The maximum tangential strain criterion is selected to determine the fracture initiation and propagation

and the incremental crack growth method is proposed to simulate the hydraulic fracturing propagation process. Numerical results show that the proposed method can effectively simulate the path of fracture propagation during hydraulic fracturing. By using the proposed crack growth method

we discussed the effects of the perforation length

the perforation angle

the stress anisotropy coefficient

Poisson’s ratio and the water injection pressure on the initial critical water pressure

the fracture path and the deflection angle. According to the initial critical water pressure and the fracture propagation path

the suitable perforation geometry can be optimized. It leads to a decrease in the initial critical water pressure but an increase in the contact area with the formation by decreasing the stress anisotropy coefficient. Poisson’s ratio has significant influence on fracture path under the critical water pressure conditions but does not have an effect on the fracture initiation angle under high water injection pressure. The sensitivity analysis indicates that the perforation angle is a critical factor to affect the fracturing. The numerical model provides a comprehensive understanding of the characteristics of hydraulic fracturing under complex loading conditions. The results also provide a basis for quantitative investigations of the engineering design of hydraulic fracturing treatments.