LIFE-CYCLE COST ANALYSIS SYSTEM FOR PAVEMENT MANAGEMENT – SENSITIVITY NALYSIS TO THE PAVEMENT FOUNDATION ADELINO FERREIRA, DEPARTMENT OF CIVIL ENGINEERING, UNIVERSITY OF COIMBRA, [email protected]JOÃO SANTOS, DEPARTMENT OF CIVIL ENGINEERING, UNIVERSITY OF COIMBRA, [email protected]This is an abridged version of the paper presented at the conference. The full version is being submitted elsewhere. Details on the full paper can be obtained from the author.
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LIFE-CYCLE COST ANALYSIS SYSTEM FOR PAVEMENT MANAGEMENT –SENSITIVITY NALYSIS TO THE PAVEMENT FOUNDATION
ADELINO FERREIRA, DEPARTMENT OF CIVIL ENGINEERING, UNIVERSITY OF COIMBRA, [email protected]ÃO SANTOS, DEPARTMENT OF CIVIL ENGINEERING, UNIVERSITY OF COIMBRA,
This is an abridged version of the paper presented at the conference. The full version is being submitted elsewhere.Details on the full paper can be obtained from the author.
Life-cycle cost analysis system for pavement management FERREIRA, Adelino; SANTOS, João
13th WCTR, July 15-18, 2012 – Rio de Janeiro, Brazil
1
LIFE-CYCLE COST ANALYSIS SYSTEM FOR PAVEMENT MANAGEMENT – SENSITIVITY ANALYSIS TO THE
PAVEMENT FOUNDATION
Adelino Ferreira
Department of Civil Engineering, University of Coimbra, [email protected]
João Santos
Department of Civil Engineering, University of Coimbra, [email protected]
ABSTRACT
This paper presents a LCCA system called OPTIPAV that can consider construction costs,
maintenance and rehabilitation costs, user costs, and the residual value of the pavement. The
OPTIPAV is constituted by a deterministic segment-linked optimization model that is solved
by an heuristic method based on genetic-algorithm principles. The OPTIPAV system has the
following components: the objectives of the analysis; the data and the models about the road
pavements; the constraints that the system must guarantee; and the results. One objective that
can be considered in the analysis is the minimisation of total costs, i.e., construction costs,
agency costs, user costs, and the residual value of the pavements.
The OPTIPAV uses the deterministic pavement performance model of the AASHTO flexible
pavement design method to predict the future quality of pavements in terms of the Present
Serviceability Index (PSI). The OPTIPAV was applied to the alternative flexible pavement
structures included in the Portuguese Road Administration pavement design catalogue. The
analysis was carried out using construction costs and information on maintenance strategies
adopted on flexible pavement structures in the main road network of Portugal.
The final part of the paper contains the main conclusions and presents the developments
Life-cycle cost analysis system for pavement management FERREIRA, Adelino; SANTOS, João
13th WCTR, July 15-18, 2012 – Rio de Janeiro, Brazil
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INTRODUCTION
The alignments for most of the highway projects do not always follow the site topography.
