Numerous efforts have been made to improve intersection operations under signal-free control enabled by connected autonomous vehicles (CAVs). However, vehicle crossing paths in existing literature primarily followed conventional geometric design. The performance of unconventional intersections with alternative conflict layouts under signal-free control remains a knowledge gap.To address this problem,we model the operations of three unconventional (signal-free) autonomous intersections and compare their operational performance with one conventional autonomous intersection. Results show that unconventional vehicle crossing paths at intersections are likely to reduce vehicle delay and fuel consumption compared with conventional intersections in most scenarios. Three crucial intersection layout factors, i.e. the number of conflicts, the distance between conflicting points, and the conflict angle, are investigated, which provides new insights into the mechanism of the performance change of unconventional intersections under the CAV environment. Our analysis suggests vehicle path design offers new space for operational performance enhancement of autonomous intersections.