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Reliability-based
Design Procedure for
Flexible Pavements
Yared Hailegiorgis Dinegdae
Licentiate Thesis
KTH Royal Institute of Technology
Engineering Sciences
Department of Civil and Architectural Engineering
SE -100 44 Stockholm, Sweden
TRITA-JOB LIC 2027
ISSN 1650-951X
© Yared H. Dinegdae
E-print, Stockholm 2015
Akademisk avhandling som med tillstånd av KTH I Stockholm framlägges till offentlig
granskning för avläggande av teknisk licentiatexamen fredagen den 8 maj kl. 13.00 i sal
B23, KTH, Brinellvägen 23,Stockholm.
i
Abstract
Load induced top-down fatigue cracking has been recognized recently as
a major distress phenomenon in asphalt pavements. This failure mode
has been observed in many parts of the world, and in some regions, it was
found to be more prevalent and a primary cause of pavements failure.
The main factors which are identified as potential causes of top down
fatigue cracking are primarily linked to age hardening, mixtures fracture
resistance and unbound layers stiffness. Mechanistic Empirical analytical
models, which are based on hot mix asphalt fracture mechanics (HMAFM) and that could predict crack initiation time and propagation rate,
have been developed and shown their capacity in delivering acceptable
predictions. However, in these methods, the effect of age hardening and
healing is not properly accounted and moreover, these models do not
consider the effect of mixture morphology influence on long term
pavement performance. Another drawback of these models is, as analysis
tools they are not suitable to be used for pavement design purpose. The
main objective of this study is to develop a reliability calibrated design
framework in load resistance factor design (LRFD) format which could be
implemented to design pavement sections against top down fatigue
cracking.
For this purpose, asphalt mixture morphology based sub-models were
developed and incorporated to HMA-FM to characterize the effect of
aging and degradation on fracture resistance and healing potential. These
sub-models were developed empirically exploiting the observed relation
that exist between mixture morphology and fracture resistance. The
developed crack initiation prediction model was calibrated and validated
using pavement sections that have high quality laboratory data and
observed field performance history. As traffic volume was identified in
having a dominant influence on predicted performance, two separate
model calibration and validation studies were undertaken based on
expected traffic volume. The predictions result for both model calibration
and validation was found to be in an excellent agreement with the
observed performance in the field.
A LRFD based design framework was suggested that could be
implemented to optimize pavement sections against top-down fatigue
ii
cracking. To achieve this objective, pavement sections with various design
target reliabilities and functional requirements were analyzed and
studied. A simplified but efficient limit state equation was generated
using a central composite design (CCD) based response surface
methodology, and FORM based reliability analysis was implemented to
compute reliabilities and formulate associated partial safety factors. A
design example using the new partial safety factors have clearly
illustrated the potential of the new method, which could be used to
supplement existing design procedures.
Key Words
Top-Down fatigue cracking; asphalt mixture morphology; fracture
mechanics; response surface; reliability analysis; load resistance factor
design
iii
Preface
The thesis presented here has been carried out at the department of
Highway and Railway Engineering at the Royal institute of Technology
KTH, Stockholm.
I am grateful to the Swedish road administration (Trafikverket) for
providing the funds necessary for the project under which this thesis was
carried out.
My sincere appreciation goes to my supervisors Proff Björn Birgisson,
Ass.Proff Nicole Kringos and Ass.Proff Nils Ryden for their
encouragement, guidance and support, without which this work might
not be realized. I am also thankful to Ass.Proff Denis Jelagin for his
contribution in the success of this work.
I would also like to express my sincere thanks to Mr. Bruce Dietrich for
providing some of the data necessary and for facilitating the acquisition
of other important inputs.
It is also my wish to express my sincere appreciation for the Friday
meeting participants for their valuable expertise opinions and insights.
My colleagues at the division also deserve recognition for creating a
wonderful team spirit and working atmosphere.
Last but not least, I would like to express my deepest thanks to my family
back in Ethiopia and to my friends here in Stockholm for their constant
encouragement and support.
