DEVELOPMENT OF A MECHANISTIC-EMPIRICAL FRAMEWORK TO ASSESS THE RESILIENCY OF FLEXIBLE PAVEMENTS AT PROJECT AND NETWORK LEVELS AGAINST FLOODING By Seyed Farhad Abdollahi A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Civil Engineering – Doctor of Philosophy 2025 ABSTRACT As a consequence of climate change, the frequency and intensity of flooding events across the United States have been increasing over the past decades. Understanding the impact of these flooding events on the performance of flexible pavement networks is crucial for the design and maintenance of these structures. Flooding increases the degree of saturation of pavement layers, which affects the mechanical behavior of the materials and accelerates the deterioration rate. The focus of this dissertation is the impact of flooding events on the performance of flexible pavement structures at both the project and network levels, using a Mechanistic-Empirical (ME) pavement analysis framework. A comprehensive literature review highlighted the limitations in current modeling approaches and underscored the need for an improved analysis system. To address these gaps, a framework was developed to incorporate the effects of flooding events on the performance of flexible pavement structures using the ME analysis procedure. This framework proposed four major modifications to the standard Mechanistic-Empirical Pavement Design Guide (MEPDG) approach, including (i) a hybrid analysis increment scheme to capture short-term flooding effects, (ii) adjustments to the Resilient Modulus (MR) of unbound layers due to increased saturation levels, (iii) modifications to the rutting prediction model for saturated pavement materials, and (iv) accounting for changes in traffic patterns during flooding events. The Unified Pavement Distress Analysis and Prediction System (UPDAPS) program, which is a ME-based pavement analysis tool, was developed as a baseline for the analysis of this research. The proposed framework was implemented into the analysis engine of the UPDAPS program, resulting in a modified version called the UPDAPS-Flood program. The distress prediction results of the UPDAPS-Flood program were validated by simulating several pavement structures from the New Orleans area under the flooding caused by hurricanes Katrina and Rita. At the project level, the UPDAPS-Flood program was used in a case study in Miami-Dade County, Florida, to simulate the effects of nine major flooding events on a newly constructed flexible pavement structure. The findings showed significant increases in rutting, fatigue cracking, and International Roughness Index (IRI) distresses due to these flooding events. The results emphasized the advantages of the UPDAPS-Flood program in analysis and design of the flexible pavement structures in the flood-prone areas. At the network level, UPDAPS-Flood program was employed to evaluate the resiliency of 10,650 flexible pavement structures across the contiguous United States. The simulation results showed a higher loss of service life for pavement networks in the Long-Term Pavement Performance (LTPP) Wet/Freeze region, areas near major U.S. rivers (e.g., the Missouri and Mississippi rivers), and along the eastern coastline. This observation was attributed to the more frequent and severe flooding events recorded in these areas, primarily caused by river flooding, coastal flooding, or high precipitation. The analysis showed an average nationwide loss of service life of nine months for pavement structures due to flooding events. Additionally, the results indicated that highly flooded sections experienced significant performance losses, emphasizing the importance of considering flooding events in pavement design and maintenance frameworks, particularly in flood-prone areas. Moreover, a sensitivity analysis was conducted to evaluate the impact of key input parameters in the UPDAPS-Flood program on the calculated resiliency of the flexible pavement network against flooding events. The results showed a direct correlation between the reduction in MR of saturated unbound layers and the accumulated flooding damage. The results also highlighted the critical role of the effective drainage systems in mitigating the flooding damage to the pavement network. Geosynthetic reinforcement of the unbound base layer was also investigated as a potential strategy to improve pavement resiliency against flooding events. Laboratory test results showed that geosynthetic reinforcement increased the MR of base materials by 47% and reduced plastic strain by 23.4%, offering a promising solution to improve pavement performance under flood conditions. In addition, a geosynthetic reinforcement model was implemented in the UPDAPS- Flood program by integrating a Finite-Element Method (FEM)-based pavement structural response model. The simulation results on two typical pavement structures in Michigan showed that effect of geosynthetic reinforcement on improving the pavement resiliency against flooding events was dependent on the structural capacity of the pavement. In the thinner pavement sections, the geosynthetic reinforcement not only mitigated flooding damages but also improve the overall performance of the pavement, while in the thicker pavement sections, it did not show significant improvement in the predicted distresses under flooding scenario. Copyright by SEYED FARHAD ABDOLLAHI 2025 This dissertation is dedicated to my father, mother, and brother, for their support and belief in me. It is also dedicated to all the invaluable lives lost for freedom in Iran, in honor of the “Woman, Life, Freedom” movement. v ACKNOWLEDGEMENTS First and foremost, I would like to express my gratitude to my advisor, Prof. M. Emin Kutay, for his guidance, mentorship, and support during throughout my doctoral studies. I would also like to acknowledge my committee members, Prof. Karim Chatti, Prof. Bora Cetin, and Prof. Thomas Pence, for their insightful comments and feedback, which greatly improve this dissertation. I also want to thank my colleagues and friends in the GeoPave group, who have shared this journey with me and provided both academic and emotional support. A special thank you to my friends here in East Lansing, who made this city a home for me. The funding support from the FHWA and USDOT is also gratefully acknowledged. vi TABLE OF CONTENTS LIST OF ABBREVIATIONS ..................................................................................................... ix CHAPTER 1. INTRODUCTION............................................................................................. 1 1.1. Objective and Scope ...................................................................................................... 2 1.2. Dissertation Organization ............................................................................................ 3 CHAPTER 2. LITERATURE REVIEW ................................................................................ 5 2.1. Climate Change ............................................................................................................. 5 2.2. Flooding ....................................................................................................................... 16 2.3. Flooding Effects on Flexible Pavement Structures .................................................. 21 2.4. Modeling of Flooding Effects on Flexible Pavement Performance ........................ 31 2.5. Chapter Conclusion .................................................................................................... 35 CHAPTER 3. MOTIVATION OF STUDY AND RESEARCH METHODOLOGY ....... 36 CHAPTER 4. UPDAPS PROGRAM ..................................................................................... 39 4.1. Background ................................................................................................................. 39 4.2. Model Improvements in UPDAPS Program ............................................................ 41 4.3. Parallel Computing and Run Time Efficiency ......................................................... 86 4.4. Chapter Conclusion .................................................................................................... 87 CHAPTER 5. UPDAPS-FLOOD PROGRAM ..................................................................... 89 5.1. Proposed Framework ................................................................................................. 89 5.2. Development of UPDAPS-Flood Program................................................................ 97 5.3. Validation of UPDAPS-Flood Program .................................................................... 99 5.4. Project-Level Results ................................................................................................ 101 5.5. Runtime Evaluation of UPDAPS-Flood Program ................................................. 104 5.6. Chapter Conclusion .................................................................................................. 104 CHAPTER 6. NETWORK-LEVEL RESILIENCY MAPS .............................................. 106 6.1. Resiliency Metric ....................................................................................................... 106 6.2. Proof of Concept of Methodology and Sensitivity Analysis .................................. 107 6.3. National Wide Network-Level Resiliency Analysis ............................................... 120 6.4. Chapter Conclusion .................................................................................................. 131 CHAPTER 7. RESILIENCY OF GEOSYNTHETIC-REINFORCED FLEXIBLE PAVEMENTS AGAINST FLOODING EVENTS ................................................................ 134 7.1. Laboratory Testing ................................................................................................... 134 7.2. Numerical Simulations ............................................................................................. 149 7.3. Chapter Conclusion .................................................................................................. 162 CHAPTER 8. CONCLUSION AND RECOMMENDATION .......................................... 165 8.1. Summary and Conclusion ........................................................................................ 165 8.2. Recommendations for Future Research ................................................................. 172 REFERENCES .......................................................................................................................... 173 vii APPENDIX A CLIMATE CHANGE PROJECTION MODELS ................................. 186 APPENDIX B SUMMARY OF MODELS USED IN UPDAPS PROGRAM .............. 190 APPENDIX C INPUT PROCESSING FOR UPDAPS-FLOOD PROGRAM ............. 213 viii LIST OF ABBREVIATIONS AC Asphalt Concrete CESM Community Earth System Model DOE Department of Energy E3SM Energy Exascale Earth System Model EdGCM Educational Global Climate Model EM-DAT Emergency Events Database ESDM Empirical Statistical Downscaling Method FEA Finite Element Analysis FEMA Federal Emergency Management Agency FMS Flexible Modeling System GCM Global Climate Model GFDL Geophysical Fluid Dynamics Laboratory GHG Green House Gases GISS Goddard Institute for Space Studies HERS Highway Economic Requirements System HMA Hot-Mix Asphalt HPMS Highway Performance Monitoring System iDMC Internal Displacement Monitoring Center IPCC Intergovernmental Panel on Climate Change IRI International Roughness Index LEA Layered-Elastic Analysis MAE Mean Absolute Error ME Mechanistic-Empirical ix MEPDG Mechanistic-Empirical Pavement Design Guide MERRA Modern-Era Retrospective analysis for Research and Application MIT GCM MIT General Circulation Model MPM Michigan Paving and Materials Company MR Resilient Modulus NAPCOM National Pavement Cost Modes NASA National Aeronautics and Space Administration NEMO Nucleus for European Modeling of the Oceans NOAA National Oceanic and Atmospheric Administration NPS National Park Service PMS Pavement Management System PSI Pavement Serviceability Index RCM Regional Climate Model RCP Representative Concentration Pathway RLPD Repeated Load Permanent Deformation RMSE Root Mean Squared Error SEE Standard Error of Estimates SRES Special Report on Emission Scenarios SSA Surface Shortwave Absorptivity UPDAPS Unified Pavement Distress Analysis and Prediction System VECD Viscoelastic Continuum Damage x CHAPTER 1. INTRODUCTION Climate change has a significant impact on multiple facets of human life, including the political, social, and economic spheres. The implications of climate change have captured the interest of climatologists and policy makers as well as international media outlets, who consistently report on a wide range of events linked to climate change. Although rising global temperatures are the primary observable indicator of climate change, there are many other effects such as rising sea levels, rising groundwater levels, changing patterns of precipitation, widespread droughts, and a variety of extreme weather events, such as heatwaves, floods, storm surges, and intense rainfall events, to name a few. Among many different consequences of climate change, it has been observed that the frequency and intensity of the flooding events are increasing globally. This can be attributed to the intense precipitation patterns coupled with the sea level and groundwater level rise, especially in the coastal regions. In the United States, several coastal regions, such as Florida, Louisiana, etc., have experienced an increased frequency and intensity of flooding events, which can significantly affect the infrastructure systems and surrounding communities. The pavement network is an important part of the transportation infrastructure and a necessary component for national economic growth and social development. The performance of pavement structures can be severely impacted by flooding events. It is noted that more than 94% of the pavement network in the United States consists of flexible pavement structures, which exhibit higher vulnerability to flooding events, compared to rigid pavements. Flexible pavements are multilayered systems consisting of Asphalt Concrete (AC) layers over unbound base or subbase layers. These pavement layers are susceptible to a severe reduction in performance when exposed to prolong inundation from floodwaters. During a flooding event, the floodwater can infiltrate the pavement structure and increase the degree of saturation of the underlying pavement layers. These increased saturation levels can significantly reduce the stiffness and damage resistance of unbound layers, resulting in a loss of pavement structural capacity. Though the AC layers are typically less susceptible to flooding events than unbound layers, they remain prone to premature deterioration, caused by stripping and raveling. These distresses can result in safety issues for the road users, and increased maintenance costs for the road agencies. 1 Given the significant impacts of flooding events on pavement performance and the increasing trend in the frequency and intensity of flooding events due to climate change, it is important to develop a comprehensive understanding of the mechanisms of damage to different pavement layers and reduction in pavement performance due to flooding. Furthermore, it is also critical to study the potential mitigation strategies to improve the resiliency of the pavement structures against flooding events. Such efforts can significantly help road agencies and stakeholders in assessing the resilience of pavement networks against flooding events and thereby prioritize their investment decisions accordingly. This research aims to address these challenges by developing a quantitative framework that helps understand the flooding effects on pavement performance integrating this framework into a practical pavement analysis tool and providing a broader overview of the pavement resiliency at the network level. 1.1. Objective and Scope The main objective of this research was to improve the understanding of the impacts of flooding events on the performance of flexible pavement structures, assess their resilience against such events at the project and network levels, and evaluate the effectiveness of geosynthetic reinforcement as a mitigation strategy for flooding events. To achieve this goal, the research plan was organized into several interconnected steps. Initially, a Mechanistic-Empirical (ME)-based pavement analysis model was developed to establish a baseline for the analysis. Subsequently, different components of this model were modified to incorporate the potential effects of flooding on the predicted pavement performance. A comprehensive review of the existing literature was performed, leading to the creation of a structured approach to incorporate the impacts of flooding into the Mechanistic-Empirical Pavement Design Guide (MEPDG) methodologies. A modified pavement analysis model was employed to evaluate the resilience of the nationwide pavement network against flooding events. Finally, the geosynthetic reinforcement was incorporated into the developed model to its efficiency in improving the resiliency of the pavement structures against flooding events. While this research aims to provide pavement engineers and road agencies with a practical tool for designing and analyzing flexible pavement structures under flooding conditions, its scope is limited to newly constructed and rehabilitated overlayed flexible pavement structures. This research specifically focuses on quantifying the impact of flooding on pavement performance with an emphasis on moisture-related effects. Factors such as the velocity of floodwaters, water force, 2 and potential clogging in the drainage system caused by flood debris have not been included within the scope of this study. In addition, although an indirect validation process was performed during this research, an extensive Pavement Management System (PMS) data is required to accurately validate the results and developed models. Moreover, the tool developed in this study can help with the evaluation of flooding damages and their associated costs for flexible pavement networks at regional, state, and national scales, thereby providing insights into network-level resiliency of the pavement network against flooding events. However, this research does not include the evaluation of uncertainties from prospective climate change scenarios. 1.2. Dissertation Organization This document is divided into seven chapters. A brief description of each chapter can be found below: • Chapter One includes the introduction of the research and problem statement, as well as its objective and scope. • Chapter Two summarizes the results of a comprehensive literature review and the state of the practice to better understand the flooding effects and its modeling for flexible pavements. • Chapter Three identifies the current gap in the literature about mechanistic-empirical modeling of the flooding effects on flexible pavements and how this research tries to address this gap. • Chapter Tour includes the development of the Unified Pavement Distress Analysis and Prediction System (UPDAPS) program, which is a mechanistic-empirical pavement analysis tool. • Chapter Five provides the development of a framework to implement the flooding effects into the ME-based pavement analysis tools and the implementation of the developed framework into the UPDAPS program, herein called the UPDAPS-Flood program. • Chapter Six includes the analysis results at the network level on 10,650 pavement sections across the contiguous United States. This chapter also discussed the resiliency metric and generation of the resiliency maps against the flooding events across the United States. • Chapter Seven evaluates the effectiveness of geosynthetic reinforcement in improving resiliency against flooding events. This chapter includes laboratory testing results on the 3 mechanical behavior of a geosynthetic-reinforced unbound base material and the results after incorporating geosynthetic reinforcement into the developed models. • Chapter Eight summaries the activities conducted throughout this research and provides the conclusions and recommendations for future research. 4 CHAPTER 2. LITERATURE REVIEW This chapter presents a thorough review of the literature and current state of the knowledge regarding the flooding effects on flexible pavement structures. It begins with an examination of climate change and flooding, proceeds to an analysis of the impact of flooding on flexible pavements, and includes modeling of these effects. Finally, the possible corrective actions against flooding have been reviewed. 2.1. Climate Change According to the terminology of the Intergovernmental Panel on Climate Change (IPCC), the climate change has been defined as the change in the state of the climate that can be identified by shifts in the average and/or variability of its properties, persisting for prolonged intervals, usually spanning decades or more (IPCC 2023a). Such changes in climate may arise from natural processes, such as fluctuation of solar cycles and volcanic activities. However, since the 19th century, human activities have been recognized the main factor behind the climate change, primarily due to usage of fossil fuels such as coal, oil, and natural gas (IPCC 2023b, United Nations 2023). It is crucial to differentiate between the terms ‘climate’ and ‘weather', where 'weather' typically refers to the transient states of atmospheric conditions, manifesting as daily fluctuations in temperature, wind, cloud cover, precipitation, etc. Whereas 'climate' refers to the aggregated long- term averages, the pattern of seasonal distribution, and annual variability of the weather (Dawson 2014). Therefore, the occurrence of a cold weather in some years does not contradict the broader trend of climate change and global warming (increase in the mean annual temperature of the earth’s atmosphere). Furthermore, while the broad definition of climate change includes long-term shifts in climate patterns, the pavement community typically focuses on changes over decadal periods. Although the climate change is usually translated in public as an increasing temperature of the earth’s atmosphere, it is also associated with a range of other climatic effects. An increase in global temperature contributes to the warming of sea waters, which can eventually result in more evaporation and higher precipitation potential. Moreover, increase in global temperature increases the energy in the atmosphere, which can generate more vigorous winds and increase the storm formation potential (Dawson 2014). Climate redistribution is another outcome of global temperature rising, an example of which is the warmer winters and cooler summers observed at the coastal California regions (Lebassi et al. 2009, Neelin et al. 2013). More details on the climate 5 change observations and their specific impact on the pavement performance has been discussed in the next sections. 2.1.1. Historical Climate Change The past climate can be studied through the climate proxies, such as ice cores, sedimentary deposits, dendrochronology (tree rings), and coral formations. For instance, dendrochronology offers an opportunity to investigate the past climate change; the growth patterns of trees, which are intrinsically influenced by climatic variables such as precipitation and solar radiation, provide insights into historical climate dynamics. As another example, stratified ice within ancient glaciers captures water and air bubbles over extended periods. By studying the hydrogen and oxygen isotopes in these trapped water and air, paleoclimatologists can infer the historical climate change based on the relation between the isotopic composition and temperature (Petit et al. 1999). Utilizing this approach enables the scientists to reconstruct the past climate, specifically temperature variations. Figure 1 shows the historical atmospheric carbon dioxide concentration and estimated historical temperature records over the past 400,000 years. As this figure shows, the variation of atmospheric temperatures reveals four distinct natural cycles corresponding to glacial periods, characterized by significantly reduced global temperatures. Each significant temperature drop indicates an ice age, which is an extremely cold periods on the earth. According to this temperature pattern, the temperature increases to a high temperature peak after the most recent ice age and it is expected to drop again (Petit et al. 1999). The temperature pattern in this figure is categorized under the long-term climate change trend. This is while, the short-term climate change trends were always existed and is of the greater importance for the pavement community. The concept of ‘climate balance’ has been used to study the reasons of climate change. In this concept, the earth’s climate is assumed as a system governed by the principle of energy balance. The solar radiations are the system inputs, which is either absorbed by the earth’s surface/atmosphere or reflected back into the outer space. The ‘radiative forcing’ is then defined as the net difference between the incoming solar radiation and the fraction that is reflected. The system balance, especially the absorption and reflection processes, can be interrupted by different influential factors and resulted in climate change. Orbit of the earth, solar output variability, changes in ocean current, and volcanism are some examples for natural influential factors (Crowley 2000). 6 Figure 1. Isotopic temperature at the atmosphere during the past 400,000 years (data source: Petit et al. 1999) In the recent decades, it has been found that the earth is experiencing a steady increase in surface temperature, which is associated with the increased concentration of Carbon-dioxide (CO2), methane (CH4), nitrous-oxide (N2O), and water vapor (H2O) in the atmosphere (Dawson 2014). Similar trends were found between the concentration of the CO2 and CH4 with the atmosphere temperature during the past 420,000 years (Petit et al. 1999). The higher concentration of these gases in the atmosphere significantly increases the absorption process, as these gases can trapped the radiation in the earth’s atmosphere. This phenomenon is called “greenhouse effect” and the above-mentioned gases are known as greenhouse gases (GHG) (Toth and Hillger 2013). As the CO2 is the most common GHG, the amount of GHG in atmosphere is usually quantified in terms of equivalent CO2 (CO2 equiv) using Equation (1) (Dawson 2014). 𝐶𝑂2 𝑒𝑞𝑢𝑖𝑣 = ∑(𝐺𝑎𝑠 × 𝐺𝑊𝑃𝐺𝑎𝑠) 𝐺𝑊𝑃𝐶𝑂2 (1) where: CO2 equiv = equivalent amount of CO2 (tones). Gas = amount of GHG gas of interest (tones). GWPCO2 = global warming potential of CO2 gas. GWPGas = global warming potential of GHG gas of interest. 7 It is believed that most of the observed increase in the GHG emissions over the past few decades was predominantly attributed to the human activities, hence it is called ‘anthropogenic’. This significant increase in anthropogenic GHG emission started with industrial revolution and is mainly related to the combustion of fossil fuels, cement manufacturing, gas flaring, and change of the land-use. IPCC has documented that from 1750 to 2011, over 2,000 gigatons of anthropogenic CO2 equiv have been added to the atmosphere (IPCC 2014). For instance, Figure 2 shows the average annual CO2 emissions from natural volcanic activities with those from fossil fuel combustion (anthropogenic source) over the past 250 years. This figure shows the significant impact of industrial revolution on increasing the CO2 emissions (Burton et al. 2013). Such significant anthropogenic radiative forcing is implicated in a global temperature increase of approximately 1.01ºC since 1880 (NASA 2022a) and a sea-level rise exceeding 4-inches since 1993 (Frederikse et al. 2020). 2.1.2. Climate Change Projection Scenarios Climate change projections are formulated through the climatic models, which are based on a range of scenarios for increasing the GHG emissions and other factors affecting the earth’s climate energy balance. The use of term ‘projection’ rather than ‘prediction’ highlights the conditional nature of these climatic models; they are mainly linked to the input scenarios that are themselves functions of GHG emissions and a suite of socioeconomic determinants. These climate change projections are the result of quantitative evaluation of the climate change concept. As such, they serve as the major inputs for many studies to evaluate the risk of specific climate event or trend (Collins et al. 2012, Dawson 2014). Climate change projections are complex models for simulating the climate system, where variability among these models can lead to different forecasts of future climate. There are lots of uncertainties in the projected future climate which can be attributed to the incomplete understanding of climate system dynamics or limitations in the models and observations (Collins et al. 2012). A significant source of uncertainty also arises from the input projection scenarios, which are the results of ambiguity regarding human decisions. This uncertainty is reflective of the challenges in forecasting socioeconomic behaviors and the resultant GHG emissions (Dawson 2014, Hayhoe et al. 2017). 8 Figure 2. CO2 emission of volcanic activities and fossil fuel combustion human activities (data source: Burton et al. 2013) Climate change projection models are developed and used to estimate the future climate based on a range of potential future scenarios. These scenarios are constructed to model possible trajectories of global society development including variables such as human population growth, land use patterns, technological evolutions, and economic trends at both global and regional scales. Projections of future GHG emissions are then derived from these variables (NOAA 2022a). In 2000, the IPCC released a Special Report on Emissions Scenarios (SRES) in which four different scenarios were described as A1, A2, B1, and B2. These scenarios were developed under various assumptions based on distinctive combination of economic, technological, and demographical parameters (Qiao 2015). The SRES scenarios have been extensively used as an input to the climatic models for more than a decade. Subsequently, in 2013, the IPCC (2014) published an updated set of scenarios in its Fifth Assessment Report (AR5), which focused on the level of GHG emissions in the atmosphere by 2100. These updated scenarios were quantified in terms of radiative forcing and referred to as Representative Concentration Pathways (RCP). Each RCP was named based on the estimated amount of radiative forcing by 2100, as listed below (IPCC 2018). • RCP 2.6: This scenario is usually referred to as the ‘very stringent’. During this pathway, radiative forcing reaches a peak of about 3.0 W/m2 before receding to 2.6 W/m2 by 2100. It is also identified as ‘RCP 3-PD’, where ‘PD’ stands for peak followed by a declined. • RCP 4.5: This scenario represents an intermediate scenario, in which the emissions peak occurs around 2040 and then declines. During this pathway, radiative forcing is anticipated to stabilize at approximately 4.5 W/m2 by 2100 or potentially earlier, around the year 2080. 9 • RCP 6.0: In this scenario, emissions are projected to peak by the year 2080 and then they will decline. During this pathway, radiative forcing is predicted to stabilized at about 6.0 W/m2 by the year 2100. • RCP 8.5: In this scenario, emissions are projected to increase consistently throughout 21st century. During this pathway, radiative forcing is expected to exceed 8.5 W/m2 by the year 2100, with a predicted continuation of this upward trend beyond that timeframe. Recently in 2021, the IPCC released its Sixth Assessment Report (AR6) regarding the physical science basis of climate change (IPCC 2021). This report introduces five distinct scenarios that project the future state of climate change. These scenarios were developed based on complex models and calculations to reflect the potential trajectories of GHG emissions, as well as socioeconomic shifts in variables such as human population, urbanization, education, land utilization, and wealth, etc. These scenarios were then called Shared Socioeconomic Pathways (SSPs) and served to enhance the previously established RCPs. The SSPs were labeled as ‘SSP XX-YY’, where 'XX' represents the scenario family, and 'YY' indicates the projected radiative forcing by the year 2100. While these five SSP scenarios have been described as the latest update to the time, the RCP scenarios continue to be extensively used in the available pavement related literature. These five SSP scenarios are explained below (IPCC 2021). 2.1.2.1. SSP1-1.9: 1.5ºC by 2050 This scenario, characterized as the most optimistic of projections, envisions global CO2 emissions reaching net-zero by the year 2050. This scenario is associated with societies switch towards sustainability, where focus shifts from economic growth to overall well-being. Such a shift includes more investments in education and health care, coupled with efforts to reduce inequality. Under the SSP1-1.9 scenario, the extreme weather events are expected to happen more frequently, while the most severe consequences of climate change are anticipated to be averted. It is also noted that SSP1-1.9 stands as the only scenario aligning with the objectives of the Paris Agreement, aiming to limit global warming to approximately 1.5ºC above pre-industrial levels. This scenario projects a global temperature rise of 1.4ºC above pre-industrial levels by the year 2100. 10 2.1.2.2. SSP1-2.6: 1.8ºC by 2100 The SSP1-2.6 represents the next-best scenario, where CO2 emissions are projected to decrease significantly but will not achieve net-zero by the year 2050. The socioeconomic sustainability assumptions for SSP1-2.6 are similar to those of SSP1-1.9. During this scenario, global warming is predicted to stabilize at approximately 1.8ºC above pre-industrial levels by the year 2100. 2.1.2.3. SSP2-4.5: 2.7ºC by 2100 The SSP2-4.5 scenario is known as a 'middle of the road' scenario, where CO2 emissions are estimated to maintain around the current levels until 2050, followed by a gradual decline. However, this scenario does not foresee CO2 emissions reaching net-zero by the year 2100. Socioeconomic developments under SSP2-4.5 are expected to continue along historical trends, indicating a modest shift towards sustainability. Consequently, this scenario predicts a global temperature rise of 2.7ºC above pre-industrial levels by the year 2100. 2.1.2.4. SSP3-7.0: 3.6ºC by 2100 The SSP3-7.0 scenario assumes a steady increase in emissions and temperature, such that the CO2 emissions are expected to double from current levels by the year 2100. This scenario envisions a world where geopolitical competition intensifies, with nations primarily orienting their policies towards national security and self-sufficiency in food production. As a result, an increase in global temperatures of 3.6ºC above pre-industrial levels is projected by the year 2100 under the SSP3-7.0 scenario. 2.1.2.5. SSP5-8.5: 4.4ºC by 2100 The SSP5-8.5 scenario represents the worst-case scenario, wherein CO2 emissions are predicted to double from current levels by the year 2050. This scenario is attributed to the rapid global economy growth, predominantly driven by an increased usage of fossil fuels and high- energy-consuming lifestyles. Under this scenario, the predicted average global temperature increases by year 2100 is estimated to be 4.4ºC or possibly even higher. 2.1.3. Climate Change Observations and their Effects on Flexible Pavements Climate change has direct and indirect impacts on the environmental conditions and weather across the world, which refers to as “climate change observations”. According to the reviewed literature in the climatology science, the main climate change observations can be categorized as follows (NOAA 2021, EPA 2023, NASA 2024): 11 • Global temperature rise. • Precipitation irregularities. • Coastal regions sea level/groundwater level rise. • Shrinkage of glaciers. • Change in availability of fresh water. • Change in cloud cover and wind speed. • Change in population and demographic properties in different regions. • Extreme weather events, including but not limited to: o Heat extremes and marine heat waves1. o Wildfires. o Droughts. o Intense precipitations. o Flooding. o Storm-surge. o Hurricanes. However, the pavement community has shown particular interest in some of these climate change observations due to their direct impact on pavement performance, which includes global temperature rise, precipitation irregularities, see level rise, groundwater level rise, change in cloud cover and wind speed, and some extreme events like flooding, hurricanes, storm-surge and heat waves (Dawson 2014, Qiao 2015, Qiao et al. 2020). Moreover, change in the traffic loading patterns is also recognized in the literature as an indirect consequence of the climate change. These changes may be attributed to demographic and population changes driven by climate change or the necessity for road closures and detours in response to extreme events such as flooding and wildfires (Qiao et al. 2020). 1 A heat extreme is period of usually hot and humid weather, while the marine heat waves is a prolong period when ocean water temperatures are warmer than normal. Marine heat waves can last for last for weeks or months and can extend over large areas (FEMA 2024a, NPS 2024). 12 2.1.3.1. Temperature-Related Effects of Climate Change on Flexible Pavements Pavement temperature profile (variation of temperature with depth) is an important component of analysis and design of the flexible pavements. Primarily, the temperature profile is used in computing the dynamic modulus (|E*|), which serves as the representative modulus of the AC sublayers. This computation uses the temperature at the mid-depth of each AC sublayer along with the AC master curve to estimate the corresponding dynamic modulus. This modulus is subsequently integrated into the pavement structural response model to calculate the strain/stress responses, which eventually feeds into the pavement distress prediction models. This process is illustrated as shown in Figure 3. This approach aims to incorporate the viscoelasticity behavior of the AC materials into the pavement analysis and design through a simple and practical approach. Hourly pavement temperature profile is usually calculated by climatic models that apply the principles of energy equilibrium at the pavement surface and heat conduction through the pavement layers (ARA Inc. 2004, Kutay et al. 2023). A detailed review of these climatic models can be found in chapter 4 (see page 47). The increase in global temperatures may cause the AC sublayers to soften, leading to an elevated stress state in the layers beneath as the softened upper layers become less effective at distributing traffic loads (ARA Inc. 2004). On the other hand, it is noted in the literature that the changes in the stiffness of the AC materials and pavement structural responses might not be significant in the short-term (e.g., daily or weekly basis), but the cumulative impact of sustained temperature increase over the pavement service life may be considerable (Qiao et al. 2020). Figure 3. Conceptual illustration for effect of temperature profile in pavement analysis 13 The softer AC sublayers due to the increased temperature profile can also reduce resistance of these bituminous materials against rutting (ARA Inc. 2004, Huang 2004). Occurrence of heatwave extreme weather events, in which the temperature drastically increases over hourly/daily intervals, can further accelerate the evolution of AC rutting (Long 2001). Another observation linked to climate change is the widening of temperature ranges, where the gap between daily minimum and maximum temperatures becomes more pronounced. This phenomenon can increase the thermal stresses and cracking in AC sublayers (Lytton et al. 1983, Dave and Hoplin 2015). Cloud cover is another important factor in calculation of the pavement temperature profile, which is subject to change by climate change. Cloud cover appears twice in the energy balance equations, which are used to calculate the pavement temperature profile. First, it inversely affects the amount of shortwave radiation from the sun reaching to the pavement surface, where higher cloud cover can reduce these solar radiations and thereby reducing the pavement temperature profile. In addition, cloud cover has a direct impact on the air temperature, where lower air temperatures are expected with high cloud coverage. Finally, cloud cover can reflect some part of the longwave radiations emitted from the pavement surface back toward the pavement surface. Therefore, although higher cloud cover can reduce the amount of solar shortwave radiations into the pavement system and result in lower pavement temperature profiles, it also increases the amount of the longwave radiations which can slow down this cooldown process (Walker and Anderson 2016, Alam-Khan et al. 2022). In summary, changes in the cloud cover patterns due to the climate change phenomenon can significantly affect the pavement temperature profile. Wind speed is another factor that impacts the pavement temperature profile by affecting the heat convection from the pavement surface. Higher wind speeds can increase the heat convection and therefore, reduce the pavement temperature profile (ARA Inc. 2004, Kutay et al. 2023). It has been reported that wind speed can change the pavement temperature profile for up to 20F, where the highest effect of wind speed can be observed during the high air temperatures (Qin and Jacob 2013). It is noted that typical changes in the wind speed due to the climate change can be captured by the current climatic models, if proper projection data is available. However, the extreme wind speeds due to the extreme weather events (i.e., tornado, storm-surge, hurricanes, etc.) which may dump debris on pavement or caused severe damages, are generally not considered in the pavement analysis and design models. 14 2.1.3.2. Moisture-Related Effects of Climate Change on Flexible Pavements Different climate change observations can significantly change the moisture content of the pavement materials in short- or long-term periods. Precipitation, either as rainfall or snowfall, can introduce moisture into the pavement system from the sides or by penetrating to the lower pavement layers through the cracks and potholes. Similarly, surface runoff can also enter the pavement structure in the lack of proper drainage system or when the water volume exceeds the drainage system capacity (Dempsey and Elzaftawy 1976). Moreover, climate change-induced extreme weather events such as intense precipitation, flooding, storm-surge, or hurricanes can introduce high volume of the water to the pavement structure in a relatively short period of time, which increases the moisture level of the pavement materials, especially the unbound layers. This increased moisture content can be drained out of the pavement system in the presence of the proper drainage system (Dawson 2009). The groundwater level rise is another important source of water intrusion to the pavement system, especially subgrade and base layers (Dempsey and Elzaftawy 1976). In coastal regions, sea level rise is the primary factor contributing to the long-term increase in the groundwater levels. Short-term weather phenomena such as flooding, storm surges, and hurricanes can also lead to a temporary rise in groundwater levels, thereby elevating the moisture content in the unbound layers of pavement. High moisture levels can lead to accelerated damage to the flexible pavements via different mechanisms. Intrusion of excess water into the unbound layers can significantly reduce their resilient modulus (MR), which eventually lowers the pavement foundation support (Dawson 2009). Lower MR and shear strength of the unbound materials at higher moisture contents can increase the rate of permanent deformation accumulation and reduce the rutting resistant of unbound materials, particularly when they contain high fine contents (Dawson 2014). In addition, moisture can accelerate the asphalt stripping (raveling) by contributing to the buildup of pore water pressure under traffic loading and weakening the adhesion between the asphalt binder and aggregates (Little and Jones 2003). More detailed discussion about the moisture effects on flexible pavements can be found in section 2.3 (see page 21). A combined moisture- and temperature-related effects on flexile pavements can be seen in the freeze-thaw cycles in cold regions. During these cycles, moisture within the pavement unbound layers freezes due to the low temperatures in form of the ice lenses. Later in the spring, these ice 15 lenses melted and trapped in the pavement layers until the completion of thawing process. During this interval, the MR and shear strength of the pavement unbound layers can significantly reduce up until the excess moisture from the thawing process drained out the pavement system. This softer pavement support can result in accelerated pavement distresses, especially rutting (Dawson 2009, Salour 2015). The climate change can extend the thawing period in certain regions, allowing moisture to be retained within the pavement structure for longer periods. Such behavior results in accelerated pavement damage accumulation and may necessitate extended load restrictions during the thawing period (Daniel et al. 2018). Furthermore, the climate change impact on global temperature rise can also affect the freeze-thaw dynamics in traditionally colder regions and delay the freezing time or result in more freeze-thaw cycles (Chen et al. 2019). On the other hand, climate change can also result in eliminating the whole freeze-thaw cycles in certain regions. Although such impact is considered beneficial in terms of pavement damage evolution, many businesses in the colder regions (e.g., timber industry) rely on the frozen local roads without any load restriction. 