Airfield and highway pavements 2021 pavement design, construction, and condition evaluation

Darter Calibration of Fatigue Cracking and Rutting Prediction Models in Pennsylvania Using Laboratory Test Data for Asphalt Concrete Pavement in AASHTOWare Pavement ME Design ...37 Bi

Selected Papers from the

Proceedings of the International

Airfield and Highway Pavements

John F Rushing, Ph.D., P.E.

Pavement Design, Construction,

and Condition Evaluation

A IRFIELD AND H IGHWAY

SELECTED PAPERS FROM THE INTERNATIONAL AIRFIELD AND

HIGHWAY PAVEMENTS CONFERENCE 2021

June 8–10, 2021

SPONSORED BY

The Transportation & Development Institute

of the American Society of Civil Engineers

Published by the American Society of Civil Engineers

Published by American Society of Civil Engineers

1801 Alexander Bell Drive

Reston, Virginia, 20191-4382

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Preface

Airfield and highway pavements are critical components of our transportation infrastructure Increasing demand on these assets creates a unique challenge for researchers and practitioners to find sustainable solutions to managing their life-cycle The airfield and highway pavements specialty conference is a unique setting where the world’s foremost experts in pavement design, construction, maintenance, rehabilitation, modeling, management, and preservation meet and present most recent developments in the pavement engineering area Building on the success of our past conferences, the 2021 International Airfield and Highway Pavements Conference of ASCE’s Transportation and Development Institute (T&DI) displayed the adaptive nature of our profession as we held our first completely virtual event from June 8-10, 2021

The 2021 virtual conference was designed to feature plenary sessions and panel discussions on important topics facing government agencies and industry Technical breakout sessions allowed researchers and practitioners to present deeper technical content on breakthrough practices and technologies The virtual poster session allowed “on-demand” access to cutting edge research

The proceedings of the 2021 International Airfield and Highway Pavements Conference have been organized into three publications and are described as follows:

Vol I: Airfield and Highway Pavements 2021: Pavement Design, Construction, and Condition Evaluation

This volume includes papers concerning mechanistic-empirical pavement design methods and advanced modeling techniques for highway pavements, construction specifications and quality monitoring, accelerated pavement testing, rehabilitation and preservation methods, pavement condition evaluation, and network-level management of pavements

Vol II: Airfield and Highway Pavements 2021: Pavement Materials and Sustainability

This volume includes papers describing laboratory and field characterization of asphalt binders, modifiers and rejuvenators, asphalt mixtures and modification, recycled and waste materials in asphalt mixtures, unbound base/subgrade materials and stabilization, pavement life-cycle management, interactions of pavements and their environment, and recent advances in cementitious materials characterization and concrete pavement technology In this volume, we also included papers introducing cutting edge innovative and sustainable technologies used in pavement applications

Vol III: Airfield and Highway Pavements 2021: Airfield Pavement Technology

This volume includes papers on recent advances in the area of airfield pavement design, construction, and rehabilitation methods, modeling of airfield pavements, use of

accelerated loading systems for airfield pavements, and airfield pavement condition evaluation

The papers have undergone a rigorous peer review by at least two to three international highway pavement and airfield technology experts and a quality assurance process before becoming a publication of ASCE – the world’s largest publisher of Civil Engineering content

The success of the conference is a tribute to the incredible efforts of the leadership team consisting of Conference Co-Chairs (Hasan Ozer, John Rushing, and Zhen Leng) and Advisory Board (Imad Al-Qadi and Scott Murrell) along with an outstanding Conference Steering Committee (Amit Bhasin, Rick Boudreau, Zeijao Dong, Jeffrey Gagnon, Tom Harman, Andreas Loizos, Geoffrey Rowe, Injun Song, Leif Wathne, and Richard Willis) and terrific support from ASCE T&DI staff The efforts of the Conference Scientific Committee are graciously acknowledged for their role in reviewing papers and providing critical feedback to the authors

We thank everyone who attended the virtual conference and hope to see everyone again in 2023!

Hasan Ozer, Ph.D., A.M.ASCE, University of Illinois at Urbana-Champaign

John Rushing, Ph.D., P.E., M.ASCE, U.S Army Engineer Research and Development Center

Zhen Leng, Ph.D., M.ASCE, Hong Kong Polytechnic University

Contents

Influence of Tire Footprint Contact Area and Pressure Distribution on

Flexible Pavement 1

Ainalem Nega and Daba Gedafa

Monte Carlo Simulation for Flexible Pavement Reliability 13

Anastasios M Ioannides and Jeb S Tingle

Calibration of Transverse Cracking and Joint Faulting Prediction Models

in Pennsylvania for JPCP in AASHTOWare Pavement ME Design 26

Biplab B Bhattacharya and Michael I Darter

Calibration of Fatigue Cracking and Rutting Prediction Models in

Pennsylvania Using Laboratory Test Data for Asphalt Concrete

Pavement in AASHTOWare Pavement ME Design 37

Biplab B Bhattacharya and Michael I Darter

Probabilistic Viscoelastic Continuum Damage Approach for Fatigue Life

Prediction of Asphalt Mixtures: Challenges and Opportunities 49

Ayat Al Assi, Husam Sadek, Carol Massarra, and Carol J Friedland

Multiscale Modeling of Heterogenous AC and Damage Quantification 61

Zafrul Khan and Rafiqul Tarefder

Implementation of Fracture Mechanics-Based Reflection Cracking Models for

Asphalt Concrete Overlay of Existing Concrete Pavement in AASHTOWare

Pavement ME Design 71

Biplab B Bhattacharya; Leslie Titus-Glover, and Deepak Raghunathan

Service Life Prediction of Internally Cured Concrete Pavements Using

Transport Properties 82

Fariborz M Tehrani

Quality Control of Hot Mix Asphalt Pavement Compaction Using In-Place

Density Measurements from a Low-Activity Nuclear Gauge 92

Linus Dep, Robert Troxler, Sumuna Mwimba, Chris Croom, and Wes Langston

Application of Fourier Transformation to Identify the Onset of Fatigue

Damage of Bitumen 103

M Jayaraman and A Padmarekha

Characterization of Curling and Warping Influence on Smoothness of Jointed

Plain Concrete Pavements 110

Kexin Tian, Bo Yang, Daniel King; Halil Ceylan, and Sungwhan Kim

Utilization of Finite Element Analysis towards the Evaluation of the Structural

Capacity of Flexible Pavements 120

Nitish R Bastola, Mena I Souliman, and Samer Dessouky

Intelligent Pavement Roughness Forecasting Based on a Long Short-Term

Memory Model with Attention Mechanism 128

Feng Guo and Yu Qian

Performance Comparison of HMA Mixes Used on Different Levels of North

Dakota’s Highway Performance Classification System 137

Jun Liu, Robeam Melaku, Daba Gedafa, and Nabil Suleiman

Influence of Slow-Moving Nature of Super Heavy Load (SHL) Vehicles on the

Service Life of Pavement Structures 146

Ali Morovatdar and Reza S Ashtiani

Durability of Concrete Pavements Exposed to Freeze-Thaw Cycles in Different

Saline Environments 159

Mohammad Pouramini, Fariborz M Tehrani, Saman Sezavar Keshavarz, and Arjang Sadeghi

A Quantitative Investigation of the Durability of Asphalt Pavement Materials

Using Experimental Freeze-and-Thaw Weathering Data 169

Rojina Ehsani, Alireza Miri, and Fariborz M Tehrani

Enhancing the Resilience of Concrete Pavements Using Service Life Prediction

Models 178

Sara Kalantari and Fariborz M Tehrani

Performance Characteristics of Asphalt Mixes Containing High Percentage of

RAP Material 186

Gargi P Jagad, Ambika Behl, and Sanjay M Dave

Field Performance Evaluation of Pavement Sections with High Polymer-Modified

Asphalt Concrete Overlays 197

Jhony Habbouche, Ilker Boz, Brian K Diefenderfer, and Sayed Adel

Comparison of Unconventional and Conventional HMA Mixes’ Performance in

North Dakota 209

Rabindra Pariyar, Nabil Suleiman, Daba Gedafa, and Bishal Karki

Adoption of 3D Laser Imaging Systems for Automated Pavement Condition

Assessment in the United States: Challenges and Opportunities 219

Ryan Salameh and Yichang (James) Tsai

GPR Application for Moisture Content Prediction of Cold In-Place Recycling 231

Lama Abufares, Uthman M Ali, Qingqing Cao, Siqi Wang, Xin Sui, and Imad L Al-Qadi

