NUMERICAL INVESTIGATION OF DESIGN

STRATEGIES TO ACHIEVE LONG-LIFE PAVEMENTS

By

Grace G. Abou-Jaoude, Assistant Professor

Department of Civil Engineering, Lebanese American University,

Blat, Byblos - Lebanon PO Box 36- Phone: (961)

E-mail: grace.aboujaoude@lau.edu.lb

&

Ziad G. Ghauch, Undergraduate Student

Department of Civil Engineering, Lebanese American University,

Blat, Byblos - Lebanon PO Box 36-0051

E-mail: zdghaouche@gmail.com

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ABSTRACT

Increasing the HMA base thickness and modifying the HMA mixture properties

to improve the resistance to fatigue cracking are among the most popular methods for

achieving long-lasting pavements. Such methods are based on the idea of reducing the

tensile strain at the bottom of the HMA layer below the Fatigue Endurance Limit (FEL), a

level of strain below which no cumulative damage occurs to the HMA mixture. This

study investigates the effectiveness of several design strategies involved in long-life,

perpetual pavement design. A 3D Finite Element model of the pavement involving a

linear viscoelastic constitutive model for HMA materials and non-uniform tire contact

stresses is developed using ABAQUS 6.11. The effects of asphalt base course thickness

and mixture type, rich binder layer, and aggregate subbase layer are examined. Four

asphalt base course mixture types, namely dense graded, polymer modified, high

modulus, and standard binder, are studied as a function of the asphalt base course

thickness. The results underline a better performance of the high-modulus asphalt base, as

compared to the other base course mixtures. The aggregate subbase layer on top of

subgrade soil showed a relatively minor effect on the longitudinal and lateral strain

response at the bottom of asphalt base course. The addition of a rich binder layer at the

bottom of the asphalt base course showed a significant reduction in tensile strains. Tables

are provided as a guideline to assess the different alternatives in design of long-life

perpetual pavements.

Keywords: long-life pavement, perpetual pavement, strain response, finite element method, linear viscoelastic theory, fatigue endurance limit

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Introduction

Research on long-life pavements, also known as perpetual pavements, has

evolved over the last decade. APA (2002) defined a perpetual pavement as “an asphalt

pavement designed and built to last longer than 50 years without requiring major

structural rehabilitation or reconstruction, and needing only periodic surface renewal in

response to distresses confined to the top of the pavement”. The advantages of such

pavements were clear when Full-Depth1 and Deep-Strength2 asphalt pavements started

showing superior performance after being in service for several decades. The design

concept of Full-Depth and Deep-Strength pavements was based on the idea of substituting

the thick layers of gravel in conventional pavements by layers of HMA, thus reducing the

total pavement thickness (Yoder and Witczak 1975).

The primary purpose of long-life pavements is two-fold: 1) resist bottom-up

fatigue cracking in the hot-mix asphalt layers, and 2) resist rutting of the subgrade. They

are considered the most cost-effective and long-lasting solution for roads subjected to

heavy traffic. If properly rehabilitated through periodic repair for surface distress, these

pavements present no major structural failures. A typical cross-section of a long-life

pavement structure is shown in Figure 1. The description of each layer is based on the

Asphalt Pavement Alliance definition of a long-life, perpetual, pavement (Harm 2001).

Figure 1 - Typical cross‐section for a long‐life, perpetual pavement

The long-lasting characteristics of these pavements has led researchers to

investigate the presence of a Fatigue Endurance Limit (FEL) below which the HMA

structure does not endure any permanent fatigue damage for an infinite number of load

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repetitions. The concept of a FEL was based on the observation that bottom-up fatigue

cracking does not occur in thick pavements where asphalt tensile strains were relatively

low. Monismith and McLean (1972) and Thompson and Carpenter (2006) conducted a

series of laboratory fatigue tests and observed from a log-log plot of strain versus bending

cycles that the fatigue life dramatically increased below the FEL. Thompson and

Carpenter (2006) considered the FEL as the balance point between healing and damage of

the HMA. When the strains were below the FEL, the healing potential of the HMA

overcame the damage inflicted by the loading cycles. For strains higher than the FEL, the

healing potential of HMA was exceeded by the damage done.