Yared Hailegiorgis Dinegdae
Stockholm, May 2015
iv
v
List of Acronyms
AC
Asphalt concrete
CCD
Central composite design
CI
Crack initiation
COV
Coefficient of variations
CR
Crack rating
DCSE
Dissipated creep strain energy
ESALs
Equivalent single axle loads
FM
Fracture mechanics
FOS
Factor of safety
FORM
First order reliability method
FOSM
First order second moment
HMA
Hot mix asphalt
LRFD
Load resistance factor design
LSE
Limit state equation
M-E
Mechanistic Empirical
PEM
Point estimate method
PS
Primary structures
R-F
Rackwitz-Fiessler
RSM
Response surface method
vi
vii
Appended Papers
Journal:
Paper I
Dinegdae, H. Y., Onifade, I., Jelagin, D. and Birgisson, B., ‘Mechanicsbased top down fatigue cracking prediction framework for asphalt
pavements’ (Submitted manuscript and under review in Road Materials
and Pavement Design, 2014)
Paper II
Dinegdae, H. Y. and Birgisson, B., ‘Reliability-based calibration for the
mechanics-based fatigue cracking design framework’, (Submitted
manuscript and under review in Road Materials and Pavement Design,
2014)
viii
ix
Contents
ABSTRACT _____________________________________ I
PREFACE ______________________________________ III
LIST OF ACRONYMS_____________________________ V
APPENDED PAPERS____________________________ VII
CONTENTS ___________________________________ IX
1. INTRODUCTION _____________________________ 1
2. TOP-DOWN FATIGUE CRACKING _______________ 3
3. RELIABILITY-BASED CALIBRATION ____________ 7
4. SUMMARY OF APPENDED PAPER _____________ 11
5. DISCUSSION AND CONCLUSIONS _____________ 19
REFERENCES __________________________________ 1
x
Introduction |1
1. Introduction
Fatigue cracking is one of the dominant distress modes in asphalt
concrete (AC) pavements. The conventional approach assumes cracks to
initiate at the bottom of AC layer and to propagate further upward to the
surface. However, core samples from multiple site investigations have
revealed cracks that occur in the reverse direction. This failure
phenomenon, called top-down fatigue cracking was recognized recently
as a failure mode and it was shown to be prevalent in many parts of the
world. The mechanism and failure process of top down fatigue cracking is
not fully understood and established, thus making it difficult to consider
this failure mode effectively in the design process.
Previous research has identified traffic-induced lateral or horizontal
stress, near-surface age-hardening, temperature induced stiffnessgradient, low fracture resistance and soft unbound layers as factors which
may contribute for the onset and propagation of top-down fatigue
cracking. Once initiated, these cracks widen up while propagating
downwards thus increasing the surface roughness and facilitating water
infiltration. These compounded factors further accelerate the rate of
damage and finally result in pavement section failure.
Research regarding top-down fatigue cracking has been ongoing through
the years. In the last decade, Hot Mix Asphalt Fracture Mechanics (HMAFM) based Mechanistic-Empirical analysis models were established that
could predict crack initiation time and crack propagation rate (Birgisson,
Wang, & Roque, 2006; NCHRP,2004; NCHRP,2010). Though these
newly developed models have shown their capacity in delivering results
which are in a good agreement with the observed performance in the
field, still more work is needed to enhance, calibrate and validate these
models. Moreover, as shown in recent research, the morphology of
asphalt mixtures which plays a critical role in governing and controlling
mixture aging properties and consequently the mixture long term
fracture characteristic is missing in these models.
Another factor which limits the application of these M-E models is, as
analysis tools, they may not be readily implemented for design purposes.
The absence of an appropriate design procedure to mitigate and control
top-down fatigue cracking can cause premature failure in pavements.
Introduction |2
This is a major concern for transportation departments as it is usually
associated with high maintenance and repair costs. In addition, there has
been a shift in civil engineering design procedures to a simpler, user
friendly and reliability-based design formats. Load resistance factor
design (LRFD) has been adopted in many structural design specifications
(AASSHTO1197b; ACI, 1995; AISC, 1989; CGS, 1985 & OHD, 1991).
However, its adoption and implementation in pavement analysis and
design is at its early phase (Kim, Harichandran & Buch, 1998; Kim and
Buch, 2004).
The objective of this thesis is to develop, calibrate and validate a
mechanics-based top down fatigue cracking initiation prediction
framework which is based on fundamental material behavior and that
encompasses key factors and design parameters. In addition, this
research proposes a reliability-based calibration in LRFD format that
could be used to supplement existing design procedures for mitigating
and controlling top-down fatigue cracking. These objectives were
achieved by undertaking further enhancement to HMA-FM and
implementing a two component reliability analysis methodology while
using observed performance of field pavement sections.
