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Prediction of flow rutting in asphalt concrete layersSafwat F. Said a , Hassan Hakim a , Erik Oscarsson b & Mattias Hjort aa Swedish National Road and Transport Research Institute, Highway Engineering , Linköping,Swedenb Department of Technology and Society , Lund University , Lund, SwedenPublished online: 04 Apr 2011.

To cite this article: Safwat F. Said , Hassan Hakim , Erik Oscarsson & Mattias Hjort (2011) Prediction of flow rutting in asphaltconcrete layers, International Journal of Pavement Engineering, 12:6, 519-532, DOI: 10.1080/10298436.2011.559549

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Prediction of flow rutting in asphalt concrete layers

Safwat F. Saida*, Hassan Hakima, Erik Oscarssonb and Mattias Hjorta

aSwedish National Road and Transport Research Institute, Highway Engineering, Linkoping, Sweden; bDepartment of Technology andSociety, Lund University, Lund, Sweden

(Received 16 April 2010; final version received 28 January 2011)

This paper evaluates an approach for predicting rut formation in asphalt concrete (AC) layers. The approach is based on alinear viscoelastic model for predicting permanent vertical strain in AC layers subjected to a moving load. The input data aretyre pressure, loading speed, lateral wandering of loading wheel, shear modulus and phase angle of AC layer. The analyticalapproach takes into consideration the change in material characteristics in respect of temperature and changes in the air voidcontent of AC layers due to repeated loading. The approach is verified by a full-scale accelerated loading test at differenttemperatures. The approach has shown good agreement as regards the prediction of flow rutting in AC layers. In addition,the approach is capable of calculating rutting profiles including the upheaval, which is important for estimating rut depth.

Keywords: modelling; asphalt concrete; flow rutting; viscoelastic; shear modulus; phase angle

1. Introduction

In spite of the generally cold climate in Sweden, the

temperature in flexible pavement can reach 508C at the

pavement surface (,308C in the binder layer), and flow

rutting is, therefore, one of the most frequent types of

distress on high-volume roads. For example, Figure 1

illustrates rutting on the E4 motorway, which is the main

road between the north and south of Sweden and down into

Europe. The rutting is primarily due to the use of bitumen

binders with relatively high penetration (160/220 and

70/100 according to EN 12591 2009). Flow rutting is

defined as an excessive deformation in the wheel paths,

which gradually increases with increasing number of

vehicle load repetitions. Flow rutting in an asphalt concrete

(AC) layer is caused by two mechanisms: densification,

which is a decrease in volume and increase in density of an

AC layer, and shear deformation with formation of

upheavals, which are displacements of material caused by

load-induced shear stresses. In addition to traffic history

and climate factors, flow rutting is affected by the

properties of asphalt mixtures, especially at high

temperatures and under loading of relatively long duration,

when the mix properties are dominated by the viscous

character of the material (Sybilski 1996, Blab and Harvey

2002). Flexible pavements should, therefore, be designed,

among other things, with respect to resistance and to

permanent deformation. Read and Whiteoak (2003)

pointed out that reduction in permanent strain can be

achieved by stiffening the bitumen so that the viscoelastic

response of the AC is reduced and/or by increasing the

elastic component of the bitumen, thereby reducing the

viscous component. Elastic and viscous components can be

measured by means of the phase angle of the material under

test conditions (Read and Whiteoak 2003, Bahia 2009,

Biligiri et al. 2010). Addition of bitumen modifiers has the

purpose of improving one or both of these properties.

Therefore, both stiffness and phase angle, and conse-

quently viscosity, should ideally be accounted for in a

permanent deformation model for AC.

Figure 2 shows typical test results from a repeated

load test. It can be seen that the permanent deformation

development can be divided into three zones: initial,

secondary and tertiary. The mechanism of permanent

deformation (flow rutting) in AC layers was described by

many investigators, for example Eisenmann and Hilmer

(1987), Sousa et al. (1991), Verstraeten (1995), Kaloush

and Witczak (2002), Blab and Harvey (2002), NCHRP 1–

37A (2004) and Oscarsson (2007). The initial deformation

zone is primarily caused by an increase in density, called

post-compaction from repeated traffic loading. Some of the

initial deformation is also related to plastic deformation

(NCHRP 1–37A 2004). This zone might be chiefly related

to construction work (Bjorklund 1984, Eisenmann and

Hilmer 1987) due to shortcomings in compaction. In the

secondary zone, the deformation grows with time although

at a decaying rate (depending on the stress level). The

deformation is primarily related to the lateral movement of

material associated with minor changes in AC properties.

The lateral movement or displacement of material is

induced by repeated shear stresses. In the third (tertiary)

ISSN 1029-8436 print/ISSN 1477-268X online

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http://dx.doi.org/10.1080/10298436.2011.559549

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*Corresponding author. Email: safwat.said@vti.se

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zone, the deformation rate increases rapidly, indicating a

type of failure.

