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yanghowdofreewaytunnel2025.md

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category: literaturenote citekey: yanghowdofreewaytunnel2025 title: How do freeway tunnel portal locations and the corresponding horizontal alignment affect traffic safety? Insights from driving simulation experiment and reliability analysis authors: "Yang, Yonghong; Hu, Yixi; Xu, Chuangbo; Zhang, Yu; Zheng, Tao" year: 2025 date: 2025-00-00 2025 doi: 10.1016/j.aap.2025.108082 publication: "Accident Analysis & Prevention" url: "https://doi.org/10.1016/j.aap.2025.108082" zotero_key: 9GEH6DIR zotero_storage: FAK6TUQ5 collections: transpordi_planeerimine folder: 001_artiklid firstAuthor: "Yang, Yonghong"

status: converted

Contents lists available at ScienceDirect

Accident Analysis and Prevention

journal homepage: www.elsevier.com/locate/aap

  • a School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, China
  • b Guangdong Provincial Key Laboratory of Tunnel Safety and Emergency Support Technology & Equipment, Guangzhou, China

ARTICLE INFO

Keywords: Traffic safety Horizontal alignment Freeway tunnel portal Driving simulation Reliability Driving behavior

ABSTRACT

Previous research has indicated that freeway tunnel portals are prone to traffic accidents, with alignment at tunnel portal being a significant factor influencing crash occurrence. However, how to ensure safe design of freeway tunnel portal alignment remains unclear. This study developed a freeway model with five tunnels, whose portals are located at different positions along a tangent-curve section, to comprehensively investigate the impact of portal locations on driving behavior and traffic safety. Microscopic driving parameters were obtained through experiments and further analyzed using reliability analysis. Based on real-world crash data, two failure modes were considered: insufficient stopping sight distance and excessive lane departure. The probability of failure (PoF) was calculated using the Monte-Carlo sampling algorithm as an effective indicator of driving risk. To further explore various features affect tunnel portal traffic safety, sensitivity analysis was conducted on four key indicators, include curve radius, spiral length, pavement friction coefficient, and driving speed. The results show that the design locations of the tunnel portal significantly affect drivers' speed and lane departure behavior. When the portal is located on a tangent section, the distribution of driver speed and lane departure behavior are the most concentrated. In contrast, when the portal is situated on a circular curve or spiral section, the distribution becomes more dispersed. The failure modes and PoF are related to the portal location. Besides, the PoF based on insufficient stopping sight distance increases continuously with the curvature at the portal, while the PoF based on excessive lane departure increases with the deviation of curvature. The synthetic PoF indicates that when the portal is located 3/4 of the spiral section, the PoF is the highest, reaching up to 35.66% at the entrance and 25.31% at the exit. The curve radius, spiral length, pavement friction coefficient, and driving speed all influence the PoF at the tunnel portal. Among these factors, increasing the curve radius and ensuring a sufficient pavement friction coefficient have the most significant impact on reducing the PoF. This study proposes recommendations for the alignment design of freeway tunnel portals and traffic safety management, providing valuable references for road designers and freeway administrators to enhance the traffic safety of freeway tunnels.

1. Introduction

1.1. Background

By the end of 2023, China had completed the construction of 27,297 highway tunnels, with a total length of 302,318 km, including 2,050 extra-long tunnels with a total length of 9,240 km (MoT, 2024). The construction of tunnels has significantly improved road accessibility, but it has also brought immense traffic safety pressures. According to statistics, in 2023, there were a total of 254,738 road traffic crashes, resulting in 60,028 deaths, 253,895 injuries, and direct property losses of 11.793 billion yuan, causing a severe impact on society (NBSC, 2024). Previous studies have indicated that tunnel sections are prone to crashes on highways, especially the transition sections at the tunnel entrances and exits, which tend to have a higher crash rate compared to other parts of the tunnel (Pervez et al., 2020; Pervez et al., 2021). This is mainly due to the significant changes of driving environment at the portal sections. Specifically, compared with open, high visibility outside tunnel, the

* Corresponding author at: School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, China. E-mail address: yangyh@scut.edu.cn (Y. Yang).

driving environment inside tunnel is relatively enclosed and has limited visibility, low navigation positioning accuracy, which may lead to tension mood of drivers, leading to unconscious changes in driving behavior, altering the vehicle's dynamic movement compared to open sections, thereby affecting traffic safety. Meanwhile, the transition between bright lighting and dim lighting environment causes "black hole" and "white hole" effects, which affects drivers' visual adaption and prevent drivers from obtaining road information in a timely manner (Broz et al., 2025; Han et al., 2024; Zheng et al., 2024). Therefore, comprehensively exploring the mechanism of how the horizontal alignment of tunnel portals affects driving risk and proposing design and traffic safety management suggestions are of great significance for improving the overall safety level of roads.

However, current specifications have limited regulations regarding these hazard sections. Relevant specifications in China (MoT, 2017, 2018) and the US (AASHTO, 2017, 2018) have limited provisions for the alignment design of highway tunnels, with only a few recommended quantitative indicators. This leads designers to often rely on subjective experience when designing the alignment of highway tunnels, which can result in unreasonable designs and potential traffic safety issues.

1.2. Related works

Previously, numerous studies have been conducted on highway tunnel traffic safety. Some researchers have collected historical crash data to establish models that explore the relationship between crash factors and crash rates, finding that road alignment is an important factor affecting tunnel driving safety (Cai et al., 2022; Feng et al., 2020; Hou et al., 2018a; Tang et al., 2021), and bridge-tunnel sections are more prone to crashes (Y. Hu et al., 2023; Min et al., 2022). Based on the function of the road section, some scholars have further divided the tunnel section using six-zone (Pervez et al., 2020) and seven-zone method (Pervez et al., 2021), pointing out that tunnel entrance and exit sections tend to have higher crash rates and more severe crashes (Pervez et al., 2022; Pervez et al., 2022). Meanwhile, by analyzing crash data, previous research aimed at finding the relationship between road alignment and crashes, but limited by dataset, which cannot cover various kinds of alignment, leading to some contradictory research conclusions (Anastasopoulos and Mannering, 2009; Cai et al., 2022; Garach et al., 2016; Hosseinpour et al., 2014; Hou et al., 2018a; Hou et al., 2018b; Tang et al., 2021), and the mechanism of how alignment impact driving risk remains unclear.

Regarding the alignment issues at tunnel portals, previous studies have typically verified the consistency of the horizontal alignment from a mathematical theoretical calculation perspective. Specifically, Yang et al. (2012) proposed a method of freezing the steering wheel for 3 s to observe vehicle lateral offset behavior, calculating and proposing a lane departure control threshold. Li et al. (2021) also fixed the steering wheel for 3 s to observe vehicle deviation using simulation methods, proposing indicators to judge the consistency of the alignment design at freeway tunnel. Yang and Guo (2006) measured speed changes at entrances and exits based on self-developed accelerometers, analyzed the impact of road alignment on speed changes. Yang et al. (2017) analyzed the adaptation distance of the portal, reaction time, and the distance from the start of the spiral to the portal, combining the vehicle lane departure threshold, proposing a calculation method for the minimum spiral parameters at the portal as a function of the distance from the start of the spiral to the portal. Guo et al. (2013) analyzed speed changes at tunnel portals, considering alignment design indicators, pavement transition indicators, and lighting transition indicators to analyze the transition situations at tunnel portals. Wu et al. (2012) analyzed the impact of tunnel horizontal and vertical alignment design on speed distribution, driver physiological and psychological indicators based on natural driving tests, proposing a safety evaluation method based on average speed difference and driver heart rate changes. The above series of studies have fully demonstrated the important impact of tunnel portal alignment on driver behavior and traffic safety. However, due to the constraints of actual engineering, previous studies have not conducted research on the impact on driver behavior and safety under the same alignment conditions with different tunnel portal locations.

