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Mechanistic-Empirical Modelling of Flexible Pavement Performance:

Verifications Using APT Measurements

Abubeker Worake Ahmed

PUBLIC DEFENCE OF PHD DISSERTATION

As a courtesy of the Royal Institute of Technology, KTH, Stockholm, the public defence of the

PhD dissertation will takes place on the 23rd

of May 2014 at 13:30 in room Q2, Osquldas väg 10,

KTH. The defence will be conducted in English.

External Examiner: Professor Hervè Di Benedetto, University of Lyon, France

Supervisor: Professor Sigurdur Erlingsson, KTH, VTI, and University of

Iceland

TRITA-TSC-PHD 14-003

ISBN 978-91-87353-39-0

Mechanistic-Empirical Modelling of Flexible Pavement Performance:

Verifications Using APT Measurements


Division of Highway and Railway Engineering, Department of Transport Science, Royal Institute

of Technology, Stockholm, Sweden

ABSTRACT

Mechanistic-Empirical (M-E) pavement design procedures are composed of a reliable response

model to estimate the state of stress in the pavement and distress models in order to predict the

different types of pavement distresses due to the prevailing traffic and environmental conditions.

One of the main objectives of this study was to develop a response model based on multilayer

elastic theory (MLET) with improved computational performance by optimizing the time

consuming parts of the MLET processes. A comprehensive comparison of the developed program

with two widely used programs demonstrated excellent agreement and improved computational

performance. Moreover, the program was extended to incorporate the viscoelastic behaviour of

bituminous materials through elastic-viscoelastic correspondence principle. A procedure based on

collocation of linear viscoelastic (LVE) solutions at selected key time durations was also proposed

that improved the computational performance for LVE analysis of stationary and moving loads. A

comparison of the LVE responses with measurements from accelerated pavement testing (APT)

revealed a good agreement.

Furthermore the developed response model was employed to evaluate permanent deformation

models for bound and unbound granular materials (UGMs) using full scale APTs. The M-E

Pavement Design Guide (MEPDG) model for UGMs and two relatively new models were

evaluated to model the permanent deformation in UGMs. Moreover, for bound materials, the

simplified form of the MEPDG model for bituminous bound layers was also evaluated. The

measured and predicted permanent deformations were in general in good agreement, with only

small discrepancies between the models.

Finally, as heavy traffic loading is one of the main factors affecting the performance of flexible

pavement, three types of characterizations for heavy traffic axle load spectrum for M-E analysis

and design of pavement structures were evaluated. The study recommended an improved approach

that enhanced the accuracy and computational performance.

Keywords: Flexible Pavement; Pavement Performance Models; Multilayer Elastic Theory; Linear

Viscoelasticity; Rutting; Accelerated Pavement Testing; Heavy Vehicle Simulator.

Mechanistic-Empirical Modelling of Flexible

Pavement Performance: Verifications Using

APT Measurements


Doctoral Thesis

KTH Royal Institute of Technology

School of Architecture and the Built Environment

Department of Transport Science

Division of Highway and Railway Engineering

SE-100 44 Stockholm

Stockholm 2014

© Abubeker Worake Ahmed, 2014

Doctoral Thesis

Division of Highway and Railway Engineering

Department of Transport Science

TRITA-TSC-PHD 14-003

ISBN 978-91-87353-39-0

To my father Worake Ahmed

Summary

i

Summary

In the last few decades, Mechanistic-Empirical (M-E) pavement design methods

have gained considerable interest due to their ability to model the actual

pavement characterization. M-E design procedures are primarily composed of a

reliable response model to estimate the state of stress in the pavement and distress

prediction models in order to predict the different types of pavement distresses

due to the prevailing traffic and environmental conditions.

One of the objectives of the study presented here was to develop a response

model based on multilayer elastic theory (MLET) with improved computational

performance by optimizing the time consuming parts of the MLET processes. The

convergence and accuracy of responses in the vicinity of the surface of the top

layer were improved using Richardson’s extrapolation. An iterative approach to

model stress dependency of unbound granular materials was also incorporated. A

comprehensive comparison of the program with two frequently used programs

demonstrated excellent agreement and improved computational performance.

Moreover, the program was extended to incorporate the viscoelastic nature of

bituminous materials the through elastic-viscoelastic correspondence principle. A

procedure based on collocation of linear viscoelastic (LVE) solutions at selected

key time durations was also proposed that improved the computational

performance for LVE analysis of stationary and moving loads. A comparison of

the LVE responses with measurements from accelerated pavement testing (APT)

revealed good agreement.

The second objective of this study was to evaluate permanent deformation (or

rutting) models for bound and unbound granular materials (UGMs). The

Mechanistic Empirical Pavement Design Guide (MEPDG) model for UGMs and

two relatively new models were evaluated to model the permanent deformation in

UGMs. Furthermore, for bound materials, the simplified form of the MEPDG

model for bituminous bound layers was also evaluated. A total of three series of

full scale accelerated pavement tests (APT) using a heavy vehicle simulator (HVS)

Mechanistic-Empirical Performance Modelling Abubeker W. Ahmed

ii

was used to evaluate the models. In addition, test results from an extra-large

wheel tracking (ELWT) device were employed for the purpose of verification of

model parameters for bituminous bound layers. The permanent deformation,

wheel loading, pavement temperature and other material properties were

continuously controlled during the HVS and ELWT tests. Stress dependent

behaviour of unbound materials and traffic wandering were also taken into

account during the evaluations and a time hardening approach was applied to

accumulate the permanent deformation contributions from different stress levels.

The measured and predicted permanent deformations were in general in good

agreement, with only small discrepancies between the models. Model parameters

were also estimated for three different types of unbound granular materials.

Finally, as heavy traffic loading is one of the main factors affecting the

performance of flexible pavement, this study evaluated three distinct types of

characterizations of heavy traffic axle load spectrum (ALS) for M-E analysis and

design of pavement structures. The characterization of the entire ALS using an

equivalent number of standard axle loads (ESALs) of 80 kN (US) and 100 kN

(Europe) is generally employed in most empirical and few M-E design

procedures. The other alternatives are to characterize the entire ALS by Constant

Contact Area (CCA) or Constant Contact Pressure (CCP). These

characterizations were evaluated based on the predicted rutting and fatigue

cracking of several pavement structures subjected to heavy traffic ALS data

collected from bridge-weigh-in-motion stations. The results indicated that for

layers below the top 25 cm, all characterizations produced similar values of

predicted rutting. However, for the top 25 cm, the methods produced significantly

different values of predicted rutting and fatigue cracking. Even though the CCP

approach is a relatively realistic representation of the actual traffic compared to

the ESAL and CCA characterizations, it was shown that the CCP characterization

is computationally very expensive. The study proposed an improvement to the

CCA approach that enhanced the accuracy while maintaining the same level of

computational performance.

Acknowledgements

iii

Acknowledgements

First and foremost, I would like to express my special gratitude and appreciation

to my supervisor Prof. Sigurdur Erlingsson, who created the opportunities for me,

and I am honoured and privileged to have been able to work so closely with him. I

am indebted to him for his guidance, encouragement and invaluable advice over

the years.

I would like to acknowledge the substantial financial support from the Swedish

Transport Administration (Trafikverket) and the Swedish National Road and

Transport Research Institute (VTI).

I would also like to thank Hassan Hakim, Andreas Waldemarson, Håkan

Arvidsson, Tomas Halldin and Henrik Hellman at the Division of Pavement

Technology at VTI, who contributed invaluable assistance during the specimen

preparation and laboratory testing in the second half of the project.

I would also like to thank my colleagues at the Division of Pavement

Technology (väg och banteknik) at VTI. Each of you contributed to making the

Division a nice working place. Special thanks to Dr Safwat Said for his fruitful

technical discussions and encouragement. My fellow colleagues Farhad Salour,

Jonas Wennström and Shafiqur Rahman are also acknowledged for their excellent

company and for reviewing my thesis. In addition, I also want to thank my friends

Abateneh Yitayew, Markus Svensson (currently working at the Swedish Defence

Research Agency FOI), Tariku Mehari (Ericsson) and Tigist Fetene (KTH) for

their support and encouragement.

Further, I would like to extend my sincere gratitude to the staff at the VTI for

all administrative and other kinds of support that they have provided me over the

years.

Finally, I would like to express my special thanks to my mother Jemila Redi,

who has always believed in me, her support has been tremendous; words cannot

express how grateful I am.

List of Acronyms

v

List of Acronyms

AASHTO American Association of State Highway and Transport Officials

ALS Axle Load Spectra

APT Accelerated Pavement Testing

BWIM Bridge Weight-in-Motion

CalME California Mechanistic-Empirical Pavement Design Program

CCA Constant Contact Area

CCP Constant Contact Pressure

ELWT Extra-Large Wheel Tracking

ERAPAVE Elastic Response Analysis of Pavements

ESAL Equivalent Standard Axle Load

FEM Finite Element Method

FWD Falling Weight Deflectometer

HMA Hot Mix Asphalt

HVS Heavy Vehicle Simulator

LVE Linear Viscoelastic

M-E Mechanistic–Empirical

MEPDG Mechanistic-Empirical Pavement Design Guide

MLET Multilayer Elastic Theory

PEDRO Permanent Deformation of asphalt for Roads

PMS Pavement Management System

STA Swedish Transport Administration

UGMs Unbound Granular Materials

VEROAD Viscoelastic Road Analysis Delft

VTI Swedish National Road and Transport Research Institute

WIM Weigh-in-Motion

Table of Contents

vii

Table of Contents

Summary ................................................................................................................... i

Acknowledgements ................................................................................................. iii

List of Acronyms ..................................................................................................... v

Table of Contents ................................................................................................... vii

List of Publications ................................................................................................. ix

1. Introduction .......................................................................................................... 1

