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Procedía

Social and Behavioral Sciences

ELSEVIER Procedía - Social and Behavioral Sciences 48 (2012) 331 - 340

Transport Research Arena - Europe 2012

Life-cycle cost analysis system for pavement management Joâo Santosa9 Adelino Ferreiraa*

aDepartment of Civil Engineering, University of Coimbra, Rua Luis Reis Santos, 3030-788 Coimbra, Portugal

Abstract

This paper presents a new Life Cycle Cost Analysis (LCCA) system based on an optimization model considering pavement performance, called OPTIPAV, developed and programmed to help pavement designers to choose the best pavement structure for a road or highway. The LCCA system considers the serviceability concept adopted by the American Association of State Highway and Transportation Officials (AASHTO) for use in the design of flexible pavements. The OPTIPAV can solve the problem of making LCCA for typical design periods (20 years) but also for longer periods (40 years or more), in order to compare different pavement solutions in terms of global costs for the final choice of the pavement structure for a national road or highway. Additionally, the OPTIPAV system provides a good solution to the pavement design problem considering not only design criteria but also construction costs, maintenance costs, user costs and the residual value of pavement structures. The results obtained by the application of the new LCCA system clearly indicate that it is a valuable addition to the road engineer's toolbox.

© 2012 Published by Elsevier Ltd. Selection and/or peer review under responsibility of the Programme Committee of the T ransport Research Arena 2012

Keywords: pavement design; life-cycle cost analysis; deterministic pavement performance models; pavement maintenance and rehabilitation; optimisation models; genetic algorithms.

1. Introduction

Despite the fact that the design period for flexible pavements is normally considered as 20 years, the Portuguese manual of pavement structures (JAE 1995) states the importance of making a Life Cycle Cost Analysis (LCCA) for a period of no less than 40 years, called project analysis period, in order to compare different pavement solutions in terms of global costs for the final choice of the pavement structure for a

* Corresponding author: Tel.: +351.239797101; fax+351.239797142. E-mail address: adelino@dec.uc.pt.

1877-0428 © 2012 Published by Elsevier Ltd. Selection and/or peer review under responsibility of the Programme Committee of the Transport Research Arena 2012

doi:10.1016/j.sbspro.2012.06.1013

national road or highway. It also states that the following costs must be considered in the LCCA: construction costs; maintenance costs throughout the project analysis period; user costs throughout the project analysis period; and the pavement residual value at the end of the project analysis period. The problem is that until now this analysis has never been done in Portugal. This paper presents a new LCCA system based on an optimization model considering pavement performance, called OPTIPAV, developed and programmed to help pavement designers to choose the best pavement structure for a road or highway. The paper is divided into four sections. The first section consists of a brief introduction. The second section contains a detailed description of the OPTIPAV system. The third section presents the results obtained with the application of the OPTIPAV system to the pavement structures of the Portuguese Manual. The final section comprises a synthesis of the conclusions reached so far and a statement of prospects for future research.

2. Proposed Life-Cycle Cost Analysis System

2.1. Introduction

The proposed LCCA system, called OPTIPAV, consists of the following components: the objective of the analysis, the road pavement data and models, the constraints that the system must guarantee and finally the results. The OPTIPAV system was implemented using Microsoft Visual Studio programming language adapting and introducing new functionalities to an existing genetic algorithm program called GENETIPAV-D (Ferreira 2001, Ferreira et al. 2002) previously developed to solve deterministic optimization models. The results of the application of the OPTIPAV system consist of the optimal pavement structure, the predicted annual pavement quality, the construction costs, the M&R plan and costs, the user costs, and the pavement residual value at the end of the project analysis period.

