Safety threshold quantification for mountainous freeways: a CatBoost-SHAP framework for crash frequency modeling on...

Geometric design critically influences mountainous freeway safety. Undulating terrain forces complex horizontal-vertical alignments that approach design limits, impairing operational safety and increasing crash risks. This necessitates examining how these combined parameters affect safety. However, critical limitations exist in current research and practice: (1) design specification limitations (a lack of empirical crash data validation for specified geometric parameter limits and interactive effects) and (2) methodological shortcomings (qualitative models masking risk heterogeneity on different combined sections). Thus, this study proposed a quantitative crash frequency analysis framework to investigate crash frequency relationships with combined horizontal and vertical curve alignments. Specifically, geometric alignments were classified into four distinct section types: tangent-sag curve (T-SC), tangent-crest curve (T-CC), curve-sag curve (C-SC), and curve-crest curve (C-CC). Using crash, geometric, and operational data from two typical Chinese mountainous freeways (5228 crashes), CatBoost regression models were developed for each section type. Shapley Additive exPlanations analysis and robustness check were then applied to quantify risk trends and identify high-risk thresholds for key geometric parameters. Key findings revealed significantly increased crash frequency associated with specific parameter interactions per section type: (1) T-SC/T-CC: short tangents, steep grade change rates, and small vertical curve radii. (2) C-SC/C-CC: high horizontal radius-to-curve length ratios, large horizontal curve average curvatures, steep grade change rates, and small vertical curve radii. (3) T-SC/C-SC: tangents exert a more significant influence on crash frequencies at sag vertical curves than horizontal curves. (4) T-CC/C-CC: crash risk on crest vertical curves is exacerbated more by horizontal curves than by tangents. These findings provide quantitative reference values and localized support for optimizing geometric design and safety management on mountainous freeways.