Impact of Seasonal and Diurnal Profile Measurements on Surface

Roughness of Rigid Pavements—LTPP SMP Study 240

Hamad B Muslim and Syed W Haider

Pavement Image Data Set for Deep Learning: A Synthetic Approach 253

Haitao Gong and Feng Wang

Evaluation of the Effect of Interlayer Shear Strength of a Layered Asphalt

Pavement on Observed Distresses in the Field: A Case Study 264

R Ghabchi and M Mihandoust

Evaluation of Fiber-Reinforced HMA Mixes’ Performance in North Dakota 272

Zeenat Nahar, Nabil Suleiman, and Daba Gedafa

The Effects of Automated Vehicles Deployment on Pavement Rutting Performance 280

Ali Yeganeh, Bram Vandoren, and Ali Pirdavani

Field Performance Analysis of Open Graded Friction Course: A Case Study in

Shreveport, Louisiana 293

Sajidur Rahman Nafis and Nazimuddin M Wasiuddin

Comparison of Inverted Pavements with Different Types of Crack Relief Layers 306

Rajan Singh Baghel, Sridhar Kasu Reddy, and Anush K Chandrappa

Evaluation of International Roughness Index Measurement Using Cell Phone

App and Compare with Pavement Condition Index 317

Mohammad Hossain and Kerrie Schattler

Machine Learning Approach to Identifying Key Environmental Factors for

Airfield Asphalt Pavement Performance 328

A Z Ashtiani, S Murrell, and D R Brill

Influence of Tire Footprint Contact Area and Pressure Distribution on Flexible Pavement

Ainalem Nega, Ph.D.1; and Daba Gedafa, Ph.D.2

1Dept of Civil Engineering, Curtin Univ., Perth, WA, Australia Email:

pavement contact stress and interaction model were simulated using 3D finite element for five layers (asphalt concrete, unbound base and subbase, compacted, and natural subgrade) of flexible pavement at various loads An axisymmetric and tire-pavement 3D finite element model was developed A good correlation agreement between contact area and deflection was observed For thin and thick pavement in the static analysis, contact area reduced 3.5% and 3.8%, respectively, while the static deflection for thin pavement decreased from 43.5 mm when 𝐸 = 0.01 to 30.5 mm when 𝐸 = 100 GPa, reduction of 29.9% Whereas for thick pavement, the deflection between static and rolling analysis was not significant, similar trends of deflection between thin and thick pavement were obtained The tire’s finite element model was validated using measured contact area and deflection The results of analysis were then compared to simplify the results of the modeling considering its effects on flexible pavement This finding may have important implication for design of relatively thin asphalt surface layered than thick pavement

Keywords: Tire-pavement contact stress; flexible pavement; tire foot print contact area;

axisymmetric; thin pavement, thick pavement; finite element model

INTRODUCTION

The importance of road transportation and development has been growing in the entire world since the past three decades – not only as the result of the development of the road infrastructure but also as a result of the technical development of trucks (Hernandez and Al-Qadi 2016; Hernandez et al 2015; Huhtala et al 1989) Transportation vehicles have become heavier and heavier, and their load – carrying capacity has also become greater and greater Engines are more powerful, cabs more comfortable, and important developments have been made in axles, tires and suspensions (Hernandez and Al-Qadi 2016; Huhtala et al 1989)

Where the deteriorating flexible pavement infrastructure and investigation load conditions are, tire-pavement contact stresses usually receives a special attention (Hernandez and Al-Qadi 2016) not clear Pavement contact stresses are not the only directly affect related to several and/or various types of distresses as discussed by Hernandez’s but are also the only feasible

manner to compare the effect of various tire types on pavement damage (Al-Qadi and Wang 2011; Nega and Nikraz 2017) such as conventional dual-tire and wide-base tires

The increased traffic roads and heavier urban vehicles cause much more distress to road pavements than ever before in history The regulation of weights and dimensions are even more significant in the wake of substantial pressure from the development and transportation industry

to allow on the highways pavements (Gungor et al 2016; Nega and Nikraz 2017)

The effect of tire-pavement contact pressure distribution on flexible pavement is generally complex and dynamic, and it is affected by axles, tires, geometry configurations, and vehicles types including load – carrying capacity (Dessouky et al 2014; Nega and Nikraz 2017) There are several inconsistences in data analysis from several experimental studies to understand and evaluate the influence of tire-pavement contact area and pressure distribution between the tire and pavements including setting the acceptable standard for thin and thick pavements

The main purpose of this study is to evaluate the influence of tire print contact area and pressure distribution on flexible pavements Tire-pavement contact stress interaction model was simulated using 3-D finite element for five layers An axisymmetric and tire-pavement 3D finite element model was developed, and deflection for thin and thick pavements was determined using the statics analysis

TIRE-PAVEMENT FE MODEL DESCRIPTION

The tire-pavement pressure distribution is generally known to be complex and affected by tire type There are many inconsistencies in the data from various experimental studies measuring the distribution of contact pressure between tire and pavement Simplifying assumptions have been used in literatures, including the use of a circular contact with contact pressure equal to the tire pressure (Nega 2016; Nega and Nikraz 2017)

The flexible pavement was composed of five layers: Asphalt concrete (AC), unbound base and subbase, compacted and natural subgrade Each layer’s thickness changes depending on the type of flexible pavement considered In the case of a thick pavement, the thickness of the AC and unbound base were 50 and 100 mm, respectively The thickness of unbound subbase, compacted and natural subgrade were 250, 75 mm and infinite, respectively Regarding the material properties, the AC layer was assumed linear elastic with varying modulus between 1.2 and 1.5 GPa Assuming AC as linear elastic material instead of viscoelastic is not expected to have a negative consequence on the conclusion of this particular study (i.e second step for validation) because the main objective is not the study of flexible pavement behavior, but analyzing the impact of tire-inflation pressure on the flexible pavement

Unbound subbase, compacted and natural subgrade were determined by the Mohr Coulomb and Drucker-Prager model (Nega et al 2015) because the illustration of the typical cross section

of the five layer linear elastic of the flexible pavement model is considered a viscoelastic on the pavement area, which means the unbound base was considered nonlinear for the thin pavement and linear elastic for a thick pavement (Hernandez and Al-Qadi 2016; Nega 2016)

The model was verified using Falling Weight Deflectometer (FWD) data from seven main roads and creep test to assure the integrity of the in site experimental data were used in the verification of the finite element (FE) model in ABAQUS The detail experiments can be found (Mulungye et al 2007; Nega et al 2015; Nega et al 2016; Owende et al 2001) For a thin pavement, the stress level in base layer is significant (Hernandez and Al-Qadi 2016), so the stress-dependency of the resilient modulus becomes significant However, in the case of thick

pavement, the stress levels in unbound base are low and the difference between linear and nonlinear model is not significant at all (Hernandez and Al-Qadi 2016)

FE PAVEMENT MATERIAL PROPERTIES

A constitutive law is required for pavement material in the nonlinear finite element simulation The asphalt surface is viscoelastic and elastoplastic material of high complexity (Nega et al 2015; Nega et al 2013; Uddin et al 1994) It exhibits sensitivity to both temperature and rate of loading (Deacon et al 1994; Diefenderfer et al 2006; Mulungye et al 2007) However, many methods for analysis of pavement employ simple linear elastic theory as a first approximation to the evaluation of the pavement response model The elastic material properties

of flexible pavement layers and the measured static, wheel load, tire contact area and average contact dual tires inflation pressures are shown in Table 1 and 2, respectively

Viscoelasticity for the asphalt surface is also considered in this study, and the results compared to the corresponding pavement response of linear elastic material model The viscoelastic material curve fitting tool in ANSYS (ANSYS 1999) was used to determine the material constraints constants of the prony series expansion for shear modulus option from the experimental data The Viscoelastic data was obtained from creep and/ or bending fatigue tests, which was performed at temperature 25oC with a void content of 7% and a frequency of 5 Hz The experimental data in cycles were converted to time and then, stiffness modulus was converted to shear modulus

Table 1 Material Properties for Flexible Pavement Model

Pavement Layer Moduli ,

E (Pa)

Poisson's Ratio (v)

Thickness (mm)

Density, p (kg/m3)

