Applied Science, Faculty of
Civil Engineering, Department of
DSpace
UBCV
Liu, Youjia
Master of Applied Science - MASc
University of British Columbia
Empirical quantification of how autonomous driving will affect road safety, particularly whether current road designs can accommodate autonomous vehicles (AV), remains under-researched. This research addresses the gap by proposing a three-dimensional (3D) risk assessment framework that integrates reliability theory and mobile Light Detection and Ranging (LiDAR) scans, focusing on how sight distance limitations interact with vehicle autonomy. Using data from 308 curves along a rural highway in British Columbia, Canada, the framework was applied in three phases. First, a voxel-based 3D LiDAR method was developed to estimate available sight distance (ASD) in complex terrain, with results compared against traditional two-dimensional (2D) methods. Second, three vehicle types were defined to represent different automation levels, including human-driven vehicles (HDV), transition-stage AVs, and fully developed AVs, followed by a reliability-based risk assessment comparing ASD with stopping sight distance (SSD) required by these vehicles. The resulting probability of non-compliance (Pnc) served as a quantitative measure of design risk from insufficient sight distance. Finally, sensitivity analyses were conducted to explore how operational parameters and sensor configurations influence highway design risk levels. The research found that the 3D method provided a more accurate, location-sensitive evaluation of ASD, while the 2D method often overestimated sight distance, especially on combined horizontal and vertical curves. The 3D-based risk assessment indicated an overall reduction in risk with increasing automation, although some cases showed higher risk for fully developed AVs. Segment- and curve-level analyses showed that fully developed AVs face higher risks on sharp curves with limited visibility due to assumptions of strict speed compliance and comfort-based braking rates. Sensitivity analysis showed that increasing deceleration rates can substantially reduce AV risks, while raising sensor height offers limited benefits. This integrated framework highlights the value of combining LiDAR technology and reliability theory for estimating Pnc as a 3D risk index. P𝚗c can guide manufacturers in adjusting operating parameters (e.g., speed and braking rates) or provide targeted system training at high-risk locations, while also helping road agencies prioritize design improvements to support road infrastructure readiness and safer transitions to full driving automation.
TOWARDS HIGHWAY DESIGN READINESS FOR VEHICLE AUTOMATION: A 3D RISK ASSESSMENT APPROACH USING RELIABILITY THEORY by Youjia Liu B.Eng. in Civil Engineering, McMaster University, 2021 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Civil Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) October 2025 © Youjia Liu, 2025 ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled: Towards Highway Design Readiness for Vehicle Automation: A 3D Risk Assessment Approach using Reliability Theory submitted by Youjia Liu in partial fulfilment of the requirements for the degree of Master of Applied Science in Civil Engineering Examining Committee: Dr. Tarek Sayed, Professor, Department of Civil Engineering, UBC Supervisor Dr. Suliman Gargoum, Assistant Professor, Civil Engineering, School of Engineering, UBC Co-supervisor iii Abstract Empirical quantification of how autonomous driving will affect road safety, particularly whether current road designs can accommodate autonomous vehicles (AV), remains under-researched. This research addresses the gap by proposing a three-dimensional (3D) risk assessment framework that integrates reliability theory and mobile Light Detection and Ranging (LiDAR) scans, focusing on how sight distance limitations interact with vehicle autonomy. Using data from 308 curves along a rural highway in British Columbia, Canada, the framework was applied in three phases. First, a voxel-based 3D LiDAR method was developed to estimate available sight distance (ASD) in complex terrain, with results compared against traditional two-dimensional (2D) methods. Second, three vehicle types were defined to represent different automation levels, including human-driven vehicles (HDV), transition-stage AVs, and fully developed AVs, followed by a reliability-based risk assessment comparing ASD with stopping sight distance (SSD) required by these vehicles. The resulting probability of non-compliance (Pnc) served as a quantitative measure of design risk from insufficient sight distance. Finally, sensitivity analyses were conducted to explore how operational parameters and sensor configurations influence highway design risk levels. The research found that the 3D method provided a more accurate, location-sensitive evaluation of ASD, while the 2D method often overestimated sight distance, especially on combined horizontal and vertical curves. The 3D-based risk assessment indicated an overall reduction in risk with increasing automation, although some cases showed higher risk for fully developed AVs. Segment- and curve-level analyses showed that fully developed AVs face higher risks on sharp curves with limited visibility due to assumptions of strict speed compliance and comfort-based iv braking rates. Sensitivity analysis showed that increasing deceleration rates can substantially reduce AV risks, while raising sensor height offers limited benefits. This integrated framework highlights the value of combining LiDAR technology and reliability theory for estimating Pnc as a 3D risk index. Pnc can guide manufacturers in adjusting operating parameters (e.g., speed and braking rates) or provide targeted system training at high-risk locations, while also helping road agencies prioritize design improvements to support road infrastructure readiness and safer transitions to full driving automation. v Lay Summary As self-driving cars become more common, it is important to assess whether highways are ready for them. This study used 3D laser scanning to capture what vehicles can actually see on the road and applied a risk index to flag design elements, such as stopping sight distance, that may not meet operational needs of road users. Since this index is linked to measurable safety outcomes, it offers a practical way to evaluate road safety for both human drivers and self-driving systems. The study found that higher levels of automation generally reduce risk, but fully autonomous vehicles can still face elevated risks under specific conditions, such as sharp curves with limited visibility. These risks can be mitigated through localized speed and deceleration adjustments or targeted system training at high-risk locations, while the risk index helps identify priority areas for design or infrastructure improvements to support safer roads as automation advances. vi Preface Versions of Chapters 3 through 7 have been submitted for publication, with portions of Chapters 1, 2, and 8 also contributing to the manuscript. I was responsible for software coding, data processing, data analysis, and drafting of the manuscript. Dr. Suliman Gargoum, my co-supervisor, provided the original data used in this research and offered methodological guidance during the data processing stage. Together with Dr. Gargoum, Dr. Tarek Sayed, my other research co-supervisor, contributed to the conceptualization of the study and provided essential guidance on research design, data interpretation, and validation. Generative artificial intelligence tools were not used in the methodological development, data analysis, or drafting of this thesis. vii Table of Contents Abstract ......................................................................................................................................... iii Lay Summary .................................................................................................................................v Preface ........................................................................................................................................... vi Table of Contents ........................................................................................................................ vii List of Tables ................................................................................................................................ xi List of Figures .............................................................................................................................. xii List of Abbreviations ................................................................................................................. xiv Acknowledgements .................................................................................................................... xvi Dedication ................................................................................................................................. xviii Chapter 1: Introduction ................................................................................................................1 1.1 Background & Motivation .............................................................................................. 1 1.1.1 Preparing Transport Systems for Long-Term Disruptions ..................................... 1 1.1.2 Road Infrastructure Readiness for Vehicle Automation ......................................... 3 1.1.3 From Deterministic to Risk-Based Road Design .................................................... 6 1.1.4 Using LiDAR Data for Highway Infrastructure Assessment ................................. 8 1.2 Problem Statement .......................................................................................................... 9 1.3 Research Objectives ...................................................................................................... 10 1.4 Thesis Structure ............................................................................................................ 13 Chapter 2: Literature Review .....................................................................................................15 2.1 Influence of Vehicle Automation on Highway Designs ............................................... 15 2.1.1 Shifts in User Characteristics and Operating Behaviors ....................................... 15 viii 2.1.2 Impact on Sight Distance as a Critical Design Criterion ...................................... 17 2.2 Highway Sight Distance Evaluation Approaches ......................................................... 20 2.2.1 Two-Dimensional (2D) Analytical Methods ........................................................ 20 2.2.2 Three-Dimensional (3D) Estimation Methods ...................................................... 21 2.3 Reliability-Based Risk Assessment in Highway Design .............................................. 23 2.3.1 Limitations with Existing Design Assumptions ................................................... 23 2.3.2 Reliability Theory and Applications to Geometric Design Elements ................... 24 2.3.3 Linking Risk Index to Measurable Safety Outcomes ........................................... 25 2.4 Broader Applications of LiDAR in Transportation Engineering .................................. 27 2.4.1 Extraction of Highway Geometric Elements ........................................................ 27 2.4.2 Design Safety Assessment using LiDAR Data ..................................................... 29 2.4.3 Simulation of AV Driving Environment Using LiDAR ....................................... 30 Chapter 3: Data Description .......................................................................................................32 3.1 Description of the Study Area ....................................................................................... 32 3.2 LiDAR Data Collection and Pre-Processing ................................................................. 33 Chapter 4: Methodology..............................................................................................................36 4.1 Vehicle Categorization by Automation Level .............................................................. 37 4.2 Estimation of Available Sight Distance (ASD) ............................................................ 37 4.2.1 2D Estimation Approach....................................................................................... 38 4.2.2 3D Estimation Approach....................................................................................... 39 4.3 Risk Assessment of Insufficient Sight Distance ........................................................... 42 4.3.1 Limit State Functions ............................................................................................ 42 4.3.2 Input Parameters ................................................................................................... 43 ix 4.3.2.1 Speed (V) .......................................................................................................... 43 4.3.2.2 Perception-Reaction Time (PRT) ..................................................................... 47 4.3.2.3 Deceleration Rate (a) ........................................................................................ 49 4.3.3 Reliability Analysis ............................................................................................... 51 Chapter 5: Comparison of 2D and 3D ASD Estimation Results .............................................54 5.1 Comparison by Sight Obstruction Type ....................................................................... 55 5.2 Comparison by Alignment Conditions ......................................................................... 57 5.3 Curve-Level Comparisons ............................................................................................ 59 5.4 Implications of ASD Evaluation Methods .................................................................... 63 Chapter 6: Reliability-Based Risk Assessment Results ............................................................65 6.1 Comparison of Risk Index between 2D and 3D Methods ............................................ 65 6.2 Comparison of Risk Index Across Vehicle Types ........................................................ 68 6.3 Identification of High-Risk Locations .......................................................................... 72 6.3.1 Segment-Level Analysis ....................................................................................... 72 6.3.2 Curve-Level Analysis ........................................................................................... 75 6.4 Implication of Automation on Highway Design Risk .................................................. 77 Chapter 7: Sensitivity Analysis ...................................................................................................79 7.1 Risk Sensitivity to Deceleration Rate ........................................................................... 79 7.2 Risk Sensitivity to Sensor Configuration ...................................................................... 81 Chapter 8: Conclusion .................................................................................................................83 8.1 Research Summary and Conclusions ............................................................................ 83 8.2 Key Contributions ......................................................................................................... 86 8.3 Limitations and Future Research Opportunities ........................................................... 88 x Bibliography .................................................................................................................................90 xi List of Tables Table 2.1: Typical Ranges for LiDAR Setup Parameters ............................................................. 19 Table 4.1: Operating Speed Models Used for HDVs and Transition-Stage AVs ......................... 46 Table 4.2: Summary of Derived Statistics for Input Parameters across Three Vehicle Types ..... 51 Table 5.1: Comparison of ΔASD by Radius Group ........................................................................ 59 Table 5.2: Comparison of ΔASD by Overlapped Vertical Alignment Type ................................... 59 Table 6.1: Average Values of Sensitivity and Importance Measures of Input Parameters Across Three Vehicle Types ..................................................................................................................... 72 Table 6.2: Geometric Characteristics of 25 Consecutives Curves ................................................ 73 xii List of Figures Figure 1.1: General Process for Resilience Planning with Readiness Emphasis (adapted from USDOT, 2024) ................................................................................................................................ 2 Figure 1.2: Planning Road Infrastructure Readiness for Vehicle Automation ............................... 5 Figure 1.3: Influence Diagram for How This Research Contributes to Ultimate System Readiness and Resilience ............................................................................................................................... 12 Figure 2.1: Illustration of Voxel-Based Sightline Obstruction Search ......................................... 23 Figure 3.1: Google Street View of the Studied Roadway, Northbound (Top) and Southbound (Bottom) ........................................................................................................................................ 33 Figure 3.2: Illustrative Example of the LiDAR Point Cloud: 3D View and Top View with Object Classification................................................................................................................................. 34 Figure 3.3: Count of Curves Categorized by (a) Horizontal Curve Radius; (b) Overlapping Vertical Alignment Type .............................................................................................................. 35 Figure 4.1: Overall Research Framework ..................................................................................... 36 Figure 4.2: Line of Sight for Horizontal Curves in the Studied Roadway ................................... 38 Figure 4.3: Flowchart for Determining Critical 3D ASD and Obstruction Type per Curve ........ 41 Figure 5.1: Comparison of ASD Estimated using 2D VS. 3D Methods with Typical Outlier Conditions ..................................................................................................................................... 55 Figure 5.2: Example Outlier Curves with 3D ASD Significantly Longer than 2D ASD ............. 55 Figure 5.3: Comparison of the Count of Obstruction Types Identified by Two Methods ............ 56 Figure 5.4: Illustration of Visibility Obstruction Caused by Road Surface .................................. 