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Procedía - Social and Behavioral Sciences 53 (2012) 1174 - 1183
SIIV - 5th International Congress - Sustainability of Road Infrastructures
LCCA system for pavement management: sensitivity analysis to the discount rate
Adelino Ferreiraa*, Joâo Santos a
aDepartment of Civil Engineering, University of Coimbra, Rua Luís Reis Santos, 3030-788 Coimbra, Portugal
Abstract
This paper presents a life-cycle cost analysis system, called OPTIPAV, which can consider construction costs, maintenance and rehabilitation costs, user costs, and the residual value of the pavement. The OPTIPAV was applied to the flexible pavement structures of the Portuguese pavement design manual. The paper also presents a sensitivity analysis to the discount rate. The results obtained by the application of the new LCCA system clearly indicate that, for any combination between traffic and pavement foundation, the optimum pavement structure always remains the same or decreases in terms of structural capacity with the increase of the discount rate value.
© 2012 TheAuthors.Published by Elsevier Ltd.Selection and/or peer-review under responsibility of SIIV2012 Scientific Committee
Keywords: Pavement design, life-cycle cost analysis; infrastructure management, discount rate, maintenance and rehabilitation.
1. Introduction
Life-cycle Cost Analysis (LCCA) has received increasing attention as a tool to assist transportation agencies in order to be able to make more economical investment decisions. When analyzing long-term public investments, we must compare costs and benefits that occur in different time periods. As time has a money value, a dollar spent in the future is worth less than the present dollar [1]. Therefore, the LCCA process uses an economic technique known as "discounting" to convert different costs and benefits occurred at different times at a common point in time [2]. This technique applies a financial variable called discount rate (d) to represent the time value of the money. The discount rate used in a LCCA application can have quite a large impact on the analysis and in the conclusions that can be reached. Therefore, it is important to apply the correct discount rate for each particular decision problem. This paper presents a sensitivity analysis to the discount rate that was carried out on the
* Corresponding author. Tel.: +351.239797101; fax: +351.239797142. E-mail address: adelino@dec.uc.pt
1877-0428 © 2012 The Authors. Published by Elsevier Ltd. Selection and/or peer-review under responsibility of SIIV2012 Scientific Committee doi:10.1016/j.sbspro.2012.09.966
application of a new LCCA system, called OPTIPAV, developed and programmed to help pavement designers to choose the best pavement structure for a road or highway [3].
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 by the sensitivity analysis to the discount rate considered in the application of the OPTIPAV system to the pavement structures of the Portuguese Manual. The final section consists of a synthesis of the conclusions reached so far and a statement of prospects for future research.
Nomenclature
CCso construction cost of a pavement structure 5 in year 0 in function of the layer's material and thickness
d discount rate
Msl material of layer l of pavement structure 5
MCrst maintenance cost for applying operation r to pavement structure 5 in year t
Nmaxs maximum number of M&R operations that may occur in pavement structure 5 over the project analysis
period
PSIt Present Serviceability Index in year t
PSIt+i Present Serviceability Index in year T+1
R number of alternative M&R operations
RVs,T+1 residual value for a pavement structure 5 in year T+1
S number of pavement structures generated for analysis
T number of years of the project analysis period
Thsi thickness of layer l of pavement structure 5
UCst user cost for pavement structure 5 in year t (€/km/vehicle)
Xrst is equal to one if operation r is applied to pavement structure 5 in year t, otherwise it is equal to zero
Zst condition variables for pavement structure 5 in year t
Z warning levels for the condition variables of pavement structures
0 pavement condition functions
0 residual value functions
To construction cost functions
Wa agency cost functions for M&R
are the user cost functions
Q feasible operations sets
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 [4,5] 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 maintenance and rehabilitation (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:
T R T Min CCs0 + y y -xMCrst xXrst +y -xUCst--xRV,T+1
s0 ¿¿r (1+d)t rst rst ¿Mi+d)t st (1+d)T+! s'T+1 (1) Subject to:
Zst = O (Zso,Xisi,...,Xist,...,XRsi,...,XRst),s = 1,...,S;t = 1,...,T (2)
Zst {¡¡^ s = u, t = 1,..., T (3)
Xrst ),r = 1,...,R;s = 1,...,S;t = 1,...,T (4)
^XrSt = 1, s = 1,...,S; t = 1,...,T (5)
CCso = Wc (Msi,Thsi),s = 1,...,S (6)
MCrst = Wa (Zst,Xrst),r = 1,...,R;s = 1,...,S;t = 1,...,T (7)
UCst = Wu {zst),s = 1,...,S;t = 1,...,T (8)
RVsT+1 = 0 (cCso, Zs,T+J s = 1,..., s (9)
^^ Xrst < N max,, Vs = 1,..., 5 (10)
UC = 0.39904-0.03871 xPSI + 0.00709xPSlj -0.00042xPSI3 (11)
tSt It /
PSIT+1 -1.5 ( 4.5-1.5
Equation (1) expresses the minimization 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
r=2 t=1
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 [6,7], and other municipal PMS [8,9], uses the pavement performance model of the flexible pavement design method developed by the American Association of State Highways and Transportation Officials [10] to predict the future quality of pavements. Thus, this application of the LCCA system will consider the AASHTO flexible pavement design method. Constraints (3) are the warning level constraints which define the maximum (or in relation to the Present Serviceability Index (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.
