# A Novel Method of Calibrating Micro-Scale Parameters of PFC Model and Experimental Validation  
[PERSON]  
1 School of Resources and Safety Engineering, Central South University, Changsha 410083, China; [EMAIL_ADDRESS] (H.W. ); [EMAIL_ADDRESS] (G.Z. )1 School of Resource Environment and Safety Engineering, University of South China, Hengyang 421000, China; [EMAIL_ADDRESS] (Y.C. ); [EMAIL_ADDRESS] (Y.T. )1  
[PERSON]  
2 School of Resource Environment and Safety Engineering, University of South China, Hengyang 421000, China; [EMAIL_ADDRESS] (Y.C. )[EMAIL_ADDRESS] (Y.T. )[EMAIL_ADDRESS] (Y.T. )[EMAIL_ADDRESS]  
employed to study the mechanical characteristics of granular assemblies, and the results indicated that the obtained force vector plots by a computer program show good agreement with those from photoelastic disc tests [19]. Later on, a series of versions of DEM-based PFC software was released by Itasca Consulting Group, Inc. This piece of promising software has a wide range of applications, e.g., slope stability, rock fracture, underground mining, hydraulic fracturing, and flow simulation. In PFC model, the medium is idealized as an assembly of various sized rigid particles and the bonds between them. The motion and interaction of the particles affect the macromechanical behavior. The shape of the particles is circular in PFC2D (Two-dimensional PFC) and spherical in PFC3D (Three-dimensional PFC). There are two types of bonds: contact bond and parallel bond [20] (Figure 1). For the contact-bond model, the adjacent particles are connected by point-formed bonds; that is, the particles can only move in translation and not in rotation. As long as the particles are in contact, the contact stiffness remains the same regardless of whether the bond is broken [21]. Clearly, this is not realistic in rock mechanics. With regard to the parallel-bond model, particles are contacted via a bond with a certain thickness and radius. When particles translate or rotate, both the force and moment can be transmitted through the bond. Once the normal or tangential stress on the bond exceeds its normal or tangential strength, fracture will occur as tensile or shear cracks. This behavior is consistent with the actual fracture of the rock. Hence the parallel-bond model was selected for PFC modeling in this study. During modeling, the macroscopic physical and mechanical properties as well as the constitutive model of the material are not required to predefine. The reason is that the mechanical response is controlled by the motion and interaction of the particles. Thus, determining a set of micro-scaled physical and mechanical parameters of the particle and contact to match the macro-response of the material is essential. Obviously, the accuracy of PFC simulation is strongly associated with these parameters. Currently, the trial-and-error method is commonly used to calibrate the micro-scale parameters of the PFC model based on uniaxial compression test results of rock specimens; that is, they need to repeat performing uniaxial compression simulation by adjusting these parameters until the simulated uniaxial compressive strength, elastic modulus, Poisson's ratio, and failure mode of the model are consistent with the laboratory test results. Indeed, the number of the micro-scale parameters is quite large, and determining a proper set of micro-scale parameter values is extremely time consuming and troublesome. Therefore, it is meaningful to find an approach to address this issue quickly and reliably. To explore the relationship between micro-scale parameters and macroscopic mechanical properties, a few attempts have been made by some researchers. [PERSON] [22] applied the Plackett-Burman design method to analyze the sensitivities of micro-scale parameters to macro-response of contact-bond model, and singled out two most significant micro-scale parameters for each macroscopic property. By using Taguchi method, [PERSON] et al. [23] performed a calibration on micro-structural parameters of parallel-bonded agglomerates in both 2D and 3D models.