1

A Model for Pavement Design and Management Based on the

AASHTO Guide and HDM Regressions

Paper submitted to the Transportation Research Record

Prof. Rgis Martins Rodrigues (Aeronautics Technological Institute, ITA, Brazil)

ABSTRACT

This paper describes the technical base of the performance prediction model that is at the core

of a pavement management system developed for Brazilian highways, which main feature is

to reduce to a minimum a major shortcoming of existing systems: the usually great

discrepancy between maintenance solutions and costs established for planning purposes at

network level and the ones that are effectively detected after studies are made at the project

level. This was accomplished through close attention to the pavement structure-traffic

interaction feature of the performance prediction model that is employed in the system. For

this purpose, a generalization of the 1986 AASHTO Guide model was developed, introducing

long-term pavement performance effects through the use of World Bank HDM-III empirical

models. Application of the model to a set of independent pavement performance cases gave a

strong support for its reliability. It was also possible to extend the applicability of this model

to airport pavements, since its results are in good agreement with FAA design procedures and

USACE models.

Key words:

Highway pavements airport pavements pavement design and management

1 - Introduction

At network level, when a Pavement Management System (PMS) applies performance

prediction models, they are usually of a simplistic nature, due to the requirement of keeping

the monitoring of field data at low costs per kilometer. Besides, several systems attempt only

to detect, at one side, the pavement segments where minor maintenance measures can be

applied and, at the other side, the ones where a major rehabilitation should be scheduled. In

2

these versions of a PMS there is no need for truly reliable performance prediction models at

network level, but the usefulness of such systems is severely restricted to prioritization of

maintenance interventions at a moment when filed monitoring data are available. Nothing can

be done about multi-year planning and budget analyses. For these, remaining life estimates are

a critical requirement.

On the other hand, experience with a PMS applied to several highway networks in

Brazil led to the need for performance models that go further: they should have the capability

to anticipate structural needs that will not be grossly over- or underestimated when

rehabilitation designs are performed at project level. A complete agreement between network

and project level solutions is impossible, since additional factors must be taken into account at

project level, such as localized environmental (climatic, drainage, pavement geometry) and

traffic conditions, pavement history and detailed pavement condition and layers materials

mechanical properties. However, when managerial characteristics impose the need for a good

agreement between these two levels of decision, the performance models to be applied at

network level must have adequate accuracy to deal properly with structural parameters (traffic

loads and their interaction with the pavement structure). This is particularly important in

Brazil due to the broad range covered by the bearing capacities of highway pavements, with

major extensions of highways operating, due to budget constraints, with relatively thin

pavements under heavy traffic loading conditions.

In fact, applications of the World Bank HDM system in Brazil have been deemed to

failure due to misconceptions on its use. Instead of running the program only for pre-selected

strategies, generated after sound technical considerations have been made regarding pavement

performance, strategies were implemented based solely on least initial cost and the resulting

expected benefits due to vehicle operation costs decrease. This led, for example, to thin

resurfacings applied over severely cracked pavements without anti-reflection cracking inter-

layers, or to thin overlays applied to structures experiencing bad performance due to excessive

plastic strains developing in the layers below the surfacing layer. Besides, lack of a proper

consideration regarding traffic-structure interaction by the empirical correlations on HDM led

to false expectations about rehabilitated pavement service lives under the use of these thin

overlays. Such experience highlights the importance of a PMS with sound performance

prediction models and reliable decision trees for the detections of pavement maintenance

needs.

The PMS here mentioned has been in use for over 14 years, mainly for the following

purposes:

3

(a) For budged estimates in the near future, and sometimes at longer analysis periods;

(b) As an aid in rehabilitation designs at project level, furnishing diagnoses, maintenance

solutions and pavement and traffic data;

(c) On special studies, so that ones involving simulations of different performance

patterns required for the pavements on the network and the costs associated with the

attainment of these patterns;

(d) As a tool for designs made before an actual design at the project level is conducted, so

that a fast and reasonable estimate of rehabilitation needs can be obtained, as well as to

avoid gross mistakes at project level.

Pavement construction and its subsequent maintenance involve consumption of precious

natural resources and of energy. To avoid a wasteful use of these resources is a central task for

any PMS, which requires truly reliable pavement performance prediction models in order to

optimize the allocation of limited funds to the purpose of maintaining an adequate service

level for the highway users.

The final purpose of a PMS is the discovery of the most effective pavement

maintenance strategy, for which a measure of the relative efficacy of different strategies is

required. A parameter to be maximized on a pavement construction or rehabilitation strategy

is the Benefit-cost Ratio (BCR) associated with the investment, which can be defined as:

[1]

where PSIav is the average pavement serviceability and Ceq is the equivalent uniform annual

maintenance cost, associated with the investment during its service life (Lf), or:

[2]

Such a definition for BCR allows the comparison to be made of different design periods

(Lf) and different standard levels for pavement performance (PSI0 and PSIt on Figure 1) so

that the most efficient solution can be found.

eq

av

CRC

PSIB =

f

eq

L

f

av

L

COSTC

dttPSIL

PSI

f

=

= 0

)(1

4

The achievement of a certain pavement performance is not, however, a certainty, due

to the stochastic nature of pavement behavior. Each design has its proper reliability level (RL),

which represents the probability of the outcome expressed by PSIav. Therefore, the best

solution is the one that maximizes the Expected Utility, defined by:

[3]

The maximization of this parameter involves the application of reliable models for the

prediction of pavement performance in relation to its reliability level.

Figure 1 Serviceability with time for a pavement investment

2 Development of the Performance Prediction Models

Based on the previous discussion, the following characteristics were judged useful for the

performance prediction models:

(1) The models must be able to describe the long-term performance of highway

pavements;

(2) The interaction between pavement structure and traffic loads must be accurately dealt

with;

(3) Inputs for the model should be the data usually available from network monitoring

programs;

PSI

PSI0

t 0

PSIt

Lf

eq

av

LCRLrUC

PSIRBRUpE ===

5

(4) The models should be easily calibrated, so that remaining life estimates could be

made using pavement past performance;

(5) Pavement condition should be adequately and easily described, as well as its

modification through pavement maintenance or rehabilitation;

(6) Due consideration must be given to the stochastic nature of pavement performance, so

that a desired reliability level for the performance predictions can be established as a

fundamental parameter for the conception of a maintenance strategy.

Existing performance prediction models aimed at pavement management applications,

such as the HDM models (Paterson, 1987), have limited applicability due to their empirical

nature and their close association with a limited set of field data. They have, however, the

advantage of being able to describe long-term pavement performance. On the other side, a

design model such as the AASHTO Design Guide (1986 or 1993) is strong at describing

traffic-structure interaction, but is not compatible to long-term pavement performance effects,

due to the accelerated nature of the AASHO Road Test (1958-1960), since layers material

properties change continuously with pavement age, so that strength parameters may increase

by 50% ten years after construction (Croney and Croney, 1991). Therefore, the procedure here

adopted for the development of the performance prediction models was to associate these two

powerful models, avoiding their shortcomings and using their strengths.

The present condition of a pavement can be described in a comprehensive manner by

the use of three indicators:

(a) A serviceability parameter, related to user riding comfort and vehicle operation costs;

(b) A pavement distress index, useful as a gauge to anticipate pavement maintenance

needs and to keep the risks of a sudden pavement failure under control;

(c) Security related indexes, so that the ones related to directional control (hydroplaning

potential), breaking distance (friction on wet surfaces) and obstacles (potholes,

surfacing disintegration).

The third set of indicators should be addressed through proper network monitoring of

the pavement surface condition, whereas the first two are affected by traffic-structure

interaction, so that they will be the ones addressed in this paper for development of

performance prediction models.

6

The first parameter can be the AASHTO Present Serviceability Index (PSI). Use of the

PSI has the advantages of being linked to a sound model describing the traffic-structure

interaction, present at the 1986 or 1993 AASHTO Guide for Design of Pavement Structures,

and of being in a close relationship with riding comfort, as expressed by:

= 5.715QI

ePSI

[4]

where QI is the Quarter-Car Index, in counts per km, that measures longitudinal roughness

(QI = 13IRI, where IRI is the International Roughness Index, m/km). This correlation was

derived in a World Bank experimental study (Paterson, 1987).

The second parameter should be a function of the nature, extent and severity of

pavement distresses, as given by a Surface Condition Index (SCI), which will be here defined

on the same scale of the PSI, from 0 to 5, and with the same meaning regarding their

respective levels, as shown in Table 1.