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 (11) was adopted for calculating the user costs because it is already used in some Portuguese PMS for calculating this type of costs [9]. 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 (12) 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.
Table 1. Maintenance and rehabilitation operations
M&R operation Description Cost (€/m2) M&R actions involved Cost (€/m2)
1 Do nothing 0.00 No actions 0.00
Wearing layer (5 cm) 6.69
Tack coat 0.41
Base layer (10 cm) 8.63
2 Structural rehabilitation 21.29 Tack coat Membrane anti-reflection of cracks Tack coat Surface levelling (2 cm) Tack coat 0.41 1.88 0.41 2.45 0.41
3. Sensitivity analysis to the discount rate
3.1. Introduction
Santos and Ferreira [3] applied the OPTIPAV system in order to compare different pavement structures defined by the Portuguese manual [11] in terms of global costs for the final choice of the pavement structure for a national road or highway. Thus, the aim of that analysis was to select the pavement structure that minimizes Net Present Value (NPV) of total costs, 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 pavement PSI value above the warning level of 2.0. This economic analysis was carried out using a discount rate equal to 3%. The flexible pavement structures considered by the Portuguese manual (16 in the total) were initially designed using the Shell pavement design method [12], with verification by using the University of Nottingham [13] and Asphalt Institute [14] pavement design methods. These pavement structures are recommended for different combinations between traffic and pavement foundation. The traffic class varies between T1 and T6 and 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). The pavement foundation class is defined by the California Bearing Ratio (CBR) value and the design stiffness modulus (E).
In [3] were used the input parameters shown in Table 2 and Figure 1. Table 2 presents the economic and traffic inputs parameters while Figure 1 shows the characteristics of the sixteen pavement structures (type of material, thickness, stiffness modulus, Poisson's ratio, CBR, etc.) recommended by the Portuguese manual of pavement structures. These characteristics were considered in the pavement design process using the Shell and the other two pavement design methods (University of Nottingham and Asphalt Institute) to define the Portuguese manual of pavement structures. Table 3 presents the rehabilitation operations to be applied in the sixteen pavement structures during the entire project analysis period considering two traffic classes (T5 and T1) and a pavement foundation F3.
Table 2. Input parameters considered in the application of the OPTIPAV system
Input parameters Value
Project analysis period 40 years
Discount rate (%) 3
Pavement foundation F3 (E=100MPa)
AADTh 300
T5 gh (%) 3
Traffic ESAL (20 years) 0.88x107
class AADTh 2000
T1 gh (%) 5
ESAL (20 years) 13.28x107
Flexible Pavement Design Alternatives
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16
4 4 4 5 5 4 5 5 6 5 6 5 6 6 6
Stiffness Modulus (MPa) 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000
lllf.l ^^ 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
a 1 m Material AC AC AC AC AC AC AC AC AC AC AC AC AC AC AC AC
Thickness (cm) 8 12 14 14 16 18 17 19 18 20 20 23 22 24 26
HMA |== Stiffness Modulus (MPa) 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000
_ase §== 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
ayer hi Material AC AC AC AC AC AC AC AC AC AC AC AC AC AC AC AC
Thickness (cm) 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
,u Stiffness Modulus (MPa) 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200
_ase 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
ayer 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
grac 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 3.43316 3.60639 3.87411 3.96860 4.00797 4.27569 4.31506 4.40955 4.58278 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 Table 3. Rehabilitation operations to be applied in pavement structures for traffic class T5 and T1
Rehabilitation plan
Pavement structure Foundation F3 (E = 100 Mpa)
Traffic class
T5 T1
Year PSI final Year PSI final
P1 4 3.23 2/20 2.92
P2 10 3.54 2/23 3.09
P3 27 4.10 4/24 3.23
P4 34 4.34 6/26 3.50
P5 38 4.47 7/32 4.08
P6 - 2.51 10/34 4.19
P7 - 2.66 11/35 4.25
P8 - 2.71 11/37 4.38
P9 - 2.97 14 1.77
P10 - 2.99 15/38 4.43
P11 - 3.06 16/39 4.50
P12 - 3.17 17 2.64
P13 - 3.29 20 2.78
P14 - 3.31 20 2.99
P15 - 3.43 23 3.28
P16 - 3.54 26 3.56
3.2. Results of the sensitivity analysis to the discount rate