Previous studies have found that infrastructure design significantly influences driver behavior. Therefore, some studies have analyzed driving data collected from drivers on specific roadways to more comprehensively assess road traffic safety. Among these, speed and lane departure are crucial and commonly used indicators. Previous scholars have conducted driving simulation experiments to comprehensively evaluate the impact of infrastructure design on these two indicators. For example, based on an 8 Degree of Freedom (DoF) driving simulation platform, past scholars have comprehensively studied the impact of longitudinal and transverse alignment combinations on driver acceleration and deceleration behavior (Wang and Wang, 2018; Wang et al., 2019), lateral acceleration (Wang et al., 2015), and vehicle lane departure (Chen et al., 2018; Guo et al., 2020). Specifically, Wang et al. (2019) conducted a driving simulation test and found that the combination of horizontal and vertical alignment significantly influences the acceleration, deceleration and speed change behavior of drivers. At the same time, another study reported that road alignment design significantly affects speed change behavior (Wang and Wang, 2018). However, some studies also indicate that when the curve radius increases beyond a certain threshold, further enlarging the radius has less pronounced effects on the driver's speed behavior (Wang et al., 2018). Bei et al. (2025) observed that drivers tend to actively decelerate when approaching a tunnel entrance, especially after recognizing the tunnel and its speed limit signs by conducting driving tests. Chen et al., 2018 found that road design has a significant impact on lane departure, with greater curvature of curves leading to larger lane departure deviations. The foregoing studies collectively confirm that, under certain conditions, alignment design of tunnels can exert some notable influence on driver behavior. Still, most studies have focused only on open road sections, and to authors' understanding, there is still relatively little research on driving simulation under tunnel environments. Some researchers investigated how tunnel environment affect driving behavior (Bassan, 2015; Calvi et al., 2012; He et al., 2025; Qin et al., 2023), other studies mainly focuses on tunnel lighting (Mingwei et al., 2023), visual guidance systems (Bei et al., 2024; Wang et al., 2024; Zheng Haoran et al., 2025), and landscape design (Su et al., 2023), with very limited research related to tunnel alignment design. Specifically, Zhao et al. (2022) conducted simulation driving tests and found that sidewall decoration has a significant impact on driver speed adjustment ability, operational stability level, and attention distraction level, believing that reasonable sidewall decoration can improve the level of tunnel driving safety. Wen et al. (2024), based on simulation driving tests, found that coordinated portal colors have a positive effect on maintaining driver attention and stable vehicle speed. Wang et al., 2024 and Bei et al. (2024) both confirmed the role of various visual guidance systems in improving tunnel driving safety through simulation driving tests. Focusing on extra-long spiral tunnel, Xing et al. (2024) conducted simulation driving tests on the combined effects of horizontal and vertical alignment on driving behavior, finding that small radii and steep slopes are unfavorable for driving, and the driving risk at the exit of ultra-long spiral tunnels is higher than that of general tunnel exits, and provided recommendations for alignment design. Shao et al. (2022) explored the impact of lighting and longitudinal slopes on driver behavior based on simulation driving tests, finding that longitudinal slopes mainly affect driving behavior, lighting mainly affects physiological indicators, and in situations with darker lighting and larger slopes, the risk of rear-end collisions will increase.

In addition, reliability indicator has been widely used in research related to the field of transportation engineering (Chen and Chen, 2011; Essa et al., 2016; Jalayer and Zhou, 2016; Xiaoxiang et al., 2022; Xiong and Chen, 2024; Yasanthi et al., 2022). This indicator can reflect the occasional nature of road hazards and reflect the overall safety level of

roads through probability. In the 1990s, Navin (1990) was one of the earlier researchers to introduce reliability theory into road design for evaluating the safety of road geometric design. Zhang et al. (2023) combined the probability empirical distribution of vehicle trajectory deviation obtained from past research, calculated the reliability of tunnel portals based on the two failure mode, include limited stopping sight distance failure and excessive lane departure. Sun and You (2013) determined three failure modes of rollover, skidding, and insufficient sight distance, established a multi-failure mode fault tree model, and explored the driving risk of curve sections. Dhahir and Hassan (2019) used reliability analysis based on four design indicators, include vehicle stability, driver comfort, sight distance, and vehicle rollover to develop a probabilistic, explicit safety horizontal curve design method. The above studies have confirmed the effectiveness of reliability in road safety analysis, but past studies have mainly been based on probability empirical distribution solutions, to some extent ignoring the heterogeneity between the sections being studied and past research sections.

1.3. Research gap and contribution

In summary, existing studies have mainly explored of the horizontal alignment design of tunnel portals from the perspective of mathematical models, or investigated the impact of tunnel alignment on crash rates and severity. However, they have not effectively revealed the internal quantitative relationship between alignment, driver behavior, and tunnel driving risk, especially the impact of horizontal alignment design at freeway tunnel portal on traffic safety. Meanwhile, limited by actual engineering constraints, it is difficult to conduct actual driving tests to explore the impact of different tunnel portal locations on driving risk. Subsequently, it is essential to carry out research to investigate how tunnel portal locations and horizontal alignment of tangent-curve section affect traffic safety.

Based on the foregoing research background, to bridge the gap, this paper employed driving simulation equipment, established road models, and conducted simulation driving comparative tests to explore how the locations of tunnel entrances and exits on tangent-curve sections affect driving behavior. Subsequently, based on the simulation results, a reliability model was established to quantitatively evaluate the impact of portal locations on driving risk. Finally, this paper conducted sensitivity analysis to quantify the impact of risk features on tunnel entrances and exits safety. Specifically, this paper aimed to address the following questions:

  • How do different tunnel portal locations on tangent-curve sections affect driving behavior and which location is relatively safer?
  • How do horizontal alignment of tangent-curve section with tunnel portals affects traffic safety?
  • From the perspectives of design and traffic management, what methods can help alleviate the traffic safety pressure at tunnel portals?

2. Methods

In this part, the methods involved in this paper would be introduced, which can be divided into two parts, driving simulation experiment and reliability analysis.

2.1. Driving simulation experiment

Previously, driving simulation experiment has been proven to be a powerful tool for traffic safety analysis (Wang and Wang, 2018; Wang et al., 2015; Xing et al., 2024). This paper aimed to leverage driving simulation experiments to explore how the locations of freeway tunnel portal on tangent-curve section affect drivers' behavior and to serve as a basis for quantifying driving risks at tunnel portals.

2.1.1. Apparatus

The driving simulation apparatus used in this experiment is a sixdegree-of-freedom (6-DoF) driving simulation platform produced by Jiangsu Delauney Information Co.,Ltd.