1.1. Distresses in Pavements ................................................................................ 2

1.2. Use of Distress Models in Pavement Management System ......................... 5

1.3. Objectives and Scope of the Research .......................................................... 6

2. Pavement Performance Modelling ....................................................................... 9

2.1. Response Model for M-E Design Procedures ............................................... 9

2.2. Performance Modelling of Unbound Granular Materials ........................... 13

2.3. Modelling Permanent Deformation in UGMs ............................................ 17

2.4. Performance of Asphalt Bound Materials .................................................. 19

2.5. Modelling Permanent Deformation in Asphalt Mixtures ........................... 21

2.6. Characterization of Traffic .......................................................................... 22

2.7. Time Hardening Procedure ......................................................................... 26

3. Test Equipment, Structures and Materials ......................................................... 29

3.1. Full Scale Accelerated Pavement Tests ...................................................... 29

3.2. Extra-Large Wheel Tracking Tests ............................................................. 31

4. Response Models for Flexible Pavements ......................................................... 33

4.1. Multi-Layer Elastic Theory ........................................................................ 33

4.2. Linear Viscoelastic Theory ......................................................................... 36

5. Evaluation of Permanent Deformation Models ................................................. 39

5.1. Permanent Deformation Models for UGMs ............................................... 39

5.2. Permanent Deformation Model for Bituminous Bound Layers .................. 41

6. Characterization of Heavy Traffic Axle Load Spectrum ................................... 43


viii

7. Conclusions and Recommendations .................................................................. 47

7.1. Response Model .......................................................................................... 47

7.2. Permanent Deformation Models ................................................................. 48

7.3. Heavy Vehicle Characterization ................................................................. 49

7.4. Limitations and Recommendations for Future Studies............................... 49

References .............................................................................................................. 51

List of Publications

ix

List of Publications

Paper I Erlingsson, S., and Ahmed, A. W., 2013. Fast layered elastic

response program for the analysis of flexible pavement structures,

Road Materials and Pavement Design, 14(1), pp. 196-210, DOI:

10.1080/14680629.2012.757558. The author of this thesis carried out the development of theory, the

programming, and was involved in the write-up.

Paper II Ahmed, A. W., and Erlingsson, S., 2013. Evaluation of permanent

deformation models for unbound granular materials using

accelerated pavement tests, Road Materials and Pavement Design,

14(1), pp. 178-195, DOI: 10.1080/14680629.2012.755936. The author of this thesis carried out the analysis of the data, the

development of theory and the write-up.

Paper III Ahmed A. W., and Erlingsson, S., 2012. Modeling of flexible

pavement structure behaviour–Comparisons with HVS

measurements In D. Jones, J. Harvey, A. Mateos, and I. Al-Qadi,

(Eds). Advances in Pavement Design through Full-scale Accelerated

Pavement Testing, pp. 493-503, New York: CRC Press. The author of this thesis analysed the data, carried out the development of

theory and the write-up.

Paper IV Ahmed, A. W., and Erlingsson, S., 2013. Characterization of heavy

traffic axle load spectra for mechanistic-empirical pavement design

applications. Accepted for publication in International Journal of

Pavement Engineering. The author of this thesis carried out the data analysis, the development of

theory and the write-up.

Paper V Ahmed, A. W., and Erlingsson, S., 2014. Viscoelastic modelling of

pavement structure behaviour in a full scale accelerated pavement

test. Submitted to International Journal of Pavement Engineering. The author of this thesis carried out the analysis of the data, the implementation of

the viscoelastic approach used and the write-up.

Paper VI Ahmed A. W., and Erlingsson, S., 2014. Evaluation of a permanent

deformation model for asphalt concrete mixtures using extra-large

wheel tracking and heavy vehicle simulator tests. Submitted to Road

Materials and Pavement Design. The author of this thesis carried out the ELWT tests, performed the analysis of

data from both the ELWT and HVS tests, and was involved in the write-up.

Introduction

1

1. Introduction

Flexible pavement flexes or deforms when subjected to wheel loads. A flexible

pavement is typically constructed of several layers of materials, traditionally with

the stiffer layers (usually made of asphalt materials) placed at the top and weaker

layers at the bottom. The major functions of flexible pavements are, among

others, to distribute the traffic loading in order to protect the subgrade from

excessive stress and to provide a better ride quality.

When subjected to excessive traffic loading and/or severe climatic condition,

pavements start to deteriorate and as a result the performance of pavement starts

to decline, which in turn affects the safety of road users.

Permanent deformation on the pavement surface along the wheel path, usually

referred to as rutting, is one of the major deteriorations that affect the ride quality

as well as safety of road users by leading to hydroplaning, which decreases the

skid resistance of the surface and eventually makes steering difficult as the rutting

increases in depth.

Pavements are designed using either the pure empirical or Mechanistic-

Empirical (M-E) procedures. The empirical procedures developed from the 1950

road test by the American Association of State Highway and Transport Officials

(AASHTO) are the basis for most existing empirical design procedures in use

worldwide. However these procedures are subjected to growing uncertainties due

to the fact that today’s pavement design data exceed the data used in the 1950s

AASHTO road test. In addition, these procedures have no mechanistic basis to

verify that the stresses, strains or deformations which are induced due to traffic

loads and environmental conditions are within the allowable limits.

The M-E design philosophy, on the other hand, applies a more realistic

characterization of pavement structures and the related variables. The responses

(stresses and strains) in the pavement due to traffic loading, and prevailing

environmental conditions are calculated using a response model. Distresses are


2

then predicted using M-E distress (performance) prediction models which

empirically relate the pavement performance to the pavement responses, traffic

volume and the environment. Finally the M-E procedure attempts to limit the

distresses or damage to pavement within the desirable tolerances. Therefore the

response model and performance prediction models are vital to M-E pavement

design methods. Figure 1 shows the flow chart of a typical M-E pavement design

procedure.

Figure 1. Flow chart for Mechanistic - Empirical pavement design procedure.

1.1. Distresses in Pavements

Pavements are built to provide safe and good ride quality for road users. The

safety and ride quality are affected due to different types of distresses during the

service life of the pavements. A more detailed description of different types of

distresses can be found in textbooks such as Huang (2004) or in handbooks of

highway engineering. The subsequent sections present the two distress modes that

most M-E design procedures attempt to control.

1.1.1. Permanent deformation

Permanent deformation of the surface of the pavement along the wheel path, also

referred to as rutting, is a gradual accumulation of small unrecoverable

Foundation Climate

Pavement

Geometry

&

Material

Properties

Traffic

Pavement Response Model

Deterioration/Distress

Prediction Models

Damage Accumulation with

Time/Load Cycles

Maintenance Strategies

Pavement

Performance

Analysis

Life Cycle Cost Analysis

Inputs

Life Cycle

Assessment

Introduction

3

deformations, in both bound and unbound granular pavement layers, as a result of

applied traffic load (Huang, 2004; Sousa et al., 1991). Rutting occurs when the

pavement layers consolidate (or change in volume) due to traffic loading. Rutting

may also have associated transverse displacement due to shear failure (FHWA,

2003).

Some of the causes of rutting, among others, are an unstable asphalt layer and

densification of the asphalt layer due to inadequate compaction during

construction. Rutting is considered as a load related or structural distress and is

included as a failure criterion in most M-E pavement design procedures. Figure 2

presents the profile of a tested pavement structure after several load passes were

carried out using a Heavy Vehicle Simulator (HVS) testing (Wiman, 2006). The

figure demonstrates that as the number of load passes increased, the rutting

increased.

Figure 2. Rut measurements from HVS Testing.

1.1.2. Fatigue cracking

Fatigue cracking is a series of longitudinal and interconnected cracks caused by

repeated application of tensile strains due to the traffic load. These tensile strains

are usually below the tensile strength of the material.

Fatigue cracking may be initiated at the bottom (bottom-up cracking) of an

asphalt layer or stabilized base where tensile stress or strain becomes highest

following traffic loading (Mobasher et al., 1997; Huang, 2004). These

-6

-5

-4

-3

-2

-1

0

1

0 500 1000 1500 2000 2500

Per

man

ent

def

orm

atio

n [

mm

]

Distance [mm]

0

20000

40000

120000

200000

300000

Load Repetitions


4

microscopic cracks propagate through the material to the top of the layer and form

one or more longitudinal wheel path cracks which, after repeated application of

loading, interconnect with each other and form cracks with a pattern like the skin

of an alligator (Huang, 2004). It is also observed that fatigue cracking may be

initiated at or near the surface of the pavement and propagate downward (top-

down cracking), which commonly occurs in hot mix asphalt pavements (Wang et

al., 2003; Wang et al., 2007).

Fatigue cracking, in general, is described as a two-phase process, initiation

followed by propagation. The initiation phase of fatigue cracking on the surface is

characterized by microcracks that are instigated in places where high cyclic shear

or tensile stress occurs (Daniel et al, 2001). The mechanism of top-down cracking

is very complicated; however, Wang el al. (2003) indicated that both tensile-type

and shear-type cracking may initiate top-down cracking. Once the crack initiation

develops and starts to propagate, further loading may lead to the propagation

phase which is characterized by macrocracks. Fatigue cracking occurs mostly in

areas which are subjected to repeated traffic loading. Therefore fatigue cracking is

considered as a structural (load related) distress and it is incorporated in most M-E

pavement design methods.

1.1.3. Modelling distresses in pavements

In pavement structures, it is believed that each passage of traffic load contributes a

certain amount of damage to the pavement that gradually accumulates over time

and eventually leads to pavement failure. Therefore pavements are designed to

span a specific amount of design life, after which the pavement is assumed to be

no longer serviceable.

The prediction of pavement life for rutting and fatigue cracking was first

introduced by Shell’s pavement design method (Dorman, 1962; Sousa et al., 1991;

Huang, 2004). The damage calculation is performed according to Miner’s law

where failure due to the combined loading occurs when:

Y

i

S

j ji

ji

RN

nD

1 1 ,

, (1)

Introduction

5

where DR, 0 ≤ DR ≤ 1 is the damage ration; Y denotes the analysis period; S is the

number of seasons per year; ni,j is the number of applied load cycles and Ni,j is the

number of load cycles to failure. If DR > 1, the pavement has reached its ultimate

carrying capacity and can no longer be serviceable.