2.2. Flooding The term “Flood” is defined as a natural phenomenon during which a considerable volume of water overflows onto a normally dry land. Traditionally, flooding was defined to be caused by the overflow of the inland waters or tidal waters (NOAA 2024a, NSSL 2024a). However, the Federal Emergency Management Agency (FEMA) expands this definition to include the unusual and rapid accumulation of the runoff waters from any source, mudflows, and body of water as a result of waves or current water (FEMA 2024b). The NOAA further distinguishes “flash flood” as a specific variant, which caused by heavy or excessive rainfall in a short period of time. While flooding events can last for days or weeks, the flash flooding events usually expected in shorter periods of less than 6 hours. The flash floods can occur within minutes to few hours of excessive rainfall or due to structural breaches like dam or levee failures (NOAA 2024a). It should be recognized that flash floods may inflict greater environmental damage due to their rapid currents, which amplify the inherent destructive force of the flooding. However, for the purpose of this study, the terminology “flood” or “flooding” includes both concepts and refer to the overflow of water on a normally dry land. Flooding is the most frequent natural disaster on a global scale (Abdullahi and Yue 2018). The Internal Displacement Monitoring Center (iDMC) reported that in 2022 alone, flood-related 16 incidents were responsible for the displacement of over 19.2 million individuals worldwide, which is about 59% of all displacements attributed to natural disasters (iDMC 2023). Within the United States, analysis of the data from NOAA dataset shows the significant economic impact of flooding as the costliest natural disaster. Figure 4 shows the cumulative costs of all natural disasters and flooding events to the United States for a timespan of 2000 to 2023. As this figure shows, flooding events costs over $1,324 billions to the United States, with the average annual cost of $75 billions over the past decade. It is noted that the cost of flooding events was about 62% of costs for all natural disasters during this period. Figure 4. Flooding costs to the US compared to all natural disasters (data from: NOAA 2024) During the past decades, the intensity and frequency of the flooding events followed an increasing trend due to the climate change impacts. These changes in the frequency of the flooding events attributed to the combination of several factors, including shifts in the weather conditions (e.g., intensity, seasonality, and type of precipitation events), changes in the snow melting patterns, changes in land use and land cover (e.g., due to urbanization and agriculture activities), and anthropogenic modifications of the water cycles (e.g., due to water management plans and construction of dams) (Slater and Villarini 2016). As an example, Figure 5 shows the frequency of the major flood events around the world based on the data reported by the Emergency Events Database (EM-DAT) agency. This figure 17 clearly shows the increasing trend of the flood frequency over the past decades, where the average annual number of flooding events in 2010s was about 20 times higher compared to the 1950s. It is noted that EM-DAT defines a major flooding events based on meeting at least one of the following conditions: (i) kills at least 10 people, (ii) affects at least 100 people, (iii) leads to a state of emergency declaration, or (iv) leads to call for international aid (EM-DAT 2024). Similar increasing trend in the frequency of the flooding events was also reported in the United States (Slater and Villarini 2016). Figure 5. Frequency of the flooding events worldwide for timespan of 1950 to 2023 (data from: EM-DAT 2024) Nowadays, the increasing trend of the frequency and intensity of the flooding events become more noticeable in the society. Figure 6 shows pictures of some of the recent major flooding events in the United States that have been widely covered in the media. These events, alongside many other similar flooding events, have significant social, environmental, and economic impacts on people lives, including but not limited to the traffic disruption, accidents, road closures, loss of structural integrity of the infrastructures, etc. 2.2.1. Flooding Sources The occurrence of a flooding event can attribute to different sources, each with different mechanism and impact. The main flooding sources can be classified in six different categories, including fluvial (river) flooding, pluvial (surface water) flooding, coastal flooding, reservoir flooding, groundwater flooding, and blocked drainage system flooding (Lu et al. 2020). 18 2.2.1.1. Fluvial Flooding Fluvial (river) flooding attributed to the water-level rise in the rivers and streams that surpass the confines of the riverbanks and let the water to overflow the neighboring low-lying areas (natural floodplains). Fluvial flooding typically caused by heavy and intense rainfalls that results in runoff volumes exceeding the river capacity (NSSL 2024b). The dynamics of fluvial flooding is influenced by the river morphology. For example, in short and steep rivers, the flooding can occur in a relatively short periods and proximity of the intense rainfall event, while in the larger rivers with more gradual water flows, the water-level rise and the resultant fluvial flooding can occur in longer periods and at the distance from the rainfall event. The fluvial flooding can also be attributed to the river blockages, such as those caused by ice jams (accumulation of the floating ice). In this mechanism, the water flow to the downstream significantly reduces and caused upstream flooding. In addition, sudden release of such blockages can also cause downstream flooding (Lu et al. 2020). Figure 6. Some recent major flooding events in United States: (a) flooded I-275 highway in Detroit area, MI in August 2023 (credit: K.P. Mitchell from Detroit Free Press); (b) flooded neighborhood in Merced, CA in January 2023 (credit: J. Edelson from AFP); (c) flooded airport in Fort Lauderdale, FL in April 2023 (credit: Miami-Herlad News); (d) flooding damage to I-10 highway near Desert Center, CA in August 2022 (credit: Fox Los Angeles) 19 2.2.1.2. Pluvial Flooding Pluvial (surface water) flooding occurs when the runoff caused by heavy and intense precipitation exceeds the capacity of the drainage system or absorption rate of the ground. The exceed water from the pluvial flooding can overflow on the neighboring lands and cause damages and disruptions to the daily lives of people. It is noted that the pluvial flooding typically occurs in relatively short periods from the intense precipitation (NSSL 2024b). As an example, the recent flooding in Detroit area, MI in 2023 was categorized as pluvial flooding [see Figure 6 (a)]. 2.2.1.3. Coastal Flooding Coastal flooding occurs along the coast when the sea-level rises higher above the neighboring lands. There are several weather events and mechanisms that can cause coastal flooding, some of which are explained below: • Storm-surge, which is defined as an abnormal sea-level rise during the storm. The storm- surge is mainly caused by the high-speed winds during the storm event. • Hurricane, which is defined as tropical cyclone with the maximum sustained wind speeds reach 74 mph. Intense rain, high wind speed, and thunderstorms are typically expected during the hurricane event. It is noted that a tropical cyclone is defined as low-pressure weather system that forms over the tropical or sub-tropical waters. • Tsunami, which is defined as giant wave approaching to the coast and caused by earthquake or volcanic eruption under the sea. • High-tide food, which is attributed to the combined effect of sea-level rise and local factors to push the water-levels higher than normal. Due to the sea-level rise, as a consequence of climate change, the coastal flooding can occur with less intense and minor local factors, such as storms, winds, or ocean currents. Therefore, a coastal flooding may occur even in a sunny day (NOAA 2024c). 2.2.1.4. Reservoir Flooding Reservoir flooding is mainly due to the failure of the reservoir structures, e.g., dam failure or overtopping of the water over a dam structure due to the heavy and intense rainfall (Qiu et al. 2021). Dam or levee failures can release a significant body of water and reservoir flooding in the downstream lands. In the less extreme case, heavy and intense precipitation can also input high 20 amount of water that exceeds the dam capacity and results in overtopping the water and reservoir flooding in the downstream. 2.2.1.5. Groundwater Flooding Groundwater flooding occurs when the groundwater-level in the underground aquifers rises, typically as the result of heavy and prolong precipitation. In other words, this type of flooding occurs when the recharge rate exceeds the underground aquifers capacity and therefore, overflow of the groundwater water onto the surface. It is noted that although the groundwater-level rise is typically happened in longer periods to cause groundwater flooding, once occurred, it is also last for extended periods. 2.2.1.6. Blocked Drainage System Flooding Flooding from a blocked drainage system happens when channels become obstructed, preventing water from being effectively expelled from the system. Such blockage can occur from debris accumulation carried by the flood waters, improper maintenance of drainage system, or complete inundation of the system. The blocked drainage system flooding typically occurs concurrently with other types of flooding and exacerbating the overall severity of the flooding. 2.3. Flooding Effects on Flexible Pavement Structures There are several studies in the pavement literature investigating the effect of flooding on the performance of flexible pavements, which found that flooding can cause considerable damage to the pavement structures through different mechanisms. These mechanisms include but not limited to erosion of the unbound layers, wash out of the pavement section, structural reduction, damages to the bituminous layers, etc. (Tao and Mallick 2020). This section aims to review the available literature and current state-of-knowledge on these mechanisms. Generally, the flooding damages to the pavement structures can be categorized in four patterns in terms of how fast the damage will occur to the pavement. Figure 7 conceptually shows these four flooding damage patterns, including: (i) Direct failure effect: This damage pattern is attributed to the rapid and severe loss of the pavement performance below the acceptable thresholds or immediate failure of the pavement sections due to the complete washout. Direct failure flooding effects are most expected in flash flooding events, in which the high-speed flood water can apply significant flood velocity load and damage the pavement structure. 21 Figure 7. Flooding damage patterns to the flexible pavement structures (regenerated based on similar figure in Lu et al. 2020) (ii) Delayed effect: This pattern of damage suggests that the immediate impact of flooding on pavement performance is negligible; however, the rate of deterioration in the pavement structure tends to accelerate after the flooding event. Delayed effects of flooding are anticipated when inundation leads to a higher degree of saturation in pavement layers, altering the structural response and causing increased damage over extended periods of time. (iii) Jump effect: This damage pattern represents the case where the pavement performance drops significantly after the flooding, while it can recover its normal state soon after the flooding event. Thus, the long-term performance of the pavement structure is not significantly affected. 22 (iv) Jump & delayed effect: This damage pattern is a combination of the jump and delayed damage patterns by which the pavement performance can drop significantly after the flooding event in short-term, while the deterioration rate of the pavement performance also increases in long-term periods (Lu et al. 2020). The direct failure flooding damage pattern to the pavement structures is typically caused by the flood velocity (water force) load. A study on the effect of flood velocity on the damages to pavement structures was conducted in 2009 on 134 pavement structures in Germany. Although details of the pavement sections (e.g., their type, age, structural properties, traffic, etc.) were not provided, it was reported that the flood velocity is the key parameter for flooding damages to the pavement structures (Kreibich et al. 2009). However, it is noted that the direct failure of the pavement structures due to the flood velocity loads is not the main focus of this research, as in most cases, such damaged pavement section reaches to the end of life and requires reconstruction. 2.3.1. Flooding Effects on AC layers Inundation is one of the effects of flooding on the pavement structures, in which a considerable body of water penetrates in the AC layers and increase their degree of saturation. Cracks and potholes can further facilitate this process. Several studies have investigated the moisture effects on the bituminous materials in AC layers. Little and Jones (2003) studied the chemical and mechanical processes of moisture damage in bituminous materials, in which they first reviewed the literature and classified the moisture damage mechanisms in six different groups, as provided below: • Detachment: Separation of the asphalt binder film from an aggregate surface by a thin film of water without an obvious break in the film (Majidzadeh and Brovold 1968). This mechanism also known as debonding. • Displacement: Displacement of the asphalt binder at the aggregate surface through breakage of the asphalt binder films by the water film (Fromm 1974, Tarrer and Wagh 1991). It is noted that although the detachment mechanism has more chemical and thermodynamic nature, the displacement mechanism has more of a mechanical nature (Mehrara and Khodaii 2013). 23 • Spontaneous emulsification: An inverted emulsion of water droplets in asphalt binder when the asphalt binder films are immersed in water which can break the adhesive bonds (Fromm 1974). • Pore pressure: Damage due to the development of the pore pressure in the trapped water within the asphalt mixture voids. Repeated traffic loading and thermal shuck can further aggravate this pore pressure buildup and accelerate the distress accumulation (Bhairampally et al. 2000). • Hydraulic scour: Suction of the water under the tire into the pavement by the tire action. The hydraulic scour occurs at the pavement surface (Fromm 1974, Kettil et al. 2005). • Environmental effect: Damage due to the environmental factors such as air temperature fluctuation, freeze-thaw cycles, aging of the asphalt, precipitation (Terrel and Al-Swailmi 1994). However, it has been emphasized that the occurrence of the moisture damage is not typically limited to only one mechanisms, while combination of several mechanisms can attribute to such damage (Little and Jones 2003). In other hand, the saturation of the AC layer during the flooding events can almost aggravate all the above-mentioned mechanisms, especially the development of the pore pressure and hydraulic scour. In particular, inundation of the pavement structure due to the flooding can saturate the AC layers by filling the asphalt mixture voids with water. Application of the traffic loading on such pavement structure applies compressive forces to the AC layers and leads to the buildup of the higher water pore pressures. This high pore pressure pushes the water out of the voids (toward out of asphalt mixture) which also can break the asphalt binder and aggregate bonds in their way out (Dawson 2014). Similarly, application of the traffic loading on the flooded pavement structure which still has at least a thin film of water on its surface can lead to the hydraulic scour effect. In this process, the water under the tire can be pushed into the asphalt mixture voids with a relatively high pressure because of the tire; subsequently, it can be expelled back through surface voids as the tire passes. Such process can break the aggregate and asphalt binder bonds. Moreover, the process of breaking the asphalt binder-aggregate bonds can be further facilitated with the aging of asphalt binder (Little and Jones 2003). 24 Flooding events can induce moisture damage to the AC layers through a combination of the before-mentioned mechanisms, which leads to the loss of bonding between the asphalt binders and aggregates. This bonding loss can eventually accelerate different pavement distresses, including asphalt stripping, raveling, degradation, etc. Asphalt stripping is defined as the separation of asphalt binder from the aggregates or rupture of the asphalt texture under the traffic load in presence of water (Mehrara and Khodaii 2013). It has been reported that the inadequate subsurface drainage system can allow the water and water vapor to accumulate in pavement layers and increase the asphalt stripping potential (Kandhal et al. 1989). The flooding event can inundate the pavement section for long periods, ranging from couple of hours to days or weeks. The intrusion of the flood water to the pavement section, especially when coupled with the traffic loading, can weaken the bonding between asphalt binder and aggregate and accelerate the asphalt stripping damage through various mechanisms, i.e., hydraulic scouring and pore pressure buildup. Raveling is another pavement distress, which is defined as the aggregate loss from the pavement surface due to the loss of mastic bridges between coarse aggregate particles. Raveling can reduce the ride quality of the road users and cause safety problems, e.g., its can lead to a pothole (Abouelsaad and White 2022). It has been reported that raveling damage grows with a “domino-like” trend. In other words, the removal of the first coarse aggregate particle diminishes support for adjacent aggregates, potentially hastening further aggregate loss and, consequently, leads to the formation of potholes (Kneepkens et al. 2004). Flooding events may also accelerate raveling distress by weakening the mastic bonds. This effect, combined with the deterioration of aged asphalt binder and damage from stripping, contributes to the mechanisms driving the raveling process. It has been reported that the areas on pavement surface that are exposed to standing water have higher raveling potential (Wolters 2003). The moisture effects on the fatigue cracking behavior asphalt mixtures have been evaluated using the laboratory testing and various advanced modeling methods (i.e., Viscoelastic Continuum Damage (VECD) theory), and it has been reported that the fatigue cracking resistant and fatigue life of the asphalt mixture materials significantly reduces in the presence of the moisture (Kim et al. 2004, Lee and Kim 2014, Yang et al. 2021). The moisture effect on fatigue damage can be observed in both higher levels of initial damage, as well as higher rates of damage evolution (Kim et al. 2004). This lower fatigue cracking resistance of the asphalt mixture in the presence of the 25 moisture can be represented with steeper pseudo stiffness versus damage, C(S), curves. In addition, moisture can also impact the rutting resistance of the asphalt mixtures. It has been reported that only one cycle of vacuum saturation can significantly reduce the rutting resistant of the asphalt mixtures (Sarsam and Alwan 2014). As previously noted, the impact of moisture on rutting and fatigue cracking in asphalt mixtures has been thoroughly investigated; however, the specific effects of flooding events on these types of distress in AC layers have not been directly documented in the literature. However, flooding events can introduce a significant body of water to the pavement structure which increases its moisture content. Therefore, an accelerated moisture damage can be expected during the flooding events and post-flood recovery time, up until the flood water drain out of the pavement structure. Finally, it has been reported that the flooding events can bring debris and cause safety issues, as well as erosion of the culverts and drainage system which reduce the water drainage rate from the pavement structure and aggravate the moisture induced damages (Vennapusa et al. 2013, Tao and Mallick 2020). 2.3.2. Flooding Effects on Unbound Layers Intrusion of the flood waters into the pavement structure can significantly change the moisture profile during the flooding events and post-flood recovery time, especially the unbound pavement layers can experience full saturation during the flooding events. This increased degree of saturation is either caused by infiltration of the flood water from the pavement surface or pavement lateral sides, and/or elevated groundwater tables. Reduction in the stiffness and rutting resistance of unbound pavement layers are the main consequence of increased degrees of saturation in these layers. Traditionally, the stiffness of the unbound materials is typically represented by the resilient modulus (MR) parameter. The moisture dependent nature of MR for unbound materials has been well-recognized in the geotechnical engineering literature. It has been reported by many studies that the MR of unbound materials reduces as the moisture contents increase above the optimum value (Hicks and Monismith 1971, Vuong 1992, Heydlinger et al. 1996). However, the amount of reduction in MR is highly sensitive to the soil type. For example, a 50% reduction in the MR of gravel and crushed stone soils used in AASHTO road test was reported when the degree of saturation increased from 70% to full saturation (Haynes and Yoder 1961), while another study 26 reported similar reduction of MR with only 5% increase in the degree of saturation (from 87% to 92%) for some Tennessee subgrade soils (Drumm et al. 1997). There are several models in the literature for predicting the MR of unbound materials as a function of moisture content or degree of saturation. In 1997, Drumm et al. evaluated 11 different subgrade soil samples throughout the state of Tennessee and proposed a linear model to predict the MR of fine-grained subgrade soils, as shown in Equation (2). In addition, they also proposed an empirical equation for estimating the rate of change in MR based on the subgrade soil classification (Drumm et al. 1997). 𝑀𝑅(𝑤𝑒𝑡) = 𝑀𝑅(𝑜𝑝𝑡) + 𝑑𝑀𝑅 𝑑𝑆 𝛥𝑆 𝑑𝑀𝑅 𝑑𝑆 = 1690 − 194 (𝐶𝐿𝐴𝑆𝑆) − 11.2 𝑀𝑅(𝑜𝑝𝑡) (2) (3) where: MR(opt) = resilient modulus at the optimum moisture content measured using confined deviatoric stresses of 41 kPa and 28 kPa (MPa). MR(wet) = resilient modulus at the increased moisture content state measured using confined and deviatoric stresses of 41 kPa and 28 kPa (MPa). 𝑑𝑀𝑅 𝑑𝑆 = rate of change in the resilient modulus with respect to the changes in the degree of saturation, as estimated in Equation (3). ΔS = change in the degree of saturation (decimal). CLASS = a real number representing the AASHTO soil classification, (e.g., for A-4, CLASS=4.0; for A-7-5, CLASS = 7.5). A sigmoid model for predicting the MR of both fine- and coarse-grained unbound materials as a function of degree of saturation was developed during the NCHRP 1-37A project and implemented in the early versions of the AASHTOWare Pavement ME. This model uses a sigmoid function in a log-log scale to estimate the ratio of the MR values at given degree of saturation over the optimum moisture content state, as shown in Equation (4) (ARA Inc. 2004). log 𝑀𝑅 𝑀𝑅𝑜𝑝𝑡 = 𝑎 + 𝑏 − 𝑎 1 + exp (𝛽 + 𝑘𝑠 ∙ (𝑆 − 𝑆𝑜𝑝𝑡)) (4) 27 where: MR = resilient modulus at the degree of saturation of interest (psi). MRopt = resilient modulus at the optimum moisture content (psi). a b β ks S = lower bound of sigmoid function, minimum value of the log(MR/MRopt). = upper bound of sigmoid function, maximum value of the log(MR/MRopt). = location parameter obtained as ln(-b/a). = calibration coefficients. = degree of saturation of interest (decimal). Sopt = degree of saturation at the optimum moisture content (decimal). In the lack of more material-specific data, NCHRP 1-37A proposed using the calibration coefficients as shown in Table 1. It is noted that the stress state at which the MR is calculated/measured is not direct input to this sigmoid model. However, the implementation procedure into the AASHTOWare Pavement ME showed that the MR at the optimum moisture content and stress state of interest is first calculated using the MR prediction models, and then Equation (4) used to estimate the MR at the same stress state and given degree of saturation (ARA Inc. 2004). Table 1. Calibration coefficients proposed by NCHRP 1-37A for Equation (4) Parameter a b β ks Coarse-grained material Fine-grained material -0.3123 0.3 -0.0401 6.8157 -0.5934 0.4 -0.3944 6.1324 Although the NCHRP 1-37A model for predicting the MR of unbound materials at different saturation levels used by many studies in the literature, there are many other models developed for this purpose, where some of them are listed below. • Jones and Witczak model for fine-grained subgrade soils (Jones and Witczak 1977). • Rada and Witczak model for base materials (Rada and Witczak 1981). • Li and Selig model for fine-grained subgrade soils (Li and Selig 1994). • Jin et al. model for coarse-grained subgrade soils (Jin et al. 1994). • Santha model for coarse- and fine-grained materials (Santha 1994). 28 • CRREL model for frozen coarse- and fine-grained materials (Berg et al. 1996). • Muhanna et al. model for fine-grained subgrade soils (Muhanna et al. 1998). • Liang et al. model for fine-grained subgrade soils (Liang et al. 2008). • Cary and Zapata model as improved MEPDG model for coarse- and fine-grained soils (Cary and Zapata 2010). On the other hand, it has been reported that the reduced MR of the unbound materials due to the increased moisture content is fully recoverable as the excess moisture drains from the pavement structure (Wang et al. 2015, Tao and Mallick 2020). In particular, Wang et al. conducted the MR testing on a localized subgrade soils in Hong Kong that were subjected to two wet/dry cycles. The results showed that the measured MR of the control samples were statistical the same as those experience one or two wet/dry cycles (Wang et al. 2015). The time needed for excess water to drain from unbound pavement layers and restore their initial stiffness can vary significantly. This variation depends on the properties of the materials and the drainage system. In this context, 'recovery time' is defined in the literature. It refers to the period from when flood water drops below the pavement surface until the moisture profile of the pavement structure returns to its pre-flood levels (Dawson 2014, Nivedya et al. 2020, Tao and Mallick 2020). Several studies have investigated the recovery time of the inundated pavement sections and reported that it can range from days to years, depending on physical and hydraulic material properties (e.g., permeability and gradation), as well as the efficiency of the pavement drainage system (Nivedya et al. 2020, Asadi et al. 2021). After the flood water recedes below the pavement surface, the pavement section experiences a loss of structural support due to the reduction in unbound material stiffness during the recovery time. Therefore, road agencies may consider restricting the heavy traffic loading on the flooded sections for a certain period of time, which is called “load restriction time”, to prevent accelerated structural damage accumulation. However, the recovery time of a pavement section to fully recover its initial structural capacity can last up to several months. Therefore, it might not be feasible to restrict the heavy traffic loading (usually truck traffic) on the flooded section during the recovery time. Thus, determination of the “load restriction time” after the flooding events is an important subject for the road agencies to minimize the structural damages while maintaining the functionality of the road network. It is also noted that although the recovery time is a function of 29 the material and drainage system properties, the “load restriction time” is determined by the road agencies and considered as the human decision effects on flooding damage to the infrastructures. The flooding events can also impact the rutting behavior of the unbound pavement layers. It has been reported that the rutting resistant of the unbound materials significantly reduces as the moisture content exceeds its optimum value (Ba et al. 2015). The current rutting model for the unbound layers includes two material-dependent calibration coefficients (ARA Inc. 2004). Several empirical equations have been developed for different unbound materials to estimate these model parameters as a function of water content, resilient modulus, stress state, etc. (Tseng and Lytton 1989, Wen et al. 2013, Ba et al. 2015). However, a comparison between the results of these studies shows that the rutting model parameters are highly dependent on the material type. In addition, full saturation was not considered in any of these studies. 2.3.3. Flooding Effects on Traffic Changes in the traffic patterns is the main indirect effect of the flooding events on the pavement performance. During the flooding event, the regular traffic is usually disrupted on the flooded pavement section. However, the traffic loading from the emergency vehicles and typically heavy debris removal trucks are usually inevitable. Application of this traffic loading on the flooded pavement section, which experience a significant reduction in structural capacity, can accelerate the damage accumulation. The data from the PMS in District 02 of Louisiana highlighted the significant impact of heavy debris removal trucks on accelerating damage to flooded pavement sections during hurricanes Katrina and Rita. (Chen and Zhang 2014). In addition, the occurrence of flooding events can also impact the neighboring unflooded pavement sections in the network. This impact is mainly due to the road closures and traffic detours which can overload the neighboring pavement sections. As an example, when a flooding event hits a major highway in an area, the relatively high traffic should follow the detours through the local pavement sections which are not initially designed for highway traffic loading. Therefore, although the neighboring local pavement sections are not actually flooded, they can experience accelerated damage accumulation due to the detours and road closure caused by flooding event on the major highway section. 30 2.4. Modeling of Flooding Effects on Flexible Pavement Performance Several studies tried to model the effects of flooding events on the performance of the flexible pavement sections using different analysis approaches. Although these approaches can widely differ from each other, each tries to address a certain problem ranging from designing more resilient pavement structures against flooding events to provide a network-level decision-making framework for road agencies during and after the flooding events. The current research classifies these different analysis approaches into four groups, including the pavement structural response- based models, mechanistic-empirical models, quantitative risk analysis models, and system dynamic models. 2.4.1. Pavement Structural Response-Based Models Some studies used the pavement structural responses, especially surface deflection, as an indicator of the pavement performance to model the flooding effects. Simplicity is the main advantage of this modeling approach, in which a LEA-based pavement structural response analysis model can be used to calculate some indicative pavement response, e.g., surface deflection, to evaluate the pavement performance under flooding conditions. Moreover, the flooding condition can be simply modeled by adjusting the modulus and interlayer bonding properties of the pavement layers. As an example, Elshaer et al. (2018) evaluated the flooding effects on the performance of 13 different pavement sections with three different base and three different subgrade soil types. This study uses two different analysis methods including, (i) AASHTO 1993 method in which the structural number (SN) is used as an indicator of performance, and (ii) LEA-based pavement structural response models in which the vertical and horizontal critical strain responses were used as an indicator of the pavement performance. The results of the analysis showed higher sensitivity of the rutting distress to the flooding events, where an increase of 15-80% was observed in critical vertical strain responses for saturated condition, while the increase in critical horizontal strains were about 6-15% (Elshaer and Daniel 2018). 2.4.2. Mechanistic-Empirical Models Some studies used the MEPDG approach for modeling the flooding effects on pavement performance, using the AASHTOWare Pavement ME software. The Enhanced Integrated Climatic Model (EICM) was deployed within this software to handle the climatic data for calculation of the pavement temperature and moisture profile during the pavement service life. According to the 31 MEPDG formulations, the moisture profile of the pavement can be used to predict the stiffness of the unbound layers, as previously discussed in section 2.3.2 (see page 26). Therefore, to study the flooding effects on pavement performance using the MEPDG approach, it is required to simulate the flooding condition with high precipitation input to the EICM model during the flooding event such that the degree of saturation in the pavement layers considerably increases. As the result, the MR of the unbound materials significantly reduces, which eventually changes the critical structural responses and accelerated damage accumulation. Lu et al. (2020) uses the AASHTOWare Pavement ME version 2.3 to model the effects of various flooding events on typical collector and arterial flexible pavement structures in Canada. They have modified the precipitation inputs to the EICM model based on the expected extreme values corresponds to the intense flood magnitudes with recuring periods of 50 to 200 years. The results of 72 different simulation scenarios were presented in terms of loss of pavement service life (based on IRI distress), which showed that a short-term flooding does not significantly damage the pavement structures, while the damage from long-term and repeated flooding events can be considerable (Lu et al. 2020). In another study in 2013, the sensitivity of the predicted pavement performance to the climatic inputs was studies using the MEPDG software version 1.1.0. More than 300 different simulations were performed for different climate inputs, traffic loadings, pavement types, etc. The results showed that the temperature range is the most sensitive input parameter, while the precipitation has a neglectable effect of the predicted performance of asphalt pavements (Li et al. 2013). However, it is noted that the MEPDG software used in this study did not consider the effect of surface infiltration in modeling the moisture profile and therefore, the insignificancy of the precipitation input cannot be fully valid. Qiao (2015) uses the MEPDG software version 1.1.0 to model 5 different typical flexible pavement structures across the United States. The results of an extensive sensitivity analysis for the climatic inputs showed that temperature is the most sensitive input, while the precipitation can only slightly affect the rutting and IRI distresses. The final conclusion states that the precipitation can have an influential effect on the pavement performances when coupled with high groundwater levels (Qiao 2015). Haider and Masud (2018) evaluated the precipitation effects on the performance of 44 flexible pavement structures across the United States from the LTPP database using the AASHTOWare 32 Pavement ME. Although the focus of this study was on the increased rate of precipitation infiltration in the presence of the pavement surface cracks, it has been reported that infiltrated moisture can reduce the MR of the base layer up to 33% and leads to about 30% higher surface cracking (Haider and Masud 2018). Matini et al. (2022) evaluated the effect of different flooding scenarios on the performance of typical pavement structures in North Carolina using the FlexPAVE version 2.0, which is an ME- based pavement analysis tool developed at North Carolina State University. Similar to the other studies with MEPDG formulation, the effect of flooding events in this study were also captured by increased moisture profile and reduction in MR of unbound pavement layers. The results showed that the predicted rutting during 10 years of analysis period can increase up to 19%, depending on the pavement structure, as well as the intensity and frequency of the flooding events (Matini et al. 2022). According to the reviewed literature, the effect of precipitation and flooding on the pavement performance could be underestimated using the MEPDG formulations. Main reason for this observation can be explained by the limitations of the MEPDG formulations, where they can only account for the loss of structural support (reduction in MR of unbound materials) during the flooding events, while the changes in damage resistance of pavement materials and traffic patterns are not implemented in this type of analysis. 2.4.3. Quantitative Risk-Analysis Models Quantitative risk-analysis models were developed due to the previous models' failure to account for the random nature of flooding events. Specifically, while other modeling approaches treat the start time, duration, and intensity of flooding events as deterministic inputs, the occurrence of future flooding events is inherently random. Wang et al. (2015) evaluated the flooding effects on the pavement performance using a quantitative risk-analysis model. In this model, the expected flooding damage during the pavement service life is calculated using Equation (5). where: 𝑘 𝐸𝑋𝑃(𝐷) = ∑ 𝐷𝑖 × 𝑛 × 𝑃𝑖 𝑖=1 𝑃𝑖 = 1 𝑇𝑖 33 (5) (6) EXP(D) = expected flooding damage during the pavement service life. n k Pi Ti = pavement analysis period (years). = number of flooding events during the pavement analysis period. = probability of the occurrence of ith flooding event. = recurrence interval of the ith flooding event. Di = damage caused by the ith flooding event. In this formulation, the damage is calculated using the Miner’s damage accumulation law, in which the critical pavement structural response under each flooding event is calculated using a LEA-based pavement response model for calculating the maximum number of allowable traffic passes. Then the damage is defined as the ratio of the traffic loading passes to the maximum number of allowable traffic passes. In addition, the confidence interval of the expected damage was then added based on the assumption of standard normal distribution. It is noted that these formulations assume the time independent flooding effects, which means similar floods occurs at different times will equally damage the pavement section. The results of this study showed that increasing the pavement thickness can reduce the detrimental effect of the flooding events (Wang et al. 2015). 2.4.4. System Dynamics models System dynamics is a computer-aided modeling method used to analyze and better understand complex systems and the effect of different components and inputs on the outcome of system. This analysis method is widely used with systems that involves feedback processes and time delays. System dynamics analysis method is typically characterized by its emphasis on stock-and-flow structures and feedback loops, which provide a detailed simulation of complex interactions in the system over time (Azar 2012). In system dynamics modeling of pavement structures, the interdependency of main and most sensitive input parameters and variables are modeled using different mathematical equations. Such model provides a mechanistically informed model with real-time analysis that integrates main pavement input parameters that affect the overall performance of the system. Mousavi et al. (2021) developed a system dynamic model to evaluate the flexible pavement performance under different moisture variations, using pavement surface deflection as an indicator. The model comprises three main components: (i) a hydrological component analyzing 34 moisture movements within the pavement structure, (ii) a geotechnical component adjusting the stiffness of unbound layers based on real-time moisture content, and (iii) a pavement response component employing a LEA-based structural response model to predict surface deflection. The results of a sensitivity analysis showed higher surface deflections during the flooding events. They have proposed the developed system dynamic model for preservation of the pavement structures during the flooding events and determination of the load restriction time for the flooded pavements (Mousavi et al. 2021). It is noted that the developed system dynamic model was published online, which is called PaveSafe™ software. 2.5. Chapter Conclusion This chapter provided the analysis results of a comprehensive literature search to evaluate the current practice and state-of-the-knowledge about the flooding effects and its modeling for flexible pavement structures. The literature search began by examining the climate change phenomenon, including its historical trends and future projections. The climate change observations and consequences were then reviewed with focus on the flooding events. In the second section, the significance of the flooding events, the flooding sources and damages, and the recent increasing trend of the floods were discussed. The third section focused on the major effects of flooding on pavement performance which is classified as the flooding effects on AC layers, unbound layers, and traffic patterns. Although the reviewed literature provided a big picture of the flooding effects on pavement structures, it is still required more research to better understand the effect of flooding and excess moisture on material and structural behavior of the flexible pavements, especially the AC layers. The next section provided different modeling approaches used for analyzing the flooding effects on pavement performances. These modeling approaches were then classified in four different groups, including the empirical pavement response-based models, mechanistic-empirical models, quantitative risk analysis models, and system dynamics models. The results of the reviewed literature showed that these different groups of models are not competitors of each other, while each group tried to address a particular aspect of the problem using a specific solution. 35 CHAPTER 3. MOTIVATION OF STUDY AND RESEARCH METHODOLOGY Climate change is a globally recognized phenomenon, and its extensive impacts on infrastructure, economics, and society have become increasingly evident. Among many different consequences of climate change, flooding can significantly damage the pavement infrastructure. Historical data showed an increasing trend in the frequency and intensity of flooding events across the United States. As the result, regions previously unaffected by major flooding events are now experiencing flooding damages. Chapter 2 included a comprehensive review of the literature regarding the effects of climate change and flooding on flexible pavement performance. However, an analysis of the reviewed literature revealed significant knowledge gaps in two critical areas: (i) the lack of unified ME- based pavement analysis tool to accurately quantify the flooding effects on flexible pavement distresses at both project and network levels, and (ii) the lack of a practical tool to evaluate the resiliency of the pavement network against the flooding events in national-level. Therefore, the main goal of this research is derived from the identified literature gaps to improve the understanding of the effects of flooding events on the performance of flexible pavements and evaluate the resiliency of the pavement network against the flooding events. To accomplish this goal, several specific objectives has been defined and illustrated in Figure 8. The first objective addresses the need for a ME-based pavement analysis tool to model the flexible pavement structures and predict the distress evolution during their service life. For this purpose, the MEPDG method was selected among different pavement analysis procedures, due to its well-established and widespread acceptance within pavement community. While several tools developed based on the MEPDG formulations (e.g., AASHTOWare Pavement ME), the main analysis engine of these tools are not publicly available for modifications and improvements. Therefore, the first objective of this research focused on the development of a pavement analysis program based on improved MEPDG formulations. To accomplish this objective, the Unified Pavement Distress Analysis and Prediction System (UPDAPS) program was developed during this research under a contract with Federal Highway Administration (FHWA). 