The prediction of three-dimensional hydraulic fracturing morphology and extension is the main factor to evaluate the effects of hydraulic fracturing; adopting the method that combining damage mechanics and fracture mechanics to describe the mechanical behavior of cracks in the surface rock

and then the damage criterion and damage evolution equation in the crack surface are established. The equation is solved by using the method combining Newton-Raphson and the linear search; and then the dynamic crack extension process and the final morphology of hydraulic fracturing three-dimensional are obtained; and the mechanical essence is revealed. The correctness of the theory and calculation is verified through numerical examples; based on which

the main factor of crack extension is analyzed. The results provide more reliable and accurate prediction methods for hydraulic fracturing design

so as to improve reservoir hydraulic fracturing success rate.