Miner’s law is used to predict the life of a pavement with respect to both

rutting and fatigue cracking and it is implemented for pavement damage

calculation in several pavement analyses and design programs such as KENPAVE

(Huang, 2004).

Barksdal (1972) presented an approach to predict the rutting in pavement

layers. The method involves dividing the layer into sub-layers and the permanent

strain at the mid-points of the sub-layers is then used to estimate the total

pavement rutting by summing up the contribution to rutting from each layer or

sub-layer as shown in Equation (2).

n

i

iippp zdzz

1

,

0

(2)

where εp,i denotes permanent strain in sublayer i calculated from M-E

performance prediction model (permanent strain model); Δzi is the thickness of the

ith

layer or sub-layer; n is the total number of sub-layers and δp is the rut depth.

1.2. Use of Distress Models in Pavement Management System

The pavement management system (PMS) involves a set of techniques for

monitoring, collecting, analysing and providing post-construction conditions of

pavements so as to assist decision makers in selecting efficient and cost-effective

maintenance strategies or intervention level (Haas et al., 1994). Therefore

evaluation or prediction of the performance of new or in-service pavements is an

essential part of PMS in order to determine the best possible cost-effective

maintenance alternatives. PMS usually involves rigorous computations of life

cycle cost analyses of several alternatives, thus leading to high- performance M-E

performance prediction procedures. Figure 3 illustrates a typical performance

curve and the possible intervention levels depending on the predicted

performance.


6

Distress models have also gained importance in performance-based contracts

for pavement maintenance and rehabilitation projects. This is due to the fact that

performance-based contracts specify the desired levels of pavement performances

or fundamental engineering properties. Therefore distress prediction models

provide an objective means to assist contractors to achieve a structural design that

fulfils the required levels of pavement performance (Pidwerbesky, 2004).

Figure 3. Pavement conditions and intervention levels for pavement management

system (Huang, 2004).

1.3. Objectives and Scope of the Research

The main objective of this research project was to develop an M-E performance

prediction procedure or framework which adequately predicts the performance of

thin asphalt pavements under prevailing traffic and environmental conditions. The

tasks included:

1. Developing and evaluating high efficiency response programs based on

multi-layer elastic and viscoelastic theories for predicting flexible

pavement responses.

2. Evaluation of performance prediction models for rutting in bound and

unbound layers using measurements of full scale accelerated pavement

testing (APT).

3. Evaluation of different characterizations of heavy vehicle axle load spectra

(ALS) for M-E pavement analysis and design applications.

Even though there are several other types of distresses such as thermal and

fatigue cracking, the present work mainly concentrated on rutting as it is

Pavement age

Pav

emen

t co

ndit

ion

Preventative

maintenance

Light

rehabilitation

Performance without treatment

Medium

rehabilitation

New construction

is necessary

Introduction

7

considered the most important distress mode. Furthermore, the framework was

designed in such a way that other types of distresses can easily be incorporated in

the future.

Pavement Performance Modelling

9

2. Pavement Performance Modelling

The subsequent sections present a short literature review of the selected works

which are deemed essential for M-E performance modelling of flexible pavement

structures. The survey focused on the response model for pavement analysis and

permanent deformation (rutting) behaviour of unbound granular materials

(UGMs) and asphalt mixtures.

2.1. Response Model for M-E Design Procedures

The multilayer elastic theory (MLET), first introduced by Burmister (1943, 1945),

is by far the most common response model employed for analysis of layered

systems, as shown in Figure 4 (Acum and Fox, 1951; Ahlvin and Ulery, 1962;

Jones, 1962; Peattie, 1962; Verstraeten, 1967; Hunag, 1968; Bufler, 1971; Van

Cauwelaert and Lequeux, 1986; Maina and Matsui, 2005; Khazanovich and

Wang, 2007). Other alternatives for analysis of layered pavement systems include

Odemark’s method of equivalent thickness (Ullidtz, 1987) and the 3D finite

element method (FEM). The FEM is more comprehensive in its ability to model

characteristics of real pavement structures such as a wide variety of nonlinear

material behaviour; however it is computationally expensive when compared to

the MLET (ARA, 2004). Therefore most M-E pavement design procedures

employ the MLET due to its simplicity and computational performance. For

instance the US Mechanistic-Empirical Pavement Design Guide (MEPDG)

implements a layered elastic program JULEA (ARA, 2004).


10

Figure 4. Layered system subjected to a circular distributed load.

In Figure 4, Ei and vi denote the elastic modulus and Poisson’s ratio of layer i (i =

1, 2,..n); n is the number of layers; zi is the distance from the surface to the bottom

of layer i; H is the distance from the surface to the top of the lowest layer; q is the

circular distributed contact pressure and a denotes the contact radius.

2.1.1. Summary of MLET

An axisymmetric solution of a multilayer elastic system as in Figure 4 can be

solved by assuming a stress function that satisfies (Timoshenko and Goodier,

1951):

04 (3)

where the Laplace operator 4 for axially symmetrical stress distribution is

defined as:

22

2

2

2

2

24 11

zrrrzrrr (4)

Each of the constituent layers must satisfy Equation (3) and the axisymmetric

responses, stresses and displacements can be obtained from (Timoshenko and

Goodier, 1951; Maina and Matsui, 2005):

q

E2, v2

E1, v1

z

H zn-2

z2 z1

En-1, vn-1

En, vn

a

∞

r


11

2

2

2

2

2

2

2

2

3

3

10

1121

1

)1(

1

)2(

zrE

rrrEE

zrr

rrzz

rzz

zz

u

w

rz

t

r

z

(5)

in which v and E are the Poisson’s ratio and modulus of elasticity of the material,

respectively; and σ, τ, w and u are normal stress, shear stress, vertical

displacement and radial displacement, respectively. The stress function for the

ith

layer (i = 1 to n) which satisfies Equation (3) is given by (Huang, 2004):

)()(

)()(

2

03

1

1)(,

ii

ii

mi

mi

mi

mi

iemDemC

eBeA

m

mJHzr

(6)

where ρ = r/H, λ = z/H, λi = zi/H; Ai, Bi, Ci and Di are integration constants for the

ith

layer which are obtained from the boundary and continuity condition; J0 is the

Bessel function of the first kind and order 0 and m is the Hankel parameter (Van

Cauwelaert, 2003). The integration constants are determined from the solution of

a matrix equation of the form ZX = Y where Z and Y are matrix of 4n-2 4n-2 and

4n-2 1, respectively, which are assembled from the boundary and continuity

conditions; X is a column vector of the unknown integration constants.

Introducing Equation (6) into Equation (5) yields the solution of the layered

system under concentrated load P = -mJ0 (mρ). Therefore the responses due to a

circular distributed load q over radius a can be found by integrating:

0

1 )( dmH

amJ

m

S

H

aqS

c

(7)

where S is the response due to a distributed load of q and Sc is the response due to

a concentrated load of P = -mJ0 (mρ).

The infinite integral in Equation (7) is evaluated using numerical integration

(Van Cauwelaert and Lequeux, 1986; Hayhoe, 2002; Huang, 2004; Maina and


12

Matsui, 2005; Khazanovich and Wang, 2007). The integral in Equation (7) is a

time consuming process for M-E pavement design applications where a repeated

application of response computation is needed. In addition, for locations close to

the surface of the top layer, the convergence of the integral is very slow (Maina

and Matsui, 2005; Khazanovich and Wang, 2007). Khazanovich and Wang (2007)

thus suggested the use of interpolation and tabulated values of stresses in order to

improve the computational performance of MLET. Maina and Matsui (2005)

employed Richardson’s extrapolation to improve the convergence of near surface

responses.

2.1.2. Extension of MLET for problems involving linear viscoelasticity (LVE)

Asphalt mixtures exhibit unique characteristics of both viscous and elastic

properties, and hence are categorized as viscoelastic materials. Moreover,

understanding the viscoelastic properties of asphalt mixtures is important to

achieve performance-based structural design of bituminous layers (ARA, 2004).

Therefore it is important to extend the theory of MLET to account for the effect of

viscoelasticity. This can be achieved by means of the elastic–viscoelastic

correspondence principle which states that the solutions of linear viscoelastic

(LVE) problems can be derived from corresponding solutions of linear elastic

problems in Laplace space (Chou, 1969; Huang, 2004; Kim, 2011).

The constitutive equation for an LVE material is given, in terms of the

convolution integral, as:

dtEt

t

0

(8)

where (t) is time dependent stress at time t; E(t-) is the modulus as function of

time t; () is the strain and is a dummy variable. The Laplace transform of

Equation (8) yields:

ssEsdtELtLs

t

ˆˆˆ

0

(9)


13

where L is the Laplace transform operator; s is a complex number; s , s , and

sE are the stress, the strain and modulus, respectively, expressed in the Laplace

domain.

It is the similarity between Equation (9) and the constitutive equation for linear

elastic problems (i.e., = E) that led to the elastic – viscoelastic correspondence

principle. Therefore Equations (3) to (7) can be employed to solve LVE problems

provided that v and E are replaced with their corresponding Laplace transform vs

and Es ˆ respectively.

The LVE solutions described above can also be extended to solve problems

involving moving loads through Boltzmann’s superposition. However, this

approach is generally time consuming (Huang, 2004; Kim, 2011). Another

alternative for analysis of pavement structures subjected to moving load includes

the use of a simplified load function, which varies with time, in order to simulate

a moving load. For instance, in the VESYS and KENLAYER codes, a haversine

function P(t) has been employed. The load function is given by (Papagiannakis et

al., 1996; Huang, 2004):

t

DAtP

2sin2

(10)

where D =

is the duration of the load in sec; a is the contact radius; V is the

speed of the moving load; A is the amplitude and

, is the time in sec.

2.2. Performance Modelling of Unbound Granular Materials

Unbound granular materials (UGMs) consist of continuously graded crushed rock

or natural aggregates that also contain some amount of fines. The term unbound

means that no binding agent such as cement or bitumen is used in UGMs. UGMs

in pavement structure are used primarily to transfer the heavy traffic loads from

the surface to the underlying subgrade. The resistance to load in UGMs is mainly

a result of the aggregate interlock and the internal friction between aggregates,

and their performance is affected by several factors presented in the subsequent

sections.