An extensive literature review on the value of the FEL showed that no single

value existed for this limit; however numerous researchers talked about a range between

60 and 100 µε for flexible pavements depending on the mix type (Monismith and McLean

(1972), Nunn (1997), Monismith and Long (1999), Nishizawa et al. (1997), Mahoney

(2001), and Carpenter et al. (2003)). Most recently, the NCHRP 646 report, published in

2010, presented a detailed study that investigated the presence of an endurance limit and

recommended a procedure to incorporate its effects into mechanistic pavement design

methods. Moreover, this report underlined three strategies that were found successful in

prolonging the pavement fatigue life: 1) use of high modulus asphalt mixtures in the base

layer, 2) use of fatigue-resistant bottom layers, and 3) use of polymer modified asphalt

binder. The effectiveness of these design strategies has been shown through laboratory

and field experiments. Molenaar et al. (2009) showed that the use of a high modulus, stiff,

base layer could reduce the asphalt thickness by up to 40%. Monismith et al. (2001)

measured the fatigue life of asphalt mixtures using beam fatigue testing according to

AASTHO T321, at 20°. The results showed that the fatigue life approximately doubled as

the asphalt binder content was raised by 0.5% and the air voids lowered by 3%. Anderson

and Bentsen (2001) and Harvey et al. (2004) reported similar findings of increased fatigue

life with higher asphalt binder content. Goodrich (1988) observed from flexural beam

fatigue tests that the fatigue life of modified asphalt mixtures was an order of magnitude

higher than that of conventional asphalt mixtures. Lee et al. (2002) observed a ten times

greater fatigue life for mixtures made with SBS-modified PG 76-22 asphalt binder, as

compared to conventional asphalt binders.

It is, thus, clear that prolonging the pavement design life is greatly dependent on

limiting the flexural strain at the bottom of the asphalt base layer. Being able to meet this

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goal without excessive costs is a critical issue. This paper presents a parametric study on

the performance of Full-Depth and Deep-Strength pavements under a moving wheel load

using three dimensional finite element modeling. The effect of asphalt base thickness and

asphalt mixture type on the tensile strain response of the bottom asphalt layer is

investigated. Four asphalt mixtures, namely dense graded, polymer modified, high

modulus, and standard binder are used in the asphalt base layer. The advantage of using a

rich bottom layer in the perpetual pavement section is also investigated. Visco-elastic

material properties are used to characterize the HMA layers and to include the time and

temperature dependent behavior of the asphalt material. This numerical investigation is

intended to assess different design alternatives and to provide a roadmap for an efficient

design based on the type and cost of available materials.

Material Properties

To achieve long-life asphalt pavement structures with typical service lives in

excess of 50 years, the selection of proper materials for each of the surface course,

intermediate course, and base course is crucial. Although resurfacing the pavement every

20 years or so is acceptable, each asphalt layer should provide minimum durability in

order to sustain a long-lasting performance without structural failure. Newcomb et al.

(2001) stated that the upper layers of the pavement should provide enough stiffness to

eliminate rutting potential, while the lower layers of the asphalt pavement should provide

enough flexibility in order to avoid bottom-up fatigue cracking. The total thickness of the

pavement should be sufficient to ensure that tensile strains at the bottom of the asphalt

layers are below the FEL.

High performance graded (PG) binders, such as the stone matrix asphalt (SMA),

are commonly used in the wearing course to provide proper aggregate-to

aggregatecontact to achieve a load carrying capacity, and enough binder and filler content

to provide the surface mix enough impermeability and stiffness. The High performance

graded (PG) binders, such as the stone matrix asphalt (SMA), are commonly used in the

wearing course to provide proper aggregate-to aggregate contact to achieve a load

carrying capacity, and enough binder and filler content to provide the surface mix enough

impermeability and stiffness. The intermediate course is usually composed of an asphalt

mixture that combines the stiffness of the upper layer with the flexibility of the lower

layers. The intermediate course provides a minimum level of rut resistance and durability.