Fig 1 Sketch of simulated pavement structure for cyclic loading

In this study, linear elastic and viscoelastic theory are used The vehicle speed was directly related to duration of cyclic loading, and at the same time, the resilient and shear modulus of each paving materials were considered so that material selected can communicate with the vehicle speed The greater the speed, the larger the modulus, and the smaller the strain is in a flexible pavement Figure 1 shows the sketch of simulated pavement structure for cyclic loading

Experimental Truck

Tire Pressure (kPa)

Wheel Loading (kN)

Contact Area (m2)

Mean Contact Pressure

(kPa) Front Middle Rear Front Rear Front Middle Rear

in the driving direction

The three-dimensional FE mesh that contains an 8-node, first-order quadratic element with reduce-integration (C3D8R) (linear) and a 20-node quadratic reduced-integration (C3D20R) (nonlinear) was used in ABAQUS because they are not susceptible to locking, even when they are subjected to complicated state of stress Therefore, these element types are generally the best choice for most general stress and/ or displacement simulations As the result of this appropriate choice of element type, all the elements have converged, because of hourglassing that were used through the width

The size of an element is 0.0508 m x 0.0508 m and 0.0254 m x 0.0254 m within the course and fine mesh, respectively From the FE model area, it can be assumed that the FE mesh contains around 14,500 elements and 520 infinite elements This is a rough assumption to preload the model in ABAQUS Figure 2 and 3 show the assembly of five-layers of flexible pavement and the three-dimensional nonlinear FE mesh in the order given The deformed shape for nonlinear viscoelastic model is shown in Figure 4 The simulated model indicated that the vertical strain on the top of the subgrade layer and the tensile strain at the bottom of the asphalt surface in this simulation are about 9% more in stiffness than that predicted by linear viscoelastic

analysis (Nega 2016) Control of Mises stress on deformed shape of flexible pavement using a nonlinear viscoelastic model for the dual tires analysis is displayed in Figure 5 From the model analysis, the contours’ stretch of the linear viscoelastic response by Nega (2016) has low maximum stress (i.e., 2.17 x 10-7 to 1.56 x 106) as compared to nonlinear viscoelastic model (i.e., 2.51 x 10-1 to 1.57 x 106) on this study This indicated that the vertical strain and the tensile strain, which are on the top of the subgrade layer and at the bottom of the asphalt surface, respectively in this simulation are about 9% less in stiffness than that predicted by nonlinear viscoelastic analysis

Fig 2 Assembly of five-layers of Fig 3 Nonlinear finite element mesh flexible pavement (3D-FE) model (three-dimensional) of flexible pavement

Fig 4 Deformed shape of nonlinear Fig 5 Contour plot of Miss Stress on deformed viscoelastic response for dual tires shape of nonlinear viscoelastic response for dual

using FE analysis tires using FE analysis

The model results were similar to the experimental results and analysis was appropriate and reasonable match to the measured one Comparison of experimental stiffness modulus and shear modulus with simulated stiffness modulus and shear modulus using finite element model are shown in Figure 6 From the model analysis, prediction using finite element method in ABAQUS correlates well with experiment results The measure of goodness for an experiment and model analysis was (R2 = 1) It is showed that an increase in stiffness modulus and shear modulus results in a reduction in structural failure of asphalt pavement Additionally, it improves shear cracking resistance and low stiff of flexible pavement Pellinen and Witczak (2002) analyzed the use of stiffness and shear of flexible pavement (hot-mix asphalt) using simple performance test that limit the stiffness values because of the power law and sigmoidal function and found good correlation (R2 =0.9981)

Fig 6 Comparison of stiffness and shear Fig 7 Sketch for simulated vehicle modulus of experiment with FE analysis speed for each cyclic loading

The full tire/pavement model was subjected to monotonic tire loading of magnitude 40 kN for dual tire and tire inflation pressure of 700 kPa (see Figure 1and Table 2) The magnitude of the spring constant was calculated as average of the stresses in perpendicular direction divided

by the average displacement in the same direction The magnitude of the spring constant for thin and thick flexible pavement and various elastic modulus of the AC layer are shown in Table 3

Table 3 k – Values for Thin and Thick Flexible Pavement

Thin Flexible Pavement k(MPa/mm)

Thick Flexible Pavement k(MPa/mm)

of 10 second with a loading of 0.1 s and 0.9 s resting, and a torque of zero magnitude at the tire’s axis as it is shown in Figure 9

To improve the computational efficiency, friction was defined in the final phase, which was free rolling resistance analysis using the Mohr Coulomb model with coefficient of friction of 0.35 It would be insignificant if it is not mentioned that tire-pavement is influenced by several factors For example, some of the factors include: pavement texture, temperature, contact pressure, speed, viscoelastic material properties of tire and pavement and slip ratio Although the

material model considered, linear elastic and hyperelastic, are not sensitive to speed In addition, the influence of speed on the friction coefficient was also ignored since it is not expected to have

an effect on the proposed model

Fig 8 Axisymmetric model

Cartesian elements were used along the circumference of the tire Hybrid and rebar element modeled rubber incompressibility and tire reinforcement were also used Mesh sensitivity analysis was also determined to the optimum size and distribution of finite element based on the computational time and accuracy The optimum mesh included the strain energy of ± 5% of a very fine mesh and the least amount of elements Finally, the pavement was meshed with full-

integration cubic element with a 20 mm side (C3D20)

Fig 9 Tire/flexible pavement 3D finite element model (a) undeformed surface (b) deformed

surface

Tire’s finite element was validated using measured contact area and deflection A good correlation agreement between contact area and deflection was observed and the mean average percentage error was 4.7% and 8.7%, respectively Hernandez and Al-Qadi (2016) developed a tire/pavement interaction model using the finite element in ABAQUS, and a good agreement

between contact area and deflections was observed The mean average percentage error was 4.2% and 8.5%, respectively Hernandez and Al-Qadi (2016) also validated a tire’s finite element model using measured contact area and deflection where the applied load and tire inflation pressure were fixed at 44.4 kN and 758 kPa The elastic modulus of the pavement was between 0.102 and 0.108 GPa, while the elastic foundation constant was determined based on static analysis of the full tire-pavement model Analysis was also performed for the tire contacting of the analytical rigid surface

CONTACT AREA AND DEFLECTION

The rate of highway pavement deterioration has been accelerating over the last five decades (Huang 1993; Yoder and Witczak 1975) A variety of factor have been identified as contributing

to the accelerated rate of pavement damage, including increased truck weight, sizes, wheel load, and tire inflation pressure Tire contact pressure distribution and its eroding effect (deflection) on the flexible pavement has and, until recently, received very little attention It is now increasingly recognized that tire-pavement contract pressure distribution is an important factor in pavement deterioration and, consequently, a major consideration in new pavement and rehabilitation design

The variation of contact area, (𝐴𝑐) and tire deflection, (𝛿) for different values of elastic modulus, (𝐸) are shown in Figure 10 and 11 There are different types of materials in each plot that represent: monotonic tire loading on thin pavement, monotonic on a thick pavement, rolling tire on a simplified thick pavement and tire rolling on a rigid pavement As it can be seen from the developed model data, for instance for static and rolling analysis, most of the influence of 𝐸 occurred between 𝐸 = 0.01 and 𝐸 = 1 GPa

independent of the pavement stiffness When the tire is deforming, it tries to match the deformed shape of the pavement As the consequence, the created curvature increases the amount of contact points in between the tire and pavement, resulting in an increment in contact area Whereas with the rigid surface case, no such deformation of the pavement exists, thus 𝐴𝑐 was the least possible for given applied load and tire inflation pressure Hernandez and Al-Qadi (2016) got a contact area reduced by 2.9% for thin pavement and 3.3% for thick pavement in the static analysis on the tire-pavement interaction model

Fig 11 Pavement deflection with type of thin and thick pavement versus elastic modulus

deformation surface

The contact area for thin and thick pavements and static analysis shows similar trends and also concurrent and/ or coincident for all the values of elastic moduli This indicated that higher influence on pavement’s surface’s stiffness on contact area than the rest of the pavement structure Regarding the rolling analysis, the 𝐴𝑐 approached a constant value as a pavement’s stiffness increased However, the value did not match the rigid surface case It can also be seen that the stiffest pavement surface deflection was slightly affected by the contact area