36 Figure 8. Main goal and related objectives of this research Development of a framework to integrate the flooding effects on pavement performance into the ME analysis procedures is the second objective of this research. This framework was developed based on an extensive literature review aimed at identifying the specific impacts of flooding events on different pavement materials and traffic patterns, and subsequently incorporating these effects into the modeling procedure of MEPDG formulations. The third objective of this research focused on implementation of the proposed framework within a ME-based pavement analysis tool. For this purpose, the analysis engine of the UPDAPS program was modified to implement the proposed framework. The resulting modified version with the implementation of the proposed framework was named UPDAPS-Flood program. Ultimately, the results of the UPDAPS-Flood program underwent a validation process to successfully achieve this objective. The development of the UPDAPS-Flood program significantly enhances our ability to quantitatively analyze the effects of flooding on flexible pavement structures. However, to fully accomplish the main goal, the fourth objective of this research was to run UPDAPS-Flood program for thousands of pavement sections across the United States and evaluate the impacts of the flooding events on pavement performances at different geological locations subjected to different flooding patterns. The results of this analysis provide a baseline for assessing the resiliency of the 37 pavement network at the national level against the flooding events, through the concept of resiliency maps. The final objective of this research was to evaluate a potential corrective action to improve the resiliency of flexible pavements against flooding events. Among various strategies, this study focused on evaluating the effectiveness of geosynthetic reinforcement in enhancing the resiliency of flexible pavement structures under flooding conditions. To achieve this, a series of laboratory experiments were conducted to evaluate the mechanical behavior of geosynthetic-reinforced unbound base material. In the next step, the effect of geosynthetic reinforcement was modeled and integrated into the UPDAPS-Flood program. Finally, to fully accomplish this objective, two typical pavement structures in Michigan were simulated under both no-flood and flood scenarios to evaluate the impact of geosynthetic reinforcement on the resiliency of these pavement sections. In conclusion, the methodology of this research was designed to accomplish the objectives and main goal using several steps, as illustrated in the flowchart of Figure 9. Figure 9. Flowchart for the methodology of this research 38 CHAPTER 4. UPDAPS PROGRAM The development of Unified Pavement Distress Analysis and Prediction System (UPDAPS) program is detailed in this chapter. The UPDAPS program is an ME-based pavement analysis and design tool that was developed during this research under a contract with the Federal Highway Administration (FHWA). The UPDAPS program was developed in Python programming language for analysis of flexible, rigid, and composite pavement structures, encompassing both newly constructed and rehabilitated pavements. UPDAPS program uses the incremental damage accumulation approach to predict pavement distresses over time. Both Layered-Elastic Analysis (LEA) and Finite-Element Analysis (FEA) pavement response models were implemented into the UPDAPS program to calculate the critical pavement structural responses. In addition, the Viscoelastic Continuum Damage (VECD) theory was also implemented to calculate the fatigue cracking in the AC layers. It is noted that the UPDAPS program was developed and customized for running thousands of pavement sections through the parallel computing. It is noted that the UPDAPS program was originally developed based on technical procedures and distress prediction models of the Mechanistic-Empirical Asphalt Pavement Analysis (MEAPA) web-application. A comprehensive review of these models and procedures used in MEAPA web-application can be found elsewhere (Kutay et al. 2023). However, there were several improvements made during the development of the UPDAPS program. In order to efficiently organize the structure of the dissertation, a summary of these models and technical procedures used in UPDAPS program are moved to Appendix B, while this chapter mainly provides the improvements made during this research. In conclusion, a list of different components of the UPDAPS program for flexible pavements can be found in Table 2. This table also specifies the state of improvement of each component, where the unmodified components are provided in Appendix B. 4.1. Background A pavement analysis and design tool was required to achieve the main objective of this research to evaluate the flooding effects on the flexible pavement performance. For this purpose, two commonly used pavement analysis and design methods were reviewed to evaluate the possibility of implementing a framework with which the flooding effects can be incorporated in pavement design or analysis. The reviewed pavement analysis and design procedures include, AASHTO 39 1993 pavement design guide (AASHTO 1993), and MEPDG method from the NCHRP 1-37A (ARA Inc. 2004). Table 2. Components of the UPDAPS program No. Component name Process traffic data 1 Calculate dynamic modulus master curve 2 Define pavement structure sublayers 3 Calculate loading frequencies 4 Process climate data 5 Run global aging system model 6 Calculate undamaged state moduli of AC sublayers 7 Define critical analysis locations 8 Run thermal cracking model 9 Run pavement structural response model 10 Calculate fatigue cracking 11 Calculate reflective cracking 12 Calculate rutting 13 Calculate IRI 14 Improvement state Detailed discussion No No No Yes Yes No No Yes No Yes Yes No No No page 190 page 194 page 196 page 41 page 47 page 198 page 201 page 53 page 204 page 55 page 65 page 206 page 208 page 210 The AASHTO 1993 method requires much less input parameters compared with the MEPDG method. In addition, the MEDPG method employed more advanced models, which makes it more complicated and required trained staff for proper application. Therefore, it was preferable to use the simpler AASHTO 1993 method for evaluation of the flooding effects on pavement structures. However, the main inputs of the AASHTO 1993 method are traffic and structural properties, while the environmental inputs are not directly implemented. On the other hand, the AASHTO 1993 method is still used by many state DOTs and road agencies around the world. Therefore, in the first step, it was tried to improve the AASHTO 1993 method by incorporating the climate data analysis and asphalt mixture dynamic modulus master curve, which resulted in new procedure called “AASHTO 1993 Plus” pavement design method. More details about the development of this improved procedure and its results were published in 2023 (Abdollahi, Lanotte, et al. 2023). Although the enhanced AASHTO 1993 plus version incorporates climate data analysis, it remains insufficient for capturing the high-resolution effects of climate variations, including flooding, on pavement performance. Consequently, the more sophisticated MEPDG method was chosen for the analysis of flexible pavement structures, serving as a foundation for developing a framework to accurately assess the impact of flooding. 40 4.2. Model Improvements in UPDAPS Program According to Table 2, UPDAPS program for analysis and design of the flexible pavement structures consists of 14 different components, where major improvements were conducted on five components. These improvements and modifications are discussed below. 4.2.1. Improvements in Calculation of Loading Frequencies The traffic operational speed on the pavement surface is one of the key inputs to the flexible pavement analysis procedure, which directly affect the stiffness of the AC sublayers and pavement structural response as the result. The applied traffic load on the pavement surface produces stress pulses in the underlying layers that duration of which depends on the vehicle operation speed, pavement structure properties, and depth of the sublayer of interest. Figure 10 conceptually shows the stress pulse distribution due to a single wheel loading throughout a typical pavement structure. As this figure shows, the deeper sublayers experience higher duration of the stress pulse. Determination of the stress pulse duration (or loading frequency) at the middle of the AC sublayers is an important factor in pavement analysis, as the modulus of the AC sublayers are estimated from the |E*| master curves and is a function of stress pulse duration (or frequency) and temperature of AC sublayers. The loading frequency at the point of interest under the pavement surface is calculated by MEPDG method using the reciprocal of stress pulse duration. The UPDAPS program calculates the loading frequencies based on two different approaches; (i) the commonly used MEPDG formulation, and (ii) an improved approach based on the formulations of Losa and Natale (2012). Figure 10. Stress pulse duration distribution in a typical flexible pavement structure 41 4.2.1.1. MEPDG Approach MEPDG approach assumes a haversine shape for the stress pulse, duration of which defines as a function of vehicle operation speed and the depth of the point of interest bellow the pavement surface (ARA Inc. 2004). The effective length of the stress pulse (Leff) is defined as the extent of the stress pulse at a specific depth within the pavement structure. The slope of the stress distribution within the pavement structure is a function material stiffness, which is required for calculation of the Leff. The UPDAPS program employs a similar concept for calculating stress pulse duration, based on the principal assumption that stress loading is distributed in the soil at a 45- degree angle. Also, Odemark’s method is utilized to convert the actual pavement structure into the equivalent structure constructed of subgrade soil. The Odemark’s method was established in 1949 based on the assumption that in a multilayer system, the stresses and strains below a layer depend only on the bending stiffness of that specific layer. In other words, considering the change in the modulus and Poisson’s ratio of layer, one can keep the stresses and strains at the bottom of that specific layer constant by adjusting the thickness so that the same bending stiffness is provided. The concept of Odemark’s equivalent thickness is illustrated in Figure 11. The equivalent thickness of the upper layer using the Odemark’s method is calculated with Equation (7). Figure 11. Concept of equivalent thickness in Odemark's method 3 ℎ𝑒 = ℎ1 √ 𝐸1 𝐸2 × 2 1 − 𝜈2 2 1 − 𝜈1 (7) where: h1 he E1 = initial thickness of the upper layer (in). = equivalent thickness of the upper layer (in). = stiffness of the upper layer (psi). 42 E2 ν1 ν2 = stiffness of the lower layer (psi). = Poisson’s ratio of the upper layer. = Poisson’s ratio of the lower layer. Using the Odemark’s method, a pavement structure can be converted into another equivalent pavement structure with the modulus and Poisson’s ratio of the subgrade soil materials. Then, the effective length of the stress pulse can be calculated using the assumption of 45 slope of the stress distribution. 4.2.1.1.1. Effective Depth and Length for Different Axle Types After converting the actual pavement structure to the equivalent pavement structure, the effective length of the stress pulse (Leff) is calculated at the effective depth (Zeff) corresponding to the depth of interest in the actual pavement structure. It is noted that the effective depth is calculated using the Odemark’s method in inverse approach. The effective length of the stress pulse (Leff) at a specific depth under the wheel load is a function of the axle configuration. For a single axle, Leff is simply estimated using the 45 slope of stress distribution, while for multiple tire loading schemes, the effective length of the stress pulse is calculated based on the following assumptions: 1. It is assumed that there is no overlap between axles when the effective depth is less than half of the clear spacing between tandem axle wheels. 2. It is assumed that there is complete overlap between axles when the effective depth exceeds twice the tandem axle spacing. 3. It is assumed that there is partial overlap between axles when the effective depth is greater than half but less than twice the clear spacing between tandem axle wheels. Figure 12 conceptually shows the layout of the tandem wheel configuration in which Sxt represents the tandem axle spacing in the direction of the traffic. As this figure shows, there is no overlap between the stress slopes in the areas close to the pavement surface (effective depths less than clear space between the tandem axle wheels), while a complete overlap is assumed at the effective depths greater than twice of Sxt. 43 Figure 12. Effective length of stress pulse under tandem axle load Few details regarding the illustration in Figure 12 are listed below. • No overlap zone (Zeff < 0.5 Sxt - ac): The Leff at the no overlap zone is simply calculated using the 45 slope of stress distribution. It is also noted that two distinct stress pulses can be observed for the tandem axle load within the no overlap zone. Therefore, to account for the twin stress/strain peaks experienced by the pavement sublayers within the no overlap zone, the number of passing traffic tandem axle load are multiplied by the correction factor of two. Similar logic is also applied for the tridem and quad axle types, with correction factors of three and four, respectively. • Complete overlap zone (Zeff > 2 Sxt): It is assumed that the pavement structure experiences only one haversine stress pulse within the complete overlap zone. Therefore, the Leff at the complete overlap zone is calculated using the 45 slope of stress distribution with the loading area increased to the boundaries of both tire loadings. Also, a correction factor of one is also applied to the passing traffic tandem, tridem, and quad axle types. • Partial overlap zone (0.5 Sxt – ac < Zeff < 2 Sxt): Any point of interest within the partial overlap zone cannot experience neither two distinct stress pulse nor one haversine stress pulse. Therefore, a linear interpolation function in logarithmic scale is used for calculation of the Leff and traffic count correction factor within the partial overlap zone. Similar logic is also applied to the tridem and quad axle types. 44 4.2.1.1.2. Selection of the Loading Frequency for Analysis The calculated loading frequencies using the MEPDG approach are one of the main inputs to the dynamic modulus master curve for estimating the AC sublayer moduli values. However, the calculated loading frequencies depends on different factors, including axle load level, axle type, and stiffness of the sublayers (through the Odemark’s method). In other words, selection of the proper loading frequencies for the pavement analysis required realistic simplifications. Therefore, the MEDPG uses the calculated loading frequencies based on the 18-kips single axle dual tire load and predefined layer moduli values for calculation of the loading frequencies. Figure 13 shows the results of a sensitivity analysis of calculated loading frequencies to the axle load levels at different depths (mid-depth of different AC sublayers) using a single axle dual tire loading. As this figure shows, calculated loading frequencies are highly affected by the axle load level. One main reason for such high sensitivity to the axle load level is the assumption of constant 120 psi for tire pressure, which causes the tire contact radius to change considerably for different axle load levels. Figure 13. Loading frequency at different depths within a pavement structure, for different single axle load levels 4.2.1.2. Improved Approach Even though the MEPDG approach accounts for the influence of material stiffness, depth, and loading area radius on the calculated loading frequencies, these loading frequencies were observed to be relatively high (see Figure 13). An independent review of MEPDG approach for calculating the loading frequencies found that the resultant dynamic moduli are overestimated (Thompson et al. 2006). In an effort to address this issue, Al-Qadi et al. (2008) proposed a set of correction 45 factors to apply to the loading frequencies calculated by the MEPDG approach and calibrated on results obtained by a three-dimensional finite element (3D FE) viscoelastic model (Al-Qadi et al. 2008). In another effort, Losa and Natale (2012) proposed a set of empirical equations to estimate the loading frequencies based on the vehicle operational speed, loading area radius, temperature profile, and depth of the interest point (Losa and Natale 2012). The proposed formulations proposed by Losa and Natale are implemented into the UPDAPS program for estimating the loading frequency at the mid-depth of AC sublayers. For this purpose, the loading frequencies in X-, Y-, and Z-directions are calculated using Equations (8) to (10), respectively (Losa and Natale 2012). 𝑓𝑥 = 0.027 ∙ 𝑉𝑚𝑠 ∙ ( 1 2𝑎 + 1 2𝑏 ) ∙ exp(−3.14 ∙ 𝑧 + 𝛼(𝑇)) 𝑓𝑦 = 0.042 ∙ 𝑓𝑧 = 0.043 ∙ 𝑉𝑚𝑠 2𝑎 𝑉𝑚𝑠 2𝑎 ∙ exp(−3.34 ∙ 𝑧 + 𝛽(𝑇)) ∙ exp(−2.65 ∙ 𝑧 + 𝛽(𝑇)) α(𝑇) = 2.12 × 10−5 𝑇3 − 2.6 × 10−3 𝑇2 + 12.8 × 10−2 𝑇 𝛽(𝑇) = 1.25 × 10−5 𝑇3 − 1.6 × 10−3 𝑇2 + 9.2 × 10−2 𝑇 (8) (9) (10) (11) (12) where: fx fy fz = loading frequency in X-direction (Hz). = loading frequency in Y-direction (Hz). = loading frequency in Z-direction (Hz). Vms = vehicle operational speed (m/s). a b z T α β = half-length of the rectangular footprint in the motion direction (m). = half-width of the rectangular footprint in the transverse direction (m). = depth of the point of interest in asphalt concrete layer (m). = temperature at the point of interest (ºC). = effect of the temperature on the loading frequency in X-direction. = effect of the temperature on the loading frequency in Y- and Z-direction. 46 UPDAPS program calculates the length (or width) of the corresponding rectangular loading area for the proposed formulation using the area equivalency approach, as shown in Equation (13). where: 𝑎 = 𝑏 = √𝜋 2 𝑟 (13) r = radius of the equivalent circular loading area (in). It is noted that by using the improved approach, the correction factors for the passing traffic axle loads are still calculated using the MEPDG approach. 4.2.1.3. Comparison Between the MEPDG and Improved Approaches Figure 14 shows the distribution of calculated loading frequencies at the mid-depth of the AC sublayers of the HPMS MI2954 section using both MEPDG and improved approaches. It is noted that the vehicle’s operational speed in this pavement section was 60 mph, and it consists of 4 of the AC layer. As this figure shows, the MEPDG method computes a single frequency regardless of the temperature of each AC sublayer, whereas the improved method calculates a range of loading frequencies for different temperatures. The comparison of the results showed that the calculated loading frequencies using the improved approach were significantly lower than those calculated with the MEPDG approach. However, the difference between these two approaches is less in the deeper AC sublayers. 4.2.2. Process Climate Data The climatic model implemented into the UPDAPS program is almost identical to the Enhanced Integrated Climatic Model (EICM) in the MEPDG, except for three notable improvements. The climatic model is a one-dimensional finite difference procedure that simulates the diurnal and seasonal fluctuations in the temperature profiles within the pavement structure during the design life. Key inputs for the climatic model include hourly air temperature, wind speed, precipitation, and cloud cover, all of which are sourced from the Modern-Era Retrospective analysis for Research and Application, Version 2 (MERRA-2) database, provided by NASA. Details of the climatic model can be found either in the MEPDG (ARA Inc. 2004) or MEAPA web-application documentations (Kutay et al. 2023). However, the improvements to the climatic model are provided in the subsections below. 47 Figure 14. Comparison of the estimated loading frequencies at the middle of AC sublayers using the MEPDG and improved approaches 4.2.2.1. Improvements in Energy Balance at Pavement Surface The temperature at the pavement surface is mostly affected by the convection and radiation. The governing equation for the heat transfer phenomena between the pavement surface and the air during a sunny/partly cloudy day is shown Equation (14). 𝑄𝑠 + 𝑄𝑎 − 𝑄𝑒 ∓ 𝑄𝑐 ∓ 𝑄ℎ ∓ 𝑄𝑔 = 0 (14) where: Qa = heat flux resulting from long-wave radiation by atmosphere (Btu/ft2.hr). Qc = heat flux resulting from convection heat transfer (Btu/ft2.hr). Qe = heat flux resulting from long-wave radiation by pavement surface (Btu/ft2.hr). Qg = heat flux conducted into the pavement (Btu/ft2.hr). Qh = heat flux resulting from transpiration, condensation, evaporation, and sublimation (Btu/ft2.hr). 48 Qs = net short-wave radiation entering the energy balance at the pavement surface (Btu/ft2.hr). The net radiation flux is the sum of total short-wave radiations entering the energy balance and long-wave radiations emitted by the atmosphere minus long-wave radiation emitted by the pavement surface. Also, the net short-wave radiation is calculated by subtracting the incident short- wave radiations from reflected short-wave radiations, in which the percent sunshine, solar radiation and absorptivity coefficients are the main parameters. The climatic model of the UPDAPS program has two options for calculating the heat flux resulting from the long-wave radiations, including the original MEPDG formulations and the improved version with consideration of the cloud cover effect (Sugita and Brutsaert 1993, Forman and Margulis 2010, Alam-Khan et al. 2022). The heat flux resulting from long-wave radiation by atmosphere is calculated in the MEPDG formulations as a function of air temperature, vapor pressure, and some empirical constants. In addition, the heat flux resulting from long-wave radiation emitted by the pavement surface in the MEPDG formulation is calculated as a function of temperature of the surface node, emissivity, and Stephan-Boltzmann constant. This is while the improved formulation uses a correction factor as a function of the could base factor and percent sunshine to correct for heat fluxes resulting from long-wave radiations by the atmosphere and emitted from the pavement surface. Details of this correction can be found in MEAPA web- application documentation (Kutay et al. 2023). 4.2.2.2. Incorporation of the Sunrise/Sunset Time Algorithm Another improvement to the climatic model of the UPDAPS program is the inclusion of an algorithm for calculating the sunrise/sunset times for each specific location during the year. Such calculation is important in the calculation of the net radiation flux at the pavement surface. In the original MEPDG formulations, the average daily solar radiation is distributed over the daytime. For this purpose, Dempsey (1969) assumed the daytime as times between 6:00 AM and 6:00 PM and used a parabolic function to distribute the solar radiation over the daytime, as conceptually shown in Figure 15. 49 Figure 15. Hourly distribution of solar radiation between 6:00 AM to 6:00 PM (data source: Dempsey 1969) UPDAPS program incorporate an algorithm to calculate the sunrise/sunset times (and daytime as the result) as a function of the location and date to improve the distribution of the solar radiation over the daytime and the accuracy of the calculated pavement temperature profile. This algorithm was originally developed in MATLAB, then converted to Python programming language and implemented into the climatic model of the UPDAPS program. As an example, Figure 16 shows the calculated sunrise and sunset times for Lansing, MI within a whole year. Figure 16. Sunrise and sunset times over one year for Lansing, MI 4.2.2.3. Improvement of Surface Shortwave Absorptivity (SSA) Surface shortwave absorptivity (SSA) is an important input to the climatic model in ME-based pavement analysis procedures. SSA is an indicator of solar radiation absorbed by a pavement 50 surface and quantified as the coefficient of absorption. The coefficient of absorption is defined as the ratio of absorbed solar radiation by a body per unit area and unit time to the total incident solar radiation per unit area and unit time (Bohren and Clothiaux 2006). Many studies reported SSA in terms of albedo, which is the ratio of reflected solar radiation to the total solar radiation (albedo = 1 - SSA). SSA is a direct input to the climatic model of the ME-based pavement design procedures (i.e., EICM in MEPDG) for estimating the hourly temperature profile of a pavement section within its service life. Several studies evaluated the sensitivity of SSA on the predicted flexible pavement performance, focusing on the International Roughness Index (IRI), rutting, and cracking. These studies identified SSA as a significant input parameter (Hall et al. 2005, Schwartz et al. 2011). In a sensitivity analysis study performed in 2011 on about 26 different input parameters of AASHTOWare Pavement ME for flexible pavements, the SSA was found to be among the top five most sensitive input parameters for all predicted performances (Schwartz et al. 2011). Typically, the SSA values of a new or rehabilitated flexible pavements vary between 0.88-0.95 (Li 2012, Li et al. 2013), while it decreases with time down to a value of 0.6-0.7 by the end of the pavements service life (Richard et al. 2015, Alleman and Heitzman 2019, Garcia Mainieri et al. 2022). This reduction of SSA is mainly attributed to the change in the color of pavement surface due to the traffic action and/or environmental effects. It has been reported that the exposed aggregates on the pavement surface are prone to lose their coated asphalt binder, which changes the overall pavement surface color (Garcia Mainieri et al. 2022). Almost all ME-based pavement design software considers a constant SSA value as an input to compute the pavement structure temperature profile (ARA Inc. 2004), where an SSA value of 0.85 is typically assumed. However, given the significance of the SSA on pavement performance and its change during pavement service life, there is a gap in the literature regarding the implementation of the variable SSA parameter and its effect on the pavement performance. A time dependent SSA parameter was implemented in UPDAPS program to improve the accuracy of the calculated pavement temperature profile during the pavement service life. For this purpose, the SSA parameter in the UPDAPS program was modeled using Equation (15), which was originally developed based on the field observation results in the literature (Richard et al. 2015). 51 𝑺𝑺𝑨 = 1.1042 − 0.0133 ln(𝒕) (15) where: SSA = vector of the SSA values corresponding to the vector of the times t. t = vector of time values during the pavement life with monthly resolution (years). Later, the calculated SSA values are normalized between the minimum and maximum likely values of the SSA during the pavement life (e.g., starting at 0.95 and decreased to 0.70) using Equation (16). As an example, Figure 17 shows the variation of the time-dependent SSA values used in the UPDAPS program during 20 years of pavement service life. 𝑆𝑆𝐴𝑖 = 𝛼 − max(𝑺𝑺𝑨) − 𝑆𝑆𝐴𝑖 max(𝑺𝑺𝑨) − min(𝑺𝑺𝑨) (𝛼 − 𝛽) (16) where: α β = maximum expected value of the SSA. = minimum expected value of the SSA at the end of service life. SSAi = SSA value at the ith month during the pavement service life. Figure 17. Time dependent SSA parameter during 20 years of pavement service life In order to evaluate the implementation of the time-dependent SSA parameter, the UPDAPS program was run for 79,209 flexible pavement sections from the HPMS dataset using the time- dependent SSA, as well as the constant SSA values of 0.95, 0.85, and 0.70. Figure 18 shows summary of the results of the analysis, shown in terms of boxplots. As this figure shows, application of a higher constant SSA value resulted in higher prediction of total fatigue cracking and AC rutting, while the effect of SSA on the unbound rutting was minimal. However, the 52 predicted distresses using the implementation of time dependent SSA parameter showed closer alignment with those obtained using SSA value of 0.70. This is primarily attributed to major reduction of the SSA parameter during the early years of the pavement service life, which was imposed by the time-dependent SSA model as reported in the literature (Richard et al. 2015). Figure 18 also demonstrates that the predicted distresses using an SSA value of 0.85, extensively referenced in pavement literature, were considerably higher than those predicted when implementing a time-dependent SSA parameter. Specifically, the prediction of total fatigue cracking, AC rutting, and IRI using an SSA value of 0.85 were about 10.8%, 31.9%, and 5.1% higher, compared to those predicted using time-dependent SSA parameter, respectively. These findings indicate that employing a constant SSA value of 0.85 in the MEPDG may result in an overestimation of distress predictions. Consequently, it is recommended to implement a time- dependent SSA parameter or use an SSA value of 0.70 to enhance the accuracy of pavement performance analysis. 4.2.3. Define Critical Analysis Locations Pavement structural responses are evaluated at critical analysis locations, where extreme structural responses are expected. Determination of critical analysis locations for single wheel loading is usually straightforward, i.e., the critical analysis location for tensile horizontal strain is expected at the bottom of AC layer (vertically) and the center of the loading wheel (radially). However, the critical analysis locations for multiple-wheel loadings are a function of wheel configuration and load level. Therefore, UPDAPS program searches among the potential analysis locations to find the critical pavement structural responses. The critical analysis locations for single axle dual tire loading are shown in Figure 19. These critical analysis locations are selected using the intersection of the vertical and radial coordinates listed below. • Vertical (Z) direction (depth): pavement surface, 0.1 from the pavement surface (for top- down fatigue cracking), center of each sublayer, 0.1 from bottom of AC layer (for bottom- up fatigue cracking), top of subgrade layer, and 6.0 deep into the subgrade layer. • Radial (X) direction (transverse): center point between the dual tires, halfway between the center point of dual tires and the inner edge of the tire, inner edge of the tire, center of the 53 tire, outer edge of the tire, and then 4.0, 8.0, 16.0, 24.0, and 32.0 away from the outer edge of the tire. Figure 18. Effect of SSA parameter on (a) total fatigue cracking, (b) AC rutting, (c) unbound rutting, and (d) IRI Figure 19. Critical analysis locations for dual tire loading 54 The critical analysis locations for the tandem, tridem, and quad loading configurations are also shown in Figure 20, which are selected using similar criteria. In Z- and X-directions, the critical analysis locations are selected with the same criteria as for single axle dual tire, which herein called the XZ point cloud. In tandem axle configuration, three sets of XZ point clouds are placed in Y- direction at the centerline of the dual tires (only one of the axles) and at the midpoint between the axles. Similarly, in tridem and quad axle configurations, the XZ point clouds are placed along the centerlines of the dual tires for one of the outer axles and one middle axle, as well as the midpoint between these XY point clouds in Y-direction. This resulted in three and four sets of XZ point cloud for tridem and quad axle configurations, respectively. Figure 20. Critical analysis locations for (a) Single axle dual tire, (b) tandem axle dual tire, (c) tridem axle dual tire, (d) quad axle dual tire 4.2.4. Run Pavement Response Model Traditionally, the UPDAPS program, like many other ME-based pavement analysis tools, used the LEA-based pavement structural response model, called MatLEA. However, in order to model the stress-dependent nonlinearity of the unbound layers and geogrid-reinforcement, an efficient FEA-based pavement structural response model was developed and implemented into the UPDAPS program. This model, called MatFEA, uses an iterative approach to capture the stress- dependent nonlinearity and extra confinement due to the geogrid reinforcement. More details about 55 the development and verification of the MatFEA model can be found elsewhere (Abdollahi, Kutay, et al. 2023). 4.2.4.1. MatLEA (Layered-Elastic Analysis) MatLEA is a computationally efficient LEA program, which is implemented in UPDAPS program as a pavement structural response model. MatLEA was originally developed at Michigan State University using MATLAB programming language (Kutay et al. 2020). It was later converted into Python programming language to be more compatible with UPDAPS program. The matrix-based methodology, formulations, and computational steps of MatLEA is almost identical with those implemented in MnLayer program (Khazanovich and Wang 2007). Computational efficiency was the main goal behind the development of MatLEA. The “Numba” library was utilized to convert the MatLEA Python code into the machine code and improve its run time. As an example, the UPDAPS program calls the MatLEA 1200 times (20 years × 12 months per year × 5 temperature quantiles per month) during the analysis of HPMS MI2954 section, and it was found that the average run time of MatLEA was 144.9 milliseconds. 4.2.4.2. MatFEA (Finite-Element Analysis) MatFEA is a computationally efficient finite-element program specifically developed for analysis of flexible pavement structures using the 2D axisymmetric geometry. It is developed to serve as a pavement structural response model in the UPDAPS program. MatFEA was developed using the MATLAB® programming language, but it will be converted into the Python programming language to be more compatible for its implementation into the UPDAPS program. Details of formulations and development of the MatFEA model are published in the journal of “Transportation Research Record” (Abdollahi, Kutay, et al. 2023). The main objectives for the development of the MatFEA are capturing the effects of stress-dependent nonlinearity of the unbound layers, geogrid reinforcement, and improve computational efficiency. 4.2.4.2.1. Stress-dependent Nonlinearity of Unbound Layers It is well-known that the resilient modulus (MR) of unbound materials depends on the applied stress state. The unbound granular materials mainly exhibit stress-hardening behavior (Rada and Witczak 1981, Uzan 1992, Yau and Von Quintus 2002), where the MR values increase as the stress state increases. On the other hand, fine-grained unbound materials often exhibit stress-softening behavior (Thompson and Elliot 1985, Santha 1994, Yau and Von Quintus 2002), where the MR 56 decreases with increasing stress state. There are several models to estimate the MR of the unbound materials at different stress states, including but not limited to the k-θ model (Hicks and Monismith 1971), universal model (Witczak and Uzan 1988), NCHRP 1-37A model (ARA Inc. 2004), and bilinear model (Thompson and Robnett 1979). The analysis engine of the MatFEA program was developed to calculate the stress-dependent nonlinearity of the unbound materials through an iterative process. In other word, the stiffness of each element in each iteration updates based on the calculated stress state of that specific element in the previous iteration. For this purpose, although MatFEA can use any nonlinear model for updating the elemental stiffness matrix, the NCHRP 1-37A model was implemented as the default nonlinear model. As an example, Figure 21 shows the distribution of the MR within an unbound base layer of a typical pavement section with 4.0 AC layer and 8.0 base layer. As this figure shows, the modulus of the unbound base materials varies in a range of 15,000 to 40,000 psi, where higher MR are observed at the regions closer to the loading with higher stress states. Figure 21. Modulus distribution in a nonlinear base layer using MatFEA Application of the MatFEA as a pavement structural response model also offers the additional benefit of modeling the modulus of the AC layer in Z- directions for each finite element. Therefore, 57 there is no need to divide the AC layer into several thinner sublayers. An example distribution of the modulus within the AC layer is demonstrated in Figure 21. 4.2.4.2.2. Geogrid-Reinforcement It is well known that the Geogrids provide lateral reinforcement within the unbound materials, creating a zone that resembles confining stress. Based on this principle, NCHRP 1-50 project developed a model to calculate the extra confinement provided by the Geogrids within an unbound layer (Luo et al. 2017). This model was implemented into the MatFEA program to compute the structural responses of the Geogrid-reinforced pavements. However, it is noted that although the Geogrid-reinforcement is already implemented in MatFEA program, its final implementation into the UPDAPS program is still on-going. As an example, Figure 22 shows the distribution of the MR within a Geogrid-reinforced base layer of a typical pavement section, with layer thicknesses of 4.0 for the AC layer and 8.0 fir the base layer. As this figure shows, the Geogrid’s additional confinement resulted in a high modulus region around the Geogrid. However, this additional confinement effect diminishes as the distance from the geogrid increases, depending on the influence zone of the Geogrid. Figure 22. Modulus distribution in a geogrid-reinforced nonlinear base layer using MatFEA 58 4.2.4.2.3. Computational Efficiency During an ME analysis of a flexible pavement section, the pavement structural response model is called several times. For example, the pavement structural response model is called 1,200 for 20 years of simulation (1,200 = 20 years × 12 months per year × 5 quantiles per month). Most of the FEA-based pavement structural response models are relatively time-consuming which make them impractical for implementation in the ME pavement analysis procedures. However, a specialized dynamic mesh generation algorithm was developed and implemented in the MatFEA program, enabling the accurate calculation of pavement structural responses within a relatively short runtime. Figure 23 conceptually illustrates this dynamic mesh. As this figure shows, the mesh density is dynamically adjusted based on the expected stress state, where a fine mesh is provided at the areas close to the loading load centerline and geogrid. The average runtime for analysis of 12,000 different flexible pavement structures with the MatFEA program is about 1.13 seconds (Abdollahi, Kutay, et al. 2023). Figure 23. Conceptual illustration of dynamic mesh used in MatFEA 4.2.5. Pavement Structural Response Superposition Implementation of the pavement structural response superposition for the nonlinear structural responses is another improvement in the UPDAPS program. The application of the superposition concept to linear elastic materials is a common practice in pavement literature. However, applying this concept in conjugation with nonlinear pavement structural responses requires more caution. This is because the additional tire loading can change the modulus distribution within the nonlinear pavement layers, which eventually changes the pavement structural responses. 59 4.2.5.1. Superposition Principal The structural response of the pavement under multiple loadings is required for predicting pavement performance. The axisymmetric LEA and FEA pavement structural response models simulate a circular load due to a single tire on a pavement surface. Due to assumption of axisymmetry, it is not possible to directly simulate multiple tire loadings (e.g., dual tires, tandem axles, etc.) using this solution. Applying the concept of linear superposition, it is possible to use the structural responses under a single tire loading to calculate the critical structural responses under multiple loading. This principle assumes linear elastic behavior for the materials in the pavement layers during each temperature quantile of each month. Figure 24 illustrates the tire layout for different axle types, and the location of a point of interest for superposition. The center of the ith tire, and the point of interest, are located at coordinates (Xi, Yi) and (x, y), respectively. Figure 24. Loading tire layouts for different axle types, and illustration of a point of interest, in the XY plane In the superposition procedure, the distance (di) and angle to the X-axis (θi) for the point of interest for the ith loading tire are calculated using Equations (17) and (18), respectively. 𝑑𝑖 = √(𝑋𝑖 − 𝑥)2 + (𝑌𝑖 − 𝑦)2 𝜃𝑖 = tan−1 ( 𝑌𝑖 − 𝑦 𝑋𝑖 − 𝑥 ) (17) (18) where: 60 (rad) di θi Xi Yi x y = distance from point of interest to the center of ith loading tire (in) = angle to the X-axis for point of interest with respect to center of ith loading tire = X-coordinate of the center of ith loading tire (in) = Y-coordinate of the center of ith loading tire (in) = X-coordinate of the point of interest (in) = Y-coordinate of the point of interest (in) The di and θi parameters are calculated for every critical analysis location (see page 53) corresponding to each axle type (single, tandem, tridem, and quad). The structural responses under the single tire loading at radial distance of di and depth of the point of interest are extracted (or interpolated) from the MatLEA outputs to create the local strain matrix, as shown in Equation (19). The global strain matrix for each critical analysis location due to the ith loading tire is calculated based on the rotation matrix [Equation (20)] using the Equation (21). [𝜺]3×3 = [ 𝜀𝑟 0 𝜀𝑟𝑧 0 𝜀𝑡 0 𝜀𝑟𝑧 0 𝜀𝑧 ] [𝑹]3×3 = [ cos 𝜃 − sin 𝜃 0 0 sin 𝜃 1 0 cos 𝜃 0 ] 𝜀𝑥𝑥 𝜀𝑦𝑥 𝜀𝑧𝑥 [ 𝜀𝑥𝑦 𝜀𝑦𝑦 𝜀𝑧𝑦 𝜀𝑥𝑧 𝜀𝑦𝑧 𝜀𝑧𝑧 ] = [𝑹] × [𝜺] × [𝑹]𝑇 R = rotation matrix (19) (20) (21) ε εxx εxy εxz εyx εyy εyz εzx = local strain matrix = global normal strain component in X-direction = global shear strain component in Y-direction and perpendicular to YZ-plane = global shear strain component in Z-direction and perpendicular to YZ-plane = global shear strain component in X-direction and perpendicular to XZ-plane = global normal strain component in Y-direction = global shear strain component in Z-direction and perpendicular to XZ-plane = global shear strain component in X-direction and perpendicular to XY-plane 61 εzy εzz εr εt εz = global shear strain component in Y-direction and perpendicular to XY-plane = global normal strain component in X-direction = local radial strain = local tangential strain = local vertical strain εrz = local shear strain For each critical analysis location, the final step in the calculation of the superposed strains is to sum up the calculated global strain components due to the different loading tires in the axle layout. A similar approach is used for superposition of the stresses under multiple loading tires. 4.2.5.2. Superposition Principal for Nonlinear Pavement Systems The application of the linear superposition method is only valid for linear elastic solutions, i.e., the results of the MatLEA pavement structural response model. Therefore, more cautious required when the superposition method used on the results of nonlinear solutions, e.g., results of the MatFEA with nonlinear unbound layers or Geogrid-reinforcement. To overcome this issue and use the superposition concept with MatFEA results, the superposition of the dual tires was incorporated within the nonlinear convergence iteration of the MatFEA program. 4.2.6. Nonlinear Load-Strain Behavior The UPDAPS program enhances the accuracy of calculating critical structural responses by accounting for nonlinear load-strain behavior. In contrast, the original MEPDG and MEAPA formulations assume a linear load-strain relationship to simplify the modeling of flexible pavement structures and reduce computational effort. In MEPDG and MEAPA, in each temperature quantile in each month, pavement structural response (stresses and strains) is computed using a standard 18-kip single axle load. The strains are then assumed to be linearly proportional to the applied axle load, allowing extrapolation of critical strains for the entire traffic load spectrum based on the standard 18-kip single axle load. Although the superposition concept allows consideration of different axle configurations – such as tandem tridem, and quad axles – the LEA analysis is only conducted for the 18-kip single axle load. In order to evaluate the linear load-strain behavior assumption, four analysis points of A, B, C, and D were considered under the tandem axle configuration and at the bottom of the AC layer for the HPMS MI2954 section, as shown in Figure 25. 62 Figure 25. Top view of the points used to evaluate the linear load-strain behavior under tandem axle loading Figure 26 compares the linear load-strain behavior assumption against the actual calculation of the strain response after running MatLEA and the superposition algorithm for each load level. This figure shows that the application of linear load-strain behavior can result in a significant deviation from the actual strain responses at the critical locations close to the loading tire (points A and B), while this difference is mitigated in the areas far from the loading tires (points C and D). In particular, Figure 26 (b) shows that the linear load-strain behavior assumption can lead to a non-representative trend in the prediction of critical strain responses. Thyagarajan et al. (2009) showed that the assumption of linear load-strain behavior has a considerable impact on rutting predictions. They also introduced a ‘three-point extrapolation method’ to calculate the critical strain responses at three distinct load levels (Thyagarajan et al. 2009). 63 Figure 26. Evaluation of linear load-strain behavior for tandem axle at the bottom of AC layer. HPMS MI2954 section. (a) Principal strain at point A, (b) strain XX at point B, (c) strain ZZ at point C, (d) shear strain XZ at point D This three-point extrapolation method was implemented in UPDAPS program. Figure 27 shows a comparison between the pavement responses using the application of the three-point extrapolation against the actual strain responses calculated by running MatLEA at each load level. The three-point extrapolation method in UPDAPS program used the 4,000, 18,000, and 30,000 lbs single axle loads, and their corresponding load levels in tandem, tridem, and quad axle types. As the results shows, the application of the three-point extrapolation method improved the accuracy of the prediction of the strain responses at different load levels. Finally, it is noted that the three- point extrapolation method is used for both LEA and FEA pavement structural response models. 64 Figure 27. Evaluation of 3-point extrapolation method for tandem axle at the bottom of AC layer in HPMS MI2954 section using: (a) principal strain at point A; (b) strain XX at point B; (c) strain ZZ at point C; (d) shear strain XZ at point D 4.2.7. Calculation of Fatigue Cracking Implementation of the Viscoelastic Continuum Damage (VECD) theory in the fatigue cracking model is one of the most significant improvements in the UPDAPS program. This model uses the VECD theory to calculate the damaged state of AC sublayers and transfer functions to convert the induced damage to the observed fatigue cracking in the field. An overview of the fatigue cracking model is shown in Figure 28, where this model can be summarized into three basic steps listed below. 1. Calculation of the representative critical strain of each AC sublayer at each temperature quantile under different axle types and load levels. 