In this sensitivity analysis, the discount rate value varied between 0 and 5%, incremented by 1%, while keeping all the other input values. Using this methodology, the decision-maker can understand the variability in the ranking of pavement structures, associated with the choice of the discount rate value. Figures 2 and 3 show, for each pavement structure and for both traffic classes T5 and T1, the impact caused by adopting different discount rate values on costs directly related to a highway operator or highway agency, i.e. construction costs, M&R costs, and residual value of pavement structures. Analysing Figure 2, if we look at traffic class T5, we can see that the differences between agency costs using different discount rates become more pronounced with the increase of the pavement structural capacity, and this is particularly significant for lower discount rates. On the other hand, contrary to what might be expected, for traffic class T5 and for almost all the pavement structures, the agency costs increase when the discount rate value also increases. This happens because the residual value is deducted from the other components (construction costs and M&R costs) in the computation of the agency costs, and the residual value always decreases with the increase of the discount rate.
Lett: ■ T1 1-0% ■ T1 i-l % ■ T1 1-2% ■ T] I-3W ■ T1 r-4% TL t-5%
Right: ■ T5 t-0% ■ T5 r-l% ■ Ti T—2% ■ 1") T- Wa ■ T5 T5 1=5%
Fig. 2. Agency costs for each pavement structure and different discount rates values
For traffic class T5, Figures 2 and 3 also show that pavement structures P2 and P3 present a maximum agency costs value for a discount rate equal to 3%. In addition, it may still be observed that the discount rate has an impact on the ranking of the alternative pavement structures. This is proved by the interception of the curves when the discount rate is higher than 1% (the first break-even point). Considering traffic class T1, Figures 2 and 3 show that the adopted discount rate value has different effects on the agency costs of each pavement structure and that impact tends to change with pavement structural capacity. Figure 3 shows that pavement structures with a lower structural capacity (for example, P1 to P4) present agency costs that always decrease with the increase of the discount rate value. On the other hand, pavement structures with a higher structural capacity (for example, P16) present agency costs that always increase with the increase of the discount rate value. Figures 2 and 3 also show that almost all pavement structures with intermediate structural capacity present a maximum agency costs value for a specific discount rate value that increases with the structural capacity of the pavement structure. For traffic class T1, just as for traffic class T5, the discount rate also has an impact on the ranking of the alternative pavement structures. Nevertheless, this impact is less pronounced for traffic class T1 than for traffic class T5 and it occurs at higher discount rate values.
Table 4 presents the pavement structures recommended by the Portuguese manual and also the optimum pavement structures defined by using the OPTIPAV system considering the agency costs computed by using different discount rate values. This Table shows that the optimum pavement structure can change with the discount rate value. For traffic class T5 and pavement foundation F3, increasing the discount rate value, the optimum pavement structure has less or at best the same structural capacity. The optimum pavement structures are P16, P13, P7, P5, P5, and P4 for discount rate values 0%, 1%, 2%, 3%, 4%, and 5%, respectively. For traffic class T1 and pavement foundation F3, as the discount rate value increases, the optimum pavement structure also has less or at best the same structural capacity. The optimum pavement structures are P16, P16, P16, P16, P16, and P11 for discount rate values 0%, 1%, 2%, 3%, 4%, and 5%, respectively. Analysing Table 4, we can see that the optimum pavement structures are structurally weaker with the increase of the discount rate value for all combinations between traffic class and pavement foundation. Two factors contribute to this: (1) the difference between M&R costs and the residual value of different pavement structures decreases with the increase of the discount rate value; (2) the pavement structures with less structural capacity have smaller construction costs which are independent of the discount rate value. Therefore, the agency costs are lower for weaker pavement structures, despite the fact that these pavement structures may have higher M&R costs because the M&R operations may occur earlier (Table 3).