Table 1 Scale for the PSI and the SCI

Range Pavement Condition

4 5 Excellent

3 4 Good

2 3 Regular

1 2 Bad

0 1 Very bad / Pavement failure

For this purpose, the SCI was determined from a relationship with a global distress

index known as the IGG, Global Gravity Index, (Pereira, 1979), given by:

[5]

The IGG is thus determined from the nature, extent and severity of the existing surface

distresses, as the summation of the products of the corresponding frequency (fi) versus

weighing factor (pi) of the n existing defects. Table 2 shows these weighing factors as used in

IGG

IGGSCI

+

=844,61

616,022,309

=

=n

i

ii pfIGG1

7

Brazil. A close relationship exists between this parameter and the USACE Pavement

Condition Index: PCI = -2.7E-6 * (IGG ^ 3) + 0.0025 * (IGG ^ 2) - 0.8109 * IGG + 100.

Table 2 Weighing factors for the IGG (Pereira, 1979)

Distress Type Code fi pi Low severity cracks FC-1, TRR fi 0.2

Raveling D fi 0.3 Average Rutting RD 1.33 RD mm ( 30 mm)

Medium severity cracks FC-2, TB fi 0.5 Rutting Variance RDV Variance ( 50 mm

2)

Bleeding EX fi 0.5 Repairs R fi 0.6

High severity cracks FC-3, TBE fi 0.8 Depressions ALP, ATP fi 0.9

Potholes and Corrugation P, O fi 1

A model for roughness progression can be written in terms of traffic, expressed as the

number of accumulated standard 80 kN axle loads N until pavement age t is reached, as:

N

0eIRI)N(IRI=

[6]

where is a function of the pavement structural strength and of the environmental conditions

(climate, geometry, drainage). In this model, the product N expresses the traffic-structure

interaction, which controls the increase of IRI with time. IRI0 is an intercept at pavement age

equal to zero and is nearly equal to the initial pavement roughness. This functional shape is

supported by several pavement performance data (see, for example, Figure 2), especially

during periods of time when IRI > 0.5 m/km. For the initial years after construction or

rehabilitation, a linear rate of growth establishes after the short term consolidation, but an

exponential rate of growth is the norm as pavement deterioration advances with pavement

age, so that the function of equation [6], with only two parameters, is adequate for practical

purposes.

Merging equations [4] and [6] leads to:

( )NPSIPSINPSI

exp0

55)(

=

[7]

8

y = 0.6231e0.0853x

R2 = 0.9962

2

3

4

5

15 17 19 21 23 25

Age (years)

IRI (m/km)

Section SHRP_ID = 3005, STATE_CODE = 6

y = 0.798e0.0225x

R2 = 0.8404

1.00

1.05

1.10

1.15

1.20

1.25

11 12 13 14 15 16 17 18 19

Age (years)

IRI (m/km)

Section SHRP_ID = 1001, STATE_CODE = 4

y = 0.0682e0.2524x

R2 = 0.9258

1.0

1.5

2.0

2.5

3.0

3.5

11 12 13 14 15

Age (years)

IRI (m/km)

Section SHRP_ID = 1002, STATE_CODE = 25

Figure 2 Sections from LTTP DataPave 3.0

9

with PSI0 being the initial pavement serviceability index. The functional shape of equation [7]

has all the desirable features surrounding parameter PSI evolution with time, as revealed by

long-term pavement performance data, a critical feature on any reliable performance

prediction model (Lytton, 1987). Similarly, a hypothesis will be launched here involving the

practical applicability of writing:

( )NSCISCINSCI

exp0

55)(

=

[8]

where SCI0 is the initial (new or newly rehabilitated pavement) Surface Condition Index. Up

to this point, nothing can prove the validity of equation [8], but as will be shown here its

calibration to several pavement data bases has been possible with an acceptable degree of

accuracy.

Besides, this functional shape has the advantage of being associated with a recursive-

incremental type of performance prediction model, since it can be rewritten, in differential

form, as:

[9]

The rate of change of the PSI with traffic (PSI/N) is entirely a function of the

present condition (PSI) and of the structural parameter (PSI). This has a clear convenience on

PMSs, since the present condition can be updated from field monitoring data, increasing the

performance prediction reliability for subsequent years.

In equations [7] and [8], if the structural parameters PSI and SCI are known, then

future performance of the pavement can be predicted. In this respect, emphasis must be given

to the determination of how these values vary with pavement structural parameters.

The AASHTO Design Guide (1986) model can be applied in the context of

determining parameter PSI, since it was derived from a test especially designed to evaluate

the traffic-structure interaction. The AASHTO model is not, however, reliable as a

performance prediction model, due to the accelerated nature of the AASHO Road Test, where

long-term effects could not be evaluated. Therefore, this model will be here applied

exclusively with the objective of arriving at a nominal pavement traffic bearing capacity,

leading to a first estimate of the parameter, capable of including in the prediction process

=5

lnPSI

PSINPSI PSI

10

the key variables related to pavement structure and traffic loads. Long-term second order

effects will be taken into account after these key effects are included in the model. In this

respect, the AASHTO design model will be here applied in the same context as it is intended

for in The AASHTO Guide (1986): to furnish an estimate of the accumulated traffic that is

required for a pavement global serviceability loss from a new pavement condition (PSI0) until

pavement failure (PSIf), when a rehabilitation, such as a major asphalt concrete overlay,

will be needed. Therefore, the first estimate of the parameter, as given by the AASHTO

Guide, will be:

=

5

5.2ln

5ln

ln1

0

18

PSI

WA

[10]

where W18 is the 18 kips single axle load accumulated number of repetitions associated with a

condition change from PSI0 to PSIf = 2.5. According to the 1986-1993 AASHTO Design

Guide, in the case of asphalt pavements:

[11]

where SN (= aihi) is the pavement Structural Number for the layers above a certain layer,

MR is the roadbed resilient modulus of this layer (MR < 40,000 psi or 280 MPa) and PSI0 is

the initial Present Serviceability Index. ZR and S0 parameters deal with the stochastic nature of

pavement performance and with the desired design reliability level.

With the most important variables already included in the model by this process

(equation [11] for PSI and the AASHTO load equivalency factors for N), it is time now to

deal with long-term effects, environmental conditions and other factors not included through

the use of equations [10] and [11]. This will be done by defining a calibration factor FC

applied to the parameter, or:

APSI Fc = [12]

( )

( ) 19.5

32.21

0

36.9

18

1

109440.0

30005.12.4

5.2

0512.1

110 0

++=

+=

SN

psi

MPSISNW R

SZR

11

A major effort in this research was at establishing the functional dependence of FC on

its controlling variables. The performance prediction model here proposed can be considered

reliable only if patterns can be identified of FC variation with environmental (climatic,

geometric, drainage) and construction (materials, construction quality and construction

processes) conditions.

3 Calibration from HDM Models

The HDM-III models (Paterson, 1987) are good predictors of long-term pavement

performance, as revealed by several studies, such as the one by Rodrigues (2009), who

applied and recalibrated these models using data from 8,000 km of highways in Brazil.

Changes had to be made on some models, such as in the case of prediction of the first cracks

appearance on overlaid pavements. One of HDM models for such prediction is:

( )42 0141,00157,0exp54,2 PCRHTY Rcr = [13]

where:

HR = HMAC overlay thickness (mm);

PCR4 = percent area cracked of the old pavement (AASHTO Class 4).

This formula has a serious drawback, as it does not include two central parameters in

the process: traffic and pavement deflections. Due to this, the model that actually is applied on

HDM-III is:

( )0402 02,121,1exp8,10 DYEDTYcr = [14]

where D0 is the pavement deflection under the 80 kN standard axle load (in mm) and YE4 is

the annual traffic rate, in 106 equivalent 80 kN axle loads.

In order to incorporate both these models, it can be written:

)5.11(

)5.10.1( )14.(2)13.(

2

2 +

+=

eq

cr

eq

cr

cr

TYTYTY

[15]

12

as revealed by applications of these models to several Brazilian highways. Such model will

allow consideration of the presence of anti-reflective cracking interlayers, since in this case it

will be possible to state PCR4 = 0 for interlayers capable of filling the upper part of the most

severe pavement cracks. These models were developed for the following set of parameters:

50 HR 125 mm

4 Age 16 anos (pavement age at the time of rehabilitation)

0,02 YE4 1,59

For the prediction of the pavement age in years (TYcr2) at the first crack appearance at

the pavement surface on flexible pavements:

=2

42 1,17139,0exp21,4

SNC

YESNCTYcr

[16]

where SNC is the structural number corrected for subgrade bearing capacity:

43,1log85,0log51,3 21010 += CBRCBRSNSNC

[17]

The HDM models for rutting and raveling prediction were applied directly, without

any corrections. That was also the case for the longitudinal roughness progression (Paterson,

1987):

( ) ( ) ttIRIVPOTPATHCRRDNESNCetIRI Pt +++++= 023.016.0003.00066.0114.0134 40.5023.0 [18]

where:

IRI(t) = International Roughness Index at year t (m/km);

t = pavement age since construction or last rehabilitation (years);

NE4 = traffic rate during the time interval t, expressed in 80 kN axle loads

repetitions, in millions;

IRI = increase in the pavement longitudinal roughness (m/km) during the time

interval t (years);

RD = increase in rut depth during the time interval t (mm);

13

CR = increase in surface cracking during the time interval t (% of area cracked with

high severity cracks);

PAT = increase in the area with patching, with mean depth or elevation equal to HP

(mm), in percent area of the pavement;

POT = increase in volume of potholes during the time interval t (m3).

