A simplified road user costs model for Portuguese highways

Proceedings of the Institution of Civil Engineers

http://dx.doi.org/10.1680/tran.12.00057

Paper 1200057

Received 19/06/2012 Accepted 14/02/2013

Keywords: management/mathematical modelling/roads & highways

ICE Publishing: All rights reserved

Transport

Refinement of a simplified road-user costmodelBatista dos Santos, de Picado Santos and PissarraCavaleiro

Refinement of a simplifiedroad-user cost modelj1 Bertha Maria Batista dos Santos PhD

Assistant Professor, Department of Civil Engineering andArchitecture, University of Beira Interior, Covilha, Portugal

j2 Luıs Guilherme de Picado Santos PhDProfessor, Department of Civil Engineering, Architecture andGeoresources, Instituto Superior Tecnico, Technical University ofLisbon, Lisbon, Portugal

j3 Victor Manuel Pissarra Cavaleiro PhDProfessor, Department of Civil Engineering and Architecture,University of Beira Interior, Covilha, Portugal

j1 j2 j3

Two Portuguese universities (University of Beira Interior and University of Coimbra) researched and developed a

simplified road-user costs model for inclusion in a pavement management system, as well as input data for

Portuguese trunk road networks, between 2004 and 2007. The model can be used to calculate the average road-user

costs in relation to vehicle operating, accident, time and toll costs. This paper describes the main activities that led to

the model formulation and the input data, and presents a new development to simplify user costs estimation

considering changes in pavement condition and the influence of road work zones. These scenarios can then be easily

and reliably utilised within the process of road maintenance and rehabilitation, evaluating the needs and

consequences of road intervention actions for consideration in the cost–benefit and life-cycle cost analysis. This

paper also confirms the importance of these additional costs through a model application to a Portuguese road

network under private concession, comparing average costs with those for specific work zones and pavement

condition scenarios.

NotationAADT annual average daily traffic (vehicles/day)

AC accident cost ((A/km)/day))

AC j accident j cost ((A/km)/vehicle))

ac j accident j cost (police time cost) (A/accident)

ANA annual number of accidents with casualties

(accidents/year)

ANA j annual number of accidents j (accidents/year)

ANCk average number of casualties k by accident

(casualties/accident)

AR j accident j rate ((accidents/vehicle)/km))

C total cracked pavement area (m2/100 m2)

CCk casualty k cost ((A/km)/vehicle))

cck casualty k cost (A/casualty)

Cdi vehicle depreciation cost for vehicle i (A/km)

Cfi fuel cost for vehicle i (A/km)

cfi fuel consumption for vehicle i (l/km)

Cmi maintenance cost for vehicle i (A/km)

Cmdti total depreciation market price for vehicle i (less

tyres) (A)

Cmfi fuel market price (gasoline or diesel) (A/l)

Cmmti total maintenance market price for vehicle i (A)

Cmti tyre market price for vehicle i (A/tyre)

Cti tyre cost for vehicle i (A/km)

ctolli toll cost for vehicle i ((A/km)/vehicle)

dCf incremental increase in fuel cost owing to

maintenance and rehabilitation (M&R) actions

((A/km)/day)

dVOT incremental increase in the value of time owing to

M&R actions ((A/km)/day)

EA annual exposure to accidents in sections and

intersections (total) ((vehicles km)/year)

FVOC,PSI VOC correction factor for a given PSI value

((A/km)/vehicle)

i vehicle class: i ¼ 1 for passenger car; i ¼ 2 for

utility; i ¼ 3 for heavy truck; i ¼ 4 for heavy bus

IRI international roughness index (mm/km for PSI

calculation)

j accident class: j ¼ 1 for accident with slight injury;

j ¼ 2 for accident with serious injury; j ¼ 3 for

accident with fatalities

k casualty class: k ¼ 1 for slight injury; k ¼ 2 for

serious injury; k ¼ 3 for fatalities

kmai annual average kilometrage for vehicle i (km/year)

1

L section length (km)

LM&R maintenance and rehabilitation zone length (km)

LPSI section length with a certain present serviceability

index (PSI) value (km)

m travel purpose: m ¼ 1 for travel in work time; m ¼ 2

for travel in non-work time

NAW national average wage ((A/h)/person)

NCk number of casualties k (casualties/year)

nti number of tyres for vehicle i

ORi,m occupancy rate for vehicle i and travel purpose m

(occupants/vehicle)

P pavement patching area (m2/100 m2)

PSI present serviceability index (0–5)

pi vehicle proportion for class i and AADT considered

R mean rut depth (mm)

RUC road-user cost ((A/km)/day)

RUCM&R road-user cost in maintenance and rehabilitation

zones ((A/km)/day)

RUCPSI incremental increase or decrease in RUC owing to

PSI ((A/km)/day)