The first part of this thesis presents the development, calibration and
validation of a mechanics based top down fatigue cracking initiation
prediction framework (Paper I). This part provides information on the
framework and the incorporated asphalt mixture morphology based sub
models that are used to predict the age-induced change in mixture
fracture properties and healing potential. In addition, full description is
given about the field pavement sections that were used for model
calibration and validation and how well predicted results are compared
with the observed performance in the field. The second part of the thesis
deals with the development of a reliability-based calibration in load
resistance factor design (LRFD) format which could be used to design
pavement sections against this kind of failure (Paper II). Detailed
information is provided in this part about the various uncertainties and
variabilities involved in the pavement design process and how these
variabilities were modeled. Moreover, discussion is given on the
reliability analysis computation and finally how the reliability-based
calibration was done to generate the partial safety factors.
Background |3
2. Top-down fatigue cracking
Most mechanistic empirical design procedures estimate the fatigue life of
asphalt pavements expecting fatigue cracks to initiate at the bottom of
asphalt layer and to propagate upwards to the surface (Brown & Dawson,
1992; Gillespie et al., 1993; Papagiannakis, Amoah, LeBlanc, &
Woodrooffe, 1993). However, core samples in many parts of the world
including Japan, UK, Europe and the United States have exhibited topdown fatigue cracks, where cracking initiates at the top and propagates
downwards to the bottom (Gerritsen, Van Gurp, Van Der Heide,
Molenaar, & Pronk, 1987; Matsuno & Nishizawa, 1992; Uhlmeyer,
Willoughby, Pierce, & Mahoney, 2000). In Florida, USA, top-down
cracking has been observed to be a dominant form of failure, accounting
over 90% of the cracking in asphalt pavements (Myers & Roque, 2002;
Roque, Birgisson, Drakos, & Dietrich, 2004).
Researchers have tried to identify potential mechanisms and key factors
that could result in top-down fatigue cracking (Collop & Roque, 2004;
Mollenhauer & Wistuba, 2012; Myers, Roque, & Ruth, 1998; Wang,
Myers, Mohammad, & Fu, 2003; Zou, Roque, & Byron, 2012). In
addition, other studies have suggested experimental methods that can
evaluate the susceptibility of mixtures to this kind of failure (Baek,
Underwood, & Kim, 2012; Chen, Tebaldi, Roque, Lopp, & Su, 2012;
Roque, Zhang, & Sankar, 1999). Recently, hot mix asphalt fracture
mechanics (HMA-FM) based Mechanistic-Empirical analysis models
have been established that could predict crack initiation time and crack
propagation rate (Birgisson, Wang, & Roque, 2006; NCHRP, 2004;
NCHRP, 2010). The underlying concept in HMA-FM is the existence of a
threshold dissipated creep strain energy limit (DCSE_lim) which when
exceeded by the traffic induced damage creates a non-healable macro
crack (Zhang, Roque, Birgisson, & Sangpetngam, 2001; Roque, Birgisson,
Sangpetngam, & Zhang, 2002). In HMA-FM, the effect of healing and
degradation on viscoelastic material properties due to aging are not
accounted for fully during the service life of the pavement, thus limiting
its ability of assessing the performance of AC pavements against topdown fatigue cracking.
Background |4
The morphology of asphalt mixtures has been shown to influence key
mixture properties that are important to fracture resistance. By
controlling mixture aging characteristics, the morphology of asphalt
mixtures affects the performance and long term durability of pavement
sections(Guarin, Roque, Kim, & Sirin, 2012; Onifade, Jelagin, Guarin,
Birgisson & Kringos, 2013; Kumar Das, Birgisson, Jelagin, & Kringos,
2013). Lira, Jelagin, & Birgisson, 2012 developed an asphalt mixture
morphological framework that utilizes aggregate packing arrangements
and aggregate gradations to evaluate mechanical properties and
performance of asphalt mixtures. In this framework, a morphological
parameter called primary structure coating thickness (PS coating
thickness) was introduced to describe the mix of bitumen and fillers that
surround the primary load carrying structure of the asphalt mixture.