2. Performing VECD analysis to calculate the damage parameter and pseudo-stiffness of each AC sublayer at each temperature quantile during the pavement life. 65 3. Translating the calculated damage into the corresponding fatigue cracking observed in the field. Figure 28. Flowchart for fatigue cracking model in UPDAPS program 66 4.2.7.1. Calculation of Representative Critical Strain Calculation of the representative critical strains for each AC sublayer due to the loading of a given axle types and load level can be summarized in four steps, as listed below. • Running the pavement structural response model (either MatLEA or MatFEA) for a given temperature quantile during the pavement service life to calculate the structural responses under single tire loading at the reference axle load levels. The damaged state modulus of each AC sublayer is used for calculating the structural responses. • Calculating the principal tensile strains at the mid-depth of each AC sublayer and critical analysis locations using the superposition concept. The principal tensile strain is used as a critical strain representation of each AC sublayer. • Defining the critical strain of each AC sublayer under a given loading condition (combination of all axle types and reference load levels) as the maximum principal tensile strain among the corresponding critical locations. • Calculating the critical strain for each AC sublayer under each loading condition (combination of all axle types and load levels) by interpolating/extrapolating the calculated critical strains in the previous step. 4.2.7.1.1. Running Pavement Structural Response Model In this step, the structural responses of the pavement structure are calculated under single tire loading at the reference load levels. Depending on the material properties (existence of the nonlinear unbound layer), the MatLEA or MatFEA pavement structural response models can be used. The modulus for each AC sublayer in undamaged state is calculated using the |E*| master curve based on the corresponding equivalent loading frequency and temperature at the mid-depth of that AC sublayer (see page 201). However, as the AC sublayers are damaged during the pavement service life, the damaged state modulus is used in pavement structural response model to calculate the structural responses. The damaged state modulus of each AC sublayer is calculated based on the Pseudo-stiffness (C) concept using Equation (22). More details about the VECD theory are provided later (see page 74). |𝐸∗|𝑖,𝑗 = 𝐶𝑖,𝑗 × |𝐸∗|LVE 𝑖,𝑗 (22) 67 where: |E*|i,j = damaged state modulus of the jth AC sublayer at the ith temperature quantile (psi). |E*|LVE i,j= undamaged state modulus of the jth AC sublayer at the ith temperature quantile (psi). Ci,j = pseudo-stiffness of the jth AC sublayer at the ith temperature quantile. It is noted that the pseudo-stiffness parameter for each AC sublayer is updated at the end of each temperature quantile during the pavement service life. This parameter is used to calculate the damaged state modulus of AC sublayers at the beginning of the next temperature quantile. 4.2.7.1.2. Calculating Principal Tensile Strain at Critical Analysis Locations In this step, the principal tensile strain at the mid-depth of each AC sublayer and critical analysis locations is calculated using the superposition concept. More details of the critical analysis locations (see page 53) and superposition procedure (see page 59) are provided in the previous sections. As an example, the principal tensile strains were calculated at the lowermost AC sublayer of the HPMS MI2954 section, for the first temperature quantile, for single (18-kips) and tandem (36-kips) axle types. The results are shown in Figure 29 and Figure 30, respectively. These figures plot the principal tensile strains calculated at different critical analysis locations in the X- and Y- directions. These results are used in wheel wander analysis, as well as in the definition of the critical strains for each AC sublayer. 68 Figure 29. Lowermost AC sublayer, section HPMS MI2954 under a 36-kips tandem axle load. (a) Critical analysis locations, (b) principal tensile strains calculated at the critical analysis locations Figure 30. Lowermost AC sublayer, section HPMS MI2954 under a 36-kips tandem axle load. (a) Critical analysis locations, (b) principal tensile strains calculated at the critical analysis locations 69 4.2.7.1.3. Defining Critical Strain Representation of Each AC Sublayer The MEPDG method used the horizontal tensile strain (either in X- or Y-directions) at the bottom of the AC layer and pavement surface in the bottom-up and top-down fatigue cracking models, respectively (ARA Inc. 2004). On the other hand, the fatigue cracking model of UPDAPS program uses the principal tensile strain at the mid-depth of each AC sublayer to represent the strain state of that specific AC sublayer. The principal tensile strain was selected because it reflects the true three-dimensional strain state regardless of the user-defined cartesian coordinate system. This is based on the premise that the material will crack in the direction it chooses, not necessarily in the direction of a cartesian coordinate system user/modeler chooses. In addition, there is a considerable shear strain field around the tire edges which is neglected by the fatigue cracking models using horizontal strains, which is a user-selected cartesian direction. Application of the principal tensile strains takes the ture 3D strain state of the material into account. The principal tensile strain was also used in the top-down fatigue cracking model of the Mechanistic-Empirical Asphalt Pavement Analysis (MEAPA) web application (Ghazavi et al. 2022, Kutay et al. 2023). Similarly, the application of the principal tensile strain at the mid-depth of the AC sublayers can effectively simulate the strain state and potential damage vulnerability of each AC sublayer. This is the case because the amount of principal tensile strain maximizes at the surface and bottom of the AC layer. This makes sense as the cracks are expected to initiate from the surface (top-down fatigue cracks) or bottom (bottom-up fatigue cracks) of the AC layer. In this regard, Figure 31 compares the radial and major principal strain fields under an 18-kips single axle load for the first temperature quantile in section HPMS MI2954. As shown, more tensile strains are observed when major principal strain is used (see area with dashed line in Figure 31 (b)). These ‘excesses’ of tensile strains are also observed close to the tire edge near the pavement surface, where they propagate toward the centerline, and from there down towards the bottom of AC layer. The critical strain in this study is defined for a given AC sublayer and each of the critical analysis locations in the X-direction as the maximum of the principal tensile strains calculated at different points along the Y-direction. The main reason for calculating critical strains as a function of X-coordinates is the wheel wander analysis. Figure 32 shows the critical strain as a function of X-coordinates for the HPMS MI2954 section under different axle types and standard axle load levels (4,500 lbs per tire). As this figure shows, loading from different axle types resulted in similar critical strain responses. It is noted that in the case of the compressive major principal strain at the 70 mid-depth of any AC sublayer, the critical strain is assumed to be zero (to avoid negative values for critical strain). Figure 31. MatLEA results for structural strain responses, HPMS MI2954 section. Positive values indicate compression. (a) Radial strain, (b) major principal strain Figure 32. Critical strain at the lowermost AC sublayer, section HPMS MI2954 under different axle types. (a) Pavement section in the XZ plane. (b) Critical strains as a function of X-coordinate for different axle types 71 4.2.7.1.4. Calculating Critical Strains at Different Axle Load Levels Considering the nonlinear load-strain behavior, the critical strains at different X-coordinates are calculated at three different axle load levels, which are selected based on the three-point extrapolation method (see page 62). In this step, the critical strains are linearly inter-/extrapolated for all axle load levels. Figure 33 shows the results of linear interpolation and extrapolation of the critical strain under a tandem axle in a three-dimensional plane. The reference axle load levels are also shown in the figure as blue, red, and black lines. 4.2.7.2. Performing VECD Analysis The fatigue cracking model in the UPDAPS program is based on the VECD analysis. The VECD constitutive model adopts the elastic-viscoelastic correspondence principle and Schapery’s work potential theory (Schapery 1990) to model the mechanical behavior of the asphalt mixture. The VECD modeling approach can describe the fatigue cracking behavior for traditional and polymer-modified asphalt mixtures (Underwood et al. 2006, Kutay et al. 2008). Figure 33. Results of inter-/extrapolation of the critical strains at the lowermost AC sublayer, section HPMS MI2954 72 4.2.7.2.1. C versus S curve The C versus S curve is one of the key elements of the VECD analysis. The pseudo-stiffness (C) is a VECD parameter to quantify the deviation of the stress response of the material from its pseudo-strain (εR) as damage accumulates in the continuum material, as shown in Equations (23) and (24). 𝐶(𝑡) = 𝜎(𝑡) 𝜀𝑅(𝑡) 𝜀𝑅(𝑡) = 𝑡 1 𝐸𝑅 ∫ 𝐸(𝑡 − 𝜏) 0 𝜕𝜀 𝜕𝜏 𝑑𝜏 (23) (24) where: C(t) = pseudo-stiffness at loading time t. εR(t) = pseudo-strain at load time t (psi). σ(t) = stress function at loading time t (psi). ER = reference modulus of the material (psi). ε(t) = strain function at the loading time t. τ = time variable of integration (s). More practical definition of C is the ratio of modulus at a certain loading cycle to the initial (undamaged state) modulus of the asphalt mixture, as shown in Equation (25). 𝐶(𝑁) = |𝐸∗|𝑁 |𝐸∗|LVE (25) where: |E*|N = dynamic modulus of the asphalt mixture at Nth load cycle (psi). |E*|LVE = undamaged state (initial) dynamic modulus of the asphalt mixture (psi). On the other hand, the damage parameter (S) is a fictitious parameter representing the extent of the microcracks within the material (Kutay and Lanotte 2018). Figure 34 shows a conceptual C vs. S curve for an asphalt mixture. The main idea of the VECD modeling is that the C vs. S curve for a particular asphalt mixture is independent of temperature, magnitude, loading rate, and mode of loading, as illustrated in Figure 34. In other words, once the C vs. S curve of an AC is calculated using a single test run at a certain temperature/loading rate/loading mode, the stress-strain behavior 73 of that AC can be calculated under any other temperature, loading rate or loading mode (Kutay and Lanotte 2018). The C vs. S curve is usually modeled using an exponential function, as shown in Equation (26). However, Kutay and Lanotte (2018) use Equation (27), which significantly reduces the mathematical effort during the VECD analysis. Figure 34. Conceptual C vs. S curve for an asphalt mixture material 𝐶(𝑆) = exp(𝑎𝑆𝑏) 𝐶(𝑆) = 1 − 𝑎 ∙ 𝑆𝑏 (26) (27) where: a, b = model coefficients. It is noted that the a and b coefficients of these two models are not identical, which means that for a given asphalt mixture, a separate set of coefficients should be fitted for each of these models. 4.2.7.2.2. VECD model formulation at Material-Level Lanotte and Kutay developed a step-by-step procedure for modeling the fatigue cracking of the pavement section in the accelerated pavement testing (APT) facility of the Turner-Fairbank highway research center (Lanotte and Kutay 2018). The original formulations are based on the 74 methodology developed by Kutay et al. (2008). A modified version of this method is implemented in the fatigue cracking model of UPDAPS program. In the implemented VECD model, the mathematical relationships between the damage parameter, pseudo-stiffness, and the number of loading cycles are shown in Equation (28), which was developed based push-pull fatigue testing (Lanotte and Kutay 2018). 𝑑𝑁 = (− 1 2 (𝜀0 ∙ |𝐸∗|𝐿𝑉𝐸)2 𝜕𝐶 𝜕𝑆 −𝑛 ) 𝑓𝑟𝑒𝑑𝑑𝑆 (28) where: N = number of loading cycles. ε0 = peak strain value during the push-pull fatigue testing. fred = reduced frequency (Hz). n = damage growth rate. The simplified power model for the C vs. S curve [Equation (27)] is used in the VECD model, where its partial derivative with respect to damage parameter is shown in Equation (29). 𝜕𝐶 𝜕𝑆 = −𝑎 ∙ 𝑏 ∙ 𝑆𝑏−1 (29) where all parameters were previously defined. After substituting the partial derivative of the C vs. S curve into the Equation (28), and integrating between zero and the number of load cycles at time t (Nt), it can be rewritten as shown in Equation (30). 𝑁(𝑡) = 𝑓𝑟𝑒𝑑 −𝑛 ∙ 𝑏 + 𝑛 + 1 𝑎 ∙ 𝑏 ( 2 −𝑛 ) (𝜀0 ∙ |𝐸∗|𝐿𝑉𝐸)−2𝑛𝑆(𝑡)−𝑛∙𝑏+𝑛+1 (30) where: N(t) = number of applied load cycles at the time t. S(t) = damage parameter at the time t. In order to simplify the calculations in the VECD modeling, Equation (30) is rearranged as shown in Equation (31). 𝑁(𝑡) = 𝐴 ∙ 𝐵 ∙ 𝑆𝜓(𝑡) −𝑛 𝐴 = 𝑓𝑟𝑒𝑑 𝜓 𝑎 ∙ 𝑏 ( 2 ) 75 (31) (32) 𝐵 = (𝜀0 ∙ |𝐸∗|𝐿𝑉𝐸)−2𝑛 𝜓 = −𝑛 ∙ 𝑏 + 𝑛 + 1 (33) (34) where all parameters were previously defined. In the rearranged form for the equation of the number of load cycles, the A parameter is a function of the reduced frequency, while the B parameter is a function of the applied peak strain. Moreover, Equation (31) can be rearranged to calculate the damage parameter from the applied number of load cycles as shown in Equation (35). 𝑆(𝑡) = ( 1 𝜓 ) 𝛮(𝑡) 𝛢 ∙ 𝛣 (35) where all parameters were previously defined. 4.2.7.2.3. VECD Fatigue Cracking Model Implementation in UPDAPS Program In order to implement the VECD model formulations into the fatigue cracking model of UPDAPS program, the damage parameter for each AC sublayer is updated based on the passing traffic axle loads during each temperature quantile. For this purpose, first the A, B, and ψ parameters are calculated for each temperature quantile during the pavement service life. It is noted that the A parameter is a function of the reduced frequency, which is unique for each AC sublayer during a given temperature quantile. The applied peak strain in the push-pull fatigue testing corresponds to the critical strain at each AC sublayer, as calculated using the pavement structural response model (see page 65). Therefore, the B parameter is a function of the critical strains due to the loading condition (combination of axle types and axle load levels). Moreover, the B parameter is also a function of X-coordinates, and it is used in the implementation of the effect of wheel wander. In the next step, the incremental damage parameter (ΔS) is calculated for each temperature quantile and AC sublayer as a function of X-coordinates. However, the damage parameter of each AC sublayer (Sj) is updated with every application of an axle loading, as it has an increasing- behavior due to the growth of damage. Therefore, the ΔS as a function of X-coordinates is calculated using the current Sj (current damage state) before the application of the axle loading. For this purpose, the equivalent number of load cycles as a function of X-coordinates is calculated for each temperature quantile and AC sublayer for the specific loading conditions, as shown in the Equation (36): 76 𝑒𝑞 𝑁𝑖,𝑗,𝑘,𝑙 (𝑋) = 𝐴𝑖,𝑗 ∙ 𝐵𝑖,𝑗,𝑘,𝑙(𝑋). 𝑆𝑗 (36) Neq i,j,k,l(X) = equivalent number of loading cycles at the ith temperature quantile, jth AC sublayer, kth axle type, and lth axle load level as a function of X-coordinates. Ai,j = A parameter at the ith temperature quantile and jth AC sublayer. Bi,j,k,l(X) = B parameter at the ith temperature quantile, jth AC sublayer, kth axle type, and lth axle load level. Sj X = current damage parameter at the jth AC sublayer. = coordinate along X-axis (in). The ΔS as a function of X-coordinates is calculated using Equation (37): 𝛥𝑆𝑖,𝑗,𝑘,𝑙(𝑋) = ( 𝑒𝑞 𝑁𝑖,𝑗,𝑘,𝑙 (𝑋) + 𝛥𝑁𝑖,𝑘,𝑙 𝐴𝑖,𝑗 ∙ 𝐵𝑖,𝑗,𝑘,𝑙(𝑋) 1 𝜓 ) − 𝑆𝑗 (37) ΔSi,j,k,l(X) = incremental damage parameter at the ith temperature quantile and jth AC sublayer due to the passing of kth axle type with lth axle load level as a function of X-coordinates. ΔNi,k,l = number of passes of kth axle type with lth axle load level during the ith temperature quantile. The ΔS values are used to calculate the effect of wheel wander and update the current damage parameter (Sj) of the AC sublayer. The current Sj for the ith temperature quantile and jth AC sublayer due to the kth axle type with lth axle load level is updated using Equation (38). 𝑆𝑗 = max [( 𝑒𝑞 𝑁𝑖,𝑗,𝑘,𝑙 (𝑋) + 𝛥𝑁𝑖,𝑘,𝑙 𝐴𝑖,𝑗 ∙ 𝐵𝑖,𝑗,𝑘,𝑙(𝑋) 1 𝜓 ) ] (38) where all parameters were previously defined. It is noted that the damage parameter of the jth AC sublayer during the ith temperature quantile is updated for each combination of axle types and axle load levels, which means the equivalent number of passes [Equation (36)] and the corresponding updated damage parameter [Equation (38)] are calculated for all combinations of k and l indicators. In the next step, the pseudo-stiffness parameter of each AC sublayer is updated at the end of each temperature quantile using Equation (39). The updated pseudo-stiffness is used for 77 calculating the damaged state modulus of the AC sublayers, which is an input to the pavement structural response model for the analyses in the next temperature quantile. 𝑏 𝐶𝑖,𝑗 = 1 − 𝑎 ∙ 𝑆𝑗 (39) where: Ci,j = pseudo-stiffness of the jth AC sublayer at the end of the ith temperature quantile. Sj = damage parameter of the jth AC sublayer at the end of the ith temperature quantile. As an example, Figure 161 shows the evolution of the pseudo-stiffness and damage parameters for the uppermost and lowermost AC sublayers of section HPMS MI2954 during the 20 year pavement analysis period. Figure 35. VECD model results for section HPMS MI2954. (a) Damage parameter, (b) pseudo-stiffness 4.2.7.2.4. Inclusion of Wheel Wander Effects In the next step, the maximum value of the ΔS distribution in the X-direction for each axle type/load level is calculated with consideration of the wheel wander effect, where details of which are provided in page 82. Then, this updated value is used to update the damage parameter at a specific temperature quantile and AC sublayer. 4.2.7.3. Transfer Induced Damage to Field Fatigue Cracking The fatigue cracking model in UPDAPS calculates the damage parameter and pseudo-stiffness of each AC sublayer during the pavement analysis period. The pseudo-stiffness is a normalized parameter (0.0-1.0) that describes the remaining stiffness of each AC sublayer. The complement 78 of the pseudo-stiffness (1 - C) is used in the fatigue cracking model to represent the damaged state of each AC sublayer, and to predict the observed amount of fatigue cracking in the field. Transfer functions are empirical equations used to estimate the distresses observed in the field based on mechanistic damage parameters (in this case, 1 - C). The fatigue cracking model of UPDAPS uses the complement of the pseudo-stiffness at the uppermost AC sublayer as the mechanistic input of the transfer function to predict top-down fatigue cracking. Similarly, the complement of pseudo-stiffness at the lowermost AC sublayer is the mechanistic input of the bottom-up fatigue cracking transfer function. 4.2.7.3.1. Bottom-Up Fatigue Cracking The California department of transportation (CalTrans) developed an incremental-recursive software, called CalME, for the analysis and design of flexible pavement structures. The effect of damage was reflected as a reduction in the upper asymptote of the |E*| master curve (Wu and Harvey 2012). A damage parameter was defined in CalME based on the ratio of applied traffic axle passes to the maximum allowable axle passes. This damage parameter was used as part of a transfer function to predict the field bottom-up fatigue cracking (Wu and Harvey 2012). The bottom-up fatigue cracking transfer function of CalME was modified in this study to make it compatible with VECD parameters. The modified version of this transfer function is shown in Equation (40). 𝐹𝐶𝑖 𝑏𝑢 = 𝐷𝑃 − 𝜔initial 𝐹𝐶max 𝐷𝑃 − 1) 𝑏𝑢 × (𝜔initial 𝑏𝑢 𝐹𝐶max 𝑏𝑢 − 1) [(1 − 𝐶𝑖) ∙ 𝑆𝐹]𝐷𝑃 𝐹𝐶initial 𝑏𝑢 𝐹𝐶max 𝑏𝑢 + ( 𝐹𝐶initial 𝜔initial = (1 + ( 𝛼ref ) ℎ𝐴𝐶 ℎref −1 ) 𝐷𝑃 = 𝑛 × 𝐶1 𝑏𝑢 𝑆𝐹 = 1 + ( 𝑅𝑝 𝑅ref 𝑎(𝑇) ∙ ( 𝜂(𝑡ref) ) 𝜂(𝑡) 𝛷 ) where: FCi td = predicted bottom-up fatigue cracks in the field at the ith month (%). Ci = pseudo-stiffness of the lowermost AC sublayer at the ith month. 79 (40) (41) (42) (43) FCmax bu FCinitial bu = maximum predicted fatigue cracks in the field (%). = predicted fatigue cracks in the field, corresponds to crack initiation (%). ωinitial = damage level corresponding to crack initiation. DP = damage parameter. n = damage growth rate. hAC = total thickness of the AC layer (in). href αref = reference AC layer thickness, equal to 250 mm (9.84 in). = model constant, equal to -2.0. C1 bu = model calibration coefficient. Rp = applied rest period (s). Rp,ref = reference rest period, equal to 10.0 s (s). Tref = reference temperature of the asphalt mixture master curve (ºF). T = temperature of the interest (ºF). a(T) = shift factor at the temperature T. φ = model constant, equal to 0.40. η(T) = viscosity of the binder at the temperature T (cP). A rest period Rp = 10.0 s is used in the bottom-up fatigue cracking model in UPDAPS, and the model coefficient (C1 bu) is calibrated based on geographical location (e.g., each state of USA) and the functionality of the pavement structure. The initial C1 bu = -1.0 is used as an input to the optimization algorithm. Figure 36 shows the bottom-up fatigue cracking transfer function for a 4.0 AC layer of HPMS MI2954 section using the initial calibration coefficient. 80 Figure 36. Bottom-up fatigue cracking transfer function with initial coefficients 4.2.7.3.2. Top-Down Fatigue Cracking MEPDG documentation uses a sigmoid function to transfer from top-down fatigue damage to observed top-down fatigue cracks in the field (ARA Inc. 2004). The fatigue cracking model of the UPDAPS program uses similar sigmoid function, this time to transfer from the complement of the pseudo-stiffness at the uppermost AC sublayer to observed top-down fatigue cracking in the field. The top-down fatigue cracking transfer function is shown in Equation (44). 𝐹𝐶𝑖 𝑡𝑑 = where: 𝑡𝑑 𝐶3 1 + exp(𝐶1 𝑡𝑑 − 𝐶2 𝑡𝑑 × log(100 × (1 − 𝐶𝑖))) (44) FCi td = predicted top-down fatigue cracks in the field at the ith month (%). Ci = pseudo-stiffness of the uppermost AC sublayer at the ith month. C1 td, C2 td, C3 td = transfer function coefficients. The coefficients of the top-down fatigue cracking transfer function are calibrated based on the geographical location (e.g., each state of USA) and the functionality of the pavement structure. However, the initial coefficients of this transfer function (to be used into the optimization algorithm) are selected such that a maximum of 50% top-down fatigue cracks are predicted at the extreme damaged condition (C = 0.30). Therefore, the initial coefficients of the top-down fatigue 81 cracking transfer function are selected as C1 td = 6.0, C2 td = 2.8, C3 td = 50.0. Figure 37 shows the top-down fatigue cracking transfer function using the initial coefficients. Figure 37. Top-down fatigue cracking transfer function with initial coefficients As an example, Figure 38 shows the top-down and bottom-up fatigue cracking of the section HPMS MI2954 during a 20-year pavement analysis period. 4.2.8. Improvement of Wheel Wander Effect Another improvement in the UPDAPS program includes more precise calculations of the wheel wander effects on the critical pavement structural responses. Wheel wander effect occurs when vehicle tires on the pavement surface do not always pass along the same exact path, which can be attributed to different axle widths for different vehicle types, individual driving habits, wind effects, and mechanical alignment of the trailers, among other reasons (Siddharthan et al. 2017). Traditionally, MEPDG uses a standard normal distribution to simulate the effect of wheel wander for the fatigue cracking and rutting models. For this purpose, it is assumed that the distribution of traffic axles passing over the pavement surface follows a normal distribution perpendicular to the direction of traffic. Therefore, the standard deviation of the lateral wheel wander is an input to the MEPDG, and similarly UPDAPS program. 82 Figure 38. Bottom-up and top-down fatigue cracking prediction for section HPMS MI2954 In the next step, the standard normal distribution is divided into five equal segments (with the same areas) with the center points -1.2816, -0.5244, 0.0000, 0.5244, and 1.2816. These center points are then used to shift the tire locations in the X-direction (perpendicular to the traffic direction). In the MEPDG formulation, the frequency of the traffic is uniformly distributed between these center points. In other words, the assumption of the normal distribution is not fully implemented in the MEPDG formulations, and it results in underestimation of the critical pavement structural responses. This issue is resolved in the UPDAPS program by incorporating the frequencies from the normal distribution graph. In this section, the implementation of the wheel wander effect for the fatigue cracking model is discussed. A similar approach is used to incorporate the wheel wander effect into the critical structural responses of the rutting model. According to the VECD implementation of the fatigue cracking model, the ΔS parameter for a given AC sublayer, temperature quantile, axle type, and axle load level is calculated as a function of X-coordinates using Equation (37). As an example, Figure 39 shows the distribution of ΔS for the HPMS MI2954 section, at the first temperature quantile and lowermost AC sublayer, caused by a 36-kips tandem axle load. 83 Figure 39. Incremental damage parameter distribution of lowermost AC sublayer, section HPMS MI2954 caused by a 36-kips tandem axle loading In order to calculate the effect of wheel wander on the damage parameter at that specific combination of temperature quantile, AC sublayer and loading condition, the calculated ΔS values are horizontally shifted using the Equation (45). The direct multiplier (wm) corresponds to each of the horizontal shifts which is calculated using the standard normal distribution. The shifted X-coordinates are obtained using the center points of the area segments in the standard normal distribution. It is noted that linear interpolation may be needed to calculate the value of ΔS at the shifted X-coordinate. 𝛥𝑆𝑖,𝑗,𝑘,𝑙,𝑚 = 𝑤𝑚 ∙ 𝛥𝑆𝑖,𝑗,𝑘,𝑙(𝑋 − 𝑠𝑑. 𝜌𝑚) (45) where: ΔSi,j,k,l,m(X) = incremental damage parameter at the ith temperature quantile and jth AC sublayer, due to the passing of kth axle type with lth axle load level as a function of X-coordinates shifted to the mth shifting step m = shifting step counter, which represents each of the area segments in the standard normal distribution Sd ρm = standard deviation of wheel wander (in) = center points of each area segment in the standard normal distribution. Equal to - 1.2816, -0.5244, 0.0000, 0.5244, 1.2816 for m values of 1 to 5, respectively. wm = weight multiplier for each shift. Equal to 0.1214, 0.2406, 0.2760, 0.2406, 0.1214 for m values of 1 to 5, respectively. 84 Figure 40 shows the shifted ΔS values as a function of X-coordinates, for the HPMS MI2954 section at its first temperature quantile and lowermost AC sublayer, caused by a 36-kips tandem axle loading. Figure 40. Shifted ΔS values for lowermost AC sublayer of section HPMS MI2954 caused by 36-kips tandem axle loading. (a) 1st shifting step, (b) 2nd shifting step, (c) 3rd shifting step, (d) 4th shifting step, (e) 5th shifting step The next step is the calculation of the ΔS values as a function of X-coordinates, at the temperature quantile, AC sublayer, axle type, and axle load level of interest. This is achieved by summation of all shifted ΔS values using Equation (46). 85 𝛥𝑆𝑖,𝑗,𝑘,𝑙(𝑋) = ∑ 𝛥𝑆𝑖,𝑗,𝑘,𝑙,𝑚 (𝑋) 𝑚 (46) where all parameters were previously defined. It is noted that ΔSi,j,k,l in this equation includes the effect of wheel wander, and it is different from the one in Equation (37). Figure 41shows the effect of wheel wander on the calculated values of ΔS as a function of X-coordinates. The inclusion of wheel wander in the analysis not only reduces the maximum value of ΔS but also broadens the ΔS distribution along the X-direction, which represents the field conditions better. Figure 41. Effect of wheel wander on the calculated ΔS values. Lowermost AC sublayer, section HPMS MI2954 36-kips tandem axle loading 4.3. Parallel Computing and Run Time Efficiency One of the main advantages of the UPDAPS program over similar ME-based pavement analysis alternatives (e.g., AASHTOWare Pavement ME or FlexPave™) is its compatibility with parallel computing on supercomputing remote servers. The analysis engine of the UPDAPS program was developed in Python programming language. In addition, the input and output files of each analysis run of a single pavement section were structured in a text file with JSON formatting. Therefore, another script was developed to upload the UPDAPS program and all JSON input files to the High-Performance Computing Center (HPCC) servers at the Michigan State University and submit parallel jobs to run the analysis. According to the HPCC policies, each user account has access to 1024 CPUs concurrently. The developed script puts all input JSON files in a queue to run with UPDAPS program using all available CPUs. As the result, the average run time for analysis of each pavement structure can 86 reduce significantly. As an example, 79,209 flexible pavement structures were extracted from HPMS dataset. The average runtime of the analysis using the UPDAPS program was about 12 minutes. However, by concurrently exploiting 1024 CPUs, the whole dataset was analyzed in less than 16 hours. In other words, the average runtime of UPDAPS program was reduced from 12 minutes (in single processor computing) to about 0.7 seconds (in parallel computing). 4.4. Chapter Conclusion This chapter summarized the development of the UPDAPS program as an ME-based pavement analysis and design tool. UPDAPS program consists of 14 different components that was originally developed based on the MEPDG formulations. However, several improvements were made to some of these components during the development of the UPDAPS program. These improvements were discussed in this chapter and details of the other components can be found in Appendix B. The improvements of UPDAPS program are summarized below: • Calculation of the loading frequency in pavement layers was improved by implementing the proposed method of Losa and Natale (2012). • The climatic model was improved in three different sub-components as listed below. o Implementation of the revised energy balance at the pavement surface. o Implementation of the new sunrise/sunset time algorithms for better distribution of solar radiation over the daytime. o Implementation of the time-dependent SSA parameter for more accurate calculation of the pavement temperature profile during the pavement service life. • Critical analysis locations for the bottom-up and top-down fatigue cracking model were improved by using the analysis points at the depth of 0.1 from the pavement surface (top- down fatigue cracking) and 0.1 from bottom of AC layer (bottom-up fatigue cracking). • Pavement structural response model was improved by developing an axisymmetric FEA- based model, called MatFEA, and its implementation into the UPDAPS program. This improvement allows the UPDAPS program to capture the nonlinear stress-dependent behavior of the unbound pavement layers, as well as the geogrid-reinforcement. 87 • To accurately model the impact of multi-tire loading (e.g., tandem, tridem, and quad axle types), a superposition scheme for pavement structural response was developed and incorporated into the nonlinear convergence iterations of the MatFEA model. • Assumption of the linear load-strain behavior for calculating the critical pavement responses at different axle load levels was improved by implementing the nonlinear load- strain behavior through three-point extrapolation method. • Fatigue cracking prediction model was improved by implementing the VECD theory to calculate the pseudo-stiffness and damage parameters for each AC sublayer during the pavement service life. The corresponding transfer functions for converting the damage to the pavement fatigue cracking was also developed. Finally, it is noted that the UPDAPS program was developed to be compatible with parallel computing on supercomputing remote serves, especially HPCC at Michigan State University. As a result, the average runtime of each pavement analysis with UPDAPS program significantly reduce from about 12 minutes (for single processor computing) to about 0.7 seconds (using 1024 CPUs concurrently). 88 CHAPTER 5. UPDAPS-FLOOD PROGRAM This chapter outlines a description of the development of a framework designed to integrate flooding effects in mechanistic-empirical pavement analysis and design procedures. It also covers the implementation of this framework in the UPDAPS program, referred to as the UPDAPS-Flood program. Additionally, the process of collecting flooding data inputs for the UPDAPS-Flood program is discussed. 5.1. Proposed Framework This framework is based on four major modifications to the ME analysis procedure as listed below. These modifications were proposed based on a comprehensive literature review on the effects of flooding events on pavement performance, where more details can be found in section 2.3 (see page 21). • Modification of analysis increments: This adjustment is necessary to enhance the resolution of damage accumulation calculations during flooding events and the subsequent recovery period. • Modification of resilient modulus of unbound layers: This modification is needed to account for the loss of support in pavement structure due to the increased moisture content in the unbound layers. • Modification of distress prediction models: This modification is aimed to incorporate the changes in resistance of unbound materials against irrecoverable distresses such as permanent deformation, due to excess moisture contents. • Modification of traffic: This modification is suggested to account for the changes in the traffic patterns during the flooding events and post-flood time. 5.1.1. Modification of Analysis Increments The current ME analysis procedures use an incremental damage accumulation approach to predict pavement distress during its service life. For this purpose, the climatic model (e.g., EICM in MEPDG) calculates the hourly temperature profile within the pavement structure, which can be used to estimate the hourly modulus of AC sublayers. In the next step, the pavement structural response model can calculate the critical pavement structural responses to estimate the accumulated damages and predict the pavement performance. However, conducting the hourly analysis for predicting the pavement performance is computationally expensive and makes the 89 analysis impractical. As an example, for a typical 20-year analysis of a flexible pavement section, it is required to call the pavement structural response and damage accumulation models 175,200 times (= 20 years × 365 days per year × 24 hours per day). Considering approximately 0.2 s for running the pavement structural response (LEA-based) and damage accumulation models for a typical flexible pavement structure, the ME analysis can take up to 10 hours. To reduce the computational cost in ME analysis procedures, NCHRP 1-37A suggested a monthly analysis scheme, in which the hourly temperature profile of the pavement structure for each month (~720 hourly results) is statistically transformed into five quantile increments. The main assumption behind this statistical transformation is that these five quantiles can represent the temperature profile of the pavement within a given month (ARA Inc. 2004). This monthly analysis scheme is conceptually shown in Figure 42, in which the distribution of the hourly temperatures at the mid-depth of the uppermost and lowermost AC sublayer of HPMS MI2954 is shown as a histogram, with five temperature quantiles shown with red star symbols. Figure 42. An example of statistical analysis of temperature profiles for HPMS MI2954 section during ninth month (June) of its service life for: (a) uppermost AC sublayer, (b) lowermost AC sublayer Application of this monthly analysis scheme can significantly reduce the computational cost of the ME analysis procedure. As an example for a typical 20-year analysis, the pavement structural response and damage accumulation models are required to run only 1,200 times (= 20 years × 12 months per year × 5 quantiles per month), compared to 175,200 times in an hourly analysis scheme. It is noted that this monthly analysis scheme is currently used in the UPDAPS program. 90 On the other hand, the duration of the flooding events usually ranges between a couple of hours to days. Therefore, the current monthly analysis scheme may not be suited to capture the variations of the pavement material properties during and after the flooding events. To overcome this limitation, the developed framework proposes using a hybrid analysis scheme, in which the monthly analysis increments are downscaled into daily analysis increments during the flooding event and post-flood recovery time, while the monthly analysis increments are used during the rest of the pavement service life. The hourly temperature profiles are statistically transformed into five quantiles for each day, instead of each month, during the flooding event and post-flood recovery times. It is also noted that the unaffected days of each month are also treated as an individual month. As an example, Figure 43 conceptually illustrates this hybrid analysis scheme with a hypothetical flooding scenario. In this scenario, the flooding event occurs on August 10th and inundates the pavement structure for 3 days till August 13th. The recovery period also takes 60 days till October 13th. As Figure 43 shows, the daily analysis increments (with five quantiles per day) are used between August 10th to October 13th. In addition, this proposed modification downscales the before-flood (August 1st to August 10th) and after-flood (October 13th to October 31st) times into five representative quantiles, while all other months (no flooding) follow the monthly analysis scheme. Figure 43. Conceptual illustration of the hybrid analysis scheme As shown in Figure 43, the application of the hybrid scheme for this hypothetical scenario results in 330 quantiles within four months of pavement service life, while the monthly analysis scheme uses only 20 quantiles. This observation shows that although the application of the hybrid analysis scheme can potentially increase the accuracy of the ME analysis procedures to capture the flooding effects on pavement performance, it also can significantly increase the computational effort. However, this increase in computational cost is unavoidable given the constraints of the monthly analysis scheme. 91 5.1.2. Modification of Resilient Modulus of Unbound Layers The modification of the resilient modulus of the unbound pavement layer was proposed based on a literature search on the moisture effects on unbound pavement materials. During flooding events, the increased moisture content in the unbound pavement layers reduces their MR and lowers the pavement structural support. However, the excess moisture can drain out the pavement structure during the post-flood recovery time, by which the MR of the unbound pavement layers can fully recover to their normal state before the flooding event. More details about this mechanism can be found in section 2.3.2 (see page 26). Implementation of the modified MR of unbound pavement layers and daily analysis results in higher accuracy in the calculation of critical pavement structural responses due to the reduced structural support during the flooding events and post-flood recovery time. Figure 44 illustrates the changes in the degree of saturation and MR of the unbound pavement layer during a flooding event. This figure shows a rapid increase in the degree of saturation of the unbound pavement layer right after the flooding event, which is attributed to the intrusion of a considerable amount of water into the pavement structure in a short period. This increased saturation level results in a significant reduction in MR of unbound materials. However, when the water level above the pavement surface recedes during the post-flood period, the excess moisture starts to drain out of the pavement structure with time. Therefore, the degree of saturation in unbound layers decreases and eventually, the MR of unbound pavement layers can fully recover to their normal values. 92 Figure 44. Illustration of changes in (a) degree of saturation and (b) modulus of unbound pavement layer during flooding event and post-flood recovery time (Abdollahi et al. 2024) Figure 44 (a) also shows that the degree of saturation gradually reduces during the recovery time via various paths. Although this figure is just a conceptual illustration of the saturation and recovery processes, the actual duration and rate of these processes are a function of the physical properties of unbound material (e.g., permeability and gradation) and drainage properties and vary from one material to another. Therefore, a moisture profile prediction model is required for an accurate determination of the changes in the degree of saturation of pavement structure. However, such a model is not currently available as a part of the UPDAPS program. Due to the lack of the moisture profile prediction model, the proposed framework makes a major assumption by which (i) the unbound pavement layers are assumed fully saturated with an occurrence of a flooding event, and this increased degree of saturation is fully recovered to its normal level during the post-flood recovery time; (ii) a recovery time of 20 days for the granular base and 60 days for the subgrade materials have also assumed to account for different physical properties of the base and subgrade materials. Although the assumption of recovery time duration 93 might not truly represent all variety of the unbound materials, this assumption has been made based on the results of a recent study in which the degree of saturation profile of unbound layers with different gradation properties was simulated after the flooding event (Nivedya et al. 2020). The recovery rate is another important factor in modeling the flooding effects on pavement performance. Unbound materials with low permeability in pavement structures with poor drainage systems can retain excess water in the pavement structure for extended durations, resulting in softer support and accelerated accumulation of the damages. As mentioned before, an accurate determination of the recovery rate requires a moisture profile prediction model, which is not currently available in this research. However, the effect of the recovery rate may be modeled with three different recovery paths, as illustrated in Figure 44. The first path (Path 1) leads to a faster recovery, which applies to permeable materials and/or an existence of an efficient drainage system. On the contrary, Path 3 indicates a slow recovery, potentially due to low permeability of the unbound materials or poor performance of the drainage system after the flooding events (e.g., due to the clogging or elevated water level around the pavement section). In addition, the second path (Path 2), which simulates a linear recovery, was introduced to represent the average behavior of the previous two recovery rates. It is also noted that recovery rates in Paths 1 and 3 are modeled using parabolic functions. As an example, the recovery of the MR of unbound materials in Paths 1, 2, and 3 are modeled using Equations (47), (48), and (49), respectively. 𝑀𝑅(𝑡) = −𝑡2 + (𝑀𝑅 max − 𝑀𝑅 𝑇𝑅 min) + 𝑇𝑅 2 𝑡 + 𝑀𝑅 min 𝑀𝑅(𝑡) = 𝑀𝑅(𝑡) = 𝑡2 + (𝑀𝑅 min) max − 𝑀𝑅 𝑇𝑅 𝑡 + 𝑀𝑅 min (𝑀𝑅 max − 𝑀𝑅 𝑇𝑅 min) − 𝑇𝑅 2 𝑡 + 𝑀𝑅 min where: MR(t) = resilient modulus of unbound layer at time t (psi). MR min = minimum resilient modulus value of the unbound layer (psi). MR max = maximum resilient modulus value of the unbound layer (psi). t = time after the recovery process starts (days). 94 (47) (48) (49) TR = duration of the recovery process (days). 5.1.3. Modification of Distress Prediction Models The material-specific calibration coefficients of the different distress models are traditionally determined through laboratory testing and field calibration without considering moisture damage. However, inundation of the pavement layers during flooding events and post-flood recovery time increases the degree of saturation and changes the resistance of the pavement materials against major distresses. The effect of flooding on the properties of AC layers is typically assumed to be negligible (Wang et al. 2015, Mallick et al. 2017, Nivedya et al. 2020), as this layer contains a relatively low air void content or the excess moisture can quickly drain out after flooding (Wang et al. 2015). In addition, the moisture effect on the AC layer is not incorporated in the MEPDG formulation. This is while the excess moisture in the AC layer can result in detrimental effects ranging from weakening aggregate-bitumen bonding to a higher rate of damage accumulation (Dawson 2014), where a more detailed discussion can be found in section 2.3.1 (see page 23). Although more research is required to better understand the behavior of the inundated asphalt mixtures, the developed framework proposed using a new set of material-specific calibration coefficients to calculate the damage accumulation in saturated AC layers during the flooding events. In other words, the ME analysis procedure is modified to use two sets of calibration coefficients for each distress prediction model, which reflects the damage-resistant behavior of the asphalt mixtures during normal and saturated conditions. In addition, the damage-resistant behavior of the AC layers during the recovery time can be adjusted proportional to the changes in the degree of saturation, as illustrated in Figure 44 (a). As an example, Figure 45 illustrates the concept of using two different material-specific C(S) curves to model the flooding effects on the fatigue cracking performance of AC layers. This figure illustrates a simple scenario in which the blue and red solid lines show the C(S) curves for the original and saturated (flooded condition) asphalt mixture samples. In this scenario, the flooding event occurs at the point where the asphalt sample is already damaged by about 22% (C = 0.78). During the flooding event, the saturated C(S) curve is used for calculating the fatigue cracking damage accumulation, by which the pseudo-stiffness parameter is reduced to 0.61. However, by achieving the full recovery, the original C(S) is used for the rest of the pavement service life. 95 Figure 45. Conceptual illustration of using two different C(S) curves for considering the flooding effects in fatigue cracking model On the other hand, rutting is the only pavement distress that is directly calculated for the unbound layers. It has been reported that the rutting resistance of the unbound materials significantly reduces as the moisture content exceeds its optimum value (Ba et al. 2015). The developed framework proposed a similar approach to account for the rutting behavior of the unbound materials during the flooding events and post-flood recovery time, which includes using a new set of material-specific calibration coefficients to calculate the plastic strain accumulation at the mid-depth of saturated pavement unbound sublayers. Therefore, the ME analysis procedure is modified to use two sets of material-specific calibration coefficients for the rutting prediction model of unbound layers, each representing either the normal or saturation conditions. Similarly, it is noted that the accumulation of the plastic strain in unbound pavement layers during the post- flood recovery time is also adjusted proportional to the changes in the degree of saturation, as illustrated in Figure 44 (a). As mentioned before, the developed framework proposed to use of a new set of material- specific calibration coefficients for different distress prediction models to account for the increased degree of saturation in the pavement structure during the flooding event and post-flood recovery times. These calibration coefficients can be obtained by running pavement material performance tests at different moisture contents (other than the optimum moisture content), as well as various preconditioning of the testing samples. 