RUCtotal total road-user cost ((A/km)/day)

S total pavement disintegrated area (with potholes and

ravelling) (m2/100 m2)

si average operating speed for vehicle i (km/h)

sM&Ri average operating speed in M&R sections, for

vehicle i (km/h)

TCm time cost for travel purpose m ((A/h)/occupant)

Toll toll cost ((A/km)/day)

tsli tyre service life for vehicle i (km)

VOC vehicle operating cost ((A/km)/day)

VOCi VOC for vehicle i (A/km)

VOT value of time ((A/km)/day)

VOTi value of time for vehicle i ((A/km)/vehicle)

VOTM&Ri value of time in M&R sections, for vehicle i

((A/km)/vehicle)

vsli vehicle i service life (years)

1. IntroductionA sustainable pavement system requires a comprehensive evalua-

tion framework that takes into account environmental, economic

and social indicators. The road-user costs are included in the social

class of indicators and can be defined as the costs experienced by

users when travelling along a certain length of a road. These costs

typically include costs related to the value of the travel time spent

by the driver and passengers, expenses of operating the vehicle and

costs of accidents. In some systems the costs of tolls and discomfort

are also considered. The sum of all or part of these costs (usually

the most significant) constitutes the road-user costs (RUC).

At this time the Portuguese Road Administration does not

consider the RUC in the evaluation process of road design,

maintenance or rehabilitation and therefore estimation of road life

cycle costs in Portugal, as in many other countries, does not

include this important aspect.

However, in road management, several RUC models with differ-

ent degrees of formulation and data requirements have been used

with good results around the world. Between 2004 and 2007

some of the most important ones were analysed to provide the

conceptual basis for a new simplified RUC model developed in a

doctoral thesis (Santos, 2007) and tested on the Portuguese trunk

road network (Santos et al., 2011a, 2011b).

The models considered in the definition of the conceptual frame-

work of the model were: the World Bank HDM-RUE – ‘Model-

ling road-user and environmental effects in HDM-4’ (Bennett and

Greenwood, 2004); the New Zealand vehicle operating cost

model (NZVOC) (Transfund, 2003); the Cost Benefit Analysis –

COBA (DfT et al., 2006a); the Manual ‘Techniques for manually

estimating road-user costs associated with construction projects’

used in the Texas department of transportation (TxDOT) (Daniels

et al., 1999); and the cost model integrated in the former

pavement management system (early 1990s) of the Portuguese

road administration (designated, at the time, as JAE – Junta

Autonoma de Estradas) (GEPA, 1995).

The review showed, as expected, that beyond the basic methodo-

logical approaches, there are three fundamental components of

RUC to be considered in an RUC model: vehicle operating costs,

accident costs and time costs. In general terms, this relationship

can be expressed as

RUC ¼ VOCþ ACþ VOT1:

These three main components, as well as a component related to

the tolling costs, were considered in the simplified RUC model

proposed in 2007. The model was developed aiming at simplicity,

reduced data requirements (selected data are usually available),

easy calibration, easy application and trustworthy results, provid-

ing average RUC values.

The main objective of this study is the refinement of the

simplified RUC model to fully integrate, in a sustained, simple

but reliable way, not only the average RUC but also the costs

related to the effect of work zones and pavement condition.

This improvement will enable a more realistic road cost analysis,

since these scenarios are not explicitly considered in the initial

formulation.

To sustain the refinements proposed, the paper presents

(a) a brief description of the main activities that led to the

original model formulation and input data definition

(b) an analysis to identify the critical parameters of the model

(c) a study of the approaches taken by some international

formulations, models and manuals in use such as ASTM,

HDM-4, TXDOT, NJDOT and TRB (ASTM, 1983; Bennett

2

Transport Refinement of a simplified road-user costmodelBatista dos Santos, de Picado Santos andPissarra Cavaleiro

Offprint provided courtesy of www.icevirtuallibrary.comAuthor copy for personal use, not for distribution

and Greenwood, 2004; Daniels et al., 1999; NJDOT, 2001;

The World Bank, 2010; Zaniewski, 1983)

(d ) the results and discussion of a case of application.

2. Road-user costs modelThe simplified road-user costs model proposed in Santos (2007)

was developed taking into account several main aspects: the

recognised conceptual principles; the application to trunk roads;

the impact of each component on the total user’s costs; the

availability of Portuguese official information; and four vehicle

classes as representative of the total traffic composition (passen-

ger car (PC), utility (U), heavy truck (HT) and heavy bus

(HB)).

The model framework adopted was essentially based on the

simplifications of the HDM-4 equations for the VOC, on the

COBA and the HDM-4 approach for the AC, and on the JAE

model and the HDM-4 equations for the VOT definition.