The HDM-III models have several shortcomings as true performance prediction

models, especially when considering their narrow experimental base and lack of mechanistic

considerations, both leading to a loss of prediction power. The effects of a change in thickness

of the asphalt concrete surfacing layer are not properly dealt with by such models, since its

increase only slightly increases pavement service life as predicted by them. Therefore, these

models were here applied only for a selected set of reference conditions, chosen to represent

the experimental data base. It is believed that, for such conditions, the models predictions are

not biased and will reflect the life expectancy under those conditions. This procedure is a need

dictated by the purely empirical nature of HDM models and from the fact that they employ

only few data parameters for the consideration of traffic loading and pavement structure

effects on pavement performance. Because of this, the models are too simplistic to reliably

describe reality, leading them to suffer from a fundamental lack of accuracy to consider the

effects of variations of pavement materials mechanical properties and of pavement layers

thicknesses on pavement performance. Therefore, HDM models can be trusted as a source of

reliable long-term pavement performance data only for pavement sections with similar

characteristics of the ones that comprised the data base that was used in the regression

analyses that led to those models. These data refer to pavements situated on Brazilian

highways, which were designed using the DNER Method (DNIT, 2006), a version of the

original USACE-CBR method. This method requires a total pavement thickness in terms of

granular base materials as given by:

( )H cm NCBR

T P( ) , , log , ,= + +

9 02 0 23 0 05

7011234 3310

12

[19]

for the pavement to support NP equivalent 80 kN single axle load repetitions for a subgrade of

bearing capacity described by its CBR value. Besides, Table 3 shows the minimum surfacing

layer thickness required by the method and this thickness must be converted to equivalent

14

granular base layer thickness using a coefficient equal to 2, so that: HT = 2h1 + h2 + h3 for the

total pavement thickness of a section with surfacing (h1), base (h2) and sub-base (h3) layers.

Table 3 Minimum surfacing layer requirement on DNER Method (DNIT, 2006)

NP (USACE load equivalency factors) Surfacing Layer

106 Surface treatments

106 < NP 5 10

6 5 cm of asphalt concrete

5 106 < NP 107 7,5 cm of asphalt concrete

107 < NP 5 10

7 10 cm of asphalt concrete

NP > 5 107 12,5 cm of asphalt concrete

The resilient modulus of the subgrade soil will be given by: E4 = 10 CBR (MPa). For

the granular base layer (crushed stone), the Shell formula was applied for estimating the

resilient modulus E2, as given by:

[20]

for the base thickness (h2) in mm. The granular subbase modulus E3 was estimated as the

average value from equation [20], E3 = 0.2h30.45

E4, and E3 = 5 CBRSB(MPa).

It was also required that the selected pavement sections met a maximum deflection

under the 80 kN axle load as expressed by: Dmax (0.01 mm) = 10(3.01-0.176logNp)

, which is also a

part of DNER method for pavement design and evaluation.

These cases were also selected imposing the condition that fatigue life, associated with

percent area cracked TR = 20%, was around (70 to 125%) the pavement service life, defined

by a terminal condition given by PSIt = 2.5 for low traffic conditions, 2.7 for medium ones

and 2.9 for high traffic volumes. This was considered to be a normal requirement to be met by

a well balanced pavement structure. Fatigue life was calculated using equation [16] plus 4

years for a condition given by TR = 20% area cracked. This condition was employed to find

the calibration factor Ff for the following mechanistic-empirical model:

TAI

fthickff NFFN =

[21]

where NfTAI

is the MS-1 (1982) fatigue equation from The Asphalt Institute and Fthick is equal

to 1 for HMAC surfacing thicknesses h1 7 cm and Fthick = (h1/10)2 for h1 < 7 cm. Dynamic

45.0

2

3

2 2.0 hE

E=

15

modulus of the asphalt concrete was calculated from T.A.I. dynamic modulus formula for

traffic speeds at 90 km/h and surfacing layer average temperature of 770F, and the maximum

tensile strain under the HMAC layer was given by:

max11

2

1

31

2

1

2

1

52

42

323

1

2

10

ln3187476.0ln10651531.44698504.0250563.9ln

ln1500

1500

DEhh

E

E

h

hR

RaE

ar

haa

Eaa

flex

flex

flex

t

++=

=

+

+

++

+=

[22]

with:

r2 = 0.894 (coefficient of determination)

SE = 2.684586 10-5 (standard error of estimate)

SE/SY = 32.6% (SY = standard deviation of the dependent variable)

a0 = -3.8853 10-5 a1 = 1.093891 a2 = -9.543262 10

-2

a3 = 1.411541 10-5 a4 = 2.545568 10

-7 a5 = 3.507885 10

-5

E1 = modulus of elasticity of the asphalt concrete surfacing layer (kgf/cm2)

E2 = resilient modulus of the base layer (kgf/cm2)

h1 = surfacing layer thickness (cm)

h2 = base layer thickness (cm)

Dmax = vertical pavement deflection under the 80 kN axle load (10-2 mm)

r = 10.8 cm = radius of the loaded area under one wheel of the 80 kN dual wheel axle

load.

for a total of 2647 data cases generated using FLAPS program (Finite Layer Analysis of

Pavement Structures), which was applied for the combinations:

h1 = 3 6 9 12 15 cm

h2 = 5 10 15 20 30 cm

E1 = 40000 60000 80000 100000 150000 kgf/cm2

E2 = 1500 5000 10000 30000 90000 kgf/cm2

Ef = 500 1000 2000 3500 7000 kgf/cm2 = foundation elastic modulus,

comprised of subbase and subgrade layers.

16

Considering a set of pavement sections that were generated according to this

procedure, Table 4 shows the resulting calibration factors required in order that the model

here proposed could reproduce pavement performance as described through HDM empirical

models. Three values for FC were calculated, each corresponding to the pavement layer with

resilient modulus MR above which the structural number SN was computed for use on

equation [11]. The low variability of the Fcs values indicate that the calculated average are

representative enough of the 16 selected cases to be taken as the calibration factors to be

applied for pavement design and analysis. A value for Fc = 1.89 can be taken, irrespective of

the way the pavement structure is described in the model.

The FC values on Table 4 were determined so that the empirical performance predicted

using HDM-III models could be nearly replicated for the analysis considering the whole

pavement structure supported by the subgrade soil with resilient modulus given by: MR = 10

CBR (MPa). The other two analyses were conducted with a generalization of the MR

parameter to be used on equation [11]:

( )2

10 CBREM

eq

R

+=

[23]

for Eeq and MR in MPa, with Eeq being the equivalent elastic modulus of the foundation that

supports the structure with Structural Number SN (subbase and subgrade layers if SN =

a1h1+a2h2, layers below the surfacing one if SN = a1h1). For the subgrade analysis nothing

changes, since MR = Eeq = 10CBR.

The equivalent modulus Eeq(i) of the system comprised of the layers situated from layer

i and below was calculated using the formula for the semi-infinite elastic half space:

( )( )

( )

( ) ( ) ( ) ( )

++

+

+=

R

h

R

h

R

h

pRE

ieq

i

ieq

i

ieq

i

iieq

21121

1

112

12

2

12

[24]

17

where i is the vertical deflection under the center of a circular applied load (of pressure p and

radius R) at depth heq(i), which is the equivalent thickness of the pavement layers situated

above layer i, of Poissons ratio i. Using Odemarks method:

( )( )( )

=

=

1

1

31

2

2

1

1i

j j

i

i

j

jieqE

Ehh

[25]

The vertical deflection on top of the subgrade can be calculated directly from equation

[24], using the soil resilient modulus for Eeq. For the other layers:

( ) ( )( )2

1

111

iviv

i

ii

i

iiiiiii

E

h

Ehh

++=+=+= ++++

[26]

where the vertical compressive stress on top of layer i is given by:

( )

( )

+

=2

32

1

11

ieq

iv

h

R

p

[27]

Table 4 also shows that it was possible to calibrate equation [21] using Ff = 0.57 to

predict the first cracks appearance at the pavement surface, and using Ff = 1.15 for the

condition given by TR = 20%. The selected reference pavement sections have average fatigue

life Vf, associated with TR = 20%, nearly equal to the service life VS, defined in terms of a

terminal condition for the PSIt = 2.7 under medium traffic conditions. Under light traffic

conditions, PSIt was chosen to be 2.5 and Vf/VS 1.3, whereas under heavy traffic conditions:

PSIt = 2.9 and Vf/VS 0.7. This assures consistency between performance in terms of both

parameters, since it is expected that the increase in commercial traffic will lead to more

fatigue cracking.