Rutting in the AC layers of pavements can be

estimated by a number of models (Sousa et al. 1991,

Verstraeten 1995). In the case of AC layers, rutting

originates primarily from shear deformations in the layer

under traffic loading. Linear viscoelastic theory that makes

use of shear deformation was adopted by several

investigators. Bjorklund (1984) studied a linear visco-

elastic approach for behaviour of AC when subjected to a

moving load on a halfspace. The asphalt mix property is

defined through the steady state viscosity of the AC

material (zero-shear-rate viscosity, ZSV) in which the ratio

of shearing stress to the rate of shearing strain is constant

and called Newtonian behaviour. Hopman (1996) devel-

oped a linear viscoelastic multi-layer program called

VEROAD for analysis of stresses and strains in pavements.

Hopman used Burger’s model for determination of the

viscoelastic properties of AC. Viscoelastic models have

the capability to discriminate between different bitumi-

nous materials under moving loads and, therefore, give

reasonable pavement responses (stress and strain; Hopman

1996, Hopman et al. 1997, Nilsson 2001), which are

important for evaluating mixes against flow rutting. The

constitutive relationship used in MEPDG (NCHRP 1-37

2004) to predict rutting in the AC layer is based upon

analysis of laboratory repeated load permanent defor-

mation tests. Both plastic and resilient strains of the

asphalt material as a function of temperature, rate of

loading and number of load applications are used to

predict rutting. The CalME software (Deacon et al. 2002,

Ullidtz et al. 2008) has adopted a shear-based approach for

predicting rutting in the AC layer. The permanent shear

strain is determined from repeated shear tests at constant

height as a function of the shear stress, the elastic shear

strain and the number of load applications.

Bjorklund’s approach and VEROAD are capable in

predicting rutting profile, including the upheavals, which is

valuable in predicting rut depth. In Bjorklund’s approach,

rutting caused by post-compaction (decrease in volume)

and flow rutting (no change in volume) is calculated

separately, showing the effect of each mechanism alone,

which is interesting for future development. MEPDG and

CalME use a power function in simulating rut development

with respect to the load applications. Interesting feature

produced in CalME is an incremental recursive procedure

in which the material’s properties are updated in terms of

damage for each time increment and used as input to the

next time increment.

In this work, the algorithms of a linear viscoelastic

model reported by Bjorklund (1984) were adapted for

prediction of permanent vertical strain in AC layers

subjected to a moving load using ZSV (Newtonian

Figure 1. Flow rutting on the E4 motorway.

Initial

Per

man

ent s

trai

n ε p

Load repetitions

Secondary Tertiary

Figure 2. Typical test results from repeated load test.

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behaviour) of AC material. Although the AC characteristic

is non-linear (non-Newtonian behaviour) for the environ-

mental conditions under which flow rutting develops, see

for example Uzan (1996). The procedure developed in

this study for calculation of the permanent deformation

of AC layers is called permanent deformation of AC layer

for roads (PEDRO). The approach is evaluated using a

full-scale accelerated loading test (heavy vehicle simu-

lator, HVS) at different temperatures. The permanent

deformations of the AC layers were measured separately

at intervals of wheel passages for verification of the

approach. In order to verify the adapted model in this

work, two test sections were built at VTI (the Swedish

National Road and Transport Research Institute in

Linkoping). This work is limited to prediction of rutting

in AC layers.

2. Objective

The purpose of this study is to evaluate an analytical

approach for predicting flow rutting in AC layers using a

full-scale accelerated loading test with HVS. The

structural sections are instrumented for measurement of

the deformation in each AC layer. The predictive model,

PEDRO, is based on the number of passages of wheel

loads, the pavement structure and the mixture properties at

various temperatures. The aim is to present a procedure

(model) which can be used in routine engineering work to

evaluate flow rutting in AC pavement layers.

3. Mechanistic rutting approach

Bjorklund (1984) proposed the use of a linear viscoelastic

theory to calculate permanent vertical strain caused by a

moving wheel load over a viscoelastic halfspace. The

permanent vertical strain at a particular point in the AC

layer can be calculated as a function of the steady state

viscosity of AC as well as traffic load and speed. The ZSV

of the AC was determined from oscillatory shear test of

AC cores in evaluation of an AC layer’s resistance to

rutting. The permanent deformation of each layer or sub-

layer is then integrated over the AC layer.

The permanent vertical strain (1p), encountered in the

initial and secondary zones, can be calculated at various

depths and transversal positions in the pavement structure

under a moving load. The relationship, Equation (1), was

described by Bjorklund (1984) for the calculation of

permanent vertical strain as follows:

1p ¼s0·ð1 2 2vÞ

V ·hA

·Re

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðzþ ixÞ2 þ a2

q2 ðzþ ixÞ

� �

þs0·z

V ·hA

·Re 1 2zþ ixffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðzþ ixÞ2 þ a2p

" #;

ð1Þ

where 1p represents the permanent vertical strain (mm/m);

s0, tyre pressure (Pa); a, radius of contact area (m); n,

Poisson’s ratio; z, depth from road surface (m); V, vehicle

speed (m/s); hA, ZSV of asphalt mix (Pa s); x, distance

from loading centre (m); i ¼ffiffiffiffiffiffiffi21

p:

The model can take changes in volume or compres-

sibility of asphalt mix into consideration using Poisson’s

ratio during the loading history. The model, as presented is

Equation (1), consists of two terms: one for calculation of

compressibility representing the initial zone when a

substantial change in volume is expected and one for

calculation of the flow rutting part of the deformation

when almost no change in volume is expected. At the end

of the first zone (Figure 2), Poisson’s ratio is supposed to

reach 0.5 and then the term for compressibility vanishes.