The variation of tire deflection, δ with respect to the elastic modulus of the pavement (see Figure 11) From the developed model presented, it can be seen that the static deflection for the thin pavement increases with an increase in 𝐸 in the logarithmic scales, and decreased from 43.5

mm when 𝐸 = 0.01 to 30.5 mm when 𝐸 = 100 GPa, a reduction of 29.9% Whereas for thick pavement, the deflection difference between static and rolling analysis was not significant and followed similar trend Contact area and deflection wouldn’t greatly depend on rolling condition but on type of pavement

CONCLUSIONS

The investigation of influence of tire footprint contact area and pressure distribution on flexible pavements and its effect on pavement was successfully investigated Tire-pavement contact stresses were measured in laboratory experiment and also simulated using 3-D finite element for five layers of flexible pavement in ABAQUS at various loads 40 kN wheel load to represent a set dual tire was assumed to be uniformly distributed over the contact area between

tire-pavement surface In addition, the full tire-pavement model was also developed and validated using experimental data The effect of tire inflation pressures was used to investigate the effects of tire-pavement structure, loading, and inflation pressure on surface loads and was successfully assessed Finally, four different types of tire inflation pressures were used (350, 490,

630, and 700 kPa, and some of its effects on flexible pavement were also briefly described

Computed deflection showed similar trend variation at different cyclic loading time and also showed a reducing vertical surface deflection and critical tensile strain in asphalt concrete layer Flexible pavement layer something is missing as the function of time due to applied load was also quite reasonable and it is also within the standard All the predictions are reasonable and also matched with laboratory experiment Experimental and simulated stiffness and shear modulus correlates well with R2 = 1 The increase in stiffness and shear modulus implies to reduction in asphalt pavement failure and improved stiffness and shear cracking resistance with flexible pavement structure

The axisymmetric and tire-pavement 3D finite element was also developed, and tire’s finite element was validated using measured contact area and deflection A good correlation agreement between contact area and deflection was observed, and the mean average percentage error was 4.9% and 8.7%, respectively For thin and thick pavement in the static analysis, contact area reduced by 3.5% and 3.8% in the same order and similar trends were also obtained This finding may have important implication for design of relative thin asphalt surface layer for pavement

For thin and thick pavement in the static analysis, 𝐴𝑐 reduced 3.5% and 3.8%, respectively, if

𝐸 increased from 0.01 to 1 GPa The reduction in contact area becomes less than 4.2% for the other values of elastic modulus When 𝐸 of the deformable shape exceeded 100 GPa, 𝐴𝑐 was almost constant This indicated that the constant area become self-sustaining and/ or independent

of the pavement stiffness When the tire is deforming, it tries to match the deformed shape of the pavement As the consequence, the created curvature increases the amount of contact points in between the tire and pavement, resulting in an increment in contact area

The contact area for thin and thick pavements using static analysis was similar trends for all values of elastic modulus This indicated pavement’s surface has higher influence stiffness on contact area than the rest of the pavement structure Regarding the rolling analysis, the 𝐴𝑐

approached a constant value as a pavement’s stiffness increased However, the value did not match the rigid surface case It can also be seen that the stiffest pavement surface deflection slightly affected the contact area

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Inc., New York

Monte Carlo Simulation for Flexible Pavement Reliability

Anastasios M Ioannides, Ph.D., P.E.1; and Jeb S Tingle, P.E.2

1Research Civil Engineer, Engineer Research and Development Center, Airfields and Pavements

Branch, Geotechnical and Structures Laboratory, Vicksburg, MS Email:

Anastasios.M.Ioannides@USACE.Army.mil

2Senior Research Civil Engineer, Engineer Research and Development Center, Airfields and

Pavements Branch, Geotechnical and Structures Laboratory, Vicksburg, MS Email:

Jeb.S.Tingle@ERDC.dren.mil

ABSTRACT

Monte Carlo simulation is used to elucidate the relationship between reliability and safety factor in the AASHTO 86/93 flexible pavement design procedure, for any given level of variability

in material properties and traffic This relationship is found to be much more sensitive to variability

in material properties, than to traffic variability The methodology developed is simple to implement and leads to practical values of the elusive overall standard deviation, So, required in AASHTO 86/93 designs, in a manner responsive to prevailing variability levels The success or failure of a flexible pavement is found to depend more on the accuracy of the predictions of the Office of Engineering, which is responsible for materials-related aspects of flexible pavement design, than to those pertaining to traffic, as provided by the Bureau of Statistics Additional insights are extracted with respect to the recommended range of So, the effect of quality control, and the remaining life of a pavement beyond its design period

INTRODUCTION

The publication of the 1986 AASHTO pavement design guide (AASHTO, 1986) represented

a significant revision of its predecessor (AASHTO, 1972), inasmuch as the new version incorporated reliability considerations for the first time To quantify the combined effect of errors

at the time of design in the predictions of traffic demand and of pavement capacity, submitted by the Bureau of Statistics and by the Office of Engineering, respectively AASHTO (1986) introduced the term overall standard deviation, So, whose units are log (ESAL), i.e., a number of Equivalent 18-kip Single Axle Loads, expressed on a logarithmic scale In combination with the standard normal deviate, ZR, corresponding to the design reliability level, R, this term leads to the reliability design factor, FR The 1993 revised version (AASHTO 1993) left the reliability analysis untouched Therefore, these two guides will be termed together as AASHTO 86/93 in this paper

It is apparent that selection of So must not be arbitrary, but needs to be the outcome of serious consideration of the statistical variability of all pertinent design factors Ioannides and Rodriguez (2017), however, have argued that “estimation of So is impossible” because “in any given pavement case, the pavement either fails or it does not, and this allows the determination of only three of the four required inputs for So” Two of these parameters pertain to pavement capacity; they are denoted herein by capital letters N and W The other parameters refer to traffic demand; they are represented in this paper by lower case symbols, n and w Moreover, the letters w and W pertain to predictions made at the time of design, whereas the letters n and N relate to actual values, established at the end of a pavement’s life Thus, (n-w) stands for the error (or difference) between

the actual values of the traffic demand and the corresponding predictions made at the time of design, whereas (N-W) signifies the error (or difference) between the actual and predicted values

of pavement capacity

To overcome the limitation they had identified, Ioannides and Rodriguez (2017) outlined a methodology involving Monte Carlo Simulation (MCS) and “relying only on three of the [four] required pieces of information, plus an assumed conventional factor of safety or FR value.” A computer spreadsheet is developed in the present study to implement the proposed methodology, incorporating flexible pavement design input parameters and their respective coefficients of variation (COV), as extracted from the literature

AASHTO RELIABILITY AND SAFETY FACTOR

The 1986 AASHTO pavement design guide (AASHTO, 1986) presented for the first time the following design equation incorporating reliability for flexible pavements:

𝑙𝑜𝑔(𝑊18) = 𝑍𝑅𝑆𝑜+ 9.36 𝑙𝑜𝑔 (𝑆𝑁 + 1) − 0.20 + 𝑙𝑜𝑔[

𝛥𝑃𝑆𝐼 2.7 ] 0.40+ 1094

(𝑆𝑁+1)5.19

+ 2.32𝑙𝑜𝑔 𝑀𝑅− 8.07 (1)

where:

W18 = predicted traffic demand in 18-kip Equivalent Single Axle Loads (ESAL);

ΔPSI = drop in the Present Serviceability Index (PSI) permitted during the design life of the pavement = (po - pt), in which po is the initial PSI at the time of construction and pt is the anticipated terminal PSI at the end of the design life of the pavement;

SN = structural number of the pavement defined as: SN = a1D1 + a2D2m3 + a3D3m3

in which a1, a2 and a3 are layer coefficients for the surface, base and subbase courses,

respectively, while D1, D2 and D3 are the thicknesses of the surface, base and subbase layers (in

inches), respectively, and m2 and m3 are the drainage coefficients for base and subbase;

MR = subgrade resilient modulus (in psi);

So = overall standard deviation, in log (ESAL); and

ZR = standard normal deviate corresponding to the design reliability level, R

Given that Eq (1) is exclusively statistical/empirical, it is not possible to convert it to SI units,

in conformity to the Conference requirements

For simplicity, Eq (1) may be re-written as:

𝑙𝑜𝑔 𝑤 = −log 𝐹𝑅+ 𝑙𝑜𝑔 𝑊 (2) where:

w = predicted traffic demand (ESAL), denoted as W18 in Eq (1);

FR = reliability design factor, given by 𝐹𝑅 = 10−(𝑍𝑅 𝑆𝑜) (3)