18

Table 4 Results for PSI prediction on new asphalt pavements

Case

Ff eq. [21]

Ff for TYcr2

Vf/VS

Nyear (AASHTO)

Subgrade CBR

VS (years)

Fc Subgrade

Fc Subbase

Fc Base

1 0.500 0.285 1.91 5.0E+05 10 11 1.850 2.297 2.657

2 0.973 0.585 0.90 5.0E+05 5 13 1.630 2.249 2.104

3 1.544 0.707 0.90 1.0E+06 12 6 1.650 1.841 2.238

4 1.484 0.704 0.83 1.0E+06 10 7 1.610 1.793 2.013

5 1.879 0.708 0.86 1.5E+06 10 5 1.450 1.688 1.946

6 1.189 0.681 0.89 7.0E+05 5 10 1.350 2.108 1.844

7 1.155 0.625 0.95 5.0E+05 15 9 1.770 1.522 1.946

8 0.792 0.459 1.05 3.0E+05 15 13 2.220 1.930 2.489

9 1.758 0.814 0.60 1.5E+06 5 8 1.400 2.045 2.001

10 1.484 0.704 0.83 1.0E+06 10 7 1.600 1.863 2.148

11 1.603 0.726 0.86 1.0E+06 13 6 1.700 1.736 2.326

12 1.591 0.690 0.72 1.5E+06 7 7 1.550 2.027 1.402

13 0.362 0.224 2.06 3.0E+05 7 16 1.980 2.505 3.179

14 0.748 0.466 0.95 3.0E+05 5 17 1.710 1.658 0.891

15 0.680 0.405 1.27 3.0E+05 10 13 1.800 1.831 0.899

16 0.654 0.341 1.82 7.0E+05 12 8 1.700 2.026 2.589

Average = 1.150 0.570 1.089 Average = 1.686 1.945 2.042

Std.Dev. = 0.484 0.181 0.442 Std.Dev. = 0.217 0.259 0.600

Cv (%) = 42.1 31.7 40.6 S0PP

= 0.129 0.133 0.294

Equation [23] indicates that MR, to be used on the AASHTO model (equation [11])

when analyzing the pavement structure above the base or above the subbase layers, should not

be simply the base or the subbase resilient modulus, but an average value between the

equivalent elastic modulus of the system that supports the structure described by SN and the

expected resilient modulus as a function of the layer strength. This last parameter was given

by the relationship that can be applied only to soils (MR = 10 CBR in MPa), but that was

here adopted for the base and subbase analyses due to the fact that the value of FC on Table 4

is nearly constant, irrespective of the way the pavement structure is described, such as

consisting only of the surfacing and base layers supported by the foundation (subbase and

subgrade layers), the surfacing layer over the system comprised of the layers below it, or as

the complete structure supported by the subgrade. Such result indicates that a granular base or

subbase layer has much more value in the pavement structure due to its shearing strength than

due to its resilient modulus. There was a loss of prediction accuracy for base and subbase

analysis (but not for the subgrade analysis) when the AASHTO design formula was expressed

in terms of the resilient modulus, instead of in terms of a soil support value, more associated

with shearing strength. Equation [23] is a generalization which corrects this problem.

The calibration factor FC is, therefore, nearly equal to 1.89, irrespective of the way the

pavement structure is described, if equation [11] is used with the MR definition of equation

[23]. This result means that use of the AASHTO design equation for the base and subbase

19

analyses must consider MR not as the base or subbase resilient modulus (this can be done only

for the subgrade analysis), but as a function of the foundation equivalent elastic modulus and

of the layer shearing strength, as described by its CBR value.

Application of this model for pavement design or performance prediction requires

determination of the maximum value of = 1.837 A from these three different ways of

describing the pavement structure, since this maximum value for will be the one controlling

pavement performance for a specific pavement structure being analyzed. Besides, such

determination will tell which pavement layer is the critical one that controls design. Such

finding will be an invaluable tool for pavement rehabilitation designs, if reliable data can be

gathered about the in situ effective elastic moduli of the pavement layers, since in this case the

critical layer will be weakest link to be reinforced in order to assure traffic-structure

compatibility.

Table 4 also shows a measure of the uncertainty regarding performance prediction

using the proposed model, in terms of the ratio S0PP = StdDev / Average for FC at the several

cases here analyzed. The AASHTO Guide overall standard deviation parameter S0 has

recommended values around 0.4 - 0.5, which makes sense, since part of this value is due to

the uncertainties solely associated with the act of performance prediction (described by S0PP

on Table 4 from 0.13 to 0.30), mainly associated with pavement layers variation in terms of

their thicknesses and the mechanical properties of the comprising materials. The remaining

part is due to uncertainties from future traffic.

Table 5 and Figure 3 show these calculations for reference Case 2. The procedure here

adopted was to find, by trial and error, the best FC value for the subgrade analysis. The other

two FC values, corresponding to the sub-base and base layers, were simply given by: FC =

/A, with being the value required for pavement performance reproduction. This

procedure forces the model to predict the same output in terms of pavement performance

irrespective of the way in which the pavement structure is described in the model by the pair

of parameters MR and SN.

20

Table 5 Analysis of Case 2 for PSI prediction

Layer h1 (cm) ai MR (kgf/cm2) Average CBR

HMAC 10 0.44 79131

Granular Base 18 0.14 3086 100

Granular Subbase 40 0.11 1491 30

Subgrade 500 5

PP (years) = 13 CBRp subgrade = 3.8

HTp (DNER) = 78.1 cm HT (cm) = 78

Nyear = 5.00E+05 SN = 4.415

QI0 = 17 RH = 0

PSI0 QI = 3.942 MR (psi) = 7112.38

Np (USACE) = 1.95E+07

h1_mn. = 10 cm SNC = 5.023

VDMc = 913 TYcr2 = 6.03

D0 mm = 0.491

(Subgrade) Dmax = 53.3

AlphaA = 9.411E-02 Vs (TR=20%) = 10.0

W18 = 1.137E+01 Epst_HMAC = 1.79E-04

Bheta = 5.705E-01 Vf (years, TAI) = 8.4

Fc = 1.630 Vf (years) = 9.5

Alpha = 1.534E-01 Vf / Vs = 0.73

(Subbase)

AlphaA = 6.822E-02 SN = 2.71

W18 = 1.568E+01 MR (psi) = 27766

Bheta = 1.621E+00

Fc = 2.249

(Base)

AlphaA = 7.291E-02 SN = 1.73

W18 = 1.468E+01 MR (psi) = 81477

Bheta = 6.335E+00

Fc = 2.104

2.7

2.9

3.1

3.3

3.5

3.7

3.9

4.1

0 1 2 3 4 5 6 7 8 9 10 11 12 13

PSI

Year

Model

HDM-III

Figure 3 Results for the analysis of Case 2 of PSI prediction with time

Such requirement was not made when the AASHTO design formula was developed, as

the formula was derived with a single view of the pavement structure: MR as the subgrade

resilient modulus and SN associated with the whole pavement structure, comprised of the

21

surfacing, base and subbase layers. This requirement must be applied, however, for pavement

design using the AASHTO Guide, as the pavement layers must be determined imposing the

attendance of the design formula for every possible (SN, MR) combination. Therefore, the

AASHTO Guide forces the user to apply the design formula in ways that are only partially

supported by the experimental evidence at the AASHO Road Test, since the extension of the

original formula for other subgrade conditions was made through an analysis involving some

pavement sections with large granular base thicknesses, by considering them to be supported

on a high quality granular subgrade. In the model here developed, such procedure is

generalized by imposing that once the pavement performance is known, it must be predicted

by the model irrespective of the way the pavement structure is described by the pair (SN, MR).

This will lead to a model that can be rigorously applied for determination of all pavement

layers thicknesses.

Following the same procedure and using the same reference pavement sections, Table

6 shows the resulting calibration factors for the case of SCI prediction along time. Table 7 and

Figure 6 illustrate for one of the cases the calculations that were done in order to arrive at

these results. For the 16 reference cases, fatigue life of the HMAC surfacing layer at TR =

20% was nearly equal to the condition defined by SCI = 2.0 (associated with IGG = 70).

Table 6 shows that a calibration factor equal to FC = 4.73 can be adopted for SCI

predictions when considering the whole pavement structure supported by the subgrade soil,

with a coefficient of variation equal to 22%, a value consistent with the component

exclusively associated with performance predictions on the AASHTO overall standard

deviation S0. For the subbase analysis, a value for FC around 3.72 can be adopted, which

becomes FC = 3.15 for the base analysis, all of them with acceptable standard errors.