This does not necessarily mean that Poisson’s ratio is 0.5

during the entire test but implies that the AC layer behaves

as a viscoelastic material in dilatation without a permanent

change in volume (Bjorklund 1984). Figure 3 illustrates

the distribution of permanent vertical strains for both terms

of the relationship in relation to the depth from the surface.

Depending on the variables, the maximum permanent

vertical strain (1p) occurred at a depth of 5–12 cm from the

surface. Other investigators also found that the shear

deformation in pavement is greatest in the upper part of

pavements and gradually decreased in lower parts. See for

example the State-of-the-Art report by Sousa et al. (1991)

and Monismith et al. (2006). Figure 4 illustrates an

example of permanent vertical strain in a semi-infinite AC

layer subjected to HVS loading at 12 km/h with a single-

wheel load of 60 kN and a tyre pressure of 900 kPa under

the assumption that viscosity is constant at 1 GPa s.

Positive strains give rise to rutting in the wheel path and

negative strains give rise to upheavals at the sides of the

wheel path.

The ZSV of the AC layers was calculated as a function

of the shear modulus and phase angle of the AC mixtures

in respect of the test conditions. Mix properties were

0.0 5.0 10.0 15.0

Term 1Term 2Term 1&2

20.00

0.1

0.2

0.3

0.4

Dep

th (

m)

Permanent vertical strain × 10–9

Figure 3. Contribution of terms 1 and 2 of Equation (1) topermanent vertical strain distributions in relation to depth inpavement.

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determined experimentally by testing cores from AC

layers in the laboratory. The ZSV of AC mixtures which is

needed to calculate rutting using the viscoelastic model

has to be determined for temperatures in the field.

Investigators using viscoelastic models earlier used simple

rheological models related to binder viscosity for

estimation of the AC viscosity (Collop et al. 1992). For

Newtonian material (steady state viscosity), the complex

viscosity of material h* is equal to the complex shear

modulus of material G* divided by angular frequency.

Sybilski (1996) and Anderson et al. (2002) used frequency

sweep test on asphalt binders to determine the ZSV using

the cross model. Sybilski (1996) used ZSV to characterise

asphalt binders with respect to rutting resistance of AC

mixtures in the laboratory. For the determination of the

ZSVof AC materials, Oscarsson and Said (2010) analysed

data from frequency sweep shear test on AC specimen and

the use of the Cross model. However, as noted above in the

range of temperatures of interest in pavement applications,

the asphalt materials behave as non-Newtonian material

and the viscosity is thus a function of temperature and

loading time. A correction factor is, therefore, needed to

account for non-Newtonian behaviour of asphalt binder

(Bonaquist et al. 1998, NCHRP 2004).

In this work, the ZSV (h*0) is determined as the

absolute viscosity related to the loss of compliance of

shear modulus (J00) at low angular frequencies (Bjorklund

1984, Anderson et al. 2002, Mezger 2006). Oscarsson and

Said (2010) described a procedure for estimation of the

ZSV of AC material based on loss compliance of shear

modulus (J00) determined as the imaginary part of Equation

(2) (Chehab and Kim 2009). The value of hv is determined

by Equation (5) and making use of Cross model, Equation

(6), for estimation of the ZSV and constants K and m

(Sybilski 1996, Anderson et al. 2002)

ðG0ðvÞ þ iG00ðvÞÞ £ ðJ 0ðvÞ2 iJ 00ðvÞÞ ¼ 1; ð2Þ

G0 ¼ G *�� ��·cos ðfÞ; ð3Þ

G00 ¼ G*�� ��·sin ðfÞ; ð4Þ

hv ¼1

2·v·J 00v: ð5Þ

As v ! 0 then hv ¼ ZSV,

hv ¼h0

1 þ ðK·vÞm; ð6Þ

where G* is the dynamic shear modulus (MPa); G00, loss

component of shear modulus (MPa); G0, storage com-

ponent of shear modulus (MPa); f, phase angle in degrees;

J00, loss compliance of shear modulus (MPa21); J0, storage

compliance of shear modulus (MPa21); h0, ZSV (MPa s);

hv, viscosity (MPa s); v, angular frequency (rad/s); K and

m, constants.

The rut depth is calculated by integrating the

permanent deformation over the thickness of the AC

layer or layers. However, the effects of densification/

hardening/ageing of asphalt mixes are also crucial for rut

prediction. These effects result in better resistance of AC

(increased stiffness) to permanent deformation and should

be taken into consideration as accurately as possible for a

good prediction of rutting.

3.1 Stiffening of mix due to post-compaction

It is worth bearing in mind that using physical properties of

AC layers to predict rutting (or deterioration in general) is a

dilemma. Asphalt concrete materials change many of their

Figure 4. Illustration of permanent vertical strain in m1 in a semi-infinite AC layer without lateral wander. Upper and lower sectionsrepresent terms 1 and 2, respectively, in Equation (1).

