Modified Intersection Method for Solving Alignment Problems Containing Incomplete Transition Curves

To address the issue that the asymmetric basic type calculation model, which the intersection method relies on in highway alignment design, fails to perform calculations when turning curves include incomplete transition curves, the asymmetric basic type calculation model was used as the foundation. By analyzing the causes of the model’s failure in solving incomplete transition curve scenarios, the structure and solution logic of the calculation model were optimized and improved, and an asymmetric general type calculation model was further proposed. This new model introduced a novel definition of transition curve direction. It classified transition curves into two categories, positive and negative, by judging the relationship between the curvature change trend of the transition curve and the route’s traveling direction. Then, based on the positional order of the transition curve within a single curve, a special local coordinate system was established. Through geometric derivation, the tangential growth value and curve offset value of the incomplete transition curve were obtained, enabling the subsequent use of the asymmetric basic type calculation model for further solution. The research has shown that the asymmetric general type calculation model eliminates the restrictions of the asymmetric basic type model on alignment combination types, allowing the curvature radii at the start and end points of transition curves to be arbitrary values. By comparing the calculation results of the same complex curve segment with those obtained using the traditional element method, the differences in the calculated mileage values and coordinates of the control stakes are both less than 1 mm, which meets the engineering accuracy requirements.