2.2. Optimization model formulation

The optimization model introduced above can be formulated as follows:

(1) (2)

Zst - soj^Mv,Xlst,...,XRsl,...,XRst),5 -1,...,S;t - l,...,T

xrSt e Qizst)>r = i,-,R',s = i,-,S;t = 1 ,...,T

£ ^ = * = U-,S-t = 1 ,...,T

Si > Thsi )>s = S MCrst = ¥a{Zst, Xrst), r = 1,..., R; s = 1,..., S; t = l,...,T UCst = Wu{Zst), í = 1,..., S; t = 1 ,...,T

(8) (9)

^^ Xrst < N max,, V* = 1,..., S (10)

Where: R is the number of alternative M&R operations; S is the number of pavement structures generated for analysis; T is the number of years of the project analysis period; CCs0 is the construction cost of a pavement structure 5 in year 0 in function of the material and thickness of each layer; MCrst is the maintenance cost for applying operation r to pavement structure 5 in year t; UCst is the user cost for pavement structure 5 in year t; RVsJ+l is the residual value for a pavement structure in year T+1; Xrst is equal to one if operation r is applied to pavement structure 5 in year t, otherwise it is_equal to zero; d is the discount rate; Zst are the condition variables for pavement structure 5 in year t; Z are the warning levels for the condition variables of pavement structures; Mst is the material of layer / of pavement structure 5; Thsl is the thickness of layer I of pavement structure 5; ^max, is the maximum number of M&R operations that may occur in pavement structure 5 over the project analysis period; O are the pavement condition functions; 0 are the residual value functions; ¥fc are the construction cost functions; are the agency cost functions for M&R; % are the user cost functions; Q are the feasible operations sets.

Equation (1) expresses the minimisation of total discounted costs over the project analysis period, while keeping a pavement structure above specified quality standards. Total costs include construction costs, M&R costs, user costs and the residual value of a pavement structure, i.e. its value at the end of the project analysis period. Constraints (2) correspond to the pavement condition functions, expressing pavement condition in each year as a set of functions of the initial pavement state and the M&R operations previously applied to the pavement. These functions can describe the pavement condition with regard to variables such as cracking, rutting, longitudinal roughness, surface disintegration (potholing and ravelling) and overall quality of pavements, etc. In Portugal, the Pavement Management System (PMS) of the Portuguese Road Administration (Picado-Santos and Ferreira 2008, Ferreira et al. 2011), and other municipal PMS (Ferreira et al. 2009a, Ferreira et al. 2009b), uses the pavement performance model of the flexible pavement design method developed by the American Association of State Highways and Transportation Officials (AASHTO 1993) to predict the future quality of pavements. Thus, this application of the LCCA system will consider the AASHTO flexible pavement design method. The basic design equation used for flexible pavements is Equation (11) which can be transformed into Equation (12) to be directly used in the prediction of the present serviceability index value in each year of the design period. Equation 13 is used to calculate the SN value for each pavement structure. Equation (14) is used to compute the number of 80 kN equivalent single axle load (ESAL) applications until any year of the project analysis period.

logofao) = ZR ■ s0 +9.36- log0(>W+l)-0.2+-

APSI 4.2-1.5

0.40+-

- + 2.32-log0(A4 )-8.07

PSIt = PSI0- (4.2-1.5)xl0-

SN = YJ Ht x C¡ x C¡

(SN+l)

(loä0(w8ti )-Zj¡^,-9.36<log0(.SA{+l)+0.2-2.32<loa^Mí)+8.07U 0.4-

(SAf+l)5'

(12) (13)

wm = 365X AADTh X (1 + 8h) ' 1 xa

8h (14)

Where: Wso is the number of 80 kN equivalent single axle load applications estimated for a selected design period and design lane; ZR is the standard normal deviate; S0 is the combined standard error of the traffic prediction and performance prediction; APSI is the difference between the initial or present serviceability index (PSI0) and the terminal serviceability index (PSIt); SN is the structural number indicative of the total required pavement thickness; MR is the sub-grade resilient modulus (pounds per square inch); Cj is the layer (structural) coefficient of layer /; c/ is the drainage coefficient of layer /; and Ht is the thickness of layer /; PSIt is the Present Serviceability Index in year t; PSI0 is the Present Serviceability Index of a pavement immediately after construction (year 0); Wg0 is the number of 80 kN equivalent single axle load (ESAL) applications in year t (million ESAL/lane); SNt is the structural number of a pavement structure in year t; AADTh is the annual average daily heavy traffic in the year of construction or the last rehabilitation, in one direction and per lane; gh is the annual average growth rate of heavy traffic; Yt is the time since the construction of the pavement or its last rehabilitation (years); a is the average heavy-traffic damage factor or simply truck factor.