14

2.2.1. State of stresses and stress history of UGMs

Several studies have indicated that the stress state of UGMs substantially

influences the rutting performance of UGMs. The state of stress at an arbitrary

point in UGM, as shown in Figure 5, can be expressed in tensor form as:

zzyzx

yzyyx

xzxyx

S

(11)

Figure 5. Stress state of UGMs subjected to traffic loading.

The mean stress (also referred to as hydrostatic stress) is defined as the mean of

the normal stresses and is given by:

3

zyx

m

(12)

Then the stress tensor in Equation (12) can be expressed as the sum of two

components, namely, the deviatoric stress and the mean stress, given by:

m

m

m

mzzyzx

yzmyyx

xzxymx

zzyzx

yzyyx

xzxyx

S

00

00

00

(13)

Deviatoric stress Mean stress

The mean stress and the deviatoric stress components are the key to

understanding the deformation mechanisms in UGMs. For instance, from repeated


15

triaxial tests performed on various UGMs, it is reported that the accumulation of

permanent strain in UGMs increases when the deviatoric stress increases and

decreases when the confining stress increases (Morgan, 1966; Barksdale, 1972;

Brown and Hyde, 1975).

Moreover, the state of stress at a single point in UGMs varies with the position

of the wheel, as shown in Figure 6, which leads to shear reversal or the rotation of

the principal planes (planes with zero shear stress). To investigate the effect of the

shear reversal on the permanent deformation behaviour of UGMs, Chan (1990)

conducted a hollow cylindrical test on crushed limestone and a higher permanent

strain was observed for load cases with shear reversal.

Figure 6. Stress condition in unbounded granular materials (Lekarp et. al., 1998).

In addition to the stress state, the permanent deformation behaviour of UGMs

is also affected by the stress history. This is due to the fact that the stiffness of the

material gradually increases due to the compaction effect of the repeated loading,

resulting in a reduction in permanent deformation for subsequent loadings. Brown

and Hyde (1975) reported that the permanent strain resulting from successive

increases in stress level is considerably smaller than the permanent strain that

occurs due to abrupt loading of higher stress.


16

Uzan (1985) has shown that the stiffness of UGMs increases as the

confinement level increases and has recommended a stress dependent resilient

stiffness. One of several forms of stress dependent stiffness is given by ARA

(2004):

32

13

1

k

a

oct

k

a

mar

pppkM

(14)

where Mr is the resilient stiffness; k1, k2, and k3 are material constants; pa = 100

kPa; m is the mean stress in kPa; oct =

√( ) ( ) ( )

is the octahedral shear stress in kPa and 1, 2 and 3 are the principal stresses in

kPa.

2.2.2. Load cycle

Pavement materials are subjected to repeated traffic loading with each passage

contributing to a small amount of unrecoverable strain. The permanent

deformation in UGMs is therefore a gradual accumulation of these contributions

through the service life of the pavement.

Several studies have indicated that the permanent deformation of UGMs is

highly influenced by the number of load repetitions (Morgan, 1966; Barksdale,

1972; Sweere, 1990). Paute et al. (1996) concluded that the rate of increase of

permanent strain in UGMs under repeated loading decreases constantly to such an

extent that it is possible to define a limit value for accumulation of permanent

strain. However, Lekarp (1997) and Lekarp and Dawson (1998) reported that

stabilization of the accumulation of permanent strain is attained only at a low

applied stress level, and at high stresses which are above some threshold value

known as the shakedown limit the material experiences a continuous incremental

permanent strain and eventually leads to failure. Kolisoja (1998) revealed that the

development of permanent deformation is complex and may not be expressed as a

simple function, as the materials that seem to be stable at some loading cycle may

indicate unpredictable behaviour under further loading.


17

2.2.3. Moisture content and physical properties

Moisture content in its optimum amount promotes better compaction of the

UGMs. However, the actual moisture content in UGMs in pavements varies from

time to time due to the ingress of water from the surroundings, depending on the

permeability of the material and the drainage conditions. Generally, an increase in

moisture content decreases the shear resistance or resistance to permanent

deformation (Barksdale, 1972; Thom and Brown, 1988; Lekarp et al., 2000a and

2000b; Erlingsson, 2010b).

Physical properties such as density, degree of compaction, fine contents,

grading, aggregate type and aggregate surface conditions also affect the

performance to rutting of UGMs. Several studies have indicated that as the

density increases the resistance to permanent deformation increases this is

particularly true for angular aggregates (Dunlap, 1966; Holubec, 1969; Thom and

Brown, 1988; Lekarp et al., 2000a and 2000b).

2.3. Modelling Permanent Deformation in UGMs

As discussed in the previous sections, permanent deformation in UGMs is

influenced by a number of factors and several attempts have been made to develop

analytical or M-E permanent strain predictive models for UGMs in pavements. A

detailed summary of the permanent strain prediction models for UGMs can be

found in Lekarp et al. (2000b) and SAMARIS (2004). The subsequent sections

present the commonly used and recently developed permanent strain models.

2.3.1. Regression-based permanent deformation models

Regression-based models for permanent deformation in UGMs relate the

pavement responses (stresses or strains) with the permanent strain in the UGM

layers using empirical equations. These models are usually some function of the

stress state, load cycles and material constants. This section presents the Tseng

and Lytton (1989), the Gidel et al. (2001) and the Korkiala-Tanttu (2005, 2008)

models. In these models, the permanent strain p is expressed as the product of

two functions as:

Nfgp , (15)


18

where g(, ) is some function of pavement responses (stresses or strains) and

f(N) is some function of load repetition N.

The Tseng and Lytton (1989) model, Equation (16), is a function of resilient

strain r and the number of load repetitions N. This model has been implemented

for estimating the permanent strain in base, subbase and subgrade layers in

MEPDG (ARA, 2004):

rN

p e

)(

01

(16)

in which 1 is the laboratory to field correlation factor; ε0, β and ρ are material

parameters.

The model by Gidel et al. (2001), Equation (17), was developed based on

repeated multistage triaxial tests conducted on UGMs and is a function of the

maximum deviatoric stress (qmax) and mean stress (pmax).

Bn

ap

N

N

p

q

p

sm

p

L

0

1

max

max

max

max01 1 (17)

where 1 is the laboratory to field correlation factor; N0 is the reference number of

load applications (N0 = 100); 2max

2maxmax qpL and pa = 100 kPa; n, B and 0

are

material constants; m = 6(sin/(3 - sin) and s = 6(c)(cos/(3 - sin), where

and c are the angle of internal friction and the cohesion of the material,

respectively; pmax = (1+23)/3, qmax = 1-3, 1, 2 and 3 are the principal

stresses.

In the Korkiala-Tanttu (2005) model, it is presumed that the permanent strain

in UGMs is directly proportional to the distance from the state of stress (stress

point) to the Mohr-Coulomb failure line expressed in deviatoric stress – mean

stress (q-p) space. The permanent strain is then expressed as a hyperbolic function

of the deviatoric stress ratio, Equation (18). This model accounts for the effect of

the number of load cycles through the log-log approach, as recommended by

Sweere (1990).

bp N

RA

RCN

1)( (18)


19

in which 1 is the laboratory to field correlation factor; C and b are material

constants; A is a parameter independent of the material (A = 1.05) and R is the

deviatoric stress ratio given by:

max

maxmax

mps

q

q

qR

f (19)

where m, s, qmax, pmax and s are as defined above.

2.3.2. Advanced models

The two most studied advanced group of models used for UGMs are the Elasto-

plastic and the Shakedown models. The elasto-plastic models apply the concept of

plasticity theory to model the cyclic behaviour of UGMs (Bonaquist et al., 1997;

Hornych et al., 1998; Desai, 2002).

The shakedown concept employs the fact that if progressive increase in plastic

strain (also known as ratcheting) under cyclic loading occurs then the structure

will eventually fail. The critical load level below which the structure shakes down

(or the plastic strain progressively stabilizes under cyclic loading) and above

which ratcheting is instigated is called the shakedown limit. This limiting value is

used for estimating the permanent strain in the UGMs (Hornych et al., 2007).

2.4. Performance of Asphalt Bound Materials

The three building blocks of asphalt bound materials (or asphalt mixtures) are

aggregate, binder, and air. In dense graded asphalt mixtures the aggregate

constitutes around 90% of the mixture volume. Asphalt mixtures are one of the

principal components of flexible pavement structure which are used to transfer the

heavy traffic loads from the surface to the underlying base and subbase layers and

provide a smooth ride when used as a surface layer.

One of the major distresses affecting the ride quality of asphalt pavements is

rutting. Rutting in asphalt layers occurs when the pavement under traffic loading

consolidates due to compaction. Rutting may also arise due to lateral movement

of the hot-mix asphalt (HMA) due to shear failure which generally occurs in the

upper portion of the pavement surface. The performance of asphalt mixtures to

rutting is affected by several factors which are presented in the following section.


20

2.4.1. Temperature and binder

The quantity and type of the binders are determinant factors of the performance of

an asphalt mixture. Generally a binder content higher than the optimum makes the

asphalt layer prone to rutting. On the other hand low binder content decreases

workability during construction and makes compaction of the HMA difficult,

which in turn leads to excessive air void, thus making the mix vulnerable to

rutting. Furthermore, at high pavement temperatures the asphalt binder becomes

less viscous. This in turn reduces the stiffness which leads to shear failure.

Some performance tests performed on asphalt mixtures indicated that asphalt

mixtures with modified binder might have better resistance to rutting and low

temperature susceptibility than unmodified mixtures (Corte et al., 1994; Tayfur et

al., 2007; Oscarsson, 2011).

2.4.2. Physical properties

Studies indicated that aggregate selections and gradations play a significant role in

the performance of asphalt mixtures. In addition, the shape and texture of the

aggregate also influence the performance of the mixture. In general, a rough-

textured cubical-shaped aggregate performs better than a smooth, rounded

aggregate as it produces a better aggregate interlock. This help decrease the

potential for rutting (Matthews and Monismith, 1992).