Figure 1. Mechanics-based crack initiation prediction framework
A general outline of a mechanics based analysis framework that utilizes
HMA-FM is suggested in Figure 1. This framework has five main
components and predicts time of crack initiation in asphalt pavements.
The inputs module, material property sub-model, pavement response
sub-model, damage accumulation and recovery sub-model and crack
initiation prediction sub-model constitute the five main components of
the framework. Detail description of the components is presented as
follows.
Background |5
Inputs module: The inputs module provides all the information that is
required to compute the crack initiation time for a given pavement
system. These inputs comprises of asphalt mixture properties, pavement
cross-sectional information, environmental factors and traffic volume.
Material property predictive sub-models: Without laboratory testing,
these material property predictive sub-models provide the input
parameters which are required to analyze the pavement response and the
damage accumulation and recovery sub-models. The predictive submodels that are incorporated are asphalt stiffness aging, dissipated creep
strain energy limit (DCSE_lim), healing potential and creep strain rate.
Pavement response sub-model: Computes the response of the pavement
system. The axisymmetric linear elastic analysis tool primarily tries to
obtain bending-induced maximum surface tensile stress as bending is the
main mechanism which is attributed to top-down cracking failure.
Damage accumulation and recovery sub-model: Computes damage on
hourly basis by considering maximum surface tensile stress, creep strain
rate and hourly traffic. Equation 1 is used to compute load associated
damage per cycle:
0.1
DCSE L cycle =
∫s
* sin(10p t ) * e p max * sin(10p t ) dt
•
AVE
(1)
0
Crack initiation sub-model:
DCSE remain ( t ) with that of
Thus, by comparing the accumulated
DCSElim ( t ) on an hourly basis, this model
estimates the crack initiation time tinit in asphalt pavements:-
tinit = DCSE remain ( t ) − DCSElim ( t ) ≥ 0
(2)
Background |6
Background |7
3. Reliability-based calibration
In some design specifications, pavement design is performed assuming
the design process to be deterministic (Shell, 1978; PMS Objekt, 2008 &
Austroads 2004). However, pavement design in reality involves a large
number of variables, and the combined effects of the variances associated
with these variables can have a significant influence on predicted
pavement performance (Darter, McCullough & Brown, 1972; Noureldin,
Sharaf, Arafah & Al-Sugair, 1994, Timm, Birgisson & Newcomb, 1998;
Kenis &Wang, 2004). Huang (2004) attributed the uncertainties and
variabilities associated with pavement design to three major sources:
inherent variability, model uncertainty and statistical uncertainty.
The significance of reliability analysis in pavement design was already
recognized in the 1970s and research was underway to address its
application and implementation (Lamer & Moavenzadeh, 1971; Darter,
McCullough, Brown, 1972; Darter, Hudson, & Brown, 1973). Chou (1990)
and Divinsky, Ishai, and Livneh (1998) incorporated reliability principles
to the CBR method of pavement design, and the 1993 AASHTO design
guide for flexible pavements have accounted for reliability in its design
procedure (AASHTO, 1993). Limited studies, which were based on
numerical simulation, were also undertaken to incorporate reliability
concepts into the pavement design process (Chua, Kiuredhian,
Monismith, 1992; Timm, Newcomb, Birgisson & Galambos, 1999; Kenis
&Wang, 2004). Moreover, further research using analytically based
reliability analysis tools such as first order second moment (FOSM), point
estimate methods (PEM) and first order reliability method (FORM) have
been conducted to compute pavement performance reliability (Kim,
Harichandran & Buch, 1998; Kim & Buch, 2003; Retherford &
McDonald, 2010).
In an early attempt to develop a codified pavement design procedure,
Harr (1987) introduced the factor of safety (FOS) for estimating the
failure risk involved in pavement performance evaluation. Nevertheless,
representing the various uncertainties involved by a single factor may not
ensure designs with uniform reliability as the various random variables
influence the predicted performance in different ways. To address this
problem, a load resistance factor design (LRFD procedure was suggested.
LRFD addresses this problem by assigning reliability-based partial safety
Background |8
factors to each significant parameter based on theirs degree of influence,
associated variability and on the level of safety required. Most structural
design specifications have already adopted the LRFD format
(AASSHTO1197b; ACI, 1995; AISC, 1989; CGS, 1985 & OHD, 1991).