W = predicted pavement capacity (ESAL), as computed by the right-hand-side of Eq (1), without the (ZRSo) term

Alternatively, one may write:

This explains why AASHTO 86/93 calls log FR “a positive spacing factor” (p I-56) and a

positive “spacer” (p I-60), which in Eq 2 represents a reduction in the predicted pavement capacity, or, alternatively, in Eq (4) an increase in the predicted traffic demand, in order to ensure the survival of the pavement to the end of its design life Finally, Eq 4 may be recast as:

𝐹𝑅 = 𝑊

𝑤 (5) This elucidates why AASHTO 86/93 refers to FR as a “multiplier of the traffic prediction” (p I-60) The definition of FR as a ratio leads to the recognition that it is a safety factor of sorts, whose purpose is to ensure that capacity always exceeds demand

Unlike conventional factors of safety, FR depends on the selected reliability level, R, but also involves the overall standard deviation, So, as indicated by Eq (3) In this manner, FR accounts for the statistical distributions of all variables entering pavement design, including those pertaining to traffic estimation (the purview of the Bureau of Statistics), as well as those associated with laboratory testing for material properties, but also those related to shortcomings in the current state-of-the-art of pavement design (from the Office of Engineering) Selection of the safety factor with due consideration to all these uncertainties is the primary reason for transitioning from safety factors to reliability in engineering design, as first advocated by Freudenthal (1947)

Adopting the ranges in So stipulated by AASHTO 86/93 for flexible and for rigid pavements (So = 0.40 to 0.50 and So = 0.30 to 0.40, respectively, p I-62), it is possible to establish the relationship between reliability and safety factor (i.e., FR) implicit in Eq (3) This relationship is shown in Fig 1, indicating that flexible and rigid pavements of the same reliability are designed

by AASHTO 86/93 with different safety factors, presumably reflecting greater uncertainty and ignorance in the case of the former pavement type

A remaining life factor, RLF, may be introduced at this point This factor provides a measure

of the remaining service capacity in a pavement upon completion of its design life, and may be expressed as a fraction of the pavement’s design life using the following expression:

METHODOLOGY OF PRESENT STUDY

The MCS methodology outlined by Ioannides and Rodriguez (2017) provides a means for establishing the elusive So parameter for flexible pavements These authors also present a brief history of MCS, while its basic formulation is described in multiple textbooks, e.g., Haldar and Mahadevan (2000) Table 1 lists the flexible pavement design input parameters, along with their respective means and coefficients of variation (COV), as adopted in the present study

Fig 1 – Relationship between Reliability, R and AASHTO’s Reliability Design Factor, F R

Table 1: Pavement Properties

(after Huang, 2004) (Huang, 2004)

Surface thickness, D1 (in or mm) 6 152 10.0

Subbase thickness, D3 (in or mm) 16 406 10.0 Asphalt concrete modulus, E1 (psi or GPa) 450,000 3.103 21.0*

Base modulus, E2 (psi or MPa) 30,000 206.8 14.0*

Subbase modulus, E3 (psi of MPa) 15,000 103.4 16.0*

Subgrade resilient modulus, MR (psi or MPa) 4,500 31.03 15.0

†: Arbitrarily adopted in this study, to conform to the corresponding COV value provided by

Huang (2004) for po

*: Values from Darter, et al (1973); E2 and E3 are not used in this study, since layer coefficients,

a1, a2 and a3, are employed directly, instead

CONVERGENCE STUDY

The screenshot in Fig 2 shows the first 20 rows of a MCS simulation for an assumed safety factor, SF, of 1.75 Each row of represents a distinct flexible pavement design according to the AASHTO 86/93 equation The number of rows in this spreadsheet were set to 10,000, but using the “Data Table” feature of the spreadsheet, these rows may be filled multiple times, rendering any desired total of simulation iterations SF-values from 0.5 to more than 15 were considered To begin with, the convergence of the spreadsheet results as the number of iterations increases was examined, using the Table 1 input values More specifically, five quantities were investigated, as explained below: reliability, R; standard error of traffic (or demand) prediction, SS (subscript S stands for Bureau of Statistics); standard error in pavement performance (or capacity) prediction,

SE (subscript E stands for Office Engineering); overall standard deviation, So (subscript o stands for overall, i.e., from both S and E); and remaining life factor, RLF

Reliability, R: The convergence of spreadsheet results toward the theoretical relationship in

Eq (3) is depicted in Fig 3, as the number of iterations increases from 100 to 1M It is observed that the difference between 100,000 and 1M iterations is hardly discernible and that even at 10,000 iterations a smooth line is obtained, evincing that the bulk of numerical instability in the spreadsheet has already been eliminated The average absolute value of the difference in reliability between the latter and the theoretical So = 0.5 curve is 0.5 percentage reliability points, demonstrating the robustness of the spreadsheet simulations

Fig 2 – Sample Screenshot from MCS Spreadsheet for Flexible Pavement Design

Fig 3 – Convergence of Reliability curve, as the number of iterations increases

this quantity is possible using MCS, even though no theoretical predictions exist against which to gage the veracity of the results Consequently, comparisons in Table 2 assume that the results obtained “in the limit of refinement”, i.e., using the maximum number of iterations stipulated in this study, are adequately precise for the purposes of this study It is observed that S2S is a constant, independent of the safety factor or reliability level selected Any variations in the calculated value

of S2S are simply numerical instabilities inherent in the MCS, and disappear quickly as the number

of iterations increases The final value of S2S, obtained at 2.4M iterations, is 0.06903

Iterations Minimum Maximum Average COV (%)

error (or statistical variance) inherent in the prediction of the anticipated pavement capacity (or structural performance), S2E, shows that its calculated values are constant and independent of SF, for each level of iterations performed (see Table 3) The final value of S2E, obtained at 2.4M iterations, is 0.1893 Table EE.4 of Appendix EE to AASHTO 86/93 quotes an S2E value of 0.1938 for flexible pavements, which is barely 2% different from the MCS result

Table 3: Convergence of traffic prediction variance, S 2

Iterations Minimum Maximum Average COV (%)

In Method A, So is calculated per its definition by AASHTO 86/93, i.e., as the standard deviation

of the difference in the logarithmic values of actual capacity, N, and actual demand, n:

In Method B, So is backcalculated from the values of FR (= SF) and of R (whence, ZR), using Eq

(3) Method C relies on the following Equations (9), (10) and (11):

𝑆𝐸2 = 𝑉𝑎𝑟(log 𝑊 − log 𝑁) , and (10)

In all three cases, So emerges as independent of the assumed safety factor, converging toward

a final value “in the limit of refinement” These final So values, obtained after 2.4M iterations, are: Method A‒ So = 0.508199; Method B‒ So = 0.484394; Method C‒ So = 0.508223 Each Method exhibits distinct convergence characteristics, the fluctuations of Method B being much more pronounced than those of the other two This is especially true for SF near unity In contrast, the

So-values from Methods A and C are essentially identical, at So = 0.5082; this value compares well

to the AASHTO 86/93 upper limit of 0.50 for flexible pavements In most cases, a minimum of

10,000 iterations suffices to dampen the preponderance of observed numerical fluctuations

(or FR) selected; RLF increases monotonically with the value chosen for this parameter Moreover,

as the number of iterations increases, the simulation is better able to capture the effect of the variability assumed (per Table 1), and the RLF from MCS converges to a curve below the theoretical (no variability) one The final RLF versus SF curve obtained after 2.4M iterations may

be fitted with the following regression equation, permitting a comparison to the theoretical expression, Eq (7), above (R2 = 1.000):

𝑅𝐿𝐹 = 1 − 1.7527

SENSITIVITY STUDY

The preceding convergence study demonstrated that the spreadsheet developed to perform 2.4M iterations in a MCS of the AASHTO 86/93 flexible pavement design algorithm can be a reliable tool in examining further the effect of traffic and material variability on the five quantities explored above A sensitivity study was, therefore, conducted for which the results using 2.4M iterations obtained above using the COV values in Table 1 were used as a baseline Accordingly, these variability measures were multiplied by factors ranging from 0.5 to 2.0 and additional analyses were conducted (each employing 2.4M iterations) The COV for traffic in Table 1 was treated as belonging to a category of its own (managed by the Bureau of Statistics), while the rest

of the values given were clustered as pertaining to material variability levels (in the purview of the Office of Engineering) Letters T and M are used to denote these two categories of inputs Sometimes the two categories of data were altered in tandem; other analyses treated them separately

