Mixture effects of multiple exposures on driving safety at tunnel entrances and exits: A Bayesian kernel machine regression (BKMR) method.

Tunnel entrances and exits are widely recognized as safety-critical zones due to abrupt environmental transitions. However, most prior work examines single domains (e.g., spatial or lighting) and often assumes linear, additive effects, leaving mixed, non-linear and interactive association patterns insufficiently understood. To address this gap, this study proposes a comprehensive framework that couples a continuous Driving Safety Margin Index (DSMI) with mixed-exposure modelling. A naturalistic driving experiment with 35 drivers collected synchronized spatial proximity to the portal (distance-to-entrance/exit, DTE), driver-view relative luminance proxy, visual fixation intensity, and physiological load. DSMI was derived via fuzzy clustering of multi-channel vehicle control behaviors, yielding a continuous measure of instantaneous safety margin. Bayesian Kernel Machine Regression (BKMR) was applied to quantify joint, nonlinear and interactive effects of mixed exposures on DSMI, separately for entrances and exits. The results reveal pronounced entrance-exit asymmetry in model-estimated risk-related association patterns at tunnel portals. At entrances, the joint effect increases monotonically, suggesting a cumulative association pattern in which DTE and physiological load show stronger relevance. At exits, the joint effect follows a nonlinear inverted-U pattern: safety margin is highest under moderate exposure but decreases under both low and high stimulation. Exposure-response results suggest a role reversal of illuminance: excessive brightness is associated with lower DSMI at exits, whereas stronger fixation intensity is associated with larger safety margins. Model-estimated interaction patterns are largely additive or compensatory at entrances, whereas they appear more synergistic and potentially vulnerability-amplifying at exits. Overall, this study suggests that driving risk at tunnel portals is associated with complex, nonlinear, and asymmetric mixed-exposure patterns rather than single-factor associations. The framework advances tunnel safety research by linking a continuous safety margin to mixed exposures, informing differentiated entrance-exit design and traffic management.