However, the adoption of LRFD procedures for pavement design is at its
early stages and there are limited studies regarding its development and
implementation (Kim, Harichandran & Buch, 1998; Kim and Buch,
2004).
Modeling of design inputs variability is a prerequisite to any reliability
analysis. There are limited studies regarding variability of flexible
pavement design inputs such as AC layer thickness, base modulus and
traffic. According to these studies, AC layer thickness variability can be
modelled with a normal distribution with coefficient of variation (COV)
range of 3%-25% (Bush, 2004; Darter, Hudson & Brown, 1973; Timm,
Newcomb, Birgisson & Galambos, 1999; Noureldin, Sharaf, Arafah & AlSugari, 1994). In the case of base modulus, lognormal distribution with a
COV range of 5%-60% was suggested (Timm, Newcomb, Birgisson &
Galambos, 1999; Bush, 2004). Traffic, according to Maji & Das (2007)
and AASHTO (1985), could be best characterized with a log normal
distribution with COV range of 30%-42%.
A suggested design flow-chart for a mechanics-based design framework is
presented as shown in Figure 2. Design is performed by comparing the
factored DCSE_lim with the corresponding factored DCSE_acum.
Reliability based partial safety factors, resistance safety factor ( ϕDCSE_lim )
and global load factor (γglobal ) represent design inputs variability.
=
PE ( t ) φDCSE _ lim * DCSE _ lim(t) − g global * DCSE _ acum ( t )
(3)
Background |9
Figure 2. Mechanics-based design framework flow-chart
Background |10
Summary of papers |11
4. Summary of appended paper
4.1 Mechanics-based crack initiation prediction
framework (Paper I)
The purpose of this paper is to develop a mechanics-based top-down
fatigue cracking initiation prediction framework for asphalt pavements.
This is achieved by undertaking further enhancement to HMA-FM
(Zhang, Roque, Birgisson, & Sangpetngam, 2001). Asphalt mixture
morphology-based sub-models were developed and incorporated into
HMA-FM to consider age induced degradation in mixture fracture
resistance and healing potential. Calibration and validation of the
developed model was achieved using field pavement sections that have a
well-documented performance history and high quality laboratory data.
For this purpose, 28 different pavement sections were used. These
pavement sections comprise of state roads, turn-pikes and interstates
with a wide range in traffic, mixture types, materials, structures and
climate.
Dissipated creep strain energy limit (DCSE_lim): This is the threshold
energy that governs the fracture resistance of asphalt mixtures. The new
morphology based predictive sub-model was achieved in two steps. First,
a relationship between PS coating thickness and DCSE_lim was
established using data from 15 pavement sections. Based on this
relationship and using additional asphalt mixtures, a non-linear
regression was undertaken to establish the following analytical equation
which relates DCSE_lim with PS coating thickness (tp) and age (t).
k2
 1   1 ( k3 +k4 *logt p )
DCSE _ lim(t) = k    
 tp   t 
(4)
1
Where k1 = 2.38, k 2 = 0.79, k 3 = 0.33 and k 4 =0.12.
Healing potential of asphalt mixtures: Based on findings from previous
research and utilizing mixture healing potential properties, a simplified
healing potential equation that accounts for asphalt mixture morphology
is developed. The developed sub-model predicts yearly healing potential
values by taking PS coating thickness, initial dissipated creep strain
Summary of papers |12
energy and time of year. An unknown aging factor k, that determines the
healing potential trend, was introduced to be used later for the purpose of
model calibration.
t
h ym (t ) = 1 − ([exp( p ) − DCSE ]norm ) k
(5)
t
i
The pavement sections were divided into two random groups for the
purpose of model calibration and validation. It was obvious from
preliminary analysis that traffic induces a significant impact on predicted
crack initiation (CI) time. This was evident in the calibration process as it
was not possible to obtain an optimum calibration equation that
effectively accounts the expected variations in traffic. Taking this into
account, model calibration and validation was achieved by dividing the
pavement sections into two traffic categories based on annual traffic
volume. The low traffic volume group includes sections that have an
annual traffic volume of 100,000 ESALs and less while the medium to
high volume group has an annual traffic volume of more than 100,000
ESALs.