Reliability, R: To begin with, the COV values in Table 1 (with the exception of COV = 42%

for traffic, T) were varied, by applying a multiplier, whose value ranged from 0.5 to 2 The resulting relationship between R and SF after 2.4M iterations is shown in Figure 4 It is observed that at any given safety factor above 1.0, reliability decreases as variability material increases, and

it increases with decreasing variability For the range of multipliers considered, the effect of variability can be up to 30 percentage points of reliability This Figure illustrates the advantage of using reliability in design rather than the traditional safety factor: reliability does not just depend

on the safety factor, but it is also quite sensitive to material variability

In contrast, the sensitivity of this relationship to altering the COV for traffic alone, while retaining the remainder of the baseline inputs in Table 1 (collectively referred to as Material, M)

is considerably less pronounced There is hardly a 5 percentage reliability points change for the range of multipliers considered

In each of the aforementioned cases, the trend line representing the relationship of R with SF was fitted with a three-term exponential function of the following form:

𝑅(%) = 𝑅0+ 𝑎 [1 − 𝑒𝑥𝑝(−𝑏 𝑆𝐹)] (13) The trend line regression coefficients are reproduced in Table 4

the selected safety factor, once enough iterations have been allowed to ensure the attenuation of numerical fluctuations in its value This is certainly the case when 2.4M iterations are performed,

as was done in this sensitivity study Consequently, it is found that a single (constant) value of So

corresponds to each adopted value of the multiplier, as indicated in Table 5 Moreover, these So

-values appear to vary linearly with the multiplier selected, as indicated by the linear regression coefficients also presented in the same Table; the functional form of the regression formula is in this case:

𝑆𝑖 = 𝑑 + 𝑓 × (𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟) (14)

in which subscript i stands for o, S or E, as the standard deviation case may call for These observations hold true for each of the three Methods employed in the determination of So, as well

as changes in variability of materials and of traffic separately or in tandem

Fig 4 – Sensitivity of the relationship between R and FS to various levels of material

variability Table 4: Trend Line Regression Coefficients (Eq 13)

Baseline 0.5(M) 1.5(M) 1.75(M) 1.875(M) 1.9375(M) 2(M) 0.5(T) 2(T) 0.5(M&T) 2(M&T)

R 0 -3.3912 -50.054 13.7914 18.1407 19.7942 20.5568 21.1538 -10.732 7.2652 -78.704 21.5084

A 98.6024 150.567 73.3623 64.9171 61.3297 59.6177 58.0895 106.341 86.9754 179.574 57.7043

B 0.7579 1.1585 0.5853 0.5421 0.5235 0.5154 0.5096 0.7763 0.6779 1.2998 0.509

R 2 0.9988 0.9987 0.9969 0.9963 0.9961 0.996 0.9959 0.9991 0.9985 0.9974 0.9959 SEE 0.8945 1.1496 1.1334 1.1051 1.0731 1.0591 1.0441 0.8318 0.8925 1.8313 1.0375

As an example, the variation of So from Method A as a function of the variability multiplier for materials, M, only (traffic, T, COV = 42%) is shown in Fig 5 Also altering the traffic COV seems to have a very limited effect More importantly, the values of So determined by MCS for variability levels worse than those prescribed for the baseline case in Table 1 may lie well above the upper limit of 0.50, suggested by the AASHTO 86/93 range for flexible pavements This range may, therefore, underestimate the sensitivity of So to the variability conditions prevailing during the design of any particular pavement section On the other hand, So values for decreased variability compared to the baseline values in Table 1 may lie well below the lower limit of 0.4 suggested by AASHTO 86/93, evincing than in such cases the beneficial effect of tightening quality control may be underestimated

components, along with SE, SS does not depend on the assumed safety factor, nor on the variability

of any parameter except for traffic, whose COV is set at 42% for the baseline case in Table 1 The variation of S2S with changes in the variability multiplier is examined in Table 6 As anticipated,

when only material variability is altered while traffic COV is kept at 42%, S2S is unaffected by the multiplier, retaining an average value of 0.06905 (with COV = 0.05%) for the cases considered

In contrast, when only traffic variability is adjusted while the baseline material inputs are maintained at the values in Table 1, S2S is found to be sensitive to, and to vary linearly with the value of variability multiplier selected Identical sensitivity is observed when both traffic and material COV values are altered, since S2

S is not affected by material variability

Multiplier S o (A)(M) S o (A)(T) So

(A)(M&T) So (B)(M) S o (B)(T) So

(B)(M&T) So (C)(M) S o (C)(T) So

(A)(M&T) 0.5 0.23609 0.44550 0.23609 0.24248 0.48029 0.24248 0.23610 0.44551 0.23610

quantity from the Office of Engineering to changes in variability is analogous to that of its counterpart from the Bureau of Statistics, SS Thus, SE does not depend on the selected safety

factor, but only on the variability multiplier applied to the COV values for material inputs in Table

1, i.e., excluding the traffic COV Table 7 shows that S2E increases rapidly with increasing variability multiplier, but its variation is not as linear as that of S2

S and So In contrast, S2

E is independent of the multiplier applied to the traffic COV of 42%, remaining constant at 0.189; similarly, when the multiplier is applied to both the materials and traffic (M&T) COV values, S2E

tracks the response it exhibits for materials only

Table 6: Variation of S 2

Multiplier S2S (M) S2S (T) S2S (M&T) 0.5 0.06908 0.00949 0.00949

1 0.18927 0.18927 0.18927 1.5 0.45302

1.75 0.65059 1.875 0.77239 1.9375 0.83629

2 0.90339 0.18910 0.90413

d -0.32190 0.18910 -0.31120

f 0.57790 0.00003 0.59230

R 2 0.95890 0.02640 0.96890

Remaining life factor, RLF: This factor exhibits much more sensitivity to variability changes

than any other quantity explored in this study, especially when the multiplier applied to the COV values in Table 1 (not including traffic) exceeds about 1.3 For this reason, the results presented in this section refer to the median RLF values, calculated over the 2.4M iterations conducted, in contrast with all other values reported in this study, which pertain to average values calculated over the given number of iterations in each case To begin with, only materials variability was altered, with traffic COV set at 42% Even for safety factors around 8, median RLF values never exceed zero when the variability multiplier exceeds about 1.6 Applying the multiplier to both materials and traffic COV values in Table 1 has a minor effect on median RLF values In general,

adjusting the traffic COV in tandem with those for material inputs, lowers the RLF at any safety factor by no more than 0.25 RLF points, especially at higher multiplier values This behavior evinces again the minor influence of traffic variability

CONCLUSIONS

In the context of AASHTO 86/93 flexible pavement design, this investigation examined the effect of traffic and materials variability on estimates of reliability, R; standard error of traffic (or demand) prediction, SS; standard error in pavement performance (or capacity) prediction, SE; overall standard deviation, So; and remaining life factor, RLF The convergence of the results from

a spreadsheet implementation of MCS as the number of iterations increases was examined first It

is found that in most cases hardly any numerical fluctuations persist beyond 10,000 iterations Moreover, S2

S is shown to be constant, independent of the safety factor or reliability level selected, being sensitive only to the traffic coefficient of variation The final value of S2S, obtained at 2.4M iterations, is 0.06903, and this may be expected to be the same for rigid pavements, as well Correspondingly, S2

E is found to be sensitive only to the material coefficients of variation, but its final value of 0.1893 is probably considerably different from that pertaining to rigid pavements This assertion is attributable to the different materials employed in the construction of the respective pavement types, and their associated variabilities

From the MCS data, as well as the So values recommended by AASHTO 86/93, one may conclude that compared to the error expected from the Bureau of Statistics, the contribution of the Office of Engineering to the overall standard deviation is much greater for asphalt than for concrete pavements This is essentially an admission that material variability is much greater in flexible pavement construction The So-value from MCS is 0.5082, which compares well to the AASHTO 86/93 upper limit of 0.50 for flexible pavements Recall that for rigid pavements the corresponding AASHTO 86/93 upper limit for So is only 0.40

A sensitivity study was then conducted, using 2.4M iterations in each case, with baseline variabilities (Table 1) multiplied by factors ranging from 0.5 to 2.0 Reliability is shown to be quite sensitive to variability, in addition to depending on the safety factor assumed For the range of multipliers considered, the effect of variability can be up to 30 percentage points of reliability Most of this is attributable to materials inputs: when traffic variability is considered by itself, there

is hardly a 5 percentage reliability points change for the range of variability multipliers considered For its part, S2