Due to a great variety of cuts and fills that will be required, the lithology nature of the soils
found at project site it is not the same in both depth and length. Consequently, the in-situ
geotechnical conditions available to build the pavement structure support are not always the
best, and as it is known the conditions and the preparation of the foundation are extremely
important to ensure a long-lasting pavement structure that does not require excessive
maintenance costs. To overcome these limitations many highway agency have as current
practise to build, upon the roadbed, a layer of compacted roadbed soil or selected borrow
material, called subgrade (Christopher et al. 2006). The main purpose of the subgrade is to
provide a platform for construction of the pavement and to support the pavement without
excessive deflection that would impact the pavement‟s performance. For pavements constructed on-grade or in cuts, if the in-situ natural soils present good qualities, the subgrade
is the natural in-situ soil at the site (Christopher et al. 2006). The stiffness of this layer must
be sufficient to allow compaction of the overlying pavement structure in order to obtain
adequate density in the granular and asphalt layers to ensure a good performance of the
pavement (APA 2010). Although there is a consensus about the importance of the foundation
strength and stiffness for the design, construction and performance of the pavement, until now
there are few research works in the literature that have assessed the impact of structural
capacity of pavement subgrade in pavement design and pavement performance prediction
(Khogeli and Mohamed 2004, Tarefder et al. 2008). Moreover, the research studies that have
been carried out are based on pavement design methods which consider only design criteria,
usually fatigue and rutting modes of pavement failure. Reddy and Moorthy (2005) assessed
the adequacy of flexible pavement design thickness based on California Bearing Ratio (CBR)
method against possible risk of shear failure in clayey subgrade. The pavement thickness
designs based on CBR method over clayey subgrades of different compressibility were
compared with a methodology proposed for flexible pavement design based on safe bearing
capacity (SBC) of subgrade soils. They concluded that it is preferable to adopt higher design
thickness values obtained from SBC approach to construct flexible pavements that are safe
against the aspects of shear failure and excessive settlement in subgrade. However, in case of
lime treated soils, the risk against shear failure of subgrade may not be there and hence design
based on CBR value of subgrade may be valid and used. Sidess and Uzan (2009) presented a
design method of perpetual flexible pavement in Israel. The total perpetual pavement
thickness is calculated using the Israeli design method. The HMA layers thickness is
determined as the minimum thickness at which the tensile strain at the bottom of the HMA
layer meets one of the following two criteria: (1) crack initiation at the end of the 30 years
design period or (2) an „endurance‟ limit of 70 µS. The effect of subgrade strength on HMA layers was studied. The authors verified that the value of the HMA thickness decreased by
only 30 mm when the CBR of the subgrade increased from 2 to 10%.
This paper is a step forward in the evaluation of the influence of pavement subgrade soils in
pavement design since the study presented here was carried out on the application of a new
LCCA system, called OPTIPAV (Santos and Ferreira 2011), which considers pavement
performance and the following costs: construction costs; maintenance costs throughout the
Life-cycle cost analysis system for pavement management FERREIRA, Adelino; SANTOS, João
13th WCTR, July 15-18, 2012 – Rio de Janeiro, Brazil
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project analysis period; user costs throughout the project analysis period; and the pavement
residual value at the end of the project analysis period.
LIFE-CYCLE COST ANALYSIS SYSTEM
Introduction
The LCCA system called OPTIPAV, proposed by Santos and Ferreira (2011), consists of the
components shown in Figure 1: the objective of the analysis, the road pavement data and
models, the constraints that the system must guarantee and the results. The OPTIPAV system
was implemented using Microsoft Visual Studio programming language (David et al. 2006,
Randolph and Gardner 2008) adapting and introducing new functionalities to an existing
genetic algorithm program called GENETIPAV-D (Ferreira 2001, Ferreira et al. 2002,
Ferreira et al. 2009a) previously developed to solve deterministic optimisation 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. The
objective of the analysis, the road pavement data and models, and the constraints that the
system must guarantee are described in the following section.
Minimisation of total costs
(construction costs, M&R costs, user costs, residual value of pavements)
Verifying the minimum quality levels
Using only the M&R actions defined by the infrastructure manager
Not exceeding the maximum number of M&R actions during the project analysis period
Number of years of the project analysis period
Discount rate
Traffic
Pavement width and length
Admissible pavement layers and construction costs
M&R actions and unit agency costs
Pavement foundation class
Performance model
User costs model
Residual value model
Minimum quality levels to guarantee
Optimal pavement structure
Predicted annual pavement quality
Construction costs
M&R plan and costs
User costs
Residual value in the end of the project analysis period
Data and models
Objective
Constraints
Results
Figure 1 – OPTIPAV system components
Life-cycle cost analysis system for pavement management FERREIRA, Adelino; SANTOS, João
13th WCTR, July 15-18, 2012 – Rio de Janeiro, Brazil
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Optimisation model formulation
The optimisation model introduced above can be formulated as follows:
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 s 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 s in year t; UCst is the user cost for pavement structure s in year t; RVs,T+1 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 s in year t, otherwise it is equal to zero; d is the discount rate;
Zst are the condition variables for pavement structure s in year t; Z are the warning levels for
the condition variables of pavement structures; Msl is the material of layer l of pavement
structure s; Thsl is the thickness of layer l of pavement structure s; Nmaxs is the maximum
number of M&R operations that may occur in pavement structure s over the project analysis
period; Φ are the pavement condition functions; Θ are the residual value functions; c are
the construction cost functions;a are the agency cost functions for M&R; u are the user
cost functions; are the feasible operations sets.