Constraints (3) are the warning level constraints which define the maximum (or in relation to the PSI, the minimum) level for the pavement condition variables. The warning level adopted in this study considering the AASHTO pavement design method was a PSI value of 2.0 which corresponds to the PSI terminal value for national roads. A corrective M&R operation appropriate for the rehabilitation of a pavement structure must be performed when the PSI value is lower than 2.0. Constraints (4) represent the feasible operation sets, i.e. the M&R operations that can be applied to maintain or rehabilitate the pavement structure in relation to its quality condition. In this study two M&R operations will be considered (Table 1). The M&R operation 1, that corresponds to "do nothing", is applied to a pavement structure if the PSI value is above the warning level; that is, if the PSI value is greater than 2.0. The M&R operation number 2 is the operation that must be applied to a pavement structure when the warning level is reached; that is, this operation is applied to rehabilitate the pavement structure. The M&R operation costs, in the same way as the construction costs, were obtained from the PMS of the Portuguese road administration and correspond to the 85th percentile.

Table 1. Maintenance and rehabilitation operations

M&R operation Description Cost M&R actions involved Cost

1 Do nothing €0.00/m2 No actions €0.00/m2

Wearing layer (5 cm) €6.69/m2

Tack coat €0.41/m2

Base layer (10 cm) €8.63/m2

2 Structural rehabilitation €21.29/m2 Tack coat Membrane anti-reflection of cracks Tack coat Surface levelling (2 cm) Tack coat €0.41/m2 €1.88/m2 €0.41/m2 €2.45/m2 €0.41/m2

Constraints (5) indicate that only one M&R operation should be performed per pavement structure in each year. Constraints (6) represent the construction costs, which are computed in relation to the material and thickness of each pavement layer. Constraints (7) represent the M&R costs, which are computed in relation to the pavement condition and the M&R operation applied to the pavement in a given year. Constraints (8) represent the user cost functions. They express the costs for road users as a function of the pavement condition in a given year. Equation (15) was adopted for calculating the user costs because it is already used in some Portuguese PMS for calculating this type of costs (Ferreira et al. 2009b).

UCt = 0.39904 - 0.03871x PSIt + 0.00709 x PSlf - 0.00042 x PSlf (15)

Where: UCt are the user costs in year t (€/km/vehicle); PSIt is the Present Serviceability Index in year t.

Constraints (9) represent the residual value functions. They express the value of the pavement structure at the end of the project analysis period as a function of the construction cost and the pavement condition at that time. Equation (16) is used for calculating the residual value of pavements structures, which is also used in Portuguese PMS for the same purpose. Constraints (10) were included in the model to avoid frequent M&R operations on the same pavement structure.

RVT+1 = CC0 X PSIt+1 15 T+l 0 4.5 -1.5

Where: RVT+Ï is the residual value for a pavement structure in year T+1; CC0 is the construction cost of a pavement structure in year 0 depending on the material and thickness of each layer; PSIT+1 is the Present Serviceability Index in year T+1.

3. Case Study

3.1. Introduction

In the Portuguese manual (JAE 1995), a pavement structure is recommended depending on traffic class, which varies between T1 and T6, and pavement foundation class, which varies between F1 and F4. The traffic class is defined by the number of 80 kN equivalent single axle load (ESAL) applications for a design life or design period calculated in relation to the annual average daily heavy-traffic (AADTh), the annual average growth rate of heavy-traffic (gh) and the average heavy-traffic damage factor or, simply, truck factor (a). On the other hand, the pavement foundation class is defined by the California bearing ratio (CBR) value and the design stiffness modulus (E). The Portuguese manual considers 16 different flexible pavement structures for different combinations between traffic and pavement foundation. These pavement structures were defined using the Shell pavement design method (Shell 1978), with verification by using the University of Nottingham (Brunton et al. 1987) and Asphalt Institute (AI 2001) pavement design methods. In order to compare different solutions in terms of global costs for the final choice of the pavement structure for a national road or highway, the OPTIPAV system was applied to 384 combinations of traffic (6 different values), foundation (4 different values of the foundation stiffness modulus) and pavement structure (16 different flexible pavement structures) using a total costs optimization approach. The objective of this analysis is to select the pavement structure that minimizes net present value (NPV), calculated by adding the construction costs, the annual maintenance costs, the annual user costs and deducting the residual value of pavements at the end of the project analysis period,