As shown in Fig. 1, the driving simulation apparatus primarily consists of display system, steering system, braking and acceleration pedal, computer host, driving seat, 6-DoF hydraulic control system, and foundation. Specifically, the display system is composed of three 60 Hz, 43-inch, 1080p monitors, covering approximately 135 degrees of the driver's forward field of view. The operation of the steering system, throttle, and brake pedals is consistent with that of a real vehicle. The computer host is equipped with an Intel Core i7-13700 K CPU, a GeForce RTX 4070 Ti GPU, and 32 GB of DDR5 memory. The 6-DoF hydraulic control stick can control the motion of the simulation platform along three coordinate axes. The foregoing apparatus ensures that the driving simulation experience closely approximates real driving conditions, thereby enhancing the precision of the experiment.

2.1.2. Participant

Considering the purpose of this experiment, factors such as age, gender, and driving experience of the drivers were not included as variables in the study. Prior to the commencement of the experiment, participant recruitment notices were posted within the campus of South China University of Technology. Referenced to sample size in previous researches (Shao et al., 2022; Wang and Wang, 2018; Zhao et al., 2022), a total of 32 participants were recruited for this simulated driving experiment. Their ages ranged from 18 to 45 years old, including 22 males and 10 females. All participants held valid motor vehicle driving licenses of the PRC and had experience driving through freeway tunnels within the past year.

2.1.3. Tunnel scenario design

In order to investigate the impact of horizontal alignment at tunnel portal on driving behavior, the research team established a roadway model via EICAD and AIRoad, whose basic information is shown in Table 1.

Due to the relative difficulty in modeling tunnel sections compared to general open sections, to reduce the complexity of modeling, the research team surveyed the alignment design of eight tunnels (as shown in Table 2) along a certain expressway in Guangdong Province, totaling 32 portals. After investigation, this paper selected a radius of 2500 m and a spiral length of 400 m as typical tunnel portal alignment design parameters. In this experimental road model, a total of five tunnels were set up. The tunnel entrances and exits are located on tangents, spiral, and circular curves, as shown in Fig. 2.

In Fig. 2(a), both the tunnel entrance and exit are located on tangents, with the entrance portal 100 m from the beginning point of tangent-to-curve (T-to-C) spiral and the exit portal 100 m from the ending point of curve-to-tangent (C-to-T) spiral (approximately a 3-second journey), marked as portal location A; in Fig. 2(b), both the tunnel entrance and exit are located at the 1/4 point of the spiral, with the entrance 100 m from the BP of the T-to-C spiral and the exit 100 m from the EP of the C-to-T spiral, marked as portal location B; in Fig. 2(c), both the tunnel entrance and exit are located at the 1/2 point of the spiral, with the entrance 200 m from the BP of the T-to-C spiral and the exit 200 m from the EP of the C-to-T spiral, marked as portal location C; in Fig. 2(d), both the tunnel entrance and exit are located at the 3/4 point of the spiral section, with the entrance 100 m from EP of the T-to-C and the exit 100 m from the BP of the C-to-T spiral, marked as portal location D; in Fig. 2(e), both the tunnel entrance and exit are located on the circular curve, with the entrance 100 m from the EP of the T-to-C spiral and the exit 100 m from the BP of the C-to-T spiral, marked as portal location E.

To conserve space, the subsequent text will refer to the tunnel portals as positions A, B, C, D, and E.

To prevent the influence of extraneous variables on the results of this

Fig. 1. Driving simulation apparatus.

Table 1 Geometric parameter of experiment road model.

Parameter (Unit) Value Parameter (Unit) Value
Road Type Freeway Design Speed (km/h) 120
Freeway Length (m) 9493 Turnings 5
Tunnel Number 5 Max Gradient (%) 0.723
Lane Numbers 3 Lane Width (m) 3.75

Table 2 List of investigated freeway tunnel.

Tunnel Tunnel Classification Direction Tunnel Length (m)
Tunnel I Extra-Long North 5190
South 5225
Tunnel II Middle North 880
South 958
Tunnel III Long North 1010
South 1010
Tunnel IV Middle North 593
South 530
Tunnel V Short North 375
South 135
Tunnel VI Short North 335
South 310
Tunnel VII Short/Middle North 492
South 508
Tunnel VIII Extra-Long North 5181
South 5120

Notation: According to relevant specification in China (MoT, 2017), short tunnels denote tunnels length shorter than 500 m, middle tunnels denote tunnels longer than 500 m and shorter than 1000 m, long tunnels denote tunnels longer than 1000 m and shorter than 3000 m, extra-long tunnels denote tunnels longer than 3000 m.

experiment, the following considerations were specifically taken into account during the design of the roadway model:

  • (1) The longitudinal slope of the entire roadway is controlled within ± 1 %;
  • (2) Each tunnel contains only one horizontal curve, and there is an open section exceeding 500 m between adjacent tunnels, which includes at least a 300 m long tangent to ensure independent operation between tunnels.
  • (3) The other geometric parameter of the roadway model strictly complies with the provisions of relevant specification for highway alignment design (MoT, 2017).

Simultaneously, to simulate the effects of black holes and white holes

effects at freeway tunnel portals as closely as possible, triggers were set at the entrances and exits of every tunnel to adjust the experimental system's time. When the simulated vehicle passes through the triggers, at the entrance, the trigger causes the system to lower the brightness to simulate the "black hole effect". Similarly, when the vehicle passes through the trigger at the exit, the system increases the brightness to simulate the "white hole effect", making the light changes more noticeable for the drivers when driving at the tunnel portals. Additionally, the tunnel itself can have a psychological and physiological impact on the driver when they approach it, which in turn affects their driving behavior. Therefore, this paper posits that the established roadway model can reproduce the state of the driver when driving at the real tunnel portals, the comparison between the tunnel portal in the modeling software and the real portal is shown in Fig. 3.

In summary, this paper established a road model for driving simulation tests. The model is approximately 10 km long and includes five tunnels, all of whose portals are located at different locations on tangentcurve sections. Quantitative analysis was conducted based on the sampled data from the ten portals of the five tunnels on this freeway.

2.1.4. Experiment procedures

The experiment procedure, which was formulated strictly based on the Declaration of Helsinki and have been admitted by the Ethic Committee of the South China University of Technology, consists of the following steps:

  • (1) Upon arrival at the laboratory, the participants are verified by the experimenters, who then introduce the experimental equipment, operation methods, and other basic information about the experiment, and have the participants sign a consent form;
  • (2) Practice with simulated driving: The research team had previously established a 15 km-long freeway segment for participants to practice and familiarize themselves with the equipment, in order to reduce experimental errors due to unfamiliarity with the equipment;
  • (3) Formal experiment: The subjects complete the entire experimental roadway driving task in one go, according to their driving habits.

After the formal experiment, a questionnaire was carried out to investigate whether participants came across any physical or psychological discomfort during the experiment. Only data collected from participants who did not come across any discomfort will be used for further evaluation.

Each experiment is expected to take about 30 min, and upon completion, the research team will distribute compensation (RMB 60/ hour) to all participants.