57 Figure 5.5: Boxplots of ΔASD (a) by Radius Group; (b) by Overlapped Vertical Alignment Type....................................................................................................................................................... 58 xiii Figure 5.6: Comparison between ASDs and SSD for an Example Curve A ................................ 61 Figure 5.7: Comparison between ASDs and SSD for an Example Curve B ................................ 63 Figure 6.1: Comparison of Pnc Values Computed using 2D ASD and 3D ASD (a) Density Plot; (b) CDF Plot; (c) Parity Plot ......................................................................................................... 67 Figure 6.2: Comparison of Pnc Values Computed Using 2D ASD and 3D ASD along Example Curve A ......................................................................................................................................... 68 Figure 6.3: Distributions of Pnc Values for Three Vehicle Types (a) Density Plot; (b) CDF Plot 70 Figure 6.4: Parity Plot of Pnc Values between Vehicle Types (a) HDV and Transition-Stage AV; (b) HDV and Fully Developed AV ............................................................................................... 71 Figure 6.5: Variation of Pnc Values Across Three Vehicle Types for 25 Consecutive Curves .... 75 Figure 6.6: Variation of Pnc Values along Length of Example Curve A ...................................... 77 Figure 7.1: CDF Plot of Pnc Values for Fully Developed AVs Computed Using Three Deceleration Rates ........................................................................................................................ 80 Figure 7.2: Parity Plot of Pnc Values (a) Comfort and Emergency Braking for Fully Developed AVs; (b) HDV and Fully Developed AV using Emergency Braking Rate .................................. 81 Figure 7.3: Cumulative Distributions of Pnc for Fully Developed AVs Using Three Observer Heights .......................................................................................................................................... 82 xiv List of Abbreviations AASHTO American Association of State Highway and Transportation Officials ACC Adaptive Cruise Control ADAS Advanced Driver-Assistance System ADS Automated Driving System AEB Automatic Emergency Braking ASD Available Sight Distance AV Autonomous Vehicle CAD Computer-Aid Design CDF Cumulative Distribution Function CMF Collision Modification Factor CWS Curve Warning System DSM Digital Surface Model DTM Digital Terrain Model FCW Forward Collision Warning FHWA Federal Highway Administration GIS Geographic Information System GNSS Global Navigation Satellite System HASD Available Sight Distance for Horizontal Curve HD High Definition HDV Human-Driven Vehicle IMU Internal Measurement Unit LiDAR Light Detection and Ranging xv Pnc Probability of Non-Compliance PDO Property-Damage Only PRT Perception-Reaction Time SPF Safety Performance Function SSD Stopping Sight Distance TAC Transportation Association of Canada VASD Available Sight Distance for Vertical Curve V2V Vehicle-to-Vehicle Communication 2D Two-Dimensional 3D Three-Dimensional xvi Acknowledgements I would like to sincerely thank my research supervisor Dr. Tarek Sayed for giving me the opportunity to pursue this degree as I transitioned from a course-based program. Your encouragement allowed me to explore my interests and strengths in the field of road safety, and I am truly grateful for your patience, your generosity with time and knowledge, and the way you always helped me work through my confusion with understanding and care. I am also very grateful to my co-supervisor, Dr. Suliman Gagroum, for your guidance in tackling technical challenges and for constructive feedback at every stage of the research. Thank you both for your continuous support, confidence, and mentorship. I have been inspired by your dedication, diligence, and strategic perspectives in your fields of research, and I feel privileged to have learned from you. I am also thankful to the transportation engineering and planning faculties at UBC, including Dr. Omar Swei, Dr. Amy Kim, Mr. Clark Lim, Dr. Terje Haukaas, as well as to Michelle Babiuk from TransLink. Through your graduate courses, I not only built technical knowledge but also grew in my ability to think critically. Your diverse insight into the broad field of transportation enriched my learning experience and supported my development in this specialization. Special thanks to the BITSAM lab team for your friendship, encouragement, and inspiration. Thank you, Elena Abu Khuzam, for being by my side through challenges and for sharing such a memorable part of this degree. Thank you, Depeng Niu, Tarek Ghoul, Gabriel Lanzaro, Ahmed Kamel, as well as Ali Faisal from the SALMALIS lab for sharing your knowledge and inspiring me through your own dedication to research. I would also like to thank Dr. Alex Biagazzi for organizing the Graduate Seminar series, which I greatly enjoyed and through which I learned from the diverse research and project presentations of my peers. xvii I would also like to thank my loving partner and close friends for your companionship and constant moral support throughout this journey, and for sharing the thoughts, feelings, and learnings that have allowed us to grow together. Lastly and most importantly, I offer my deepest gratitude to my parents, who offer unconditional love and support. You have always believed in me and walked beside me in moments of doubt. Your wisdom has been a steady light, and your encouragement has given me the strength to keep moving forward. Thank you for cheering me on from afar and for everything you have given me. The completion of this thesis has been made possible through the support, guidance, and kindness of many, to whom I extend my heartfelt thanks. xviii Dedication To my beloved family. To all transportation professionals dedicated to making this world a safer, better, and more resilient place.1 Chapter 1: Introduction 1.1 Background & Motivation 1.1.1 Preparing Transport Systems for Long-Term Disruptions Transportation systems face both short-term shocks (e.g., disasters, system shutdowns) and long-term disruptions (e.g., climate change, technological advancements) that must be managed constantly. Short-term shocks strike suddenly and cause a temporary performance decline before the system recovers, while long-term disruptions build up slowly and may lead to lasting changes that are not yet fully understood. These challenges highlight the importance of ensuring resilience, broadly defined as the system’s capacity to withstand, cope with, recover from, and adapt to disruptions (Mattsson & Jenelius, 2015). With long-term disruptions, focusing on recovery is less meaningful given the uncertainty of their impacts. What matters more is equipping the system with the capacity to respond as disruptions evolve, a perspective described in literature as readiness. Hollnagel (2009), in his book “Resilience Engineering Perspectives”, emphasizes that this capacity is enabled by the ability to anticipate challenges and monitor critical situations, and is further reinforced through learning from past responses. Figure 1.1 presents a general resilience planning framework synthesized from multiple studies (EFC, 2020; USDOT, 2024). In this framework, readiness is defined through the initial stages, which involve assessing evolving conditions, identifying systemic gaps, and planning strategies. These stages represent the proactive dimension of resilience, focused on building capacity before disruptive impacts fully unfold. Given the uncertain timing, scale, and form of long-term disruptions, they provide the essential groundwork for guiding future implementation. 2 Figure 1.1: General Process for Resilience Planning with Readiness Emphasis (adapted from USDOT, 2024) Vehicle automation represents one such long-term disruption, moving forward at a rapid pace even though many of its consequences remain unclear. This technological shift introduces lasting impacts on transportation systems because it challenges the traditional definition of driving behavior and responsibility, and it is further complicated by the advancement and interdependence of sensors, perception systems, driving algorithms, and artificial intelligence (Saeed, 2019). Preparing for the rollout of vehicle automation therefore requires anticipating how conditions may evolve, identifying emerging safety risks, and planning responsive strategies. In line with these needs, many public agencies have already begun developing readiness plans and policy frameworks to guide their response (Ontario Ministry of Transportation, 2020; USDOT, 2021; Labi et al., 2023). changing con itions critical gaps responsive strategies through policies programs an esign evolving con itions to minimi e impacts from outcomes to inform future ecisions Emphasis of Reasiness3 1.1.2 Road Infrastructure Readiness for Vehicle Automation Readiness planning for vehicle automation begins with assessing changing conditions, this includes understanding potential deployment timelines and application scenarios. While these predictions vary, they are commonly framed around the levels of automation defined by the Society of Automotive Engineers (SAE International, 2021). These levels range from Level 0, represented by fully human-operated vehicles (HDV), to Level 5, represented by fully autonomous vehicles (AV). Levels 1 and 2 provide driver assistance with tasks such as braking, lane keeping, and parking, while Level 3 allows the system to manage most driving tasks but still requires the driver to intervene when prompted. At Levels 4 and 5, vehicles operate independently within defined or all driving environments, relying entirely on system detection, perception, path planning and decision-making without human intervention. Despite the growing excitement surrounding these technologies, the timeline for widespread adoption of higher levels of automation remains uncertain. This uncertainty arises from interdependent challenges spanning technological maturity, infrastructure compatibility, regulatory frameworks, and public acceptance (Fagnant & Kockelman, 2014; Litman, 2025). At the core of these challenges lies safety, with associated risks stemming from altered driver perception-reaction during the transition to automation, the limitations of automated driving systems (ADS) in complex environments (Campbell et al., 2016), and unresolved questions of liability in the event of incidents (Taeihagh & Lim, 2019). Recent studies reinforce this concern: Khan et al. (2024) reported that 99% of disengagements in highly automated vehicles are attributable to ADS-related issues, such as localization, perception, prediction, planning, and control. Among these, perception is particularly critical because it encompasses the widest range 4 of error types, depends heavily on the system’s interaction with its surroun ing infrastructure, and can impact downstream systemic performance (Marti et al., 2019). Dixit (2016) similarly emphasized the role of road infrastructure under vehicle automation, noting that poor roadway conditions contributed to nearly 10% of ADS disengagements. Together, these findings highlight that road infrastructure quality remains an essential factor in the safety of automated operations. Within this broader context, it is important to evaluate whether existing design standards remain valid under automation. Existing geometric standards were built on empirical evidence of human perception, driving behavior, and visibility, reflecting the historical dominance of human factors in shaping safety outcomes (Campbell et al., 2008). With automation, however, safety risks are shifting from human behavior to system performance, making it critical to reassess whether current roadway designs can accommodate evolving vehicle technologies and user characteristics (Tengilimoglu et al., 2023). Although recent discussions have considered how road infrastructure might be adjusted based on potential system needs, ranging from maintenance practices to redesign strategies, they remain largely qualitative. To advance road design readiness planning through quantitative evaluation, researchers have often used sight distance as a starting point (Othman, 2021). Sight distance is a fundamental geometric design element that links roadway geometry with safety by embedding a margin for variations in driving behavior. In practice, evaluating sight distance involves checking whether the available sight distance (ASD) provided by the roadway exceeds the stopping sight distance (SSD) required by road users, both of which depend on user characteristics that will evolve under automation (TAC, 2017). 5 Sensitivity analysis is commonly used to evaluate how sight distance requirements may change under automation by varying the input parameters of SSD and ASD across different operating assumptions. SSD depends on factors such as perception-reaction time (PRT), speed, and deceleration rate, while ASD is shaped by roadway geometry and user perspective, including observer height and detection range. Relevant analyses have indicated that automated vehicles at higher levels often exhibit shorter PRTs and more consistent speed profiles due to ADS systems, which may lower SSD requirements (Urmson, 2006; Ye et al., 2021). At the same time, their reliance on sensor-based perception challenges traditional assumptions about observer heights and detection ranges, directly affecting ASD estimation (Khoury et al., 2019). These studies demonstrate how automation can alter design assumptions, but they offer limited insight into safety outcomes, a gap that reflects a broader issue in current practice: the reliance on deterministic assumptions in design. Figure 1.2: Planning Road Infrastructure Readiness for Vehicle Automation Assess changing conditions: Automation is altering vehicle operational parameters and reshaping the demands placed on road infrastructureIdentify critical gaps:Current road design practices need to be revisited to ensure they can support the safe deployment of AVsPlan responsive strategies:A quantitative approach is needed to guide strategies for adapting standards and targeting improvements6 1.1.3 From Deterministic to Risk-Based Road Design In current practice, sight distance evaluation is based on estimating SSD using fixed values for vehicle operating parameters such as PRT, speed, and deceleration. These values are drawn from empirical studies of driver behavior, with conservative upper-end values selected to ensure coverage of most users (TAC, 2017; AASHTO, 2018). While this approach provides some safeguards, it does not reflect the variability in driver performance and operating conditions, raising doubts about whether compliance with such standards can truly ensure safety. To address these limitations, reliability theory has been introduced as a framework for explicitly accounting for variability in key design parameters. Navin (1992) was among the first to demonstrate its use in road design, illustrating the approach with sight distance as an example. In this framework, critical inputs can be modeled as random variables, and the probability that ASD is less than SSD can be estimated to produce a risk index for insufficient sight distance. Building on this foundation, subsequent studies applied reliability-based methods to assess risks associated with geometric design elements such as sight distance at intersections and curves (Easa, 2000; Richl & Sayed, 2006). The framework has also been extended to support benchmarking and calibration of design standards by linking geometric requirements to predefined acceptable risk levels (Ismail & Sayed, 2009). Empirical studies further demonstrate the value of this approach, reporting statistically significant associations between risk levels and crash frequency or crash rates (S. E.-B. Ibrahim & Sayed, 2011; Alsaleh et al., 2023), thereby linking these probabilistic measures directly to observed safety outcomes. Given this evidence, the risk-based approach provides a promising way to quantify the safety of road design under vehicle automation. Until recently, most applications of this approach used input 7 parameters derived from human driver behavior. However, emerging empirical tests with higher-level automated vehicles now make it possible to incorporate AV-specific data. For instance, a recent study by Sarran and Hassan (2025) incorporated AV operational parameters into a reliability-based risk model to examine how traffic volume and speed combinations influence sight-distance safety at uncontrolled intersections in mixed traffic with AVs and HDVs. While this represents a step forward in adapting reliability methods to automation, it also opens up two key opportunities for extending the approach. First, the analysis is confined to rural intersections, whereas highways represent an equally critical context for reliability-based design risk assessment. SSD is a fundamental element of highway geometric design and is especially consequential on horizontal curves. According to FHWA (2023), horizontal curves account for more than 25% of fatal crashes, with crash rates nearly three times higher than tangent segments. The risks are further elevated on highways where horizontal and vertical alignments overlap, creating compounded sight distance challenges. Extending reliability analysis to highways, and particularly to curves, is therefore essential for a comprehensive evaluation of design readiness under automation. Second, the study relied on simplified 2D formulas for ASD evaluation based on roadway geometry and driver assumptions such as eye height and visibility. Even when adjusted for AVs by incorporating sensor placement, 2D methods remain limited because they cannot capture the influence of vertical alignment, roadside obstructions, and combined geometries, representing factors that substantially affect sight distance. Continued reliance on these 2D formulas risks introducing inaccuracies in risk indices and misinforming design evaluation (Hassan & Easa, 2003). To provide a more reliable basis for safety assessment under automation, robust three-8 dimensional (3D) methods are needed. Prior research has explored approaches ranging from analytical models using finite elements to advanced spatial tools such as Geographic Information Systems (GIS) and Light Detection and Ranging (LiDAR), with LiDAR gaining attention for its dual role in reliable roadway evaluation and in representing how AVs perceive their environment (Yue et al., 2018). 