The results of all these considerations led to a model with the

three main cost components identified above: the VOC, including

costs for fuel, tyres, vehicle preventive maintenance and deprecia-

tion; the AC, considering costs for accident, police and medical

assistance for accident type and casualty costs (fatalities, serious

and slight injuries); and the VOT for work and non-work travel.

Eventually, when appropriate, a component related to tolling costs

may also be added.

The input values for the Portuguese average situation were

defined for 2006, the costs being updated in 2010. This definition

took into account the values used and recommended by the

existing methodologies and, in particular, the values obtained

from the Portuguese Road Haulage Association, companies and

official bodies such as ANTRAM (National Association of

Transportation of Goods), ANTROP (National Association of

Transportation of Passengers), INE (National Institute of Statis-

tics), the police and emergency services.

To validate the model, the Portuguese average values of the RUC

were computed with the proposed and reference models and the

results were compared (Santos et al., 2011a). The values obtained

confirmed that the contributions of the vehicle operation and the

value of time costs in total RUC for passenger cars (66% for

VOC and 34% for VOT) and heavy trucks (84% for VOC and

16% for VOT) are similar to those obtained in the reference

models. In terms of accident costs, no comparison study was

made because they usually comprise characteristic costs and

information from the network or section in analysis, so values for

different countries or even different regions of the same country

may be diverse.

The model was also tested with real data and for a real network.

The outcome was analysed by the network managers and accord-

ing to them the figures obtained were very acceptable.

The complete formulation of the model and the input data for

Portuguese conditions, which permit the calculation of average

values of the RUC, can be found in Appendix 1.

3. Sensitive parameters of the modelSeveral variability studies were carried out to identify the

sensitive parameters of the model. Tables 1 and 2 present some

results that show that the proposed model, as most of the existing

ones, is mainly sensitive to changes in the average operating

speed defined for each class of vehicle and type of road and to

consumption and fuel cost.

Besides being identified as critical parameters, speed and fuel

consumption and cost are also the main parameters in the

definition of the vehicle operating cost and the value of time, and

those that best reflect the main changes in the RUC due to

pavement condition and maintenance actions in the network

(work zones).

Thus, a careful consideration of these parameters in the RUC

calculations and the definition of correction factors in the values

Road type PC HT

Operating speed:

km/h

2/3 of operating

speed: km/h

˜VOT: % Operating speed:

km/h

2/3 of operating

speed: km/h

˜VOT: %

EN, ER 70 46.7 +50 50 33.3 +50

IC 80 53.3 +50 60 40.0 +50

IP 90 60.0 +50 80 53.3 +50

AE 120 80.0 +50 100 66.7 +50

PC, private cars; HT, heavy trucks; VOT, value of time; EN/ER, national and regional roads with two lanes (one in each direction) and ‘medium’design standards; IP and IC, main roads (principal and complementary roads) with two lanes (one in each direction) and ‘high’ design standards;AE, motorways with at least four lanes (two in each direction), median and ‘high’ design standards.

Table 1. Variability study for operating speed

3



defined for an average situation are essential to forecast additional

RUC in sections where maintenance actions are planned, or to

compute the benefits associated with a better pavement condition.

4. Additional RUC due to work zones andpavement condition

Additional RUC due to maintenance intervention periods (work

zones) and changes in pavement condition can be included in the

proposed RUC formulation by considering specific parameter

values defined for a certain maintenance strategy or for a

particular pavement quality index.

4.1 Work zones

The main parameters that can lead to additional RUC in work

zones have been identified in several models and manuals in use,

such as HDM-4, TXDOT and NJDOT (Bennett and Greenwood,

2004; Daniels et al., 1999; NJDOT, 2001), as being the decrease

of operating speed leading to traffic delays, which increases the

VOT, and the consequent additional fuel consumption associated

with traffic congestion, increasing the VOC values.

In the 2007 model, the speed values were defined for each type

of road based on posted speed limit and typical Portuguese values

(for each type of vehicle), and were considered constants. For

fuel consumption, average consumption by type of vehicle was

adopted.

Work zone additional accident costs are also considered in some

approaches, such as Quadro (DfT et al., 2006b), by comparing

work zone accident rates with those for normal conditions;

however, rates in work zones are not commonly available, so they

are not considered in the proposed simplified model.

Nonetheless, from the parameters identified, the most significant

influence on RUC values in work zones is changes in operating

speeds. For the refinement of the RUC model formulation, these

changes and the consequent additional travel time (delay) were

incorporated by the consideration of work zone length, duration

of interventions and work zone posted speed limit. This last

depends on the timing of restrictions (hours of the day and days

of the week) and the legal framework of each country, which

normally applies lower posted speed limits at night. The values

adopted for work zone speed (constant values by road class and

time with restriction) also reflect the operating characteristics of

the traffic affected and configuration of the work zones.