2.4.3. Other factors

Other factors influencing the performance of asphalt mixtures include traffic load

and axle configurations, truck speed, contact pressure and wheel wandering. It is

well known that slow moving trucks are more damaging due to the longer

duration of loading. Furthermore, truck loading and axle configurations are also

important factors. For instance, Corte et al. (1994) reported that axles with wide

single wheels, super single wheels, might be more aggressive than dual wheels

with respect to rutting resistance. Finally excessive wheel wander may also lead to

wider and perhaps deeper ruts in the asphalt layers (Donovan and Tutumluer,

2008).


21

2.5. Modelling Permanent Deformation in Asphalt Mixtures

Simple M-E analytical and advanced models have been developed in an effort to

predict rutting in asphalt mixtures which are discussed in the subsequent sections.

2.5.1. Regression-based models

One of the commonly used regression-based rut predictive models for asphalt

layers is the AASHTO model which was developed as a part of the M–E

Pavement Design Guide developed under the National Cooperative Highway

Research Program (NCHRP). Equation (20) presents the simplified version of the

model. This model is a function of pavement temperature, number of load cycles

and vertical elastic strain calculated using a response model (ARA, 2004).

r

aa

p NTaN 3211)( (20)

where p is the permanent strain; 1 is a calibration factor; T is the temperature; N

is the load repetitions; a1, a2 and a3 are the regression constants and r is the

vertical elastic strain calculated using a response model.

Other models include the shear based incremental-recursive CalME model

which is employed in the M-E design program by the California Department of

Transportation (Ullidtz et al., 2006) and the PEDRO model which was developed

based on viscoelastic densification and flow (Said et al., 2011). Oscarsson (2011)

evaluated the MEPDG, CalME and PEDRO models based on permanent

deformation measurements from test pavement structures.

2.5.2. Advanced models

Advanced models for predicting permanent deformation in asphalt mixtures

consider the viscous nature of asphalt mixtures through viscoelastic or

viscoelastoplastic constitutive equations. Both linear and nonlinear viscoelasticity

approaches have been examined. One such example is the linear viscoelastic

model employed in the viscoelastic multilayer computer program VEROAD,

viscoelastic road analysis Delft, (Hopman, 1996). However, being

computationally expensive the nonlinear viscoelasticity has gained little usage

(Collop et al., 1995).


22

Collop et al. (1995) used VESYS to predict rutting in asphalt concrete and they

reported that there was a good agreement between the measured and the predicted

rutting except at the initial stage of the loading. This was attributed to the fact that

the initial stage rutting is a result of densification which the theory of

viscoelasticity is unable to take into account. Furthermore, research from Shell

indicated that utilizing viscoelastic properties of asphalt is not sufficient due to the

fact that the influence of the aggregate and its interaction with the asphalt is not

included in viscoelastic modelling (Lijzenga, 1997; Long, 2001).

Viscoelastoplastic models, on the other hand, take into account the influence of

aggregate and asphalt-aggregate interaction through elastoplastic components.

2.6. Characterization of Traffic

Traffic is one of the major factors affecting the performance of flexible pavements

and it is certainly one of the important parameters in pavement design procedures.

In the empirical pavement design procedure which was developed based on the

1950’s AASHTO road test, the mixed traffic is converted into the number of an

Equivalent Standard Axle Loads (ESAL) of usually 80kN (US) and 100 kN

(Europe). The conversion is made based on empirical relations developed from

the AASHTO road test. The conversion of mixed traffic into ESALs depends on

several factors such as the pavement type and the distress type under

consideration.

As pavement design procedures advance toward a more mechanistic approach,

the use of a more detailed traffic count and characterization is inevitable. The

subsequent sections present the common traffic counting method and its

characterizations.

2.6.1. Weigh-in-motion instruments

Weigh-in-motion (WIM) instruments are installations or attachments on or under

the pavement which are used to record the daily, weekly, seasonal and yearly

variations of traffic data while the vehicle is in motion (Cebon and Winkler, 1991;

Bouteldja et al., 2008).


23

The bridge weigh-in-motion (BWIM) system, first introduced by Moses

(1979), is a WIM system mounted on a concrete bridge. The system consists of

extensometers (strain gauges) and a data logger. Strain gauges and extensometers

attached to the bottom surface of the bridge slab are used to measure and detect

traffic information such as vehicle speed, axle load and configurations, and time.

The various recordings are stored in the data logger. It is essential to note that,

even though BWIM or WIM instruments provide detailed information regarding

traffic characteristics, these instruments do not record other important parameters

such as traffic wander pattern, wheel configurations (i.e. single or dual), and

contact pressure which are also important for pavement design procedures.

The axle loads and configurations from WIM instruments are usually presented

in the form of the axle load spectra (ALS) or frequency distribution of the axle

load groups of a given axle configuration (steering, single, tandem, tridem or quad

axle). Therefore raw WIM or BWIM data must be analysed to produce the ALS.

The analysis of the BWIM data is carried out in two steps; first the data from each

axle configuration are grouped into different axle load intervals (load groups). The

axle loads may be grouped using a desired load interval or bin width. In MEPDG,

for instance, 4.4 kN (1000 lb) for single axle, 8.9 kN (2000 lb) for tandem axle

and 13.3 kN (3000 lb) for tridem and quad axle are used (APA, 2004). The

frequency distributions for the load groups are then determined in order to

produce the ALS.

Few studies have been carried out to characterize the statistics of ALS and their

contribution to the pavement deterioration process. Based on the ALS data from

the USA, Haider and Harichandran (2009) concluded that fatigue damage is

related to the heavy load wings of the ALS while the rutting behaviour is

primarily the result of the number of load applications. Similarly, Prozzi and

Hong (2006) has shown that the ALS of a given project site can be represented by

a mixed lognormal distribution function and it is reported that the performance of

the pavement can be predicted by the statistical characteristics of the ALS

distribution functions.


24

2.6.2. Characterization of heavy traffic in a Swedish road network

In 2004, the Swedish Road Administration established a national BWIM network.

The BWIM network consists of motorways, arterials or trunk roads as well as one

county road and measurements were made during one week every year between

2004 and 2008 (Erlingsson, 2010a; Erlingsson et al., 2010; Winnerholt and

Persson, 2010). Erlingsson et al. (2010) analysed the BWIM data to generate ALS

of national BWIM sites and studied their characteristics. A time series analysis of

these stations for the time period between 2004 and 2008 was also carried out to

investigate how the ALS changes over time and to estimate the annual growth

rate. Figure 7 shows the ALS for a national BWIM site at Mjölby, South of

Stockholm.

Figure 7. ALS of the national BWIM site at Mjölby for the period 2004 – 2008 for

a) Steering axles, b) Single axles, c) Tandem axles and d) Tridem axles

(Erlingsson, 2010a).

From Figure 7 it can be observed that the distribution of steering axles was

fairly normally distributed; this might be attributed to the fact that steering axles

are single wheel and the load carried by steering axles, the front compartment of

the trucks, is fairly uniform from truck to truck while the load transferred to other

axle configurations varies depending on the loading conditions.

0

0

0

1

1

1

1

0 0.2 0.4 0.6 0.8 1 1.2

0

10

20

30

40

0 50 100 150Axle Weights [kN]

Fre

quency [

%]

20042005200620072008Mean

a)

0

5

10

15

0 50 100 150 200Axle Weights [kN]

Fre

quency [

%]

20042005200620072008Mean

b)

0

2

4

6

8

10

0 50 100 150 200 250 300

Axle Weights [kN]

Fre

quency [

%]

20042005200620072008Mean

c)

0

2

4

6

8

10

0 50 100 150 200 250 300 350

Axle Weights [kN]

Fre

quency [

%]

20042005200620072008Mean

d)


25

2.6.3. Characterization of heavy traffic ALS for M-E applications

As mentioned in the preceding sections, traffic is one of the key factors

influencing the performance of flexible pavements and it is one of the main input

parameters for pavement design procedures. Various design procedures adopt

different characterizations of the traffic. Most M-E procedures characterize the

entire heavy traffic ALS by converting into an equivalent number of standard

axles ESALs; thus this standard axle is used for analysis and design of the

pavement. This characterization is generally computationally efficient as the

analysis of the pavement is performed only for the chosen standard axle. On the

other hand, in more comprehensive M-E design procedures such as MEPDG, the

entire ALS is used to analyse the pavement. However, these procedures are

computationally expensive. Thus, to improve the computational performance, in

MEPDG the ALS is characterized by a constant contact area (CCA); in this way,

as indicated in Equation (7), response analysis for only one set of axle load-

contact pressure combinations is performed. The responses for other axle loads in

the ALS are estimated from the linear relation between contact pressure and the

response. As reported by Morton et al. (2004), a relatively more accurate

characterization for the ALS is to assume a constant contact pressure (CCP) for

the entire traffic. However, this characterization requires the analysis of the

pavement structure for the entire axle loads in the ALS and therefore

computationally inefficient for practical applications.

2.6.4. Heavy traffic lateral wander

Pavements are subjected to wandering traffic loads that do not follow a straight

course or channelized traffic. Several studies have shown that traffic wandering

has a significant effect on the development of rutting (Blab and Litzka, 1995; Wu

and Harvey, 2008). It is therefore necessary to take the effect of a wandering

pattern into account both during testing and modelling of the permanent

deformation behaviour of the pavement structures. Studies based on field

measurements have indicated that the lateral wander pattern can be modelled as

normally distributed (Erlingsson et al., 2012). Figure 8 shows the measured lateral

wander distributions of one-lane and two-lane sections of a state road. The


26

approximate normal distribution curve and its standard deviation of the data are

also included in the figure.

Figure 8. Normalized frequency of the lateral positions of the right wheel of heavy

vehicles on one-lane and two-lane sections of a state road (Erlingsson et al.,

2012).