Fig. 2. Schematic diagram of tunnel portal position. Notation: BP denotes beginning point, EP denotes ending point, T-to-C spiral denotes tangent-to-curve spiral.

2.1.5. Driving data acquisition

During the experiment, the computer collects micro driving parameters at a frequency of 50 Hz, including the vehicle's position, velocity, acceleration, and displacement data in three axes (driving direction, lateral, and vertical to the road surface). After all subjects have completed the experiment, and through observation during the experiment and data curation after the experiment, two participants were not able to complete the experiment normally were excluded, and eventually, a total of 30 sets of valid data were collected from the driving simulation experiment.

For data extraction scope, considering that the alignment design specification (MoT, 2017) requires that the alignment consistency should be ensured within 3 s of travel distance inside and outside the tunnel portal, as a result, this paper focuses on studying this range. The designed speed for the experimental road is 120 km/h (the design speed

for the tunnel section is 100 km/h). A 3-second journey is approximately 100 m, so this paper selects a data sampling range of 100 m inside and outside the tunnel entrance and exit, that is, 200 m long for each tunnel portal.

For each sampling range, the average driving speed and lane departure values of the drivers are calculated separately. Furthermore, Kolmogorov-Smirnov (KS) test is carried out to verify the normality distribution of driving behavior.

2.2. Reliability analysis

Reliability refers to the ability of a system to perform its intended functions within a specified time frame and under defined conditions. It encompasses structural safety, applicability, and durability, and when measured probabilistically, it is referred to as reliability. Reliability

Fig. 3. Comparison of tunnel portal in AIRoad and reality.

theory has been widely applied in structural design, and some scholars have attempted to introduce reliability theory into traffic safety analysis (Chen and Chen, 2011; Xiong and Chen, 2024). By treating traffic safety issues as a system and defining traffic accidents as system failures, reliability theory can be used to quantitatively analyze traffic safety levels. To ensure safe passage on roads, the actual supply value (S) provided by the road for vehicle travel must be greater than the demand value (D) for safe vehicle travel. In this paper, the reliability function T is given by Eq. (1):

$$T = S - D \tag{1}$$

When the supply value S is greater than the demand value D, and T is greater than 0, it indicates that the system can operate normally. Conversely, when S is less than D, and T is less than 0, the system fails. In the context of this study, it is considered that when T is greater than 0, the road can meet the safety requirements for vehicle passage; when T is less than 0, it suggests that the road poses a certain level of danger, potentially leading to crashes.

To identify failure modes, the research team analyzed 648 traffic crashes in 8 tunnels located on a freeway in Guangdong Province from 2019 to 2023 and found that rear-end and side collisions were the main types of crashes, accounting for approximately 93 % of all crashes. Previous studies have indicated that the main causes of such crashes are insufficient stopping sight distance, which prevents drivers from braking in time, and excessive lane departure of vehicles (Chen et al., 2018; Yonghong et al., 2020). Therefore, this paper aims to establish functional equations based on insufficient stopping sight distance and excessive lane departure, and to calculate the probabilities of failure for both scenarios as well as the combined PoF.

2.2.1. PoF based on insufficient sight distance

During the driving process, drivers need to have a good line of sight to understand the road conditions ahead and make decisions. The distance from a driver's position on the road to the farthest point they can see is called the available sight distance, which is usually related to the road alignment design. During driving, the driver's available sight distance should be greater than the stopping sight distance to ensure that the driver can brake in time when they spot a hazard on the road ahead, preventing rear-end collisions. Therefore, the functional equation based on insufficient stopping sight distance can be expressed as Eq (2):

$$F1 = f(SD{av}, SDs) = SD{av} - SD_s \tag{2}$$

In which, *F*1 denotes the insufficient sight distance based functional equation, SDav denotes the available sight distance, SDs denotes the stopping sight distance.

It is worth noting that although the black hole and white hole effects have a certain adverse impact on the driver's available sight distance, this effect is difficult to quantify. Therefore, in this paper, when calculating the available sight distance and stopping sight distance, the research team only considers the impact of the black and white hole effects on the stopping sight distance, details of which are provided below.

Firstly, this paper calculates the available sight distance for the driver. In the example calculations of this paper, the driver's viewpoint may be located on the tangent, spiral, and circular curve. Among these, when the driver's viewpoint is on the tangent and the spiral, the calculated value of the sight distance may be very large, which obviously does not conform to reality. Therefore, referring to past research, when driving at about 100 km/h, the farthest useful sight distance is 400 m (AASHTO, 2018; Zhao, 1998). That is, when the calculated value of the sight distance is less than 400 m, the available sight distance value is the calculated value. When the calculated value exceeds 400 m, the available sight distance value is recorded as 400 m.

Consequently, when the driver's viewpoint is on the tangent, the sight distance value is taken as 400 m. When the driver's viewpoint is on the spiral curves, the sight distance value is calculated by establishing a road model on the computer and then calculated by the EICAD software. When the viewpoint is on the circular curve, past research has indicated that the available sight distance has the following relationship with the radius of driver's viewpoint and side clearance distance, expressed as Eq. (3):

$$W_c = Rs \left[ 1 - \cos \left( \frac{S{av}}{2R_s} \right) \right] \tag{3}$$

Transform the foregoing Eq. (3), the calculation of available sight distance is expressed as Eq. (4):

$$S_{av} = 2R_s \arccos\left(1 - \frac{W_c}{R_s}\right) \tag{4}$$

In which, Wc denotes the side clearance distance, in this paper, this value equals to the distance between visual point and tunnel side wall, m; Rs denotes the radius of the driver visual point, m;Sav denotes the available sight distance, m.

To consider the most unfavorable condition, the point with the smallest view radius in each sampled section is selected to calculate the available sight distance. When calculating the distance from the visual point to the side wall, it is assumed that the vehicle is traveling in the center of the innermost lane of a curve. The design width of a small passenger car is taken as 1.8 m, resulting in a calculated distance of 3.8 m from the viewing point to the tunnel side wall.

The stopping sight distance refers to the distance required for a vehicle to come to a complete stop after the driver spots a hazard while driving normally and applies full braking force. It is typically calculated using the following Eq. (5):

$$SD_s = v_0 t_r + \frac{v0^2}{2a{brake}} \tag{5}$$

In which, v0 denotes the travel speed before braking, m/s; tr denotes the driver reaction time, s; abrake denotes the acceleration when braking, m/s2 .

During the braking process of a vehicle, the acceleration is not a constant value and should include the braking rise phase and the full braking phase. That is, the actual braking process involves a change in vehicle acceleration as shown in Fig. 4. Additionally, previous studies have indicated that drivers experience visual vibration phenomena when driving through tunnel entrances and exits, influenced by the black hole and white hole effects. This phenomenon refers to a type of blindness that occurs when a driver passes through the tunnel entrance and exit, where the intense transition from light to dark causes difficulty in accurately focusing the pupils, thereby preventing clear imaging on the retina, which can prolong the reaction time (Du et al., 2007). Therefore, taking into account the actual variation in braking force and the impact of visual vibration phenomena, Eq. (5) can be further revised as shown in Eq. (6) below:

$$SD_s = v_0 \left( t_1 + t_2 + \frac{t_3}{2} \right) + \frac{v0^2}{2a{brake}} - \frac{a_{brake}t3}{2} + \frac{1}{8}a{brake}t_3^2$$

In which, t1 denotes the reaction time, s; t2 denotes the visual fluctuation time, s; t3 denotes the braking ascending time, s.

