The significant advantages of the rotary drilling rig for boring have attracted increasing attention. However, achieving ideal fragmentation efficiency in practical drilling remains challenging. Therefore, it is crucial to understand the fragmentation mechanism in the stratum environment. By solving the Boussinesq problem, the force and displacement exerted on the picks by the power head, as well as the penetrating force and cutting force under picks fragmentation conditions, have been determined. Additionally, a 3-Dimension numerical model for a single pick has been proposed to analyze the variation in penetrating force and cutting force. The results have been calibrated with theory to validate their reliability. Furthermore, a numerical simulation involving two picks has been conducted to describe the mechanical response and cracking evolution, thus revealing the mechanism of the pick fragmentation. In addition, the fragmentation forces exerted by picks with different arrangements have been extensively discussed, highlighting that the pick inclination or deviation angle has a significant impact on fragmentation force. Finally, the fragmentation efficiency with considering the picks arrangement in different strata has been thoroughly investigated. The findings demonstrate that specific work increases as the machine drills from soft to hard formations, while maintaining the same pick inclination, deviation angle or spacing. Furthermore, the corresponding value firstly decreases, then increases for a given stratum, indicating that the optimized arrangement of picks yields the highest efficiency. These achievements provides theoretical support for the optimization of picks and improvement of fragmentation efficiency.