96 5.1.4. Modification of Traffic ME analysis procedures incorporate the traffic in damage accumulation models in terms of the number of different axles (axle types and load level) that goes over the pavement section during each analysis increment, which is calculated using different traffic input parameters including AADTT, vehicle class distribution, axle load spectra, etc. More details about the processing of traffic data can be found in section 0B.1 (see page 190). However, the traffic pattern could considerably change after a flooding event, which can be attributed to the need for emergency vehicles, traffic detours for road closures, and relatively heavier trucks during the debris removal process. As an example, it has been reported that the relatively heavy debris haul trucks were loading the weakened pavement network of New Orleans after Hurricane Katrina and caused damage to both submerged and unsubmerged pavement sections (Chen and Zhang 2014). In addition, the pavement structural support can significantly reduce after the occurrence of a flooding event, which accelerates the damage accumulation. Therefore, the road agencies may restrict the heavy traffic loading on the flooded pavements for certain periods, which is called “load restriction time”. The developed framework proposed using two different sets of traffic input parameters to account for the effects of flooding events on the traffic pattern, as listed below. • Regular traffic input parameters that reflect the normal condition, which applies to the analysis increments before flooding events and after the load restriction time. • A new set of traffic input parameters that reflect the changed traffic pattern due to the flooding event. These traffic input parameters are applied to the analysis increments during the flooding event and load restriction time. These traffic input parameters also represent the loading from the emergency vehicles and relatively heavy debris removal trucks. It is noted that the duration of the “load restriction time” is an additional input for the developed framework. 5.2. Development of UPDAPS-Flood Program UPDAPS program is an ME-based pavement analysis and design program that was developed during this research under a contract with the FHWA. The analysis engine of the UPDAPS program was developed based on the original formulations of the MEPDG, while several improvements were made to different models. More details about the development of the UPDAPS 97 program and its improvements compared with the original MEPDG formulation can be found in Chapter 4 (see page 39). This research proposed a framework to incorporate the effects of flooding events on pavement performance in the ME analysis procedures using four major modifications, as described earlier. This framework was implemented into the analysis engine of the UPDAPS program, and the modified version is named the “UPDAPS-Flood” program. Three main distresses are predicted by the UPDAPS-Flood program to evaluate the flooding effects on pavement performance, including rutting, fatigue cracking, and IRI. The UPDAPS-Flood program uses the same JSON formatted text file to load the required inputs for running the analysis. However, some additional inputs about the flooding data are also required. These additional inputs account for different modification steps of the proposed framework. In response to the first modification (modification of analysis increments), UPDAPS-Flood requires the number, start dates, and durations of each flooding event within the pavement service life. It also requires inputs regarding the recovery time of each unbound layer during which the excess moisture content fully recovered to its normal level. These inputs are then used to modify the analysis increments within the UPDAPS-Flood program. In response to the modification of the MR of unbound layers, the UPDAPS-Flood program uses the NCHRP 1-37A model to calculate the MR of unbound layers at different saturation levels. However, the application of this model requires a dedicated moisture profile model, which is not currently available in the UPDAPS-Flood program. In the lack of such a moisture profile model, the percent reduction in MR of the unbound layers and the recovery path are inputs to the UPDAPS- Flood program. Using these parameters, the UPDAPS-Flood reduces the MR of unbound layers during the flooding event, while it follows the recovery path to regain its normal level modulus within the recovery time. In response to the third and fourth modifications, UPDAPS-Flood was developed to take different sets of material-specific calibration coefficients for different distress prediction models of AC and unbound layers that represent the normal and saturated conditions. It also takes two different sets of traffic input parameters to account for the traffic patterns during normal conditions, as well as flooding events and load restriction time. 98 However, these material-specific calibration coefficients of the saturated pavement materials and traffic input parameters during the flooding event are not currently available in this research. Therefore, simplified modifications were made based on expert knowledge and understanding of the average changes in the traffic patterns. These simplified modifications are listed below. • The rutting model of AC and unbound pavement sublayers was modified by adjusting the local calibration coefficients (k1 coefficient, which is a direct multiplier to the rutting model). This coefficient was increased by 50% to account for the accelerated plastic strain accumulation of the saturated materials. However, this increase is dissipated with the recovery path during the recovery time. It is also noted that a limited sensitivity analysis was also conducted to better understand the effect of this coefficient on the pavement performance by increasing it by 25%, 50%, 75%, and 100%. • Traffic was modified by adjusting only the AADTT parameter using a multiplier factor to account for the flooding events on the traffic patterns. Another major assumption is using a similar duration for the recovery time and load restriction time. The traffic multiplier factor of 2.0 for the major flood events and 1.25 for flash flooding events was used in this research. It is noted that the UPDAPS-Flood program results using these simplified modifications should considered a limited study for the current stage of the research, as it was only performed on the rutting model and traffic patterns, while changes in fatigue cracking resistant behavior of the asphalt mixtures are ignored. Moreover, laboratory efforts are required to provide more accurate input parameters to the UPDAPS-Flood program. 5.3. Validation of UPDAPS-Flood Program The literature search revealed that there is a lack of publicly available measured performance data on the flexible pavements that are subjected to flooding events. Therefore, an “indirect” approach was employed to validate the results of the UPDAPS-Flood program. It is noted that a direct validation approach refers to a comparison between the direct measurements of distress in the field against the predicted distress from the ME analysis procedure. However, this indirect validation process refers to a comparison between the indirect IRI distress measurements from the field against the UPDAPS-Flood IRI predictions of a flooded pavement section. 99 The hurricanes Katrina and Rita events were selected for this indirect validation process. Hurricane Katrina hit the New Orleans area on August 23rd, 2005, with 15 days of inundation, followed by hurricane Rita which occurred on September 18th, 2005 with 20 days of inundation. As a result, it has been reported that more than 2,000 miles of roadways were inundated for about five weeks (Zhang et al. 2008, Chen and Zhang 2014). Louisiana State Department of Transportation (DOT) performed Falling Weight Deflectometer (FWD) tests on the New Orleans road network closely before the occurrence of these hurricanes. Similar FWD testing was carried out on the road network weeks after these two hurricanes. Although the detailed FWD test results are not available online, the analysis of the results showed an average 20% loss in the Structural Number (SN) of the flooded flexible pavement structures (Zhang et al. 2008, Chen and Zhang 2014). HPMS database includes 18 flexible pavement sections within the New Orleans area, LA. The information on these pavement structures was extracted from the HPMS database, and they were analyzed with the UPDAPS-Flood program by only including flooding data on hurricanes Katrina and Rita (all other flood data, if any, were not included). The IRI was selected for validation purposes as it includes the combined effect of the fatigue cracking and rutting distresses. It is also noted that the analysis of the UPDAPS-Flood program used inputs of 50% reduction in MR of saturated unbound pavement layers with linear recovery, traffic multiplication factor of 2.0 during the flooding events, and 20-days and 60-days of recovery time for base and subgrade materials, respectively. On the other hand, almost all these 18 pavement sections were designed by the AASHTO 1993 pavement design guide. Therefore, the AASHTO 1993 formulation was used to calculate the changes in the Pavement Serviceability Index (ΔPSI) of these 18 pavement sections considering a 20% reduction in the SN. In the next step, the ΔPSI values were converted into the ΔIRI using the empirical conversion equation developed by Gulen et al. (1994), as shown in Equation (50). 𝑃𝑆𝐼 = 9 ∙ exp(−0.008784 ∙ 𝐼𝑅𝐼) (50) where: PSI = pavement serviceability index. IRI = international roughness index. 100 As an example, Figure 46 (a) shows the predicted IRI with time for the LA1262 section in the New Orleans area which experienced hurricanes Katrina and Rita. In this graph, the thick red line shows the predicted IRI during hurricanes Katrina and Rita events as well as post-flood recovery time. Similarly, the light blue area shows the predicted change in IRI, converted from the ΔPSI in AASHTO 1993 methodology caused by a 20% reduction in structural number. As this figure shows, the predicted change in IRI using the AASHTO 1993 method was slightly higher than that predicted using the UPDAPS-Flood program. On the other hand, the predicted changes in IRI due to the hurricanes Katrina and Rita on all 18 pavement sections in the New Orleans area are also shown in boxplots of Figure 46 (b). This figure shows that, although the two methodologies show different variability of the predicted ΔIRI, the median values are similar. In other words, the majority of the pavement sections showed a consistent change in the predicted IRI calculated directly from the UPDAPS-Flood program and indirectly from the AASHTO 1993 pavement design guide. Considering the lack of detailed field-measured distresses before and after a hurricane or flood event, the results from this approach validated the UPDAPS-Flood program reasonably well. 5.4. Project-Level Results The UPDAPS and UPDAPS-Flood program were used to analyze the HPMS FL806 pavement section in Miami-Dade County of Florida. This pavement section consists of a 2.0 AC layer, followed by an 8.0 granular base layer, where the modulus of the base and subgrade layers at their normal condition are 24,000 and 22.929 psi, respectively. The vehicle design speed on this pavement section is 30 mph, with the expected total traffic of about 4.1 million ESALs. This pavement was modeled for a time frame of August 2002 to August 2022, during which it experienced six major flooding events with at least two days of inundation and 40 minor flooding events with less than one-day inundation. However, as the UPDAPS-Flood program uses the daily analysis increments, these minor floods were modeled with one-day inundation. This pavement section was modeled using both UPDAPS and UPDAPS-Flood programs to predict the pavement performance with and without consideration of the flooding events. Figure 47 shows the predicted rutting, total fatigue cracking, and IRI for this section. It is also noted that the UPDAPS-Flood program used a 50% reduction in MR of saturated unbound layers with linear recovery function, as well as a traffic multiplier of 2.0 during the flooding events. 101 Figure 46. Validation results: (a) predicted IRI for LA1262 section during hurricanes Katrina and Rita using UPDAPS-Flood and AASHTO 1993 method; (b) comparison of predicted ΔIRI of 18 flexible pavement sections in the New Orleans area due to Hurricanes Katrina and Rita using AASHTO 1993 and UPDAPS-Flood (Abdollahi et al. 2024) In Figure 47, the thick red line represents the pavement analysis results with the effect of flooding events (UPDAPS-Flood program results), while the dashed blue line shows the results without implementing the effects of flooding events (UPDAPS program results). As shown in part (a), the predicted rutting from the UPDAPS-Flood program with considering flooding effects was 102 considerably higher than that of the UPDAPS program with no flood scenario. Visual inspection of the predicted rutting with consideration of the flooding events also showed some significant increases in rutting during a short time (major jumps in the graph). These jumps indicate major flooding events during which the pavement section was inundated for longer periods, and therefore, more plastic strains were accumulated in the unbound pavement layers. This observation means that although this pavement section experienced 46 flood events during its service life, most of them affected the pavement structure for short periods, while the major increases in the rutting (jumps) were the results of major flooding events with longer duration. Figure 47. Results of UPDAPS and UPDAPS-Flood for FL806 section: (a) rutting, (b) total fatigue cracking, and (c) IRI (Abdollahi et al. 2024) 103 Similarly, Figure 47 (b) shows the predicted total fatigue cracking with and without the impact of flood events. It was found that the effect of flooding events on predicted fatigue cracking was less noticeable than rutting. It is worth reminding that the UPDAPS-Flood uses the VECD theory to predict fatigue cracking, which relies on material-characteristic C(S) curves. As the effect of flooding on these curves has not been evaluated in the literature, UPDAPS-Flood uses the same C(S) curves during and after the flooding events, which means the effect of increased saturation on the cracking behavior of the asphalt mixture has been ignored. Still, the higher predicted fatigue cracking in the presence of the flooding events is due to the loss of bearing capacity of the unbound layers which lowers the pavement structural response and potentially increases the critical structural strain responses at the AC level. The effect of flooding on IRI is shown in Figure 47 (c). It is worth noting that the IRI considers both rutting and fatigue cracking, but its value is not a mere sum of the distresses. The impact of flooding events on IRI was observed to lie within an intermediate range, where it was not as significant as that of rutting, nor was as low as that of fatigue cracking. 5.5. Runtime Evaluation of UPDAPS-Flood Program The same pavement section (HPMS FL806) was analyzed using both UPDAPS and UPDAPS- Flood programs using a single processor computing on an AMD EPYC 7H12 processor (2.59 GHz) on the HPCC computing facilities at Michigan State University. The results showed that the UPDAPS program runtime for this pavement section was 334 seconds, while the UPDAPS-Flood program took 1066 seconds to run similar analysis with consideration of the flooding events. The main reason for the higher runtime of the UPDAPS-Flood program is attributed to the implementation of a daily analysis scheme during the flooding events and post-flood recovery time, as mentioned in section 5.1.1 (see page 89). For this purpose, only 1,200 analysis increments were used in the UPDAPS program (monthly analysis scheme), while the UPDAPS-Flood program had 4,215 analysis increments according to the hybrid analysis scheme. 5.6. Chapter Conclusion This chapter included the details of development of the UPDAPS-Flood program as an ME- based pavement analysis and design tool to incorporate the effects of flooding events on flexible pavement performance. For this purpose, a framework for incorporating the effects of flooding events on pavement performance using the ME analysis procedures was first discussed in this chapter. This framework proposed four major modifications to the ME analysis procedures, 104 including (i) modification of the analysis increments through the hybrid analysis scheme, (ii) modification of the MR of unbound pavement layers, (iii) modification of the distress prediction models for the saturated pavement materials, and (iv) modification of the traffic. In the next step, the proposed framework was implemented into the UPDAPS program and called the UPDAPS-Flood program. It is noted that the UPDAPS-Flood program was developed in a general way to accommodate all modifications in the proposed framework. However, due to the lack of a moisture profile model and accurate material-specific and traffic pattern input during the flooding conditions, several simplified assumptions were made to run the UPDAPS-Flood program and evaluate the flooding effects on the flexible pavement performance. It is noted that these assumptions were made based on expert knowledge and understanding of average changes in material behavior with saturation and traffic patterns during the flooding events. Moreover, an indirect approach was used to validate the results of the UPDAPS-Flood program by analyzing 18 flexible pavement structures located in the New Orleans area, which experienced hurricanes Katrina and Rita. For this purpose, the changes in the IRI were modeled with the UPDAPS-Flood program and compared those indirectly calculated using the AASHTO 1993 pavement design guide method. The results indicate that although these two methodologies showed different variability in the prediction of the ΔIRI, most of the pavement sections showed consistent results using both methods. Therefore, considering the lack of field-measured distresses before and after flooding events, this indirect validation approach reasonably supports the UPDAPS-Flood program. Finally, the UPDAPS-Flood program was used to analyze the flooding effects on a flexible pavement section in Miami-Dade County in Florida, which experienced 6 major flooding events. The results of the analysis showed that the UPDAPS-Flood program can effectively model these flooding effects, where the predicted distress considerably increased compared to the results of the UPDAPS program without consideration of flooding effects. 105 CHAPTER 6. NETWORK-LEVEL RESILIENCY MAPS This chapter details pavement network resiliency against flooding events, emphasizing their capacity to withstand and recover from such disruptions. For this purpose, it includes two main parts: (i) proof of concept of the methodology and evaluation of the sensitivity of the results to the primary input assumption, and (ii) performing a national-wide network-level resiliency analysis for the United States. 6.1. Resiliency Metric The concept of resiliency is typically used to evaluate the functionality and quality of infrastructure components that experience a reduction in service capacity due to natural or manmade disasters. In other words, it evaluates how fast service capacity can return to equilibrium after a disruption occurs (Pimm 1984). A recent study on pavement resiliency against flooding events utilized total surface deflection under the Falling Weight Deflectometer (FWD) to assess resilience. In this study, the resiliency curve was defined as the trend of changes in the total surface deflection over time. A resiliency index parameter was introduced, calculated as the ratio of the area under the resiliency curve to recovery time, providing a quantitative measure of structure resilience (Nivedya et al. 2020). However, this resiliency index does not apply to the predicted pavement distress after flooding, as the accumulation of distress over time is not irreversible and does not recover after the flooding event. To address this limitation, the loss of pavement service life based on specific distress can be used as an alternative resiliency metric. A similar approach has been used in the literature to evaluate the resiliency of the pavement structures against flooding events, where the loss of service life was calculated based on predicted IRI distress using the AASHTOWare Pavement ME software (Lu et al. 2020). Similarly, this study evaluated the resiliency of pavement sections against flooding events using the loss of service life concept based on the predicted IRI distress. For this purpose, the resiliency metric, denoted as RIRI, is calculated by comparing the pavement age at which the predicted IRI of the flooded sections (UPDAPS-Flood program results) reaches the predicted IRI of the no-flood scenario (UPDAPS program results) at the end of the pavement service life. The process of calculating the RIRI is illustrated in Figure 48. As this figure shows, the loss of service life for the HPMS FL806 section is approximately three years. 106 Figure 48. Procedure for calculating the RIRI of HPMS FL806 section (Abdollahi et al. 2024) This methodology for calculating the resiliency metric can also be adapted to different types of pavement distress, such as rutting or fatigue cracking. However, this study selected the resiliency metric based on the predicted IRI distress since IRI effectively incorporates all pavement distress types and environmental site factors. It is noted that a higher RIRI value indicates more damage and lower resilience of the pavement structure against flooding events. 6.2. Proof of Concept of Methodology and Sensitivity Analysis This section provides a proof of concept for generating resiliency maps and assessing the sensitivity of the results to key input variables. Data from 7,655 pavement sections across three regions of the United States were extracted from the Highway Performance Monitoring System (HPMS) database, and corresponding flooding information for these pavement sections was obtained from the National Oceanic and Atmospheric Administration (NOAA) databases. Resiliency maps for these regions were then generated based on the definition of pavement resiliency against flooding events, as discussed in section 6.1. Finally, a sensitivity analysis was conducted to evaluate the impact of primary assumptions in the UPDAPS-Flood program on the resiliency of the pavement network against flooding events. 6.2.1. Information of Extracted Pavement Sections The HPMS is a national database developed and maintained by the FHWA. It provides comprehensive data on the extent, condition, performance, usage, and operational characteristics of over 129,000 pavement sections across the United States. The HPMS database contains administrative and extent of system information for all public roads, while other characteristics, 107 such as condition and performance, are represented through a combination of complete (universe) and sample data for arterial and collector functional systems (FHWA 2021). As one of the key objectives of this research is to evaluate the effects of flooding events on pavement performance at the network level, the HPMS database was primarily used to extract pavement properties across the United States and prepare input files for the UPDAPS-Flood program. The information on 7,655 flexible pavement sections was extracted from the HPMS database, representing three regions across the United States: (i) the coastal areas along the Gulf of Mexico, including parts of Florida, Alabama, Mississippi, Louisiana, and Texas; (ii) the state of Minnesota; and (iii) the state of California. These three regions were selected to reflect the different flooding patterns expected across the United States, with the first region representing coastal flooding (i.e., hurricanes, storm surge, etc.), the state of Minnesota representing flash flooding in the northern United States, and the state of California representing flooding events at the western United States. The HPMS database showed that there were 3,164, 555, and 3,946 pavement sections available for these three regions, respectively, where the spatial distribution is shown in Figure 49. It is noted that a small blue dot marked each pavement section, while the thin black lines indicate county boundaries. The extracted pavement sections from all three regions consist of either newly constructed AC layers over a gravel base or AC overlays on an existing HMA layer. These pavement sections were modeled using the UPDAPS and UPDAPS-Flood programs for a service life spanning from August 2002 to August 2022. It is noted that the missing traffic, environmental, material, and pavement structure data were obtained from various sources, including the National Pavement Cost Model (NAPCOM), Highway Economic Requirements System (HERS), and Long-Term Pavement Performance (LTPP). Further details on preparing input JSON files for each pavement section can be found in Appendix C (see page 213). A summary of the structural, traffic, and climate characteristics of the extracted pavement sections is provided in Table 3. 108 Figure 49. Spatial distribution of the HPMS pavement sections in different regions: (a) coastal line counties in the Mexican Gulf, (b) the State of Minnesota, and (c) the State of California (Abdollahi et al. 2024) Table 3. Summary information about the structural, traffic, and climate properties of the extracted pavement sections (Abdollahi et al. 2024) Property Average annual daily truck traffic (AADTT) Equivalent single-axle load (ESAL) (×106) Vehicle speed (mph) AC thickness (in) Base thickness (in) Mean annual air temperature (ºF) Section length (mile) Gulf of Mexico Min 1282 Avg 2642 California Minnesota Max Min 2013 10000 Avg 4725 Max Min 1859 10000 Avg 3946 Max 9882 4.01 5.95 23.10 6.92 8.69 8.80 4.02 9.62 27.13 20 2.00 2.00 64.6 46.7 3.60 7.69 71.5 75 12.5 15.0 77.0 15 4.00 6.00 37.9 45.7 6.21 11.93 59.9 80 8.00 12.0 73.3 25 2.00 2.5 37.5 45.5 4.39 8.23 42.4 70 13.0 34.0 45.4 0.2 1.14 18.6 0.2 3.8 25.56 0.8 1.78 14.0 109 6.2.2. Information of Extracted Flooding Records The characteristics of the flooding events were obtained from the NOAA database (NOAA 2023). Data on ‘flood’ and ‘hurricane’ events were pulled for the Gulf of Mexico region and the State of California, while ‘flash flood’ event data were retrieved for the State of Minnesota. Since all pavement sections were modeled from August 2002 to August 2022, only flooding events within this timeframe were considered. One major limitation of the NOAA storm event database is its spatial resolution. While the extracted flooding data offers relatively high temporal resolution, measured in hours, the spatial resolution is provided at the county level. As a result, it was assumed that all pavement sections within a flooded county were affected by the flooding event. This assumption overlooks several factors, such as the exact location of the flooding event and the elevation of the pavement section. However, given that higher spatial resolution data is currently unavailable, this assumption represents a worst-case scenario. Another assumption made during the extraction of flooding data was that any flooding event lasting less than a day is assumed to result in at least one full day of inundation. This assumption is necessary due to the hybrid analysis scheme in the UPDAPS-Flood program, which downscales the analysis into daily increments during flooding events. Therefore, the UPDAPS-Flood program cannot model flooding events shorter than one day. This assumption can lead to overestimating flash flooding events, which typically inundate affected areas for six hours to one day. The extracted flooding data showed 2,132 flooding event records across 223 counties in the studied regions, where a statistical summary of the extracted records is provided in Table 4. In this research, pavement sections experiencing more than 30 days of inundation during their service life are classified as highly flooded sections. As shown in Table 4, only 24% of the pavement sections fall into this category. 110 Table 4. Summary of extracted flooding data from NOAA database (Abdollahi et al. 2024) Region No. sections No. flood records1 Min 1 Avg 9.8 Max 46 Inundation duration2 (days) No. highly Min 1 flooded sections3 1,075 (34%) Max 104 Avg 28.2 3,164 Gulf of Mexico Minnesota California All regions 1Number of flood records per section. 2Total inundation duration per section during the service life (August 2002 to August 2022). 3Number of sections with more than 30 inundation days during their service life. 555 3,946 7,665 6.9 15.4 12.9 7.1 20.8 25.4 26 80 104 26 44 46 1 1 1 1 1 1 0 (0%) 779 (20%) 1,854 (24%) Table 4 also shows that number of occurrences and total duration of flooding events in Minnesota were considerably lower than those in the Gulf of Mexico and California. This difference is primarily due to the geographical location of Minnesota, which results in a distinct climatic pattern. While fluvial and flash floods are more common in Minnesota, more severe coastal flooding events are expected along the Gulf of Mexico coastline. Supporting the previous observation, Table 4 also shows that while the number of flooding events in California was comparable to those in the Gulf of Mexico coastal region, the duration of these events was significantly shorter. This suggests that more severe floods occurred in the Gulf of Mexico coastal region. It is also noted that the intensity of the flooding events was unavailable in the NOAA dataset. However, as NOAA defined a flood event as an overflow of water onto normally dry land (NOAA 2024a), the duration of the flood event is the primary parameter considered in this study. 6.2.3. Resiliency Maps A resiliency map is a visual geographic representation that illustrates varying levels of resilience or resiliency metrics across different areas in response to a specific disaster. In this research, resiliency maps were generated using a color gradient technique based on the resiliency metric of pavement service life loss (RIRI) across three regions in the United States. Resiliency maps serve different purposes, including planning and preparedness, resource allocation, public awareness and engagement, and disaster responses (Cimellaro et al. 2010). However, the primary purpose of the pavement resiliency maps in this study is to assist road agencies in identifying flood- vulnerable regions and implementing unique design and mitigating strategies for those areas. To generate the resiliency maps, data from 7,655 flexible pavement sections and their corresponding flooding events between August 2002 and August 2022 were extracted from the 111 HPMS and NOAA databases, and input JSON files for each pavement section were created. In the next step, these pavement sections were analyzed under the no-flood scenario using the UPDAPS program, followed by an analysis using the UPDAPS-Flood program, accounting for flooding events. Due to the different configurations of the recovery path, reduction in the MR of the unbound layer, and distress calibration coefficients in the UPDAPS-Flood program, the simulations required more than 50,000 CPU hours. These simulations were run in parallel on the HPCC computing remote servers at Michigan State University. In the next step, the resiliency metric (RIRI) was calculated for each pavement section by comparing the predicted IRI distress from the UPDAPS-Flood program with the no-flood scenario from the UPDAPS program. The location and corresponding RIRI values were then used to generate the resiliency maps, as shown in Figure 50. It is noted that this figure is generated based on RIRI values under the assumptions of a 50% reduction in the MR of the saturated unbound layer with linear recovery and a traffic multiplier factor of 2.0 during flooding events. This figure provides a general representation of the resiliency maps against flooding events. As shown, a more significant loss of pavement service life is observed in Florida, likely due to more severe flooding events. 112 Figure 50. Resiliency maps for (a) coastal line of Gulf of Mexico, (b) Minnesota, (c) California Each resiliency map includes the results from many individual pavement sections, with higher densities in certain areas, such as the high density of pavement sections in the San Francisco area of California. In addition, pavement sections within the same geographic region, exposed to similar flooding patterns, could have considerably different functionality, traffic, and structural properties, leading to different levels of resiliency against flooding events. Therefore, an effective analysis of these detailed and overloaded resiliency maps can be challenging for road agencies. To overcome this issue, the K-Means clustering algorithm was employed to group pavement sections based on their proximity. Using this approach, the pavement sections in the Gulf of Mexico, Minnesota, and California regions were divided into 45, 30, and 50 distinct clusters, respectively. Figure 51 shows the summarized resiliency maps that were post-processed using this method. In this figure, each 113 circle represents the centroid of a group of pavement sections, where the size of the circle indicates the number of sections within that group. The color of the circle reflects the average RIRI value for the group. Comparing Figure 50 and Figure 51 shows that the summarized resiliency map is more accessible for road agencies to use in the decision-making and identifying flood-vulnerable areas. Figure 51. Summarized resiliency map using the K-Means clustering algorithm for (a) costal line of Gulf of Mexico, (b) Minnesota, (c) California To better analyze the resiliency of different regions against flooding events, boxplots were generated to show the statistical distribution of the calculated RIRI values for pavement sections in the Gulf of Mexico, Minnesota, and California, as shown in Figure 52. The figure shows that the pavement network in the coastal area of the Gulf of Mexico experienced higher flooding damage, as indicated by higher RIRI values. The results also show that the average resiliency index in this region was about two times greater than those in California and Minnesota. This observation aligns 114 with data from the NOAA database, which reported more frequent and severe flooding events in the Gulf of Mexico region. Figure 52. Distribution of the resiliency metric (RIRI) in different regions (Abdollahi et al. 2024) Figure 52 (for all sections) also shows that, on average, the flexible pavement network in Minnesota experienced slightly higher flooding damages than those observed in California. This observation opposes the relatively more frequent and longer-duration flooding events in California. However, further investigation of the HPMS database showed that pavement sections in California were approximately two inches thicker than those in Minnesota (see Table 3). This increased thickness could result in lower critical structural strain responses within the unbound layers during flood events and the post-flood recovery time. Since pavement design and structural properties can significantly influence resiliency against flooding, it is noted that comparing the resiliency of pavement sections across different states or regions is not the focus of this research. The primary objective is to develop a framework and practical tool for assessing pavement resiliency to flooding events at both the project and network levels. 115 As mentioned in section 6.2.2, a highly flooded pavement section is defined as a pavement section with more than 30 days of inundation during its service life. As shown in Figure 52, the highly flooded pavement sections showed significantly higher RIRI values, as expected. In the Gulf of Mexico and California, highly flooded pavement sections experienced an average increase in the resiliency index of 1.5 and 2.4 times, respectively, compared to the regional average. These findings emphasize the importance of implementing flooding events into the design of pavement structures in flood-prone areas. It is noted that all pavement sections in Minnesota had less than 30 days of inundation during their service lives, meaning the state did not have any highly flooded pavement sections. Figure 52 also shows a wide range of RIRI values across different regions. For example, the RIRI for the 3,164 pavement sections in the Gulf of Mexico ranges from 3 to approximately 40 months. The variation in RIRI for Minnesota and California was still considerable but lower than that observed for the Gulf of Mexico. Similarly, the RIRI for highly flooded sections exhibited a wide range, though the average RIRI was higher than that for all sections. These variations are primarily attributed to the diversity of pavement designs in the HPMS dataset, which includes a broad spectrum of road types, from robust interstate highways to thin local roads. This diversity in pavement design explains the significant variation in RIRI values. Nonetheless, the average RIRI still provides a valuable measure of the overall resiliency of the network against flooding events, with higher average RIRI values expected in regions with more frequent and prolonged floods. 6.2.4. Sensitivity Study at Network-Level Modeling the effects of flooding on pavement structures using the UPDAPS-Flood program requires several inputs, ranging from the characteristics of flooding events to the materials’ responses. In this study, several assumptions were made regarding these input parameters. Therefore, a sensitivity analysis is needed to evaluate the sensitivity of the results of the UPDAPS- Flood program to its inputs. Specifically, this sensitivity analysis evaluates the changes of the predicted IRI performance from the UPDAPS-Flood program by change in (i) resilient modulus variation in the unbound materials, (ii) recovery function, and (iii) variation of rutting coefficients presented. 6.2.4.1. Sensitivity to Reduction in MR of Saturated Unbound Layers The literature showed that the MR of the unbound materials reduces significantly with increasing moisture contents, ranging from 40% (partially saturated) to 80% (near saturation) 116 (Wang et al. 2015, Khan et al. 2019). This sensitivity analysis considered 30%, 50%, and 70% reductions in the modulus of saturated unbound materials. Figure 53 shows the effect of the MR reduction on the resiliency index across all three regions. According to this figure, a higher saturation level corresponds to higher MR reduction, leading to increased damage accumulation and a higher deterioration rate of the pavement structures. Therefore, the highest loss of service life (RIRI) was observed in pavement sections modeled with a 70% reduction in modulus of saturated unbound layers. Figure 53. Effect of resilient modulus reduction on the distribution of RIRI (Abdollahi et al. 2024) 6.2.4.2. Sensitivity to Recovery Path It has been reported that the reduced modulus of the saturated unbound layers can fully recover as the water drains from the pavement system and the moisture content of the unbound materials returns to pre-flood level (Wang et al. 2015). However, the rate and duration of the drainage 117 process can significantly affect the deterioration rate of the pavement structure. To evaluate the effect of the drainage rate on pavement performance, three recovery functions were implemented in the UPDAPS-Flood program. These three recovery functions are shown in Figure 44, in which paths 1 and 3 represent the highest and lowest drainage rate, while path 2 represents the average condition with a linear function. Figure 54 shows the sensitivity of RIRI to the drainage rate within pavement sections. The results of this figure refer to the 50% MR reduction to avoid the superposition of different variables. As this figure shows, the loss of service life (RIRI) values for pavement sections with a lower drainage rate (Path 3) were about two times greater than those with a higher drainage rate. This observation highlights the importance of proper subsurface drainage system design during the post-flood recovery time, which can improve the resiliency of the pavement system against flooding events. Figure 54. Effect of recovery function on the distribution of RIRI (Abdollahi et al. 2024) 118 6.2.4.3. Sensitivity to Unbound Materials Rutting Model Coefficients Recent studies showed that the rutting resistance of the unbound materials decreases rapidly at higher water content levels (Ba et al. 2015). This phenomenon can be modeled by recalibrating the rutting distress prediction model in the laboratory under higher saturation levels. The sensitivity analysis was conducted by varying the rutting calibration coefficient between 1.25 and 2.00. This coefficient acts as a direct multiplier of the rutting function, with higher values indicating an increased rate of rutting accumulation. The sensitivity analysis results, as shown in Figure 55, demonstrate the high sensitivity of the UPDAPS-Flood program to this coefficient. As this figure shows, increasing the coefficient from 1.50 to 2.00 resulted in an average loss of pavement service life that was four times greater. These findings highlight the need for further laboratory research to better understand the rutting behavior of pavement materials at higher water content levels. Figure 55. Effect of rutting model coefficients on the distribution of RIRI (Abdollahi et al. 2024) 119 6.3. National Wide Network-Level Resiliency Analysis This section presents a nationwide evaluation of the resiliency of the pavement network against flooding events. For this purpose, data from 10,650 pavement sections across the contiguous United States and their corresponding flooding records were extracted from the HPMS and NOAA databases. The UPDAPS and UPDAPS-Flood program results were used to generate resiliency maps based on the definition of pavement resiliency against flooding events, as discussed in section 6.1. It is noted that the results in this section are based on primary UPDAPS-Flood input assumptions, including a maximum 50% reduction in the MR of unbound materials following the linear recovery path (Path 2), and a rutting model calibration coefficient of 1.5. 6.3.1. Information of Extracted Pavement Sections The HPMS database was primarily used to extract the properties of flexible pavement sections across the United States and prepare the input files for running the UPDAPS and UPDAPS-Flood programs. This database contains information on 71,141 flexible pavement sections nationwide. To reduce computational expense, a representative sample of 16,869 pavement sections was randomly selected while maintaining the spatial distribution of sections within each state. However, due to missing data—such as climatic information, pavement material properties, or flooding records (e.g., some sections were not exposed to flooding events)—the final analysis included 10,650 flexible pavement sections. Figure 56 shows the spatial distribution of these pavement sections across the United States. Each pavement section is represented by a small blue dot, with thick and thin black lines indicating state and county boundaries, respectively. The extracted pavement sections consist of either newly constructed AC layers over a gravel base or AC overlays on an existing HMA layer, and they were modeled using the UPDAPS and UPDAPS-Flood programs for a service life from August 2002 to August 2022. These 10,650 pavement sections are distributed across 45 states in the contiguous United States. It is noted that there was not enough information for the selected pavement sections in the District of Columbia (D.C.), Iowa, Mississippi, and Wisconsin. For the remaining pavement sections, missing data on traffic, environmental conditions, material properties, and pavement structure were supplemented from various sources, including defaults inputs used in NAPCOM, HERS programs as well as LTPP data. Further details on preparing input JSON files for each pavement section can be found in Appendix C (see page 213). A summary of the structural, traffic, and climate characteristics of the extracted pavement sections is provided in Table 5. 120 Figure 56. Spatial distribution of the HPMS pavement sections across the United States 6.3.2. Information of Extracted Flooding Records The NOAA database was utilized to extract flooding event records from August 2002 to August 2022 (NOAA 2023). For this purpose, only ‘flood’ and ‘hurricane’ events were pulled for all states within the contiguous United States. As discussed in section 6.2.2, one of the main limitations of the NOAA database is its spatial resolution, which reports flooding events at the county level. Since more precise flood data is not currently available, it has been assumed that all pavement sections within a flooded county are affected by the flooding event. The extracted flooding data showed 27,726 flooding event records across 2,787 counties in the contiguous United States, where a statistical summary of these records is shown in Table 6. Pavement sections with more than 30 days of inundation during their service lives are classified as highly flooded sections. As shown in Table 6, 30.09% of the extracted pavement sections fall into this category. In addition, Figure 57 and Figure 58 show the number of flooding events and the total duration of flooding inundation for each county. 