The cases on Table 6 showed a strong trend towards the SCI parameter being

explained by t0, the number of years for the first fatigue cracks appearance on the AC

surfacing layer, as shown on Figure 5. This is a reasonable result, since the onset of fatigue

cracking controls the IGG increase with time. This gives another procedure for SCI prediction

for overlay design, if a reliable model for t0 can be applied in order to predict the first

reflective cracks appearance at the overlay surface. In practice, it will be better to use the

relationship of Figure 5 for overlay design, since it can be expected a strong dependence of

SCI on the reflection cracking process.

22

Table 6 Results for SCI prediction on new asphalt pavements

Case Nyear

(AASHTO) Subgrade

CBR Design

period (years) Fc

Subgrade Fc

Subbase Fc

Base

1 5.0E+05 10 11 4.800 4.403 4.201

2 5.0E+05 5 13 6.200 4.639 3.390

3 1.0E+06 12 6 3.800 3.474 3.631

4 1.0E+06 10 7 4.100 3.467 3.297

5 1.5E+06 10 5 4.000 3.382 3.217

6 7.0E+05 5 10 5.600 4.364 2.813

7 5.0E+05 15 9 3.400 2.498 2.836

8 3.0E+05 15 11 4.300 3.160 3.587

9 1.5E+06 5 8 4.900 3.972 2.263

10 1.0E+06 10 7 4.100 3.467 3.297

11 1.0E+06 13 6 3.750 3.195 3.734

12 1.5E+06 7 7 5.300 4.589 2.481

13 3.0E+05 7 16 6.900 5.032 5.122

14 3.0E+05 5 17 6.300 3.197 1.415

15 3.0E+05 10 13 4.250 3.090 1.262

16 7.0E+05 12 8 4.000 3.657 3.822

Average = 4.731 3.724 3.148

Std.Dev. = 1.043 0.699 0.978

S0PP

= 0.220 0.188 0.311

y = 3.195x-0.891

R = 0.9944

2

3

4

5

6

7

0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3

t0 (years)

Alpha x Nyear (10^6)

Figure 5 Relationship between SCI and surfacing layer fatigue life

23

Table 7 Analysis for Case 2 for SCI prediction

Layer h1 (cm) ai MR (kgf/cm2) Average CBR

HMAC 10 0.44 79131

Granular Base 18 0.14 3086 100

Granular Subbase 40 0.11 1491 30

Subgrade 500 5

PP (years) = 13 CBRp subgrade = 3.8

HTp (DNER) = 78.1 cm HT (cm) = 78

Nyear = 5.00E+05 SN = 4.415

QI0 = 17 RH = 0

PSI0 QI = 3.942 MR (psi) = 7112.38

Np (USACE) = 1.95E+07

h1_mn. = 10 cm SNC = 5.023

VDMc = 913 TYcr2 = 6.03

D0 mm = 0.491

(Subgrade) Dmax = 53.3

AlphaA = 1.632E-01 Vs (TR=20%) = 10.0

W18 = 2.922E+01 Epst_HMAC = 1.79E-04

Bheta = 5.705E-01 Vf (years, TAI) = 8.4

Fc = 6.200 Vf (years) = 9.5

Alpha = 1.012E+00 Vf / Vs = 0.73

(Subbase)

AlphaA = 2.181E-01 SN = 2.71

W18 = 2.186E+01 MR (psi) = 27766

Bheta = 1.621E+00

Fc = 4.639

(Base)

AlphaA = 2.984E-01 SN = 1.73

W18 = 1.598E+01 MR (psi) = 81477

Bheta = 6.335E+00

Fc = 3.390

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0 1 2 3 4 5 6 7 8 9 10 11

Year

SCI

Model

HDM-III

Figure 6 Results for the analysis of Case 2 on SCI prediction with time

In the case of a rehabilitated pavement, this same model can be applied, since the

configuration of an asphalt concrete overlaid pavement resembles the performance prediction

24

made for a new pavement considering now the pavement structure as consisting only of the

surfacing layer supported by the base layer. Therefore:

(a) The Structural Number will be given by: SN = a1HR, where a1 = 0.44 is the asphalt

concrete overlay structural coefficient and HR is its thickness (in inches);

(b) The roadbed resilient modulus will now be given by:

[28]

where Eeq is calculated as the semi-infinite elastic space equivalent modulus of the pavement

structure (before rehabilitation), and DC is the pavement deflection, measured under a circular

applied load of pressure p and radius R, as in the FWD. The Poissons ratio of this

equivalent system can be fixed at an average typical value for pavement materials (such as

0.35). CBRef is the effective in situ CBR value of the upper layers of the pavement. DCP test

data could be employed for its evaluation on thin surfacing pavements, with a default value

CBRef = 150 for thick asphalt concrete surfacing layers over high quality crushed stone bases.

The idea behind considerations (a) and (b) is that deterioration of a rehabilitated

pavement is essentially the generation of distresses inside the applied asphalt concrete

overlay, with the old pavement behaving only as an elastic platform which gives a support

described by its equivalent elastic modulus MR, calculated by equation [28]. Such

consideration will lead to an underestimate of pavement performance only if the old pavement

has a significant remaining life, since in this case it cannot be degenerated simply as an

elastic platform. Practical applications of this model in such cases can be made by adding

an effective overlay thickness to the actual applied overlay thickness HR, with this effective

thickness calculated using the model for new pavements in order to reproduce its remaining

service life.

For the final overlay design, it will be also necessary to analyze the overlaid pavement

structure using the model for new pavements, in order to verify if there is a combination SN -

MR which is more critical to pavement performance than the one above described on items (a)

and (b). The layer materials in situ elastic moduli from Falling Weight Deflectometer tests

( )C

eq

efeq

R

D

pRE

CBREM

212

2

)10(

=

+=

25

will be required for these analyses. This requirement will be critical if the old pavement has

been showing poor performance, if it has been left with extensive cracking for too long time

or if it is expected the passage in the future of significantly higher loads than in the past.

These are all situations under which the existing pavement can not be regarded as a stable,

consolidated platform, over which the HMAC overlay will be safely supported.

It is unlikely that the value of FC for a new pavement can also be applicable to a

rehabilitated one, since an existing pavement has already suffered the conditioning effects due

to traffic loads, as well as long-term climatic and ageing effects. It can be anticipated that FC

for a new pavement must be greater than the value for an overlaid one, since the conditioning

effects that the traffic loads apply to all pavement layers lead to a pavement structure more

stable than a new one, which has been subjected only to the stress history applied by the

compaction equipment.

The procedure here adopted was to consider the overlay case with the same view of a

new pavement, which means FC = 1.824 for PSI prediction and SCI = (106/Nyear)

(t0/3.2063)-1.125

, as indicated on Figure 5.

The expected overlay age at first cracks appearance (t0) will be estimated from: t0 = Ff

Lf, where Lf is the fatigue life calculated applying the recalibrated T.A.I. fatigue law

(equation [21]), with t given by equation [22] and Ff = 0.919 is the fatigue calibration factor

from HDM cases, as shown in Table 8. These analyses were conducted using the followin

expression to calculate pavement deflection after application of the AC overlay:

4315352.09555741.03

0 1068636.8= lK ef

[29]

with r2 = 0.9761, SE = 0.1175181 and SE/SY = 15.4%, which is a regression developed from

several cases generated using FLAPS program. This formula was developed using

Westergaards equations for calculating the vertical deflection of a slab on a Winkler

foundation, where the effective reaction modulus of the existing pavement can be calculated

from the measured deflection by: Kef = p/c, with p = 5.8 kgf/cm2 under the 41 kN load on

FWD tests. Therefore, 0 = Q/(Kefl2)f(l), where Q is the applied load and l4 = E0HR

3/[12(1-

02)Kef] is the fourth power of the radius of relative stiffness.

A calibration of the model for PSI prediction in the case of overlaid pavements cannot

be done using HDM empirical models, since these models could not discriminate between the

new pavements from the rehabilitated ones, except in the case of TYcr2 estimation (equations

26

[13] and [14]). Therefore, empirical data concerning the performance of overlaid pavements

will be plotted against the predictions of the model here developed to analyze its implications.

