Reliability-based Design Procedure for Flexible Pavements

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 (HMA- FM) 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., ‘Mechanics- based 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 stiffness- gradient, 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 (HMA- FM) 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 top- down 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 top- down 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 sub- models 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:

(1) Crack initiation sub-model: Thus, by comparing the accumulated

remain( )

DCSE t with that of DCSElim

( )

t on an hourly basis, this model estimates the crack initiation time tinitin asphalt pavements:-

(2)

0.1

max 0

* sin(10 ) * * sin(10 ) dt

L AVE p

DCSE cycle=

∫

s pt e^• pt

( ) lim( ) 0

init remain

t =DCSE t −DCSE t ≥

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 & Al- Sugari, 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 (γ_global) represent design inputs variability.

(3) PE t( )=φ_{DCSE_ lim}*DCSE_ lim(t)−g_global*DCSE_acum t( )

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).

(4)

Where k₁= 2.38, k₂ = 0.79, k₃ = 0.33 and k₄ =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

1

2 ( 3 4*logt )

_ lim(t) 1 1

p

k k k p

DCSE k

t t

+

=            

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.

(5)

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.

(6) Where k1= 15.5 and k2 = 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.

( ) 1 ([exp( )

^{p DCSEi}

] )

k

ym norm

t t

h t

= −

⁻

1 2

( *tp )

( ) 1 ([ exp( )

^{p DCSEi}

] )

ym norm

k k

t t

h t = −

^{− +}

Summary of papers |13

Figure 3. Predicted and observed CI times for medium to high volume roads

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.

0 5 10 15

CI time (year)

Pavement section Observed Predicted

0 5 10 15

CI time (year)

Pavement section Observed Predicted

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.

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.

(7) 0.0

0.2 0.4 0.6 0.8 1.0 1.2 1.4

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Damage_acum (RSM predicted)

Damage_acum (Real model)

_ lim _ lim _

DCSE DCSE globalDCSE acum

φ

≥

g

Summary of papers |17

In Equation 8,

φ

_{DCSE_ lim}and

g

_globalare 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:

_ ( _ACH_AC

,

_B

E ,

_{B h h}

)

DCSE acum= f φ

φ g

N (8)

In the above equation,

φ

_AC,

φ

_B and

g

_hare partial safety factors introduced to reduce the effect of

H

_ACand

E

_bon DCSE_acum while increasing the influence of

N

hrespectively.

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 (%)

φ

^{DCSE_ lim}

φ

_Hac

φ

_Eb

g

_ESALs

g

_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 betweenthe target and computed reliabilities.

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.

50 60 70 80 90 100

75% 80% 85% 90% 95%

Reliability, %

Pavement sections R_target R_calculated

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.

References

1. AASHTO, 1993. Guide for Design of Pavement Structures, American Association of State Highway and Transportation Officials, Washington, D.C.,

2. AASHTO, 1997b, Standard Specifications for Highway Bridges, American Association of State Highway and Transportation Officials, Washington, D.C., 16th Edition (1996 with 1997 Interims).

3. ACI, 1995, Building Code Requirements for Reinforced Concrete, American Concrete Institute, Detroit.

4. AISC, 1994, Load and Resistance Factor Design Specification for Structural Steel Buildings, Chicago, IL, 2nd Edition.

5. Austroads, Pavement Design, Sydney, 2004.

6. Baek, C., Underwood, B. S., & Kim, Y. R. (2012). Effects of oxidative aging on asphalt mixture properties. Transportation Research Record: Journal of the Transportation Research Board, 2296, 77–85.

7. Birgisson, B., Wang, J. & Roque, R. (2006b). Implementation of the Florida cracking model into the mechanistic empirical pavement design. Gainesville: University of Florida.

8. Brown, S. F. and Dawson, A. R. Two-stage mechanistic approach to asphalt pavement design. Proceedings of Seventh International Conference on Asphalt pavements, Nottingham, 1992.

9. Canadian Geotechnical Society, 1985, Canadian Foundation Engineering Manual, Bitech Publishers, Ltd., Second Edition

10. Chen, Y., Tebaldi, G., Roque, R., Lopp, G., & Su, Y. (2012). Effects of interface condition characteristics on open-graded friction course top-down cracking performance. Road Materials and Pavement Design, (Sup. 1), 56–75.