121 Figure 57. Number of flooding event records in different counties across United States between August 2002 to August 2022 Figure 58. Total inundation duration in counties across United States due to the flooding event records between August 2002 and August 2022 As shown in Figure 57, the number of flooding event records in the LTPP Wet/Freeze region is significantly higher than in other areas in the United States, with some counties experiencing up to 50 flooding events over 20 years. This observation agrees with the general expectations, as higher precipitation levels in this region increase the likelihood of flooding. However, Figure 58 indicates that the average inundation duration for frequent flooding events in the LTPP Wet/Freeze region is typically one to two days. On the other hand, the longest total inundation durations were 122 observed in counties along the Missouri and upper Mississippi rivers, likely due to river flooding events impacting surrounding pavement sections. This observation further highlights the major limitation of the NOAA storm event database, where flooding records are reported at the county level, lacking finer spatial resolution. 123 Table 5. Summary information about the pavement structural, traffic, and climate properties used in national wide network- level resiliency analysis State Alabama Arizona Arkansas California Colorado Connecticut Delaware Florida Georgia Idaho Illinois Indiana Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Missouri Montana Nebraska Nevada New Hampshire New Jersey New Mexico New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania # of Sections 357 186 224 601 395 101 65 527 499 277 90 335 129 245 169 265 93 37 417 258 264 346 160 180 153 133 292 210 294 256 220 152 336 160 AC thickness (in) Min 4.5 4 6 4 4 2 2 2 4 2 4 4 2 2.5 2.7 4 2 3 2 2 5 2 2 2 2 2 4 5.5 2 2 3 2 2.5 2 Avg 8.6 8.9 8.4 6.2 7.1 7.1 5.8 3.3 7.0 6.1 9.4 7.5 4.8 9.5 8.0 7.4 9.0 8.6 3.0 6.9 10.4 5.3 5.9 5.3 3.9 5.8 5.4 11.9 9.4 6.6 7.3 6.0 6.9 7.5 Max 22 16 12 8 14 17 17.8 14 12 14.8 13 14 14 22 22 17 18 13 11.5 13.0 14 13.5 20 14.5 9 15 12 12 21 16 14 15 16.5 22 Base thickness (in) Min 4 6 6 6 6 1 0.5 2 6 2.4 4 6 1 4 0.1 6 4 5 1 2.5 4 4 3 4 6 6 4 6 2 1 6 4 5 1 Avg 5.9 6.4 6.5 11.9 16.0 7.3 5.8 7.7 7.2 12.2 5.9 7.6 4.9 4.9 7.8 11.9 7.7 5.6 15.4 8.6 6.0 13.8 7.1 10.2 8.0 7.3 6.3 8.4 7.3 7.7 6.0 6.2 8.1 8.6 Max 12 20 11 12 30 18 16 12 10 34 6 12 16 16 21.3 28 27 6 24 34 6 36 17 30 36 30 12 12 18 20 6 10 23 36 124 Traffic (106 ESALs) Min 7.0 6.4 8.6 8.6 6.3 4.0 4.0 4.0 6.3 4.1 6.4 6.3 4.0 4.7 4.9 6.3 4.0 5.2 4.0 4.0 7.5 4.0 4.1 4.0 4.0 4.1 6.3 8.1 4.1 4.0 5.2 4.1 4.7 4.1 Avg 11.7 12.0 11.4 8.7 9.9 10.0 8.4 5.6 9.9 8.8 12.6 10.4 7.4 12.7 10.9 10.3 12.1 11.7 5.3 9.7 13.7 7.9 8.6 7.9 6.3 8.4 8.0 15.4 12.4 9.3 10.2 8.7 9.7 10.3 Max 27.1 20.2 15.7 8.8 18.0 21.4 22.3 17.9 15.7 18.8 16.9 18.0 17.9 27.2 24.9 21.4 22.5 16.7 15.1 22.0 17.9 17.4 24.9 18.5 12.3 19.1 15.6 15.7 26.0 20.3 18.0 19.1 20.8 23.9 Mean annual air temp. (F) Min 59.0 49.9 57.9 39.7 31.2 47.6 54.7 67.8 56.6 34.8 47.9 49.8 53.6 54.1 65.1 39.0 53.1 45.9 40.5 38.7 52.0 33.2 49.7 45.4 44.0 49.8 46.1 42.3 54.0 39.1 49.7 58.6 42.1 45.2 Max 69.4 74.2 65.6 75.2 56.6 51.9 56.7 77.9 69.0 53.1 57.5 56.8 58.0 59.3 70.3 48.8 58.4 51.9 50.1 47.0 60.4 49.0 54.2 64.5 48.8 56.7 64.2 53.1 65.5 46.6 55.5 63.6 54.0 53.5 Avg 63.7 64.8 61.9 60.9 48.4 49.7 56.5 72.6 63.3 46.3 53.5 52.4 55.9 56.2 67.4 45.9 56.3 48.2 47.7 43.6 56.0 42.1 51.5 50.8 47.1 54.3 57.4 48.1 60.2 43.3 51.3 61.7 49.1 48.9 State Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington West Virginia Wyoming Summary # of Sections 31 187 241 181 361 387 66 183 356 113 118 10650 AC thickness (in) Min 2 4 2 6.3 3 6.5 4 2 2 2 3 2 Avg 6.2 10.2 5.8 12.5 3.6 7.1 6.5 9.4 5.5 9.9 6.4 7.17 Max 14 14 14 16 6 12 9 21.7 13.8 16 14 22 Table 5 (cont’d) Base thickness (in) Min 4 6 0.7 6 6 8 6 3 1 4 2 0.1 Avg 6.7 7.2 8.3 9.9 8.6 17.9 6.0 5.8 6.9 7.2 6.4 8.2 Max 18 16 32.7 10 12 18 6 7 28 16 12 36 Traffic (106 ESALs) Min 4.0 6.4 4.1 9.0 5.2 9.3 6.4 4.0 4.0 4.1 5.2 4.0 Avg 8.9 13.5 8.5 16.2 5.9 10.0 9.3 12.5 8.1 13.2 9.1 10.0 Max 17.9 18.0 17.9 20.3 8.8 15.7 12.2 26.8 17.6 20.2 17.9 27.2 Mean annual air temp. (F) Min 48.9 60.6 44.1 52.4 59.5 37.3 42.0 50.8 34.7 49.6 33.7 31.2 Max 51.7 68.1 50.8 61.2 76.2 62.3 44.9 60.3 54.0 55.5 49.3 77.9 Avg 50.5 64.3 47.9 57.9 68.2 49.5 44.0 56.2 48.9 53.3 44.2 53.8 Table 6. Summary of extracted flooding data from NOAA database State Alabama Arizona Arkansas California Colorado Connecticut Delaware Florida Georgia Idaho Illinois Indiana Kansas Kentucky Louisiana Maine Maryland Massachusetts # of Sections 357 186 224 601 395 101 65 527 499 277 90 335 129 245 169 265 93 37 Number of flood records1 Max Avg Min 22 7.5 1 20 11.7 1 22 7.3 1 39 14.2 1 9 4.3 1 29 10.7 3 8 8.0 8 41 7.9 1 17 6.1 1 20 7.6 1 15 6.1 1 39 12.8 1 46 18.0 2 41 10.6 1 12 5.0 1 28 12.6 5 52 12.8 2 39 21.0 13 Inundation duration2 (days) No. highly flooded sections3 Min 1 1 1 1 1 3 8 1 1 2 3 1 2 1 1 8 2 14 0 (0.0%) 0 (0.0%) 149 (66.52%) 151 (25.12%) 72 (18.23%) 12 (11.88%) 0 (0.0%) 130 (0.0%) 0 (0.0%) 181 (65.34%) 34 (37.78%) 125 (37.31%) 65 (50.39%) 67 (27.35%) 69 (40.83%) 47 (17.74%) 11 (11.83%) 23 (62.16%) Max 29 28 86 82 63 56 8 56 19 212 130 226 128 226 151 38 52 64 Avg 11.7 13.9 35.6 18.2 16.8 13.6 8.0 18.7 9.3 80.5 37.3 37.5 37.7 28.1 31.6 20.9 13.0 32.9 125 Table 6 (cont’d) State # of sections 417 258 264 346 160 180 153 133 292 210 294 256 220 152 336 160 31 187 241 181 361 387 66 183 356 113 118 10650 Number of flood records1 Max Avg Min 14 5.7 1 27 6.4 1 47 16.7 1 13 6.4 1 17 10.5 1 8 4.8 1 14 11.8 7 22 15.0 8 10 3.6 1 30 9.7 1 24 5.7 1 24 7.7 1 33 14.1 1 30 5.5 1 34 11.9 1 30 12.5 2 22 13.6 5 19 5.4 1 31 12.4 3 12 6.6 1 27 7.6 1 9 4.2 1 19 13.3 7 48 8.2 1 37 6.3 1 34 20.8 4 11 5.4 1 52 9.68 1 Michigan Minnesota Missouri Montana Nebraska Nevada New Hampshire New Jersey New Mexico New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington West Virginia Wyoming Summary 1Number of flood records per section. 2Total inundation duration per section during the service life (August 2002 to August 2022). 3Number of sections with more than 30 inundation days during their service life. Inundation duration2 (days) No. highly flooded sections3 Min 2 1 1 1 1 1 7 10 1 1 1 1 1 1 1 5 5 1 13 1 1 1 7 1 1 4 1 1 96 (23.02%) 108 (41.86%) 201 (76.14%) 192 (55.49%) 105 (65.62%) 108 (60.00%) 91 (59.48%) 34 (25.56%) 0 (0.0%) 72 (34.29%) 0 (0.0%) 244 (95.31%) 79 (35.91%) 11 (7.24%) 133 (39.58%) 24 (15.00%) 8 (25.81%) 13 (6.95%)) 229 (95.02%) 0 (0.0%) 90 (24.93%) 86 (22.22%) 0 (0.0%) 11 (6.01%) 97 (27.25%) 37 (32.74%) 0 (0.0%) 3205 (30.09%) Avg 26.0 43.6 61.1 35.0 102.6 25.4 24.4 29.3 4.6 30.2 8.1 112.7 27.8 8.6 25.6 25.7 25.3 8.2 104.8 9.7 20.8 18.3 14.2 9.8 27.9 24.4 14.1 29.63 Max 158 182 181 109 193 59 32 50 16 121 29 223 103 45 107 109 30 49 215 16 98 52 20 50 134 38 28 226 126 6.3.3. Resiliency Maps Based on the simulation results for 10,650 flexible pavement sections across the contiguous United States, nationwide resiliency maps of the pavement network against flooding events were generated. For this purpose, the pavement sections were first evaluated under a no-flood scenario using the UPDAPS program, followed by analysis with the UPDAPS-Flood program, which accounted for flooding events. These simulations were run in parallel on the HPCC remote computing servers at Michigan State University, with a total runtime of over 38,000 CPU hours. The results from the UPDAPS and UPDAPS-Flood programs were analyzed to calculate the RIRI for each pavement section by comparing the predicted IRI distress under both flooding and no-flood scenarios. The locations and corresponding RIRI values of these pavement sections were then used to generate the nationwide resiliency maps, as shown in Figure 59. This figure is based on the assumptions of a 50% reduction in the MR of the saturated unbound layer with linear recovery and a traffic multiplier factor of 2.0 during flooding events. This figure provides a general form of the resiliency maps against flooding events. This figure shows that a higher RIRI was observed for sections within the LTPP Wet/Freeze region, near major U.S. rivers, and along the eastern coastline. This observation is attributed to the higher frequency of flooding events and longer inundation times in these counties. Figure 59. Resiliency map for the contiguous United States 127 The resiliency map shown in Figure 59 was generated by plotting the RIRI for each pavement section (10,650 data points) across the contiguous United States. However, as discussed earlier in section 6.2.3, such a detailed resiliency map may be complex for road agencies to interpret. To address this issue, the K-Means clustering algorithm was applied to group the pavement sections based on their proximity. As a result, the 10,650 sections were divided into 300 distinct groups. Figure 60 shows the summarized resiliency map generated using this approach. In this figure, each circle represents the centroid of a group of pavement sections, with the size of the circle indicating the number of sections in that group. The color of each circle reflects the average RIRI value for the group. A comparison between Figure 59 and Figure 60 shows that the summarized map is much easier for road agencies to use in decision-making processes and identify potential flood- vulnerable areas. Figure 60. Summarized resiliency map using the K-Means clustering algorithm for the contiguous United States Figure 61 presents the resiliency of the analyzed pavement sections as boxplots for each state across the contiguous United States. These boxplots show the statistical distribution of the calculated RIRI values for the pavement sections. As shown, the highest RIRI values, indicating higher flooding damage, were observed in the pavement networks of Nebraska, followed by Kansas, South Dakota, Maryland, and Missouri. These findings are consistent with data from the NOAA database, which reported more frequent and severe flooding events in certain counties within these states. The results indicate that the average RIRI values for Nebraska, Kansas, South 128 Dakota, and Missouri are 20, 22, 18, and 16 months, respectively—significantly higher than the national average of 9.15 months. As mentioned previously, the spatial resolution of NOAA flooding records is limited to the county level. Due to the lack of more detailed flooding data, severe local river or coastal flooding may be assumed to impact all pavement sections within a county, potentially overestimating the predicted damage. As a result, these findings should be viewed as representing a worst-case scenario. Figure 62 shows the distribution of calculated RIRI values of highly flooded pavement sections within the six states with the highest RIRI values. It is noted that this study defined a highly flooded section as one with more than 30 days of inundation during its service life. As shown in this figure, except for the pavement network in South Dakota, the highly flooded sections exhibited significantly higher RIRI values, with an average increase of 1.66 times. It is noted that 95% of the pavement sections in South Dakota were classified as highly flooded, which explains why no significant difference was observed between the distribution of RIRI values for highly flooded sections and all sections in that state. 129 Figure 61. Distribution of the resiliency metric (RIRI) in different states divided into three groups alphabetically 130 Figure 62. Effect of high inundation period on the distribution of the resiliency metric (RIRI) for six states with highest resiliency metric values 6.4. Chapter Conclusion This chapter provided examples of the application of the UPDAPS-Flood program to evaluate the resiliency of the flexible pavement network against flooding events. Based on predicted IRI distress, the loss of service life was selected as the resiliency metric (RIRI). The chapter is divided into two main phases: (i) a proof of concept for the methodology and a sensitivity analysis of key input assumptions, and (ii) an evaluation of the nationwide resiliency of the United States pavement network to flooding. For this purpose, the pavement structural, traffic, and environmental properties of the sections were primarily extracted from the HPMS database, with missing data supplemented from various sources, as described in Appendix C (see page 213). Additionally, flooding information was pulled from the NOAA database. The extracted data were used to create input JSON files for each pavement section. The UPDAPS-Flood program was run on the HPCC remote computing servers at Michigan State University using 1,024 CPUs concurrently. The calculated RIRI values were utilized to generate network resiliency maps, which can assist road agencies in decision-making and identifying flood-vulnerable areas. To facilitate the interpretation of these maps, the K-Means algorithm was applied to cluster pavement sections based on spatial proximity, enabling better analysis of average RIRI values without the interference of noise effects. 131 In the first phase, the UPDAPS-Flood program was used to simulate 7,655 flexible pavement sections across three regions in the United States: (i) the coastal regions along the Gulf of Mexico, known for more frequent and severe flooding events, (ii) the state of Minnesota, which experiences frequent flash floods, and (iii) the state of California, where flooding events have shown an increasing trend in the past decade. The results indicated a higher loss of service life along the Gulf of Mexico compared to Minnesota and California, attributed to the more severe and frequent flooding events in that region. Although California has recorded more frequent and intense flooding events, its pavement network showed higher resiliency against flooding compared to Minnesota. This is likely because, on average, California pavement structures are thicker than those in Minnesota, which significantly influenced the structural analysis results. In addition, the results showed that the highly flooded sections suffered significant performance loss, highlighting the importance of accounting for flooding events in pavement design and maintenance frameworks, especially in flood-prone areas. The first phase of this chapter also discussed a limited sensitivity analysis to evaluate the primary assumptions in the UPDAPS-Flood program, specifically: (i) the reduction in the MR of saturated unbound layers, (ii) the shape of the recovery path, and (iii) the k1 local calibration coefficient in the rutting model. The results showed a direct correlation between the reduction in MR of saturated unbound layers and the accumulated flooding damage. Additionally, the analysis showed that improving drainage systems, resulting in a higher drainage rate during the post-flood recovery time, could significantly reduce the loss of pavement service life, potentially by a factor of two, thereby improving the resiliency of the pavement network against flooding events. Finally, the study found that the distress prediction models used in the MEPDG are highly sensitive to the model coefficients. This finding highlights the need for further laboratory research to better understand the rutting behavior of unbound materials under higher water content conditions. In the second phase, the UPDAPS-Flood program simulation results for 10,650 flexible pavement sections across the contiguous United States were used to generate nationwide resiliency maps. These maps were based on assumptions of a 50% reduction in the MR of the saturated unbound layer with linear recovery and a traffic multiplier factor of 2.0 during flooding events. The results showed a higher loss of pavement service life for pavement networks within the LTPP Wet/Freeze region, areas near major U.S. rivers, and the eastern coastline, which can be attributed to the more frequent and severe flooding events recorded in these counties. The analysis found that 132 the average loss of service life for the pavement network across the contiguous United States was approximately nine months. However, the highest flooding damage was observed in Nebraska, followed by Kansas, South Dakota, Maryland, and Missouri. These findings align with data from the NOAA database, which reported more frequent and severe flooding events in certain counties within these states. It is noted, however, that the spatial resolution of the NOAA flooding records is at the county level. With the lack of more detailed flooding data, severe local river or coastal flooding may be assumed to affect all pavement sections within a given county, potentially increasing the predicted flooding damage. Therefore, these results should be interpreted as representing a worst-case scenario. 133 CHAPTER 7. RESILIENCY OF GEOSYNTHETIC-REINFORCED FLEXIBLE PAVEMENTS AGAINST FLOODING EVENTS This chapter evaluates the effect of geogrid reinforcement on improving the resiliency of flexible pavements against flooding events. For this purpose, a limited laboratory study was conducted to evaluate the mechanical behavior of a selected granular base material, both with and without geosynthetic reinforcement. The Resilient Modulus (MR) and Repeated Load Permanent Deformation (RLPD) tests were conducted to predict the material's behavior. The results from these laboratory tests were then used to simulate the resiliency of two typical flexible pavement sections in Michigan under flooding conditions. A FEM-based pavement structural response model was integrated into the UPDAPS-Flood program to account for the stress-dependent nonlinearity of the unbound base materials and the geosynthetic reinforcement. 7.1. Laboratory Testing This section presents the methodology and results of the detailed laboratory efforts to determine the physical properties and mechanical behavior of the granular base materials used in this study. The experimental plan involved basic soil index tests, Resilient Modulus (MR), and Repeated Load Permanent Deformation (RLPD) tests conducted with and without geosynthetic reinforcement. 7.1.1. Materials The granular base material used in this study was obtained from the Michigan Paving & Materials (MPM) company, an asphalt paving contractor in Michigan. The base material was collected to meet the specifications for dense-graded aggregate (21A) according to the Michigan Department of Transportation (MDOT) standard specifications for construction (MDOT 2020). Basic soil index tests, including grain size distribution and Proctor compaction, were conducted to determine the physical properties of the collected material. 7.1.1.1. Grain Size Distribution The ASTM D422 (2012), the standard test method for particle-size analysis of soils, was followed to measure the grain size distribution of the base material. This procedure involves sieve analysis to determine the percentage of different soil fractions, such as gravel, sand, and fines. The sieve analysis results, performed with four repetitions for the collected base material, along with the MDOT specification requirements for 21A dense-graded aggregates, are presented in Table 7, and plotted in Figure 63. This table shows the collected soil met the MDOT specifications, except 134 for the fine content. The analysis showed that the base material consists of 50.37% gravel, 48.87% sand, and 0.76% fine content, with a coefficient of uniformity and coefficient of curvature of 17.84 and 0.37, respectively. Therefore, the base material is classified as poorly graded gravel (GP) soil. Sieve number 1½ 1 3/4 3/8 #4 #8 #16 #30 #50 #100 #200 Table 7. Sieve analysis results Sieve size (mm) 38.10 25.40 19.05 9.52 4.75 2.36 1.15 0.6 0.3 0.15 0.075 Passing percent (%) 100 98.70 86.40 64.84 49.63 37.64 25.41 11.76 4.44 1.45 0.76 MDOT Specification Minimum Maximum 100 85 - 50 - 20 - - - - 4 100 100 - 75 - 45 - - - - 8 Figure 63. Grain size distribution of granular base material and MDOT specification requirements 7.1.1.2. Standard Proctor Compaction test The standard Proctor compaction test was performed according to ASTM D698 (2021) to determine the Optimum Moisture Content (OMC) and Maximum Dry Density (MDD) of the 135 collected base material. Three repetitions of the Proctor compaction test were conducted Table 8 shows the results of the standard proctor tests, where the OMC and MDD of the sample are 6% and 161 pcf, respectively. These results were used during the sample preparation for the MR and RLPD tests. Figure 64 also shows the moisture-density relationship for the collected base material at different trials. Table 8. Results of standard Proctor compaction test Property OMC (%) MDD (pcf) 158.57 Trial 1 6.00 Trial 2 6.20 161.38 Trial 3 5.88 162.69 Average value 6.03 160.88 Figure 64. Moisture-density relationship of granular base material 7.1.1.3. Geosynthetic This study selected a commonly used commercial geosynthetic product to reinforce the base materials, as shown in Figure 65. This geosynthetic is made from high-grade polyester yarn, known for its high tenacity and low creep properties, and is knitted into a stable network. According to the manufacturer's catalog, the product is characterized by its low elongation, superior stress-strain behavior, and high permeability performance. The technical properties of the selected geosynthetic, as reported by the manufacturer, are provided in Table 9. It is noted that the relatively small aperture opening size of this geosynthetic makes it well-suited for use with the 6- inch diameter triaxial samples. 136 Figure 65. Geosynthetic product used in this study Table 9. Technical properties of the selected geosynthetic Property Minimum ultimate tensile strength in X-direction Minimum ultimate tensile strength in Y-direction Elongation at minimum ultimate tensile strength Creep reduction factor at 20 C and 120 years design life Creep limited strength Values 6,850 lbf/ft 6,850 lbf/ft 10% 1.4 4,893 lbf/ft Testing standard ASTM D4595 ASTM D4595 ASTM D4595 - - 7.1.2. Resilient Modulus (MR) test The resilient modulus (MR) test was performed using a cyclic triaxial test setup according to the AASHTO T307, the 'Standard Method of Test for Determining the Resilient Modulus of Soils and Aggregate Materials'. This procedure involves applying cyclic loads to the compacted material during 15 different sequences with varying stress states and measuring the displacement response to calculate the nonlinear, stress-dependent MR behavior. Figure 66 shows the triaxial setup and the prepared base material sample used for the MR and RLPD tests. According to the AASHTO T307 procedure, 6-inch diameter and 12-inch height samples were prepared by compacting the base materials at their OMC of 6% using six equal lifts. The required weight of moist material for each lift was calculated based on the MDD and OMC results from the Proctor compaction test, targeting a 95% compaction ratio. A vibratory compaction hammer was used to compact the materials to 2-inch height increments for each lift. For the geosynthetic- reinforced samples, the geosynthetic layer was placed in the middle of the sample, between the third and fourth lifts. To ensure proper installation, the surface of the compacted material at the third lift was lightly scratched with a spatula before placing the geosynthetic. Half of the material from the fourth lift was placed on top of the geosynthetic layer and manually compacted with a standard Proctor hammer, after which the remaining material from the fourth lift was added and 137 compacted with the vibratory hammer. Finally, after compaction of the fifth and sixth lifts, the prepared sample was weighed to verify the compaction ratio, where the results are presented in Table 10. As this table shows, the compaction ratios of the prepared samples were within 1 % of the target value of the target compaction ratio (95%). Figure 66. Triaxial setup used for MR and RLPD tests Table 10. Compaction ratio of the prepared samples for MR and RLPD tests Property Dry density (pcf) Compaction ratio (%) Control sample (no geosynthetic) Trial 3 Trial 2 Trial 1 151.23 152.01 154.28 94.0 94.5 95.9 Geosynthetic-reinforced sample Trial 3 Trial 2 Trial 1 154.28 153.32 151.39 95.9 95.3 94.1 The compacted samples were sealed within the triaxial cell and placed in the Material Testing System (MTS) to conduct the MR test. The MR test, conducted according to the AASHTO T307 procedure, included 500 loading cycles for sample conditioning, followed by 15 sequences of 100 loading cycles to measure the strain response under various stress states. These stress states were applied by adjusting the triaxial cell confinement pressure and the vertical cyclic deviatoric stress 138 from the machine actuator. The details of the applied confining and deviatoric stresses to the sample are shown in Table 11. Each loading cycle included two phases: a haversine cyclic stress applied for 0.1 seconds, followed by a 0.9-second rest period during which a constant axial stress was applied to the sample. These phases are illustrated in Figure 67, where Pmin and Pmax represent the minimum (constant) and maximum axial stresses, respectively. Table 11. Stress state during different loading sequences of MR test Sequence No. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Confining stress (psi) 15 3 3 3 5 5 5 10 10 10 15 15 15 20 20 20 Cyclic deviatoric stress (psi) 13.5 2.7 5.4 8.1 4.5 9.0 13.5 9.0 18.0 27.0 9.0 13.5 27.0 13.5 18.0 36.0 Maximum axial stress (psi) 15 3 6 9 5 10 15 10 20 30 10 15 30 15 20 40 Constant (minimum) axial stress (psi) 1.5 0.3 0.6 0.9 0.5 1.0 1.5 1.0 2.0 3.0 1.0 1.5 3.0 1.5 2.0 4.0 No. of loading cycles 500 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 Figure 67. Loading cycle pattern during the MR and RLPD tests During the MR test, the applied deviatoric load and the measured deformation of the sample were recorded and used to calculate the deviatoric stress and axial strain by dividing the load and deformation by the sample's cross-sectional area and height, respectively. The MR was then calculated for each loading cycle as the ratio of peak-to-peak applied deviatoric stress to peak-to- peak measured axial strain, as shown in Equation (51). 139 𝑀𝑅 = 𝜎𝑑 𝜀𝑟 (51) where: MR = resilient modulus of the loading cycle of interest (psi). σd εr = peak-to-peak applied deviatoric stress during the loading cycle of interest (psi). = peak-to-peak measured axial strain during the loading cycle of interest. It is noted that the representative MR value for each of the 15 test sequences was reported as the average MR from the last five loading cycles. For example, Figure 68 shows the applied deviatoric stress and measured axial strain response for the control sample (Trial 1). Figure 68 (a) shows the range of applied deviatoric stresses for each test sequence, where the magnitude of the applied deviatoric stresses increases for each level of confining stress. Similarly, Figure 68 (c) presents the corresponding measured strain responses, showing the increasing trend in strain as the deviatoric stress increases. In the next step, the MR test raw data was analyzed to calculate the MR value for each test sequence. It is well-known that the MR of unbound materials depends on the applied stress state. Therefore, the NCHRP 1-37A model was used as MR prediction model, as shown in Equation (52) to (54). 140 Figure 68. Raw data from MR test for the control sample (Trial 1): (a) applied deviatoric stress during the entire test, (b) zoomed view of the applied deviatoric stress for the end of the third test sequence, (c) measured axial strain during the entire test, and (d) zoomed view of the measured axial strain during for the end of the third test sequence. 141 𝑀𝑅 = k1 ∙ 𝑝𝑎 ( 𝜃 𝑝𝑎 𝑘2 ) 𝜎𝑜𝑐𝑡 ( 𝑝𝑎 𝑘3 + 1) 𝜃 = 3 × 𝜎𝑐 + 𝜎𝑑 𝜎𝑜𝑐𝑡 = 1 3 2 √2 × 𝜎𝑑 (52) (53) (54) where: MR = predicted resilient modulus (psi). pa θ = air atmospheric pressure (psi). = bulk stress (psi). σoct = octahedral shear stress (psi). σc σd = confined stress (psi). = deviatoric stress (psi). k1, k2, k3 = model calibration coefficients. According to this model, the bulk stress (θ) and octahedral shear stress (σoct) represent the stress state of the sample. As an example, Figure 69 shows the correlation between the calculated MR values and both θ and σoct for the control sample (Trial 1) at different test sequences. Visual inspection of this figure shows a clear correlation between the MR and both θ and σoct, indicating stress-hardening behavior. The NCHRP 1-37A model was fitted to the MR test results for different samples, where the calibrated model coefficients are presented in Table 12. These calibration coefficients were calculated by minimizing the mean absolute error of the fitted NCHRP 1-37A model to the measured MR values at different test sequences for each test trial. The summary coefficients were calibrated by fitting the NCHRP 1-37A model to combined data from all three trials, which were then used in the subsequent numerical modeling. 142 Figure 69. Correlation between the measured MR values of the control sample (Trial 1) and (a) bulk stress, (b) octahedral shear stress Table 12. Calibrated coefficient of the NCHRP 1-37A model Property Control sample (no geosynthetic) Geosynthetic-reinforced sample k1 k2 k3 Trial 1 539.19 0.52 0.46 Trial 1 522.36 0.27 0.97 Trial 1 564.98 0.72 0.16 Summary Trial 1 488.71 541.34 0.64 0.52 0.59 0.50 Trial 1 518.03 0.66 0.60 Trial 1 739.57 0.68 0.22 Summary 580.43 0.66 0.46 Although the calibrated coefficients of the NCHRP 1-37A model are required and used in numerical simulations, these numerical values are not easily interpretable when assessing the effect of geosynthetic reinforcement on the MR of granular base materials. In addition, according to the NCHRP 1-37A model, MR is a function of both θ and σoct, meaning neither of these stress variants alone can fully reflect the stress state within the sample. Therefore, both must be considered in any visual representations used for interpretation. To address this issue, the MR test results are presented using a newly designed 2D plot, where the vertical axis shows the laboratory-measured MR values for different test sequences of each sample, and the horizontal axis shows the corresponding reference MR values for the same stress state. The reference MR values are calculated using the NCHRP 1-37A model and the summary calibrated coefficients from the control sample. Figure 70 shows the distribution of the laboratory-measured MR values with their corresponding reference MR values for both control and geosynthetic-reinforced samples. As shown in Figure 70 (a), the measured MR data points are clustered around the line of equality, where the slope of the best-fit line is equal to 1. This observation was expected, as the reference MR values were calculated using the summary calibration coefficients for all trials of the control 143 samples. However, Figure 70 (b) shows that the measured MR data points for the geosynthetic- reinforced samples are generally above the line of equality, with an average increase of 47% compared to their corresponding reference MR values (slope of best-fit line is 1.47). This observation indicates the beneficial effect of geosynthetic reinforcement on the stiffness of the samples, which is primarily attributed to the local stiffness increase within the influence zone of the geosynthetic. This observation aligns with geosynthetic mechanism theory, as detailed in section 7.2.1. Figure 70. Distribution of laboratory measured MR compared with reference MR for: (a) control sample, (b) geosynthetic-reinforced sample Considering the stress-hardening behavior of the unbound base material used in this study, Figure 70 (b) also shows that the effect of geosynthetic reinforcement on increasing MR is more pronounced at higher stress states. This is primarily due to the concept of particle mobilization, where Poisson’s effect at higher stress states causes higher horizontal mobilization of soil particles. Due to the interlock between the geosynthetic and soil particles, such higher horizontal mobilization increases the additional confinement by the geosynthetic. This phenomenon is thoroughly discussed in the geosynthetic-reinforcement theory in section 7.2.1 (see page 154). 7.1.3. Repeated Load Permanent Deformation (RLPD) test The Repeated Load Permanent Deformation (RLPD) test was conducted using a cyclic triaxial test setup according to the NCHRP 1-50 recommended procedure (Luo et al. 2017). This test was performed on control and geosynthetic-reinforced samples, with three replicates. The RLPD test was conducted immediately after completing the MR test on the same samples. Since the MR test involves a relatively low number of loading cycles (100 cycles per sequence), the sample is 144 considered undamaged after the MR test, allowing the RLPD test to be conducted on the same specimen. According to the NCHRP 1-50 recommended procedure, the RLPD test consists of two test sequences, as shown in Table 13. The first sequence involves conditioning the sample with 500 loading cycles, similar to test sequence zero in the MR test, to ensure continuity between the MR and RLPD tests (Luo et al. 2017). The second sequence consists of 10,000 loading cycles to evaluate the permanent deformation behavior of the sample. The NCHRP 1-50 procedure proposes six different stress states for conducting the RLPD test, and it recommends selecting one for the test. The confining stresses of these six stress states range from 4 to 13 psi (Luo et al. 2017), and for this study, a stress state with a 10 psi confining stress was selected. Table 13. Stress state during different loading sequences of MR test Sequence No. 0 1 Confining stress (psi) 15 10 Cyclic deviatoric stress (psi) 13.5 25.2 Maximum axial stress (psi) 15 28 Constant (minimum) axial stress (psi) 1.5 2.8 No. of loading cycles 500 10,000 It is noted that the deviatoric stress loading pattern is identical to that of the MR test, with a 0.1- second haversine loading followed by a 0.9-second resting period at constant (minimum) stress, as illustrated in Figure 67. During the RLPD test, the deformation of the sample was recorded and used to calculate the plastic deformation and plastic strain (εp) response. The plastic deformation for each of the 10,000 loading cycles was determined as the difference between the initial deformation at the start of the first loading cycle and the deformation at the end of each subsequent cycle, as conceptually illustrated in Figure 71. The calculated plastic deformations were then divided by the sample length to compute the plastic strains. 145 Figure 71. Conceptual scheme of procedure for calculating the plastic deformation The evolution of plastic strain (εp) in all samples was calculated using the measured plastic deformation, as shown in Figure 72. This figure shows the average εp for each sample from three replicates, with error bars indicating the variation in the results. As this figure shows, the average εp for the control and geosynthetic-reinforced samples after 10,000 loading cycles was 0.0334 and 0.0256, respectively, indicating that geosynthetic reinforcement reduced plastic strain by 23.4%. Although the variation in εp for the geosynthetic-reinforced samples was higher than for the control samples, the geosynthetic reinforcement still provided better resistance to permanent deformation, as the error bars do not overlap. Figure 72. Plastic strain (εp) response of control and geosynthetic-reinforced sample during RLPD test 146 The plastic strain model of the NCHRP 1-50, shown in Equation (65), was fitted to the average of measured εp of the control and geosynthetic-reinforced samples to calibrate the ε0, ρ, and β coefficients. The calibrated coefficients are presented in Table 14, and the fitted model is shown in Figure 73. It is noted that the default model coefficients for the stress state components (n=- 2.16 and m=1.7) were used to calibrate the NCHRP 1-50 plastic strain model. Table 14. Calibrated coefficients of NCHRP 1-50 plastic strain model Sample type Control (no geosynthetic) Geosynthetic-reinforced ε0 0.6061 0.6665 ρ 1021.36 4128.01 β 0.3908 0.2957 As shown in Figure 73 (a), the NCHRP 1-50 plastic strain model was adequately fitted to the average of the measured εp response of the control and geosynthetic-reinforced samples within the 10,000 loading cycles of the RLPD test. Since this model is directly used to calculate the additional confinement provided by the geosynthetic within the FEM-based pavement structural response model, it is crucial to assess its extrapolating behavior at a higher number of loading cycles. Figure 73 (b) shows the extrapolated prediction of the εp response for up to 100,000 loading cycles. As this figure shows, the evolution of the εp response almost stabilizes and the predicted εp values after 100,000 loading cycles for the control and geosynthetic-reinforced samples were 0.0428 and 0.0376, respectively. This observation suggests that geosynthetic reinforcement can provide about a 12% reduction in the predicted εp response at 100,000 loading cycles. As mentioned earlier, the geosynthetic-reinforcement mechanism is primarily based on the interlock between the geosynthetic and the unbound material aggregates at their interface. Therefore, the compatibility between the geosynthetic aperture opening size and the unbound material gradation is crucial for effective interlock. The geosynthetic used in this study has a relatively small aperture opening size, which may not ideally match the granular base materials. However, the MR and RLPD test results still demonstrated improved mechanical behavior in the geosynthetic-reinforced samples, which indicates an effective interlock. 147 Figure 73. Plastic strain model of NCHRP 1-50: (a) fitted to the laboratory measured average εp response of samples, (b) extrapolated to 100,000 loading cycles Figure 74 shows the geosynthetic extracted from the compacted sample (Trial 1) after the MR and RLPD tests. This figure shows that the geosynthetic deformed into a 3D shape of hills and valleys due to direct contact with the unbound material aggregates during compaction and testing. Additionally, the small aperture size of the geosynthetic increases the contact surface with the unbound material, enhancing friction forces, particularly when the unbound material contains higher percentages of sand and fines. These observations provide evidence of effective interlock between the geosynthetic and unbound material aggregates. 148 Figure 74. Extracted geosynthetic from the compacted sample (Trial 1) after conducting MR and RLPD tests 7.2. Numerical Simulations This section provides the numerical simulation of the effect of geosynthetic reinforcement on the resiliency of flexible pavement sections against flooding events. To achieve this, the theory of geosynthetic reinforcement was reviewed and incorporated into the FEM-based pavement structural response model within the UPDAPS-Flood program. Two typical flexible pavement structures from Michigan were selected for the pavement structure-level analysis, and corresponding flooding records were extracted from the NOAA database. Finally, the pavement structural analysis and ME pavement analysis results under the no-flood and flooding scenarios were presented. 7.2.1. Theory of Geosynthetic-Reinforcement The NCHRP 1-50 project developed a theory to quantify the impact of geosynthetic reinforcement on pavement performance. As part of this project, an analytical model was developed to predict the vertical and horizontal modulus of geosynthetic-reinforced unbound materials using the concept of additional lateral confinement provided by the geosynthetic (Gu et al. 2016, Luo et al. 2017). This section provides details of this model and its application in pavement structural analysis. Figure 75 shows a schematic plot of a cylindrical geosynthetic-reinforced unbound material under a confining pressure of σ3 and an axial stress of σ1. Compression of the sample in the axial 149 direction (due to σ1) causes lateral movement of the unbound materials, driven by Poisson’s effect and both plastic and resilient deformation. This lateral movement is restrained by the geosynthetic, which generates shear stresses due to the relative lateral displacement between the geosynthetic and the unbound material aggregates, stretching the embedded geosynthetic. However, the lateral movement of the unbound material aggregates and the geosynthetic are not identical. Therefore, the α coefficient is introduced to account for the difference in radial displacement between the geosynthetic and the unbound material aggregates, as described in Equation (55) (Gu et al. 2016). Figure 75. Schematic plot of geosynthetic-reinforcement of unbound material sample 𝛼 = 𝑎 𝜀𝑟𝑟 𝑔 𝜀𝑟𝑟 (55) where: εa rr = radial tensile strain of unbound material aggregate at the interface between geosynthetic and aggregate. εg rr = radial tensile strain of geosynthetic at the interface between geosynthetic and aggregate. As the lateral movement of the aggregates generates the lateral movement in the geosynthetic, it is normally expected that the α coefficient will have a value greater than 1. However, an analytical solution for determining the α coefficient has been derived in the literature, as shown in Equation (56) (Christopher et al. 2001, Perkins 2002). The α coefficient can be implicitly solved using an iterative solver. 𝛽 ∙ 𝐽0 (𝛽 𝐷 2 ) − 2 𝐷 ∙ 𝐽1 (𝛽 𝐷 2 ) = σ3 (56) 150 𝛽 = √ 2) 2 𝐺𝑎(𝛼 − 1)(1 − 𝜈𝑔 𝛿 𝑀 (57) where: Ji = Bessel function of the order i. D = diameter of the unbound material cylindrical sample (inch). Ga = shear modulus of the unbound material aggregate. σ3 = confining stress (psi). M = geosynthetic sheet stiffness (lb/ft). δ νg = influence zone of the geosynthetic (inch); typically assumed 6-inches. = Poisson’s ratio of the geosynthetic. As mentioned earlier, the stretching of the geosynthetic generates a reinforcement force (T), which provides additional lateral confinement to the unbound materials through the interlock between the aggregate and the geosynthetic. Under axisymmetric plane-stress condition, this reinforcement force is calculated using Equation (58) (Luo et al. 2017). 𝑇 = 𝑀 1 − 𝜈𝑔 2 (𝜀𝑟𝑟 𝑔 ) 𝑔 + 𝜈𝑔 ∙ 𝜀𝜃𝜃 (58) where εg θθ is the tangential tensile strain of geosynthetic at the interface between geosynthetic and aggregate. However, by assuming that the geosynthetic deforms uniformly in tangential and radial directions, Equation (58) can be simplified, as shown in Equation (59). 𝑇 = 𝑀 1 − 𝜈𝑔 𝑔 𝜀𝑟𝑟 (59) where: T = reinforcement force by the geosynthetic (lb). However, this reinforcement force is not uniformly distributed over the height of the sample. It is highest at the location where the geosynthetic is installed and gradually decreases with distance of the unbound materials from the geosynthetic. The NCHRP 1-50 model assumes a triangular distribution for the additional confinement stress, represented by Δσ3 in Figure 75, 151 where the additional confinement dissipating beyond the influence zone (δ) of the geosynthetic. The maximum additional confining stress (Δσ3,max) can be calculated using Equation (60). 𝛥𝜎3,𝑚𝑎𝑥 = 2𝑇 𝛿 = 2𝑀 (1 − 𝜈𝑔)𝛿 𝑔 𝜀𝑟𝑟 (60) where: Δσ3,max = maximum additional confinement by the geosynthetic (psi). It is noted that the assumption of a 6-inch influence zone for the geosynthetic was made during the NCHRP 1-50 project (Luo et al. 2017). By incorporating Equation (55), the maximum additional confinement can be written as a function of the radial tensile strain of the unbound materials at the geosynthetic interface (εa rr), as shown in Equation (61). 𝛥𝜎3,𝑚𝑎𝑥 = 2𝑇 𝛿 = 2𝑀 (1 − 𝜈𝑔) 𝛿 ∙ 𝛼 𝑎 𝜀𝑟𝑟 (61) The radial tensile strain of unbound materials at the geosynthetic interface (εa rr) is the sum of the radial elastic strain (εa 3,r) and radial plastic strain (εa 3,p). The generalized Hooke’s law can be applied to define εa 3,r, as shown in Equation (62). 𝑎 = 𝜀3,𝑟 (𝜎3 + 𝛥𝜎3,𝑚𝑎𝑥) 𝐸𝐻 − 𝜈13 ∙ 𝜎1 𝐸𝑉 − 𝜈33(𝜎3 + 𝛥𝜎3,𝑚𝑎𝑥) 𝐸𝐻 (62) where: εa 3,r EH EV ν13 ν33 = radial elastic strain of unbound material at the interface of geosynthetic. = modulus of the specimen at horizontal direction (psi). = modulus of the specimen at vertical direction (psi). = Poisson’s ratio to characterize the effect of axial strain on lateral strain. = Poisson’s ratio to characterize the effect of lateral strain on axial strain. On the other hand, the radial plastic strain is related to the axial plastic strain through the dilation angle concept, as shown in Equation (63) (Bolton 1987). 𝑎 = 𝜀3,𝑝 1 2 𝑎 ( 𝜀1,𝑝 1 + sin 𝜓 1 − sin 𝜓 ) (63) where: εa 3,p = radial plastic strain of unbound material at the interface of geosynthetic. 152 εa 1,p = axial plastic strain of unbound material at the interface of geosynthetic. ψ = dilation angle (º). Considering a dilation angle of 15º, the radial plastic strain of unbound materials can be written as a function of axial plastic strain, using Equation (64). This approach is preferable, as the axial plastic strain can be directly measured from the RLPD test results. 𝑎 𝛼 = 0.85 𝜀1,𝑝 𝜀3,𝑝 (64) The NCHRP 1-50 project proposed a new ME model to predict the axial plastic strain of control or geosynthetic-reinforced unbound material, as shown in Equation (65). It is noted that the default values were assumed for the m=1.7 and n=-2.16 model calibration coefficients of the stress state components according to the results presented in the NCHRP 1-50 project (Luo et al. 2017). 𝑎 = 𝜀0 ∙ exp (− ( 𝜀1,𝑝 𝛽 ) ) ∙ (√𝐽2) 𝑚 ∙ (𝛼 𝐼1 + 𝐾)𝑛 𝜌 𝑁 𝐽2 = 1 6 (𝜎1 − (𝜎3 + 𝛥𝜎3,𝑚𝑎𝑥)) 2 𝐼2 = 𝜎1 + 2(𝜎3 + 𝛥𝜎3,𝑚𝑎𝑥) 𝐾 = 𝑐 ∙ 6 cos 𝜑 √3(3 − sin 𝜑) (65) (66) (67) (68) where: Ν = number of loading cycles. J2 I1 c φ = second invariant of stress tensor (psi2). = first invariant of stress tensor (psi). = cohesion of the unbound materials (psi). = aggregate internal phase angle of unbound materials (º). ε0, ρ, β, m, n = model calibration coefficients. By substituting the elastic and plastic components of the radial tensile strain into Equation (61), a formula for calculating the maximum additional confinement due to geosynthetic reinforcement is derived, as shown in Equation (70). It should be noted that this equation is solved implicitly for Δσ3,max (Luo et al. 2017). 