Impact of grade designs of long mountainous freeway tunnel with crest vertical curve on traffic safety at tunnel portals

OBJECTIVE: Crest vertical curves are frequently employed in long mountainous freeway tunnels to facilitate drainage and ventilation, yet the mechanisms by which specific grades and grade changes within these curves influence driving behavior and traffic safety at tunnel portals remain insufficiently understood. This study aims to explore the effects of crest vertical grade designs, specifically entrance grades, exit grades, and grade changes, on driving behavior at the portals of long mountainous freeway tunnels. METHODS: Based on a survey of alignment design indicators of over 100 tunnels in Guangdong Province, this study identified that most long tunnels adopt a crest vertical grade design and their typical alignment indicators. Based on the investigation, a 26-km-long freeway model comprising 10 tunnels with distinct vertical profile was constructed. Subsequently, a driving simulation experiment was conducted with 32 recruited participants. Driving behavior data were collected within 100-meter zones inside and outside each portal. Eight key behavioral indicators, including mean and standard deviation of speed, time headway, lane departure, and acceleration, were extracted. Repeated-measures one-way analysis of variance (ANOVA) was then used to identify significant differences across various design conditions. Subsequently, indicators exhibiting statistical significance were integrated into a Fuzzy Comprehensive Evaluation (FCE) model, combining with entropy weight methods to objectively quantify the overall safety performance of each design scheme. RESULTS: ANOVA results indicated that five specific indicators showed significant variations under different grade designs: mean and standard deviation of speed, mean and standard deviation of time headway, and mean acceleration. Lane departure and standard deviation of acceleration were not significantly affected by grade designs. The Fuzzy Comprehensive Evaluation revealed distinct optimal conditions for portal safety. At tunnel entrances, uphill grades yielded significantly higher safety scores compared to flat or downhill sections, with the 1.5% uphill grade achieving the highest comprehensive score. Conversely, flat (0%) entrances resulted in the lowest safety ratings. At tunnel exits, safety scores generally decreased as the exit grade became less steep; the 1.5% exit grade produced the optimal safety outcome. Regarding internal grade changes, a moderate change of 3% resulted in the highest safety scores, whereas larger changes led to increased speed dispersion and reduced time headways, lowering the overall safety evaluation. CONCLUSIONS: This study confirms that vertical alignment design critically influences driver performance and safety at portals of long tunnels. These findings provide quantitative guidance for updating freeway tunnel design specifications, recommending that designers prioritize uphill approaches and moderate grade transitions. Furthermore, the results offer a scientific basis for traffic authorities to implement targeted safety management measures, thereby mitigating crash risks in critical tunnel portal zones.