## 4 Calibration Method for Micromechanical Parameters of Discrete Element Model and Case Application  
### Calibration Method for Micromechanical Parameters of Discrete Element Model  
Based on the analysis of the significant influencing factors of macroscopic mechanical parameters and the results of interaction among micromechanical parameters, when the \(R_{max}/R_{min}\) exceeds 2.0, its effect on the elastic modulus becomes negligible. The radius ratio determines the total number and distribution of particles in the model. Considering both computational efficiency and modeling accuracy, calibration with respect to this parameter is prioritized. The detailed calibration procedure is as follows.  
1. The uniaxial compressive strength, elastic modulus, and Poisson's ratio of the rock were determined through uniaxial compression tests. A numerical model was established based on the actual dimensions, porosity, and density of the rock.
2. Based on the research rules mentioned above and by comprehensively considering computational performance and simulation accuracy, an appropriate radius ratio was selected to determine the number and spatial distribution of particles in the model.
3. The experimentally determined Poisson's ratio is substituted into Equation (13) to obtain the stiffness ratio \(k\), which is then set as \(k=\overline{k}\). After \(R_{max}/R_{min}\) and \(k\) are determined, the actual elastic modulus is substituted into Equation (2) to calculate the micromechanical parameter, the effective modulus \(\overline{E}\), which is then set as \(\overline{E}=\overline{E}^{*}\).
4. The failure modes of rock under uniaxial compression include shear failure, tensile failure, and conjugate failure. According to the findings of [PERSON] [27], the ratio of tensile strength \(\overline{\sigma}_{c}\) to cohesion \(\overline{c}\) determines the failure mode of the rock. Specifically, when \(\overline{\sigma}_{c}/\overline{c}<1.66\), the rock exhibits tensile failure; when \(1.66<\overline{\sigma}_{c}/\overline{c}<3.0\), the rock displays conjugate failure; and when \(\overline{\sigma}_{c}/\overline{c}>3.0\), the rock undergoes shear failure. Based on the crack morphology observed in the actual rock mechanics test, the corresponding value of \(\overline{\sigma}_{c}/\overline{c}\) is selected. The experimentally measured uniaxial compressive strength (UCS) and the selected \(\overline{\sigma}_{c}/\overline{c}\) are then substituted into Equation (7) to calculate the micromechanical parameters: tensile strength \(\overline{\sigma}_{c}\) and cohesion \(\overline{c}\).
5. Since the friction coefficient (\(\mu\)) and friction angle (\(\overline{\varphi}\)) have negligible effects on macroscopic mechanical properties, initial values of \(\mu=0.5\) and \(\overline{\varphi}=30^{\circ}\) are adopted based on previous research experience [28]. The above micromechanical parameters are incorporated into the parallel-bond model to establish a particle flow model for moderately consolidated sandstone. By comparing the results of laboratory tests and numerical simulations, if the error is less than or equal to 10%, the calibration of the model's micromechanical parameters is completed. If the error is greater than or equal to 10%, iterative calibration is performed according to Formula (14).  
\[A_{k+1}=A_{k}+(A_{k}^{*}-A^{*})\cdot\lambda \tag{14}\]  
\[\lambda=\left\{\begin{array}{cc}1&(A_{k}^{*}-A^{*})\leq 0\\ -1&(A_{k}^{*}-A^{*})>0\end{array}\right. \tag{15}\]  
(where \(A_{k+1}\) is the simulated input value after No.(\(k+1\)) iteration, \(A_{k}^{*}\) is the simulated result after the No.(\(k\)) iteration, and \(A^{*}\) is the target value obtained from experiments).