153 By substituting the elastic and plastic components of the radial tensile strain into Equation (61), a formula for calculating the maximum additional confinement due to the geosynthetic reinforcement is derived, as shown in Equation (70). This equation is solved implicitly for Δσ3,max (Luo et al. 2017). 𝛥𝜎3,𝑚𝑎𝑥 = 2𝑀 (1 − 𝜈𝑔) 𝛿 ∙ 𝛼 [𝜀3,𝑟 𝑎 ] 𝑎 + 𝜀3,𝑝 𝛥𝜎3,𝑚𝑎𝑥 = 2𝑀 (1 − 𝜈𝑔) 𝛿 ∙ 𝛼 (𝜎3 + 𝛥𝜎3,𝑚𝑎𝑥) [ 𝐸𝐻 − 𝜈13 ∙ 𝜎1 𝐸𝑉 − 𝜈33(𝜎3 + 𝛥𝜎3,𝑚𝑎𝑥) 𝐸𝐻 + 0.85 𝜀0 ∙ exp (− ( 𝛽 ) ) ∙ (√𝐽2) 𝑚 𝜌 𝑁 ∙ (𝛼 𝐼1 + 𝐾)𝑛] (69) (70) where all parameters were previously defined. According to this model, the additional lateral confinement due to geosynthetic reinforcement consists of three main components, as listed below: • Geosynthetic properties: The Δσ3,max is directly related to the sheet stiffness, where stiffer geosynthetics provide higher lateral confinement. Additionally, while the Poisson’s ratio (νg) of geosynthetics does not vary significantly, more rigid geosynthetics with lower νg can offer higher lateral confinement. However, it should be noted that stiffer and more rigid geosynthetics may be more prone to fracture during lateral aggregate movement or geosynthetic installation. Therefore, most manufacturers provide flexible geosynthetics with relatively high sheet stiffness. • Stress state: The stress state of the unbound material at the geosynthetic interface can vary depending on the location of the geosynthetic and the traffic loading on the pavement section. The increasing stress state directly affects the radial elastic strain response of the unbound materials, thereby increasing Δσ3,max. This behavior aligns with expectations from the geosynthetic reinforcement mechanism, in which higher stress states enhance lateral soil particle mobilization (due to Poisson’s effect). This mobilization is restrained by the interlock between the soil particles and the geosynthetic, leading to a higher reinforcement force generated by the geosynthetic. This explains the more significant improvement in measured MR values at higher stress states (see results and discussion in section 7.1.2). 154 • Plastic strain behavior: Δσ3,max is also directly related to the axial plastic strain prediction model, where the additional lateral confinement provided by the geosynthetic increases as plastic strain develops in the sample. In other words, the model suggests that the benefit of additional lateral confinement from the geosynthetic grows as the sample undergoes more loading cycles. This behavior can be explained by the mobilization concept, in which 85% of the induced axial plastic strain occurs in the lateral direction. The interlock between soil particles and the geosynthetic further stretches the geosynthetic, enhancing the additional lateral confinement. 7.2.2. Pavement Section and Flooding Properties Two typical pavement structures from Michigan were selected to study the effect of geosynthetic reinforcement on the resiliency of flexible pavement sections against flooding events. The first pavement section consists of 8 inches of AC layers, followed by a 6-inch unbound base layer. The second pavement section has AC and unbound base layer thicknesses of 4 and 6 inches, respectively. Table 15 presents the structural properties of these two pavement sections, and details of the HMA properties used in the AC layers are provided in Table 16. As shown, the unbound base material used in the laboratory testing was also used in the base layer of these two pavement structures and modeled as a stress-dependent nonlinear base layer. The summary calibrated coefficients from the NCHRP 1-37A MR model were applied to represent the mechanical behavior of the base layers. On the other hand, the subgrade layer was modeled as an elastic layer. Table 17 presents the main input parameters for the ME pavement analysis. As this table shows, these pavement structures are located in Saginaw, MI, with traffic levels and designed vehicle speeds corresponding to rural arterial or highway roadways. 155 Table 15. Structural properties of the pavement structures Layer AC layer Unbound base layer Subgrade layer Property Thickness (in) HMA ID Thickness (in) HMA ID Thickness (in) HMA ID Thickness (in) k1 k2 k3 Modulus (psi) Pavement #1 2.0 S01 2.0 L01 4.0 B01 6.0 541.34 0.52 0.50 7000 Pavement #2 2.0 S02 2.0 L02 - - 6.0 541.34 0.52 0.50 7000 Table 16. HMA properties of the pavement structures Pavement HMA ID section Pavement #1 S01 L01 B01 Pavement #2 S02 L02 Michigan DOT mix type 5E10 4E10 3E10 5E3 4E3 Asphalt binder PG 70-22P 70-22P 58-22 70-28P 70-28P Va (%) Vbe (%) VMA (%) VFA (%) 6.5 6.5 6.4 7.1 6.7 12.0 10.6 9.6 11.2 10.9 18.5 17.1 16.0 18.3 17.6 64.9 62.0 60.0 61.2 61.9 Table 17. Main inputs for the ME pavement analysis Property Initial annual average daily truck traffic (AADTT) Equivalent single-axle load (ESAL) Lane distribution factor (LDF) Directional distribution factor (DDF) Vehicle speed Design life Location Latitude Longitude Ground water table depth Pavement #1 1,200 Pavement #2 3,500 3.4 million ESALs 90% 51% 60 mph 20 years Saginaw, MI 43.43º -83.97º 10 ft 10.7 million ESALs 90% 51% 60 mph 20 years Saginaw, MI 43.43º -83.97º 10 ft Flooding event data for Saginaw County, MI, was extracted from the NOAA database and is presented in Table 18. As this table shows, the county experienced eight flooding events, with a total inundation duration of 35 days over 20 years of service life from August 2002 to August 2022. The default UPDAPS-Flood program assumptions were used for analyzing these two pavement sections, including a 50% reduction in the MR of the saturated unbound layer with linear recovery and a traffic multiplier factor of 2.0 during flooding events. 156 Table 18. Information of flooding records at Saginaw County, MI No. Start date Start time End date End time 03/11/2006 06:00 AM 09/14/2008 02:00 PM 04/10/2013 12:00 AM 04/19/2013 12:00 AM 06/24/2017 03:31 PM 02/21/2018 12:00 PM 03/15/2006 04:00 PM 09/15/2008 12:00 PM 04/12/2013 12:00 AM 04/25/2013 12:00 AM 06/28/2017 01:42 PM 02/28/2018 11:00 PM 05/25/2019 06:00 AM 05/18/2020 11:00 PM 05/25/2019 11:00 AM 05/26/2020 10:40 AM 5 180 1 8 Exact duration (hours) 106 22 48 240 94 179 Modeled duration (days) 5 1 2 6 4 8 Flood cause N/A Heavy rain Heavy rain Heavy rain Heavy rain Heavy rain / snow melt Heavy rain Heavy rain 1 2 3 4 5 6 7 8 7.2.3. UPDAPS-Flood Simulation MatLEA, an LEA-based model, was initially integrated into the UPDAPS-Flood program as the pavement structural response model. However, typical LEA models cannot capture the stress- dependent nonlinearity of unbound materials or the additional lateral confinement provided by geosynthetic reinforcement. On the other hand, Finite-Element Analysis (FEA) is an effective approach to account for the nonlinearity of unbound materials and the additional lateral confinement by the geosynthetic reinforcement. To address this issue, an efficient FEA-based pavement structural response model, called MatFEA, was developed and implemented into the UPDAPS-Flood program. Details of the pavement structural response models are provided in section 4.2.4.2 (see page 56), or it can be found elsewhere (Abdollahi, Kutay, et al. 2023). MatFEA calculated the stiffness matrix of each element based on its stress state, according to the MR model from the NCHRP 1-37A project. Additionally, the NCHRP 1-50 model for calculating the additional lateral confinement provided by geosynthetic reinforcement was incorporated into the MatFEA. The calculated additional confinement was used to update the stress state of each element, which directly impacts the elemental stiffness matrix and pavement structural responses. In other words, this approach translated the additional lateral confinement from the geosynthetic reinforcement into increased stiffness in the base layer within the geosynthetic’s influence zone. For example, Figure 76 shows the distribution of elemental stiffness for the Pavement #2 control (no geosynthetic) and geosynthetic-reinforced scenarios. The maximum elemental stiffness in the nonlinear base layer for the control and geosynthetic- reinforced sections was 10,665 and 11,882 psi, respectively, which clearly reflects the effect of extra confinement on the base layer moduli. Visual inspection of this figure also shows a 157 significant increase in elemental stiffness in the elements near the geosynthetic. Furthermore, the change in elemental stiffness is not confined to the geosynthetic's influence zone, as elements beyond this range, e.g., those near the interface of the AC and base layers, were also affected. This was an expected observation, as changes in the elemental stiffness regime impact the structural responses of the entire pavement system, which in turn influence the stiffness in the unbound layer. Figure 76. Distribution of the elemental stiffness of the Pavement #2 structure: (a) control (no geosynthetic) scenario, (b) geosynthetic-reinforced scenario 158 Figure 77 shows the UPDAPS-Flood simulation results for the Pavement #1 section under three scenarios: (i) an unreinforced unbound base layer under the no-flood scenario, (ii) an unreinforced unbound base layer under the flooding scenario, and (iii) a geosynthetic-reinforced unbound base layer under the flooding scenario. As the figure shows, fatigue cracking predictions were most affected by the flooding events, with total fatigue cracking increasing from 8.3% under the no-flood scenario to 9.9% when flooding was considered, indicating a 19% increase in predicted fatigue cracking. In contrast, the effect of flooding on total rutting and IRI predictions was much less significant. This observation is attributed to the relatively strong structural capacity of the Pavement #1 section, which includes an 8-inch-thick AC layer. Since the stiffness of the AC layer is not affected by flooding events, a thick AC layer can significantly reduce the traffic- induced stresses transferred to the underlying layers, even when those layers experience reduced stiffness due to flooding. However, the more significant effect of flooding on predicted fatigue cracking is explained by the softer support provided by the underlying unbound layers during the flooding events, which increases the principal stresses at the top and bottom of the AC layer. 159 Figure 77. Results of UPDAPS and UPDAPS-Flood simulations for Pavement #1 section: (a) total fatigue cracking, (b) total rutting, and (c) IRI Figure 77 also shows that geosynthetic reinforcement did not significantly improve the resiliency of the section against flooding events, as the predicted fatigue cracking and IRI distresses for both the geosynthetic-reinforced and unreinforced sections under flooding scenario were almost identical. Although the predicted rutting for the geosynthetic-reinforced section was slightly lower than that of the control section, the reduction was not substantial. This observation is also attributed to the relatively strong structural capacity of the section, which resulted in a low stress state within the unbound base layer. The inefficacy of geosynthetic reinforcement under low stress states was previously observed in the MR test results (Section 7.1.2) and the geosynthetic reinforcement model (Section 7.2.1). The results of the UPDAPS-Flood simulations for the Pavement #2 section are shown in Figure 78. As this figure shows, the predicted fatigue cracking for the control (no geosynthetic) 160 section increased from 19.1% to 20.6% due to flooding events, representing a 7.3% increase. However, the predicted fatigue cracking for the geosynthetic-reinforced section under the flooding scenario was 14.4%, which is even lower than the control section under the no-flood scenario. Similar trends were observed for total rutting and IRI distresses, where the predicted distresses for the geosynthetic-reinforced section were lower than those of the control section under the no-flood scenario. This observation indicates that, for the Pavement #2 section, geosynthetic reinforcement not only mitigated the accumulated damage due to the flooding events but also improved the overall performance of the pavement structure compared to the control section under no-flood scenario. Based on the UPDAPS-Flood simulation results for the Pavement #1 and Pavement #2 sections, it was found that the beneficial effect of geosynthetic reinforcement in improving the resiliency of pavement structures against flooding events was more significant in thinner pavement sections, while its effect was almost negligible in thicker sections. This observation is primarily attributed to the stress state within the geosynthetic-reinforced unbound layer, where higher stress states allow geosynthetic reinforcement to more effectively improve pavement resiliency against flooding events. This finding well-aligns with the primary purpose of geosynthetic reinforcement, which is to reduce pavement thickness without compromising the pavement performance. That’s why the use of geosynthetic reinforcement in thick pavement structures is uncommon and the results of UPDAPS-Flood simulations also showed that it would not significantly improve resiliency of the reinforced section against flooding events. 161 Figure 78. Results of UPDAPS and UPDAPS-Flood simulations for Pavement #2 section: (a) total fatigue cracking, (b) total rutting, and (c) IRI 7.3. Chapter Conclusion This chapter focuses on the impact of geosynthetic reinforcement in enhancing the resiliency of flexible pavement structures against flooding events. A common unbound base material from Michigan and a commercial geosynthetic product were selected to evaluate the mechanical behavior of geosynthetic-reinforced unbound base material through a limited set of laboratory tests. The physical properties of the selected unbound base material were determined using grain size distribution and standard Proctor compaction tests. Subsequently, Resilient Modulus (MR) and Repeated Load Permanent Deformation (RLPD) tests were conducted on both control (no geosynthetic) and geosynthetic-reinforced samples, with three replicates for each. The results of the MR test showed that, on average, geosynthetic reinforcement increased the MR of the unbound base material by 47%. This improvement was primarily attributed to the local 162 stiffness increase within the influence zone of the geosynthetic. Additionally, the results indicated that the reinforcing effect of the geosynthetic was more significant under higher stress states. This was explained by the mobilization concept, where Poisson’s effect at higher stress states causes higher horizontal mobilization of soil particles. Due to the interlock between the geosynthetic and soil particles, such higher horizontal mobilization increases the additional confinement by geosynthetic. The results of the RLPD test showed that geosynthetic reinforcement reduced the plastic strain (εp) of the unbound base materials by 23.4% after 10,000 loading cycles. This finding was also explained using the mobilization concept. It is noted that the MR test was conducted with fewer loading cycles (100 cycles) across 15 different stress states, where higher stress states caused more lateral mobilization of soil particles and demonstrated a more significant effect of geosynthetic reinforcement. On the other hand, the RLPD test was performed under a single stress state but with a much higher number of loading cycles (10,000 cycles). As a result, the primary driver for lateral soil particle mobilization in the RLPD test was the evolution of axial plastic strain within the sample, which was directly related to lateral plastic strain through the dilation angle concept. This chapter also included a thorough explanation of the theory of geosynthetic reinforcement. According to this theory, the geosynthetic provides additional lateral confinement to the sample, distributed in a triangular pattern within the influence zone of the geosynthetic. This additional confinement is influenced by three main factors: (i) geosynthetic properties, where stiffer and more rigid geosynthetics offering greater confinement; (ii) the stress state of the sample, where higher stress states result in greater radial elastic strain and, consequently, increased lateral confinement; and (iii) the plastic strain behavior of the sample, where the evolution of plastic strain causes greater lateral soil particle mobilization and further increasing the lateral confinement. To evaluate the effectiveness of geosynthetic reinforcement in improving the resiliency of pavement structures against flooding events, the formulations from geosynthetic reinforcement theory were integrated into the UPDAPS-Flood program using a FEM-based pavement structural response model. Two typical pavement structures in Michigan were selected to simulate the effects of flooding on predicted pavement performance. The results showed that the impact of geosynthetic reinforcement on improving resiliency against flooding was highly dependent on the structural capacity of the pavement. In the thinner pavement section, geosynthetic reinforcement not only mitigated flooding damage but also improved the overall performance of the pavement 163 compared to the control section under no-flood conditions. In contrast, geosynthetic reinforcement in the thicker pavement section did not show significant improvement in the predicted distresses under flooding scenario. These findings are primarily attributed to the stress state within the geosynthetic-reinforced unbound layer, where higher stress states allow geosynthetic reinforcement to more effectively improve pavement resiliency against flooding events. 164 CHAPTER 8. CONCLUSION AND RECOMMENDATION 8.1. Summary and Conclusion The frequency and intensity of flooding events across the United States have been increasing over the past decades as a consequence of climate change. Understanding the impact of these flooding events on the performance of flexible pavement networks is crucial for planning, design and maintenance of these structures. Flooding introduces a significant amount of water into the pavement structure and increases the saturation levels of the pavement layers. This excess moisture content affects the mechanical behavior of pavement materials and their structural response to traffic loading and environmental factors, which eventually accelerates the deterioration rate in the pavement sections. A comprehensive literature review was conducted to evaluate the current practices and state of knowledge about the effects of flooding on the performance of flexible pavement structures and the available modeling approaches. A detailed review of the increasing trend in flooding events and various flooding sources was provided to emphasize the significance of this issue. The literature search results were then classified based on the effects of flooding on Asphalt Concrete (AC) layers, unbound layers, and traffic patterns. Current models for evaluating the effect of flooding on flexible pavement performance were also discussed. The Mechanistic-Empirical (ME) pavement analysis modeling approach was selected as the baseline for this research to evaluate the effects of flooding events on flexible pavement performance. The development process of the Unified Pavement Distress Analysis and Prediction System (UPDAPS) program, which is an ME-based pavement analysis tool, was summarized in Chapter Four. The UPDAPS program was originally developed based on the Mechanistic-Empirical Pavement Design Guide (MEPDG) formulations. However, several improvements were made during the development of UPDAPS program, which include improvements to the loading frequency calculations, climatic model, determination of critical analysis locations, pavement structural response model, and fatigue cracking prediction model. As an example, the Viscoelastic Continuum Damage (VECD) model was utilized within the improved fatigue cracking model. Additionally, the UPDAPS program was designed to be compatible with parallel computing on supercomputing remote servers, making computationally expensive network-level simulations feasible. In this research, the UPDAPS program served as the baseline for evaluating the effects of flooding events on the performance of flexible pavement structures. 165 A framework was developed to incorporate the effects of flooding events on the performance of flexible pavement structures using the ME analysis procedure, with four major modifications proposed to the standard MEPDG approach. The first modification involves implementing a hybrid analysis increment scheme during flooding events and the post-flood recovery period. This scheme downscales the traditional monthly analysis increments to daily increments during flooding and post-flood recovery period to capture the short-term effect of the flooding events. The second modification addresses the reduction in the resilient modulus (MR) of unbound pavement layers due to increased saturation levels during flooding and the post-flood recovery period. The third modification adjusts the rutting resistance behavior of pavement materials by modifying the calibration coefficients of rutting distress prediction model for saturated pavement materials. Finally, the fourth modification accounts for changes in traffic patterns, particularly increased traffic loads from debris removal trucks and road closures during flooding events. The proposed framework was implemented into the analysis engine of the UPDAPS program, resulting in a modified version called the UPDAPS-Flood program. Although the UPDAPS-Flood program was designed to accommodate all modifications in the proposed framework, several simplified assumptions were made to run the program and evaluate the effects of flooding on flexible pavement performance. These simplified assumptions were made because of the lack of a moisture profile model and accurate material-specific and traffic pattern inputs during flooding conditions. For instance, because detailed traffic characteristics during flooding events were unavailable, multiplication factors of 1.25 and 2.0 were applied to the traffic axle count during ‘flash flood’ and ‘major flood’ events, respectively. It is noted that these assumptions were made based on engineering judgement and a general understanding of how material behavior and traffic patterns typically change under flooding conditions. An indirect approach was used to validate the results of the UPDAPS-Flood program by analyzing 18 flexible pavement structures in the New Orleans area, which were affected by hurricanes Katrina and Rita. The changes in the International Roughness Index (IRI) were modeled using the UPDAPS-Flood program. Additionally, the AASHTO 1993 pavement design guide model was used to predict changes in the Pavement Serviceability Index (PSI) due to the same flooding events. The predicted ΔPSI values were then converted to ΔIRI using a typical conversion model from the literature and compared with the corresponding ΔIRI values from the UPDAPS- Flood simulation results. 166 The simulation results from the UPDAPS-Flood program were used to evaluate the resiliency of flexible pavement structures at the project level. A newly constructed flexible pavement structure in Miami-Dade County, Florida, was selected for such analysis, as it experienced nine major flooding events during its service life. The performance of this pavement section was first simulated using the UPDAPS program under a no-flood scenario, followed by an analysis with the UPDAPS-Flood program to predict pavement distresses considering the flooding events. A comparison of the results from these two simulations was conducted to assess the effects of flooding on the evolution of fatigue cracking, rutting, and IRI distresses. The UPDAPS-Flood simulation results were also used to assess the resiliency of pavement structures against flooding events at the network level. For this purpose, the IRI distress of each pavement section was predicted using both the UPDAPS and UPDAPS-Flood programs for no- flood and flooding scenarios, respectively. These results were then used to define a resiliency metric, called RIRI, representing the loss of service life due to flooding events. This metric was primarily used to conduct a network-level analysis of pavement resiliency against flooding events. In the first step, a proof of concept and sensitivity analysis were conducted to investigate the sensitivity of the results to the main input assumptions of the UPDAPS-Flood program. Subsequently, the resiliency of the pavement network against flooding events was evaluated across the contiguous United States. For the proof of concept and sensitivity analysis, information on 7,655 flexible pavement structures from three regions across the United States was extracted from the Highway Performance Monitoring System (HPMS) database. Additionally, flooding data for these sections was obtained from the National Oceanic and Atmospheric Administration (NOAA) storm event database. The extracted data was processed to prepare input files for each pavement section. UPDAPS and UPDAPS-Flood simulations for these pavement sections were run in parallel on the High-Performance Computing Center (HPCC) remote computing servers at Michigan State University, using 1,024 CPUs concurrently. Based on the simulation results, RIRI values were calculated for each pavement section. These calculated RIRI values, along with the locations of each pavement section, were then used to generate network-level resiliency maps, which serve as valuable tools to assist road agencies in decision-making and identifying flood-vulnerable areas. A sensitivity analysis was also conducted to evaluate the effect of key assumptions in the UPDAPS-Flood program on the results. These assumptions, which were made due to the lack of 167 detailed data for the flooded pavement sections, include (i) the reduction in MR of saturated unbound layers, (ii) the shape of the recovery path, and (iii) the k1 local calibration coefficient in the rutting model. A nationwide evaluation of the network-level resiliency of flexible pavement structures across the contiguous United States was conducted using the results of UPDAPS and UPDAPS-Flood simulations for 10,650 pavement structures. Pavement structure, traffic, environment, and flooding data for these sections were extracted from the HPMS and NOAA databases. Based on the sensitivity analysis results, the UPDAPS-Flood simulations were carried out using the assumptions of a 50% reduction in MR of the saturated unbound layer with linear recovery and a traffic multiplier factor of 2.0 during flooding events. The simulation results were then analyzed to calculate RIRI values and generate resiliency maps for the contiguous United States. Geosynthetic reinforcement of the unbound base layer was also investigated as an alternative approach to improve the resiliency of flexible pavement structures against flooding events. For this purpose, a common unbound base material from Michigan and a widely used commercial geosynthetic product were selected to evaluate the mechanical behavior of geosynthetic-reinforced unbound base material through a set of laboratory tests, including MR and Repeated Load Permanent Deformation (RLPD) tests. In the next step, the theory of geosynthetic reinforcement was reviewed and incorporated into the UPDAPS-Flood program by integrating a Finite-Element Method (FEM)-based pavement structural response model. Finally, two typical pavement structures in Michigan were selected to simulate the effects of flooding on predicted pavement performance. The following conclusions were made based on the activities performed: • The current modeling approaches in the literature for evaluating the effects of flooding events on flexible pavement performance can be classified into four groups, including empirical pavement response-based models, ME-based models, quantitative risk analysis models, and system dynamics models. The literature review revealed that these different models are not competitors, but rather each one addresses a specific aspect of the problem with its own unique solution. • The ME-based pavement analysis models used in the literature did not adequately capture the effects of flooding events on flexible pavement performance. This is mainly due to the 168 lack of material-specific models that accurately predict the response of saturated pavement materials, as well as the use of relatively long analysis increments (monthly) that fail to account for the short duration of flooding events, which typically last hours to days. • The results of the indirect validation for the UPDAPS-Flood program indicated that, although the calculated ΔIRI values from the UPDAPS-Flood program and AASHTO 1993 model showed different levels of variability, most pavement sections showed consistent results using both methods. Therefore, considering the lack of field-measured distresses before and after flooding events, the results of this indirect validation reasonably support the accuracy of the UPDAPS-Flood program. • The results of the resiliency analysis for a pavement structure in Florida at the project level showed that the predicted rutting, fatigue cracking, and IRI distresses from the UPDAPS- Flood program were significantly higher than those obtained from the UPDAPS program under the no-flood scenario. The analysis indicated that the most significant impact of flooding was on rutting predictions, followed by fatigue cracking and IRI distresses. Additionally, the results showed significant increases in predicted distresses over short periods during the pavement service life, which temporally corresponded to major flooding events. Therefore, these findings indicated that the UPDAPS-Flood program effectively models the effects of flooding events on the performance of flexible pavement structures. • The results of the network-level resiliency analysis for 7,655 flexible pavement structures during the proof-of-concept stage showed a higher loss of service life for pavement networks along the Gulf of Mexico compared to those in Minnesota and California. This was attributed to more frequent and severe flooding events near the Gulf of Mexico. Additionally, a comparison between California and Minnesota showed that, despite more frequent and severe flooding events in California, the California pavement network was more resilient against the flooding events. This observation was likely attributed to differences in structural capacity of the pavement network among these two states. According to the HPMS database, pavement structures in California were thicker than those in Minnesota, which significantly influenced the structural response and resiliency of the pavements against flooding events. 169 • The results of the sensitivity analysis on the primary assumptions in the UPDAPS-Flood program showed a direct correlation between the reduction in MR of saturated unbound layers and the accumulated flooding damage. Additionally, the findings emphasized the importance of an effective drainage system in improving the resiliency of pavement structures against flooding events. A proper drainage system, with a higher drainage rate during post-flood recovery period, can significantly reduce the loss of pavement service life, potentially by a factor of two. Moreover, the results showed that the results of the UPDAPS-Flood program are highly sensitive to the coefficients of rutting distress prediction models. This observation highlights the need for further laboratory research to better understand the rutting behavior of unbound materials under higher saturation levels. • The results of the nationwide resiliency analysis of 10,650 flexible pavement structures against flooding events showed a higher loss of service life for pavement networks in the Long-Term Pavement Performance (LTPP) Wet/Freeze region, areas near major U.S. rivers (e.g., the Missouri and Mississippi rivers), and along the eastern coastline. This observation was attributed to the more frequent and severe flooding events recorded in these areas, primarily caused by river flooding, coastal flooding, or high precipitation. The analysis showed an average nationwide loss of service life of nine months for pavement structures due to flooding events. Additionally, the results indicated that highly flooded sections experienced significant performance losses, emphasizing the importance of considering flooding events in pavement design and maintenance frameworks, particularly in flood-prone areas. • The results of the MR test on control (no geosynthetic) and geosynthetic-reinforced unbound base materials showed that, on average, geosynthetic reinforcement increased the MR of the unbound base material by 47%. This improvement was primarily attributed to the local stiffness increase within the influence zone of the geosynthetic. Additionally, the results indicated that the reinforcing effect of the geosynthetic was more significant under higher stress states. This was explained by the soil particle mobilization concept, where Poisson’s effect at higher stress states causes higher horizontal mobilization of soil particles. Due to the interlock between the geosynthetic and soil particles, such higher horizontal mobilization increases the additional confinement by geosynthetic. 170 • The results of the RLPD test on control (no geosynthetic) and geosynthetic-reinforced unbound base material showed that geosynthetic reinforcement reduced plastic strain (εp) by 23.4% after 10,000 loading cycles. This finding was also explained using the mobilization concept. It is noted that the MR test was conducted with fewer loading cycles (100 cycles) across 15 different stress states, where higher stress states caused more lateral mobilization of soil particles and resulted in a greater effect of geosynthetic reinforcement. Conversely, the RLPD test was performed under a single stress state but with a much higher number of loading cycles (10,000 cycles). As a result, the primary driver for lateral soil particle mobilization in the RLPD test was the evolution of axial plastic strain within the sample, which was directly related to lateral plastic strain through the dilation angle concept. • According to the theory of geosynthetic reinforcement used in this research, the geosynthetic reinforcement provides additional lateral confinement to the sample, distributed in a triangular pattern within the influence zone of the geosynthetic. This additional confinement is influenced by three main factors: (i) geosynthetic properties, where stiffer and more rigid geosynthetics offer higher confinement; (ii) the stress state of the sample, where higher stress states lead to higher radial elastic strain and, consequently, increased lateral confinement; and (iii) the plastic strain behavior of the sample, where the evolution of plastic strain causes higher lateral soil particle mobilization, further increasing lateral confinement. • The results of the UPDAPS-Flood program simulations on the geosynthetic-reinforced pavement structures showed that the effect of geosynthetic reinforcement on improving resiliency of the flexible pavement structures against flooding events was highly dependent on the structural capacity of the pavement. In the thinner pavement section, geosynthetic reinforcement not only mitigated flooding damage but also improved the overall performance of the pavement compared to the control section under no-flood conditions. In contrast, geosynthetic reinforcement did not show significant improvement in the predicted distresses for the thicker pavement section under flooding conditions. These findings are primarily attributed to the stress state within the geosynthetic-reinforced unbound layer, where higher stress states allow geosynthetic reinforcement to more effectively enhance pavement resiliency against flooding events. 171 8.2. Recommendations for Future Research The following research topics are recommended to succeed the activities of this research: • Although this study provides a practical framework for analyzing flexible pavement structure resiliency against flooding at the network level, the analysis results were highly sensitive to input data, i.e., the reduction in MR of unbound materials and coefficients of the rutting prediction model during flooding events. Therefore, more laboratory testing is recommended to better understand the effect of saturation levels on the reduction in MR and rutting behavior of different unbound materials. • The NOAA storm event database was used as the primary source for flooding event information; however, the spatial resolution of the flooding records is at the county level. This relatively large spatial resolution can result in overgeneralizations, such as assuming severe local river or coastal flooding affects all pavement sections within a county. Using more precise flooding records is recommended to increase the accuracy of the UPDAPS- Flood simulation results, both for network-level pavement resiliency analysis and project- level pavement design purposes. • The findings of this study regarding the beneficial effects of geosynthetic reinforcement on improving pavement resiliency against flooding were based on a limited set of laboratory tests for one unbound base material and one commonly used commercial geosynthetic product. Future research can extend these tests to a broader range of unbound materials for base and subbase pavement layers, as well as different types of geosynthetic products. • Limited observations in this research indicated that pavement structures with higher structural capacity were more resilient against flooding events. 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Conceptual illustration of the global climate models (source: NOAA 2022) The results of GCMs may not be directly applicable to climate change-related pavement analysis due to their coarse resolution, which represent large regions rather than specific project sites. Recent advancements in computational capabilities have led to a significant enhancement in the resolution of GCMs, with the size of the grid decreasing from approximately 100 miles per grid edge to about 15-30 miles. However, even the most current high-resolution models are not suitable for predicting the fine-scale climate change characteristics at the local scale (Dawson 2014, Hayhoe et al. 2017). In order to address the resolution issue of the GCM results, downscaling approach is utilized to refine the coarse-resolution outputs of GCMs to a local scale. Downscaling techniques usually adjust systematic biases in GCM projections or calibrate them against available empirical observations to generate high-resolution local climate projections (Hayhoe et al. 2017). There are two primary downscaling methods are available in the literature: dynamic and statistic. Dynamic downscaling employs Regional Climate Models (RCM), which are complex models to simulate 186 climate processes at regional scales, whereas Empirical Statistical Downscaling Methods (ESDM) offer greater flexibility and computational efficiency. A.1 Global Climate Model (GCM) The GCMs are complex mathematical frameworks based on fundamental physical principles to account for energy conservation, mass, and momentum, as well as their interaction within the climate system. These models simulate the large-scale climatic patterns, including temperature, precipitation, storm tracks, and other climatic characteristics for a given climate change scenarios. Over time, the complexity of GCMs has increased by integration of more components of the climate system. For instance, while initial versions of GCMs only accounted for the general circulation of the atmosphere, subsequent enhancements have incorporated more components, including atmospheric chemistry and aerosols, land surface interactions (e.g., soil and vegetations), land and sea ice, interactive carbon cycles, biogeochemical feedbacks, and higher spatial resolution (Hayhoe et al. 2017). Several GCMs have been developed and reported in the literature, each incorporating various components of the climate system with different resolution. The IPCC has adopted an approach by which the outputs of 29 main GCMs are aggregated to estimate the projected global warming for the 21st century (IPCC 2014). A brief summary of seven notable GCMs are provided in Table 2. 187 Table 19. Brief summary of some notable GCMs GCM name GISS GCM ModelE Reference (NASA 2022b) NCAR CESM (NCAR 2021) EdGCM (Chandler et al. 2009) NEMO (NEMO 2022) MIT GCM GFDL FMS (Campin et al. 2022) (GFDL 2022) Description This is a coupled atmosphere-ocean model to simulate different climate system components of atmospheric chemistry, aerosols, and carbon cycle, as well as atmosphere, ocean, sea ice and land surface components. The Community Earth System Model (CESM) is a fully coupled global climate model that provides state-of-the-art computer simulations of the earth’s past, present, and future climate states. The Educational Global Climate Model (EdGCM) is a fully functional GCM with educational purposes which developed at the NASA Goddard Institute for Space Studies as a joint project with Columbia University. The GISS Model II is the core of the EdGCM. The Nucleus for European Modelling of the Oceans (NEMO) is a state-of-the-art modeling framework for research activities and forecasting services in ocean and climate sciences, developed by European consortium. The MIT General Circulation Model (MIT GCM) is a numerical model designed for study of the atmosphere, ocean, and climate. The Flexible Modeling System (FMS) developed by Geophysical Fluid Dynamics Laboratory (GFDL) is a software framework for supporting the efficient development, construction, execution, and scientific interpretation of atmospheric, oceanic, and climate system models. DOE’s E3SM (US DOE 2022) DOE’s Energy Exascale Earth System Model (E3SM) is a state-of- the-science earth system model development and simulation project to investigate energy-relevant science using code optimized for DOE’s advanced computers. A.2 Regional Climate Model (RCM) Regional Climate Models (RCMs) are recognized as a subset of dynamic downscaling techniques, comprising physical components analogous to those in Global Climate Models (GCMs) but operating at heightened spatial resolutions tailored for smaller geographic extents. In a majority of RCM applications, the output fields from GCMs are utilized to define boundary conditions. RCMs, due to their intricate detail, are resource-intensive, featuring grid cells that may range from as small as 0.6 to 1.2 miles per grid box. More commonly, grid cells are approximately 6 to 30 miles in size (Hayhoe et al., 2017). There exists a diversity of RCMs within the scientific literature, each with varying degrees of correlation to their GCM counterparts. Table 3 enumerates various RCMs alongside their associated GCMs. The regional climate models (RCM) are categorized as dynamic downscaling methods which consist of similar physical components as in GCM, but simulate these components at the higher spatial resolutions for smaller regions. In many of the RCMs, the GCM fields are used as the boundary conditions. RCMs are computationally expensive models in which the size of the grid 188 cells can be as fine as 0.6 to 1.2 miles per grid box, while a more common size of the grid cell is about 6 to 30 miles (Hayhoe et al. 2017). Similar to the GCMs, there are several RCMs developed in the literature. As an example, REgional MOdel (REMO) is an RCM model developed by MPI institution which provides a high spatial (10 km grid cell size) and time (hourly) resolution and works using the results of ECHAM5 GCM model. Figure 8 shows the results of the REMO model for projected hourly air temperatures during 2001 to 2040 for the city of Braunschweig, Germany. A.3 Empirical Statistical Downscaling Models (ESDM) The empirical statistical downscaling models (ESCM) uses the historical observations to convert the results of the GCM to the high-resolution projections in the scale of the observations. These historical observations can be obtained from weather stations or gridded database. The statistical approaches in the ESDMs can be as simple as difference/delta approach (i.e., the historical simulations are subtracted from future values and the resulting delta is added to the historical simulations) to the more advanced mathematical modeling approaches such as parametric quantile mapping (Hayhoe et al. 2017). ESDMs are usually flexible and computationally efficient methods compared to the RCMs. Localized constructed analogs method (LOCA) and asynchronous regional regression model (ARRM) are examples of ESDM models (Stoner et al. 2013, Hayhoe et al. 2017). In conclusion, the climate change projection models can be categorized into the GCM and RCM/ESDM. The GCMs projected the future climate in a coarse grid which can be refined into the high-resolution climate projection in the local-scale by the use of RCM or ESDM models. Although many GCM and RCM/ESDM models have been developed for studying the climate change during the past decades, the MAGICC/SCENGEN has been used by many pavement- related studies (Li et al. 2011, Dawson 2014, Qiao 2015). The model for the assessment of greenhouse gas induced climate change (MAGICC) has been used to project the climate change stressors using the input emission scenario in the global scale, while the scenario generator (SCENGEN) downscales the results into the local-scale. 