Table 8 Calibration of the reflection cracking fatigue model from HDM

HR YE4 (106) Dc h1 Age TR f E0 MR TYcr2 t Vf Ff

(cm) (ESALs) (10-2

mm) (cm) (years) (%) (Hz) (kgf/cm2) (kgf/cm

2) (years) (10

-4) (years)

5 0.1 100 5 4 2 68.3 93746 1527 4.59 2.757 6.0 0.771

5 0.1 100 5 7 5 68.3 93746 1527 4.50 2.757 6.0 0.756

5 0.1 100 5 10 10 68.3 93746 1527 4.36 2.757 6.0 0.732

5 0.1 100 5 13 20 68.3 93746 1527 4.10 2.757 6.0 0.689

5 0.1 100 5 16 50 68.3 93746 1527 3.52 2.757 6.0 0.592

5 0.3 80 7.5 4 2 68.3 93746 1909 4.78 2.278 3.7 1.284

5 0.3 80 7.5 7 5 68.3 93746 1909 4.69 2.278 3.7 1.260

5 0.3 80 7.5 10 10 68.3 93746 1909 4.54 2.278 3.7 1.222

5 0.3 80 7.5 13 20 68.3 93746 1909 4.29 2.278 3.7 1.154

5 0.3 80 7.5 16 50 68.3 93746 1909 3.71 2.278 3.7 0.998

5 0.7 60 10 4 2 68.3 93746 2545 4.89 1.798 3.5 1.410

5 0.7 60 10 7 5 68.3 93746 2545 4.80 1.798 3.5 1.384

5 0.7 60 10 10 10 68.3 93746 2545 4.66 1.798 3.5 1.344

5 0.7 60 10 13 20 68.3 93746 2545 4.41 1.798 3.5 1.270

5 0.7 60 10 16 50 68.3 93746 2545 3.83 1.798 3.5 1.103

5 1.5 40 12.5 4 2 68.3 93746 3817 5.01 1.276 5.0 1.002

5 1.5 40 12.5 7 5 68.3 93746 3817 4.92 1.276 5.0 0.984

5 1.5 40 12.5 10 10 68.3 93746 3817 4.78 1.276 5.0 0.956

5 1.5 40 12.5 13 20 68.3 93746 3817 4.53 1.276 5.0 0.905

5 1.5 40 12.5 16 50 68.3 93746 3817 3.95 1.276 5.0 0.789

7.5 0.1 100 5 4 2 56.7 85155 1527 5.97 2.500 8.9 0.670

7.5 0.1 100 5 7 5 56.7 85155 1527 5.84 2.500 8.9 0.655

7.5 0.1 100 5 10 10 56.7 85155 1527 5.63 2.500 8.9 0.632

7.5 0.1 100 5 13 20 56.7 85155 1527 5.25 2.500 8.9 0.589

7.5 0.1 100 5 16 50 56.7 85155 1527 4.39 2.500 8.9 0.493

7.5 0.3 80 7.5 4 2 56.7 85155 1909 6.15 2.073 5.5 1.118

7.5 0.3 80 7.5 7 5 56.7 85155 1909 6.02 2.073 5.5 1.094

7.5 0.3 80 7.5 10 10 56.7 85155 1909 5.81 2.073 5.5 1.056

7.5 0.3 80 7.5 13 20 56.7 85155 1909 5.44 2.073 5.5 0.987

7.5 0.3 80 7.5 16 50 56.7 85155 1909 4.58 2.073 5.5 0.831

7.5 0.7 60 10 4 2 56.7 85155 2545 6.27 1.650 5.0 1.253

7.5 0.7 60 10 7 5 56.7 85155 2545 6.14 1.650 5.0 1.227

7.5 0.7 60 10 10 10 56.7 85155 2545 5.93 1.650 5.0 1.185

7.5 0.7 60 10 13 20 56.7 85155 2545 5.55 1.650 5.0 1.110

7.5 0.7 60 10 16 50 56.7 85155 2545 4.69 1.650 5.0 0.938

7.5 1.5 40 12.5 4 2 56.7 85155 3817 6.39 1.192 6.8 0.939

7.5 1.5 40 12.5 7 5 56.7 85155 3817 6.25 1.192 6.8 0.920

7.5 1.5 40 12.5 10 10 56.7 85155 3817 6.04 1.192 6.8 0.889

7.5 1.5 40 12.5 13 20 56.7 85155 3817 5.67 1.192 6.8 0.834

7.5 1.5 40 12.5 16 50 56.7 85155 3817 4.81 1.192 6.8 0.707

10 0.1 100 5 4 2 48.5 79131 1527 7.85 2.307 12.4 0.635

10 0.1 100 5 7 5 48.5 79131 1527 7.65 2.307 12.4 0.619

10 0.1 100 5 10 10 48.5 79131 1527 7.34 2.307 12.4 0.594

10 0.1 100 5 13 20 48.5 79131 1527 6.78 2.307 12.4 0.548

10 0.1 100 5 16 50 48.5 79131 1527 5.51 2.307 12.4 0.446

27

Table 8 Calibration of the reflection cracking fatigue model from HDM (cont.)

HR YE4 (106) Dc h1 Age TR f E0 MR TYcr2 t Vf Ff

(cm) (ESALs) (10-2

mm) (cm) (years) (%) (Hz) (kgf/cm2) (kgf/cm

2) (years) (10

-4) (years)

10 0.3 80 7.5 4 2 48.5 79131 1909 8.02 1.917 7.6 1.059

10 0.3 80 7.5 7 5 48.5 79131 1909 7.83 1.917 7.6 1.033

10 0.3 80 7.5 10 10 48.5 79131 1909 7.52 1.917 7.6 0.992

10 0.3 80 7.5 13 20 48.5 79131 1909 6.96 1.917 7.6 0.919

10 0.3 80 7.5 16 50 48.5 79131 1909 5.69 1.917 7.6 0.751

10 0.7 60 10 4 2 48.5 79131 2545 8.13 1.536 6.7 1.207

10 0.7 60 10 7 5 48.5 79131 2545 7.94 1.536 6.7 1.178

10 0.7 60 10 10 10 48.5 79131 2545 7.63 1.536 6.7 1.132

10 0.7 60 10 13 20 48.5 79131 2545 7.07 1.536 6.7 1.049

10 0.7 60 10 16 50 48.5 79131 2545 5.80 1.536 6.7 0.861

10 1.5 40 12.5 4 2 48.5 79131 3817 8.25 1.125 8.7 0.943

10 1.5 40 12.5 7 5 48.5 79131 3817 8.05 1.125 8.7 0.921

10 1.5 40 12.5 10 10 48.5 79131 3817 7.74 1.125 8.7 0.885

10 1.5 40 12.5 13 20 48.5 79131 3817 7.18 1.125 8.7 0.822

10 1.5 40 12.5 16 50 48.5 79131 3817 5.91 1.125 8.7 0.676

12.5 0.1 100 5 4 2 42.3 74622 1527 10.45 2.154 16.3 0.642

12.5 0.1 100 5 7 5 42.3 74622 1527 10.16 2.154 16.3 0.624

12.5 0.1 100 5 10 10 42.3 74622 1527 9.70 2.154 16.3 0.596

12.5 0.1 100 5 13 20 42.3 74622 1527 8.87 2.154 16.3 0.545

12.5 0.1 100 5 16 50 42.3 74622 1527 6.99 2.154 16.3 0.429

12.5 0.3 80 7.5 4 2 42.3 74622 1909 10.62 1.794 9.9 1.072

12.5 0.3 80 7.5 7 5 42.3 74622 1909 10.33 1.794 9.9 1.043

12.5 0.3 80 7.5 10 10 42.3 74622 1909 9.87 1.794 9.9 0.996

12.5 0.3 80 7.5 13 20 42.3 74622 1909 9.04 1.794 9.9 0.913

12.5 0.3 80 7.5 16 50 42.3 74622 1909 7.16 1.794 9.9 0.723

12.5 0.7 60 10 4 2 42.3 74622 2545 10.72 1.446 8.6 1.241

12.5 0.7 60 10 7 5 42.3 74622 2545 10.43 1.446 8.6 1.207

12.5 0.7 60 10 10 10 42.3 74622 2545 9.97 1.446 8.6 1.154

12.5 0.7 60 10 13 20 42.3 74622 2545 9.15 1.446 8.6 1.058

12.5 0.7 60 10 16 50 42.3 74622 2545 7.27 1.446 8.6 0.841

12.5 1.5 40 12.5 4 2 42.3 74622 3817 10.83 1.072 10.8 1.006

12.5 1.5 40 12.5 7 5 42.3 74622 3817 10.54 1.072 10.8 0.978

12.5 1.5 40 12.5 10 10 42.3 74622 3817 10.08 1.072 10.8 0.936

12.5 1.5 40 12.5 13 20 42.3 74622 3817 9.25 1.072 10.8 0.859

12.5 1.5 40 12.5 16 50 42.3 74622 3817 7.37 1.072 10.8 0.685

Average = 0.919

Std. Dev. = 0.239

Cv (%) = 26.0

One of such empirical models is the one by George et al. (1989), developed for

Mississippi highways:

37,076,043,64 RS HAGEV

= [30]

where: VS = rehabilitated pavement service life (years);

AGE = old pavement age at the time of rehabilitation, in years;

HR = HMAC overlay thickness (in).

28

This is an extremely simplistic model, with a high degree of masking of key

parameters influences. For instance, the decrease of pavement service life with the increase of

the old pavement age can be due to a higher level of pavement deterioration, which is not

described in the regression. Besides, there is not a parameter to describe the traffic rate.

Another model is the one from Hajek et al. (1987), also described in George et al.