11. Chua, K.H., Kiuredhian, A.D. and Monismith, C.L., 1992. Stochastic model for pavement design. Journal of Transportation Engineering, ASCE, 118(6), 769–785.

12. Chou, Y. T., 1990. Reliability design procedures for flexible pavements. Journal of Transportation Engineering, ASCE, 116(5), 602–614.

13. Collop, A. C. & Roque, R. (2004). Report on the prediction of surface- initiated longitudinal wheel path cracking in asphalt pavements.

Road Materials and Pavement Design, 5(4), 409–434.

14. Darter, M. I., Hudson, W. R. and Brown, J. L., 1973. Statistical variation of flexible pavement properties and their consideration in design. Proceedings of the Association of Asphalt Paving Technologists, Vol. 42, pp. 589–615

15. Darter, M. I., McCullough, B. F. and Brown, J. L., 1972. Reliability concepts applied to the Texas flexible pavement system. Highway Research Board, Record No. 407, pp. 146–161

16. Divinsky, M., Ishai, I. and Livneh, M., 1998. Probabilistic approach to pavement design based on generalized California bearing ratio equation. Journal of Transportation Engineering, ASCE, 124(6), 582–588.

17. Gerritsen, A. H., Van Gurp, C. A. P. M., Van Der Heide, J. P. J., Molenaar, A. A. A., & Pronk, A. C. (1987). Prediction and prevention of surface cracking in asphaltic pavements. Proceedings of the 6th International Conference on Structural Design of Asphalt Pavements.

Ann Arbor, MI, 378–391.

18. Gillespie, T. D, Karamihas, S. M., Cebon, D, Sayers, M. W, Nasim, M.

A, Hansen, W. and Ehsan, N. Effects of heavy vehicle characteristics on pavement response and performance. Transportation Research Board, NCHRP Report 353, 1993.

19. Guarin, A., Roque, R., Kim, S., & Sirin, O. (2012). Disruption factor of asphalt mixtures. International Journal of Pavement Eng.

doi:10.1080/10298436.2012.727992

20. Harr, M. E., 1987. Reliability-based design in civil engineering.

McGraw-Hill, New York.

21. Huang, Y., 2004. Pavement Analysis and Design, 2nd edition.

Prentice Hall, Upper Saddle River, N.J., 505 PP.

22. Kenis, W. and Wang, W., 2004. Pavement variability and reliability, http://www. ksu.edu/pavements/ TRB /A2B09/CS13-12.pdf, last visited: January.

23. Kim, H. B. and Buch, N., 2003. Reliability-based pavement design model accounting for inherent variability of design parameters, Transportation Research Board, 82nd Annual Meeting, and Washington DC.

24. Kim, H. B., Harichandran, R. S., and Buch, N., 1998. Development of load and resistance factor design format for flexible pavements.

Canadian Journal of Civil Engineering, V. 25, pp. 880-885

25. Kumar Das, P., Birgisson, B., Jelagin, D., & Kringos, N. (2013).

Investigation of the asphalt mixture morphology influence on its ageing susceptibility. Materials and Structures DOI 10.1617/s11527- 013-0209-z

26. Lamer, A.C. and Moavenzadeh, F., 1971. Reliability of highway pavements. Highway Research Board, Record No. 362, pp. 1–8, 27. Lira, B., Jelagin, D., & Birgisson, B., (2012) Gradation-based

framework for asphalt mixture. Material structure.

doi:10.1617/s11527-012-9982-3

28. Matsuno, S., & Nishizawa, T. Mechanism of longitudinal surface cracking in asphalt pavement. Proceedings of Seventh International Conference on Asphalt pavements, Nottingham, 1992.

29. Mollenhauer, K. &Wistuba, M. (2012). Evaluation of hot-mix asphalt susceptibility to temperature-induced top-down fatigue cracking by means of uniaxial cyclic tensile stress test. Road Materials and Pavement Design, 13(1), 171–190.