189 APPENDIX B SUMMARY OF MODELS USED IN UPDAPS PROGRAM This appendix includes a summary of the technical procedures and distress prediction models used in development of the UPDAPS program. It is noted that UPDAPS program was originally developed based on the Mechanistic-Empirical Asphalt Pavement Analysis (MEAPA) web- application, where more details of the models and technical procedures can be found elsewhere (Kutay et al. 2023). However, there were several improvements made during the development of the UPDAPS program. These improvements were discussed in Chapter 4, while a summary of the unmodified models and components of the UPDAPS program are provided in this appendix. A list of different components of the UPDAPS program is provided below (see table 2). • Process traffic data. • Calculate dynamic modulus master curve. • Define pavement structure sublayers. • Calculate loading frequencies. • Process climate data. • Run global aging system model. • Calculate undamaged state moduli of AC sublayers. • Define critical analysis locations. • Run thermal cracking model. • Run pavement structural response model. • Calculate fatigue cracking. • Calculate reflective cracking. • Calculate rutting. • Calculate IRI. B.1 Process Traffic Data The evolution of different distresses in the flexible pavement structures are caused either by traffic loading or environmental conditions, while typically the traffic loading is responsible for the major distresses, i.e., fatigue cracking and rutting. The traffic processing module of the UPDAPS program was developed based on the MEPDG formulation (ARA Inc. 2004). This 190 module required 24 input parameters (either scalers, vectors, or matrices), which can be categorized in five groups listed below. • General: these inputs include scaler data such as average annual daily truck traffic (AADTT), percentage of trucks in design lane and direction, operational speed, traffic opening year and month, and analysis duration. • Axle configuration: these inputs include scaler data such as average axle width, axle spacing for tandem, tridem, and quad axle types, dial tire spacing, and tire pressure. • Vehicle properties: these inputs include the percentage of vehicles in each vehicle classes, growth rate for each vehicle class, and monthly distribution factor matrix. • Number of axles per class: these inputs include vector data of the number of single, tandem, tridem, and quad axles per each vehicle class. • Axle load spectra: these inputs include matrix data of percentage of single, tandem, tridem, and quad axles corresponding to each axle load level for each vehicle class during each month of the year. It is noted that the traffic processing module of the UPDAPS program uses some assumption, similar to those used in MEPDG, which are listed below. • The normalized axle load distributions for each axle type and vehicle class remains constant from year to year. • The normalized axle load distributions for each axle type and vehicle class and normalized truck volume remains constant during the day (i.e., daytime versus night-time) and week (weekday versus weekend). B.1.1 Vehicle Classes Traditionally, MEPDG and HPMS use 13-vehicle classes for processing the traffic data as described in the FHWA traffic monitoring guide, appendix C (FHWA 2016). However, the Highway Cost Allocation Study (HCAS) uses 20-vehicle classes system for processing the traffic data after 2017 (FHWA 2017). These different vehicle classes are listed in table 20. 191 Class name Description AUTO automobiles and motorcycles Class name Description CT5 Table 20. HCAS vehicle classes LT4 SU2 SU3 Light trucks with 2-axles and 4 tires (pickup trucks, vans, minivans, etc.) single unit, 2 axles, 6 tire trucks single unit, 3 axles trucks CS6 CS7+ CT6+ SU4+ single unit trucks with 4 axles or more DS5 CS3 CS4 CT34 CS5T CS5S tractor-semitrailer combinations with 3 axles tractor-semitrailer combinations with 4 axles truck-trailer combinations with 3 or 4 axles tractor-semitrailer combinations with 5 axles, two rear tandem axles tractor-semitrailer combinations with 5 axles, two split (>8 ft) rear axles DS6 DS7 DS8+ TRPL BUS truck-trailer combinations with 5 axles tractor-semitrailer combinations with 6 axles tractor-semitrailer combinations with 7 or more axles truck-trailer combinations with 6 or more axles tractor-double semitrailer combinations with 5 axles tractor-double semitrailer combinations with 6 axles tractor-double semitrailer combinations with 7 axles tractor-double semitrailer combinations with 8 or more axles tractor-triple semitrailer or truck- double trailer combinations Buses (all types) Although any vehicle classification can be incorporated in UPDAPS program through proper traffic inputs, the HCAS 20-vehicle classes system is mainly used in this research. B.1.2 Traffic Data Processing Algorithm The main output of traffic data processing module is calculation of the actual number of single, tandem, tridem, and quad axles at each increment of analysis period per weight category. This parameter has been used in most of the performance prediction models of UPDAPS program. For this purpose, the raw traffic inputs are processed into the number of axle applications using the steps listed below. 1. Calculating the number of trucks at the design lane for each month, and vehicle class, during the base year. This is calculated by multiplication of AADTT by the percentage of trucks in design lane and direction, number of days per given month, corresponding monthly distribution factor, and corresponding percentage of trucks in the given vehicle class. 2. Calculating the number single, tandem, tridem, and quad axles for each month, and vehicle class, during the base year. This is calculated by multiplication of the number of trucks at the design year (calculated in previous step) by the corresponding average number of axles per each vehicle class. 192 3. Calculating the growth factor to estimate the traffic during the design life. This factor is multiplied with the calculated traffic in the base year to estimate the traffic during the design life. The traffic growth can be modeled by either compound or linear models. 4. Calculating the number of single, tandem, tridem, and quad axles for each vehicle class and month, during each year of the design life. This is calculated by multiplication of the calculated number of axles (step 2) by the corresponding growth factor (step 3). 5. Calculating the number of axles corresponding to each axle load level using the axle load spectra. This is calculated by multiplication of the calculated number of axles for each vehicle class, month, and year by the percentage of corresponding axles from the axle load spectra. 6. Calculating the number of single, tandem, tridem, and quad axles for all vehicle classes at each month and year, and for given axle weight. This is calculated by summing the calculated matrix for the number of axles (step 5) over all vehicle classes. As an example, figure 80 shows a three-dimensional bar chart of the distribution of the annual mean number of tandem axles, for each month, based on the axle load level for the traffic passing the HPMS MI2954 section. 193 Figure 80. Distribution of the annual mean number of tandem axles for each month based on axle load levels for the traffic passing the HPMS MI2954 section Finally, it is noted that the calculated number of single, tridem, tandem, and quad axles corresponding to each axle load level for given month and year (result of step 6) are the main parameters used in damage accumulation models for predicting different pavement distresses. These parameters are three-dimensional matrices in which the first, second, and third dimension represent each month, year, and axle load level, respectively. B.2 Calculate Dynamic Modulus Master Curve for AC Layers The temperature and loading frequency dependency of the asphalt mixture modulus can be modeled within the concept of dynamic modulus (|E*|) master curve. The UPDAPS program uses these asphalt mixture |E*| master curves to estimate the modulus of the AC sublayers for calculating the critical pavement responses. The time-temperature superposition principle is used for construction of the master curves. The time dependency of the AC modulus at the reference temperature (Tref) can be described using the sigmoid form function, as shown Equation (71). log|𝐸∗| = c1 + 𝑐2 1 + exp(𝑐3 + 𝑐4 log 𝑡𝑟) (71) where: 194 |E*| = absolute value of the dynamic modulus (psi). tr c1 c2 = reduced loading time at the reference temperature (s). = sigmoid coefficient; where log 𝑐1 = |𝐸∗|min. = sigmoid coefficient; where log(𝑐1 + 𝑐2) = |𝐸∗|max. c3, c4 = sigmoid coefficients representing the shape of the master curve. The reduced time (tr) is essentially equivalent to stress loading pulse duration at the given temperature of interest, which defines using Equation (72). log 𝑡𝑟 = log 𝑡 − log 𝑎(𝑇) (72) where: t T = loading time at the given temperature of interest (s). = temperature of interest (F). a(T) = shift factor as a function of temperature. The shift factor values at different temperature of interest are calculated using the polynomial model, as shown in Equation (73). log 𝑎(𝑇) = 𝑎1(𝑇2 − 𝑇𝑟𝑒𝑓 2 ) + 𝑎2(𝑇 − 𝑇𝑟𝑒𝑓) (73) where: Tref = reference temperature (F). a1, a2 = model coefficients. In addition, a gaussian form function is used to model the AC phase angle master curve, as shown in Equation (74). 𝛿 = 𝑑1 exp (− (𝑑2 + log 𝑡𝑟)2 2 2𝑑3 ) (74) where: δ d1 = phase angle (º). = model coefficient representing the maximum phase angle (º). d2, d3 = model coefficients representing the shape of the gaussian function. 195 As an example, the |E*| and δ master curves for the surface AC layer of HPMS MI2954 section are shown in figure 81. Figure 81. Constructed master curves for surface AC layer of HPMS MI2954 section: (a) |E*| master curve; (b) δ master curve B.3 Define Pavement Structure Sublayers According to the MEPDG guide, the pavement structure layers are divided into several sublayers. The main reasons for defining these pavement sublayers are listed below. • Calculating the pavement structural responses with higher accuracy. For this purpose, the temperature, equivalent loading frequency, and modulus of each AC sublayer is calculated using the constructed |E*| master curve and shift factor model. These sublayer properties are then inputted to the pavement structural response model (LEA-based) to have more accurate analysis results. • Calculating the rutting at the mid-depth of each sublayer. • Calculating the thermal stresses at the mid-depth of each sublayer. UPDAPS program uses both LEA- and FEA-based pavement structural response models, where the pavement sublayering is required for running the analysis using the LEA-based 196 pavement response model. The algorithm for dividing the pavement structure into several sublayers is based on the material type, layer thickness, and depth of the layer. The sublayering algorithm is developed based on specific rules, as listed below. • For top (AC) layer: o If the thickness of the top layer is greater than 1.5, two 0.5 sublayers were divided at the upper most portion, following by 1.0 sublayers and remaining thickness. o If the thickness of the top layer is less than 1.5, the entire layer is divided into two sublayers of the same thickness. • For subsequent (all) layers: o If the thickness of the layer is greater than 2.0, it is divided into multiple 2.0-thick sublayers and the remaining thickness. However, if the remaining thickness is between 2.0 and 4.0, the entire remaining thickness is treated as one sublayer. o If the thickness of the layer is less than 2.0, the entire layer is treated as one sublayer. As an example, figure 82 shows the sublayers for the HPMS MI2954 section. Figure 82. Resultant sublayers of the HPMS MI2954 section B.4 Calculate Loading Frequencies UPDAPS program uses an improved algorithm for calculation of the loading frequencies. Details of this improvement are provided in Chapter 4 (see page 41). 197 B.5 Process Climate Data UPDAPS program uses a climatic model similar to the EICM that is used by MEPDG. Detailed formulations of this climatic model can be found in MEPDG (ARA Inc. 2004) or MEAPA web- application documentation (Kutay et al. 2023). However, there are several improvements made to this climatic model, which are discussed in Chapter 4 (see page 47). B.6 Run Global Aging System Model The Global Aging System (GAS) model covers the effect of aging (due to heat and oxidation) on the modulus of the AC sublayers. In the GAS model, the aged viscosity of the asphalt binder is calculated and subsequently used in the |E*| master curve sigmoid formulation. The GAS model includes four components, as listed below. • Original viscosity to mix/lay-down viscosity model. • Surface aging model. • Air void adjustment model. • Viscosity-depth model. B.6.1 Original Viscosity to Mix/Lay-Down Viscosity Model This model estimates the viscosity of the asphalt binder at the time of HMA mixing/lay-down using the original viscosity of the asphalt binder (Mirza and Witczak 1995), as shown in Equation (75). log(log 𝜂𝑡=0) = 𝑎0 + 𝑎1 × log(log 𝜂orig) 𝑎0 = 0.054405 + 0.004082 × code 𝑎1 = 0.972035 + 0.010886 × code (75) (76) (77) ηt=0 = mix/lay-down viscosity (cP). ηorig = original viscosity (cP). code = hardening ratio (see table 21). The code variable in this model is an integer value designed to simplify the model and eliminate the exact value of the hardening ratio from the equation. Table 7 shows the corresponding hardening ratios for code values from -1 to 2. To simplify the inputs and not to require the hardening ratio, the UPDAPS program uses the average hardening quality (code = 0). 198 Table 21. Corresponding hardening ratios for each code variable value code variable -1 0 1 2 Hardening ratio range HR < 1.030 1.030 < HR < 1.075 1.075 < HR < 1.100 HR > 1.100 Mix/lay-down hardening quality Excellent to good Average Fair Poor Moreover, this model is based on the original viscosity of the asphalt binder (ηorig). However, the binder |G*| is often measured on RTFO-aged asphalt binders. In such cases, a0 = 0 and a1 = 1 are used in the model. To address this situation, the “RTFO” parameter is an input of the UPDAPS model. RTFO equal to 1 means that RTFO-aged asphalt binder was used for measuring the |G*| moduli; while RTFO equal to 0 indicates that the original asphalt binder was used for measuring the |G*| moduli, and Equation (75) used in the model. The viscosity of the asphalt binder is calculated from |G*| modulus measurements at a frequency of 10 rad/s using the Equation (78). Note that the maximum value of ηorig is 2.7×1012 cP. where: 𝜂orig = 1000 × 4.8628 |𝐺∗| 10 1 ( sin 𝛿 ) ≤ 2.7 × 1012 𝑐𝑃 (78) |G*| = absolute value of asphalt binder complex shear modulus (psi) δ = asphalt binder phase angle (º) Once ηorig is computed for different values of |G*| moduli corresponding to different temperatures (TR), the Equation (79) is fitted to the datapoints to calculate the parameters A and VTS. Note that on a log∙log scale (vertical axis) and log scale (horizontal axis), Equation (79) represents a line with slope VTS and intercept A. The values are computed by fitting a linear equation and determining the slope and intercept, using the A-VTS relationship shown in Equation (79). where: TR A log(log 𝜂orig) = 𝐴 + 𝑉𝑇𝑆 × log 𝑇𝑅 (79) = temperature at which the |G*| modulus was measured (ºRankine) = intercept of the viscosity-temperature relationship in log∙log-log scale VTS = slope of the viscosity-temperature relationship in log∙log-log scale 199 B.6.2 Surface Aging Model The evolution of asphalt binder viscosity at the pavement surface over time is estimated using Equation (80). Note that the maximum value of asphalt binder’s aged viscosity (ηaged) is 2.7×1012 cP. log(log 𝜂aged) = log(log 𝜂𝑡=0) + 𝐴 × 𝑡 1 + 𝐵 × 𝑡 ≤ 2.7 × 1012 𝑐𝑃 𝐴 = −0.004166 + 1.41213 × 𝐶 + 𝐶 × log 𝑀𝐴𝐴𝑇 + 𝐷 × log(log 𝜂𝑡=0) 𝐵 = 0.197725 + 0.068384 × log 𝐶 𝐶 = 10274.4946−193.831×log 𝑇𝑅+33.9366×log(𝑇𝑅)2 𝐷 = −14.5521 + 10.47662 × log 𝑇𝑅 − 1.88161 × log(𝑇𝑅)2 (80) (81) (82) (83) (84) where: ηaged = aged viscosity of asphalt binder (cP). t = time (months). A, B, C, D = model coefficients. MAAT = mean annual air temperature (ºF). TR = temperature (ºRankine = ºF + 459.67). B.6.3 Air Void Adjustment Model The asphalt binder viscosity at the pavement surface is corrected for air voids using Equation (85). log(log 𝜂𝑡,0 ′ ) = 𝐹𝑣 × log(log 𝜂𝑡,0) 𝐹𝑣 = 1 + 1.0367 × 10−4 × 𝑉𝐴 × 𝑡 1 + 6.1798 × 10−4 × 𝑡 𝑉𝐴orig + 0.011 × 𝑡 − 2 (85) (86) (87) 1 + 4.24 × 10−4 × 𝑡 × 𝑀𝐴𝐴𝑇 + 1.169 × 10−3 × ( 𝑡 𝜂orig,77 ) 𝑉𝐴 = where: η't,0 = aged asphalt binder viscosity at time t, on pavement surface which is corrected for air voids (cP). Fv = correction factor. 200 VA = corrected air void during time (%). VAorig = original air void of uppermost AC sublayer (%). t = time (months). ηorig,77 = original asphalt binder viscosity at 77ºF (Mega Poise, MP). B.6.4 Viscosity-Depth Model The aged asphalt binder viscosity as a function of depth is estimated based on the aged asphalt binder viscosity at the pavement surface and the asphalt binder viscosity at the time of HMA mixing/lay-down using Equation (88) (Mirza and Witczak 1995). 𝜂𝑡,𝑧 = 𝜂𝑡 × (4 + 𝐸) − 𝜂𝑡=0 × 𝐸 × (1 − 4𝑧) 4 × (1 + 𝐸 × 𝑧) 𝐸 = 23.83 × exp(−0.030 × 𝑀𝐴𝐴𝑇) (88) (89) where: ηt,z = asphalt binder viscosity at time t, and depth z (MP). E z = model coefficient. = depth from pavement surface (in). It is noted that the maximum value of asphalt binder viscosity at any depth (ηt,z) is 2.7×1012 cP. B.7 Calculate Undamaged State Moduli of AC Sublayers The undamaged state modulus of the AC sublayers can be calculated using the |E*| master curve with the inputs from previous steps, including calculation of the temperature profile, loading frequencies, and GAS model. It is noted that this modulus value is calculated for each AC sublayer during each analysis increment (i.e., temperature quantile). In particular, the loading times (frequencies) at the mid-depth of each AC sublayer are calculated by UPDAPS program (see page 41). In addition, the mid-depth temperatures of each AC sublayer at each temperature quantile are calculated using the climatic model (MClim) in the UPDAPS program (see page 47). Next, the aging of asphalt binder during the pavement service life is considered by adjusting the mid-depth temperatures of the AC sublayers through the GAS model. This procedure is summarized for each temperature quantile, as listed below. 201 • Plug the mid-depth temperatures of each AC sublayer into the A-VTS model to calculate the corresponding original viscosity of the asphalt binder [Equation (79)]. • Run the GAS model to calculate the aged viscosity of the asphalt binder at the given time (corresponds to the temperature quantile) and depth (corresponds to the AC sublayer). • Back-calculate the mid-depth temperature of each AC sublayer corresponding to the aged viscosity of the asphalt binder with Equation (90). 𝑇𝑎𝑑𝑗 = 10 log log 𝜂𝑡,𝑧−𝐴 𝑉𝑇𝑆 (90) where: Tadj = adjusted mid-depth temperature of the AC sublayer after implementing the GAS model (ºF). ηt,z = aged asphalt binder viscosity at time t (corresponds to the temperature quantile) and depth z (corresponds to the mid-depth of AC sublayer) (cP). A = intercept of the viscosity-temperature relationship in log∙log-log scale. VTS = slope of the viscosity-temperature relationship in log∙log-log scale. The adjusted temperature at the mid-depth of each AC sublayer during each temperature quantile is plugged into the shifting model [Equation (73)] to calculate the shifting factor, a(T). The reduced loading times are calculated using Equation (72) by plugging in the calculated shift factors and corresponding loading times. The calculated reduced loading times are then plugged into the corresponding |E*| master curve [Equation (71)] to calculate the |E*| values. B.8 Define Critical Analysis Locations Pavement structural responses are evaluated at critical analysis locations, where extreme structural responses are expected. Determination of critical analysis locations for single wheel loading is usually straightforward, i.e., the critical analysis location for tensile horizontal strain is expected at the bottom of AC layer (vertically) and the center of the loading wheel (radially). However, the critical analysis locations for multiple-wheel loadings are a function of wheel configuration and load level. Therefore, UPDAPS program searches among the potential analysis locations to find the critical pavement structural responses. 202 The critical analysis locations for single axle dual tire loading are shown in figure 19. These critical analysis locations are selected using the intersection of the vertical and radial coordinates listed below. • Vertical (Z) direction (depth): pavement surface, 0.1 from the pavement surface (for top- down fatigue cracking), center of each sublayer, 0.1 from bottom of AC layer (for bottom- up fatigue cracking), top of subgrade layer, and 6.0 deep into the subgrade layer. • Radial (X) direction (transverse): center point between the dual tires, halfway between the center point of dual tires and the inner edge of the tire, inner edge of the tire, center of the tire, outer edge of the tire, and then 4.0, 8.0, 16.0, 24.0, and 32.0 away from the outer edge of the tire. Figure 83. Critical analysis locations for dual tire loading The critical analysis locations for the tandem, tridem, and quad loading configurations are also shown in figure 20, which are selected using similar criteria. In Z- and X-directions, the critical analysis locations are selected with the same criteria as for single axle dual tire, which herein called the XZ point cloud. In tandem axle configuration, three sets of XZ point clouds are placed in Y- direction at the centerline of the dual tires (only one of the axles) and at the midpoint between the axles. Similarly, in tridem and quad axle configurations, the XZ point clouds are placed along the centerlines of the dual tires for one of the outer axles and one middle axle, as well as the midpoint between these XY point clouds in Y-direction. This resulted in three and four sets of XZ point cloud for tridem and quad axle configurations, respectively. 203 Figure 84. Critical analysis locations for (a) Single axle dual tire, (b) tandem axle dual tire, (c) tridem axle dual tire, (d) quad axle dual tire B.9 Run Thermal Cracking Model Low-temperature cracking, also known as thermal cracking, is a significant issue in areas characterized by cold temperatures and/or rapid temperature drops. Accumulation of the damage is the main cause of this distress, which occurs when thermal stresses within the pavement structure approach the material strength threshold, ultimately leading to the initiation of cracks. These cracks typically occur in the transverse direction and often cause more severe forms of pavement distresses, such as frost heaving during winter or subsequent cracks and potholes along the transverse cracks. Moreover, these cracks provide a pathway for moisture infiltration into the pavement structure, resulting in substantial damage. The occurrence and propagation of low- temperature cracking are mainly influenced by two key factors: the mechanical properties of the asphalt and the climatic conditions to which the pavement is exposed. An overview of the thermal cracking model is summarized into nine steps as presented below. In this model, the basic propagation of the thermal crack length (C) within the depth of the pavement is based on a simplified Paris law. Once the C is computed, a probabilistic standard normal distribution is assumed and actual observed crack on the surface, in terms of feet per mile, is computed. It is noted that the detailed formulations and technical procedure of the thermal cracking model can be found in the submitted technical report of UPDAPS program. 204 1. Convert dynamic modulus |E*| master curve to relaxation modulus E(t) master curve using the Prony-series based procedure. 2. Calculate the thermal cracking fracture growth parameter: damage growth rate (n). 3. Calculate thermal strains caused by temperature fluctuations at different AC sublayers using the coefficient of thermal expansion/contraction. 4. Calculate reduced time using |E*| master curve shift factor coefficients. 5. Calculate the thermal stresses through state variable implementation for solving the convolution integral. 6. Calculate daily incremental stress intensity factor (ΔK) using the maximum and minimum thermal stresses. 7. Calculate the A parameter based on indirect tensile strength of the AC sublayer which includes the crack tip. 8. Calculate the incremental crack length (ΔC) and update the crack length (C). 9. Calculate the observed amount of thermal cracking (Cf) using the standard normal distribution equation and crack length. As an example, figure 85 (a) and (b) show the thermal crack depth and observable thermal cracking for a HPMS MI2954 section. As this figure shows, the thermal cracking evolves very fast within the first 2 years of the pavement service life. Considering the cold climatic conditions in the State of Michigan, the results of this figure can be explained. 205 Figure 85. Thermal cracking model results for an example HPMS MI2954 section: (a) thermal crack length; (b) observed thermal cracking B.10 Run Pavement Response Model UPDAPS program uses two different pavement structural response models: (i) LEA-based model called MatLEA, and (ii) FEA-based model called MatFEA. Details of this improvement are provided in Chapter 4 (see page 55). B.11 Calculate Fatigue Cracking One of the most significant improvements in the UPDAPS program is the fatigue cracking model, which is based on the VECD theory. Details of this improvement are provided in Chapter 4 (see page 65). B.12 Calculate Reflective Cracking AC overlays are usually designed to resist fatigue and/or rutting distresses over an existing pavement structure with considerable damage. However, AC overlays may still show cracking patterns similar to the ones, which existed in the existing pavement after a short period of time. This distress is known as ‘reflection cracking.’ The discontinuities (cracks) in underlying layers cause reflection cracking, which propagate through an AC overlay due to continuous movement at the discontinuity prompted by thermal expansion and traffic loading. 206 00.20.40.60.811.21.4Time (years)0123456789Crack depth (in)00.20.40.60.811.21.4Time (years)050100150200250300350400450Crack length (ft/mile) The procedure for calculation of the reflective cracking is identical to the MEPDG formulation (ARA Inc. 2004). The reflective cracking on the AC overlay surface is modeled using a convolution-like equation, as shown in Equation (91). 𝑡−1 𝑅𝐶(𝑡) = ∑ 𝑅𝐶𝑇(𝑡 − 𝜏) × (𝐹𝐶𝐸𝐴𝐶 𝑏𝑢 (𝜏 + 1) − 𝐹𝐶𝐸𝐴𝐶 𝑏𝑢 (𝜏)) 𝜏=1 𝑅𝐶𝑇(𝑡) = 100 1 + exp(𝑎 + 𝑏 ∙ 𝑡) 𝑎 = 3.5 + 0.75 ∙ ℎAC-overlay −0.915469 𝑏 = −0.688584 − 3.37302 ∙ ℎAC-overlay (91) (92) (93) (94) where: RC(t) = reflective cracking on the AC overlay surface at age t during the pavement analysis period (%). RCT(t) = percent cracking reflected for age t during pavement analysis period (%). FCbu EAC(t) = bottom-up fatigue cracking at age t during pavement analysis period, as decimal. t = pavement age (years). a, b = RCT model coefficients. hAC-overlay = total thickness of AC layer(s) above the EAC layer. Figure 86 shows the results of reflective cracking model of UPDAPS program for the HPMS MI1682 section. As this figure shows, the observable reflective cracking on the pavement surface was predicted up to about 4%. 207 Figure 86. Predicted reflective cracking for HPMS MI1682 section B.13 Calculate Rutting The rutting model of UPDAPS program is based on the introduced rutting model in the MEPDG formulations (ARA Inc. 2004). This model uses different formulations for calculating the rutting in AC, unbound base/subbase, and subgrade layers. Detailed formulations for rutting model can be found elsewhere (Kutay et al. 2023). B.13.1 Rutting of AC layer The rutting model for AC layers is primarily based on the vertical compressive strain and temperature at the mid-depth of AC sublayers. In this model, the temperature and vertical compressive strain at the mid-depth of each AC sublayer is calculated using the climatic and pavement structural response (MatLEA or MatFEA) models, respectively. B.13.1.1 Equivalent Cycle Approach The equivalent cycle approach in the rutting model of UPDAPS program is similar to the method described in appendix GG of the MEPDG document (ARA Inc. 2004). An illustration of the equivalent cycle approach for calculation of the accumulated vertical plastic strain is provided in figure 87. 208 Figure 87. Concept of equivalent cycle approach for AC rutting model The vertical plastic strain is a function of temperature, number of applied loading cycles, and vertical compressive strain. Among these parameters, the temperature at the mid-depth of AC sublayer is constant for a given AC sublayer during a given temperature quantile, while the vertical compressive strain is a function of the applied axle loading (axle type and axle load level). Therefore, for a given AC sublayer and temperature quantile, the vertical plastic strain as a function of number of cycles can be plotted under a specific loading condition (see graphs in figure 87). In order to calculate the accumulated vertical strain due to a specific axle loading, the equivalent number of cycles (see point 2 in figure 87) corresponds to the accumulated vertical plastic strain before application of axle load (see point 1 in figure 87) is calculated. In the next step, the accumulated vertical plastic strain of the jth AC sublayer is updated (see point 3 in figure 87). It is noted that the equivalent cycle approach is repeated to update the accumulated vertical plastic strain of each AC sublayer during each temperature quantile for all axle loads (combination of axle types and axle load levels). Finally, the effect of wheel wander is also incorporated into the rutting results, detailed formulation of which can be found in page 82, as well as MEAPA web- application documentation (Kutay et al. 2023). 209 Equivalent Cycles ApproachTi-1 (Jan), ev,i-1Ti (Feb), ev,iTi+1 (Mar), ev,i+1epn (cycles)ep,i-1nt,i-1nt-eqiv.,int,iep,i123ni B.13.2 Rutting of Unbound Base/Subbase Layer The rutting model for unbound materials (base or subbase) is somehow similar to the methodology of AC rutting model. The basis phenomenological relationship is based on the model developed by Tseng and Lytton (1989), which was slightly modified during the MEPDG formulations (ARA Inc. 2004). This model is primarily based on the average vertical strain at the unbound layer, as well as moisture content and resilient modulus of the unbound material. Similar to the AC rutting model, since the resilient modulus and moisture content of the unbound materials can vary from one month to another, the equivalent cycles approach is applied to calculate the progression of accumulated vertical plastic strain (i.e. rutting) during the pavement analysis period. B.13.3 Rutting of Subgrade Layer The rutting model for the subgrade layer follows similar procedure compared to the one for unbound layers. The same phenomenological relationship developed by Tseng and Lytton (1989) is used for the subgrade rutting model. In order to calculate the rutting of the subgrade layer, two different critical analysis depths are used: (i) top of the subgrade layer; (ii) six inches below the top of the subgrade layer. The accumulated vertical plastic strains (εp,j) at these two critical analysis depths are calculated during the pavement analysis period using the equivalent cycle approach, as explained for the rutting model of unbound layers. B.14 Calculate IRI The international roughness index (IRI) model of UPDAPS program is identical to the MEPDG formulations. This model is a function of predicted rutting, fatigue cracking, reflective cracking, thermal cracking, and site factors. The IRI prediction models for the newly constructed and rehabilitated (overlayed) flexible pavement structures are shown in Equations (95) and (96), respectively. 𝐼𝑅𝐼𝑖 = 𝐼𝑅𝐼initial + 𝐶1 ∙ 𝑅𝐷𝑖 + 𝐶2 ∙ 𝐹𝐶𝑖 + 𝐶3 ∙ 𝑇𝐶𝑖 + 𝐶4 ∙ 𝑆𝐹𝑖 𝐼𝑅𝐼𝑖 = 𝐼𝑅𝐼initial + 𝐶1 ∙ 𝑅𝐷𝑖 + 𝐶2 ∙ (𝐹𝐶𝑖 + 𝑅𝐶𝑖) + 𝐶3 ∙ 𝑇𝐶𝑖 + 𝐶4 ∙ 𝑆𝐹𝑖 𝐹𝐶𝑖 = ( 𝑏𝑢 𝐹𝐶𝑖 100 + 𝑡𝑑 𝐹𝐶𝑖 100 − 𝑏𝑢 𝐹𝐶𝑖 100 × 𝑡𝑑 𝐹𝐶𝑖 100 ) × 100 𝑆𝐹𝑖 = (𝐹𝑟𝑜𝑠𝑡 + 𝑆𝑤𝑒𝑙𝑙) × 𝐴𝑔𝑒𝑖 1.5 𝐹𝑟𝑜𝑠𝑡 = ln[(𝑅𝑎𝑖𝑛 + 1) × (𝐹𝐼 + 1) × 𝑃4] 210 (95) (96) (97) (98) (99) 𝑆𝑤𝑒𝑙𝑙 = ln[(𝑅𝑎𝑖𝑛 + 1) × (𝐹𝐼 + 1) × 𝑃200] (100) where: IRIi = international roughness index (IRI) at the ith temperature quantile (in/mile). IRIinitial = initial IRI value at the time of construction (in/mile). RDi FCi = predicted total rutting at the ith temperature quantile (in). = total fatigue cracking at the ith temperature quantile (%). FCi bu = bottom-up fatigue cracking at the ith temperature quantile (%). FCi td = top-down fatigue cracking at the ith temperature quantile (%). RCi TCi SFi = total reflective cracking at the ith temperature quantile (%). = thermal cracking at the ith temperature quantile (ft/mile). = site factor at the ith temperature quantile. Agei = pavement age from construction, ith temperature quantile (years). FI = freezing index (ºF∙days). Rain = mean annual rainfall (in). P4 = percent of the subgrade materials passing sieve No. #4 (%). P200 = percent of the subgrade materials passing sieve No. #200 (%). As an example, figure 88 shows the results of IRI model for the HPMS MI1682 section. As this figure shows, the predicted IRI grows from the initial IRI value of 71 inch/mile and ended up to about 149 inch/mile, which is a reasonable range for the designed AC overlay. 211 Figure 88. Predicted IRI for HPMS MI1682 section 212 APPENDIX C INPUT PROCESSING FOR UPDAPS-FLOOD PROGRAM The NAPCOM++ input processing module generates a JSON input files for the selected HPMS pavement sections by analyzing and importing data from different sources. These JSON input files are then used within the UPDAPS module to predict the pavement distresses and compute the damage shares of different vehicle classes during the pavement service life. Various types of information are saved in each JSON input file, including pavement structure properties, traffic loading characteristics, climatic data, and measured performances of the section in the field. The NAPCOM++ input processing module uses several default JSON input files for different surface types (e.g., surface type 2 for new flexible pavement or surface type 3 for new JPCP rigid pavement, etc.) to generate the inputs for each pavement section. For this purpose, the corresponding default JSON input file of each pavement section is copied and modified using the information obtained from various sources. Details of obtaining this information for each HPMS pavement section are explained in this chapter C.1 Pavement Structural Properties Pavement structural properties is one of the main components of the JSON input files. NAPCOM++ input processing module obtained these properties different databases including HPMS, LTPP, HERS, and Michigan State University asphalt mixture testing database. These databases are summarized as follows: C.1.1 Highway Performance Monitoring System (HPMS) The HPMS database is a national level highway information system which is developed by the FHWA. This database includes data that reflects the extent, condition, performance, use, and operating characteristics for more than 129,000 pavement sections all over the United States. The processed HPMS file includes several types of information in a CSV format. Each row represents a pavement section the properties of which provided in different columns. Figure 22 shows a snapshot of the processed HPMS file (version 2018) opened in Excel software. The main pavement structural inputs obtained from the HPMS database are summarized in table 2. This information are extracted from the HPMS database and used to modify the JSON input files for each pavement section. 213 Figure 89. Processed HPMS file (version 2018) Table 22. Main pavement structural features in HPMS database Column name surface_type base_type last_overlay_thick thickness_rigid thickness_flexible base_thickness year_last_const. year_last_improv. lane_width shoulder_type Shourlder_width soil_type f_system latitude_deg longitude_deg Unit - - inch inch inch inch - - ft - ft - - º º Description Surface type code for a given section. Base type code for a given section. Thickness of the most recent pavement overlay. Thickness of the rigid layer. Thickness of the flexible layer. Thickness of the base layer. Year in which the pavement section was constructed. Year in which the pavement surface was improved. Width of the design lane. Type of the road shoulder. Width of the shoulder, if any. Soil type as defined by AASHTO soil classes. Functional system code of the pavement section. Location of the pavement section. Location of the pavement section. C.1.2 Highway Economic Requirements System (HERS) HERS is a computer model used to simulate improvement selection decisions based on the relative benefit-cost merits of alternative improvement options. It is used by the FHWA to estimate national level investment requirements for the nation's highway system. Some of the pavement structural properties are extracted from the provided data within the HERS user manual using the properties pulled from the HPMS database. As an example, the modulus of the base layers is extracted from the HERS user manual as a function of the base type code, as shown in table 3. 214 Table 23. Modulus of the base layer based on HERS data Base type code 1 2 3 4 5 6 7 8 Description No base Aggregate base Asphalt or cement stabilized Asphalt or cement stabilized with granular subbase Bituminous base Lean concrete Stabilized open-graded permeable Fractured PCC Modulus (psi) - 24,000 500,000 500,000 200,000 1,000,000 40,000 100,000 In addition, the modulus and soil properties of the subgrade, as well as the depth of the ground water table are also extracted from the HERS manual as a function of the hosting state and the AASHTO soil type, both pulled from the HPMS section. Figure 23 shows a snapshot of the CSV file used for extracting the subgrade modulus and gradation properties from the HERS user manual. Figure 90. Soil properties of the subgrade from the HERS user manual C.1.3 Long-Term Pavement Performance (LTPP) The dynamic modulus of the asphalt mixtures is required for the thermal cracking, fatigue cracking, and rutting performance prediction models in the UPDAPS module. Such information is not available neither in HPMS or HERS databases. Therefore, the NAPCOM++ input processing 215 module uses the LTPP database to estimate the dynamic modulus coefficients of the asphalt mixtures for the flexible and composite pavement sections. For this purpose, the dynamic modulus properties of 2,142 asphalt mixtures at different layers (top, leveling, and base layers) from all over the United States were pulled using the LTPP database. These extracted dynamic modulus data are then assigned to each AC layer of HPMS pavement sections through a closest distance approach. In this approach, the location of each HPMS pavement section (latitude and longitude) is extracted from the HPMS database and used to find the closest available data in the LTPP database. Figure 25 shows a snapshot of the extracted dynamic modulus and location data from the LTPP database. Figure 91. Dynamic modulus and location data extracted from LTPP database C.1.4 Michigan State University Testing Database The UPDAPS module predicts the fatigue cracking of the AC layers using the VECD theory. The Pseudo stiffness versus damage curve (C-D curve) is the key element of the VECD analysis, which is usually obtained using the fatigue push-pull tests in the laboratory. The C-S curve in the UPDAPS module is modeled using the power function as shown in Equation (101). 𝐶(𝑆) = 1 − 𝑎 ∙ 𝑆𝑏 (101) where C is the pseudo stiffness, S is the damage parameter, a and b are the model calibration coefficients. As information on the C-S curves of different asphalt mixtures were not available 216 neither in HPMS or LTPP databases, the NAPCOM++ input processing module uses an estimate of the C-S model coefficients from a database of fatigue push-pull tests in Michigan State University. This database includes the fatigue test results over a wide range of asphalt mixtures used in different pavement sections throughout the State of Michigan. This database were analyzed based on the functionality of the pavement sections to assign proper C-S model coefficients to each functional system codes in the HPMS database, as shown in table 4 Table 24. Coefficients of the C(S) curve for asphalt mixtures Functional System Description 1 2 3 4 5 6 7 Interstates Principal arterial – freeways & expressways Principal arterial – others Minor arterial Major collector Minor collector Local a 0.00063 0.00105 0.00154 0.00213 0.00280 0.00347 0.00424 b 0.596 0.555 0.527 0.503 0.484 0.470 0.457 C.2 Traffic Loading Properties NAPCOM++ input processing module obtained the traffic loading properties from different databases including HPMS, HERS, and old NAPCOM version 2006. These databases are summarized as follows: C.2.1 Highway Performance Monitoring System (HPMS) The main traffic loading inputs obtained from the HPMS database are summarized in table 5, and used to modify the JSON input files for each pavement section. It is noted that the Average Annual Daily Truck Traffic (AADTT) is calculated as a summation of the average annual daily traffic of the single unit trucks, busses, and combination trucks. Table 25. Main traffic loading features in HPMS database Column name speed_limit aadt_single aadt_combination dir_factor f_system state_code Unit mph - - % - - Description Posted speed limit on the pavement section. Average annual daily traffic of single unit trucks and buses. Average annual daily traffic of the combination trucks. Percentage of design hour volume flowing in higher volume direction. Functional system code of the pavement section. The FIPS state code of the state hosting the section. C.2.2 Highway Economic Requirements System (HERS) The HERS inputs are used to modify some of the missing fields in the JSON input files. The number of each axle types per each vehicle class and the correspondence between the 20 and 13 217 vehicle class systems are obtained through the traffic configuration inputs from the HERS. Figure 27 shows a snapshot of the CSV file that include such information. It is noted that the 13-vehicle class system was traditionally used by the FHWA, while it was recently replaced by the more detailed 20-vehicle class system. Figure 92. Traffic configuration inputs from the HPMS input database C.2.3 National Pavement Cost Model (NAPCOM) version 2006 The axle load spectra and their corresponding load levels for single, tandem, and tridem axle types are obtained from the NAPCOM version 2006 input database, in which these variables were defined as a function of the NAPCOM region and highway group. The NAPCOM++ input processing module finds the equivalent NAPCOM region of each pavement section from the hosting state FIPS code, while the highway group is determined using the functional system code and table 6. 218 Table 26. Equivalency between highway groups and functional system codes Functional class code (2006) 1 2 3 4 5 6 7 8 9 10 11 12 Description Rural interstate Rural other principal arterial Rural minor arterial Rural major collector Rural minor collector Rural local Urban interstate Urban other freeway & expressway Urban principal arterial Urban minor arterial Urban collector Urban Local Functional system code (current FHWA codes) 1 3 4 5 6 7 1 2 3 4 5 7 Highway group 1 2 2 2 2 2 3 4 4 4 4 4 Figure 28 shows a snapshot of the axle load spectra CSV files for the single axle type at different NAPCOM regions and highway groups. The NAPCOM++ input processing module used similar CSV files for obtaining the data for the tandem and tridem axle types. Figure 93. Axle load spectra data for single axles from the NAPCOM version 2006 C.3 Climate Data Climatic data are important inputs to the UPDAPS module, by which the temperature profile of the pavement structure can be modeled during its service life. The NAPCOM++ input processing module obtained the climate properties from different databases including HPMS and 219 Modern-Era Retrospective analysis for Research and Applications, version 2.0 (MERRA-2) databases. These databases are summarized as follows: C.3.1 Highway Performance Monitoring System (HPMS) The main climate properties inputs obtained from the HPMS database are summarized in table 7, and used to modify the JSON input files for each pavement section. It is noted that the location of the pavement section (latitude and longitude) is the main input that is used to find the closest weather station. Table 27. Main climate features in HPMS database Column name climate_zone county_code state_code latitude_deg longitude_deg Unit - - - º º Description Climate zone of the pavement section as defined by LTPP. The FIPS county code of the county hosting the section. The FIPS state code of the state hosting the section. Location of the pavement section. Location of the pavement section. C.3.2 MERRA-2 database Modern-Era Retrospective analysis for Research and Application (MERRA-2) is a global atmospheric reanalysis data product developed by National Aeronautics and Space Administration (NASA) that provides comprehensive and high-quality datasets of various atmospheric and climate variables spanning several decades. The weather stations all over the United States are providing the historical hourly data in the standard MERRA-2 format. The NAPCOM++ input processing module finds the closest weather station to each pavement section and uses its corresponding historical hourly database for the climatic analysis in UPDAPS module. For this purpose, a list of all weather stations and their location is the input to the NAPCOM++ input processing module, where a snapshot of this CSV file is shown in figure 29. An algorithm for finding the closest weather station to each pavement section is then utilized to modify the JSON input files with the proper weather station code. Finally, the UPDAPS module downloads the historical hourly data of the given weather station and use it for calculating the temperature profile of the pavement sections and other climate-related parameters 220 Figure 94. List of weather stations across United States and their locations C.4 Measured Performance The measured performance of the HPMS pavement sections is not a required input for the analysis within UPDAPS module; however, they are used for adaptive calibration of the performance models. These measured performances are extracted from HPMS database for each pavement section C.4.1 Highway Performance Monitoring System (HPMS) The measured performances obtained from the HPMS database are summarized in table 8, which are limited to IRI, rutting, total cracking on pavement surface, and faulting. It is noted that these distresses were measured in 2018, and some of the performance measurements may not be available for specific pavement section, based on their surface type or availability of the measured data. Table 28. Main measured performance features in HPMS database Column name psr iri rutting faulting cracking_percent % Unit - inch/mile inch inch Description Present serviceability rating in 2018. International roughness index in 2018. Measured rutting in 2018. Measured joint faulting in 2018. Measured cracking on pavement surface in 2018. 221