Additionally, the influence of the discount rate on the selection of different pavement structures increases with the structural capacity of the pavement foundation. For example, if we take the pavement foundation F1, we can see that the optimum pavement structure is always P16 for all discount rate values and traffic classes T1 to T5 (Table 4). On the other hand, considering the pavement foundation F4, the optimum pavement structures are very different for all discount rate values and traffic classes T1 to T5. In these cases, the optimum pavement structure remains the same or decreases in terms of structural capacity with the increase of the discount rate value.
Table 4. Optimum pavement structures defined by OPTIPAV system using different discount rates values
Traffic aADT (%) a ESAL Pavement class h (20 years) foundation
Pavement (Manual)
Pavement (OPTIPAV)
Minimization of the agency costs
d = 0% d = 1% d il 2 xO o1- d = 3% d il 4 xO o1- d = 5%
T6 150 3 2 0.29x107 F1 NAF P16 P16 P16 P16 P15 P13
T5 300 3 3 0.88x107 F1 NAF P16 P16 P16 P16 P16 P16
T4 500 4 4 2.17x107 F1 NAF P16 P16 P16 P16 P16 P16
T3 800 4 4.5 3.91x107 F1 NAF P16 P16 P16 P16 P16 P16
T2 1200 5 5 7.24x107 F1 NAF P16 P16 P16 P16 P16 P16
T1 2000 5 5.5 13.28x107 F1 NAF P16 P16 P16 P16 P16 P16
T6 150 3 2 0.29x107 F2 P3 P16 P16 P8 P7 P7 P6
T5 300 3 3 0.88x107 F2 P7 P15 P15 P15 P15 P13 P11
T4 500 4 4 2.17x107 F2 P11 P16 P16 P16 P16 P16 P13
T3 800 4 4.5 3.91x107 F2 P13 P16 P16 P16 P16 P16 P16
T2 1200 5 5 7.24x107 F2 P15 P15 P15 P15 P15 P15 P15
T1 2000 5 5.5 13.28x107 F2 P16 P16 P16 P16 P16 P16 P16
T6 150 3 2 0.29x107 F3 P2 P16 P3 P3 P3 P3 P3
T5 300 3 3 0.88x107 F3 P4 P16 P13 P7 P5 P5 P4
T4 500 4 4 2.17x107 F3 P6 P16 P12 P12 P11 P7 P7
T3 800 4 4.5 3.91x107 F3 P9 P15 P15 P15 P15 P13 P7
T2 1200 5 5 7.24x107 F3 P12 P16 P16 P16 P16 P13 P13
T1 2000 5 5.5 13.28x107 F3 P14 P16 P16 P16 P16 P16 P11
T6 150 3 2 0.29x107 F4 P1 P2 P2 P2 P1 P1 P1
T5 300 3 3 0.88x107 F4 P3 P16 P4 P3 P3 P3 P3
T4 500 4 4 2.17x107 F4 P5 P16 P16 P7 P5 P5 P4
T3 800 4 4.5 3.91x107 F4 P8 P16 P16 P10 P10 P7 P6
T2 1200 5 5 7.24x107 F4 P10 P14 P13 P13 P13 P9 P7
T1 2000 5 5.5 13.28x107 F4 P12 P16 P16 P16 P16 P13 P11
4. Conclusions
The results of a sensitivity analysis to the discount rate presented in this paper demonstrate the importance of a
right choice of the discount rate value in a LCCA application, in order to avoid a bad allocation of private/public funds to highway projects, particularly now that Portugal and other European countries are facing an economic
crisis. The outcomes obtained with the sensitivity analysis to the discount rate value permit us to draw the following conclusions: (1) the construction costs are independent of the discount rate value; (2) the M&R costs and the residual value of pavements always decrease with the increase of the discount rate; (3) the agency costs (the sum of the construction costs and the M&R costs, deducting the residual value of pavements) do not have
uniform behavior. Usually, for a pavement structure with high structural capacity for the traffic that uses it, the agency costs increase with the increase of the discount rate value. For a pavement structure with low structural capacity for the traffic that uses it, the agency costs decrease with the increase of the discount rate value; (4) for any combination between traffic and pavement foundation the optimum pavement structure remains the same or decreases in terms of structural capacity with the increase of the discount rate value.
In the near future, in terms of sensitivity analysis, our research will follow with the consideration of other input parameters, such as, for example, the project analysis period or the CBR value of the pavement foundation.
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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