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The asphalt base layer must present enough flexibility and fatigue cracking resistance

such that bottom up fatigue cracking does not initiate under traffic loading. In this study,

the asphalt concrete mixture types and properties for all pavement layers were extracted

from Liao (2007) and Al-Qadi et al. (2008). A rich binder mix was used in the parametric

study to investigate the effect of high asphalt binder content on the tensile strains at the

bottom of the asphalt base. Properties of this mix were also extracted from Liao (2007).

Finite Element Model

Two pavement structures were modeled in this study. The first model simulates a

Deep-Strength asphalt pavement structure. It consists of a 50 mm surface course, a 50

mm intermediate course, a 100 mm to 250 mm asphalt base course, a 180 mm aggregate

subbase, and a 2880 mm subgrade. The aggregate subbase layer was excluded in the

second model to simulate a Full-Depth pavement. In order to assess the impact of using a

rich binder mix in the base course, the parametric analysis included a 100mm thick rich

binder layer as part of the total thickness of the base course layer. The dense graded mix,

standard binder mix, polymer modified binder mix, and high-modulus mix were used to

simulate a total of 58 analysis cases in order to quantify the strain response of Deep-

Strength and Full-Depth pavements to a moving wheel load.

The pavement models were developed using the finite element software

ABAQUS 6.11 (ABAQUS 2011), as shown in Figure 2. The modeled section of the

pavement was 4,750 mm in the transverse direction and 3,600 mm in the traffic direction.

Such dimensions were selected as a compromise between minimizing boundary effect

errors and achieving accurate results at the lowest computational cost. Only half of the

pavement was modeled in the transverse direction. Symmetric boundary conditions were

adopted along the longitudinal symmetry plane. Fixed boundary conditions were assigned

for the remaining planes in the model. A graded mesh was implemented in order to

achieve the highest accuracy without increasing the computational cost. A relatively fine

mesh (20mm) was used in the upper pavement layer and in the vicinity of the vehicle load

path. The length of elements in the wheel path was on average 10 mm in the transverse

direction and 20 mm in the longitudinal direction. Larger elements were used farther from

the loading path. A total of 44,100 C3D8R elements (8-node linear brick with reduced

integration) were used in the model.

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Figure 2 - 3D Finite Element mesh configuration of a Deep‐‐‐‐Strength pavement with 100mm rich binder layer

included in the asphalt base course

To simulate the movement of an 80 kN single axle dual-tire load passage at a

speed of 8 km/h, a quasi-static approach was implemented by gradually shifting the

contact area of the load along the loading path. A total of 170 increments, each with a

duration of 9 milliseconds and a length of 20 mm, were used to model one full wheel load

passage. Longitudinal and lateral strains at the bottom of the asphalt base layer were

examined for one load passage.

In order to simulate the most critical condition for fatigue failure, a relatively high

pavement temperature distribution was adopted. Initially, the pavement temperature was

set to 20°C, and subsequently, a 15°C increase in pavement surface temperature was

simulated. An exponential function was used to simulate the thermal gradient such that

the temperature at the top of the surface course was 35°C, and the temperature at the top

of subgrade (for Full-Depth pavement) or aggregate base (for Deep-Strength pavement)

was 20°C.

Viscoelastic Material Characterization

Flexible pavements have been traditionally modeled as multilayer linear elastic

systems. However, the behavior of HMA materials is highly time and temperature

dependent. At low temperatures and short loading duration, they behave as elastic solids,

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while at high temperatures and long loading duration, they present viscous properties. At

moderate temperatures and loading durations, HMA materials exhibit both the rigidity of

elastic solids, and energy dissipation by frictional losses which are a characteristic of

viscous fluids. In this study, viscoelastic properties of HMA materials are represented

using a linear viscoelastic (LVE) constitutive model which is a simple yet sufficiently

accurate tool for modeling the behavior of asphalt materials.

All HMA materials used in the FE model are assumed to behave as

thermorheologically-simple (TRS) materials, i.e, time-temperature superposition principle

is valid. The latter implies that the material behavior at low temperatures is identical to

that at high frequency loading, while the behavior at high temperatures is the same as that

at low frequency loading. Based on this idea, the long-term behavior of viscoelastic

materials is simulated at relatively high temperatures instead of performing laboratory

tests over a long duration.

