Fracture mechanics is a vital component involved in studying the exact behavior of rock materials. Detection and assessment of the behavior of rock joints injected by grout plays an important role in numerical modelling in rock mechanic projects. The importance of mechanisms associated with initiation and propagation of cracks due to hydraulic fracturing has led to a considerable interest in investigation and analysis of this phenomenon. In this work, the process of propagation of cracks on the wall of boreholes, drilled in single and bi-material structures, was simulated in ABAQUS software employing the extended finite element method. The energy method was implemented to obtain the stress intensity factor and energy release rate through applying J integral around the crack tip. The method was applied to two rock types, diorite and granite at the Chadormalu iron mine located in the central part of Iran. It was concluded that assuming the same geometry, the possibility of crack propagation at the boundary between two materials was more than the single material medium. Therefore, in dealing with a bi-material medium, if the purpose is to measure the in situ stresses, the measurement should not be performed on the boundary between the two materials.