1.1.4 Using LiDAR Data for Highway Infrastructure Assessment Mobile Light Detection and Ranging (LiDAR) technology has emerged as one of the most promising methods for 3D roadway evaluation because of its integration of laser scanners, Global Navigation Satellite System (GNSS) receivers, and inertial measurement units (IMUs) to create dense 3D point clouds that capture roadway conditions and surrounding environments in detail. When mounted on vehicles, mobile LiDAR can scan an entire roadway corridor continuously, producing data that allows sight distance to be measured at incremental points along the route (S. A. Gargoum & El Basyouny, 2019). It also enables the identification of roadside features such as signs vegetation an structures an etermines whether they obstruct a roa user’s line of sight. In addition, researchers have developed algorithms to extract geometric characteristics from LiDAR data, including horizontal and vertical curves, further demonstrating its value for precise roadway feature evaluation (S. A. Gargoum, 2019). LiDAR also has its unique strength compared with other 3D methods for ASD evaluation. It is not only highly accurate for roadway evaluation due to its high-resolution, but it is also one of the core sensing technologies in automated vehicles. Reflecting this dual role, researchers have applied LiDAR data to build simulation environments that examine how AVs perceive roadway conditions under different levels of environmental complexity (Abohassan & El-Basyouny, 2024). LiDAR 9 has also been used to test AV visibility on existing roadway design safety by comparing point-based 3D sight distance with design values to identify non-compliant locations (Gouda et al., 2021). Despite its great potential, LiDAR has not been systematically integrated into reliability-based frameworks for evaluating roadway readiness under vehicle automation, a gap this research seeks to address. 1.2 Problem Statement Quantifying infrastructure readiness for vehicle automation is an emerging research area that is critical for safe AV deployment. Roadway design is central to this effort because design standards embed assumptions about vehicle performance and driver behavior that may not be held under automation. Highway design becomes critical in this context, since many of its design criteria such as sight distance are shaped by evolving vehicle operating parameters and require closer examination. Highways also warrant special attention where horizontal and vertical alignments intersect, as these conditions often constrain visibility and elevate safety risks. Reliability-based risk assessment provides a useful framework for linking highway sight distance sufficiency with measurable safety outcome. By treating the input parameters of SSD as random variables and estimating the probability that SSD is less than ASD, this approach produces a probabilistic risk index for insufficient sight distance. However, its current application faces two major limitations: (1) reliance on SSD parameter distributions derived mainly from human driving behaviors, often outdated and not reflective of AV behavior under various operating environments; and (2) use of simplified 2D formulas for ASD estimation, which cannot adequately capture complex roadway geometries or realistic obstruction conditions. 10 Although a recent study applying reliability-based risk assessments have incorporated AV operating parameters, they have been confined to rural intersection settings (Sarran & Hassan, 2025), leaving highway designs largely unexplored. Meanwhile, LiDAR-based 3D ASD evaluation methods provide detailed views of highway geometry and visibility obstructions that enable more accurate estimation of ASD, yet they have not been systematically integrated into reliability-based frameworks for highway design under AV operational conditions. This gap limits the ability to evaluate highway design readiness for automation and highlights the need for integrated approaches that can generate reliable evidence on whether current standards should be modified or adapted for future needs. 1.3 Research Objectives The objective of this research is to address the identified gaps through a 3D reliability-based risk assessment framework with a specific case study focusing on highway sight distance limitations. The process will involve examining 3D sight distance at highway curves as a representative design element for assessing infrastructure readiness under automation. A reliability-based risk assessment will then be conducted to evaluate the sufficiency of sight distance on a highway segment in British Columbia, Canada, using mobile LiDAR-derived roadway data and operational parameters reflecting different vehicle types and automation levels. To achieve this objective, a three-phase approach is applied: 1. ASD estimation: ASD is calculated using both the traditional 2D analytical formula and using a proposed algorithm to extract the information from a 3D mobile LiDAR scan. The two methods are compared to determine their accuracy, implications for risk estimation, and suitability as the basis for subsequent analysis. 11 2. Reliability-based risk assessment: Applying reliability theory, the selected ASD is compared with SSD values computed from operational parameters for three vehicle types representing increasing levels of automation: HDVs (SAE Level 0), transition-stage AVs (SAE Levels 1-3), and fully developed AVs (SAE Levels 4-5). The resulting probability of non-compliance (Pnc), quantifying the likelihood that ASD falls below SSD, serves as a risk index for quantifying safety under varying levels of automation. 3. Sensitivity analysis: Key input parameters, including vehicle operating characteristics and AV sensor configurations, will be varied to identify the dominant factors of risk under automation. The findings aim to provide insights for road agencies and vehicle manufacturers on how to reduce critical uncertainties and support safe AV deployment. Through this research, highway sight distance evaluation serves as an entry point to connect design-level safety risks with a broader framework for quantifying infrastructure readiness under vehicle automation. By demonstrating how reliability-based analysis and LiDAR-derived 3D methods can reveal gaps in existing practices, the study contributes to developing an evidence base that supports adaptive design practices. In turn, such practices strengthen the transportation system’s capacity to a apt to evolving technologies and build long-term resilience. 12 Figure 1.3: Influence Diagram for How This Research Contributes to Ultimate System Readiness and Resilience 13 1.4 Thesis Structure The remainder of this thesis is organized into seven chapters, as outlined below: Chapter 2 presents a review of the literature on the influence of vehicle automation on highway design, with particular attention to evolving user characteristics and operational parameters and their implications for sight distance as a key design criterion. The chapter then reviews existing evaluation approaches, including 2D analytical methods and 3D estimation methods with applications of LiDAR. It further introduces reliability-based risk assessment in highway design by explaining how reliability theory addresses limitations of traditional deterministic evaluations and how the resulting risk indices have been linked to measurable safety outcomes. The chapter concludes by examining broader applications of LiDAR in transportation engineering, including its use in extracting geometric features, supporting safety assessments, and simulating driving environments for AVs. Together, these discussions lay the foundation for why LiDAR is particularly valuable for risk assessment of highway design under automation. Chapter 3 describes the study area used in the case study that grounds this research. This includes an overview of the general geometric characteristics of the roadway, based on data obtained from mobile LiDAR scanning. Chapter 4 outlines the research methodology, using sight distance as the representative highway design element. It explains how vehicle types were defined to represent varying levels of automation, details the methods for estimating ASD using both 2D and 3D approaches, and describes the setup of the limit state function and application of reliability theory to evaluate the risk of insufficient sight distance. The chapter also presents the rationale and assumptions 14 underlying the operational parameters collected for each vehicle type, which are essential for conducting the risk assessment and for evaluating how risk evolves under increasing automation. Chapter 5 presents the results of ASD estimation using the 2D and 3D methods. Comparisons are made from multiple perspectives, including overall trends, variation by obstruction type, and variation by alignment condition. An illustrative example of ASD variation along a curve is also provided. The chapter concludes by summarizing the key implications of the two evaluation methods, particularly in the context of vehicle automation. Chapter 6 presents the findings from the reliability-based risk assessment. It first compares risk estimates when 2D and 3D ASD are used in the limit state function, confirming that 3D ASD is the more appropriate measure for further analysis. It then examines the risk index across the three vehicle types, identifying how highway design risk varies with automation level. High-risk locations are identified at both the segment and curve levels, with discussion of the main factors contributing to elevated risk. The chapter closes with an interpretation of how these findings can inform coping strategies for vehicle manufacturers and road agencies as they prepare for greater levels of vehicle automation. Chapter 7 presents a sensitivity analysis of the quantified risk. By adjusting operational parameters and sensor configurations, this chapter explores potential strategies for reducing risk associated with vehicles operating at higher levels of automation. Chapter 8 concludes the thesis by summarizing the research findings, discussing the key contributions, and outlining opportunities for future research. 15 Chapter 2: Literature Review 2.1 Influence of Vehicle Automation on Highway Designs 2.1.1 Shifts in User Characteristics and Operating Behaviors Highway systems are traditionally defined by three interdependent components: the road, traffic control, and users (Campbell et al., 2008). Safe and efficient operations depend on these components, functioning together as an integrated system. In geometric design, the user has tra itionally been assume to be human forming the basis of the ‘ esign river’s concept with design decisions guided by the capabilities and limitations of this representative figure. Key considerations include physical factors such as height and vision, cognitive factors such as PRT and decision-making, and experiential factors such as driving skill and familiarity with the road environment (TAC, 2017; AASHTO, 2018). These dimensions shape how roadway elements are perceived and navigated, forming the basis for criteria such as sight distance, clear zone, and alignment. With the growing integration of Advanced Driver-Assistance Systems (ADAS) in modern vehicles, active safety features are reshaping the traditional concept of the design driver. These systems introduce new responsibilities by requiring drivers to supervise their operation and intervene during malfunctions. Such eman s increase river workloa by requiring an appropriate “mental mo el” for effective system interaction (Pai et al., 2023). Because ADAS typically deliver alerts or maneuver recommendations through dashboard displays, they directly influence driver cognition. This influence can lead to “automation bias”, where drivers rely more on automated advice than on thorough evaluation of available information (Parasuraman & Manzey, 2010). Empirical studies based on naturalistic data, on-road experiments, and driving simulators provide 16 evidence of overreliance and reduced vigilance among drivers operating with partial automation (Louw & Merat, 2017; Kraft et al., 2018; Gaspar & Carney, 2019). Distraction is a key concern associated with these overtrust issues in automated systems. When supervising automated driving systems such as Adaptive Cruise Control (ACC), drivers exhibit long takeover times, which increase further with secondary task engagement (Merat et al., 2012; Zeeb et al., 2015). A driving simulator study by So et al. (2021) also found that stabilization time, the period required for drivers to regain stable control and return to normal driving after a takeover, was further extended because of distraction. On the other hand, some ADAS functions provide measurable benefits. Warning-based systems such as Forward Collision Warning (FCW) have been shown to mitigate driver distraction and improve reaction times in emergency situations, particularly among certain driver populations (Lyu et al., 2017; Masello et al., 2023). Taken together, this body of evidence highlights how partial automation not only alters driver responsibilities but also challenges the traditional definition of perception-reaction behavior by directly shaping cognitive engagement and takeover performance. When moving toward fully autonomous driving, these factors shift more drastically. Human perception is replaced by system-based sensing, and the assumptions underlying the design driver no longer apply. Instead of relying on human vision and cognitive processing, automated vehicles use a combination of LiDAR, radar, cameras, and other sensors, each with distinct fields of view, ranges, and mounting heights work together for perception tasks (T. Li & Kockelman 2016; Kocić et al., 2018). These sensing mechanisms can outperform human vision in certain conditions, such as night driving, but may also be constrained by weather, resolution data-processing capabilities (Yahyaei et al., 2022). Based on the sensor perception, planning and decision algorithms are 17 engaged to guide the next-step motion and vehicle control automation also modifies vehicle operational behavior (Marti et al., 2019; Velasco-Hernandez et al., 2020). It is commonly acknowledged that modern computational power enables the process from perception to reaction by the system to be way shorter than human, with theoretical time being shorter than 0.5 seconds (Urmson, 2006; Wagner, 2016; Rydzewski & Czarnul, 2021). Beyond perception, system-based driving also affects operational behaviors such as speed and braking. For instance, whereas human drivers typically display variable speed distributions, automated vehicles tend to maintain more stable and consistent speed profiles (Wei et al., 2014). Refinement of these speed algorithms remains ongoing, with approaches ranging from optimizing fuel efficiency (Anastassov et al., 2017; S. Xu & Peng, 2018), to accounting for road geometry and associated constraints (Aparicio et al., 2005; Lima et al., 2015), and to replicating human speed control in order to enhance comfort and flexibility in decision-making (Lefèvre et al., 2016; L. Li et al., 2018; Z. Chen et al., 2022). Similarly, braking algorithms under development consider passenger comfort, safety, and energy consumption (Fu et al., 2020a; Yang et al., 2020). Although these algorithms are often designed to emulate human braking behavior, they cannot fully reproduce the stochastic nature of human decision-making in all braking situations (McCall & Trivedi, 2007). 2.1.2 Impact on Sight Distance as a Critical Design Criterion Evolving user characteristics and operational parameters directly affect highway design criteria, with sight distance being one of the most critical. Stopping sight distance (SSD), for instance, depends on operating speed, PRT, and deceleration rate. These factors have been shown in the previous section to vary under different driving conditions and have been examined through 18 sensitivity analyses by several researchers (Khoury et al., 2019; Othman, 2021; Ye et al., 2021). Welde and Qiao (2020) further modeled three scenarios including current conditions, Level 3 automation, and full automation, by selecting operating parameters to represent the driving assumptions at each level and found that SSD requirements could be significantly reduced. Understanding changes in SSD requirements is crucial because they directly shape other design elements, including the length of the sightline offset or clearance for horizontal curves (Hassan & Easa, 2000; Knapp et al., 2014). SSD also governs vertical curve length, where traditional assumptions about driver vision distance and eye height are altered by the use of LiDAR sensors for object detection and classification (Welde & Qiao, 2020). For example, design standards typically assume a driver eye height of 1.08 m, but under full automation this parameter would instead reflect LiDAR sensor placement, which can range from 0.4 m to 1.85 m (Marti et al., 2019; Bastos et al., 2021; Hsu et al., 2021). Table 2.1 summarizes typical LiDAR setup configurations reported in the literature. 19 Table 2.1: Typical Ranges for LiDAR Setup Parameters Setup Description Detection Range Typically from 150m to 300m; 200m and more is considered as necessary range while moving at highway speed. Horizontal Field of View Various between 115° to 360° depending on the system, with the highest range achieved using a rotating mirror. Vertical Field of View Ranges from 20° to 26.8° depending on the model. Minimum of 20° was recommended to provide reliable obstacle detection. Accuracy and Resolution From as low as 0.2° to higher resolution of 2°. Usually, the sensitivity of measurement reduces as target distance increases. Mount height Ranges from 0.4m to 1.85m epen ing on the vehicle mo el an whether it’s mounted at the license plate, headlight, or the top part of the vehicle. Another sight distance dimension affected by automation is passing sight distance (PSD), since its design equation depends on speed and braking rates that are expected to change under automated driving. Automation also introduces added complexity through freight platooning, enabled by sensor-based perception, vehicle-to-vehicle (V2V) communication, and vehicle-following algorithms (Axelsson, 2017). highlighted the need to revise PSD equations to account for the number of vehicles in a platoon, their length, and the physical gaps between them. Similarly, Garcia and Pastor-Serrano (2022) examined the influence of truck platoons on visibility at horizontal curves and calibrated the minimum curve radius required for safe passing. 20 2.2 Highway Sight Distance Evaluation Approaches 2.2.1 Two-Dimensional (2D) Analytical Methods Traditionally, the adequacy of highway sight distance is evaluated by comparing the required SSD by road users with the ASD provided. ASD represents the actual unobstructed length of roadway visible to a driver and is typically estimated using analytical formulas provided in design guidelines (TAC, 2017; AASHTO, 2018). A key limitation of these formulas, however, is that they treat roadway geometry in isolation, evaluating sight distance separately for horizontal curves on level grades or for vertical curves along tangents, rather than capturing their combined effects in real-world conditions. For this reason, these methods are often referred to as 2D by researchers (Hassan & Easa, 2003). In addition, ASD formulas assume that sightline obstructions are always located within the curve, typically represented by roadside or median features. This simplification can cause sight distance estimates to deviate from actual field conditions where obstructions may extend beyond the curve. To address these limitations, researchers have extended 2D methods by developing analytical equations that allow sightline computations to extend beyond the curve length, provided that vertical alignment effects remain insignificant (Lovell, 1999; Lovell et al., 2001). The conventional assumption of circular horizontal curves has also been refined through advanced analytical models that determine clearance offsets for spiral arcs (Mauga et al., 2013). In addition, computer-aided design (CAD) tools have been applied to estimate ASD graphically using geometric projections (de Santos-Berbel et al., 2017). However, when horizontal curves and vertical alignments are combined, these 2D approaches still exhibit inherent shortcomings. 