.44mm, while its asphalt counterpart would be $3.25mm.

Figure 13: Florida probabilistic life-cycle cost of urban interstate roadalternatives (black line represents HMA design, gray represents JPCP design).The dashed lines represent the mean value from the analysis

Figure 14 shows the same plot for the results from the Colorado data. The probabilistic

results are much less symmetric than are the data in Florida, indicating that design

selection could potentially be impacted by one’s risk threshold. It can be seen that the

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mean cost for a JPCP design is $2.21mm per mile, while the mean cost associated with a

HMA design is $2.72mm per mile. From a risk-threshold perspective, one can say with

95% certainty that the JPCP design would be $2.87mm per mile, while the equivalent

metric for HMA design is not included on the graph due to the asymmetry of the

distribution. This discrepancy in the distribution, as compared to the Florida data, can be

attributed to the difference in standard errors in the regression data. Specifically, the

average standard error in the HMA design was approximately 43% higher in the

Colorado data than it was in the Florida data.

Figure 14: Colorado probabilistic life-cycle cost of urban interstate roadalternatives (black line represents HMA design, gray represents JPCP design).The dashed lines represent the mean value from the analysis

These data have successfully classified various uncertainties relevant to highway

pavement construction projects. Additionally, the results have been presented in a case

study framework that will be easy to interpret for the average pavement LCCA

practitioner. It was this case study that found that the JPCP design was a cost effective

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alternative to HMA for all risk thresholds, and while data varied between Florida and

Colorado, both states showed JPCP as a superior alternative (both in the deterministic and

the probabilistic case). Of course there are more factors that play a role in pavement

design selection, including government ordinances, environmental implications,

surrounding environment, single project as opposed to highway network perspective, and

more. These results will provide practitioners with a cost analysis that will prove useful

in the larger selection process.


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CONCLUSIONS AND FUTURE WORK

This research has validated out-of-sample, long-term (i.e. multiple decades) forecasting

as a viable methodology for predicting future materials prices. Moreover, economies of

scale have been quantitatively classified as a driver of variability in bid prices for

materials-intensive activities. By collating results and implementing the MEPDG

framework, this paper has assessed the relative merits of a probabilistic LCCA model. In

so doing, this research has established the shortcomings of the deterministic LCCA

approach, and has established the importance of characterizing uncertainties and risks in

any project involving materials selection and investment.

One of the limitations of this research is that the forecasts neglected a confidence

interval. Further research into the reliability of such forecasts would prove valuable to

augment the validation of backcasting. Furthermore, while state variation was briefly

mentioned, it would prove valuable to look at additional drivers of uncertainty, such as

seasonality, timing of construction (i.e. night vs. day), intrastate location (i.e. county or

north vs. south), and more. Additional characterization of such inputs would inevitably

lead to a more comprehensive understanding of the probabilistic implementation of the

LCCA model for highway construction projects.


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WORKS CITED

1. Gransberg, D.D. and C. Rierner, Impacts of Inaccurate Engineer's Estimated Quantitieson Unit Price Contracts. Journal of Construction Engineering and Management, 2009.135(11): p. 1138-1145.

2.

Swei, O., Prepared Manuscript for Review (Projections Journal Paper); 2013

3. Walls, J. and M. Smith, Life-Cycle Cost Analysis in Pavement Design - InterimTechnical Bulletin., 1998, FHWA: Washington, D.C.

4. Temple, W.H., et al., Agency Process for Alternative Design and Alternate Bid ofPavements. Transportation Research Record, 2004. 1900: p. 122-131.

5. Tighe, S., Guidelines for Probabilistic Pavement Life Cycle Cost Analysis. Transportation Research Record, 2001. 1769: p. 28-38.

6.

Lee, D.B., Fundamentals of Life-Cycle Cost Analysis. Transportation Research Record,

2002. 1812: p. 203-210.

7. Guo, H.L., H. Li, and M. Skitmore, Life-Cycle Management of Construction Projects Based on Virtual Prototyping Technology. Journal of Management in Engineering,2010. 26(1): p. 41-47.

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9. Frangopol, D.M., J.S. Kong, and G. Emhaidy, Reliability-Based Life-Cycle Managementof HIghway Bridges. Journal of Computing in Civil Engineering, 2001. 15(1): p. 27-34.

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Swei, O. December Hub Meeting Presentation; December, 2012; Cambridge, MA

11. National Highway System Designation Act of 1995, 1995, U.S. Government PrintingOffice.

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13.

Snyder, R.A.E.a.M.B., Life-Cycle Cost Comparison of Asphalt and Concrete Pavementson Low- Volume Roads. Transportation Research Record, 2001. 1749: p. 28-37.

14. Trost, S.M. and G.D. Oberlender, Predicting Accuracy of Early Cost Estimates Using

Factor Analysis and Multivariate Regression. Journal of Construction Engineering andManagement, 2003. 129(2): p. 198-204.

15.