In summary, the main factors affecting the failure modes based on stopping sight distance include vehicle speed, road surface friction coefficient, and alignment design parameters. Specifically, vehicle speed and road surface friction coefficient influence the stopping sight distance required by the vehicle, while alignment design parameters primarily affect the available sight distance for drivers.

Based on previous research, the time required for a driver to react from perceiving a hazard to initiating braking action is approximately 2.5 s (Tang et al., 2020), the time required for the rise phase of automotive braking is approximately 0.6 s (Xia, 2021; Zhang et al., 2023). Meanwhile, based on research carried out by Du et al. (2007), the visual vibration time at freeway tunnel entrance and exit is shown in Table 3.

As for the pavement friction coefficient, research team collected road surface data from 32 tunnel portals on a freeway in Guangdong Province, as shown in Table 2. After calculation, the average road surface friction coefficient is 0.482, and the standard deviation is 0.054. Kolmogorov-Smirnov (KS) test indicates that the road surface friction coefficient follows a normal distribution. Therefore, in the subsequent reliability calculations, the road surface friction coefficient will be input into the model as a normal distribution with a mean of 0.482 and standard deviation of 0.054.

Table 3 Visual vibration time at tunnel portal.

Speed (km/h) Entrance Section (s) Exit Section (s)
80 1.25 0.63
100 1.01 0.61
120 1.2 0.62

2.2.2. PoF based on excessive lane departure

Lane departure refers to the unconscious offset from the centerline of lane of drivers during driving process, which is an important cause of side collision traffic accidents (Board, 2011; Caird et al., 2018). Previous studies have pointed out that the design of the road's horizontal alignment significantly affects the driver's lane dep behavior. Therefore, to meet the needs of safe driving, it is necessary to ensure that the lane departure value during the driver's driving process is less than the safety threshold. Thus, the functional form of excessive lane deviation can be described as Eq. (7):

$$F2 = g(D{threshold}, D{drive}) = D{drive} - D_{threshold}$$ (7)

In which, Ddrive denotes the mean lane departure when drivers driving through tunnel portal, Dthreshold denotes the safety threshold of lane departure.

At the tunnel portal, due to the variation in light and darkness, drivers may not be able to timely perceive the road alignment ahead, leading to unconscious deviation behavior of the vehicle. In engineering practice, to mitigate this effect, the portal is often set on a tangent or circular curve sections with constant curvature. However, some tunnel portals are also set on spiral lines due to practical needs. When drivers are traveling at such portals, greater lane departure may occur due to the alignment, posing a danger (Eustace et al., 2014; Lord et al., 2011). In this paper, the mean value and standard deviation of drivers' lane departure behavior are obtained from driving simulation experiment. As for threshold of lane departure, previous studies have been carried out on this topic. Some studies investigated the lane departure behavior at freeway tunnel portals, based on one of the most recognized studies carried out by Yang et al. (2017), who investigated the lane departure behavior by collecting real-world driving data at tunnel portal, the threshold was selected as 0.4 m.

2.2.3. Monte-Carlo sampling solution

Based on the driving simulation results, the research team obtained the speed and lane departure data of 30 drivers under different tunnel portal arrangements. Previous studies have indicated that the microdriving parameters of drivers on the road usually follow a normal distribution (Andjus and Maletin, 1998). Considering the sample size of this experiment, we used the Kolmogorov-Smirnov (KS) test to verify that the driver samples in this experiment follow a normal distribution and calculated the mean and variance using statistical software.

After obtaining the distribution of variables, we input them into the functional equation and solved them using the Monte Carlo sampling solution. The Monte Carlo method is a computational method based on probability and statistical theory, which uses random numbers to solve various scientific problems. It assumes that the variables in the problem to be solved follow a certain probability distribution and obtains approximate solutions through random sampling. This method has been widely used in the reliability analysis and model parameter solving in the field of transportation (Sun and You, 2013; Zhang et al., 2023).

To fully consider the impact of drivers' longitudinal and lateral behaviors on the reliability of tunnel portal setting positions, we have established functional equations based on insufficient stopping sight distance and excessive lane departure as mentioned above. In actual situations, either of these two situations occurring will lead to failure. Therefore, the expressions for the PoF based on insufficient stopping sight distance, the PoF based on excessive lane departure, and the synthetic PoF are shown in equations (8–10), respectively. Fig. 4. Braking control diagram.

$$P{f1} = \frac{N{SSD}}{N_s} \tag{8}$$

$$P{f2} = \frac{N{LD}}{N_s} \tag{9}$$

$$P{sf} = \frac{N{SSD}^* + N_{LD}^* + N_B}{N_S} \tag{10}$$

In which, Pf1 denotes insufficient stopping sight distance based PoF, Pf2 denotes excessive lane departure based PoF, Psf denotes synthetic PoF, NSSD denotes sampling with insufficient stopping sight distance, NLD denotes sampling with exceed lane departure, NS denotes the overall sampling number, N*SSD denotes sampling with only insufficient stopping sight distance, N*LD denotes sampling with only exceed lane departure, NB denotes sampling with both failure mode.

In this paper, 10,000 was selected as the overall sampling number simulation. The mean value and standard deviation of speed and lane departure values obtained from the driving simulation experiment, as well as the pavement friction coefficients detected at 32 tunnel portals on a freeway in Guangdong Province, are input as random variables into the Monte-Carlo simulation.

2.2.4. Sensitivity analysis

To provide a reference for the alignment safety design of highway tunnel entrances and exits, and to offer suggestions for traffic safety management. This paper conducted a sensitivity analysis to investigate how the deviation of certain features affects traffic safety. Initially, four typical features that significantly affect traffic at freeway tunnel portal were selected, include the road design index of radius (R), the length of the spiral (Ls), the vehicle velocity (V), and the pavement friction index (ft). The specific parameters for the sensitivity analysis are shown in Table 4.

In the reliability calculation process, this paper treats speed and lateral offset as random variables input into the reliability calculation model. It is worth noting that in this section, the paper investigates the effect of changing different parameters on the failure probability by altering their values. These parameter changes, in fact, influence driving behavior, but based on previous studies, such effects are predictable. When the radius is large, alignment changes have little impact on speed, whereas when the radius decreases and the curve length shortens, lateral offset intensifies (Chen et al., 2018; Wang et al., 2018). Due to the difficulty of modeling tunnel sections under varying alignment conditions, this paper statistically derives the speed and lateral offset distributions at the entrances and exits from the foregoing driving simulation

Table 4 Analytic parameter of sensitivity analysis.

Simulation R/m Ls/m V/km*h-1 ft
1 2500 400 Based on driving
simulation results		 Based on
measured value
2 1000/
1500/
2000
2500/
3000/
3500
4000/
4500/
5000		 400 Based on driving
simulation results		 Based on
measured value
3 2500 100/
200/
300/
400/
500/600		 Based on driving
simulation results		 Based on
measured value
4 2500 400 120/100/80 Based on
measured value
5 2500 400 Based on driving
simulation results		 0.4/0.45/0.5/
0.55/0.6

experiments as random distributions for input into the model.