2.7. Time Hardening Procedure

The preceding sections discussed the various factors affecting the rutting

performance of bound and unbound pavement materials. Attempts to develop

permanent deformation models for pavement materials were also discussed. These

models are generally some function of the number of load passes, stress or strain

level and pavement temperature. Figure 9 is a graphical representation of these

models. The dashed lines in the figure represent the accumulated permanent strain

p as a function of the number of load passes N for a single pavement temperature

Ti, a single deviatoric or mean stress level qi or pi and a single strain level ri,

where i = 1, 2, 3 and 4, denoting the climate and loading conditions of period i.

However, pavements in actual field circumstances are subjected to variable

climatic and traffic loading conditions (such as ALS or wandering); therefore a

procedure must be adopted to combine the permanent strain contributions from

different temperature and stress levels.

Lytton et al. (1993) proposed a time hardening procedure to combine the

permanent deformation contributions due to various stress levels. To illustrate the

procedure, the permanent deformation in the bituminous bound layers, shown in

Equation (20), is employed to predict the permanent strain for a time period of

0

5

10

15

-1.00 -0.50 0.00 0.50 1.00

Norm

. fr

equ

ency

[%

]

Wheel position [m]

One-lane

= 24.5 cm

0

5

10

15

-1.00 -0.50 0.00 0.50 1.00

Norm

. fr

equ

ency

[%

]

Wheel position [m]

Two-lane

= 28.5 cm


27

four seasons. It is assumed that each season is characterized by a pavement

temperature Ti, a deviatoric or mean stress level qi or pi and a strain level ri where

i = 1, 2, 3 and 4. The process begins by calculating the permanent strain p1 at the

end of the first season, using the temperature T1 and strain r1, and is given by:

(21)

Then the equivalent number of passes Neq1 that would yield the same

permanent strain p1 in the second season (or dashed line 2 in Figure 9) is

calculated from:

(

)

⁄

(22)

Figure 9. The time hardening procedure.

Finally, the permanent strain contribution due to the climate and loading

conditions of the second season is calculated from:

(23a)

(

) (23b)

where N is the number of applied load repetitions during the second season. The

total permanent strain at the end of the second season is obtained from:

(24)

The above procedures are repeated until the end of the seasons is reached.

Neq1 Neq2 Ni5 Ni2

T1, q1, p1, εr1

T2, q2, p2, εr2

T3, q3, p3, εr3

T4, q4, p4, εr4 εp

N

1

2

3

4

Ni1

Test Equipment, Structures and Materials

29

3. Test Equipment, Structures and Materials

3.1. Full Scale Accelerated Pavement Tests

Full Scale APT results were used in this study. The APTs were conducted using

an HVS facility at the Swedish National Road and Transport Research Institute,

VTI (Wiman and Erlingsson, 2008). Figure 10 shows the HVS facility.

Figure 10. The HVS at the Swedish Road and Transport Research Institute, VTI,

Linköping, Sweden.

The HVS is a mobile device employed to study the behaviour of a pavement

structure under loading and environmental conditions which are close to actual

field conditions. Using the HVS it is possible to apply a single or dual wheel

moving load of magnitudes from 30 to 110 kN at speeds up to 12 km/h. Traffic

wander is simulated by moving the wheel in the transverse direction.

Environmental influences such as pavement temperature and ground water table

are controlled through add-on facilities. The responses (stresses and strains in the

pavement) in the pavement and permanent deformation measurements are

registered using various sensors installed in the test structure.

The tests used in this study were conducted on test structures built in a 3 m

deep test pit testing facility at VTI (Wiman, 2001, 2006 and 2010). The structures

consisted of a thin asphalt surface layer, bituminous bases, UGM base or subbase

layer, and a sand subgrade over a rigid bottom. A total of 6 test pavement

structures were used. Figure 11 shows the cross sections of the test structures and


30

their instrumentations.

Figure 11. Cross sections of the test structures and instrumentations.

The test structures, referred to as SE01, SE05-1, SE05-2 and SE06 in Figure

11, were used for evaluation and validation of responses and permanent

deformation models for UGMs (Paper II and Paper III) whereas permanent

SE01

0

49

138

z [mm]

Crushed aggregate base

Asphalt concrete surface

Natural till mixed with

crushed rock base

Natural gravel

Sand subgrade

SE05-1

Pressure cell (vertical stresses)

Transversal asphalt strain gauge

Longitudinal asphalt strain gauge

Inductive coils (vertical strain)

SE05-2 0

55

506

z [mm]

0

50

512

z [mm]

Deflection gauge

48

209

101

z [mm]

351

0

SE06

Bituminous base

Granular subbase

SE09

0

35

396

z [mm]

33

192

110

z [mm]

644

0

SE10

Bituminous binder

117

198

Test Equipment, Structures and Materials

31

deformation models and viscoelastic responses of bituminous layers were

evaluated using test structures SE09 and SE10, respectively (Paper V and Paper

VI).

The material properties for the different layers in the test structures were

established based on laboratory tests and/or back-calculated from falling weight

deflectometer (FWD) measurements performed on the test structures.

3.2. Extra-Large Wheel Tracking Tests

The other device employed in this study was the extra-large wheel tracking

(ELWT) apparatus at The Swedish Road and Transport Research Institute (VTI),

Linköping, Sweden. In the ETWT test, an asphalt slab specimen of size 50 cm x

70 cm x 4-12 cm is subjected to a moving single wheel load of a magnitude up to

25 kN at a speed of up to 5 km/h in either direction. The load is applied through a

small truck tyre. The load is applied for a specified number of passes. Traffic

wandering is simulated by displacing the wheel at 7 offset positions over a width

of 6 cm.

The permanent deformation on the asphalt slab is measured using a laser beam

mounted on the device. The rut measuring is carried out at five transverse profiles

along the length of the plate. The distance measurement is made at an accuracy of

0.01 mm and a maximum number of 700 measurement points per profile. The

measurement points are spaced at 0.7 mm.

Specimen and air temperature in the test chamber are continuously controlled.

The temperature in the chamber can be varied between +5 and +60 °C. The

chamber temperature is controlled so that the temperature of the specimen is

maintained at a constant level. Figure 12 demonstrates the schematics of the

device.


32

Figure 12. Schematic diagram of the ELWT test setup.

A total of nine rectangular asphalt slabs from three types of asphalt mixtures

which are commonly used as asphalt surface layer (ABT11), bituminous binder

layer (ABb22) and a bituminous base layer (AG22), respectively, were prepared.

The sizes of the slabs were determined by the size of loading area (70 cm x 50

cm) of the ELWT device and therefore, 70 cm x 50 cm x 4 cm for ABT11 mixes

and 70 cm x 50 cm x 6 cm for ABb22 and AG22 were selected. The mixes were

prepared according to the European standard and the slabs were roller compacted

to attain the desired degree of compaction, as shown in Figure 13. The mixture

properties for the asphalt slabs were selected to match the corresponding mixture

properties of the bituminous bound layers of the SE09 test structure shown in

Figure 11. The permanent deformation measurements in the asphalt slabs along

with the APT results of SE09 test structure were used to evaluate the permanent

deformation model for asphalt bound layers (Paper VI).

Figure 13. Compaction of the slabs and the actual ELWT test setup.

Figur 1 Skiss över VTI:s Wheel Tracking utrustning

Laser beam Water tank

Asphalt plate

Response Models for Flexible Pavements

33

4. Response Models for Flexible Pavements

As discussed in the preceding sections, the response model plays an important

role in M-E pavement design and performance prediction procedures. The

response model is used to estimate the stresses, strains and displacements in the

pavement structure subjected to existing traffic loading, taking into account the

material properties and prevailing environmental conditions.

4.1. Multi-Layer Elastic Theory

Paper I appended to this thesis documents the development of a layered elastic

program based on Burmister theory. As is explained in the paper, a considerable

effort was made to improve the computational performance of the MLET program

by computing the integration constants shown in Equation (6) at selected Hankel

parameters and using piecewise linear interpolation to estimate the coefficients for

other values of the Hankel parameters. This procedure considerably decreased the

number of matrix inversions required. In addition, Richardson’s extrapolation was

employed to improve the convergence and accuracy of the integral for near

surface responses. Figure 14 depicts the stress coefficients (A, B, C and D), shown

in Equation (6), for a typical four layer pavement structure. As can be observed

from the figures, the coefficients increase or decrease continuously, like

monotonic functions, thus interpolation or extrapolation of the coefficients is

valid. The procedure is implemented in an MLET program ERAPAVE (Elastic

Response Analysis of flexible PAVEments).

A comprehensive verification of the program using two frequently used layered

elastic programs, KENPAVE (Huang, 2004) and WinJulea (ARA, 2004), was

performed and the accuracy obtained was excellent. The comparison of the

computational performance of the three programs also revealed that the

ERAPAVE program has an improved computational performance, especially for a

larger number of evaluation points, as shown in Figure 15.


34

Figure 14. Coefficients of the stress function as a function of the Hankel

parameter m for a four layer structure a) A; b) B; c) C; d) D.

Figure 15. Comparison of the computational performance of ERAPAVE,

KENPAVE and WinJulea.

-10

-8

-6

-4

-2

0

2

0 10 20 30 40 50

A [

-]

Hankel parameter m

Layer-1

Layer-2

Layer-3

Layer-4

a)

-2

0

2

4

6

8

10

0 10 20 30 40 50

B [

-]

Hankel parameter m

Layer-1

Layer-2

Layer-3

Layer-4

b)

-2

0

2

4

6

8

10

12

0 10 20 30 40 50

C [

-]

Hankel parameter m

Layer-1

Layer-2

Layer-3

Layer-4

c)

-2

0

2

4

6

8

10

12

14

16

0 10 20 30 40 50

D [

-]

Hankel parameter m

Layer-1

Layer-2

Layer-3

Layer-4

d)

0

1

2

3

4

5

0 100 200 300 400 500

Tim

e [s

ec]

Number of evaluation points

WinJulea

KENPAVE

ERAPAVE


35

Moreover, a nonlinear module was also introduced to take the stress dependent

behaviour of unbound materials into account. The superposition principle was

used to handle multiple wheel loading. The comparison of the nonlinear responses

from ERAPAVE with KENPAVE revealed good agreement between the two

programs.