The aging parameter (k) that was included as an unknown calibration
factor in the healing potential sub-model was used for model calibration.
Equation 6 shows the calibrated healing potential model for the medium
to high volume traffic category.
tp
h ym (t ) = 1 − ([exp( ) − DCSE ]norm )
i
( k1*tp + k2 )
(6)
t
Where k1 = 15.5 and k 2 = 3.35
New predictions were made for the calibration sections by incorporating
the modified healing potential equation. Figure 3 compares these results
with the corresponding observed CI time in the field for the medium to
high volume traffic category. The same prediction was also done for the
validation sections in the same category. Figure 4 presents these
predicted results in comparison with the observed performance in the
field. As can be seen in the figures, there is a general agreement between
the predicted and observed CI times, though specific case studies
revealed that there is a noticeable over prediction in some section and an
under prediction in other sections. A goodness of fit evaluation revealed
that it is only two sections that exhibited a CI time that exceed 3 years.
Summary of papers |13
Observed
Predicted
CI time (year)
15
10
5
0
Pavement section
Figure 3. Predicted and observed CI times for medium to high volume roads
CI time (year)
15
Observed
Predicted
10
5
0
Pavement section
Figure 4. Predicted and observed CI times for medium to high volume roads
Based on the results from the two traffic groups, it can be concluded that
the model accurately captures the phenomena of load related top down
fatigue cracking in asphalt pavements and can be used to predict the
onset of cracking.
Summary of papers |14
Summary of papers |15
4.2 Reliability based calibration for the mechanics based
crack initiation framework (Paper II)
The main objective of this paper was to develop a reliability-based design
procedure in LRFD format for a mechanics-based analysis framework.
This is achieved by incorporating a two component reliability analysis
framework. The framework computes reliability by utilizing a response
surface methodology and a first order reliability method (FORM).
Another objective is to perform statistical characterization of design
inputs that have a significant influence on predicted performance. To
achieve the above stated goals, field pavement sections that have a wide
range in functional requirements and target reliabilities were studied and
evaluated.
Figure 5. Incorporated reliability analysis methodology
As can be seen in Figure 5, the reliability analysis methodology
implemented in this study is comprised of two main components. The
first component, using a response surface analysis, generates an efficient
analytical expression that simplifies the limit state equation (LSE). For
this purpose, a central composite design (CCD) based response surface is
implemented. CCD employs a second degree polynomial equation to
effectively surrogate the load induced accumulated damage. Once the
LSE is established, the reliability analysis component computes reliability
using the Rackwitz-Fiessler (R-F) algorithm, which is one variety of the
Summary of papers |16
FORM. The computed reliability is presented with reliability index and
probability of failure.
For this study, the full probabilistic distribution approach was used to
characterize design inputs variability. The parameters which were
identified to be dominant and subsequently modeled as random variables
are AC thickness, base modulus, traffic and DCSE_lim. Using these
design inputs variability, a surrogate model is generated to represent
DCSE_acum. A statistical analysis was performed on the fitted function
to examine its adequacy and to ensure it provides a good approximation
to the true system. Figure 6 shows a comparison between DCSE_acum
values which are predicted by the real and response surface methodology
(RSM) for a given pavement section.
1.4
Damage_acum (RSM predicted)
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Damage_acum (Real model)
Figure 6. DCSE_acum values as predicted by the real and RSM models
A design equation in LRFD format for a mechanics-based design
framework procedure is proposed as shown in Equation 7.
φDCSE _ lim DCSE _ lim ≥ g global DCSE _ acum
(7)
Summary of papers |17
In Equation 8,
φDCSE _ lim and g global are partial safety factors introduced to
reduce the effect of DCSE _ lim and to amplify DCSE _ acum influence
respectively. However, DCSE _ acum is the product of many independent
variables and could be expressed as follows:
EB , h Nh )
DCSE _ acum = f (f AC H AC , fγ
B
In the above equation, φ AC , φB
and
γ h are
introduced to reduce the effect of H AC and
increasing the influence of
(8)
partial safety factors
E b on DCSE_acum while
N h respectively.