while always keeping the pavements PSI value above the warning level of 2.0. In this application of the OPTIPAV system the following statistic design values were considered: a ZR value of -1.282 and a S0 value of 0.45.The economic analysis was done using a discount rate equal to 3%.

3.2. Results ofthe application ofthe OPTIPAVSystem

The results presented in this paper were obtained using the following data and conditions: two traffic classes (T1 and T5) characterized in Table 2; one type of pavement foundation (F3 with CBR equal to 20% and design stiffness modulus equal to 100 MPa); sixteen different pavement structures with the characteristics presented in Figure 1; a project analysis period of 40 years. Table 2 also shows the pavement structure recommended in the Portuguese manual for traffic class T5 and pavement foundation F3 (P4) and for traffic class T1 and pavement foundation F3 (P14). Figure 1 presents the characteristics of the pavement structures (type of material, thickness, stiffness modulus; Poisson's ratio, CBR, etc.) that were considered in the pavement design process using the Shell and the other two pavement design methods to define the Portuguese manual of pavement structures. Figure 2 shows the construction costs of each pavement structure. We can see that their values increase with the pavement structural capacity defined by the structural number (SN) considered in the AASHTO pavement design method. Figure 2 also presents the M&R costs during the entire project analysis period for the sixteen pavement structures and for traffic classes T5 and Tl. As expected, the M&R costs decrease with the pavement structural capacity, and for traffic class Tl the least-M&R-costs pavement structure is P16. For traffic class T5 there are several pavement structures (P6 to P16) with no M&R costs during the 40 years of the project analysis period. For traffic class Tl, pavement structure P9 presents less M&R costs than pavement structures P10 and Pll, which would not be expected. The explanation for this can be detected analyzing the rehabilitation operations and the evolution of the PSI value. Figure 3 represents the predicted PSI value over the years of the project analysis period, for each pavement structure and traffic classes T5 and Tl, as a consequence of the execution of the rehabilitation operations. It can be seen that the rehabilitation operation is applied when the PSI value reaches its minimum quality value, i.e. 2.0. Figure 3 shows, as expected, that for the lowest traffic class (T5) and for all pavement structures the degradation of the PSI value during the project analysis period is slower than for the highest traffic class (Tl). They also show that using weak pavement structures (with a small SN value) the PSI value decreases quickly in the first years of the project analysis period. Then with the application of M&R operations the PSI value decreases slowly in the remaining years of the project analysis period because the SN increases, making these pavement structures stronger. For traffic class T5, if pavement structure P4 recommended by the Portuguese manual is adopted then only one rehabilitation operation will be needed in the 34th year of the project analysis period. For traffic class Tl, if pavement structure P14 recommended by the Portuguese manual is adopted then again only one rehabilitation operation will be needed, but in this case in the 20th year of the project analysis period. This pavement structure will not require any rehabilitation operation during 20 years, the design period considered in the Portuguese Manual.

Table 2. Traffic classes and corresponding values

Traffic Pavement foundation Pavement structure

Traffic AADTh gh(%) ESAL Foundation E Manual

class a (20 years) class (MPa) V

T5 300 3 3 0.88xl07 F3 100 0.35 P4

Tl 2,000 5 5.5 13.28xl07 F3 100 0.35 P14

Flexible Pavement Design Alternatives

PI P2 P3 P4 P5 P6 P7 P8 P9 PIO Pli PI 2 P13 P14 PI 5 P16

HMA 6 6

Stiffness Modulus i"MPa1 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000