For linear isotropic viscoelasticity, the basic hereditary integral formulation is

expressed as follows:

t t. .

0 0

(t)= 2G( - ') ed '+ K( - ') d 's t t t t t f tò ò

Where

t

T0

dt'=

a [T (t')]t ò

In the above equations, ø and e are the mechanical volumetric and deviatoric strains,

respectively; K and G are the bulk and shear modulus, function of the reduced time τ; and

aT is a shift function dependent on the temperature T (ABAQUS 2011).

The time dependent behavior of asphalt concrete is simulated in ABAQUS 6.11

using the Prony (or Dirichlet) series expansion expressed in the form of shear modulus.

The shear modulus is calculated from the relaxation modulus using the following

equation:

E( )G( )=

2(1+ )

tt

u

Where G(τ) is the shear modulus, E(τ) is the relaxation modulus, and ν is the Poisson’s

ratio of asphalt concrete, assumed constant (as for isotropic homogeneous materials). A

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simple normalization of the obtained shear modulus G(τ) with respect to the instantaneous

shear moduli is done to obtain a shear modulus ratio g(τ), expressed as:

i

N -

i

i=1

g( )=1- g (1-e )

t

tt å

Where N is the number of Prony series terms (N=9), τi is the retardation time, and gi is

a dimensionless Prony series parameter.

The temperature dependent behavior of asphalt concrete is modeled using a time-

temperature shift factor. In ABAQUS 6.11, either the Arrhenius shift factor relationship

or the Williams-Landel-Ferry (WLF) equation can be used. In this study, the WLF

equation (Williams et al. 1955) is used:

1 010 T

2 0

C (T -T )Log (a )=-

C +(T -T )

where aT is the time-temperature shift factor, T0 is the reference temperature, C1 and C2 are

regression coefficients obtained by fitting the WLF equation to the corresponding shift

factors at various tests temperatures.

Tire Contact Stresses

Thompson and Carpenter (2006) observed that occasional overloads greater than

the critical 80kN single axle dual-tire load (SAL) will not significantly reduce the HMA

fatigue life and their limited occurrence will not eliminate the concept of no damage

accumulation below the FEL. Thus, an 80 KN single axle dual-tire load (SAL) is used in

this study. Also, knowing that the vertical stresses at the tire-pavement interface are not

uniformly distributed throughout the contact area, measurements of tire-pavement contact

stresses were obtained from the literature. The Goodyear 295/75R22.5 tire was used

based on the measurements of contact stress distribution that were obtained from Park et

al. (2005). Table 1 shows the tread contact stresses of the Goodyear 295/75R22.5 tire

measured using the Vehicle Road Surface Pressure Transducer Array (VRSPTA).

For the 80 kN single axle dual-tire assembly, each tire is loaded 20kN. The

corresponding values of vertical pressure at each tread/tire are interpolated from the

values in Table 1. Figure 3 shows the dimensions of the Goodyear 295/75R22.5 tire

footprint and the corresponding vertical contact stress for each tread.

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Table 1 - Table 1 Goodyear 295/75R22.5 tread contact stresses using VRSPTA (Park et al 2005)

77

6.1

80

7.4

77

5.3

68

1.1

76

5.5

182 199 145

39 31 31 31 39

8.2 8.2 8.2 10.2

Figure 3 - Figure 3 Goodyear 295/75R22.5 tire imprint

(dimensions in mm)

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Results and Analysis

Unless otherwise specified, the Deep-Strength pavement model with 100-mm Dense

Graded Asphalt Base Course is used as the reference example for presenting and

analyzing the results of this parametric study.