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mechanical properties over time due to post-compaction

(densification due to traffic loading), ageing and hardening

or curing (Nunn 1996, Jacobson and Hornwall 1999,

NCHRP 2004, Said 2005, Swedish Code 2005, Wiman et al.

2009) and this cannot be ignored in prediction models.

Stiffening of AC, especially during the early life of the

pavement, is usual and must be considered in theoretical

model for prediction of pavement deterioration. Most of the

stiffening occurs during the first year and subsequently only

moderate changes are expected. For example, Figure 5

shows changes in air void content in relation to mix type,

initial air void content and age at a temperature of 258C. Air

void content decreases significantly with time after

construction, depending on the initial air void content.

However, Ullidtz et al. (2008) reported the average

decrease in air voids over the first 12 months, for the top

and bottom lifts from cores, and was found to be 0.36 of the

original air voids. The effect of post-compaction or

densification (decrease in air voids due to loading) on the

shear characteristics of asphalt material should, therefore,

be taken into consideration when the tested specimens are

taken from areas not subjected to traffic.

In a trial to study the effect of degree of compaction on

the stiffness modulus of a frequently used mix, Karlstrand

and Neander (2006) quantified the increase in the stiffness

moduli of specimens with decreasing air void content as

shown in Figure 6. The stiffness moduli of laboratory-

compacted dense AC (ABb 16 160/220) specimens at

different compaction levels were measured using the

indirect tensile test. The compaction levels were adapted to

the decrease in air void content encountered in the field

during the initial period, which is about 1–2 years

depending on traffic volume (Jacobson and Hornwall

1999). The relationship between stiffness modulus and air

void content (Figure 6) was used in correction of shear

moduli and phase angles of the specimens. Equation (7) was

developed based on the Karlstrand and Neander (2006)

work to calculate the increase in stiffness modulus in

correlation with decrease in air void content. Decrease in

phase angle, in respect of decrease in air void content, can be

predicted by means of the relationship between stiffness

modulus and phase angle (in respect of change in stiffness

modulus), the so-called black diagram (Francken and

Vanelstraete 1997). Verification of the relationship by

testing further mixes and cores will be useful

DS ¼ DV ·4:374·e0:0445·T ; ð7Þ

whereDS is the change in stiffness modulus (%);DV, change

in air void content (%); T, AC temperature (8C).

Figure 5. Relative importance of initial air void content in relation with time at a mean annual air temperature (NCHRP 2004).

00 1 2 3 4 5 6 7 8

2000

4000

6000

8000

10000

12000

Air void content (%)

Stif

fnes

s m

odul

us (

MP

a)

10°C

5°C

20°C

Figure 6. Relationships between stiffness moduli and air voidcontent at different temperatures for dense AC (Karlstrand andNeander 2006).

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4. Testing programme

4.1 HVS testing

The VTI-accelerated loading facility, HVS– Nordic

(Wiman and Erlingsson 2008), is a linear full-scale mobile

road-testing machine (HVS Mark IV). The facility has a

heating/cooling system that uses air media. The HVS was

used to apply single-wheel loads of 60 ^ 0.5 kN using a

wide base tyre with a tyre pressure of 900 ^ 30 kPa. The

test wheel travels at a speed of 12 ^ 0.3 km h21 with bi-

directional loading. Lateral wander was accomplished with

a normal distribution of^350 mm and a standard deviation

of 123 mm. The HVS test was performed inside a climate-

controlled chamber in three constant temperature phases.

The test started at 108C, which was then increased to 20 and

308C. The loadings were halted when the temperature was

changed. In this investigation, two test pavements were

constructed in a pit (5 m £ 15 m with a depth of 3 m). The

pavement section is 8 m long and the speed is constant over

6 m of the section. Each test-pavement section in this study

was thus 3 m long as shown in Figure 7. The pavement

sections were constructed in the summer of 2004 and tested

between December 2004 and March 2005. For more

details, see Wiman (2010).

4.2 Structure and materials

The two flexible pavement sections consisted of a standard

AC pavement section according to Swedish norms and an

enhanced AC pavement section. The enhanced structure

was expected to have higher resistance to rutting. The

flexible structures consist of three AC layers: wearing,

binder and asphalt base layer constructed on an unbound

base layer and a layer of fine sand in the testing pit. The

two structures were practically identical except that the

binder layer of the enhanced AC section was polymer

modified. The pavement structures are shown in Figure 7

and asphalt mix properties are presented in Table 1.

Further details can be found in Wiman (2010) and

Oscarsson (2010). During the construction of the

pavement sections, displacement sensors were installed

in the structures (Wiman 2010). A total of 18 coil pairs of

deformation sensors were used to measure permanent

vertical deformation in the full-scale section. Three pairs

per each asphalt layer and structure were used. The

inductive coil sensors are called 1-mu, where 1-mu is an

acronym for strain (1) measuring unit, pronounced ‘emu’

(Janoo et al. 1999), and were manufactured at VTI’s

laboratory. To measure vertical displacement at one point

in an asphalt layer, one coil is attached to the bottom and

one to the surface of the AC layer at the mid-point of the

wheel track, for sending and receiving signals. The

locations of 1-mu are illustrated in Figure 7. A loose coil

was used at the pavement surface to measure permanent

deformation in the wearing course.