Field pavement sections with various target reliabilities and functional
requirements were used to establish the respective partial safety factors
of the design parameters. The directional cosines, which are the
byproduct of the reliability analysis, were used to develop the partial
safety factors for the different target reliabilities. In addition, a global
partial safety factor was introduced for amplifying the effect of
DCSE_acum that effectively substitute the partial safety factors of the AC
thickness, base modulus and traffic. Averaged partial safety factors for
the design inputs involved and for the target reliabilities can be seen in
Table 1.
Table 1. Partial safety factors for the design procedure
Target
Reliability (%)
φDCSE _ lim
φHac
φEb
γ ESALs
γ Global
75
0.902
0.977
0.890
1.169
1.501
80
0.882
0.958
0.89
1.244
1.682
85
0.854
0.948
0.864
1.268
1.871
90
0.823
0.941
0.843
1.422
2.255
95
0.780
0.914
0.798
1.502
2.842
An illustrative design was done to show how the developed LRFD
procedure could be implemented in the design of new pavement sections
against top-down fatigue cracking. For this purpose, a given section was
Summary of papers |18
designed for target reliabilities of 75%, 80%, 85%, 90% and 95%. First
LRFD procedure was implemented to design the sections for the various
target reliabilities and later based on FORM the reliability of these
sections was assessed. As can be seen in Figure 7, there is a remarkable
agreement between the target and computed reliabilities.
100
R_target
Reliability, %
90
R_calculated
80
70
60
50
75%
80%
85%
90%
95%
Pavement sections
Figure 7. A comparison between target and calculated reliabilities
Despite the limited number of pavement sections used in the
development of the partial safety factors, the result from the illustrative
example have shown clearly that the LRFD procedure could satisfactorily
deliver designs of uniform reliability. Moreover the result gives credibility
to the methodology proposed in this paper and the design procedure
could be used to supplement existing design methods.
Discussion and conclusions |19
5. Discussion and conclusions
The focus of the present study is to establish a reliability calibrated design
procedure that can be implemented for mitigating top-down fatigue
cracking in asphalt pavements. HMA-FM was selected as a basis for
model development while FORM was chosen for reliability analysis and
establishing partial safety factors. The predicted CI times have given
credibility to the notion that the morphology of asphalt mixtures plays a
key role in controlling and governing pavements long term performance.
Nevertheless, it was also obvious from the predictions that the PS coating
thickness cannot be taken as a determining parameter which could be
used to rank mixtures fracture performance. One of the key findings of
the model calibration and validation was the extent to which traffic
volume affects pavement sections susceptibility to cracking. However,
traffic volume was not able in explaining solely the observed anomalies in
the predictions, which shows the significant influence of the various
design inputs and key factors and the complicated interplay that exist
among these parameters. There is a remarkable agreement between the
predicted and observed CI times for the medium to high volume traffic
groups, but this is not the case for low volume roads. As a low reliability
design, the design inputs and material properties of low volume sections
are expected to exhibit high variations, which could result in a less
accurate prediction. In addition, this study could have benefitted from
having included low traffic volume sections. Unfortunately, these were
not readily available.
The reliability analysis has demonstrated the capability and credibility of
the two component reliability computation methodology. It is also
observed that the CCD generated surrogate model, which replaced the
true accumulated damage in the limit state equation, was shown to
deliver remarkably exact values. The wide range in reported COV of
design inputs have clearly shown how estimated reliabilities could be
influenced by the values selected. Moreover, the design examples have
clearly illustrated the importance of including various design features in
the partial safety factors formulation. This is clearly demonstrated in the
85%-95% reliabilities design, where the computed reliabilities have a
remarkable agreement with the design reliabilities. Another issue which
was important during the reliability calibration process was to develop
Discussion and conclusions |20
the new partial safety factor in conjunction with existing design manuals
as this allows the new procedure to be tied with inherent past
experiences.
Appropriate evaluation of the top-down cracking performance of asphalt
pavements is a very complex problem as it involves many factors,
material properties and design conditions. In this study, new
morphology-based sub-models were developed to address the
degradation in DCSE and healing potential. These sub-models were
developed empirically without considering the real mechanisms and
factors that govern these properties. Moreover, the partial safety factors
for the LRFD procedure were formulated using a limited number of
pavement sections that may not be enough to represent the various
design features exist in practice. Despite these limitations, and
simplifications involving other key factors, both the crack initiation
prediction model and the LRFD procedure have deliver results which are
in an excellent agreement with the field observed performance and
computed reliabilities respectively.
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