Regarding fuel consumption, data collected in several studies,

empirical models developed from this information (which usually

relate fuel consumption to the operating speed of vehicles) and

mechanistic models (which relate fuel consumption to the forces

opposing motion, allowing application under different conditions)

show that maximum fuel consumption occurs for low and high

speeds, and minimal fuel consumption for speeds of 40–60 km/h

(Bennett and Greenwood, 2004; DfT et al., 2006a) (see Figure 1).

Taking into account the patterns of fuel consumption presented in

Figure 1 and considering the Portuguese legal framework for

trunk roads with high posted speed limits (100–120 km/h and at

least two lanes in each direction), which limits the private road

concessionaires to guarantee maximum operating speeds greater

than or equal to 2/3 of the posted limit in work zones (up to

10 km per set) in the daytime (7.00 a.m.–9.00 p.m.), in this

period and situation there is actually a decrease in fuel consump-

tion.

Lower speeds, up to 1/3 of the normal posted speed limit, are

allowed in work zones during the nighttime, when the volume of

traffic is usually low.

VOC component Parameters ˜ ˜VOC: %

PC HT

Fuel +20% cf +8.0 +15.6

Tyre +25% tsl �0.9 �0.9

�25% tsl +1.4 +1.5

Preventive maintenance +20% vsl +0.07 +0.01

+25% kma �0.9 �0.04

�25% kma +1.6 +0.06

Depreciation +20% vsl 26.0 �1.3

+25% kma 27.8 �2.7

�25% kma +9.0 +4.4

VOC, vehicle operating cost; PC, private cars; HT, heavy trucks; cf, fuel consumption (l/km);tsl, tyre service life (km); vsl, vehicle service life (years); kma, annual average kilometres(km/year). The numbers in bold represent the most significant variations.

Table 2. Variability study for vehicle operating parameters

4



Taking into account the scenarios described, additional RUC in

work zones due to changes in fuel consumption were considered

for Portuguese national and regional roads, and eventually in

main roads with two lanes, operating at lower speeds (up to 1/3

of the posted speed limit). In such cases, in the daytime, there is

a high probability of frequent stops, resulting in an increased fuel

consumption associated with the movement at very low speeds.

For that reason, in this scenario, an increase of 20% in fuel

consumption was considered.

The choice of this additional consumption value is based on

representative PC vehicle manufacturer information that points to

urban fuel consumption values 20–30% higher than the combined

values (used for the definition of an average situation) and, for an

HT, the additional values of 30–40% that are commonly obtained

in fuel consumption models simulations such as those presented

above.

When traffic diversions are needed, changes in operating costs

and travel time should be considered in the same way as

described above.

The refinements proposed to consider the effects of the works

zones programmed in the RUC calculations are presented in

Equations 2–5.

RUCM&R ¼ dCf þ dVOT2:

dCf ¼ AADTX4

i¼1

(0:2 Cf ipi)

for sM&Ri<

1

3si and ER, EN

3:

dVOT ¼ AADTX4

i¼1

VOTM&Ripið Þ � VOT

4:

VOTM&Ri¼ 1

sM&Ri

X2

m¼1

TCmORi,mð Þ5:

This refinement was tested in order to evaluate, for several work

zone scenarios and Portuguese road classes, the influence of work

zones on unit RUC values (A/km), by vehicle (Teixeira, 2011).

The road classes considered were motorways (with at least four

lanes, median and ‘high’ design standards; AE), principal (IP)

and complementary (IC) main roads (with two lanes and ‘high’

design standards) and national (EN) and regional (ER) roads

(with two lanes and ‘medium’ design standards).

Some results can be observed in Figures 2 and 3. In these figures

the baseline scenario (range of 0%) represents the average unit

values of RUC for each vehicle class calculated with the initial

model formulation, and includes vehicle operating, travel time

and toll costs.

Through combined analysis of the charts and results and consid-

ering a typical traffic distribution of 80% for PC, 10% for U,

9% for HT and 1% for HB (based on traffic data provided by

road concessionaires and Portuguese average values), it can be

found that reducing the speed to 2/3 of the normal operation

speed without additional fuel consumption, during the daytime,

led to an additional cost of around 10% for motorways and 17–

20% for the remaining network. For a speed reduction to 1/3 of

0

2

4

6

8

10

12

14

16

0 20 40 60 80 100 120 140 160

Fuel

con

sum

ptio

n: li

tres

/100

km

Vehicle speed: km/h(b)

Fuel IRC empirical 1993

Fuel COBA empirical 2002

Fuel HDM mechanical Portugueseconditions 2006

0

2

4

6

8

10

12

14

16

0

Fuel

con

sum

ptio

n: li

tres

/100

km

Vehicle speed: km/h(a)