4.3 Shear characteristics

Figure 8 shows the shear test device used in this work. A

cylindrical specimen is glued between two steel plates

with epoxy glue. One of the plates can be exposed to

sinusoidal or repetitive loading over a range of

frequencies. Briquette specimens of 150 mm in diameter

may be tested. The thickness of the specimen should be

,1/4 of the diameter to come close to pure shear state

(Lundberg 1956). It is thus possible to test thin specimens

at actual pavement layer thickness. Further information on

the shear test can be found in Said (2004).

Test specimens were cored from all AC layers after

accelerated loading with HVS outside the loaded area.

Cylindrical specimens were 150 mm in diameter with a

maximum thickness of 40 mm. Specimens were tested by

sinusoidal loaded shear test (oscillatory test). The

temperatures chosen for the test were 210, 0, 10, 25 and

408C with an accuracy of ^0.58C and the frequencies

were 0.05, 0.1, 1, 5, 10 and 20 Hz. The master curves were

obtained using the time – temperature superposition

Figure 7. The standard and enhanced AC structures withlocations of the strain measuring units (1-mu) along the pavementsections.

Table 1. Properties of the asphalt mixes according to their recipes (Oscarsson 2010).

Mix type ABT ABb ABbm AG

Maximum aggregate size (mm) 11 22 22 22Binder content (%) 6.5 5.0 5.0 4.5Bitumen type Pen 70/100 Pen 70/100 Pen 70/100 modified Pen 160/220

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principle using Arrheniu’s approach (Francken and

Vanelstraete 1997). The test results obtained for all four

asphalt mixes, with at least two specimens per mix (in all

10 specimens tested at six frequencies and five

temperatures), are presented in Figures 9 and 10. Figures

9 and 10 show the master curves of shear moduli fitting to

a sigmoidal function and phase angles fitting to a beta

function (Biligiri et al. 2010), respectively, for all mixes.

The variation of the shear modulus and the phase angle at

frequency ( f ) and temperature (T) is expressed as a

function of reduced variable (log ðaT ·f Þ). These results

indicate significant differences between the layer mixes.

The master curve approach was used for calculation of the

shear modulus and phase angle of AC layers (wearing,

binder and base courses). Values of shear moduli and

phase angles of AC layer mixes were used to calculate the

ZSV of AC mixes in respect of HVS testing temperatures

for use in prediction of rut depth using Equation (1). The

estimated ZSVof the AC layers (described in Section 3) is

shown in Figure 11. The ZSV results indicate, as master

curves of shear moduli and phase angles, significant

differences between the layer mixes.

On the basis of laboratory measurements and the

influence of stiffening noted earlier (Section 3.1), Table 2

shows the assumed changes in air void content at the end

of the initial zone. The asphalt mixes ABT, ABb and

ABbm are dense mixes and a 1% decrease in their air void

content at 208C is taken to be reasonable. The base course

Figure 8. Shear box for AC.

10

100

1000

10000

–7–7 –2 3–5 –3 –1 1 3 5 7

–7 –5 –3 –1 1 3 5 7 –7 –5 –3 –1 1 3 5 7

She

ar m

odul

us (

MP

a)

10

100

1000

10000

She

ar m

odul

us (

MP

a)

10

100

1000

10000

She

ar m

odul

us (

MP

a)

10

100

1000

10000

She

ar m

odul

us (

MP

a)

AG 22

ABbmABb

ABT

X=log(aT*Fr) X=log(aT*f)

X=log(aT*Fr) X=log(aT*Fr)

Figure 9. Master curves for shear moduli of AC mixes represented by sigmoidal function with several samples per mix at Tref ¼ 108C.

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mix AG is an open-graded mix with an air void content of

about 7% according to the recipe. A 3% decrease in air

void content is, therefore, expected at 208C. The decrease

in air void content at 108C is estimated to be 0.5% for all

four mixes. The long-term effect of decreases in air voids,

presented in Figure 5, is not implemented in this work due

to the absence of data, which should have an impact on rut

growth. The measured and the adjusted values of the shear

moduli and phase angles in respect of decrease in air void

content are presented in Table 3. (Mix properties at 308C

were not analysed due to excessive rutting during the HVS

testing.) These adjustments have resulted in the increase in

the shear moduli and in the decrease in the phase angles,

which have a significant effect on the calculated viscosities

and by extension on the predicted rut depth.

According to Equation (1), Poisson’s ratio has a

significant effect on the predicted rutting in the initial

zone. Sayegh (1967) reported that Poisson’s ratio of the

AC mixes varies approximately between 0.1 and 0.5

depending on the temperature and frequency of the test.

Nilsson (2001) has shown that Poisson’s ratio of the

asphalt material is highly dependent on the strain,

temperature and frequency of the test. Consequently, in

this work, the assumed Poisson’s ratios are 0.20 and 0.35

at 10 and 208C, respectively. However, further investi-

gation of change of Poisson’s ratio with load applications

would be an improvement to PEDRO.

In this work, the test sections were tested several

months after the AC layers were laid, and cored specimens

were tested by means of shear tests at about the same time.