21 2.2.2 Three-Dimensional (3D) Estimation Methods Researchers have increasingly turned to 3D estimation methods to more accurately capture the effect of combined alignment on sight distance. For example, Hassan et al. (1996) proposed an analytical model that represents the 3D highway surface using finite elements and evaluates sightline obstructions iteratively. Building on this, Ismail and Sayed (2007) characterized the road surface with continuous mathematical equations and refined the obstruction search to critical areas. Their analysis revealed that the 2D approach can either overestimate or underestimate sight distance depending on the specific alignment configuration. In parallel, computational studies using simulated driving environments have been conducted to assess driver perception of sight distance and identify critical areas where horizontal and vertical curves overlap to reduce visibility (Hassan & Easa, 1998; Hassan et al., 2002; Bidulka et al., 2002). More recently, geospatial techniques using Geographic Information Systems (GIS) and LiDAR have been introduced for 3D ASD estimation. Early studies applied viewshed analysis to digital terrain models (DTMs) derived from aerial LiDAR, which represent the bare-earth surface. By setting conventional river’s eye height an target height accor ing to the stan ar an assigning a travelling path, the DTM model was able to return finite ASD values at discretized stations (Castro et al., 2011, 2014). Subsequent research advanced this approach by using digital surface models (DSMs), which retain roadside features such as vegetation, barriers, and cut slopes. DSMs provide a more realistic representation of roadway environments and typically yield shorter ASD values because they capture additional obstructions (Castro et al., 2016). This approach was later used to evaluate horizontal curve design safety by assessing whether the provided ASD was 22 sufficient on a highway (de Santos-Berbel et al., 2017). Notably, most applications of these approaches have relied on airborne LiDAR data. Similar estimation capabilities can also be achieved using mobile LiDAR, which collects dense point-cloud data from a moving vehicle to generate detailed 3D models of the road environment. This allows sight distance to be evaluated continuously along a vehicle’s trajectory. Gargoum et al. (2018a) developed an algorithm that extracts both ASD and PSD from a DTM created with mobile LiDAR data and compared these values with required sight distances to identify highway locations with potential safety risks due to insufficient visibility. Subsequently, Shalkamy et al. (2020) developed a voxel-based methodology that enabled 3D sight distance assessment by discretizing space into 3D grids. In this approach, a sightline is considered obstructed when it intersects with an occupied voxel representing a potential obstacle. A later study by Gargoum and Karsten (2021) automated an algorithm to detect sight distance obstructions and classify them according to morphological attributes, such as object linearity, verticality and sphericity, using principal component analysis. Gouda et al. (2021) further leveraged LiDAR-based sight distance assessment to evaluate infrastructure preparedness for automation by comparing 3D ASD estimates with SSD values derived under different vehicle operating assumptions through sensitivity analyses. 23 Figure 2.1: Illustration of Voxel-Based Sightline Obstruction Search 2.3 Reliability-Based Risk Assessment in Highway Design 2.3.1 Limitations with Existing Design Assumptions In current design standards, criteria such as SSD are computed using fixed input parameters derived from conservative assumptions. SSD is intended to ensure a safe stopping maneuver by incorporating operating speed, PRT, and braking rate of various driving populations. For instance, design guidelines in North American context recommend using design speed rather than posted speed, as it is generally higher and accounts for drivers who may exceed the posted limit (TAC, 2017; AASHTO, 2018). The PRT is commonly set as 2.5 seconds, a value supported by field studies to represent a conservative estimate across various driver age groups (Lerner, 1995). Similarly, the deceleration rate of 3.4 m/s2 is set based on empirical findings indicating that 90 percent of drivers are capable of braking at or above this rate (Fambro et al., 1997). Although these standardized values simplify the design process and embed safety buffers, they also reflect deeper limitations identified in the literature. Scholars have criticized such assumptions for equating compliance with published standards to guaranteed safety, a view reinforced in both 24 practice and legal contexts despite the lack of direct connection to crash outcomes (Navin, 1992; Hauer, 1999). More importantly, reliance on single conservative parameter values fails to represent the variability of real-world driving behavior and overlooks the inherently probabilistic nature of operating conditions (Fitzpatrick, Carlson, et al., 2000; Richl & Sayed, 2005). 2.3.2 Reliability Theory and Applications to Geometric Design Elements This limitation can be addressed using reliability theory, a method widely applied in structural engineering to quantify the margin of safety. First introduced in the context of highway design by Navin (1992), this approach treats the input parameters in the SSD equation as random variables, replacing fixed conservative values with probabilistic distributions. The resulting probabilistic SSD values are then compared with ASD values using a limit state function, which estimates the likelihood that SSD falls short of ASD. This likelihood, referred to as the non-compliance probability (Pnc), represents the probability that a given sight distance design fails to meet the operational demands of road users. A range of reliability analysis techniques and sampling methods can be employed to calculate Pnc. Buil ing on Navin’s fun amental work Easa (2000) replaced fixed operational parameters with assumed mean values, defined as specific percentiles relative to the extreme values recommended by design standards. A coefficient of variation was then applied to represent stochastic variability, enabling the evaluation of Pnc for intersection sight distance. Similarly, Echaveguren et al. (2005) extended the application of reliability theory to horizontal curve design, using upper and lower limits for skid resistance together with vehicle operating data in the design equation. In a subsequent study, Richl and Sayed (2006) advanced the approach by assessing the safety risks of narrow medians that obstruct sightlines on horizontal curves. In this study, variability in PRT and 25 braking rate was captured using empirical distributions, while operating speed was modeled with prediction equations developed in their earlier work (Richl & Sayed, 2005), which synthesized empirical speed models from various studies. Sarhan and Hassan (2008) broadened the scope by evaluating Pnc for horizontal curves overlapping with different vertical alignments. In addition to operating parameters, their analysis incorporated variability in driver eye height and object height based on prior empirical studies (Fambro et al., 1998; Fitzpatrick et al., 1998). To better integrate research findings into design practice, Ismail and Sayed (2009) proposed a risk-based code calibration framework that links each design output to a theoretical Pnc and evaluates whether that probability is acceptable from a safety perspective. A calibration factor is then applied to minimize the scatter of reliability indices around a target safety level. In their subsequent case studies, the framework was used to quantify the risk of insufficient horizontal offset distance on curves (Ismail & Sayed, 2010). By overlaying Pnc contours corresponding to different combinations of curve radius and horizontal clearance onto the design speed graph, the authors provided a clear visualization of how speed design choices map to risk levels. Hussein et al. (2016) extended this approach by applying reliability analysis to calibrate geometric design charts for the middle ordinate M, defined as the lateral distance between the edge of median barriers and the centerline of the adjacent traffic lane. Their calibration considered both design and operating speeds under different target Pnc. 2.3.3 Linking Risk Index to Measurable Safety Outcomes To bridge the gap between these probabilistic risk assessments and measurable safety outcomes, Ibrahim and Sayed (2011) integrated Pnc into safety performance functions (SPFs). Utilizing negative binomial regression modelling, their research revealed a statistically significant positive 26 association between Pnc and crash frequency, suggesting the potential of Pnc as a surrogate measure of safety. This relationship was supported by a later study employing Tobit model (Alsaleh et al., 2023). At the network level, other studies have also reported a positive correlation between noncompliance rates and crash rates, with higher risk levels observed among aging drivers (S. A. Gargoum, Tawfeek, El-Basyouny, et al., 2018; S. A. Gargoum & El-Basyouny, 2020). Other research has explored the use of Pnc in practical applications, such as optimizing highway cross-sections on horizontal curves using Collision Modification Factors (CMF) derived from Pnc (Ibrahim et al., 2012), or improving design consistency by addressing multiple failure modes beyond limited sight distance (Essa et al., 2016; Alsaleh et al., 2023). Additionally, Lanzaro et al. (2021) examined how correlations among input parameters influence the outcomes of reliability-based safety assessments. A more recent study by Sarran and Hassan (2025) leveraged the reliability theory to evaluate how automation influences the safety of intersection sight distance at uncontrolled intersections in a mixed traffic environment of HDVs and AVs. In this study, they proposed an SSD model for AVs that incorporated distribution-based operating parameters, such as rule-compliant speeds, shorter system-based PRTs, and braking rates constrained by passenger comfort, while also assuming lower variability in AV behavior compared with human drivers. The resulting Pnc was then translated into a safety index termed the probability of an unresolved conflict (PUC), which represents the likelihood of a conflict given traffic arrival volumes at an intersection. This formulation directly linked the reliability-based measure to a safety outcome. Their findings showed that PUC varied across different traffic volumes and speed combinations of HDVs and AVs, with safety risks tending to rise as AV penetration increased under higher-speed conditions. 27 2.4 Broader Applications of LiDAR in Transportation Engineering Light Detection and Ranging (LiDAR) is an optical remote sensing technology that employs laser scanners, supported by sensors, GNSS receivers, and IMU, to generate dense 3D point clouds of the surrounding environment (S. A. Gargoum & El Basyouny, 2019). Its ability to capture millions of measurements per second enables the creation of highly accurate roadway models while operating at highway speeds, minimizing traffic disruption and reducing survey time (Kemeny & Turner, 2008). Compared with traditional surveying and photogrammetry, LiDAR provides greater efficiency and accuracy (Williams et al., 2013), and its datasets can be leveraged for diverse applications in transportation engineering, including detecting highway features, conducting safety assessments, and training autonomous vehicles as a core sensing technology onboard many AV systems. 2.4.1 Extraction of Highway Geometric Elements Roadway cross-sectional elements, such as cross slopes and side slopes, are critical to the safe operation of highways. LiDAR technologies allow these features to be extracted at a network scale, addressing the limitations of traditional digital level surveys that are both time-consuming and labor-intensive. Several researchers have developed algorithms that rely on lane marking locations in mobile LiDAR data to estimate roadway slopes. For example, Tsai et al. (2013) focused on cross slope estimation within a region of interest bounded by lane markings, while Holgado-Barco et al. (2017) expanded this approach to extract additional cross-sectional features, including lane widths, number of lanes, and slope differences. More recently, Gargoum et al. (2018) noted that extracting lane markings itself could take even longer than extracting the slopes, making the process 28 inefficient. To address this, they proposed a statistical method that directly identified slope endpoints, which also allowed for the estimation of shoulder slopes. Another important application of LiDAR in transportation is the extraction of roadway profiles. Early efforts using aerial LiDAR estimated vertical grades by linearizing between two points, but this approach could not adequately capture vertical curvature (Souleyrette et al., 2003; K. Zhang & Frey, 2006). To reduce estimation errors, the roadway had to be divided into many short segments, which limited both accuracy and efficiency. Mobile LiDAR addresses these limitations by capturing continuous profiles along the vehicle’s travel path. Gargoum et al. (2018) developed a method that uses centerline point clouds and a best-fit profile feature in Civil 3D to generate vertical profiles. This approach produced grade estimates within 0.2% of those obtained from GPS surveys, demonstrating higher accuracy and a more reliable representation of roadway geometry compared to aerial LiDAR methods. The continuous nature of mobile LiDAR data also facilitates the detection and extraction of horizontal curves. Holgado-Barco et al. (2015) developed a semi-automatic method to extract horizontal alignment from LiDAR by segmenting lane-marking points into straight, circular, and clothoid sections based on curvature changes. Their approach was able to estimate radii and transition lengths with errors generally below 2% on real highway data and even smaller on simulated data. Gargoum et al. (2018b) advanced this work by defining trajectory vectors from discrete data and detecting curves based on changes in azimuth, which allowed identification of curve features such as point of intersection, point of curvature, point of tangency, curve radius, and chord length. Spiral transitions can also be identified by comparing distances from selected points along the curve to potential curve centers. When these distances converge at a new location 29 before the original center, it indicates the beginning of the circular portion of the curve, from which the circular radius can then be estimated. A similar approach has also been applied to surveying curved ramps at interchanges, where it demonstrated high accuracy and efficiency, outperforming the limitations of manual surveying (Luo & Li, 2018). 2.4.2 Design Safety Assessment using LiDAR Data Building on the reliable extraction of highway geometry from LiDAR data, researchers have increasingly used these datasets to assess roadway design and safety. In a comprehensive review of road inventory data collection methods for Highway Safety Manual implementation, Jalayer et al. (2015) highlighted that mobile LiDAR, when properly applied and efficiently processed, can serve as a valuable tool for safety analysis. This potential has been demonstrated in several contexts. For instance, Kilani et al. (2021) used LiDAR to evaluate visibility at urban intersections, quantifying vision blockage as a function of intersection control type, and found that intersections with restricted ASD exhibited an increased collision rates. In another study, Zhang et al. (2023) employed LiDAR to classify the geometric characteristics of rural roads in the Tibetan Plateau and combined these with other risk factors to identify high-risk segments, demonstrating how LiDAR can support risk assessment in remote or less accessible areas where conventional surveys are difficult. Assessing design risk can also be approached quantitatively through the application of reliability theory. Leveraging LiDAR’s capability to estimate 3D ASD as described in Section 2.2.2, Shalkamy and El-Basyouny (2020) developed a risk index to capture sight distance insufficiencies at horizontal curves in complex terrains. They further proposed a Full Bayes multivariate Poisson lognormal safety performance function to relate this index to expected collisions by severity level, 30 finding that higher risk values were most strongly associated with property-damage-only (PDO) crashes. In another study, Gargoum et al. (2022) advanced reliability-based risk assessment by applying it at a larger spatial scale. Through hot spot analysis and spatial interpolation, they identified high-risk regions within a provincial highway network, with clusters concentrated in mountainous terrain. Their findings demonstrated how such methods can help highway agencies prioritize safety improvements under resource constraints. 2.4.3 Simulation of AV Driving Environment Using LiDAR With the rise of automation, the use of LiDAR technology and the point clouds it produces is not limited to real-time perception, scene understanding, and object detection. Further applications include creating high-definition (HD) maps to support reliable localization and referencing (Y. Li et al., 2021). These datasets enable the development of deep learning frameworks for AV to perform tasks such as 3D semantic segmentation, object detection, and classification (Dewan et al., 2017; B. Li, 2017; Qi et al., 2017). To expand these capabilities, researchers have proposed simulation frameworks that generate synthetic LiDAR point clouds for AV training and testing. For example, Yue et al. (2018) developed a framework that collects data from both driving scenes and configurable scenarios, allowing point clouds to be used for training algorithms as well as systematically testing neural network vulnerabilities and improving robustness through retraining. Similarly, Fang et al. (2020) proposed a “scan-and-simulate” LiDAR simulator that automatically produce annotated point cloud for 3D obstacle perception in the AV driving scenario. This line of work has even been extended to evaluate the environmental complexity and associated workload for AV. Abohassan and El-Basyouny (2024) used LiDAR data to simulate driving environments and quantify the volume of information AVs must process to make effective decisions. 