S is unaffected by the variability multiplier when only material variability is altered; nonetheless, when only traffic variability is adjusted, S2S is found to vary significantly in a linear fashion with the value of variability multiplier selected On the other hand, S2E is independent of the multiplier applied to the traffic COV, yet it increases rapidly in a nonlinear fashion with increasing materials variability multiplier Finally, RLF exhibits much more sensitivity to material variability changes than any other quantity explored in this study, especially when the multiplier exceeds about 1.3 To accommodate this, median RLF values are reported for the 2.4M iterations, rather than average values It is shown that even for safety factors around 8, median RLF values never exceed zero when the multiplier exceeds about 1.6

These findings can guide efforts to improve on the reliability procedures adopted in the Mechanistic-Empirical Pavement Design Guide, MEPDG (ARA, 2003) The reason that the present paper deals with AASHTO 86/93, instead, is because the latter lends itself to the implementation of Monte Carlo Simulation, which is the only applicable computerized technique for pavement reliability analysis Extensive critiques of the MEPDG and proposed solutions for

its deficiencies may be found, for example, in Aguiar Moya (2011), Retherford (2012), Xiao (2012) and Dinegdae (2015) The current paper is part of a very practical and urgently needed remedy, in anticipation for future developments

ACKNOWLEDGMENTS

Funding for this research was provided by the United States Army Corps of Engineers, through Contract W912HZ-18-C-0005: Mechanistic-Based Pavement Analysis and Modeling Dr Anastasios M Ioannides was the Principal Investigator; Mr Jeb S Tingle was the Contracting Organization’s Technical Representative Mr Isaac Chigozie Oti had performed a number of proof-

of-concept analyses in an initial attempt to resolve this issue

AUTHOR CONTRIBUTIONS

The authors confirm contribution to the paper as follows: study conception and design: Dr Ioannides and Mr Tingle; data collection: Dr Ioannides; analysis and interpretation of results: Dr Ioannides and Mr Tingle; draft manuscript preparation: Dr Ioannides and Mr Tingle Both authors reviewed the results and approved the final version of the manuscript □

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(pre-doctoral) thesis, KTH Royal Institute of Technology, Stockholm, Sweden, May

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Civil Engineers, Vol 112, ASCE, Reston, VA, pp 125-180

Haldar, A., and Mahadevan, S (2000), Probability, Reliability, and Statistical Methods in

Engineering Design, John Wiley and Sons, New York, NY

Huang, H Y (2004), Pavement Analysis and Design, 2nd Edition, Pearson Prentice-Hall, NJ

Ioannides, A M., and Rodriguez, D (2017), “Reliability Demystified, At Last,” in Bearing

Capacity of Roads, Railways and Airfields, (Loizos, A., et al Eds.), Taylor & Francis Group,

London, UK, pp 549-556

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Analytical and Probabilistic Methods, Ph.D thesis, Vanderbilt U., Nashville, TN, Aug

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Pavement Design, Ph.D thesis, U of Arkansas, Fayetteville, AR, Aug

Calibration of Transverse Cracking and Joint Faulting Prediction Models in Pennsylvania

for JPCP in AASHTOWare Pavement ME Design

Biplab B Bhattacharya1 and Michael I Darter2

1Pavement Engineer, California Dept of Transportation; formerly, Senior Engineer and Principal

Investigator, Applied Research Associates, Inc., Sacramento, CA Email:

(AASHTO) Mechanistic-Empirical Pavement Design Guide (MEPDG) procedure and

accompanying software AASHTOWare Pavement ME Design (Pavement ME) into its routine pavement design practice The implementation of the Pavement ME as a PennDOT standard required modifications in some aspects of PennDOT pavement design practices such as materials testing, testing equipment, traffic data reporting, software/database integration, development of statewide defaults for key inputs, policy regarding design output interpretation, and others In addition, the implementation required local calibration of the software’s global pavement performance prediction models for Pennsylvania conditions to improve the accuracy of performance prediction for both asphalt concrete pavement and jointed plain concrete pavement (JPCP) This paper discusses the procedures and steps involved in locally calibrating the Pavement

ME global transverse cracking and mean joint faulting prediction models for JPCP to account for Pennsylvania’s unique climate, traffic, and soils conditions, and its commonly used pavement construction practices Local calibration of the Pavement ME models, using Pennsylvania input data, was performed using statistical analysis software’s nonlinear model optimization tool The calibration efforts involved derivation of new local calibration factors for each performance prediction model using Pennsylvania-specific performance data The outcome included elimination of bias (consistent over- or under-prediction), reduction of prediction error, and improvement in model prediction accuracy The results indicate that compared to Pavement ME global performance prediction models, Pennsylvania-locally calibrated models could be used to develop more accurate, reliable, and cost-effective pavement designs

INTRODUCTION

The Pennsylvania Department of Transportation (PennDOT) recently conducted a study to implement and adopt the American Association of State Highway and Transportation Officials (AASHTO) Mechanistic-Empirical Pavement Design Guide (MEPDG) [1] procedure and accompanying software AASHTOWare Pavement ME Design (Pavement ME) [2] into its routine pavement design practice Pavement ME is based on mechanistic-empirical principles and represents a significant improvement over the existing empirical design procedures The Pavement

ME successfully addresses most of the serious limitations of empirical design procedures, such as lack of consideration of climatic, lack of meaningful materials properties, lack of direct

consideration of actual traffic loadings, no distress consideration, non-Pennsylvania validated prediction models, and many others It does so by employing a mechanistic-empirical (ME) framework that requires the user of the design guide software to enter a detailed description of several variables for each type of input (traffic, climate, and materials) The program uses these inputs in mechanistic-based algorithms to compute pavement responses such as stresses, strains, truck axle load deflections, and accumulated pavement damage over the pavement design/analysis period The cumulative damage is then used to determine the pavement performance with respect

to various distresses, using empirical relationships called transfer functions The Pavement ME distress transfer functions were originally calibrated using data from the Long-Term Pavement Performance (LTPP) program under National Cooperative Highway Research Program (NCHRP) projects 1-37A [3] and 1-40D [4], and for concrete pavements more recently under NCHRP 20-07 [5]

Successful implementation of Pavement ME depends on PennDOT’s resources to obtain accurate and reliable design inputs Therefore, identifying the agency’s needs in terms of collecting information for different traffic, materials, and climatic variables plays a key role in seamlessly transitioning from the current pavement design methodology to ME-based design [6] To accomplish that PennDOT has conducted laboratory testing of typical PennDOT materials and developed a materials database In addition, a traffic database was also developed to capture the traffic distributions in Pennsylvania [7] The calibration of distress prediction models or transfer functions with local data is equally important, as global calibration factors do not consider all potential factors such as material specifications, design and maintenance strategies, climatic conditions, and traffic distributions that are specific to an agency The process of locally calibrating performance prediction models [8] will enable PennDOT to use Pavement ME for new construction and rehabilitation pavement design with a much greater degree of reliability and confidence

Figure 1 Location of LTPP and RMS JPCP sections in Pennsylvania.

