## 5 Conclusions  
This study employed the linear parallel-bond model as the particle contact constitutive law and developed a numerical model for the uniaxial compression of sandstone. Using orthogonal tests and an interaction analysis of key factors, a functional relationship between micromechanical and macroscopic mechanical parameters of moderately consolidated sandstone was established. This study proposed a micromechanical parameter calibration method for discrete element models of moderately consolidated sandstone. This method is more efficient than the conventional trial-and-error approach.  
1. The primary micromechanical parameters influencing the macroscopic mechanical properties are the maximum-to-minimum particle size ratio, effective modulus, stiffness ratio, tensile strength, and cohesion. The elastic modulus is mainly determined by the effective modulus, stiffness ratio, and particle size ratio. The uniaxial compressive strength depends on cohesion and tensile strength. [PERSON]'s ratio is most significantly affected by the stiffness ratio alone.
2. Interaction analysis shows that the elastic modulus increases with effective modulus and decreases with stiffness ratio. The effect of the particle size ratio on the elastic modulus exhibits a threshold. When the ratio exceeds 2.0, the elastic modulus is mainly controlled by the effective modulus and stiffness ratio. Uniaxial compres  
\begin{table}
\begin{tabular}{l l l l l l l} \hline
**Serial No.** & **UCS (MPa)** & **Error** & **E (GPa)** & **Error** & \(\lambda\) & **Error** \\ \hline experiment 1 & 35.75 & 2.06\% & 5.97 & 1.98\% & 0.233 & 0.85\% \\ simulation 1 & 36.49 & 2.02\% & 5.77 & 7.79\% & 0.289 & 2.42\% \\ \hline experiment 2 & 35.61 & 2.02\% & 5.32 & 7.79\% & 0.296 & 2.42\% \\ simulation 2 & 34.89 & 2.71\% & 4.22 & 4.49 & 6.39\% & 0.327 & 0\% \\ \hline experiment 3 & 25.41 & 24.72 & 2.71\% & 4.49 & 6.39\% & 0.327 & 0\% \\ \hline \end{tabular}
\end{table}
Table 4: Results and error comparison of macroscopic mechanical parameters between laboratory tests and numerical simulations.  
Figure 8: Results of laboratory tests and numerical simulations.  
sive strength increases with both tensile strength and cohesion, with a pronounced synergistic effect when both parameters are high.
* A multivariate predictive model was developed using an intelligent dynamic regression selection mechanism, achieving a goodness of fit above 90%. An iterative correction method for micromechanical parameter calibration was introduced and validated through three sets of laboratory and numerical simulation tests. The resulting macroscopic mechanical parameters show errors within 10% compared with the experimental results, and the fracture morphology of the numerically simulated rock samples is similar to that of the actual cores. These findings confirm that the proposed calibration method is both accurate and efficient.  
Methodology, P.Z.; Software, Z.M.; Validation, H.Z.; Investigation, T.W.; Writing--original draft, W.Z.; Supervision, J.D.; Project administration, S.T. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare no conflict of interest.