16014012010080604020

Fuel IRC empirical 1993

Fuel COBA empirical 2002

Fuel HDM mechanical Portugueseconditions 2006

Figure 1. Fuel consumption against vehicle speed for:

(a) passenger cars; and (b) heavy trucks

5



the normal operation speed, without additional fuel consumption

on motorways but considering an additional fuel consumption of

20% on the remaining network, at nighttime, the additional user

cost rises to 42% (motorways) and 74–85% (for the remaining

network). A combined analysis considering that road works take

place during the day and night periods, with a day/night

distribution of traffic equal to 85%/15%, leads to additional

costs of about 15% for highways and 25–30% for the remaining

network.

4.2 Pavement condition

Changes in operating speed and the consequent additional travel

time due to the pavement conditions can be incorporated into the

proposed model formulation through consideration of the section

length within a certain pavement quality index and lower operat-

ing speeds.

However, the pavement conditions of the most important net-

works, such as the national ones, do not in general reach a level

Day: 2/3 speed, without additional fuel consumption, without toll (II)

Night: 1/3 speed, without additional fuel consumption, with toll (III)

HBHTU

(I) (I)(I)

(I)

(II) (II) (II)(II)

(III) (III)

(III)

(III)

(IV)(IV)

(IV)

(IV)

�30·0�20·0�10·0

010·020·030·040·050·060·070·080·0

PC

ΔRU

C: %

Day: 2/3 speed, without additional fuel consumption, with toll (I)

Night: 1/3 speed, without additional fuel consumption, without toll (IV)

Figure 2. RUC variations on motorways for different scenarios

and vehicle classes (2010 unit values)

HBHTU

(I) (I)

(I)

(I)

(II)(II)

(II)

(II)

0

10·0

20·0

30·0

40·0

50·0

60·0

70·0

80·0

90·0

100·0

PC

ΔRU

C: %

Day: 2/3 speed, without additional consumption of fuel (I)

Night: 1/3 speed, additional consumption of fuel (II)

Figure 3. RUC variations on principal main roads for different

scenarios and vehicle classes (2010 unit values)

6



of degradation that significantly influences the normal operating

speed. On the other hand, it is also known that pavements in good

condition allow vehicles to maintain higher speeds with greater

comfort and security, reducing travel time and accident costs.

They also allow reductions in operating costs in terms of tyres,

maintenance and depreciation of the vehicle, but not necessarily

in fuel. The converse occurs for pavements in poor conditions.

To consider these scenarios, the condition of the pavements was

integrated into the initial RUC formulation only in the vehicle

operating costs calculations through a quality index representing

the functional and structural state of the pavements. The index

adopted was the ‘present serviceability index’ (PSI), which ranges

from 0 (for a pavement in a poor state) to 5 (for a new

pavement).

Equation 6 presents the PSI formulation adopted in the refine-

ment of the model. This equation was developed by Picado-

Santos et al. (2006) for the Portuguese trunk roads in order to

reflect the condition of the national road network and was used

by the Portuguese Road Administration during the first decade of

this century. The formulation is derived from the version used in

the pavement management system of the State of Nevada

(Sebaaly et al., 1996) and that developed during the AASHO

road test (HRB, 1962). Similar equations developed for and

representing other realities, can be incorporated in the model as

well.

PSI ¼ 5e�0:0002598IRI=2 � 0:002139R2

� 0:03 C þ S þ Pð Þ0:56:

The changes in VOC as a function of PSI (or IRI, the

international roughness index) have been treated in several stud-

ies by applying the regression analysis to real data, resulting in

several formulations such as those presented by HDM-4 (The

World Bank, 2010), TRB (Zaniewski, 1983), ASTM (ASTM,

1983) and by Picado-Santos et al. for Portuguese conditions

(Picado-Santos et al., 2006).

The study of these formulations, as well as an analysis of recent

data on Portuguese trunk road pavements condition (Picado-

Santos and Pereira, 2009) and average user cost (Santos, 2007),

was used to develop a mathematical model that reflects the

change of VOC as a function of PSI for Portuguese conditions.

Table 3 shows the set of correction factors that support the

proposed formulation (for PSI and IRI).

The range of PSI and IRI values was chosen to ensure that the

most extreme conceivable circumstances were examined as well

as the usual expected pavement conditions in operation. The range

examined was beyond values normally expected in Portugal.

In the range of values, ‘reference’ situation corresponds to the

current average state of Portuguese trunk road pavements, which

according to the latest available data presents a PSI of about 3.5

(Trindade and Horta, 2009), and the average vehicle operating

cost obtained by Santos (2007) for the same period. This scenario

constitutes the baseline with a correction factor of 1.

