Hydraulic fracturing technology is widely applied in shale gas extraction engineering. In this study

the state-based peridynamic theory was introduced into the modeling and analysis of hydraulic fracture in horizontal shale wells. The mechanism of the multi-fracture propagation and the formation of complex fracture networks were analyzed as well. An equivalent hydraulic pressure term was embedded in the constitutive function

which describes the interactive forces between material points

to track the applied hydraulic pressure on the new crack surfaces. Thus

a simplified state-based peridynamic model was established to describe the hydraulic fracturing. Through the proposed model

the hydraulic fracturing process of shale reservoirs was simulated to investigate the complex crack propagation paths

the formation process of crack networks

as well as the effects of natural stratification

cracks

and perforation spacing on the hydraulic crack propagation. Numerical results indicate that when the perforation spacing is sufficiently small

the cracking process is disturbed and the crack propagation along the central perforation is inhibited. Under certain fracturing pressure

a proper increase of perforation distance can significantly accelerate the hydraulic fracture process. During the hydraulic fracturing process

horizontal cracks may be formed in the horizontal stratification

and complex vertical cracks may be formed by the induction of natural cracks. The proposed model and numerical methods provide alternative and promising ways for the profound investigation into shale hydraulic fracturing and engineering applications.