Equation (1), the objective-function of this quite complex, highly non-linear discrete
optimization model, 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.
Life-cycle cost analysis system for pavement management FERREIRA, Adelino; SANTOS, João
13th WCTR, July 15-18, 2012 – Rio de Janeiro, Brazil
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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, the first application of the LCCA system (Santos and Ferreira 2011) has
also considered the AASHTO flexible pavement design method. The basic design equation
used for flexible pavements is Equation (11). This pavement design method considers the
structural coefficients (SN) presented in Table 1, the initial and terminal present serviceability
index (PSI) values presented in Table 2 and the statistic design values (ZR and S0) presented in
Table 3. Equation (11) can be transformed into Equation (12) to be directly used in the
prediction of the PSI value in each year of the design period. The PSI value ranges between
0.0 and approximately 4.5 (the value for a pavement immediately after construction).
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.
M
+SN
PSI
+SNSZ=W R0R 8.07-log2.32+
1
1094+0.40
1.5-4.2log
+0.2-1log9.36+log 10
5.19
10
108010
(11)
5.19101080101
10944.007.8log2.32-0.21log9.36log
0 101.5-4.2-+SN
M+SNSZW
tt
Rt0Rt
PSIPSI (12)
L
l
dl
ell CCHSN
1
(13)
h
tYh
hg
gAADTW
t
1)1(365
80
(14)
Where: W80 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; PSI 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); elC is the layer (structural)
coefficient of layer l; dlC is the drainage coefficient of layer l; and lH is the thickness of layer
l; PSIt is the Present Serviceability Index in year t; PSI0 is the Present Serviceability Index of
a pavement immediately after construction (year 0); t
W80
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; tY is the time since the construction of the
pavement or its last rehabilitation (years); is the average heavy-traffic damage factor or
simply truck factor.
Life-cycle cost analysis system for pavement management FERREIRA, Adelino; SANTOS, João
13th WCTR, July 15-18, 2012 – Rio de Janeiro, Brazil
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 (Table 2). 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 application of the OPTIPAV system two M&R operations were considered (Table 4).
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
Life-cycle cost analysis system for pavement management FERREIRA, Adelino; SANTOS, João
13th WCTR, July 15-18, 2012 – Rio de Janeiro, Brazil
7
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 4 – Maintenance and rehabilitation operations
Khogeli, W. and Mohamed, E. (2004). Novel approach for characterization of unbound
materials. Journal of the Transportation Research Board, Washington, D.C., USA,
1874, 38-46.
Life-cycle cost analysis system for pavement management FERREIRA, Adelino; SANTOS, João
13th WCTR, July 15-18, 2012 – Rio de Janeiro, Brazil
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Picado-Santos, L. and Ferreira, A. (2008). Contributions to the development of the Portuguese
road administration‟s pavement management system. Proceedings of the 3rd European pavement and asset management conference, Coimbra, Portugal, CD Ed., paper
1138.pdf, 1–10.
Randolph, N. and Gardner, D. (2008). Professional Visual Studio 2008. Wiley Publishing,
Inc., Indianapolis, Indiana, USA, 1-946.
Reddy, C. and Moorthy, N. (2005). Significance of bearing capacity of clayey subgrade in
flexible pavement design. International Journal of Pavement Engineering, 6 (3), 183-
189.
Santos, J. and Ferreira, A. (2011). Life-cycle cost analysis for pavement management at
project level. International Journal of Pavement Engineering, 1-14, Published online:
06 Oct 2011, DOI:10.1080/10298436.2011.618535,
http://dx.doi.org/10.1080/10298436.2011.618535.
Shell (1978). Shell pavement design manual - asphalt pavements and overlays for road traffic.
Shell International Petroleum Company Ltd., London, UK.
Sidess, A. and Uzan, J. (2009). A design method of perpetual flexible pavement in Israel.
International Journal of Pavement Engineering, 10 (4), 241- 249.
Tarefder, R., Saha, N., Hall, J. and Ng, P. (2008). Evaluating weak subgrade for pavement
design and performance predictions: a case study of US 550. Journal of