Given that the Portuguese road administration adopts a PSI equal

to or less than 2 as an indication of the need to intervene in the

pavement quality of the network, a correction factor of 1.05 was

defined for this scenario (based on the approaches studied). For

extreme scenarios a gain of 5% was considered for new

pavements and an increase of 15% for badly degraded pavements.

The analysis of the existing approaches and the characteristic

Portuguese values presented in Table 3 permitted the definition of

a new Portuguese VOC–PSI relation and thus the consideration

of this additional cost in determining the RUC, through Equations

7 and 8.

RUCPSI ¼ VOC FVOC,PSI � 1ð Þ7:

FVOC,PSI ¼ � 0:0006 PSI3 þ 0:0072 PSI2

� 0:0612 PSIþ 1:14988:

Figure 4 shows the curves obtained from the VOC correction

factors recommended by TRB-ASTM, the Portuguese model

(UC-UM) (Picado-Santos et al., 2006) and the proposed model

(RUC PT).

The aggregated correction factors presented in Figure 4 for the

TRB-ASTM approach were obtained by applying the Portuguese

VOC component distribution (for fuel, engine oil, tyres, main-

tenance and repair, and depreciation cost) obtained from data

collected in 2006 (Santos, 2007) to the disaggregated correction

factors recommended in the TRB-ASTM study. A similar proce-

dure was adopted for the distribution of traffic.

PSI IRI: m/km Correction factors for VOC

0 4.25 1.15

2.0 3.50 1.05

3.5 2.00 1.00

4.7 0.50 0.95

5.0 – 0.95

PSI, present serviceability index; IRI, international roughness index;VOC, vehicle operating cost.

Table 3. VOC correction factors, PSI and IRI for Portuguese model

calibration

7



From analysis of Figure 4 it can be concluded that the trend of

the proposed mathematical model is similar to those others

studied, even if the correction factors for the worst pavements are

smaller. This can be justified by considering technological ad-

vances in vehicles and the type of road network data used (trunk

road), where low PSI values are not common.

Analyses of changes in VOC with IRI were also carried out, since

most of the existing formulations use IRI as the main parameter

for the computed PSI and VOC variation in trunk road networks.

This analysis is presented in Figure 5, where it is possible to

observe the curves obtained from HDM-4 and JAE RUC values

when applying the models to typical Portuguese VOC component

and traffic distribution. A curve representing the quadratic equa-

tion obtained from the IRI values considered for Portuguese

calibration is also included.

For trunk roads and current values of IRI (up to 3.5 m/km), most

of the models tested produce similar results. Higher values of

IRI, such as those considered in HDM-4, are not frequent in

Portuguese motorway networks under concession.

When interpreting Figures 4 and 5, it is necessary to be aware

that the index adopted in the proposed model for the definition of

the VOC correction factor is PSI, in which the calculation

depends not only on IRI but also on the pavement’s superficial

degradation (such as rutting, cracking, potholes, ravelling and

patching).

Some results obtained by applying the proposed refinement to

motorways and principal main roads are shown in Figures 6 and

7, where the RUC variation due to the pavement condition (PSI)

is compared with the average values obtained from the initial

model formulation. The average RUC constitutes the reference

scenario and corresponds to a variation of 0%.

From the analysis of Figures 6 and 7 it is possible to observe that

for the PSI indicative of need for intervention on the quality of

pavements (PSI ¼ 2), the additional cost of RUC is about 3% (for

all vehicle classes).

5. Model applicationsThe RUC formulation and input model values proposed were

applied to two Portuguese motorway networks under concession

with good results: Scutvias (A23) and Aenor (A7, A11).

5.1 Presentation of results

Tables 4 and 5 include the data provided by the private road

concessionaire Scutvias, in order to perform the RUC calcula-

tions, and some application results.

0·8

0·9

1·0

1·1

1·2

1·3

0 1 2 3 4 5

VO

C c

orre

ctio

n fa

ctor

: %

PSI

UC_UM (aggregate)RUC_PT (aggregate)TRB_ASTM (aggregate)

Figure 4. VOC correction factors for different PSI values and

models

0·8

0·9

1·0

1·1

1·2

1·3

0 1 2 3 4 5

VO

C c

orre

ctio

n fa

ctor

: %

IRI: m/km

JAE90 (aggregate)

HDM-4 default(aggregate)

HDM-4 calibrate (aggregate)

RUC_PT (aggregate)

Figure 5. VOC correction factors for different IRI values and

models

�6·0

�4·0

�2·0

0

2·0

4·0

6·0

8·0

10·0

12·0

ΔRU

C: %

PC U HT HB

PSI 0� PSI 2� PSI 3·5� PSI 4·7� PSI 5�

Figure 6. RUC variations on motorways for different scenarios of

pavement condition and vehicle classes (2010 unit values)

8



5.2 Discussion of results

For average RUC values and comparing the results obtained from

the reference models (Bennett and Greenwood, 2004; DfT et al.,

2006a) and the proposed model (Santos, 2007), the main role of

the vehicle operation costs (approximately 60%) and the value of

time (approximately 20%) in total RUC is confirmed. Therefore,

knowing that the VOC is mostly influenced by pavement condi-

tion and the VOT by maintenance interventions (on a temporary

basis), a decrease in RUC can be expected when a pavement care

maintenance programme is applied, and at the same time a

reduction in the number of accidents.