It was, therefore, concluded that a great part of the early

ageing and/or hardening should have occurred before the

start of the HVS and laboratory testing, and the effects of

long-term ageing over a long period in-service (several

years) had not occurred in this work since the HVS testing

ABT

5

10

15

20

25

30

35

X=Log (aT, f)

Pha

se a

ngle

(de

gree

)

AG

5

10

15

20

25

30

35

–4 –2 0 2 4 6–4 –2 0 2 4 6

X=Log (aT, f)

X=Log (aT, f)

–4 –2 0 2 4 6–4 –2 0 2 4 6

X=Log (aT, f)

ABbm

0

5

10

15

20

25

30

35

Pha

se a

ngle

(de

gree

)

Pha

se a

ngle

(de

gree

)P

hase

ang

le (

degr

ee)

ABb

5

10

15

20

25

30

35

Figure 10. Master curves of phase angles for AC mixes represented by beta function with several samples per mix at Tref ¼ 108C.

1E–06

1E+13

1E+12

1E+11

1E+10

Vis

cosi

ty (

Pas

)

1E+09

1E+08

1E+071E–04 1E–02 1E+00 1E+02 1E+04 1E+06

Angular frequency (rad/s)

ZSV (20°C)

ABbmABbAGABT

Figure 11. Viscosity versus angular frequency of AC mixes inrelation to temperature.

Table 2. Assumed changes in air void content due to post-compaction in relation to temperatures.

Asphalt mix type

Temperature (8C) ABT ABb ABbm AG

10 0.5 0.5 0.5 0.520 1.0 1.0 1.0 3.0

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was completed in about 3 months. Otherwise, the ageing

impact should be taken into consideration, i.e. in the field.

5. Prediction of rutting in accelerated HVS test

5.1 Rut depth growth

The HVS testing started at the lowest temperature by

loading the pavement sections with about 150,000

passages at 108C, 300,000 passages at 208C and 100,000

passages at 308C. Shifting to a higher test temperature was

done until it was certain that the second zone (see Figure 2)

was reached. The measured permanent deformations in

relation to the number of load passages per each AC layer,

using 1-mu coils, are shown in Figures 13–15. Many

variations are apparent in the measured deformations.

The permanent deformation in the wheel path is

calculated using Equation (1) for the AC layers at 10 and

208C. (Calculation of rutting at 308C was not done due to

excessive rutting, which is unknown if the mix is in the

initial or tertiary flow zone. The deformation at the surface

of the reference section was greater than 50 mm, and

originated from unbound and bound layers, and this might

result in uneven contact pressure.) For calculation of the

deformation at the initial zone, the end of the first zone was

determined when the linear zone (secondary zone in

Figure 2) has started. In practice, this is usually

encountered after approximately 1 year of traffic

(Jacobson and Hornwall 1999, Wiman et al. 2009). The

permanent deformation of each layer is determined by

integrating the permanent deformation over the thickness

of the layer. The calculated permanent deformations at the

initial zone and the secondary zone were calibrated to the

rutting data at the HVS test.

Kc ¼ aþ bT ; ð8Þ

Kf ¼ cþ dT ; ð9Þ

where Kc is calibration factor for the compressibility; Kf,

calibration factor for the flow rutting; T, AC temperature

(8C); a, b, c and d, calibration constants.

Calibration constants were found based on curve fitting

between measured and calculated deformations for each

zone. Figure 12 shows relationships between measured and

calculated deformations for secondary zone at 208C. It is

evident that the deformations for the binder layers are

underestimated because the calculations are in linear

viscoelastic range. However, the HVS test is in nonlinear

viscoelastic range. The base course layer (AG) shows

unexpectedly overestimated deformations that are com-

mented later. The calibration constants of initial (compres-

sibility) and secondary (flow) zones for wearing, binder

and asphalt base layers are shown in Table 4. The

permanent deformation was calculated for each AC layer

and compared with the measured permanent deformation

of each layer of the HVS testing. Figure 13 shows the

comparison between measured and calculated defor-

mations versus number of load applications in the wearing

course. Measurements from two of the 1-mu gauges out of

a total of six 1-mus were rejected due to inverse values and

large variations in the measurements. The average value of

the four 1-mus was used for calculation of rutting in the

wearing course for both structures because it is the same

mix ignoring the effect of multilayer structure. Calculated

and measured deformations of the binder courses are

illustrated in Figure 14. There is variation in the measured

deformations in both structures, but on average the

Table 3. Measured and adjusted shear characteristics of AC mixes.

Shear modulus (MPa) Phase angle (degrees)

Temperature (8C) ABT ABb ABbm AG ABT ABb ABbm AG

Measured shear characteristics at initial air void content10 2644 2959 2777 2625 18.8 17.6 15.5 21.920 1457 1747 1739 1391 26.5 23.7 20.4 28.1

Adjusted shear characteristics at air void content after post-compaction10 2734 3060 2872 2715 18.0 16.9 14.9 21.420 1612 1934 1924 1835 25.1 22.5 19.3 25.4

Figure 12. Relationships between measured and predicteddeformations for secondary zone at 208C.