Additionally, when altering speed, previous studies have indicated that the mean and standard deviation of the driver's speed distribution are usually linearly related (Zhang et al., 2023). Based on the results of simulated driving experiments, this paper linearly fitted the mean and standard deviation obtained from ten portals in the simulation. Subsequently, the linear relationship between the mean and standard deviation of the speed distribution as shown in Eq. (11). In simulation scenario 4 shown in Table 4, when conducting the sensitivity analysis of driving speed (80 km/h, 100 km/h and 120 km/h), the standard deviation of the driver's driving speed at that speed is calculated using Eq. (11) and input into the model.

$$St.D{\nu} = 0.109M{\nu} \tag{11}$$

In which, St.Dv denotes the standard deviation of velocity, Mv denotes the mean value of velocity.

To compare the impact of each indicator on PoF, this paper normalizes the parameters within 0 and 1 using Eq. (12).

$$Z{ij} = \frac{Y{ij} - \min(Y_j)}{\max(Y_j) - \min(Y_j)}$$ (12)

In which, Zij denotes the i th normalized value of the j th parameter Zj, Yij denotes the i th value of the j th parameter Yj, max(Yj) denotes the max value of the j th parameter Yj, min(Yj) denotes the minimum value of the j th parameter Yj.

Consequently, this paper defined αj as impact factor, representing how PoF affected by j th parameter Yj. In this study, PoF Pf can be viewed as a function related to radius, spiral curve length, speed and pavement friction coefficient, defined as Pf = f (R, Ls, V, ft), hence, αj can be defined as the partial derivative of Pf with respect to parameter Zj, expressed as Eq. (13).

$$a_j = \frac{\partial P_f}{Z_j} \tag{13}$$

3. Results

3.1. Driving characteristic analysis

The research group processed the micro-driving parameters collected by the driving simulator, acquiring the driving speed and lane departure of the subjects within each sampling range, and plotted as boxplot as shown in Figs. 5 and 6. Here, A, B, C, D, and E represent the positions of the tunnel portals, consistent with foregoing Fig. 2.

Firstly, the research group conducted a Kolmogorov-Smirnov (KS) test on the driving behavior samples obtained from each sampling interval and found that the driver behavior at all sampling locations could not reject the hypothesis of being sampled from a normal distribution (p > 0.05). This means that the driver behavior in this experiment is significantly derived from a normal distribution. In the subsequent reliability calculations, driver behavior will be input into the functional function as a random variable that follows a normal distribution.

Fig. 5(a) and (b) respectively show the distribution of driving speed and lane departure of drivers at the portals of the tunnel. In Fig. 5(a), on average, when the tunnel entrance is located on a tangent section, the mean driving speed is high, reaching about 114 km/h, and the distribution is more concentrated. When the tunnel entrance is set on the spiral, the mean driving speed decreases slightly, ranging between 105 km/h and 115 km/h, and the distribution is more dispersed than when the entrance is on a tangent, indicating a certain negative impact on driver behavior when the tunnel entrance is set on the spiral. When the tunnel entrance is set on the circular curve, the mean speed is similar to that when the entrance is on the spiral, but the distribution is denser. In Fig. 5(b), when the tunnel entrance is set on a tangent or the first quarter of the spiral, the mean lane departure is close to 0. When the entrance is set at the 1/2 and 3/4 position of the spiral and on the circular curve, the

Fig. 5. Driving behavior distribution at Tunnel Entrance.

Fig. 6. Driving behavior distribution at Tunnel Exit.

mean lane departure is slightly larger but does not exceed 0.25 m, which is still within the safety threshold of 0.4 m for lane departure.

Fig. 6(a) and (b) respectively show the distribution of driving speed and lane departure of drivers at the exit of the tunnel. As shown in Fig. 6 (a), the driving speed gradually decreases with the increasing curvature of the tunnel exit setting. When the tunnel exit is set on a tangent, the average speed reaches 113 km/h; when the exit is set on a circular curve, the average driving speed is 109 km/h. When the exit is set on a tangent section, the speed distribution is the most concentrated, and when the exit is set on a spiral section, the distribution is more dispersed than when set on a tangent; when the exit is set on a circular curve, the speed distribution is the most dispersed. This may be the result of some drivers accelerating at the exit in order to quickly leave the tunnel and some drivers consciously decelerating when driving on curves, which is consistent with previous research (Yang et al., 2024). Fig. 6(b) shows that when the exit is set on a tangent and a circular curve, the lane departure distribution is more dispersed. Meanwhile, the mean lane departure at each exit position is less than the safety threshold of 0.4 m. When the exit is set on a spiral, larger offset values are observed, exceeding the safety threshold of 0.4 m. It is also observed that when the exit is set on tangent, the mean lane departure value is highest, this is due to the particularity of the experimental scenario, where the exit at the tangent is located after the curved segment. When drivers transition from the curved section back to the tangent, the vehicle fails to return promptly to the center of the lane due to the driver's maneuvering, resulting in this behavior.

3.2. Probability of failure

Based on Equations (2) and (7) and the Monte Carlo sampling method, the PoF for each entrance and exit based on insufficient stopping sight distance, excessive lane departure, and synthetic PoF are calculated, respectively. The reliability of each tunnel entrance is shown in Table 5, and the reliability of each tunnel exit is shown in Table 6.

In Table 5, as the curvature of the tunnel entrance position increases, the PoF based on stopping sight distance also increases. When the entrance is located on tangents, the stopping sight distance does not become a factor for tunnel entrance failure. As the curvature of the entrance further increases, the PoF due to stopping sight distance gradually increases. When the entrance is set on a circular curve, where the curvature is the greatest, the PoF is the highest, reaching 6.98 %. This is because on circular curve sections, the radius of the viewpoint is the smallest, making it easy to have poor visibility. Considering the PoF based on lane departure values, when the entrance is located on a

Table 5 Probability of failure at tunnel entrance.

Portal Position SSD Based PoF
(%)		 Lane departurebased PoF
(%)		 Synthetic PoF
(%)
A <0.001 3.45 3.45
B 0.03 1.07 1.08
C 1.04 30.71 31.18
D 4.82 33.35 35.66
E 6.98 1.73 7.54

Table 6 Probability of failure at tunnel exit.

Portal Position SSD Based PoF
(%)		 Lane departurebased PoF
(%)		 Synthetic PoF
(%)
A <0.001 9.63 5.63
B 0.02 7.15 7.16
C 0.16 19.45 19.52
D 2.19 24.77 25.31
E 4.01 6.23 8.35

tangent (A), the first quarter of the spiral (B), and the circular curve (E), the PoF based on lane departure is low. On the opposite, when the entrance is set at the halfway point (C) and three-quarters point (D) of the spiral, the PoF based on lane departure is significantly higher than when the entrance is set on a tangent or circular curve, reaching a maximum of 35.66 %. The synthetic PoF, compared with the PoF based on stopping sight distance and lane departure, shows that when the entrance is set on sections with smaller curvature changes, such as tangents or circular curves, failure is more likely to occur due to insufficient stopping sight distance. When the entrance is set on sections with significant curvature changes, such as spirals, failure is more likely to occur due to excessive lane departure.