DEVELOPMENT OF CALIBRATION DATABASE

The Pavement ME implementation process involved developing a database of selected pavement projects Jointed Plain Concrete Pavement (JPCP) projects from both LTPP and PennDOT Roadway Management System (RMS) located in Pennsylvania were included in the database The geographic distribution of both LTPP and RMS sites across the region for JPCP is shown in Figure 1 Efforts were made to collect as much as-built data as possible and use the as-

built data as input in the Pavement ME The historical performance data was collected from the RMS database as well as field surveys

JPCP TRANSVERSE CRACKING MODEL

The Pavement ME predicts transverse fatigue cracking in JPCP via two key models The first model, shown in Equation 1 [1], is used to calculate the estimated fatigue life of PCC (or number

of load repetitions to failure, N) when subjected to repeated stress for a given flexural strength,

testing data Hence, the MEPDG Manual of Practice (1) does not recommend modifying these coefficients as the extensive data used for their determination make the model applicable to a wide range of design conditions

𝐿𝑜𝑔( 𝑁𝑖,𝑗,𝑘,𝑙,𝑚,𝑛) = 𝐶1× ( 𝑀𝑅𝑖

𝜎𝑖,𝑗,𝑘,𝑙,𝑚)

𝐶2

+ 0.4371 (1)

The relationship between the accumulated fatigue damage at the top and bottom of JPCP slabs

(i.e., damage index or DI) and the field-measured cracking was defined in the form of a sigmoidal

function (S-shaped curve) The fatigue cracking transfer function for JPCP is shown in Equation

2 [1] Parameters C4 and C5 in the following equation are adjusted to remove bias and improve the

goodness of fit with field data

1+𝐶4(𝐷𝐼𝐹) 𝐶5 (2)

Local Calibration of JPCP Transverse Cracking Model

The analysis utilized the Pennsylvania database to establish the goodness of fit and bias in the Pavement ME transverse cracking model The global models showed significant bias The researchers investigated the possible causes of bias, and no obvious reasons (such as erroneous inputs) were found Thus, local calibration proceeded Calibration of the Pavement ME global models using PennDOT input data was done using nonlinear model optimization tool available in the SAS statistical software Adjusted JPCP transverse cracking global model coefficients are presented in Table 1 and shows that two of the four global coefficients were adjusted

The goodness of fit and bias statistics presented in Table 2 show an adequate goodness of fit with minimal bias for the locally calibrated JPCP transverse cracking model developed using new and rehabilitated JPCP sections [10] The bias test was performed at 5% significant level Local calibration of the transverse cracking model resulted in the development of PennDOT-specific model that predict transverse cracking distress with adequate accuracy and minimal bias Goodness

of fit characterized using R2 slightly increased from 58.52 for the global models to 58.71 percent,

while standard error (SEE) increased from 4.6 to 5.4 percent slabs cracked The very low SEE value with global models was due to under prediction and low measured cracking values in general

Table 1 Summary of Pavement ME Global and PennDOT Local Calibration Coefficients

for JPCP Fatigue Damage and Transverse Cracking Models

Model or Submodel Type Model Coefficients Global Model Values

PennDOT Local Model Values

PCC Fatigue Damage Model

JPCP Transverse Cracking Model

Table 2 Results of Statistical Evaluation of Pavement ME JPCP Transverse Cracking

Local Model for Pennsylvania Conditions

(Intercept)

p-value (Slope)

p-value (Paired t-test)

58.71% 5.4% slabs cracked 0.2543 > 0.05 0.0692 > 0.05 0.9672 > 0.05 Figures 2a and 2b present plots of predicted transverse cracking, using PennDOT local calibration coefficients versus field-measured transverse cracking for all Pennsylvania JPCP sections and PCC fatigue damage versus field-measured transverse cracking Figure 2b shows that the typical S-shaped fatigue curve achieved in many similar calibrations (e.g low fatigue cracking for low fatigue damage and rapidly increasing cracking as damage approaches 1.0) Figure 3 illustrate the PennDOT local model prediction of transverse cracking for a JPCP section The transverse fatigue cracking (combination of top down and bottom up fatigue cracking) model predicts well with the measured field cracking of the slabs

The new models will increase the accuracy of transverse cracking predictions, while minimizing bias and will produce for PennDOT more accurate and optimum (lower cost) new and rehabilitated JPCP designs at the desired design reliability

a Measured vs Predicted Slabs Cracked using PennDOT Local Transverse Cracking Model

b Measured Transverse Cracking vs Predicted Concrete Fatigue Damage using PennDOT Local

Transverse Cracking Model

Figure 2 Measured versus predicted transverse cracking using PennDOT local transverse

cracking model

0 20 40 60 80 100

R 2 = 58.71%

SEE = 5.4% slabs cracked

Figure 3 Plot showing measured versus predicted JPCP transverse cracking for LTPP

section 9027

Estimating Design Reliability for JPCP Transverse Cracking Model

The Pavement ME estimates pavement design reliability using estimates of cracking standard deviation for any given level of predicted cracking Thus, for JPCP transverse cracking model, there was a need to develop a relationship between predicted transverse cracking and the standard error of prediction The predicted transverse cracking standard error equations were developed as follows [10]:

1 Divided predicted transverse cracking into 3 or more intervals

2 For each interval, determined mean predicted transverse cracking and standard error (i.e., standard variation of predicted – measured transverse cracking for all the predicted transverse cracking that falls within the given interval)

3 Developed a nonlinear model to fit mean predicted transverse cracking and standard error for each interval

The resulting standard error of the estimated transverse cracking model developed by using the locally calibrated PennDOT transverse cracking model is presented below:

𝑆𝐸𝐸(𝐶𝑅𝐴𝐶𝐾) = 3.1306 × 𝐶𝑅𝐴𝐶𝐾0.3582+ 0.5 (3)

Where:

SEE(CRACK) = transverse fatigue cracking standard deviation, percent slabs

JPCP JOINT FAULTING MODEL

The mean transverse joint faulting is predicted using a complex incremental approach A detailed description of the faulting prediction process is presented in the MEPDG Manual of Practice [1] Pavement ME faulting is predicted using the models presented below:

Age, months

0 40 80 120 160 200 240 280 320 360 400 440 480

SHRPID=42_9027_1

PLOT PREDICTED MEASURED

𝐹𝑎𝑢𝑙𝑡𝑚 = ∑𝑚𝑖=1𝛥𝐹𝑎𝑢𝑙𝑡𝑖 (4) 𝛥𝐹𝑎𝑢𝑙𝑡𝑖 = 𝐶34× (𝐹𝐴𝑈𝐿𝑇𝑀𝐴𝑋𝑖−1− 𝐹𝑎𝑢𝑙𝑡𝑖−1)2∗ 𝐷𝐸𝑖 (5) 𝐹𝐴𝑈𝐿𝑇𝑀𝐴𝑋𝑖 = 𝐹𝐴𝑈𝐿𝑇𝑀𝐴𝑋0+ 𝐶7× ∑𝑚𝑗=1𝐷𝐸𝑗× 𝐿𝑜𝑔(1 + 𝐶5× 5 0𝐸𝑅𝑂𝐷)𝐶6 (6)

𝐹𝐴𝑈𝐿𝑇𝑀𝐴𝑋0 = 𝐶12× 𝛿curling× [𝐿𝑜𝑔(1 + 𝐶5× 5 0𝐸𝑅𝑂𝐷) × 𝐿𝑜𝑔(𝑃200 ×𝑊𝑒𝑡𝐷𝑎𝑦𝑠

𝑝𝑠 )]𝐶6 (7) Where:

during month i, in

DE i = differential deformation energy accumulated during month i

computed using various inputs such as joint LTE and dowel damage

δ curling = maximum mean monthly slab corner upward deflection PCC

due to temperature curling and moisture warping

P S = overburden on subgrade, lb

P 200 = percent subgrade soil material passing No 200 sieve

𝐶12 = 𝐶1+ C2× 𝐹𝑅0.25 (8)

𝐶34 = 𝐶3+ C4× 𝐹𝑅0.25 (9) Where FR is the base freezing index defined as percentage of time the top base temperature is below freezing, i.e less than 32°F

C 1 through C8 are calibration constants to be established based on field performance Faulting model calibration involved determination of the calibration parameters C1 through C 7 from the above equations and the rate of dowel deterioration parameter, C8, from the above equation, which

minimizes the error function

Local Calibration of JPCP Joint Faulting Model

The global joint faulting model showed poor goodness of fit along with slight bias for Pennsylvania-specific inputs The researchers investigated the possible causes of bias, and no obvious reasons (such as erroneous inputs) were found Thus, local calibration was performed Calibration of the Pavement ME global models using PennDOT input data was done using nonlinear model optimization tool available in the SAS statistical software Adjusted JPCP joint faulting global model coefficients are presented in Table 3 and shows that two of the eight global coefficients were adjusted

Table 3 Summary of Pavement ME Global and PennDOT Local Calibration Coefficients

for JPCP Joint Faulting Model

Model or Submodel Type Model Coefficients Global Model Values

PennDOT Local Model Values

JPCP Joint Faulting Model

Table 4 Results of Statistical Evaluation of Pavement ME JPCP Joint Faulting Local

Model for Pennsylvania Conditions

(Intercept)

p-value (Slope)

p-value (Paired t-test)

52.31% 0.00713 in 0.0601 > 0.05 0.8447 > 0.05 0.1276 > 0.05

Figure 4 Measured versus predicted JPCP joint faulting using

PennDOT local joint faulting model

R 2 = 52.31%

SEE = 0.00713 in