## 2 Model Establishment and Parameter Selection
### Main Parameters of the Model  
In the numerical simulation of uniaxial compression tests, the macroscopic mechanical behavior of rocks is influenced by geometric parameters and micromechanical parameters. Geometric parameters, such as minimum particle radius (\(R_{min}\)), maximum particle radius  
Figure 1: Experimental numerical core sample and model principles.  
(\(R_{max}\)), particle density (\(\rho\)), and model dimensions (height and width), determine the basic morphology and particle distribution of the model. In the Linear Parallel Bond Model (LPBM), micromechanical parameters are classified into linear micromechanical parameters and parallel bond micromechanical parameters. Linear micromechanical parameters include the effective modulus \(\overline{E}\), stiffness ratio \(k=k_{n}/k_{s}\), and friction coefficient \(\mu\), describing the elastic behavior and frictional properties of particles. The parallel bond micromechanical parameters include the radius multiplier (\(\overline{\lambda}\)), parallel bond effective modulus (\(\overline{E}^{*}\)), parallel bond stiffness ratio (\(\overline{k}^{*}=\overline{k}_{n}/\overline{k}_{s}\)), tensile strength (\(\overline{\sigma}_{c}\)), cohesion (\(\overline{c}\)), shear strength (\(\overline{\tau}_{c}\)), and friction angle (\(\overline{\varphi}\)), which characterize the cement properties between particles, especially the stiffness and strength of the bonding interface. Due to the large number of model parameters, key parameters must be selected and simplified in practical applications to streamline the calibration process. These parameters should be reasonably chosen and calibrated to ensure the accuracy of simulation results.  
In this study, the parameter settings were based on the methodology proposed by [PERSON] for Lac du Bonnet granite [26]. Specifically, the effective modulus of particles was set equal to the parallel bond effective modulus, and the stiffness ratio was set equal to the parallel bond stiffness ratio, with the radius multiplier fixed at 1. These settings not only reduce the number of experimental variables, but also ensure that the numerical models accurately reflect the mechanical properties of the rock. The particle density was set to the measured value from actual cores (2140 kg/m\({}^{3}\)), and the minimum particle radius was set at 0.2 mm. Since shear strength is determined by cohesion and friction angle, it was not treated as an independent variable [22]. Consequently, the principal micromechanical parameters used for calibration in this study were the particle radius ratio (\(R_{max}\)/\(R_{min}\)), effective modulus (\(\overline{E}\)), stiffness ratio (\(k\)), friction coefficient (\(\mu\)), tensile strength (\(\overline{\sigma}_{c}\)), cohesion (\(\overline{c}\)), and friction angle (\(\overline{\varphi}\)).  
Orthogonal experimental design is a method that enables the systematic investigation of multiple factors while reducing the required number of experimental groups. In this study, parameter levels for experimental investigation were determined by integrating findings from previous research and the material characteristics of moderately consolidated sandstone. Experimental parameters are shown in Table 1.