Surface 0.35 0.3Í 0.3Í 0.35 0.35 0.3Í 0.35 0.35 0.3Í 0.3Í 0.35 0.3Í 0.3Í 0.35 0.35 0.35

ayer Material AC AC AC AC AC AC AC AC AC AC AC AC AC AC AC AC

155 Thickness (cm) 12 14 14 16 18 17 19 18 20 20 23 22 24 26

HMA «==! Stiffness Modulus iMPal 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000

155 Poisson's ratio 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35

■■■■■■■■■■■■■■■I Material AC AC AC AC AC AC AC AC AC AC AC AC AC AC AC AC

:x::x:| Thickness (cm) 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20

XvXXd Stiffness Modulus (MPa) 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200

: ::::: :::: Poisson's ratio 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35

Material G G G G G G G G G G G G G G G G

Thickness (cm) 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100

Sub- Stiffness Modulus (MPa) 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100

grade Poisson's ratio 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35

CBR (%) 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20

Total HMA Layer Thickness (cm) 10 12 16 18 19 21 22 22 24 24 25 26 28 28 30 32

Structural Number 2.36228 2.63000 3.16544 343316 3.60639 3.87411 3.96860 4.00797 4.27569 4.31506 4.40955 4.5 8278 4.81113 4.85050 5.11822 5.38594

Key: AC - Asphalt Concrete; G - Granular Material; CBR - California Bearing Ratio; HMA - Hot Mix Asphalt

Fig. 1. Characteristics of pavement structures

Fig. 2. Construction costs of pavement structures and M&R costs throughout the project analysis period

Fig. 3. Evolution of PSI for each pavement structure and traffic class T5 (left) and Traffic class T1 (right)

Figure 4 presents the total user costs throughout the project analysis period and also the residual value at the end of the project analysis period corresponding to traffic classes T5 and Tl. It shows that the total user costs are much higher for traffic class Tl than for traffic class T5, but for the same traffic class all the pavement structures have relatively close values. The difference between the maximum and the

minimum user costs is 0.68% and 0.60% for T5 and Tl traffic classes, respectively. Taking the traffic class T5 and pavement structure P4 as a reference, the total user costs are approximately 915% higher when the traffic category is Tl. This happens because the difference between traffic volumes is enormous, and the degradation of PSI value is higher for traffic class Tl. Figure 5 presents the Net Present Value (NPV) and the highway agency costs for each pavement structure for both traffic classes T5 and Tl. Considering the NPV, the results show that the optimum pavement structure for traffic class T5 (P13) is different from the pavement structure recommended by the Portuguese manual of pavement structures (P4), although for traffic class Tl the OPTIPAV system and the Portuguese manual recommend the same pavement structure (P14). Considering traffic class T5, P13 is the least-total discounted costs pavement structure, allowing savings of €4.81 per m2 (approximately 0.32%) comparatively to P4, which is the pavement structure recommended by the Portuguese manual. For example, for a road with 100 kilometres long and 10 meters wide it corresponds to a saving of €4,810,000.00. Considering only costs directly related to a highway operator or highway agency, i.e. constructions costs, M&R costs and the residual pavement of pavement structures, we can conclude that pavement structure P5 is the optimum pavement structure for traffic class T5, while pavement structure P16 is the optimum pavement structure for traffic class Tl. For example, pavement structure P5 has the following values: construction costs (€27.59/m2); maintenance costs (€6.92/m2); residual value (€8.62/m2). Pavement structure P4 has the following values: construction costs (€26.25/m2); maintenance costs (€7.79/m2); residual value (€7.85/m2). We can see that P5 has higher construction costs (more €1.34/m2) but lower maintenance costs (less €0.87/m2) and a higher residual value (more €0.77/m2). Considering these costs, P5 allows savings of €0.3 per m2. For a road with 100 kilometres long and 10 meters wide it corresponds to a saving of €300,000.00.