Effect of Asphalt Base Binder Course Mix Type

The effect of the asphalt base course mixture on the horizontal flexural strain at the

bottom of the asphalt pavement is examined. As shown in Figure 4, the longitudinal

tensile strains levels are lowest for the high-modulus asphalt base mixture. In percentages,

the maximum tensile longitudinal strain for the high-modulus base course is 60.7 %,

111.8 %, and 150.3 % lower than that of dense graded, polymer modified, and standard

binder courses, respectively. Similar variations are obtained for the maximum lateral

strains when comparing the performance of high modulus asphalt to the other base course

types. The maximum lateral tensile strain for the standard binder asphalt base is 132.1 %

higher than that of the high-modulus layer, while that of the polymer modified and dense

graded asphalt base were 108.6 % and 65.1 % higher, respectively.

Effect of Asphalt Base Course Thickness

The thickness of the asphalt base course is directly related to the reduction in

horizontal strains at the bottom of the asphalt pavement section. Figure 5(a) shows how

the values of longitudinal flexural strains drop at a decreasing rate with increasing

thickness. The standard binder asphalt base course shows the steepest drop. The

maximum tensile longitudinal strain decreases by 1.14µε/mm when the asphalt base

thickness increases by 50 mm. This decrease becomes 0.85µε /mm for another 100 mm

increase in thickness.

Although the level of longitudinal flexural strain in the standard binder mixture is

initially higher than that of the high-modulus mixture, an increase in asphalt base

thickness is more effective in reducing the longitudinal strain for the standard binder

asphalt base mixture. The same increase in thickness is least effective for the high-

modulus asphalt base mixtures. In summary, as the asphalt base thickness increased from

100 mm to 250 mm, the level of longitudinal flexural strain in the standard binder asphalt

base dropped by 137.0 %, while it dropped by 121.9 % in the high-modulus asphalt base

mixtures.

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Figure 4 - Effect of asphalt base course mix type on the longitudinal and lateral strains

Figure 5(b) shows that as the asphalt base course thickness increases, the drop in

lateral peak strain is more pronounced at high base thicknesses. For a standard binder

asphalt base course, the maximum lateral strain drops by only 0.075µε/mm when the

asphalt base thickness increases from 100 mm to 150 mm, while it drops by 0.43µε/mm

as the asphalt base thickness increased from 150 mm to 250 mm. Similarly to longitudinal

strains, the values of lateral strain are highest in the standard binder asphalt base and

lowest for in the high-modulus asphalt base. With increasing asphalt base thickness, the

lateral strain in the high-modulus asphalt base layer decreases at a slightly lower rate than

the other asphalt mixtures.

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Figure 4 - Maximum longitudinal and lateral strain values as a function of asphalt base course mix type and

thickness

Effect of Aggregate Subbase Layer

The aggregate subbase layer in the Deep-Strength pavement model showed that it

has a positive effect in reducing the tensile strain values when the base course thickness is

small. Figure 6 shows the decrease in maximum longitudinal and lateral strains with

increasing base course thickness for both Full-Depth and Deep-Strength pavements using

the dense-graded base course mix. The results show that the aggregate subbase layer

reduced the level of longitudinal strain by approximately the same amount for all asphalt

base thicknesses. On average, the values of longitudinal flexural strain dropped by 34 %

with the addition of the aggregate subbase layer.

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Figure 5 - Maximum longitudinal and lateral strain values as a function of pavement type and asphalt

basecourse thickness

Effect of the Rich Binder Mix in the Asphalt Base Course

Figure 7 shows that the effectiveness of including a rich binder layer decreases

with increasing asphalt base thickness. For instance, for the deep-strength pavement with

dense graded asphalt base, the level of longitudinal peak strain drops 2.2 times with the

addition of the rich binder layer for a total thickness of asphalt base course of 150 mm,

while it drops 1.9 times for a 250 mm total thickness. Similarly, by including the rich

binder layer, the lateral flexural strain decreases 2.5 times for a 150 mm total thickness of

asphalt base course, and 2.2 times for a 250 mm total thickness. It is thus clear that a rich

binder layer placed at the bottom of the asphalt base course acts as a fatigue resistant

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layer that significantly decreases the strain values at the bottom of the pavement section.

The effectiveness of this layer, however, decreases as the total base course thickness

increases.