The program was also used to simulate the measured responses of a test

structure from a full scale APT conducted at several wheel loadings and pavement

temperatures (Paper III). Figure 16 presents the measured and calculated vertical

strain for dual wheel (DW) loads of 50, 60 and 80 kN at a tyre pressures of 500

kPa, 800 kPa and 900 kPa, respectively, and a pavement temperature of 10C.

Figure 16. Measured and computed vertical strain for SE06 test structure under

wheel loads of a) 50, b) 60 and c) 80 kN.

0

10

20

30

40

50

60

70

-1.0 0.0 1.0 2.0 3.0

Dep

th [

cm]

Strain εz [10-3]

DW-50kN/500kPa-measured

DW-50kN/500kPa-computed

T = 10 ºC

a)

0

10

20

30

40

50

60

70

-1.0 0.0 1.0 2.0 3.0D

epth

[cm

] Strain εz [10-3]



T = 10 ºC

b)

0

10

20

30

40

50

60

70

-1.0 1.0 3.0 5.0

Dep

th [c

m]

Strain εz [10-3]



T = 10 ºC

c)


36

Figure 17 presents the measured and calculated vertical stress for a single

wheel (SW) load of 60 kN and at tyre pressures of 500 kPa and 900 kPa,

respectively, at a pavement temperature of 10C.

Figure 17. Vertical stress for SE06 test structure under single wheel loading at

different radial locations at 17 cm depth from the surface for (a) 500 kPa and (b)

900 kPa tyre pressure and pavement temperature of 10ºC.

4.2. Linear Viscoelastic Theory

The ERAPAVE program was extended for analysis of a layered system consisting

of linear viscoelastic materials. Paper V appended to this thesis demonstrated the

application of a generalized layered LVE analysis for estimating the structural

response of flexible pavements. The procedure is based on the elastic-viscoelastic

correspondence principle using a numerical inverse Laplace transform by Abate

and Valko (2004). A comparison of the direct layered LVE responses with

approximate solutions based on the elastic collocation (LE Collocation) method

was also carried out. Furthermore, this study proposed and demonstrated the use

of a collocation method based on LVE solutions at selected time durations (or

LVE Collocation) in order to improve the accuracy of the elastic collocation

method. Figures 18 and 19 present the comparison of these approaches for a

typical four layered pavement structure subjected to a stationary load of 60 kN

(Paper V). The figures also included the LVE response from KENLAYER.

0

25

50

75

100

125

150

175

200

-40 -20 0 20 40

Str

ess

σz

[kP

a]

SW-60kN/500kPa-measured

SW-60kN/500kPa-computed

a)

Distance from centre of tyre [cm]

0

25

50

75

100

125

150

175

200

-40 -20 0 20 40

Str

ess

σz

[kP

a]

SW-60kN/900kPa - measured

SW-60kN/900kPa - computed

b)

Distance from centre of tyre [cm]


37

Maximum errors of 8% in tensile stress and 3% tensile strain at the bottom of the

asphalt layer were observed in the LVE collocation method. The corresponding

values for the LE collocation approximation were 14% for tensile stress and 5%

for tensile strain, respectively.

Figure 18. a) Tensile stress and b) tensile strain at the bottom of the asphalt layer

under the centre of the wheel.

The proposed LVE collocation method was extended for analyses of moving

loads. The HVS test pavement structure SE10, shown in Figure 11, was also

analysed to simulate the measured responses under a moving load of varying

magnitude. Figures 20a to 20d show the measured and computed longitudinal and

transversal strains at the bottom of the bituminous base layer for moving wheel

loads of 30, 50, 60 and 80 kN at tyre pressure of 800 kPa and a pavement

temperature of 20C. The LVE calculations in general agreed very well with the

response measurements.

Figure 19. a) Vertical stress and b) vertical strain at the top of the subgrade under

the centre of the wheel.

-2500

-2000

-1500

-1000

-500

0

0 2 4 6 8 10

Ten

sile

str

ess

x [

kP

a]

Time [sec]

LVE

LVE Collocation

LE Collocation

KENLAYER

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0 2 4 6 8 10

Ten

sile

str

ain

x

[1

0-3

]

Time [sec]

LVE

LVE Collocation

LE Collocation

KENLAYER

b)

0

20

40

60

80

0 2 4 6 8 10

Ver

tica

l st

ress

z

[k

Pa]

Time [sec]

LVE

LVE Collocation

LE Collocation

KENLAYERa)

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10

Ver

tica

l st

rain

z [

10

-3]

Time [sec]

LVE

LVE Collocation

LE Collocation

KENLAYERb)

a)


38

Figure 20. Longitudinal and transversal strains at the bottom of the bituminous

base under the centre of one wheel for a) 30, b) 50, c) 60 and d) 80 kN at

pavement temperature of 20C.

-100

0

100

200

300

400

500

600

0 500 1000 1500 2000 2500 3000

Ten

sile

str

ain

[µ]

Time [msec]

Measured ey

Calculated ey

Measured ex

Calculated ex

Measured y

Calculated y

Measured x

Calculated x

a)

-100

0

100

200

300

400

500

600

0 500 1000 1500 2000 2500 3000

Ten

sile

str

ain

[µ]

Time [msec]

Measured ey

Calculated ey

Measured ex

Calculated ex

Measured y

Calculated y

Measured x

Calculated x

b)

-200

-100

0

100

200

300

400

500

600

0 500 1000 1500 2000 2500 3000

Ten

sile

str

ain

[µ]

Time [msec]

Measured ey

Calculated ey

Measured ex

Calculated ex

Measured y

Calculated y

Measured x

Calculated x

c)

-200

-100

0

100

200

300

400

500

600

0 500 1000 1500 2000 2500 3000

Ten

sile

str

ain

[µ]

Time [msec]

Measured ey

Calculated ey

Measured ex

Calculated ex

Measured y

Calculated y

Measured x

Calculated x

d)

Evaluation of Permanent Deformation Models

39

5. Evaluation of Permanent Deformation Models

Permanent deformation on the pavement surface along the wheel path, usually

referred to as rutting, is one of the main deterioration mechanisms. Rutting affects

the ride quality by forming hydroplaning which decreases the skid resistance of

the surface and eventually makes steering the vehicle difficult.

A number of permanent deformation models have been developed by several

researchers for both bound and unbound granular materials (Lekarp et al., 2000;

SAMARIS, 2004; Korkiala-Tanttu, 2008). The evaluation of these models is

frequently performed using data from triaxial tests which do not fully represent

the actual field loading circumstances. The subsequent sections present the

evaluation of selected permanent deformation models for bound and unbound

granular materials using full scale APT test results.

5.1. Permanent Deformation Models for UGMs

Paper II appended to this thesis presents the evaluation the Tseng and Lytton

(1989), the Gidel et al. (2001) and the Korkiala-Tanttu (2005) permanent strain

models using permanent deformation measurements from full scale APTs

performed on three different types of base materials. The Gidel et al. model has

shown a similar trend for the three base materials, i.e. a steep slope at the initial

stage of the load repetitions and a milder slope afterwards. A good fit was

obtained for crushed rock base material. On the other hand, the models by

Korkiala-Tanttu and Tseng and Lytton have shown slight differences between

patterns of permanent deformation for the base materials. Moreover, the Tseng

and Lytton model agreed relatively well with all materials. Figures 21, 22 and 23

show the measured and the modelled permanent deformation for the three types of

base materials, respectively.


40

Figure 21. Measured and modelled permanent deformation of base layer (natural

moraine mixed with crushed rock) of SE01 test structure.

Figure 22. Measured and modelled permanent deformation of natural gravel base

layer of SE05-1 test structure.

Figure 23. Measured and modelled permanent deformation of crushed rock base

layer of SE05-2 test structure.

0.0

1.0

2.0

3.0

0 200 400 600 800 1000

Number of load repetitions in thousands

Per

man

ent

Def

orm

atio

n [

mm

] MeasuredKorkiala-TanttuGidelTseng-Lytton

0.0

1.0

2.0

3.0

4.0

0 100 200 300 400

Per

man

ent

Def

orm

atio

n [

mm

]


Measured

Korkiala-Tanttu

Gidel

Tseng-Lytton

0.0

1.0

2.0

3.0

4.0

5.0

0 100 200 300 400


Per

man

ent D

efor

mat

ion

[mm

]

Measured

Korkiala-Tanttu

Gidel

Tseng-Lytton

Evaluation of Permanent Deformation Models

41

Laboratory to field correlation factors for the three base materials and for three

models were also estimated. The influence of moisture content and degree of

compaction was not modelled in this study.

5.2. Permanent Deformation Model for Bituminous Bound Layers

An evaluation of the permanent deformation model for asphalt concrete mixtures,

shown in Equation (20), was carried out based on ELWT and full scale APT tests

performed on three different types of asphalt mixtures. The tests were performed

at several pavement temperatures and efforts were made to simulate the actual

field conditions (Paper VI).

The measured permanent deformations in the asphalt slabs were modelled

using the permanent deformation model in Equation (20) and model parameters

a1, a2 and a3 for the three types of asphalt mixtures were estimated based on least

square optimization. 1 was considered as unity for ELWT tests. The estimated

mode parameters were then used to model the measured permanent deformation

of a test structure SE09 shown in Figure 11. The test structure consisted of the

three mixtures tested using the ELWT device. The calibration parameters 1, in

Equation (20), were estimated for the mixtures. Here, it should be noted that the

1 factor was used to relate the model parameters from the ELWT and the HVS

test. Figure 24 shows the measured and modelled permanent deformations in the

bituminous bound layers of the test structure.

The estimated factors were close to unity for all mixtures which indicated

that the ELWT device fairly represented the behaviour of the full scale APT test.

It should also be noted that slight differences in 1 were observed though efforts

were made to reproduce the APT test circumstances (Paper VI). Therefore it was

demonstrated that the ELWT device can be used to evaluate the performance

asphalt mixtures as well as to establish parameters for permanent deformation

model for asphalt mixtures. The slight differences in 1 from unity might be

attributed to differences in geometry, scale, wheel load and speed.