31 Collectively these stu ies highlight LiDAR’s role beyon tra itional surveying positioning it as a promising tool for addressing AV operational needs and supporting their safe deployment. 32 Chapter 3: Data Description 3.1 Description of the Study Area This study uses LiDAR data from a 30-km segment of Westside Road, a two-lane rural highway in mountainous British Columbia, to evaluate design safety under vehicle automation. The roadway is characterized by sharp horizontal curves, narrow cross-sections, and continuous steep rock cuts along its west side, creating frequent roadside obstructions and complex vertical terrain. These features heighten the risk of insufficient sight distance design, particularly at curve locations where safe visibility is most critical. Posted speed limits range from 50 km/h to 70 km/h on tangent sections, with advisory speeds reduced to 30-40 km/h on curves, further underscoring the safety challenges. Beyond representing a high-risk corridor for motorists, Westside Road offers a challenging highway design condition well-suited for the research scope. Its combination of geometric complexity, terrain-induced obstructions, and variable speed conditions provides an opportunity to test the effectiveness of LiDAR-based methods in capturing 3D sight distance. It also allows for pinpointing specific locations and underlying causes of sight distance deficiencies, thereby generating insights not only for improving traditional design practices but also for informing AV training in environments where visibility is constrained. 33 Figure 3.1: Google Street View of the Studied Roadway, Northbound (Top) and Southbound (Bottom) 3.2 LiDAR Data Collection and Pre-Processing LiDAR point cloud data for the case study corridor was collected by driving a vehicle equipped with a RIEGL VMY-1 mobile LiDAR scanner. The resulting dataset includes detailed geospatial information and classification attributes for both the roadway and surrounding features. Pre-processing steps were carried out to extract geometric elements from the point cloud data, specifically targeting horizontal and vertical alignment characteristics, based on the methodologies proposed by Gargoum et al. (2018b; 2018). 34 Figure 3.2: Illustrative Example of the LiDAR Point Cloud: 3D View and Top View with Object Classification To extract horizontal curves, reference points were first generated along the vehicle trajectory at 5-meter intervals. These points served as input for the least-squares circular fitting method proposed by Kasa (1976), chosen for its computational efficiency and robustness to noise. Since as-built data were unavailable to verify curve radii, the fitting results were validated using AutoCAD Civil 3D. This process yielded key information for each curve, including start and end locations and radius. In total, 308 horizontal curves were identified. The estimated radii were further categorized using the Jenks natural breaks algorithm into four groups: very sharp (60–260 m), sharp (260–460 m), medium (460–660 m), and mild (greater than 660 m). 35 Vertical alignment conditions overlapping these horizontal curves were also analyzed based on changes in longitudinal grade along the vehicle trajectory. Grades were estimated using elevation values associated with the same 5-meter reference points, extracted from the surrounding point cloud data to represent the vehicle path in both directions. A moving average was applied to these elevation values to smooth out local variation and capture general grade trends. Once the longitudinal grade at each reference point was computed, changes in grade were used to classify vertical alignment types. For example, a transition from positive to negative grade indicated a crest curve, while a negative-to-positive transition was classified as a sag curve. Other vertical alignment types included consistent upgrades, downgrades, and compound profiles featuring multiple deflections, such as a crest curve followed by a sag curve within the same horizontal curve limits. Figure 3.3 presents the distribution of horizontal and vertical alignment types for the studied highway segment. Figure 3.3: Count of Curves Categorized by (a) Horizontal Curve Radius; (b) Overlapping Vertical Alignment Type 15310626 23020406080100120140160180VerySharpSharp Medium MildCountCurve Radius Category4134101 10527020406080100120Crest Sag DownwardSlopeUpwardSlopeMultipleCountType of Overlapping Vertical Alignment36 Chapter 4: Methodology Figure 4.1 presents the overall framework for this research, beginning with data collection and processing described in Chapter 3, followed by three analysis phases: ASD estimation, reliability-based SSD estimation and risk assessment, and sensitivity analysis. This chapter elaborates on the methodology for phases 2 and 3 of the framework. Figure 4.1: Overall Research Framework Collection of ighway Data through obile LiDAR Scanning an Desktop ReviewEstimation of SSD using Probabilistic etho un er Reliability TheoryComparison an Selection of the Appropriate ASD for Next Step AnalysisReliability Base Risk Assessment of Sight Distance nsufficiency for All ehicle Automation Levels D Transition Stage A Fully Develope A Categori ation of ehicle Types by Automation LevelsEstimation of 2DASD through Analytical FormulasExtraction of Key eometric FeaturesCollection of Statistics for Key perational Parameters per ehicle TypeSpee Profile ( Perception Reaction Time (PRT DecelerationRate (a Cross Sectional Dimensions Estimation of 3D ASD Directly using LiDAR Data an through a oxel Base Approach Alignment FeaturesSensitivity Analysis of the nput ParametersRoa way Data Collection & Processing Phase 1: ASD EstimationPhase 2: Reliability Base SSD Estimation & Risk Assessment Phase 3: Sensitivity Analysis 37 4.1 Vehicle Categorization by Automation Level For the purpose of this research, vehicles were categorized into three representative groups reflecting increasing levels of automation. • Human-driven vehicles (HDVs), corresponding to SAE Level 0, are fully operated by human drivers with little to no technological support, aside from warnings or momentary assistance. • Transition-stage automated vehicles (AVs), encompassing SAE Levels 1 to 3, are equipped with varying degrees of advanced driver assistance systems (ADAS), such as adaptive cruise control, lane-keeping assistance, or traffic jam chauffeur; however, the human driver remains responsible for monitoring the environment, performing driving tasks, and making critical decisions. • Fully developed AVs, aligned with SAE Levels 4 and 5, represent the full realization of autonomous driving functions. At these levels, the automated system assumes control of both operational and decision-making, either within a defined operational design domain (ODD) or across all environments, enabling the vehicle to operate independently of human input. 4.2 Estimation of Available Sight Distance (ASD) This research adopts sight distance design as the primary criterion for evaluating highway geometric elements. To determine whether existing designs adequately meet the needs of road users, the process involves estimating ASD using both 2D analytical formulas and 3D methods derived from mobile LiDAR data. A subsequent reliability-based risk assessment compares the estimated ASD against required SSD across different vehicle categories: transition-stage AVs, and fully developed AVs, based on their respective operating parameters. 38 4.2.1 2D Estimation Approach The traditional approach for estimating ASD relies on 2D analytical formulas that take into account of various geometric dimensions and driver-related parameters. For simple horizontal curves sitting on flat grade, the sight distance, expressed as HASD, is computed as: HASD = R28.65∙ cos−1(1 −MR) (1) where R is the ra ius of the curve (m an represents the lateral clearance from the lane’s centerline to a roadside obstruction on a horizontal curve (m). R for each curve is obtained from the pre-processing stage of the LiDAR data, and M is computed based on location of the vehicle. As shown in Figure 4.2, for a paint-separated two-lane rural highway, vehicles on both the inside and outside carriageways share the same line of sight, with the sight distance expected to be blocked by a roadside obstruction. Therefore, for each curve, M is measured from the centerline of the travel lane of the respective carriageway to the roadside obstruction. The obstruction type that determines the measurement of M is identified through a desktop review. Figure 4.2: Line of Sight for Horizontal Curves in the Studied Roadway Roa si e bstructionLine of Sight( utsi e Carriageway Line of Sight( nsi e Carriageway uter Shoul erLane ( utsi e Carriageway e ianLane ( nsi e Carriageway uter Shoul erCenterline of Travel Lane 39 Similarly, the formulas for computing ASD for vertical crest or sag curves at tangent alignment, expressed as VASD, are rearranged as follows based on TAC (2017): VASDcrest = √K ∙ 200(√h1 + √h2)2 (2) VASDsag = √K ∙ 200(h3 + VASDsag ∙ tan α) (3) where K is the rate of vertical curvature (m per 1% change in grade) which is computed from LiDAR-derived attributes, h1 represents height of the human river’s eye (1.08 m), h2 is the height of object critical for crest curves (0.6m), h3 is the height of headlights critical for sag curve (0.6 m) an α is the upwar angle of the hea light beam (1°) per TAC (2017). The VASD is assumed to be limited by the length of the vertical curve. Under the 2D approach, when combined alignments are encountered, the governing sight distance is the shorter of HASD and VASD, expressed as: 2D ASD = min{HASD, VASD} (4) For the studied segment, a desktop review showed that the most common sightline obstructions along horizontal curves were curbs, cut slopes, vegetation, and roadside features such as signs, utility poles, and residential buildings. In contrast, on vertical curves, the primary obstruction is the road surface itself, where the vertical geometry limits the driver's direct line of sight. 4.2.2 3D Estimation Approach A voxel-based approach is proposed to determine the critical 3D ASD and its corresponding obstruction type, integrating methodologies from Gargoum et al. (2018a) and Gargoum and 40 Karsten (2021). The process begins by generating observer points ( = i i+1 i+2 … an target points (J = j j+1 j+2 … at 1-meter offsets in the cross-sectional direction from previously established reference points, representing typical vehicle locations. Observer and target heights are set at 1.08 meters and 0.6 meters, respectively, in accordance with TAC (2017) and to ensure consistency with the values applied in the 2D method. Each observer point is mapped to its corresponding curve segment and assigned a curve ID. For each observer, sightlines are constructed by connecting it to all downstream target points in the travel direction. Meanwhile, the LiDAR point cloud is discretized into a 3D voxel grid with a voxel size of 15 centimeters, selected to match the approximate spacing between LiDAR scan lines. For each observer-target pair, visibility is assessed by checking whether any voxel intersects with the corresponding sightline. A voxel is considered obstructed if its is occupied with LiDAR points classified as valid (non-noise) object types (e.g., vegetation, road surface, etc.). The obstruction type is determined based on the classification of the first voxel that blocks the line of sight. If the sightline to target (j) is unobstructed, the algorithm proceeds sequentially downstream (j+1, j+2, … until a valid obstruction is detected. Once an obstructed sightline is identified for the observer (i), the ASD of that observer is recorded as the distance to the last unobstructed target point (j-1). This procedure is repeated for all observer points within each curve segment, producing an individual ASD value for each observer. The shortest ASD of all these is taken as the critical 3D ASD for the curve. Its associated obstruction type is defined by the classification of the obstructing voxel and is compared against predefined 2D obstruction categories (curb, cut slope, road surface, roadside feature, vegetation) as a consistency check. The described process is illustrated in Figure 4.3. 41 Figure 4.3: Flowchart for Determining Critical 3D ASD and Obstruction Type per Curve enerate Points for bserver (i an Target (j J Construct Sightlines by Connecting bserver (i to the Targets (j DownstreamAssess the ccupancy an Point Classification of the oxels s the Target bstructe by an ccupie oxel Containing Points Classifie as ali (Non Noise bjects o to the Next Target (j = j+1 NoLoa Classifie LiDAR Point Clou Data (3D oxeli e the Point Clou DataAssess Target (j isibility by Evaluating oxels ntersecting with the Sightline Target (j is bstructe : Recor the Point Classification as bstruction Type an the Distance between the bserver (i an the Previous Target (j 1 as the 3D ASDAre Sightlines enerate an Assesse for All bservers with the Curve o to the Next bserver (i = i+1 Assign the Shortest Sightline as the Curve s Critical 3D ASD an its bstruction Type as the overning bstructionNo es es42 4.3 Risk Assessment of Insufficient Sight Distance 4.3.1 Limit State Functions Reliability analysis aims to determine the probability that an engineering system will perform its intended function under defined operating condition. This evaluation is formally defined through the use of a limit state function, g(X). Establishing this function, or referred as formulating the R-S reliability problem by Der Kiureghian (2022), is the fundamental step. This function is expressed as: g(𝐗) = R − S (5) where X enotes the vector of reali ations of ran om variables R represents the system’s available supply an S represents the system’s eman or require capacity. A esign in consi ere unacceptable, or failed, when R is less than S, and otherwise acceptable (Moses, 1977). This study defines insufficient sight distance as the failure mode in the context of highway geometric design. The ASD represents the length of roadway visible to the driver (supply), while the SSD is the minimum length required for a vehicle to safely based on its operating characteristics (demand). A non-compliance is considered to occur when ASD falls below SSD. Canadian geometric design guidelines such as TAC (2017) provides the following equation to calculate SSD: SSD = 0.278 ∙ V ∙ PRT +V2254 ∙ (a9.81 + G) (6) 43 where V is the design speed (km/h), PRT is the perception-reaction time (seconds), a is the deceleration rate (m/s2), and G is the grade of roadway (m/m). These input parameters vary by vehicle types due to differences in perception and response characteristics. To evaluate design adequacy, limit state functions are defined for each ASD estimation method, as follows: g(𝐗)2D = min(HASD, VASD) − SSD (7) g(𝐗)3D = 3D ASD − SSD (8) 4.3.2 Input Parameters Three driver-related operational parameters, including V, PRT, and a, are treated as random variables and characterized by probability distributions in the limit state function. Since these parameters vary depending on automation level, this study defines V, PRT and a separately for HDV, transition-stage AV, and fully developed AV. 4.3.2.1 Speed (V) Previous studies have highlighted the importance of using operational speed rather than design speed as input variables for highway geometric design (Fambro et al., 2000). Numerous empirical studies have developed operating speed models specifically for horizontal curves, predicting speed based on various influencing factors, including road geometry, pavement condition, facility type or other roadway features (Lamm et al., 1999; Fitzpatrick, Elefteriadou, et al., 2000). However, caution should be exercised when applying these models, especially under conditions such as different posted speed limits that fall outside the range for which they were originally calibrated (TRB, 2011; Himes et al., 2013). 44 • HDV: Richl and Sayed (2005) evaluated the impact of curve speed prediction models on highway design consistency by aggregating multiple models based on a desired speed of 100 km/h. While the resulting speed statistics have been used in several highway design risk assessments (Ismail & Sayed, 2009; S. E. Ibrahim et al., 2012; Alsaleh et al., 2023), their direct applicability to the present study is limited due to differences in design speed. Specifically, the road examined in this study has a lower design speed of 70 km/h, with even lower posted speeds on tangents and advisory speeds on curves. To ensure compatibility, this study adopted a similar approach but compiled operating speed models calibrated for lower-speed roadways, as summarized in Table 4.1. These models were used to estimate the mean and standard deviation of HDV speeds for each horizontal curve radius, assuming a normal distribution. • Transition-Stage AVs: As automation advances, ADAS technologies such as Curve Warning Systems (CWS) and Adaptive Cruise Control (ACC), increasingly influence vehicle speed behavior on horizontal curves. CWS algorithms have been shown to improve driver speed compliance and reduce curve-entry speeds (McElheny et al., 2006; Glaser et al., 2007; Ahmadi & Machiani, 2019; S. Wang et al., 2020, 2023). Similarly, ACC technologies can adjust curve-entry speeds based on road geometry, vehicle dynamics, and driver inputs (Matsumoto et al., 2005; D. Zhang et al., 2013). Several studies have also evaluated the curve speeds that vehicles equipped with these technologies can maintain without triggering system disengagement (Dixit et al., 2016; García et al., 2020; Chang et al., 2024). Despite these developments, empirical speed models that directly relate curve geometry to operating speeds for ADAS-equipped vehicles remain lacking. As a results, this study applies the same operating speed models developed for HDVs to transition-stage AVs, recognizing 45 that human drivers continue to influence speed selection under partial automation. A normal distribution is used to model transition-stage AV speeds, as tests showed minimal sensitivity to the choice between normal and lognormal distributions. • Fully Developed AVs: In fully autonomous vehicles, operating speeds on curves are controlled entirely by onboard systems that rely on pre-programmed algorithms to ensure safe maneuvering. These speed-control algorithms are typically developed based on several key factors, including road geometry (Glaser et al., 2007; Lee & Deng, 2008; Narmack, 2022), lateral acceleration thresholds (Reymond et al., 2001; Levinson et al., 2011), driver behavior characteristics (Lee, 2008; Z. Chen et al., 2022), and safety considerations related to sideslip or rollover risks (Sun et al., 2016; Chu et al., 2017). To validate these algorithms against observed human driving behavior, Bosetti et al. (2015) analyzed vehicle speeds curves with radii ranging from 15 to 800 meters under a posted speed limit of 90 km/h. Their study produced calibrated coefficients for several speed prediction models, generating a speed envelope that reflects typical human speed choice on curves. Among these models, the Modified Levison model demonstrated strong alignment with empirical data and is selected in this study to represent AV operating speeds. In addition, emerging literature suggests that AVs often adopt conservative driving strategies, closely adhering to posted or advisory speed limits (Shebeeb, 2016; Sukennik, 2017; S. Wang et al., 2020). Based on this insight, Sarran and Hassan (2025) modeled AV speed using the posted speed as the mean and applied a coefficient of variation (COV) of 2% to capture the consistency of autonomous speed control. In alignment with these findings, this study defines the mean curve speed for fully developed AVs as: 46 V = min(VModel, VL) (9) where V is the mean curve speeds of AVs (km/h), VModel is the speed predicted by the Modified Levison Model (km/h) calibrated by Bosetti et al. (2015), and VL denotes the posted speed limit (km/h). A COV of 2% is used to calculate the standard deviation of AV speeds, reflecting the high degree of control and consistency provided by fully autonomous driving systems. A normal distribution is assumed for speed of fully developed AVs. Table 4.1: Operating Speed Models Used for HDVs and Transition-Stage AVs Model Speed Range (km/h) Model Equation (km/h) R2 Lamm et al. (1999) 40-80 V85 = 94.398 - 3188.656/R 0.79 Morrall and Talarico (1994) 60-120 V85 = exp (4.561 - 0.00586D) 0.631 Krammes et al. (1995) – Linear 40-100 V85 = 103.66 - 1.95D 0.8 Krammes et al. (1995) – Exponential 40-100 V85 = exp (4.66 - 0.02D) 0.81 Krammes et al. (1995) – Inverse 40-100 V85 = (0.0092 + 0.0003D)-1 0.8 Fitzpatrick et al. (1995) 64-90 V85 = 54.18 + 1.061R0.5 NA Fitzpatrick et al. (2000) 48-72 V85 = 28 + 0.02R + 0.55VL 0.67 Banihashemi et al. (2011) 40-65 V85 = min ((71.21-4796.588/R), VL+10) 0.37 Dhahir and Hassan (2019) – MC, Rolling Terrain 64-97 V85 = 80.352 - 3289.296/R + 0.261VL 0.829 Dhahir and Hassan (2019) – MC, Mountainous Terrain 64-97 V85 = 80.352 - 3289.296/R + 0.261VL + 5.969 0.829 Note: D, degree of curve (m) = 5729.58/R (Lamm et al., 1999); VL, posted speed limit (km/h) = 60 for this study; V85, operating speed (km/h); R, horizontal curve radius (m). All model parameters were converted to metric units. 