Risk-Based Calibration of Road Sag Vertical Curve Design Guidelines on Undivided Highways

Safety in highway geometric design is one of the main goals to be achieved. However, deterministic design criteria do not provide information concerning the risk associated with the design outputs proposed. To yield consistent safety levels, the sag vertical curve design model on undivided highways was calibrated using a reliability-based framework, which allows one to incorporate the uncertainty associated with the model variables. The sag curve design model contemplates the features of vehicle front lighting systems to compute the headlight sight distance (HSD), which must be equal to or greater than the stopping sight distance (SSD). A dataset of 34,238 case studies was generated. Each case study was associated with two values of the risk level, designated as the probability of noncompliance ($P_{nc}$), one per driving direction. A Monte Carlo simulation was selected to calculate the values of $P_{nc}$. Through a series of interpolating surfaces of the cloud of points, contour graphs and calibrated charts were depicted. The paper provides a new methodology to verify, design, and compare sag vertical curves, evaluating the risk level with the $P_{nc}$.