(1989), which was developed for highway pavements in Ontario:

[31]

where the pavement service life VS refers to a terminal PCR = 55, HR in mm, DESAL is the

daily number of ESALs and patch is equal to 0 under restricted routine maintenance

interventions and is equal to 1 under a regular practice. The traffic effect is not adequately

described in this model, since a 100% increase in it imply in a service life loss of only 10%.

Table 9 shows the results of these models to a set of selected design conditions. Pavement

service life for the model here developed was calculated for a terminal condition given by

SCIt = 3.0. The average values from the three models are near and around 14 to 16 years.

Figure 7 shows the comparison between the model for SCI prediction and the empirical

regressions here considered. The regression line is nearly identical with the equality line. It is

necessary to trace an envelope from 70.5% to 163% around the equality line to reach a

reliability of 70% for the predictions of overlaid pavement service life (60% for the

Mississippi data and 80% for the Ontario data). In spite of the shortcomings of the empirical

regressions [30] and [31], these results can be regarded as a support for the model here

developed.

y = 1.4069x0.9008

R = 0.821

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35

Vs (years)

Vs model (years)

George et al. Hajek et al.

Figure 7 Analysis of the model for SCI prediction

patch

RS DESALHAGEV 14,132,1097,047,033,0 =

29

Table 9 Overlaid pavements analyzed for Vs at SCIt = 3.0

HR YE4 (106) Dc h1 Age TR Vs model Vs Eq.[25] Vs Eq.[26]

(cm) (ESALs) (10-2

mm) (cm) (years) (%) (years) (years) (years)

7 0.1 100 5 7 10 11.9 21.4 10.7

7 0.1 100 5 10 20 11.9 16.3 12.1

7 0.1 100 5 15 30 11.9 12.0 13.8

7 0.1 100 5 20 50 11.9 9.6 15.2

7 0.1 100 5 25 70 11.9 8.1 16.3

7 0.3 80 7.5 7 10 6.9 21.4 9.6

7 0.3 80 7.5 10 20 6.9 16.3 10.8

7 0.3 80 7.5 15 30 6.9 12.0 12.4

7 0.3 80 7.5 20 50 6.9 9.6 13.6

7 0.3 80 7.5 25 70 6.9 8.1 14.7

7 0.7 60 10 7 10 6.2 21.4 8.9

7 0.7 60 10 10 20 6.2 16.3 10.0

7 0.7 60 10 15 30 6.2 12.0 11.4

7 0.7 60 10 20 50 6.2 9.6 12.6

7 0.7 60 10 25 70 6.2 8.1 13.5

7 1.5 40 12.5 7 10 8.9 21.4 8.2

7 1.5 40 12.5 10 20 8.9 16.3 9.3

7 1.5 40 12.5 15 30 8.9 12.0 10.6

7 1.5 40 12.5 20 50 8.9 9.6 11.7

7 1.5 40 12.5 25 70 8.9 8.1 12.5

10 0.1 100 5 7 10 18.6 24.4 12.7

10 0.1 100 5 10 20 18.6 18.6 14.3

10 0.1 100 5 15 30 18.6 13.7 16.3

10 0.1 100 5 20 50 18.6 11.0 17.9

10 0.1 100 5 25 70 18.6 9.3 19.3

10 0.3 80 7.5 7 10 10.7 24.4 11.4

10 0.3 80 7.5 10 20 10.7 18.6 12.8

10 0.3 80 7.5 15 30 10.7 13.7 14.7

10 0.3 80 7.5 20 50 10.7 11.0 16.1

10 0.3 80 7.5 25 70 10.7 9.3 17.3

10 0.7 60 10 7 10 9.4 24.4 10.5

10 0.7 60 10 10 20 9.4 18.6 11.8

10 0.7 60 10 15 30 9.4 13.7 13.5

10 0.7 60 10 20 50 9.4 11.0 14.8

10 0.7 60 10 25 70 9.4 9.3 16.0

10 1.5 40 12.5 7 10 12.6 24.4 9.7

10 1.5 40 12.5 10 20 12.6 18.6 11.0

10 1.5 40 12.5 15 30 12.6 13.7 12.5

10 1.5 40 12.5 20 50 12.6 11.0 13.8

10 1.5 40 12.5 25 70 12.6 9.3 14.8

12.5 0.1 100 5 7 10 25.3 26.5 14.1

12.5 0.1 100 5 10 20 25.3 20.2 15.8

12.5 0.1 100 5 15 30 25.3 14.8 18.1

12.5 0.1 100 5 20 50 25.3 11.9 19.9

12.5 0.1 100 5 25 70 25.3 10.1 21.4

12.5 0.3 80 7.5 7 10 14.5 26.5 12.7

12.5 0.3 80 7.5 10 20 14.5 20.2 14.2

12.5 0.3 80 7.5 15 30 14.5 14.8 16.3

12.5 0.3 80 7.5 20 50 14.5 11.9 17.9

30

Table 9 Overlaid pavements analyzed for Vs at SCIt = 3.0 (cont.)

HR YE4 (106) Dc h1 Age TR Vs model Vs Eq.[25] Vs Eq.[26]

(cm) (ESALs) (10-2

mm) (cm) (years) (%) (years) (years) (years)

12.5 0.3 80 7.5 25 70 14.5 10.1 19.3

12.5 0.7 60 10 7 10 12.4 26.5 11.7

12.5 0.7 60 10 10 20 12.4 20.2 13.1

12.5 0.7 60 10 15 30 12.4 14.8 15.0

12.5 0.7 60 10 20 50 12.4 11.9 16.5

12.5 0.7 60 10 25 70 12.4 10.1 17.7

12.5 1.5 40 12.5 7 10 15.9 26.5 10.8

12.5 1.5 40 12.5 10 20 15.9 20.2 12.2

12.5 1.5 40 12.5 15 30 15.9 14.8 13.9

12.5 1.5 40 12.5 20 50 15.9 11.9 15.3

12.5 1.5 40 12.5 25 70 15.9 10.1 16.5

14 0.1 100 5 7 10 29.8 27.6 14.8

14 0.1 100 5 10 20 29.8 21.1 16.7

14 0.1 100 5 15 30 29.8 15.5 19.1

14 0.1 100 5 20 50 29.8 12.4 21.0

14 0.1 100 5 25 70 29.8 10.5 22.6

14 0.3 80 7.5 7 10 17.0 27.6 13.3

14 0.3 80 7.5 10 20 17.0 21.1 15.0

14 0.3 80 7.5 15 30 17.0 15.5 17.2

14 0.3 80 7.5 20 50 17.0 12.4 18.9

14 0.3 80 7.5 25 70 17.0 10.5 20.3

14 0.7 60 10 7 10 14.4 27.6 12.3

14 0.7 60 10 10 20 14.4 21.1 13.8

14 0.7 60 10 15 30 14.4 15.5 15.8

14 0.7 60 10 20 50 14.4 12.4 17.4

14 0.7 60 10 25 70 14.4 10.5 18.7

14 1.5 40 12.5 7 10 18.0 27.6 11.4

14 1.5 40 12.5 10 20 18.0 21.1 12.8

14 1.5 40 12.5 15 30 18.0 15.5 14.7

14 1.5 40 12.5 20 50 18.0 12.4 16.1

14 1.5 40 12.5 25 70 18.0 10.5 17.4

Average = 14.5 15.7 14.5

4 Case Studies

The model here developed was also applied to a set of independent field data in order to see if

it is capable of giving a reliable performance prediction. For a new pavement, highway SP-

070 (Figure 8) in Brazil was analyzed. The pavement was not designed solely using the

DNER pavement design method, but use was made also of mechanistic-empirical analyses.

The new highway SP-070 (segment Taubat Jacare in So Paulo state) was opened to

traffic in 1995 between km 61.3 and km 130.4. The average condition of the pavements in

2012 on lane 2, where commercial traffic was concentrated, was given by QI = 27 counts/km

and IGG = 9 to 14, under a traffic rate of 5 105 ESALs (AASHTO equivalency factors) per

31

year. Pavement deflection was at an average value of 27 10-2 mm under 40 kN (FWD), SN

= 3.6 and subgrade elastic modulus was MR = 217 MPa. Pavement structure consisted of 12

cm AC surfacing layer, 15 cm granular base layer (crushed stone) and 17 cm cemented-treated

crushed stone subbase, above a subgrade soil with CBR 15.

Figure 8 Analysis of the new pavement on SP-070 highway

In the case of rehabilitated pavements, an interesting outcome was the overlay of SP-

160 using 3 cm of a HMAC with asphalt-rubber. Figure 9 shows the performance prediction

for lanes 3 and 4 (where commercial traffic was concentrated). The pavement was overlaid in

2006. Longitudinal roughness was at QI = 13 counts/km in 2013 and reached QI = 19

counts/km, with IGG = 8 by the next year. It can be seen that this performance was essentially

predicted with success by the model. The fatigue model here calibrated predicted the first

appearance at the pavement surface of the cracks after 8 years, which is in agreement with the

observed pavement performance. The model was also in agreement with asphalt-rubber

equivalency factors from laboratory fatigue tests, which indicate 0.7 cm of HMAC with

asphalt-rubber for 1 cm of conventional HMAC mixes.

