# Research on the Development Mechanism of Three Kinds of Cracks in Rock Cutting
## 2 Experiment and Simulation
### PFC Model  
Particle Flow Code (PFC) is a method of dynamic numerical analysis that can be utilized to simulate in-homogeneous, discontinuous, and large deformation properties in rock experiments [26]. This approach considered the motion of the block after the force was  
Figure 4: Rock-Cutting Experiment (DOC = 1.5 mm). Note: The numbers 1–5 refer to the chronological order of the cutting tests; the following figure is the same. Figure 5: Rock-Cutting Experiment (DOC = 2.5 mm). Figure 6: Rock-Cutting Experiment (DOC = 3.5 mm). applied with the consequent condition of force and block motion, then estimated the motion of the particle in accordance with [PERSON]'s Second Law of Motion and many constitutive relations. This paper adopted PFC2D to investigate the initiation and expansion of the cracks as well as the generation of crack fragmentation. In PFC2D, if the particle itself is a disc-shaped rigid body, the motion of the particles follows [PERSON]'s Second Law of Motion to conduct force and energy through contact. If the contact form between particle is overlapping, it is supposed to be calculated by the magnitude of the overlap and adheres Hooke's Law. PFC simulation material on bulk particles, including the CB-model, PB-model, and different joint models, must be put up for particle bonding. In this paper, the process of fracture propagation of sandstone rock cutting is analyzed, and the model of parallel bonding is selected after careful deliberation. The functions of parallel bonding are shown in Figure 7. The rectangular bonding shape is situated on the particle's contact plane, at the center of the contact point, and it offers rotational resistance as well as normal and shear bond stiffness. The bond contact is parallel to the linear contact of the particle body. If relative movement occurs at the contact after bonding is established, the elastic interaction can impart force and torque. The force and torque act on the contacts of two bonds and are associated with the maximum normal and shear stresses acting around the bond and within the bonded material. The particle model exhibits linear elastic tensile, compressive, and rotational behavior. If the stress of the bond exceeds the limit of its corresponding strength, the bond fracture will occur. The bonding material corresponding to the fractured bond and its accompanying forces, torques, and strengths are removed from the model, and the fracture degenerates into the linear contact models, resulting in tensile and shear cracks in the model [27; 28]. The Discrete Fracture Network was used to separate the tensile crack from the shear fracture in order to better understand the mechanism of crack initiation and expansion in rock cutting. The principle is shown in Figure 8. There are four reasons for bond fracture, which are rotation, interleaving, separation, and overlap. Among them, the bond fracture caused by rotation and interleaving will produce a shear crack in situ, and the bond fracture caused by separation and overlap is a tension crack. To better determine the parameters of the sandstone model and characterize the crack initiation process and the formation mechanism of rock fragmentation, the indoor experiments of rock sample was first conducted in this paper. The sandstone basic mechanical parameters shown in Table 1 were obtained from the UCS and BTS experiment. According to the measured mechanical parameters of the sandstone, the particle parameters and bond parameters of PFC rock model as shown in Table 2 are selected after calibration. Figure 7: Schematic Diagram of Parallel Bonding. Note: The arrows within the sphere depict the trajectory of its motion, the following figure is the same. Where emod _(E)_ is the effective modulus; k-ratio is the normal-to-shear stiffness ratio; pb-k-ratio is bond normal-to-shear stiffness ratio; friction is the friction coefficient; pb-emod (\(\overline{\textbf{E}}\)) is the bond effective modulus; pb-fa is friction angle, pb-coh is cohesion, pb-ten is tensile strength.