47 4.3.2.2 Perception-Reaction Time (PRT) The traditional definition of PRT refers to the time a driver needs to detect a roadway obstacle and initiate an appropriate response, such as braking. In North American standards, it is typically set at 2.5 seconds to reflect the ability of most drivers to perform braking under unexpected conditions (TAC, 2017). However, this conservative value does not fully capture the variability in driver behavior. Empirical studies have shown that PRT tends to be positively skewed, consistent with a lognormal distribution type (Fambro et al., 1997). • HDV: In an experimental study by Lerner (1995), participants were asked to operate their own cars on normal roadways during daytime, and any braking response to unexpected situations were recorded. The study reported a mean PRT of 1.5 seconds and standard deviation of 0.4 seconds, following a lognormal distribution. These findings have been widely cited in the reliability-based studies discussed earlier, and are used in this study to represent the PRT of HDVs. • Transition-Stage AVs: As reliance on automate riving systems increases rivers’ situational awareness and readiness to respond may decline, leading to longer reaction times when human control must be regained (Shebeeb, 2016; Körber et al., 2018). This reaction time is commonly referred to as takeover time. Studies involving Level 2 vehicles have reported mean takeover times ranging from 0.8 to 2.5 seconds, based on both field data (Young & Stanton, 2007; Kusano & Gabler, 2012; Y.-L. Chen et al., 2013; Blanco et al., 2015; Wu et al., 2021) and driving simulator experiments (Blommer et al., 2017; Lubbe, 2017; G. Li et al., 2023). For Level 3 vehicles, Testaferrata de Noto (2020) observed even longer takeover times, ranging from 2.2 to 3.2 seconds, especially when drivers were engaged in secondary tasks. 48 These findings highlight growing concerns that distraction and fatigue may further delay driver responses to takeover requests in increasingly automated systems (Dunn et al., 2021; Guo et al., 2021). In this study, takeover time is treated as the PRT for transition-stage AVs. Aggregating values from the studies above, a mean of 1.8 seconds and a standard deviation of 0.9 seconds are obtained. A lognormal distribution is assumed to remain consistent with the PRT distribution type used for HDVs. • Fully Developed AVs: For higher-level vehicles with autonomous driving capabilities, some researchers have assume PRT as short as 0.5 secon s to represent the system’s response to hazards, reflecting advancements in sensing, computing, and actuation technologies (Khoury et al., 2019; Othman, 2021; Ye et al., 2021). At this level of automation, where human intervention is no longer require PRT refers exclusively to the system’s response time. Several studies have examined system PRT from various perspectives, including assessments of vehicle-control technologies (Aki et al., 2014; Makridis et al., 2018; X. Xu et al., 2021; Riahi Samani & Mishra, 2024), braking mechanisms (Hu et al., 2023), optimization models (X. Wang et al., 2023; Bosia et al., 2024), and sensor performance (Fu et al., 2020b; Rydzewski & Czarnul, 2021; Hula et al., 2023). Reported system PRT values range from 0.2 to 1.1 seconds, demonstrating significantly faster response times than those associated with lower levels of automation, where human drivers remain part of the control (Talebpour & Mahmassani, 2016). Based on the reviewed literature, this study adopts a mean PRT of 0.7 seconds and a standard deviation of 0.5 seconds for fully developed AVs, assuming a lognormal distribution for consistency with other vehicle types. 49 4.3.2.3 Deceleration Rate (a) To calibrate the SSD model, Fambro et al. (2000) conducted a field study on driver braking performance and found that 90% of test drivers decelerated at rates exceeding 3.4 m/s² in response to unexpected obstacles on wet pavement. This value has since been adopted in North American design standards as a threshold for comfortable braking (AASHTO, 2018). An earlier study by Fambro et al. (1997) also reported mean and maximum deceleration values under various testing scenarios, emphasizing the variability in braking performance based on driver behavior, vehicle type, and roadway conditions. • HDV: To better represent the variability in deceleration rates, this study adopts braking parameters reported by Fambro et al. (1997), which have been widely used in related reliability-based research. In their study, participants drove their own vehicles along curves and braked on wet pavement, resulting in a mean deceleration of 4.2 m/s² and a standard deviation of 0.6 m/s². A normal distribution was assumed in several follow-up studies (Ismail & Sayed, 2010; Lanzaro et al., 2021). For consistency, these values and assumptions were adopted in this study to represent the braking performance of HDVs. • Transition-Stage AVs: With advancements in vehicle technologies, brake assist systems such as Automatic Emergency Braking (AEB) have been introduced, prompting research into their effect on overall braking behavior (Flannagan et al., 2018). Kidd et al. (2023) analyzed AEB performance in recent vehicle models and reported mean deceleration rates ranging from 2.5 to 7.2 m/s² epen ing on system type an test spee . n efforts to improve existing AEB systems, Yang et al. (2020) simulated braking scenarios for five AEB models and found mean eceleration rates between 2.0 an 2.5 m/s² un er normal con itions. To represent braking 50 performance for transition-stage AVs equipped with AEB under normal conditions, this study aggregates findings from the above studies. A mean deceleration of 4.8 m/s² and a standard deviation of 1.6 m/s² are used, following a normal distribution. • Fully Developed AVs: As vehicles advance toward full automation, recent research has increasingly focused on modeling deceleration rates that reflect passenger comfort (Deligianni et al., 2017; de Winkel et al., 2023). An early study by Wilson and Moyer (1941) found that rivers generally preferre a eceleration rate aroun 2.6 m/s² with higher values observe during emergency situations. Similarly, Moon and Yi (2008) i entifie 2 m/s² as a comfort threshold for developing ACC systems. Building on these insights, more recent studies have adopted comfort-based deceleration values in automated vehicle models. For instance, Rahman and Abdel-Aty (2018) applie a esire eceleration rate of 2 m/s² for mo elling connecte vehicles in platooning scenarios, while Sarran and Hassan (2025) assumed a mean deceleration rate of 2.1 m/s² to mo el A braking behavior. Base on prior work this stu y assumes that fully developed AVs follow comfort-based deceleration under normal distribution. A mean rate of 2.3 m/s² is obtained based on previous studies, with a standard deviation of 0.04 m/s² (derived from a COV of 2%) to reflect low variability in autonomous braking. To assess the impact of this assumption, a sensitivity analysis will be conducted to evaluate the implications of varying deceleration rates on the model outcomes. 51 Table 4.2: Summary of Derived Statistics for Input Parameters across Three Vehicle Types Parameter Distribution HDV Transition-Stage AVs Fully Developed AVs Mean Standard Deviation Mean Standard Deviation Mean Standard Deviation PRT Lognormal 1.5s 0.4s 1.8s 0.9s 0.7s 0.5s Deceleration Normal 4.2m/s² 0.6m/s² 4.8m/s² 1.6m/s² 2.3m/s² 0.04m/s² Speed Normal Obtained from Table 4.1per Curve Radius Obtained from Table 4.1 per Curve Radius Equation (9) Applying COV of 2% 4.3.3 Reliability Analysis In the context of highway design, the probability of non-compliance (Pnc) is used to quantify the uncertainty associated with design outputs (Navin, 1992). Pnc is related to the limit state function g(X) as the equation below: Pnc = P(g(𝐗 < 0)) = ∫ … ∫ f(𝐗)dXg(𝐗)<0 (10) where Pnc is the integration of f(X) over the domain in which g(X ≤ 0 an f(X) represents the joint probability distribution of random variables. The integral in Equation (10) can be evaluated using a range of computational methods, including First-Order Second-Moment (FOSM), First-Order Reliability Method (FORM), Second-Order Reliability Method (SORM), and sampling-based techniques such as Monte Carlo Simulation (MCS) and Importance Sampling (IS). The FOSM method uses a first-order Taylor series expansion of the limit state function around the mean values of the input variables. While 52 computationally efficient, it may yield inaccurate results for highly nonlinear functions. Both FORM and SORM transform the input variables into standard normal space, allowing for more robust handling of nonlinear function and non-normal random variables. FORM applies a linear approximation of the limit state surface at the design point (also known as the most probable point of failure), while SORM incorporates second-order curvature at the same point to improve accuracy. MCS estimates the failure probability by generating a large number of random samples from the original distributions and can be computationally extensive. IS improves efficiency by sampling from a modified distribution that concentrates on the failure region. Among these methods, FORM is selected for this study due to its balance between computational efficiency and accuracy in approximating the failure probability. Under this approach, the random variables X in the original function are transformed into standard normal space Y such that: f(𝐗) = Φ(𝐘) (11) where Φ ( enotes the cumulative ensity function (CDF of a stan ar normal variable an Y represents the transformed standard normal variables. The design point Y*, which corresponds to the point on the limit state surface with the highest probability of non-compliance, is obtained by solving the following constrained optimization problem: Y∗ = argmin{‖𝐘‖ | G(𝐘) = 0} (12) where G(Y) is the limit state function expressed in standard normal space. Using a first-order Taylor series approximation, the limit state function at Y* is expressed as a function of reliability in ex β that represents the algebraic istance from the original to the design point (Der Kiureghian, 2022). Finally, the Pnc can be computed as: 53 Pnc = Φ(−β) (13) The FORM analysis in this study is conducted using the Python module PySTRA (Caprani et al., 2025), which efficiently computes Pnc based on the procedure outlined above. 54 Chapter 5: Comparison of 2D and 3D ASD Estimation Results The first step of the analysis compares ASD estimates from the 2D analytical method and the 3D LiDAR-based method to identify the sources of discrepancy and determine which approach is more suitable for the subsequent risk assessment. Figure 5.1 presents a scatter plot of ASD values from both methods, with their difference expressed as ΔASD and calculated as: ΔASD = 2D ASD − 3D ASD (14) Approximately 70% of points fall below the 45-degree reference line, indicating that the 2D method tends to produce higher ASD estimates than the 3D method for the same curves. This trend is supporte by statistical tests: the mean ifference for ΔASD is 12.1 meters (paired t-test, p < 0.01), and the median difference is 19.1 meters (Wilcoxon signed-rank test, p < 0.001). These findings suggest that the 2D analytical approach, which relies on simplified geometric assumptions, often overestimates visibility relative to the more detailed LiDAR-based 3D method that accounts for vertical terrain and roadside obstructions. Nevertheless, a subset of outlier cases displays the opposite trend, with 3D ASD values substantially exceeding those of the 2D method, resulting in negative ΔASD values. Such cases are typically associated with curves transitioning into downgrade tangents or roadway alignments that open to expansive visibility, where vegetation, rock cuts, or other roadside barriers are minimal, as illustrated in Figure 5.2. 55 Figure 5.1: Comparison of ASD Estimated using 2D VS. 3D Methods with Typical Outlier Conditions Figure 5.2: Example Outlier Curves with 3D ASD Significantly Longer than 2D ASD 5.1 Comparison by Sight Obstruction Type Figure 5.3 compares obstruction types identified by the two ASD methods. The 2D method identified 33 roadside curbs as obstructions, while the 3D method found none. This discrepancy likely stems from the 2D metho ’s assumption that all obstructions lie within the curve. Un er this assumption, roadside curbs may be flagged as potential obstructions during desktop review, even Outlier Curve Example with 𝛥𝐴𝑆𝐷= -297.9m Outlier Curve Example with 𝛥𝐴𝑆𝐷= -221.2m 56 though they are unlikely to significantly impede sightlines in practice. In contrast, visibility limitations in real-world conditions are often caused by terrain beyond the curve, which the 3D method captures more effectively. For example, the 3D method identified 111 occurrences of road surface as the obstruction type, compared to just 22 by the 2D method. These cases typically occur in areas with overlapping vertical curves that restrict visibility, as illustrated in Figure 5.4, highlighting that simplified 2D methods often overlook the combined effect of vertical alignments on curve sight distance (Hassan & Easa, 1998). Moreover, only 39% of obstructions detected by the 3D method were located within the curve, and just 12% of those matched the obstruction types identified by the 2D method. This low level of agreement in obstruction type highlights fundamental differences between how the methods interpret visibility limitations. Figure 5.3: Comparison of the Count of Obstruction Types Identified by Two Methods 3313622 23940871112189Curb Cut Slope Road Surface Roadside Feature VegetationCountIdentified Obstruction Type2D Method3D Method57 Figure 5.4: Illustration of Visibility Obstruction Caused by Road Surface 5.2 Comparison by Alignment Conditions To assess how geometric alignment affects differences between 2D and 3D ASD estimates, comparisons were made across different horizontal curve radius groups and vertical alignment types. Figure 5.5(a presents a boxplot of ΔASD grouped by horizontal curve radii. A consistent tren of positive me ian ΔASD (i.e., 2D ASD > 3D ASD) is observed across all radius groups, indicating a general overestimation of sight distance by the 2D method, even after considering previously identified outliers. Notably, this overestimation increases as curve radii become larger. This suggests that the 2D method often overlooks visibility constraints on gentler curves, which frequently coincide with vertical alignment in roadway design (TAC, 2017). Specifically, among 21 mild curves, the 3D method identified road-surface obstructions related to vertical alignment in 13 cases, whereas the 2D method detected only two. This comparison highlights that the 2D method is less sensitive to vertical alignment effects, resulting in less accurate and often overly optimistic sight distance evaluations. 58 Table 5.1 further summari es these results an confirms that both mean an me ian ΔASD values are generally positive and statistically significant, except for sharp curves. While sharp curves show a negative mean ΔASD, this result is not statistically significant due to the large variability in ΔASD values and the influence of a few outliers, thus limiting its interpretability. Regarding vertical alignment types, Figure 5.5(b) similarly shows predominantly positive median ΔASD values. Table 5.2, summarizing statistics by vertical alignment categories, further confirms that mean and me ian ΔASD values are generally positive and statistically significant. The notable exception is curves associated with downward slopes, which exhibit statistically significant negative mean ΔASD. This exception arises due to the presence of outlier cases where the 3D method estimates substantially longer sight distances than the 2D method, attributable to extended visibility on downgrades toward open terrain. (a) (b) Figure 5.5 x ΔASD (a) by Radius Group; (b) by Overlapped Vertical Alignment Type 59 Table 5.1 C ΔASD by Radius Group Radius Group Radius Range (m) Count Mean Standard Deviation P-value (t-test) Median P-value (Wilcoxon) Very Sharp 60 to 260 155 7.32 39.5 <0.05 15.2 <0.001 Sharp 260 to 460 105 -2.45 90.0 0.781 19.1 <0.05 Medium 460 to 660 28 46.8 58.7 <0.001 59.5 <0.001 Mild > 660 20 77.7 60.8 <0.001 92.9 <0.001 Table 5.2 C ΔASD by Overlapped Vertical Alignment Type Type Count Mean Standard Deviation P-value (t-test) Median P-value (Wilcoxon) Crest 41 25.0 41.0 0.917 25.9 <0.001 Sag 34 8.92 85.2 0.994 27.1 <0.05 Downward Slope 101 -6.97 84.9 <0.05 5.65 0.592 Upward Slope 105 20.3 50.0 <0.05 19.1 <0.001 Multiple 27 36.7 38.0 <0.01 33.7 <0.001 5.3 Curve-Level Comparisons Another key difference between 2D and 3D methods lies in their analytical resolution. The 2D method produces a single ASD value for the entire curve, whereas the 3D method assesses sightline restrictions at multiple reference points along the entire alignment, yielding a detailed profile that captures localized variations. This difference is illustrated using two representative curves: Curve A in Figure 5.6 and Curve B in Figure 5.7. For Curve A, the 2D ASD exceeds the SSD, indicating 60 adequate sight distance under traditional criteria, with roadside features identified as the obstruction. However, 3D ASD reveals variations caused by local geometric and topographical influences. At the entrance of the curve, the 3D ASD falls below both 2D ASD and SSD because the alignment is near the apex of a crest curve transitioning into a sag, causing the descending roadway surface to obstruct forward visibility. Approximately 90 meters into the curve, visibility temporarily improves as the roadway descends further into open terrain, with roadside features and vegetation serving as temporary obstructions. Further along the curve, the 3D ASD again falls below the 2D estimate, approaching the SSD threshold due to cut slopes on the inside of the next curve beginning to obstruct the sightline. 