It can be seen that toll costs also make a significant contribution

to RUC in a proportion similar to the value of time and that,

despite the small contribution of accident costs in the results

obtained for the networks analysed, this component will be more

significant in low to medium design standard roads. For that

reason they must also be considered in the calculations.

To validate the refinements proposed, the model was tested in a

maintenance (work zone) and pavement condition scenario, for a

unit section 1 km long, a speed reduction to 2/3 of the posted limit

(to 80 km/h), PSI equal to 2.0 and without deviations, according to

�6·0�4·0�2·0

02·04·06·08·0

10·012·014·0

ΔRU

C: %

PC U HT HB

PSI 0� PSI 2� PSI 3·5� PSI 4·7� PSI 5�

Figure 7. RUC variations on principal main roads for different

scenarios of pavement condition and vehicle classes (2010 unit values)

Data Scutvias (A23) 2010

Network length (km) 177.5

Total AADT 10 574

pia PC 0.7972

U 0.0648

HT 0.1289

HB 0.0091

Accidents With slight injury 59

With serious injury 10

With fatalities 2

Casualties Slight injury 88

Serious injury 15

Fatalities 2

Approximate toll cost (A/km) 0.20 (virtual tollb)

a Information processed from the traffic data provided by the roadconcessionaire.b The approximate toll cost values provided by Scutvias correspond toa uniform rate for all vehicle classes for 2006.PC, private cars; U, utility vehicles; HT, heavy trucks; HB, heavy buses.

Table 4. Data provided by road concessionaire Scutvias for 2010

Scutvias (A23) Scutvias (A23)

Average values Work zone (1 km) PSI ¼ 2.0 m/km

Costs RUC: (A/km)/day RUC: % RUC: (A/km)/day RUC: %

VOC 2613.90 58.41 2743.55 54.70

AC 90.72 2.03 90.72 1.81

VOT 822.30 18.37 1233.46 24.59

Toll 948.28 21.19 948.28 18.91

RUC 4475.21 100.00 5016.01 +12.08

The value in bold represents the additional RUC.

Table 5. Portuguese RUC model application results (2010 values)

9



the Portuguese legal framework described above for a main road

network with work zones operating during the daytime.

The total RUC obtained from this scenario considers the delay

costs (VOT changes) and additional non-fuel components cost,

resulting in an increase of 12% compared with the average values

of RUC. This additional cost can be disaggregated into about 9%

due to changes in VOT and 3% due to the pavement condition

and demonstrates the importance of taking work zones and

pavement condition into account in RUC calculations.

6. ConclusionThe fact that user costs do not debit agency budgets as agency

costs do, combined with uncertainty regarding some values (value

of time, effects of agency activities on accident rates), may

incline transportation decision makers to give less credence to

user costs than to their own agency cost, restricting their ability

to find the lowest total cost solutions.

Conversely many road-user cost models with strong concep-

tual frameworks have been developed in the past and are in

use. Nevertheless, many countries or regions that wish to

consider RUC in their road life-cycle costs analysis lack the

means to obtain and update all the data required for these

models.

The simplified road-user cost model proposed solves the problem

of the amount of information needed to calibrate models such as

HDM-4, and allows easy application for different scenarios. With

the refinements proposed to include the effect of pavement

condition and work zones, the average user costs as well as those

associated with maintenance and rehabilitation intervention peri-

ods can be considered over the life of the infrastructure using

simple models.

The pavement condition was included by defining correction

factors to be applied to the vehicle operating costs (non-fuel

components). These factors reflect a variation of the average

RUC between �3% (for PSI ¼ 5) and 9% (for PSI ¼ 0), with an

additional cost of about 3% for PSI ¼ 2 (level for the need of

intervention in the pavement).

The effect of work zones was incorporated by setting lower

average speeds along the work sections (2/3 of the normal speed

for work ongoing during the daytime and 1/3 for nighttime) and

an additional fuel consumption of 20% for roads with ‘medium’

design standards operating at lower speeds (up to 1/3 of the

normal posted speed limit). When applied to the Portuguese road

network, for daytime works, these considerations result in an

additional cost of approximately 10% for motorways and 17–

20% for a two-lane type of network. For nighttime works, an

additional cost of 42% for motorways and 74–85% for a two-lane

type of network was obtained.