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enhanced binder layer (ABbm) shows less deformation

than the standard binder layer (ABb). The comparisons

between calculated and measured deformations in relation

to the number of load applications at 10 and 208C appear to

be quite reasonable for both layers, despite using the same

calibration factors (Kc and Kf) for both binder layers. On

average, the ABb layer shows 50% larger rut depth than the

ABbm layer. This should be the influence of an increased

viscosity of the ABbm mix by a factor of 1.5 compared with

the viscosity of the ABb mix. The ZSV determined from

the shear properties tested in the laboratory can thus be

useful in the evaluation of a mix property against

permanent deformation. Further investigation on relation-

ship between the ZSV and rut formation in the field would

be valuable for pavement and mix design.

Calculated and measured deformations of the base

course layer are illustrated in Figure 15. Unfortunately,

four out of a total of six 1-mu gauges were non-functional.

Nevertheless, the two 1-mu measurements are taken to be

representative of deformation in both sections, because it

is the same mix. The reason for the relatively small c

constant, less than 1 unit (Table 4), for asphalt base layer in

comparison with the other two layers is not known.

However, it is worth noting that measured temperatures

during the HVS test are missing due to a computer crash

and there was a significant fall in ambient air temperature

at the time of testing (Figure 16). The operator reported

several adjustments of temperatures in order to keep the

temperature of the binder layer at the test temperature

(^18C). It can, therefore, be concluded that the

temperatures of the base course might have been lower

than the test temperatures due to shortcoming of the

temperature chamber (isolated only from the surface of the

ground). This could have resulted in lower temperature

(,208C) of the base course layer. It is worth mentioning

that when the model is implemented in the field, the

temperature gradient in the pavement must be treated with

caution.

The total permanent deformation in the AC layers is

the sum of the permanent deformations of the asphalt

layers versus the number of load applications. Figure 17

illustrates the rut depth accumulations in the AC layers for

both sections. It is worth to note in Figure 17 that the

measured rut rate of the two structures at about 350,000

repetitions clearly decreases. This might be caused by a

decrease in temperature as noted earlier. Furthermore, one

can observe that the model predictions are linear in both

the initial and the secondary zones. Using a variable

Poisson’s ratio instead of a constant value in the prediction

of rutting in the initial zone will result in convexity

Table 4. Calibration constants for pavement layers.

Calibrationfactor Constants Wearing Binder

Asphaltbase

Kc a 2.63 49.05 1.62b 20.076 22.132 20.025

Kf c 24.50 7.93 0.76d 21.182 20.318 20.024

–1

0

1

2

3

4

5

0 100 200 300 400 500 600

No. of load applications × 103

Def

orm

atio

n (m

m)

EMU105 ABTEMU107 ABTEMU108 ABTEMU110 ABTPredicted

Figure 13. Measured and calculated rut depth development forwearing course, ABT 12 70/100 mix at 10, 20 and 308C.

0

1

2

3

4

5

6

7

8

9

10

0 100 200 300 400 500 600

No. of load applications × 103

Def

orm

atio

n (m

m)

EMU111 ABbm EMU117 ABbEMU113 ABbm EMU119 ABbEMU115 ABbm EMU121 ABbPredicted ABbm Predicted ABb

Figure 14. Measured and calculated rut depth development forbinder courses, ABb 22 70/100 and ABb PMB mixes at 10, 20and 308C.

0

2

4

6

8

10

12

0 100 200 300 400 500 600

No. of load applications × 103

De

form

atio

n (

mm

)

EMU112 AG

EMU114 AG

Predicted at 10/20°C

Figure 15. Measured and calculated rut depth development forbase course mix, AG16 70/100 mix at different temperatures.

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upwards that is comparable with the measured rutting. In

the secondary zone, the development of deformation at a

decaying rate would have been found to be more

comparable with the measured rutting if the effect of

hardening/ageing was included despite the short testing

period. Constant Poisson’s ratio was used for simplicity

and the effect of hardening/ageing was not considered

because the test lasted only a few months. It is concluded

that the model gives reasonable rut depth values and is

sensitive to mix characteristics and temperature with

regard to resistance to rutting. However, further research

considering the influence of a variable Poisson’s ratio, and

ageing would be valuable.

5.2 Influence of lateral wander

Under a moving wheel load, the asphalt material moves

vertically and horizontally; when calculating rutting under

wheel load, it is, therefore, crucial to include the influence

of lateral wandering of the traffic. Figure 18 shows the

lateral distribution of wheel load. The lateral distribution

of traffic has a significant effect on rut and air void

development in bituminous layers. In this work, the lateral

distribution results in about 38% less rut depth for both

structures compared with that if all the wheel passages

loaded only the rut centre based on calculation using the

PEDRO approach. Using PEDRO algorithms, Figure 19

illustrates predicted permanent deformations in initial and

secondary zones with total deformation of each AC layer

during the 208C testing phase. It is clear from Figure 19

that deformation in the first zone is caused by densification

(no upheaval). Indications of the upheavals in the second

zone are evident in all the layers with the largest upheaval

in the base course layer (AG) in this work. The binder

layer of the reference section (ABb) shows significantly

larger rut depth and upheaval than the enhanced binder

layer (ABbm). The enhanced asphalt mix layer (ABbm)

shows about 50% less rutting than the conventional asphalt

mix layer (ABb). This is a result of higher viscosity of the

enhanced asphalt mix by a factor 1.5 as reported earlier.