61 Figure 5.6: Comparison between ASDs and SSD for an Example Curve A Example Curve B exhibits a different pattern. The 2D ASD remains consistently below the SSD throughout the entire curve, indicating inadequate sight distance based on traditional criteria, with curbs identified as the obstruction type. In contrast, the 3D ASD offers a different conclusion, revealing that insufficient sight distance only occurs in the middle section of the curve. Initially, sightlines are obstructed by vegetation on the inside of the curve. This is followed by further reduction in visibility where the horizontal alignment overlaps with a crest vertical curve, causing 62 the road surface to block forward sight. After the vehicle passes the crest apex, visibility improves as the alignment levels out, although cut slopes on the inside of the next curve continue to obstruct the view. In both Curve A and Curve B, the ASD values estimated by the 3D method tend to approach those of 2D method in the interior portions of the curves rather than its ends. This pattern aligns with findings by Ismail and Sayed (2007), who observed that differences between 2D and 3D estimates are typically more pronounced near curve entry and exit points. However, the direction of deviation differs between the two examples. In Curve A, the 3D method yields longer sight distances in the interior section due to improved visibility along a downgrade following the crest apex. In contrast, Curve B’s 3D ASD is shorter than the 2D estimate in the mi le region primarily ue to limite visibility imposed by a crest vertical curve. These examples demonstrate the granular analytical capability of the 3D method in capturing localized variations in visibility conditions. 63 Figure 5.7: Comparison between ASDs and SSD for an Example Curve B 5.4 Implications of ASD Evaluation Methods The comparison between 2D and 3D ASD methods reveals a consistent trend: the simplified 2D approach tends to overestimate sight distance, while the LiDAR-based 3D method produces more realistic assessments by accounting for the combined influence of horizontal and vertical alignments. In addition, the 2D method often flags features such as roadside curbs as obstructions, 64 even though they rarely restrict sightlines in practice. In contrast, the 3D method more effectively identifies visibility constraints caused by road surfaces, terrain changes, and other roadside features beyond the curve. This difference reflects a broader gap in granularity: the 2D method, grounded in geometric assumptions, provides a single ASD and obstruction type per curve, whereas the 3D method estimates ASD continuously at reference points along the alignment, capturing how real-world topography and roadway geometry interact to shape driver visibility. Under the trend of vehicle automation, these differences carry important implications. Because AV perception systems rely on precise sensing and detection, with LiDAR as a primary input for object recognition, 3D ASD offers a more realistic representation of the environment than simplified 2D methods. By localizing sight distance limitations, attributing them to specific geometric or environmental factors, and capturing obstructions as they would be perceived by sensors, the 3D method provides a more operationally relevant basis for risk-based roadway design evaluation. 65 Chapter 6: Reliability-Based Risk Assessment Results 6.1 Comparison of Risk Index between 2D and 3D Methods Building on observed difference between 2D and 3D ASD estimates, a reliability analysis was carried out to quantify their implications for sight distance design risk. Figure 6.1(a) illustrates the density distribution of Pnc values obtained from reliability analysis, using 2D and 3D ASD as supply inputs and HDV parameters as the demand. It shows that the 2D-based distribution is heavily concentrated at lower Pnc values, while the 3D-based distribution is broader, spanning a wider range of risk levels. Figure 6.1(b) presents the corresponding cumulative distribution functions (CDF), demonstrating that for any given cumulative probability, the 3D ASD is consistently associated with higher Pnc values than the 2D ASD. This observation aligns with findings by de Santos-Berbel et al. (2017), who reported higher Pnc values using a 3D ASD derived from a Digital Surface Model (DSM) compared to traditional 2D estimates under Spanish design standards. Figure 6.1(c) further compares Pnc values using a parity plot, where almost 70% of the points lie above the 45-degree line. This reveals not only limited agreement between the two methods but also a systematic tendency for the 3D method to identify higher risk levels. To further demonstrate these differences in a localized context, Figure 6.2 illustrates the variation in Pnc values along the previous example Curve A. The 2D-based results exhibit minimal variation, with a modest peak of 0.02 near the middle of the curve, where the vertical profile begins to descend. In the 2D method, when the curve radius and lateral clearance remain constant, road grade is the primary factor influencing ASD; as the downgrade increases, so does the required sight distance, leading to a slight increase in Pnc. In contrast, the 3D method produces a sharp peak of 0.97 around 90 meters into the curve, reflecting elevated risk due to critical sight conditions 66 caused by the combined influence of horizontal and vertical alignments rather than a single grade factor. This highlights that the 3D method captures a broader range of risk levels and more effectively identifies high-risk areas influenced by both vehicle location and surrounding features. For fully developed AVs, which rely on precise perception to respond safely to sudden hazards under limited visibility, such context-sensitive assessments are essential for safe operation. 67 (a) (b) (c) Figure 6.1: Comparison of Pnc Values Computed using 2D ASD and 3D ASD (a) Density Plot; (b) CDF Plot; (c) Parity Plot 68 Figure 6.2: Comparison of Pnc Values Computed Using 2D ASD and 3D ASD along Example Curve A 6.2 Comparison of Risk Index Across Vehicle Types Building on the demonstrated advantages of 3D ASD in capturing detailed visibility constraints and risk variation, it was used as the supply term in the limit state function to support a consistent and realistic comparison across different vehicle types under varying levels of automation. Corresponding demand terms were defined using vehicle-specific input parameters, as detailed in Section 4.3.2. The density plot in Figure 6.3(a) illustrates right-skewed Pnc distributions for both HDVs and transition-stage AVs, with most values concentrated at the lower-risk range. In contrast, the distribution for fully developed AVs shows two peaks, with a primary peak at the lower Pnc values 69 and a smaller secondary peak at the higher values. Further analysis of this secondary peak reveals that it corresponds to curves with relatively sharp radii (mean = 253.0 m) and very low 3D ASD (mean = 56.4 m). Figure 6.3(b) presents the CDFs of Pnc for three vehicle types. The CDF for fully developed AVs rises more steeply at both ends, reflecting a distinct risk pattern compared to the other two vehicle types. The relationship between HDVs and the two AV types was evaluated using parity plots that compare their respective Pnc values. Figure 6.4(a) presents the parity plot for transition-stage AVs versus HDVs. Most points lie near the 45-degree line, indicating overall similar risk levels between two vehicle types. However, at lower Pnc values (below 0.35), transition-stage AVs tend to predict slightly higher risk than HDVs. Beyond this point, they estimate lower risk than HDVs as shown by points falling below the 45-degree line. This suggests that partial automation may offer modest safety benefits in situations with more restricted visibility, likely due to the higher braking rates assumed for AVs under such conditions. Figure 6.4(b) plots Pnc values for fully developed AVs against HDVs. In low-risk conditions, a small cluster of points appears below the 45-degree line, indicating that fully developed AVs tend to predict slightly lower risk than HDVs in these scenarios. However, as Pnc increases, this pattern diverges, with points scattering widely above and below the line, revealing much greater variability in AV risk estimates under higher risk. Curves where AVs predict substantially higher risk tend to have shaper radii (mean = 126.6 m) and very low 3D ASD (mean = 59.9 m). In contrast, curves where AVs predict substantially lower risk tend to have constrained 3D ASD (mean = 83.4 m) but feature greater gentler radii (mean = 717.3m). These widespread patterns suggest that fully developed AVs are more sensitive to geometric complexity than HDVs, amplifying risk on tight 70 curves and reducing it more on gentler ones, even when visibility is limited. One possible explanation is that AVs strictly follow the posted speed limit, travelling more slowly than HDV on gentle curves and thereby reducing risk. On sharper curves, however, that same speed compliance combined with comfort-based deceleration can lead to higher risk compared with human drivers, who often brake more aggressively when sight is constrained. (a) (b) Figure 6.3: Distributions of Pnc Values for Three Vehicle Types (a) Density Plot; (b) CDF Plot 71 (a) (b) Figure 6.4: Parity Plot of Pnc Values between Vehicle Types (a) HDV and Transition-Stage AV; (b) HDV and Fully Developed AV To better understand the influence of each input parameter on the risk outcome, we examined parameter sensitivities and importance measures. In the FORM analysis, sensitivity values quantify how changes in each parameter influence the risk estimates (Der Kiureghian, 2022). Table 6.1 presents the average sensitivity for each parameter across the three vehicle types. Negative sensitivity values for speed and PRT indicate that increases in these parameters lead to higher Pnc values. Conversely, positive sensitivities for deceleration suggest that higher deceleration rates reduce risk. These findings align with the logic of the Equation (6) as well as the previous findings. While most sensitivity values range between -1 and 1, the deceleration rate for fully developed AVs shows an exceptionally high sensitivity of 2.65, suggesting its strong influence on the Pnc distribution. 72 Parameter importance is obtained by multiplying the sensitivity values (with respect to parameter means) by their corresponding standard deviations, resulting in a unitless and statistically comparable metric. The magnitudes of these importance vectors, expressed in absolute terms, reflect each parameter’s contribution to the variance in Pnc. According to Table 6.1, the most important parameters (on average) are speed for HDVs, deceleration for transition-stage AVs, and PRT for fully developed AVs. This variation across vehicle types likely stems from differences in the underlying variability of each parameter. Since the input statistics are derived from limited empirical data, further data collection may help refine these estimates and update the relative importance rankings. Table 6.1: Average Values of Sensitivity and Importance Measures of Input Parameters Across Three Vehicle Types Vehicle Type HDV Transition-Stage AV Fully Developed AV Input Parameter V PRT a V PRT a V PRT a Sensitivity -0.08 -0.88 0.65 -0.05 -0.59 0.37 -0.23 -0.92 2.65 Importance Vector 0.81 0.36 0.39 0.55 0.49 0.59 0.28 0.89 0.13 6.3 Identification of High-Risk Locations 6.3.1 Segment-Level Analysis In addition to capturing the overall trend, the use of 3D ASD in risk assessment identifies high-risk locations. Table 6.2 summarizes the geometric characteristics of a selected segment consisting of 25 consecutive northbound curves spanning a range of radius groups and vertical alignment types. 73 Table 6.2: Geometric Characteristics of 25 Consecutives Curves ID Carriageway Effective Radius (m) Radius Category Overlapping Vertical Alignment 3D ASD (m) Obstruction Type 1 Inside 223.9 Very Sharp Downward Slope 77.5 Vegetation 2 Outside 159.1 Very Sharp Sag 99.5 Cut Slope 3 Inside 140.1 Very Sharp Crest 52.8 Cut Slope 4 Outside 249.2 Very Sharp Sag 113.7 Road Surface 5 Inside 120.3 Very Sharp Crest 58.6 Road Surface 6 Outside 169.0 Very Sharp Downward Slope 78.3 Road Surface 7 Inside 208.6 Very Sharp Downward Slope 99.4 Cut Slope 8 Outside 334.3 Sharp Downward Slope 133.6 Cut Slope 9 Inside 335.1 Sharp Downward Slope 135.9 Road Surface 10 Outside 172.9 Sharp Sag 65.9 Vegetation 11 Inside 269.7 Sharp Multiple 64.0 Vegetation 12 Outside 158.2 Very Sharp Multiple 79.8 Vegetation 13 Inside 203.1 Very Sharp Upward Slope 77.4 Vegetation 14 Outside 400.7 Sharp Upward Slope 97.6 Roadside Feature 15 Inside 249.6 Sharp Upward Slope 81.8 Vegetation 16 Outside 96.1 Very Sharp Upward Slope 51.9 Cut Slope 17 Inside 168.8 Very Sharp Upward Slope 68.4 Roadside Feature 18 Outside 113.3 Very Sharp Upward Slope 74.3 Vegetation 19 Inside 137.9 Very Sharp Multiple 60.3 Vegetation 20 Outside 98.2 Very Sharp Upward Slope 61.4 Vegetation 21 Inside 532.6 Medium Upward Slope 68.0 Road Surface 22 Outside 152.8 Very Sharp Multiple 84.6 Vegetation 23 Inside 591.9 Medium Sag 66.4 Road Surface 74 ID Carriageway Effective Radius (m) Radius Category Overlapping Vertical Alignment 3D ASD (m) Obstruction Type 24 Outside 101.0 Very Sharp Upward Slope 57.2 Road Surface 25 Inside 883.1 Mild Upward Slope 49.4 Road Surface Average Radius (m): 250.8 Average 3D ASD (m): 78.3 Figure 6.5 presents the Pnc values computed for all curves across three vehicle types. While some curves have consistent risk levels, others show elevated Pnc depending on the level of automation. For example, Curves 1, 3, and 6, which have very sharp radii (77.5 m, 52.8 m, 58.6 m, respectively) and low 3D ASD values, show substantially higher Pnc values for fully developed AVs (1.00, 0.91, 0.79, respectively). These risk values are more than twice those observed for HDVs and transition-stage AVs, highlighting potential concerns for AV operational safety under challenging geometric and topographic conditions. Unlike human drivers, who reduce speed in response to higher perceived risk in shaper curves, AVs tend to adhere to posted speed limits without making such adjustments. In this study, for a curve radius of 50 meters, the HDV and transition-stage AV speed mo els pre ict an average spee of 34 km/h while the fully developed AV model predicts 50 km/h. This higher spee increases the require SSD contributing to elevate risk. As a result the current emphasis on speed compliance in AV algorithms may leave sharp curves as persistent safety concern, calling the need for targeted training or algorithm enhancements that account for geometric complexity. 75 Additionally, Curves 23 and 25, despite having relatively large radii (591.9 and 883.1 meters), exhibit consistently high Pnc values (above 0.85) across all vehicle types. These elevated risks are linke to their low 3D ASD values measure at 66.4 m an 49.4 m respectively which result from obstructions caused by the road surface itself. This finding suggests that gentler horizontal curves do not necessarily imply safer conditions, as they are often combined with complex vertical alignments under current design practice, which can introduce visibility issues. Such conditions may warrant closer design evaluation and targeted infrastructure improvements independent of the level of vehicle automation. Figure 6.5: Variation of Pnc Values Across Three Vehicle Types for 25 Consecutive Curves 6.3.2 Curve-Level Analysis A similar comparison was performed at the curve level. Figure 6.6 illustrates the variation in Pnc values along Curve A, computed every 5 meters for three vehicle types. A clear negative association is observed between 3D ASD and Pnc, with all vehicle types reaching peak Pnc values at the point of most restricted visibility (around 90-meter mark). For transition-stage AVs, Pnc values are lower than those of HDVs in low-visibility areas (30 to 110 meters) but surpass them 76 where visibility improves (beyond 110 meters). This pattern suggests that partial automation may help reduce risk in areas with poor sight distance. On the other hand, fully developed AVs generally exhibit lower Pnc values than the other vehicle types across most of the curve, except near the point of greatest visibility restriction. This localized increase in risk is likely due to the comfort-based braking rate assumed for fully developed AVs, which becomes insufficient for braking safely where ASD is at its minimum. The implication is clear: if braking strategies are adapted to respond to localized risk rather than relying solely on comfort thresholds, autonomous vehicles could transform challenging geometric conditions into opportunities for substantial safety gains, thereby maximizing their contribution to highway design safety. 77 Figure 6.6: Variation of Pnc Values along Length of Example Curve A 6.4 Implication of Automation on Highway Design Risk The findings show that automation can reduce overall risk, but the extent of this benefit depends strongly on roadway geometry. Transition-stage AVs generally mirror the risk patterns of HDVs, with modest safety gains in low-visibility situations, suggesting that incremental automation can offer some improvement within existing design standards. Fully developed AVs show the greatest potential for overall risk reduction, particularly on gentler curves where strict speed compliance 78 lowers exposure compared with human drivers. However, they also exhibit elevated risks on sharp curves and in areas with constrained visibility, where operating at posted speeds and reliance on comfort-based braking can limit their ability to respond effectively. These results carry two key implications. First, geometric design practices that depend on traditional 2D sight distance analysis may understate risks for AVs, especially in segments influenced by vertical alignment or surface obstructions. Incorporating 3D ASD into risk-based evaluation provides a more realistic representation of how AV perception systems interpret the roadway environment and helps identify locations where design interventions may be needed. Second, AV algorithms themselves must integrate contextual risk adjustments. This could involve adopting lower speed thresholds, such as advisory speeds, or training AVs to dynamically adjust their speed in response to geometric changes, mimicking how human drivers naturally slow down when they perceive higher risk on sharper curves. This is particularly important at locations where advisory speed information is missing. Alternatively, a risk-based approach could be implemented, where a target Pnc threshold is used to back-calculate the appropriate speed ensuring that safety is proactively maintained. In parallel, braking strategies may need to be adjusted depending on the scenario as relying solely on comfort-based deceleration rates may not be sufficient under highly constrained visibility. 