The scenarios tested show that in most cases of intervention the

user costs associated with work zones may increase significantly

and are higher than those due to pavement condition. The work

zone additional costs depend mainly on day/night operating speed

and traffic distribution and pavement condition must be main-

tained above PSI ¼ 2 to minimise additional RUC.

Although the additional user cost due to work zones is established

as the most significant factor, it is recommended that the effect of

pavement condition also be incorporated in the analysis. The

inclusion of this effect is justified in order to identify, from a user

cost perspective, the best time to perform the maintenance and

rehabilitation works to improve the pavement condition.

As a result, a simplified but trustworthy model such as the one

developed for the Portuguese trunk road network can help

decision makers to include user costs in life-cycle cost analysis

(LCCA). This will permit a more accurate technical and econom-

ic planning of the maintenance and operation actions and thereby

achieve optimal solutions.

Appendix 1

A1.1 Road-user cost model

A1.1.1 Model formulation

RUCtotal ¼ RUC 3 Lð Þ þ RUCM&R 3 LM&Rð Þ

þ RUCPSI 3 LPSIð Þ9:

RUC ¼ VOCþ ACþ VOTþ Toll10:

VOC ¼ AADTX4

i¼1

VOCi pið Þ11:

AC ¼ AADTX3

j¼1

ACj þX3

k¼1

CCk

0@

1A

12:

VOT ¼ AADTX4

i¼1

VOTi pið Þ13:

Toll ¼ AADTX4

i¼1

ctolli pið Þ14:

10



Considered by vehicle class

VOCi ¼ Cf i þ Cti þ Cmi þ Cdi15:

Cf i ¼ cf i Cmf i16:

Cti ¼ nti Cmtið Þ=tsli17:

Cmi ¼ Cmmti= vsli kmaið Þ18:

Cdi ¼ Cmdti= vsli kmaið Þ19:

Data PC HT

Representative vehicle Car medium Truck articulated

Average operating speed (km/h) EN/ER IC IP AE EN/ER IC IP AE

70 80 90 120 50 60 80 100

Vehicle service life (year) 10 12

Annual average kilometrage (km/year) 20 000 85 000

Occupancy rate (occupants/vehicle) 2 (1 work driver + 1 non-work

passenger)

1 (1 work driver)

PC, private cars; HT, heavy trucks; EN/ER, national and regional roads with two lanes (one in each direction) and ‘medium’ design standards; IPand IC, main roads (principal and complementary roads) with two lanes (one in each direction) and ‘high’ design standards; AE, motorways withat least four lanes (two in each direction), median and ‘high’ design standards.

Table 6. Passenger car and heavy truck general input data values

Data PC HT

Fuel Gasoline: 5.9 litres/100 km Diesel: 44.0 litres/100 km

Diesel: 4.8 litres/100 km

Market price (31/12/2010): Market price (31/12/2010):

Gasoline 95: A1.485/litre Diesel: A1.270/litre

Diesel: A1.270/litre

Tyres nt ¼ 4 tyres/vehicle nt ¼ 12 tyres/vehicle

tsl ¼ 40 000 km tsl ¼ 200 000 km

Market price: A75/tyre Market price: A490/tyre

Preventive maintenance A1626/10 years A28 920/12 years

Depreciation A17 720/10 years A87 135/12 years

Value of time A6.93/h (work time) A9.61/h (work time)

Accident costs: A/accident Accident type With light injuries With serious injuries With fatalities

Police assistance 57.5 160.0 250.0

Medical assistance 18.0 103.50 103.5

Casualties costs (A/casualty) Light injuries: A40 000/casualty

Serious injuries: A90 000/casualty

Fatalities: A500 000/casualty

Toll cost A0.075/km A0.185/km

PC, passenger cars; HT, heavy trucks; nt, number of tyres per vehicle; tsl, tyre service life.

Table 7. Passenger car and heavy truck input data costs (2010

values)

11



VOTi ¼1

si

X2

m¼1

TCm ORi,mð Þ20:

TCm¼1 ¼ NAW21:

TCm¼2 ¼ 0:25 NAW22:

And for the set of all vehicle classes (without vehicle class

disaggregation)

ACj ¼ ARj acj23:

CCk ¼ ANCk cckð ÞX3

j¼1

ARj

24:

EA ¼ 365 AADT L25:

ARj ¼ ANAj=EA26:

ANCk ¼ NCk=ANA27:

A1.1.2 Input data for Portuguese conditions

Tables 6 and 7 present the input data defined for passenger cars

and heavy trucks. A similar process was used for the utility and

heavy bus values.

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A simplified road user costs model for Portuguese highways

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