32

Figure 9 Overlaid pavement on SP-160 highway

A final verification of the model was performed applying it to pavement sections

designed using the TRRL Road Note 29 (Croney, 1977). Table 10 shows the derived

reliability levels and the pavement terminal conditions required for the pavement sections to

be in agreement with the model here developed. It is apparent that the design reliability level

increases and the pavement acceptable conditions during service lives around 16 to 22 years

become more stringent as the design traffic increases, in ways similar to the ones

recommended by the AASHTO Guide.

Figure 10 illustrates the procedure here adopted for the cases listed on Table 10.

Table 10 Application of the model to Road Note 29

Case Np

(AASHTO) Nyear CBRsg

h1 (cm)

h2 (cm)

h3 (cm)

RL (%)

QIt (counts/km)

IGGt Life (years)

S6 1.00E+06 5.00E+04 4 6.5 16 23 50 35 80 16

S5 1.00E+06 5.00E+04 7 6.5 16 11 50 35 80 17

S2 1.00E+07 5.00E+05 5 12 22 24 70 40 40 20

S1 1.00E+07 5.00E+05 7 12 22 16 75 35 30 20

S4 1.00E+08 5.00E+06 4 21 27 37 85 45 30 20

S3 1.00E+08 5.00E+06 7 21 27 20 90 35 30 20

These results strongly support the validity of the proposed model, with its present

calibration factors, so that no reason exists up to this point to invalidate the model here

developed.

33

A final experiment was chosen for application of the model: the one conducted by

OCDE (1991) at Nantes Circular Test Track. On those accelerated tests, flexible and semi-

rigid pavements were tested under a dual wheel, traveling at speeds ranging from 60.6 to 72.0

km/h. Of importance to the analysis here performed is the behavior of Structures I and II, both

of flexible pavements with a granular base layer (thickness equal to 28 cm) and asphalt

concrete thicknesses shown on Table 11, together with the number of load repetitions

recorded at the appearance of the first cracks at the pavement surface. These cracks were

transversal to the direction of traffic, indicating a mechanism of fatigue cracking produced by

tensile stresses at the bottom of the asphalt concrete surface layer. A dual axle load was

employed, with separation distance between wheels equal to 36 cm and wheel contact area

equal to 600 cm2. Passages-to-coverage ratios were greater than one due to the 1.60 m lateral

displacement of the dual wheel at a 45 minutes time interval.

Figure 10 Analysis of a Road Note 29 case

Table 11 also shows parameter a on: RD(N) = RD0 + a N0.5 for rut depth development

(mm) after N load repetitions. For Section I, RD = 25 mm after N = 2.5 105 load repetitions

at Q = 115 kN, with N = 4.9 105 at Q = 100 kN. For Section II, RD = 7 mm after N = 6.4

105 load repetitions at Q = 115 kN, and N = 3.6 105 at Q = 100 kN.

34

Table 11 Field data at Nantes Circular Test Track (OCDE, 1991)

Pavement

Section

Sector

No.

Axle load

(kN)

Speed

(km/h)

Thickness

of A.C. layer (cm)

N0 (105)

First crack appearance

a

(103)

I 01 115 72.0 6.3 0.726 70.0

I 11 100 60.6 6.0 1.030 31.4

II 02 115 72.0 13.9 38.000 6.67

II 12 100 60.6 13.0 3.700 4.46

The tests were conducted with the asphalt concrete layer experiencing temperatures

between 8oC and 24

oC. For determination of the pavement layers elastic moduli, pavement

deflections and tensile and compressive strains on the asphalt concrete layer were measured

under a moving axle load of 115 kN at 24oC. Values of the layers elastic moduli that were

found to be more consistent with these instrumentation parameters were:

- For the asphalt concrete layer: E1 = 5610 MPa;

- For the granular base:

E2 = 260 MPa on Section I and on Sector 02 of Section II

E2 = 190 MPa on Sector 12 of Section II

- For the granular subgrade soil: E3 = 58 MPa.

Using these data, Figures 11 and 12 and Table 12 show the results from application of

the model here developed. Considering the first appearance on the surface of fatigue cracks as

associated with IGG = 20, good agreements were obtained for Section I, whereas for Section

II the predicted values are inside the experimental range, since 5.1 < (N0/N0I-01

)model < 52.3.

Table 12 Performance prediction at Nantes Circular Test Track

Section Sector N0 N0_model Rel = N0/N0I-01

Rel_model

I 1 7.260E+04 8.175E+04

I 11 1.030E+05 1.278E+05 1.42 1.56

II 2 3.800E+06 1.366E+06 52.34 16.71

II 12 3.700E+05 1.491E+06 5.10 18.24

Average = 19.62 12.17

35

Figure 11 Performance prediction on Section I at Nantes Circular Test Track

36

Figure 12 Performance prediction on Section II at Nantes Circular Test Track

5 Application to Airfield Pavements

Extrapolating the AASHTO axle load equivalency factors to aircrafts, Figures 13, 14 and 15

depict the application of the model to three traffic conditions. The resulting pavement sections

are nearly the same as the ones designed using the FAA AC-150/5320-6E procedure for a 20

years design life, in spite of the caution required on such kind of analysis. This agreement

illustrates the power of the model and of AASHTO load equivalency factors. Also, application

37

of the model here developed shows that FAA minimum thickness requirement in the case of

light aircrafts is excessive.

For these cases, it was also calculated the Cumulative Damage Factor (CDF) using the

mechanistic interpretation of the USACE CBR formula, given by (Ahlvin, Chou and

Hutchinson, 1974):

(1) Single Wheel:

max,,= 5 5 10 3 0 237N

(2) Multiple Wheels:

max,,= 3 0 10 3 0 159N

[32]

The results are presented on Table 13 and show that the adequate performance

predicted by the model is associated with CDF values well below 100%. This result gives

support to the model, as applied also to airfield pavements with AASHTO load equivalency

factors. This last result should not be a surprise if one considers the fact that AASHTO load

equivalency factors are in agreement with mechanistic ones for the case of fatigue cracking

analysis of asphalt concrete surfacing layers on flexible pavements.

Table 13 Airport pavements analyzed

Traffic Aircraft Q_wheel (kgf) L_wheel (cm) X (cm) Gamma_Subgr. Nadm CDF (%)

Light ATR-72-200 5415.0 31.1 40.9 6.896E-04 1.037E+04 80.90

Medium ATR-72-200 5415.0 31.1 40.9 2.474E-04 6.544E+06 0.32

EMB-145 11734.8 41.5 50.0 5.269E-04 5.635E+04 12.66

Heavy B 777-300 23727.4 39.6 89.8 5.213E-04 6.027E+04 28.67

A 320-100 15543.0 34.8 55.5 2.823E-04 2.854E+06 1.47

38

Performance prediction model

FAARFIELD

Figure 13 Application of the model to airfield pavements under light traffic conditions

39

Performance prediction model

FAARFIELD

Figure 14 Application of the model to airfield pavements (average traffic conditions)

40

Performance prediction model

FAARFIELD

Figure 15 Application of the model to airfield pavements (heavy traffic conditions)

References

AASHTO (1986). The AASHTO Guide for Design of Pavement Structures. American

Association of State Highway and Transportation Officials, Washington, DC.

41

Ahlvin, R.G., Chou, Y.T. & Hutchinson, R.L. 1974. Structural Analysis of Flexible Airfield

Pavements. Transportation Engineering Journal of ASCE, Vol. 100, No. TE3,

August, pp. 625-641.

Croney, D. and Croney P. The design and performance of road pavements. McGraw-Hill.

London. 1991. 2nd edn.

DNIT (1996). Manual de Pavimentao. Publicao IPR-719. Rio de Janeiro, Brasil.

George, K.P. and Rajagopal, A.S. (1989). Life Expectancy of Asphalt Overlays. Second

International Symposium on Pavement Evaluation and Overlay Design, Rio de

Janeiro. Vol. II, pp. 4.9.1 - 4.9.19.

Lytton, R.L. (1987). Concepts of pavement performance prediction and modeling. Second

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Paterson, W.D.O. (1987). Road Deterioration and Maintenance Effects: models for planning

and management. The World Bank, Washington, DC.

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superfcie de pavimentos flexveis e semi-rgidos normalizado pelo DNER.

Fundamentos metodolgicos. Algumas modificaes possveis". Simpsio

Internacional de Avaliao de Pavimentos e Projeto de Reforo, Anexos, Rio de

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Rodrigues, R.M. (2009). Modelos para previso de desempenho de pavimentos com base em

dados de concessionrias de rodovias. CBCR, Campinas.

The World Bank (1987). Description of the HDM-III Model. Volume I. Washington, DC.