79 Chapter 7: Sensitivity Analysis The distribution of Pnc values for each vehicle type depends on the assumptions made in estimating ASD and the input parameters used in the SSD Equation (6). Given the limited empirical data, sensitivity analysis on these assumptions is valuable for testing the robustness of previous results and assessing how changes in input distributions impact risk estimates. 7.1 Risk Sensitivity to Deceleration Rate The first sensitivity test examined the deceleration rate assumptions used for fully developed AVs. As previously noted, the original comfort-based value showed a high sensitivity measure of 2.65, indicating a strong influence on the Pnc distribution. To evaluate this further, two additional eceleration rates were teste : 3.4 m/s² representing the stan ar value use in current esign manuals an 4.0 m/s² reflecting emergency braking con itions as suggeste by i et al. (2002). The same COV value of 2% was applied to ensure consistency. Figure 7.1 presents the resulting CDF plot, showing a substantial increase in cumulative probability of low Pnc values when standard and emergency rates are applied. The 95th percentile of Pnc drops from 1.0 under comfort-based braking to 0.52 with standard braking and further down to 0.24 under emergency braking, reflecting considerable safety improvements. This pronounced sensitivity arises from the deceleration term appearing squared in the denominator of the limit-state function, amplifying its influences on the risk outcomes. 80 Figure 7.1: CDF Plot of Pnc Values for Fully Developed AVs Computed Using Three Deceleration Rates Figure 7.2(a) further highlights this relationship by comparing Pnc values for fully developed AVs under comfort-based versus emergency braking. All points are below the 45-degree reference line, confirming that higher deceleration consistently reduces sight-distance risk. Nevertheless, several curves still yield Pnc values above 0.5 even under emergency braking conditions, primarily corresponding to scenarios with very sharp radii (mean = 163.1 m) and severely constrained 3D ASD (mean = 40.5 m). These high-risk locations may require additional interventions, such as targeted speed reductions or geometric improvements. Additionally, Figure 7.2(b) compares fully developed AVs (under emergency-braking scenario) to HDVs. A general reduction in risk with automation is observed, with most points falling below the 45-degree line. Compared to earlier analysis with comfort-based braking in Figure 6.4(b), the number of high-risk curves is significantly reduced when AVs are modeled with emergency braking. 81 Collectively, these results emphasize the importance of carefully balancing passenger comfort with safety risk when determining appropriate deceleration rates for fully developed AVs. Adopting a dynamic braking approach that adjusts in real time based on quantified risk levels could enable AVs to switch between comfort-based and emergency profiles as needed to ensure safe operation across varying geometric conditions. (a) (b) Figure 7.2: Parity Plot of Pnc Values (a) Comfort and Emergency Braking for Fully Developed AVs; (b) HDV and Fully Developed AV using Emergency Braking Rate 7.2 Risk Sensitivity to Sensor Configuration The second sensitivity analysis evaluated the effect of observer height on risk estimates for fully developed AVs. The baseline human eye height of 1.08 m was compared to two LiDAR mounting heights: 0.6 m for headlight-mounted sensors and 1.8 m for roof-mounted sensors (K. Li et al., 2024). Figure 7.3 presents the resulting CDF plots of Pnc values. Sensors mounted at headlight 82 level (0.6 m) are associated with higher cumulative probabilities of elevated Pnc, while roof-mounted sensors (1.8 m) reduce the risk condition by shifting the cumulative distribution toward lower Pnc values, although a steep rise at the upper tail indicates some persistent high-risk cases. The median values for Pnc fall from 0.19 at 0.6 m, to 0.05 at 1.08 m, and further to 0.02 at 1.8 m. Despite this improvement, the 95th percentile Pnc values remain close to 1.0 across all sensor heights, indicating that severely restricted visibility continues to pose a high risk that cannot be mitigated by elevated sensor placement alone. For example, the average 3D ASD on certain curves remains as low as 62.6 m even with roof-mounted LiDAR sensor, highlighting the need for additional geometric or operational interventions to reduce risk arising from visibility constraints. Figure 7.3: Cumulative Distributions of Pnc for Fully Developed AVs Using Three Observer Heights 83 Chapter 8: Conclusion 8.1 Research Summary and Conclusions This research examined the readiness of existing highway infrastructure to accommodate increasing levels of vehicle automation, with a particular focus on insufficient sight distance at horizontal curves. Using a case study of 308 curves along a rural highway in British Columbia, a risk-based framework grounded in reliability theory was developed to quantify the probability of non-compliance (Pnc) between available sight distance (ASD) and stopping sight distance (SSD). The analysis was carried out in three phases. In the first phase, ASD was estimated using two methods: a traditional 2D analytical approach based on design formulas, and a 3D method that leverages mobile LiDAR data collected along the roadway to estimate sight conditions using a voxel-based approach. Comparisons reveal that the 2D method consistently overestimates ASD relative to the 3D method across most curve radius groups and combined alignment types, with the difference found to be statistically significant. This overestimation is especially pronounced on gentler curves, where vertical alignment changes are typically combined with horizontal curves under standard design practice. These results indicate that the simplified 2D method, while conservative, often produces inaccurate as it fails to capture real-world geometric and topographical complexities. In contrast, the 3D method provides a more detailed and realistic assessment of roadway visibility, allowing ASD to be evaluated at any point along the alignment rather than as a single value per curve, as demonstrated through two example curves. This higher analytical resolution allows for the identification of localized visibility constraints that the 2D method cannot capture. Moreover, the 3D approach more accurately identifies obstruction types. While the 2D method typically 84 attributes obstructions to roadside elements such as curbs or cut slopes, the 3D method more often identifies road surface as the obstruction type, which arise when vertical alignment governs the line of sight. This distinction highlights the 3D metho ’s ability to reflect the actual driving visibility conditions. Altogether, these findings support the use of 3D ASD as a more accurate and context-sensitive basis for sight distance evaluation in highway design. The second phase of the analysis assessed the safety risk associated with insufficient sight distance on existing highway designs, focusing on three levels of automation: HDV, transition-stage AV, and fully developed AV. Using reliability theory, limit state functions were formulated to compare the ASD against the required SSD for each curve. Input parameters for SSD were selected for each vehicle type based on literature to reflect their respective operational characteristics. The resulting risk metric, expressed as Pnc, quantifies the likelihood that the ASD is insufficient for safe stopping under SSD requirement. Risk estimates were first compared using 2D and 3D ASD to further examine the conclusion from phase one of the analysis. The 3D method produced consistently higher and more location-specific Pnc values levels, revealing context-sensitive risk profiles that the conservative 2D ASD failed to capture. Therefore, 3D ASD was selected as the basis for comparing risk across automation levels. Overall, Pnc tended to decrease with higher levels of automation, indicating a general improvement in safety performance from HDVs to fully developed AV. However, exceptions were observed where fully developed AVs demonstrated elevated risk levels. To investigate these special cases, a roadway segment with 25 consecutive curves was analyzed and compared. Several curves showed a sharp increase in Pnc for fully developed AVs relative to other vehicle types, particularly in locations with very sharp radii and severely limited ASD. These 85 elevated risks are likely due to AV speed behavior, as fully developed AVs tend to maintain posted speeds through sharp curves, in contrast to human drivers who are more likely to slow down in response to perceived risks. The reliance on comfort-based deceleration rates further compounds this issue, as lower braking rates increase the required SSD, thereby elevating the Pnc when ASD is limited. Additionally, some curves exhibited consistently high Pnc values across all vehicle types. These cases involved gentle curve radii but limited ASD, primarily due to visibility constraints from the effects of combined vertical alignment. This finding suggests that gentler horizontal curves do not inherently provide safer conditions. Locations with persistent risk driven by vertical alignment effects should be prioritized for more detailed design evaluation. Furthermore, a curve-level comparison among the three vehicle types revealed that transition-stage AVs demonstrated risk reduction, particularly under limited visibility conditions. In contrast, fully developed AVs, although effective in reducing risk across most of the curve length, were associated with elevated risk under the most critical sight-distance constraints. These findings highlight the need for AV manufacturers to tailor operational algorithms to extreme visibility conditions. For example, adjustments in speed when approaching limited-visibility zones or more proactive engagement of emergency braking profiles could help mitigate risk and improve safety performance. In the last phase, sensitivity analysis confirmed that the risk associated with fully developed AVs is highly sensitive to the assumed deceleration rate in the limit state function. Risk levels decreased significantly when higher deceleration rates were used in place of the comfort-based rate typically assumed for AV operation. This finding highlights the importance of carefully balancing passenger comfort with safety risk when defining AV operational parameters. One potential strategy is to establish a threshold Pnc value that triggers a shift from comfort-based to emergency braking, 86 ensuring the vehicle responds appropriately to changing risk levels. Additionally, the analysis showed that increasing the mounting height of LiDAR sensors is associated with reduced risk. However, elevated sensor placement alone may not be sufficient to ensure safe operation at locations where ASD remains limited. Overall, this research demonstrates that sight distance insufficiencies remain a critical safety challenge for both HDVs and AVs. Risk-based metrics such as Pnc can guide targeted strategies for risk reduction, including adapting AV driving algorithms through speed and braking rate adjustments based on risk conditions, as well as revisiting geometric design to identify opportunities for infrastructure improvements at locations that exhibit high risk regardless of automation level. By directly linking geometric design to a quantitative risk index and examining how risk varies with vehicle automation, this research provides a practical framework for enhancing AV readiness from both the vehicle manufacturer and the infrastructure perspectives. Implementing proactive strategies to reduce risk prior to the widespread deployment of higher-level AVs will also improve the resilience of transportation systems by mitigating potential safety risks that could otherwise degrade system performance. 8.2 Key Contributions This research makes an original contribution by being the first to evaluate highway design risk under vehicle automation through a 3D reliability-based framework. The approach is validated through a case study using sight distance as a representative design element and applying LiDAR-derived 3D data. This approach directly addresses the research gaps identified in the literature, as it provides a more realistic and context-sensitive assessment of roadway visibility than traditional 2D methods, while also reflecting the perception and sensing conditions of AVs. By aligning 87 infrastructure evaluation with AV sensing technologies, the study demonstrates the potential of LiDAR as a critical tool for future design assessment and policy guidance under automation. A second contribution lies in the methodological structure of the analysis. By differentiating between HDVs, transition-stage AVs, and fully developed AVs, and by collecting and deriving operational statistics representative of each, the study offers an evidence-based way of assessing how risk evolves with increasing automation. Integrating the data into reliability analysis grounds the assessment in realistic operating conditions rather than hypothetical sensitivity tests, thereby improving the relevance of the resulting risk estimates. This categorization clarifies the sources of risk at each automation level and guides the tailoring of design improvements to different conditions. Finally, the thesis advances quantitative readiness planning by employing Pnc as a practical index to inform design insufficiencies under vehicle automation. This index enables road agencies and vehicle manufacturers to identify when and where risks are likely to occur and to prioritize coping strategies accordingly. Readiness planning for automated vehicles requires assessing current conditions, identifying gaps, and preparing strategies, and Pnc acts as a foundational index to support this process. It can be applied to inform both vehicle-side measures, such as training AVs in high-risk environments or adapting AV operating algorithms based on a predefined risk threshold, and infrastructure-side measures, such as prioritizing or targeting design improvements at locations with persistent high risks. By enhancing the system’s responsive capacity an re ucing potential risks in advance of widespread AV deployment, this framework moves transportation systems closer to resilience. Importantly, this is also the first research to attempt linking such quantitative risk analysis directly with the broader resilience definition. 88 8.3 Limitations and Future Research Opportunities This study opens several promising avenues for future research. First, at the data processing stage, some steps relied on simplified or manual procedures. For example, elements such as lane width, shoulder width, and roadside obstructions in the 2D method were extracted through desktop review, and horizontal curve radii were estimated using simple curve assumptions. While these approaches were sufficient for the current analysis, their scalability could be improved by developing more comprehensive and automated algorithms for extracting such information from LiDAR data. Leveraging advances in point cloud processing and feature extraction would allow such datasets to provide a stronger foundation for future risk assessment work. Second, due to the lack of publicly available empirical data, particularly for the two AV types, assumptions were made regarding key input parameters for the reliability analysis. These assumptions influenced the computed Pnc values, pointing to the need for future field studies on speed profiles, PRT, and braking behavior across different AV automation levels and under different road geometric conditions. Expanding empirical datasets in these areas would help refine risk models and improve their applicability. Third, this study assumed a single representative vehicle type at each automation stage, thereby modeling a simplified scenario where roadways are dominated by homogeneous traffic. In reality, future roadways will likely feature mixed traffic environments as indicated by Sarran and Hassan (2025), where interactions between HDVs and AVs at varying levels of market penetration may influence highway safety risk in more complex ways. Extending the framework to account for mixed traffic environments and interactions among different vehicle types would provide a more robust understanding of how vehicle automation influences design-related risks 89 Finally, AV perception was represented solely through LiDAR-derived sight distance; however, real-world AV systems rely on sensor fusion that combines cameras, radar, and ultrasonic sensors for perception. This creates opportunities for future studies to evaluate how integrated sensor inputs, particularly under weather conditions that may impair LiDAR performance, affect AV visibility and associated safety outcomes on highways. Together, these opportunities highlight how future research can refine both the methodological robustness and the practical impact of this framework. As vehicular technologies continue to advance and automation becomes more prevalent, it is essential to evaluate whether existing highway infrastructure can safely accommodate higher levels of automation. This study contributes to that effort by employing sight distance as a representative design criterion and developing a framework that integrates LiDAR-based 3D sightline assessment with reliability-based risk analysis, informed by operational parameters across different automation levels. The framework demonstrates the benefits of a 3D approach for design evaluation and introduces a quantitative risk index that can guide both vehicle manufacturers and road agencies in developing targeted safety solutions. Looking ahead, it can be further strengthened by leveraging more accurate LiDAR feature extraction, incorporating empirical data from higher levels of automation, accounting for mixed traffic environments, and integrating sensor inputs beyond LiDAR. 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Thesis/Dissertation
eng
Civil Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Sayed, Tarek, 1965-
Gargoum, Suliman
Towards highway design readiness for vehicle automation: a 3D risk assessment approach using reliability theory
Text