30. Myers, L. A., Roque, R., & Ruth, B. E. (1998). Mechanisms of surface initiated longitudinal wheel path cracks in high-type bituminous pavements. Journal of the Association of Asphalt Paving Technologists, 67, 402–432.

31. Myers, L.A. & Roque, R. (2002). Top-down crack propagation in bituminous pavements and implications for pavement management.

Journal of the Association of Asphalt Paving Technologists, 71, 651- 32. NCHRP (2004). Mechanistic-Empirical design of new and 670

rehabilitated pavement structures (NCHRP Project 1-37A Final Report). Washington, DC: Transportation Research Board, National Research Council.

33. NCHRP Web-Only Document 162 (2010). Top-down cracking of Hot- Mix Asphalt Layers: Models for initiation and propagation.

Washington, DC: National Cooperative Highway Research Program, Transportation Research Board

34. Noureldin, S. A., Sharaf, E., Arafah, A. and Al-Sugair, F., 1994.

Estimation of standard deviation of predicted performance of flexible pavements using AASHTO model. Transportation Research Record, No. 1449, TRB, Washington, DC, pp. 46–56,

35. Onifade, I., Jelagin, D., Guarin, A., Birgisson, B., & Kringos, N.

(2013). Asphalt Internal Structure Characterization with X-Ray Computed Tomography and Digital Image Processing.” In Multi- Scale Modeling and Characterization of Infrastructure Materials, 139–58

36. Ontario Highway Department, 1991, Ontario Highway Bridge Design Code, Third Edition, Ministry of Transportation and Communication, Toronto, Ontario, 370 p.

37. Papagiannakis, A. T, Amoah, N., LeBIanc, P. and Woodrooffe, J.

Viscoelastic pavement response under moving dynamic loads.

Seventy-second Annual Meeting of the Transportation Research Board, Washington, D.C., 1993.

38. PMS Objekt, Vägverket, 2008. VVTK VÄG. Borlänge: Vägverket.

39. Roque, R., Birgisson, B., Drakos, C., & Dietrich, B. (2004).

Development and field evaluation of energy-based criteria for top- down cracking performance of hot mixt asphalt. Journal of the Association of Asphalt Paving Technologists, 73, 229-260

40. Roque, R., Zhang, Z., & Sankar, B. (1999). Determination of crack growth rate parameters of asphalt mixtures using the Superpave indirect tensile test (IDT). Journal of the Association of Asphalt Paving Technologists, 68 404-433

41. Shell Pavement Design Manual—Asphalt Pavement and Overlays for Road Traffic, 1978 (Shell International Petroleum Company Ltd.

London).

42. Timm, D.H., Birgisson, B. and Newcomb, D.E., 1998. Variability of mechanistic–empirical flexible pavement design parameters.

Proceedings of the 5th International Conference on the Bearing Capacity of Roads and Airfields, Vol. 1, Norway 1998.

43. Timm, D. H., Newcomb, D. E., Birgisson, B., and Galambos, T. V., 1999. Incorporation of reliability into the Minnesota mechanistic- empirical pavement design method, Final Report Prepared to Minnesota Department of Transportation, Minnesota Univ., Department of Civil Engineering, Minneapolis

44. Uhlmeyer, J. S., Willoughby, K., Pierce, L. M., & Mahoney, J. P.

(2000). Top-down cracking in Washington state asphalt concrete wearing courses. Transportation Research Record: Journal of the Transportation Research Board, 1730, 110–116.

45. Wang, L. B., Myers, L. A., Mohammad, L. N., & Fu, Y. R. (2003).

Micromechanics study on top-down cracking. Transportation Research Record: Journal of the Transportation Research Board 1853, 121-133.

46. Zhang, Z., Roque, R., Birgisson, B., & Sangpetngam, B. (2001).

Identification and Verification of a Suitable Crack Growth Law.

Journal of the Association of Asphalt Paving Technologists, 70, pp.

206-241.

47. Zou, J., Roque, R., & Byron, T. (2012). Effect of HMA ageing and potential healing on top down cracking using HVS. Road Materials and Pavement Design, 13(3), 518-533.