42

Figure 24. Measured and modelled permanent deformations for asphalt layers in

the SE09 HVS test structure a) ABT11, b) ABb22 and c) AG22.

0

2

4

6

8

0 150 300 450 600

Per

man

ent

def

orm

atio

n

[mm

]

Load cycles [Thousands]

ABT11 - HVS

ABT11- Model

30C 10C

20C

0

3

6

9

12

0 150 300 450 600

Per

man

ent

def

orm

atio

n [

mm

]


ABb22 - HVS

ABb22 - Model

30C 10C

20C

0

2

4

6

8

10

0 150 300 450 600

Per

man

ent

def

orm

atio

n [

mm

]


AG22 - HVS

AG22 - Model

10C

20C

30C

a) b)

c)

Characterization of Heavy Traffic Axle Load Spectrum

43

6. Characterization of Heavy Traffic Axle Load

Spectrum

Heavy traffic axle load spectrum (ALS) is one of the key inputs for mechanistic-

empirical analyses and design of pavement structures. For the purpose of

pavement design, the entire ALS is aggregated into Equivalent Number of

Standard Axle Loads (ESALs) or characterized by either constant contact area

(CCA) or constant contact pressure (CCP). These characterizations affect both the

accuracy and computational performance of the pavement analysis process.

Usually a standard axle load of 80 kN or 100 kN is used to convert the ALS into

ESALs or to obtain the contact area for the CCA characterizations. The CCP

characterization is a relatively accurate representation of the actual field

conditions as observed by tyre inflation pressure measurements of actual traffic

scenarios (Morton et al., 2004).

In Paper IV these three alternatives were evaluated based on the predicted

rutting and fatigue cracking performances of several pavement structures

subjected to heavy traffic ALS data collected from BWIM stations. It was

indicated that for layers below the 25 cm from the surface, the three

characterizations produced similar values of predicted rutting. However, for the

top 25 cm, the characterizations produced significant differences. Figure 25a to

25d shows the permanent deformation in the surface, base, subbase and subgrade

layers, respectively, of a typical four layered pavement structure subjected to a

heavy traffic ALS from one of the BWIM sites. The figure indicated that both the

ESAL and CCA characterizations underestimated the predicted permanent

deformation.

The Paper indicated that even though the CCP characterization is a relatively

accurate representation of the actual traffic conditions, it is computationally very

expensive and impractical for routine applications. On the other hand the ESAL


44

and CCA characterizations are computationally very efficient for M-E pavement

analysis and design applications; however, both characterizations underestimated

the calculated permanent deformation. Therefore in this study an improvement to

the CCA approach was proposed that enhanced the accuracy while maintaining

the same level of computational performance. Figure 26a and 26b presents the

predicted permanent deformation using the improved CCA approach (denoted by

modified CCA [MCCA] in the figure). From the figure it can be observed that a

significant improvement was gained when using the proposed MCCA approach.

Figure 25. Permanent deformation in a) surface layer, b) base layer, c) subbase

and d) subgrade.

0.0

2.0

4.0

6.0

8.0

0 5 10 15 20

Per

man

ent

def

orm

atio

n [

mm

]

Pavement age [year]

ESAL

CCA

CCP

a)

0.0

0.5

1.0

1.5

2.0

0 5 10 15 20

Per

man

ent

def

orm

atio

n [

mm

]

Pavement age [year]

ESAL

CCA

CCP

b)

0

0.2

0.4

0.6

0.8

0 5 10 15 20

Per

man

ent

def

orm

atio

n [

mm

]

Pavement age [year]

ESAL

CCA

CCP

c)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 5 10 15 20

Per

man

ent

def

orm

atio

n [

mm

]

Pavement age [year]

ESAL

CCA

CCP

d)

Characterization of Heavy Traffic Axle Load Spectrum

45

Figure 26. Permanent deformation using mean of the ALS as a reference axle a)

surface layer and b) base layer.

0.0

2.0

4.0

6.0

8.0

0 5 10 15 20

Per

man

ent

def

orm

atio

n [

mm

]

Pavement age [year]

ESAL

CCP

MCCA

a)

0.0

0.5

1.0

1.5

2.0

2.5

0 5 10 15 20

Per

man

ent

def

orm

atio

n [

mm

]

Pavement age [year]

ESAL

CCP

MCCA

b)

Conclusions and Recommendations

47

7. Conclusions and Recommendations

The objective of this study was to develop a mechanistic-empirical (M-E) flexible

pavement performance prediction framework. The work particularly concentrated

on evaluating the most important constituents of the M-E methods, namely, the

response model, permanent deformation models for bound and unbound pavement

materials, and heavy traffic characterization. The subsequent sections present the

conclusions, recommendations and limitations from of study.

7.1. Response Model

The response model is one of the key components of M-E design procedures. The

multilayer elastic theory (MLET) is employed in several M-E pavement design

procedures due to its simplicity and computational performance. In this study, an

MLET program ERAPAVE (Elastic Response Analysis Program for Flexible

PAVEments) which was based on the Burmister theory was developed and a

considerable effort was made to further improve the computational performance

of the program. In addition a procedure based on Richardson’s extrapolation was

introduced to improve the accuracy and convergence of near-surface responses. A

comprehensive verification of the ERAPAVE program using two frequently used

layered elastic programs, KENPAVE and WinJulea, was performed and the

accuracy obtained was excellent. The comparison of the performance of the three

programs revealed that the ERAPAVE program has an improved computational

performance, especially for a larger number of evaluation points, which is usually

the case for M-E design applications. Moreover, a nonlinear module was

introduced into the program to take stress dependent behaviour of unbound

materials into account.

Asphalt mixtures exhibit unique characteristics of both viscous and elastic

properties and hence are categorized as viscoelastic materials. Therefore the

ERAPVE program was extended to incorporate the viscoelastic behaviour of


48

bituminous layers through the elastic-viscoelastic correspondence principle. A

procedure based on collocation of linear viscoelastic (LVE) solutions at selected

time durations was also proposed that improved the computational performance

for analysis of stationary and moving loads.

7.2. Permanent Deformation Models

Rutting is one of the distresses that M-E pavement design procedure attempts to

control and it is well understood that rutting is the result of the permanent

deformation in the constituent layers of the pavement due to the prevailing traffic

and environmental condition. Therefore, it is necessary to model the permanent

deformation in bound and unbound layers of the pavement.

In this study, three M-E permanent deformation models for unbound granular

materials (UGMs) were evaluated based on three accelerated pavement tests

(APTs). The APTs were conducted on three test structures with different base

materials. The permanent deformation models evaluated were the Tseng and

Lytton (1989), Gidel et al. (2001) and Korkiala-Tanttu (2005). Models by Tseng

and Lytton and Korkiala-Tanttu showed slight differences between patterns of

permanent deformation for the base materials whereas the Gidel et al. model has

shown a similar trend for the three base materials, i.e. a steep slope at the initial

phase of the loading and a milder slope afterwards, and a good fit was obtained for

crushed rock base material. In general, the Tseng and Lytton model agreed

relatively well with all types of base materials. Laboratory to field correlation

factors for the three materials were also estimated for the models.

Furthermore, one permanent deformation model for asphalt layers was also

evaluated using an extra-large wheel tracking (ELWT) and APT tests. The model

produced reasonable magnitudes and trends for permanent deformation in the

asphalt layers. In addition, a calibration factor relating the ELWT device and the

APT facilities indicated that the ELWT device could fairly simulate the conditions

of APT and it can be employed to establish model parameters for the permanent

strain model.

Conclusions and Recommendations

49

7.3. Heavy Vehicle Characterization

Traffic loading is one of the most important factors influencing the performance

of flexible pavements. Therefore M-E pavement design procedures must account

for the effect of traffic. Due to the nature and the complexity of traffic data, M-E

pavement design procedures adopt different types of characterization and

simplification of the raw traffic data. This study discussed and evaluated three

different approaches for characterizations of heavy traffic ALS, namely, the

equivalent standard axle load (ESAL), the constant contact area (CCA) and the

constant contact pressure (CCP) approaches. Field measurement studies showed

that the CCP is a more realistic characterization of the actual traffic conditions;

however, it was shown that it is computationally very expensive for M-E

applications.

The characterizations were evaluated based on the predicted permanent

deformation and fatigue cracking performances and they produced similar results

for layers below 25 cm from the surface. However both the ESAL and CCA

approaches underpredicted the permanent deformations for the top 25 cm. The

error introduced, due to ESAL and CCA characterizations, reached up to 35% for

the permanent deformation and up to 70% for fatigue cracking. The computational

performances of the three characterizations were also evaluated; the ESAL

produced the highest performance, followed by the CCA. An improvement to the

CCA approach was also proposed that enhanced the accuracy while maintaining

the same level of computational performance.

7.4. Limitations and Recommendations for Future Studies

It is essential to state that the impact of climate such as temperature, moisture,

freezing-thawing, ground water table and drainage conditions were not fully

considered when evaluating the permanent deformation models for UGMs and

bituminous bound layers. This was due to the fact that the study mainly employed

results from full scale APT tests, where the temperature and the moisture in the

pavements were controlled. Moreover, unlike pavements under real traffic

scenarios, the APT test structures considered in the study were subjected to only a


50

single axle configuration. Therefore a validation of the models and the model

parameters using actual field conditions is recommended.

The stress dependent nature of UGMs was considered in the study; however,

the bituminous bound layers were treated as linear elastic materials and the effect

of aging was not taken into account. Furthermore, as MLET theory was employed

in the study, it was not possible to implement advanced characterization of the

materials such as anisotropic behaviours. Therefore these influences should be

assessed and incorporated through advanced materials characterizations and

rigorous modelling techniques such as the finite element method (FEM).

Finally, this study focused mainly on the M-E prediction and development of

rutting for flexible pavements and therefore other failure modes of flexible

pavements such as cracking, low temperature cracking and the international

roughness index (IRI) were not incorporated.

References

51

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