Figure 6 - Effect of rich binder layer as a function of asphalt base course thickness

Table 2 - Maximum longitudinal strains for Deep‐‐‐‐Strength and Full‐‐‐‐Depth pavements without the 100‐‐‐‐mm rich

binder layer

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Table 3 - Maximum lateral strains for Deep‐‐‐‐Strength and Full‐‐‐‐Depth pavements without the 100‐‐‐‐mm rich

binder layer

Table 4 - Maximum longitudinal strains for Deep‐‐‐‐Strength and Full‐‐‐‐Depth pavements including the 100‐‐‐‐mm

rich binder layer

Table 5 - Maximum lateral strains for Deep‐‐‐‐Strength and Full‐‐‐‐Depth pavements including the 100‐‐‐‐mm rich

binder layer

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Maximum Longitudinal and Lateral Flexural Strain

The results of the parametric study for the maximum longitudinal and lateral

flexural strains of Deep-Strength and Full-Depth pavements are shown in Table 2 and

Table 3, respectively. Table 4 and Table 5 show that the presence of a 100-mm rich

binder mix at the base of the asphalt pavement section significantly reduces both

longitudinal and lateral flexural strains.

Knowing that the Fatigue Endurance Limit (FEL) for typical HMA mixtures

varies between 60 and 100 µε depending on the mix type, values presented in these tables

can be used as a guide in selecting design alternatives that would limit the tensile strain at

the bottom of the HMA layer below the chosen FEL value in a particular design. As a

general guideline, the longitudinal and lateral tensile strains at the bottom of the HMA

layer are found to be most sensitive to a change in asphalt base course thickness. In

addition, the rich binder layer is found to have a crucial role in reducing the maximum

tensile longitudinal and lateral strain below 100 µε. The maximum longitudinal tensile

strain drops approximately 1.7 times when the mix of the 100mm asphalt base is changed

from a dense graded to a rich binder mix. Similarly, the rich binder mix layer decreases

the maximum lateral strain by approximately 1.8 times. If the rich binder layer is not

used, other design strategies can be selected in order to limit the maximum tensile

longitudinal and lateral strain below the FEL.

Conclusions and Recommendations

This study examined different design alternatives used to achieve a long-life, perpetual

pavement. A 3D FE pavement model involving Linear Viscoelastic (LVE) properties for

HMA materials and non-uniform tire contact stresses was developed using ABAQUS.

The results of the parametric study showed that the high modulus mix used in the asphalt

base course outperformed all other asphalt mixtures. It presented the lowest levels of

longitudinal and lateral strains. The dense-graded and polymer modified mixes ranked

second in reducing the values of tensile strains at the bottom of the asphalt pavement. The

longitudinal strain values in the standard binder mix were higher than that of the high-

modulus mix; however, these values decreased significantly when the asphalt base course

thickness was increased. The effect of varying the asphalt base course thickness was

lowest for the high-modulus asphalt base mix. The aggregate subbase layer on top of

subgrade soil was found to have a relatively small impact on the longitudinal and lateral

strains at the bottom of the asphalt base layer. The addition of a rich binder layer at the

bottom of the asphalt base course significantly reduced the longitudinal and lateral

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strains. Increasing the asphalt base thickness was found more effective in reducing the

strain levels in cases where the rich binder mix was not included.

The results of this parametric study can be easily compared to the results of laboratory

and field testing that were obtained from the literature review. Conclusions drawn from

this numerical assessment of design strategies used in long-life, perpetual, pavements

were found to complement the research findings of Molenaar et al. (2009), Monismith et

al. (2001), Anderson and Bentsen (2001), Harvey et al. (2004), Goodrich (1988), and Lee

et al. (2002), that were presented in the beginning of the paper.

Finally, the values of longitudinal and lateral strains presented in Table 2 toTable 5 were

provided as a guideline to assess various design alternatives to achieve a long-life

pavement. Knowing that a high positive pavement temperature distribution was used in

this model, the measured flexural strains are expected to be the highest during the seasons

of the year. Hence, values presented in Table 2 to Table 5 are considered to be

conservative, since during most of the remaining of the year, the flexural strains at the

bottom of the HMA layer will be of lower magnitude.

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