Table 6 shows the calculated probabilities of failure for exits set at various positions. From Table 6, the overall trend of failure based on stopping sight distance is similar to that of the entrance, with the PoF increasing as curvature increases and the obtainable sight distance decreases, reaching 4.01 %. From the perspective of lane departure, when the tunnel exit is set on a tangent (A), the first quarter of the spiral (B), and the circular curve (E), the PoF based on lane departure is small, all not exceeding 10 %. However, when the tunnel exit is set at the halfway point (C) and three-quarters point (D) of the spiral, the PoF based on lane departure increases, reaching 19.45 % and 24.77 %, respectively. The synthetic PoF shows that when the tunnel exit is set on a tangent (A), the first quarter of the spiral (B), and the circular curve (E), the PoF is small, while when the tunnel exit is set at the halfway point (C) and three-quarters point (D) of the spiral, the PoF is higher.

3.3. Sensitivity analysis

This section selects four significant factors that influence the safety of highway tunnel entrances and analyzes the impact of changes in different indicators on the safety of tunnel entrances at various locations. Input the sensitivity analysis parameters shown in Table 4 into the reliability calculation model to compute the synthetic Probability of Failure (PoF). This paper first normalized all indicators using Eq. (12), allowing for a direct comparison of the impact of changes in each indicator on synthetic PoF through their slopes, shown in Figs. 7 and 8, in which how PoF changes with various influencing factors were shown. Fig. 7 illustrates the trend of synthetic PoF at the entrance, and Fig. 8 shows the trend at the exit. In these figures, the x-axis represents the normalized values (0,1) of each typical influencing parameter, which allows for a clear horizontal comparison of the impact of changes in each indicator on PoF through normalization.

3.3.1. Tunnel entrance

Fig. 7(a–d) respectively present the trend of PoF at the tunnel entrance varying with the radius of the circular curve, the length of the spiral, the road surface friction coefficient, and the speed. As shown in Fig. 7(a), as the radius increases, the PoF of the entrance set on the curved section gradually decreases. However, when the entrance is set on a tangent (A), it does not affect the PoF. Fig. 7(b) indicates that when the length of the spiral increases, the PoF of the entrances set on the tangent and circular curve sections does not change significantly, while the PoF of the entrances set on the spiral gradually decreases with the

Fig. 7. Sensitivity analysis at tunnel entrance.

Fig. 8. Sensitivity analysis at tunnel exit.

increase of the spiral length. Specifically, when the entrance is set at the 1/4 (B) and 1/2 (C) of the spiral, once the spiral length reaches 200 m and 300 m, respectively, the PoF becomes similar to that of the entrances set on the tangent section. When the entrance is set at the 3/4 (D) of the spiral, even if the spiral length reaches 600 m, the PoF remains higher than that of the entrances set on the tangent. Fig. 7(c) shows that by changing the road surface friction coefficient, it is found that as the road surface friction coefficient increases, the PoF of the entrances set at the 1/2 (C), 3/4 (D) of the spiral, and on the circular curve significantly decreases. In contrast, when the entrance is set on a tangent and 1/4 (B) of the spiral, the main failure mode is lane departure failure, so the change in the road surface friction coefficient does not significantly affect the PoF. Fig. 7(d) indicates that by changing the driving speed, it is found that when the speed increases, it does not significantly affect the PoF of the entrances set on the tangent and 1/4 (B) of the spiral. However, for entrances set at locations with greater curvature (C, D, E), the PoF significantly increases.

Calculating the αk using Eq. (13), the maximum gradient of the PoF change with each indicator are − 3.56 (radius), − 0.212 (spiral length), − 0.601 (road surface friction coefficient), and 0.49 (driving speed). Comparing the effects of each influencing indicator on the PoF reveals that selecting a larger radius in the design phase and ensuring pavement friction coefficient during operational management can significantly enhance the safety level of the entrance.

3.3.2. Tunnel exit

Fig. 8 shows the sensitivity analysis results for the tunnel exit, changing the radius (a), spiral length (b), road surface friction coefficient (c), and speed (d) to explore the impact of these indicators on the PoF. When the exit is set on a tangent, it does not significantly affect the PoF. When the exit is set on the spiral and circular curves, the PoF significantly decreases as the radius increases. However, when the radius increases to 2500 m (value 0.375 in Fig. 8(a)), further increases in the radius do not significantly affect the PoF of the exits at various locations. Increasing the spiral length slightly reduces the PoF of the exits set on the spiral, but the PoF of the exit set at the 3/4 of the spiral

remains higher than that of the exits set at locations with greater curvature. The PoF of the exits set on the tangent and circular curve does not significantly change with the length of the spiral. Increasing the road surface friction coefficient does not significantly affect the PoF of the exits set on the tangent and 1/4 of the spiral. The PoF of the exits set at the 1/2 of the spiral slightly decreases, while the PoF of the exits set at the 3/4 of the spiral and on the circular curve significantly decreases with the increase of the road surface friction coefficient. Increasing the driving speed, when the speed is between 80 km/h and 100 km/h, does not significantly change the PoF of the exits set at various locations. However, when the speed further increases to 120 km/h, the PoF of the exits set on the circular curve and 3/4 of the spiral significantly increases, and the PoF of the exits set at the 1/2 of the spiral slightly increases.

The maximum slope of the PoF change with each indicator, i.e., the influence factor αk, are − 3.15 (radius), − 0.207 (spiral length), − 0.342 (road surface friction coefficient), and 0.026 (driving speed). Comparing the effects of each influencing indicator on the PoF reveals that selecting a larger radius in the design phase and ensuring pavement friction coefficient during operational management can significantly enhance the safety level of the exit.

4. Discussions and recommendations

Based on the distribution of drivers' speed behavior according to the driving characteristic analysis, the position of the tunnel portals has a significant impact on driver behavior, which is consistent with the conclusions of previous studies (Yang et al., 2012; Zhang et al., 2012). This is mainly due to when driving near the tunnel entrance, drivers notice a change in the road environment ahead and then proactively adjust their speed to ensure safety. Previous studies have also addressed this unfavorable effect of tunnel entrances on driver behavior (Bei et al., 2025). Specifically, when the horizontal alignment change at the entrance and exit is small, such as when the entrance is located on a tangent or a circular curve, the driving variability of drivers is lower, which is more conducive to traffic safety. However, when the entrance is

set on a spiral curve, the distribution of driver behavior is more dispersed, and the variability is greater. Reflected in actual traffic management, such distribution of driver behavior is likely to lead to turbulence in traffic flow, which in turn can increase the vehicle conflict rate, lead to traffic congestion, reduce passage efficiency, and even cause traffic safety issues (Tang et al., 2020; Yang et al., 2024). In summary, based on the analysis of driving speed, it is proven that setting the entrance on tangents and the exit on tangents is still the best choice as it results in a more concentrated driving behavior (Lin et al., 2008).