Swei, O. Manuscript for Review (Backcasting Validation); 2013

16. Ashuri, B. and J. Lu, Time Series Analysis of ENR Construction Cost Index. Journal ofConstruction Engineering and Management, 2010. 136: p. 1227-1237.


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17. Hwang, S., Dynamic Regression Models for Prediction of Construction Costs. Journal ofConstruction Engineering and Management, 2009. 135(5): p. 360-367.

18. Hwang, S., Time Series Models for Forecasting Construction Costs Using Time Series Indexes. Journal of Construction Engineering and Management, 2011. 137(9): p. 656-662.

19. Xu, J.-w. and S. Moon, Stochastic Forecast of Construction Cost Index Using aCointegrated Vector Autoregression Model. Journal of Management in Engineering,2013. 29(1): p. 10-19.

20. Swei, O., LCCA Prepared Manuscript for Review 2013 (TRB Publication); 2013

21. Touran, A., Probabilistic Model for Cost Contingency. Journal of ConstructionEngineering and Management, 2003. 129(3): p. 280-284.

22. Tighe, S., Guidelines for Probabilistic Pavement Life Cycle Cost Analysis. Transportation Research Record, 2001. 1769: p. 28-38.

23. Osman, H., Risk-Based Life-Cycle Cost Analysis of Privatized Infrastructure.Transportation Research Record, 2005. 1924: p. 192-196.

24.

Nason, G.P. Statistics in Volcanology, 2006; Chapter 11: Bristol, United Kingdom

25. Gneiting, T. and T.L. Thorarinsdottir, Predicting Inflation: Professional Experts Versus No-Change Forecasts, 2010, Universität Heidelberg, Germany.

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Leybourne, S.J. and P. Newbold, The Behavious of Dickey-Fuller and Phillips-PerronTests Under the Alternative Hypothesis. Econometrics Journal, 1999. 2: p. 92-106.

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Armstrong, J.S., Principles of Forecasting: A Handbook for Researchers andPractitioners. 2001, Norwell, MA: Kluwer Academic Publishers.

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35. Rayer, S., Population Forecast Errors: A Primer for Planners. Journal of PlanningEducation and Research, 2008. 27: p. 417-430.

36. Swanson, D.A., J. Tayman, and T.M. Bryan, MAPE-R: A Rescaled Measure of Accuracy for Cross-Sectional Forecasts. Journal of Population Research, 2011. 28: p. 225-243.

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APPENDIX

Table 3: Florida and Colorado MEPDG based JPCP and HMA pavement designsfor the urban interstate and local road case studies.

Florida Road Design (Initial AADTT of 8,000)

JPCP Design HMA Design

Layer Thickness Layer Thickness

JPCP 11 in (27.9 cm)HMA # in. mix with PG 76-22

2.5 in (6.4 cm)

AggregateBase

6 in (15.2 cm)HMA $ in. mix with AC-30(PG 67-22)

4 in (10.2 cm)

HMA 1 in. mix with PG 64-22

6 in (15.2 cm)

Limerock Base 6 in (15.2 cm)

Stabilized Embankment 12 in (30.5 cm)

A-3 Semi-infinite

Colorado Road Design (Initial AADTT of 8,000)


Layer Thickness Layer Thickness

JPCP 7.5 in (19.1cm)HMA # in. mix (SMA) withPG 76-28

2 in (5 cm)

Aggregate

Base4 in (10.2 cm)

HMA # in. mix (SX 100)

with PG 76-28

4 in (10 cm)

HMA $ in. mix (S 100) withPG 64-22

8 in (20 cm)

A-1-a 4 in (10 cm)

A-1-a 6 in (15 cm)

A-2-4 Semi-infinite


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Table 4: Maintenance schedule for JPCP and HMA pavement designs at MEPDGspecified 90% reliability for the urban interstate and local road case studies.

Florida Road Design (Initial AADTT of 8,000)


Maintenance

Number

Year of

OccurrenceRehab Type

Year of


1 30

100% Diamond

Grinding and Full

Depth Repair

142.5” Mill/Overlay and

Patching


Patching


Patching

Colorado Road Design (Initial AADTT of 8,000)


Maintenance

Number

Year of


Year of


132.” Mill/Overlay and

Patching

1 20 Full Depth Repair 302” Mill/Overlay and

Patching

2 40 Full Depth Repair 402” Mill/Overlay and

Patching


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Table 5: Florida Pavement Specifications

Florida Pavement Specifications*

TrafficLevel Million ESAL's Typical Applications

A < 0.3 Local roads, county roads, city streets where truck traffic islight or prohibited

B 0.3 - < 3.0 Collector roads, access streets. Medium duty city streetsand majority of county roadways

C 3.0 - < 10.0 Collector roads, access streets. Medium duty city streets

and majority of county roadways

D 10.0 - = 30.0 US Interstate class roadways

*Asphalt designs were separated by performance grade and traffic levels but not byfriction course

Note: Colorado Asphalt designs were separated by performance grade, gyration level,and aggregate gradiation specifications.


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Documents

Comprehensive Life Cycle Cost Analysis of Pavement Materials 2013