Fig. 4. User costs throughout the project analysis period and residual value at the end ofthe project analysis period

Fig. 5. Net Present Value and highway agency costs for each pavement structure

Table 3 presents the pavement structures recommended by the Portuguese manual and the optimum pavement structures defined by using the OPTIPAV system considering all the costs and considering only the highway agency costs. Considering all the costs, one can see that in eight cases the optimum pavement structure defined by using the OPTIPAV system has more structural capacity, in four cases it has the same structural capacity, and in six cases it has less structural capacity. The pavement structures recommended by the Portuguese manual and by the OPTIPAV system are different in 78% of the cases. Considering only the highway agency costs, one can see that in thirteen cases the optimum pavement structure defined by using the OPTIPAV system has more structural capacity, in five cases it has the same structural capacity, and in no case it has less structural capacity. In the most cases, pavement structures with more structural capacity allow for savings in terms of highway agency costs.

Table 3. Optimum pavement structures

Traffic class ESAL (20 years) Pavement foundation Pavement (Manual) Pavement (OPTIPAV)

AADT AADTh gh(%) a Min(NPV) Min (Agency Costs)

T6 1500 150 3 2 0.29xl07 F1 NAF P14 P16

T5 3000 300 3 3 0.88xl07 F1 NAF P16 P16

T4 5000 500 4 4 2.17xl07 F1 NAF P6 P16

T3 8000 800 4 4.5 3.91xl07 F1 NAF P15 P16

T2 12000 1200 5 5 7.24xl07 F1 NAF P16 P16

T1 20000 2000 5 5.5 13.28xl07 F1 NAF P9 P16

T6 1500 150 3 2 0.29xl07 F2 P3 P13 P7

T5 3000 300 3 3 0.88xl07 F2 P7 P7 P15

T4 5000 500 4 4 2.17xl07 F2 Pll P13 P16

T3 8000 800 4 4.5 3.91xl07 F2 P13 P16 P16

T2 12000 1200 5 5 7.24xl07 F2 P15 P7 P15

T1 20000 2000 5 5.5 13.28xl07 F2 P16 P14 P16

T6 1500 150 3 2 0.29xl07 F3 P2 P3 P3

T5 3000 300 3 3 0.88xl07 F3 P4 P13 P5

T4 5000 500 4 4 2.17xl07 F3 P6 P16 Pll

T3 8000 800 4 4.5 3.91xl07 F3 P9 P6 P15

T2 12000 1200 5 5 7.24xl07 F3 P12 Pll P16

T1 20000 2000 5 5.5 13.28xl07 F3 P14 P14 P16

T6 1500 150 3 2 0.29xl07 F4 PI PI PI

T5 3000 300 3 3 0.88xl07 F4 P3 P3 P3

T4 5000 500 4 4 2.17xl07 F4 P5 P16 P5

T3 8000 800 4 4.5 3.91xl07 F4 P8 P16 P10

T2 12000 1200 5 5 7.24xl07 F4 P10 P7 P13

T1 20000 2000 5 5.5 13.28xl07 F4 P12 P9 P16

4. Conclusions

The LCCA system for pavement management at project level proposed in this paper, called OPTIPAV, can solve the problem of making LCCA for typical design periods (20 years) but also for longer periods

(40 years or more), in order to compare different pavement solutions in terms of global costs for the final choice of the pavement structure for a national road or highway. Additionally, the OPTIPAV system provides a good solution to the pavement design problem considering not only design criteria but also construction costs, maintenance costs, user costs and the residual value of pavement structures. The application of the OPTIPAV system to the case study allows us to conclude that the pavement structures recommended by the Portuguese Manual are not always the optimum solutions. The pavement structures recommended by the Portuguese manual and by the OPTIPAV system are different in 78% of the cases. The OPTIPAV system already constitutes a useful tool to help road engineers in their task of pavement design. They can now carry out LCCA taking into account any combination of construction costs, maintenance costs, user costs and the residual value of pavement structures, in order to compare different pavement solutions for the final choice of the optimum pavement structure for a national road or highway.

Acknowledgements

The authors are grateful to the Portuguese Foundation of Science and Technology for the financial support provided to this study through Grant PTDC/ECM/112775/2009 - MODAT - Multi-Objective Decision-Aid Tool for Highway Asset Management, financed by the European Community Fund FEDER.

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