As for lane departure behavior of drivers, no obvious distribution pattern was observed for the mean lane departure. However, the dispersion of the observed distribution revealed some unusual findings, this is primarily because the radius selected under the experimental conditions fully complies with relevant design standards, allowing most drivers to pass the curve relatively centered. However, similar with the speed behavior, due to the change in the tunnel entrance environment, drivers' attention may not be fully focused on the road alignment changes, leading to more severe unconscious lane departure. When the entrance is set on tangents and circular curves, where the curvature inside and outside the tunnel is consistent, a more dispersed lane departure behavior was observed compared to when the entrance is set on a spiral curve. However, when observing the extreme values, when the entrance is set on a spiral curve, a small number of drivers exhibited larger offsets, exceeding 1 m. Considering that the upper and lower 1/4 quartile points of the driver's lane departure values at each entrance are within the offset threshold of 0.4 m, it can be concluded that even if the entrance is set on tangent and curved sections with a more dispersed distribution, it will not pose a danger. From the perspective of extreme states, the entrances set on the spiral curve (B, C, and D) showed larger maximum lane departure, indicating that these entrances are more likely to fail due to lane departure offset, which was also confirmed in subsequent reliability analyses.

From the perspective of reliability, the position of the tunnel entrance significantly affects the PoF. Specifically, under the conditions of this experiment, when the curvature at the entrance is small, the main failure mode is excessive lane departure. When the curvature at the entrance is large, insufficient stopping sight distance becomes the main failure mode, and previous studies have also reached similar conclusions (Zhang et al., 2023). It is worth noting that to consider the impact of road alignment on driver behavior, the simulation traffic conditions were set for free flow. However, in actual road operations, insufficient car-following distance can further increase the PoF caused by insufficient sight distance. Therefore, from a reliability perspective, during the design phase of the tunnel entrance, it is preferable to set the entrance in sections with less curvature, such as tangents (A), the initial part of the spiral (B), or sections with constant small curvature near the entrance. From the perspective of traffic safety management, previous studies have shown that speed is related to a vehicle's lane departure behavior (Tian et al., 2022), in situations where lane departure failure is the primary mode of failure, it is essential to strengthen speed management. Simultaneously, we have observed that the PoF at the exit is lower compared to the entrance, primarily due to the shorter visual adaptation time for drivers at the exit. Therefore, implementing measures such as installing light-shielding canopies at the tunnel entrance and enhancing the lighting at the tunnel portals to alleviate the visual adaptation phenomenon for drivers is of great significant for enhancing the safety level of tunnel traffic safety (M. Hu et al., 2023; Li et al., 2021).

Based on the results of parameter sensitivity analysis, from a design perspective, for the entrance portal, increasing the curve radius within a certain range and extending the length of the spiral can enhance the safety level of the tunnel portal. From the perspective of road operation, conducting timely road surface inspections to ensure pavement friction coefficient and implementing reasonable speed limit measures for tunnels with portals on spirals can also improve the safety level of tunnel portals, measures such as variable speed limit control strategy can be applied to enhance traffic safety (Jin et al., 2025). Comparing the

influence factors reveals that, for tunnel portals, reasonably selecting a larger curve radius during the design phase and ensuring good pavement friction coefficient are of great significant for enhancing tunnel portal safety.

It is also worth noting that changes in horizontal alignment can have a certain impact on the lateral offset behavior of drivers. Specifically, when the radius is smaller and the transition curve is shorter, the lateral offset behavior of drivers is more pronounced compared to the typical alignment design parameters selected in this study (Chen et al., 2018). Therefore, in the sensitivity analysis, the impact of changes in radius and transition curve length on the PoF may be a little underestimated. As the radius decreases, the intensification of lane departure behavior will further increase the PoF. When the transition curve length decreases and the curvature increases, drivers are more likely to experience greater lateral offset, which also leads to an increase in PoF. This further highlights the positive impact of selecting a larger radius and longer transition curves at tunnel entrances on tunnel entrance safety.

5. Limitations

Still, there is certain limitation in this study. Current driving simulation equipment simulated the black hole and white hole effects by using triggers to a certain extent, and this paper only consider horizontal alignment. In the future, simulation can be updated to better simulate the lighting environment at freeway tunnel portal, at the same time, the combined effects of horizontal and vertical alignment on driving behavior is also worth investigating. Meanwhile, the participants recruited for this study were primarily from the young adult group. In the future, additional recruitment of middle-aged and elderly drivers could be considered to make investigate how drivers' age affects driving behavior at freeway tunnel portals.

6. Conclusions

This paper aimed at investigating how the location of freeway tunnel portals on tangent-curve sections and the corresponding horizontal alignment design affects traffic safety by conducting driving simulation experiments and reliability analysis. Based on driving simulation experiment results, reliability and sensitivity analysis, this paper drawn the following conclusions.

  • (1) Regarding speed behavior, when the portal is set on a tangent, the driving speed is higher than when the portal is set on a curved section and the distribution of driver speed behavior is relatively concentrated. When the portal is set on a spiral or circular curve, the speed behavior of drivers exhibits significant fluctuations. As for lane departure behavior, when the portal is set on a tangent and circular curve, the distribution of lane departure is more dispersed. It is recommended that when deciding the freeway tunnel portal location on tangent-curve section, tangent sections and circular curve sections are still the favorable choice.
  • (2) The failure mode and PoF of tunnel portals are related to the horizontal alignment, the curvature and deviation of curvature affects PoF based on insufficient SSD and based on excessive lane departure, respectively. The PoF based on insufficient stopping sight distance increases with the curvature at the portal. According to the synthetic PoF, the portal set at the 3/4 of the spiral has the highest PoF. Under the same alignment conditions, the PoF of the entrance portal is greater than that of the exit portal. It is recommended that when conditions are limited and the portal must be set on a spiral section, the tunnel portal at the first 1/4 range of the spiral would be preferred, and select a spiral as long as possible to reduce the deviation of curvature at tunnel portals.

  • (3) The radius of circular curves, the length of spirals, pavement friction performance, and driving speed all affect the PoF of tunnel portals. Choosing larger curve radius, longer spiral,

  • making strict speed management and ensuring good pavement friction performance all do help to enhance the safety of the tunnel portals. Among the foregoing measures, enlarge radius and ensure good friction performance have the most significant impact on the tunnel portal PoF. It is recommended that at the tunnel portal, a radius greater than 2500 m should be chosen as much as possible. When conditions are limited and a smaller radius curve must be chosen, the tunnel portal should be avoided on curves.

  • (4) During the road operation management phase, speed management should be conducted reasonably according to the horizontal alignment at the tunnel portal to improve traffic safety levels and passage efficiency. It is also recommended that the pavement friction performance at the tunnel portal be regularly inspected to ensure indicators are within reasonable range.

CRediT authorship contribution statement

Yonghong Yang: Writing – review & editing, Writing – original draft, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. Yixi Hu: Writing – review & editing, Writing – original draft, Visualization, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Chuangbo Xu: Writing – review & editing, Writing – original draft, Software, Methodology, Formal analysis, Data curation. Yu Zhang: Writing – review & editing, Visualization, Formal analysis, Data curation. Tao Zheng: Writing – review & editing, Visualization, Data curation.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This work was supported by the Key Area Research and Development Program of Guangdong Province (Grant No. 2022B0101070001), the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2021A1515011788) in China.

Data availability

The data that has been used is confidential.

References