Analysis of initiation angle for fracture propagation considering stress interference

Stress interference of multiplied fractures has significant influences on the propagation behavior of hydraulic fractures in roads, bridges, clay formations, and other forms of engineering. This paper establishes a crossing criterion and initiation angle model with comprehensive consideration of remote stress, stress intensity near the tip of fracture, and stress interference of multiplied fractures. Compared with the existing crossing criterion and initiation angle model, the ability to cross natural fractures decreases. Furthermore, the secondary initiation angle decreases with consideration of multiplied fracture propagation. The length of hydraulic fractures and natural fractures has little influence on the secondary initiation angle. With the increase in fracture space, the stress interference between fractures decreases, and as a result, the initiation angle begins to increase and then decrease. Differing from the propagation behavior of single fracture, the initiation angle basically does not vary with the increasing of net pressure under the high intersection angle between hydraulic fractures and natural fractures. Under a low intersection angle condition, the bigger the net pressure is, the smaller the initiation angle is. These results have great significance when analyzing the propagation behavior of multiplied fractures in real-world applications.Mathematical Physic