Figure 20 illustrates the normalised measured surface

rutting profiles and the calculated deformations in AC layers

of the two structures at the end of the HVS testing at 208C

(include rutting at 10 and 208C). The calculated rutting

profiles consist only of deformations in the AC layers.

However, the measured profiles consist of deformations in

bound and unbound layers. There are upheavals in the

Figure 16. Ambient air temperatures when testing at 208C (Temperature 2009).

0

2

4

6

8

10

12

14

16

18

0 100 200 300 400 500 600

Number of load applications × 103

Per

man

ent d

efor

mat

ion

(mm

)

Measured enhanced structure

Measured standard structure

Predicted enhanced structure

Predicted standard structure

Figure 17. Measured and calculated rut depth development inAC layers at 10, 20 and 308C at HVS test.

0

10

20

30

40

50

60

–400 –300 –200 –100 0 100 200 300 400

Rel

ativ

e fr

quen

cy (

%)

Laternal position (mm)

Figure 18. Lateral distribution of wheel load during HVStesting.

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calculated rutting profiles of about 8% of the maximum

rutting of the AC layers for both structures. The measured

profiles show clear upheavals in the standard structure of

about 19% of the maximum rutting, but almost no upheavals

of the measured profile for the enhanced structure. The

rutting width between the upheavals’ peaks in the calculated

profiles is about 90 cm, which is somewhat narrower than

the measured rutting profiles. A broader measured rutting

profile might be an effect of the deformation in the unbound

layers of the structures. According to this study, the

measured deformation in the AC layers (Figure 17) is about

half of the measured surface rutting (Figure 20) for both

structures.

6. Conclusions

This work utilises a linear viscoelastic model for

prediction of permanent vertical strain in AC layers of

pavement subjected to a moving load. The model takes

into consideration both the initial deformation which is

primarily related to densification and the subsequent

deformation that has an almost constant growth rate. The

newly developed approach, PEDRO, which is based on the

linear viscoelastic model, takes into consideration the

change in material characteristics due to densification

(post-compaction) of AC layers as a function of repeated

traffic loading. The analytically based PEDRO approach is

verified by a full-scale accelerated loading test (HVS) at

different temperatures. Flow rutting (permanent defor-

mation) in each AC layer was measured by 1-mu coils and

predicted using the PEDRO procedure.

As expected, the flexible pavement with a modified AC

layer showed less rut development than the reference

section in the HVS testing.

The flexible structures presented in this work have

shown encouraging agreement between predicted and

measured flow rutting based on loading variables from

HVS testing and laboratory measurements on cores with

regard to temperature variation. The calculated defor-

mation developments versus the measured deformations as

regard number of load repetitions in each AC layers are

presented. The comparisons were shown to be reasonable.

It was demonstrated how sensitive the PEDRO

approach is to mix characteristics and temperature as

well as the importance of the accuracy of the input data for

the model for prediction of rutting.

The lateral wandering of traffic results in significantly

less rut depth compared with that if the wheel passages

loaded only the rut centre, indicating the importance of the

lateral wandering in prediction of rutting. In addition, the

PEDRO approach is capable of calculating rutting profiles

including the upheaval, which is important for estimating

rut depth.

Hardening of asphalt material due to ageing was not

taken into consideration in this evaluation, because the test

was completed in a relatively short time. Hardening as a

function of climate must be incorporated in the approach

for field evaluation.

–1

0

1

2

–1

0

1

–1 –0.5 0 0.5 1

–1 –0.5 0 0.5 1

Transversal distance from rut centre (m)P

erm

anen

t def

orm

atio

n (m

m)

Per

man

ent d

efor

mat

ion

(mm

)

ABT

Zone 1

Zone 2

Total

Transversal distance from rut centre (m)

ABb

Zone 1Zone 2Total

–1

0

1

–1 –0.5 0 0.5 1

Transversal distance from rut centre (m)

Per

man

ent d

efor

mat

ion

(mm

)

ABbm

Zone 1Zone 2Total

–1

0

1

2

3

4

5

6

7

–1 –0.5 0 0.5 1Transversal distance from rut centre (m)

Per

man

ent d

efor

mat

ion

(mm

)

AG

Zone 1Zone 2Total

Figure 19. Calculated transversal deformations caused bylateral wander of wheel load at 208C (about 300,000 passes).

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The ZSV is a crucial factor in predicting the permanent

deformation of pavement and the only parameter

describing the influence of a mix on rut formation

according to the PEDRO model. Further investigation on

determination of ZSV would be an improvement of rut

prediction.

Further investigations regarding increase in stiffness,

and consequently the ZSV of AC layers related to repeated

traffic loading, which results in decrease in air void content

in AC layers, would be helpful for this approach.

In this work, a number of transfer functions (regression

relationships) are used in the prediction model which have

an influence on the variability of predicted rutting. It is

recommended that this work would be extended with a

sensitivity analysis of variables for future model

improvement.

Validation of this approach under field conditions

would be valuable for evaluation of the conclusions from

this study. The effect of variation in traffic loading in

correlation to variation in climate and long-term ageing of

asphalt materials should then be included.

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–5

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