## 6 Conclusions  
Using the orthogonal test method, the L25 (4\({}^{5}\)) orthogonal design and 25 groups of similar material ratio tests were adopted, and the density test, porosity test, and compression test were carried out in this paper. The physical and mechanical indexes such as density, porosity, compressive strength, and elastic modulus of different similar material ratio tests were obtained.  
The results of the similar material proportioning test showed that the physical and mechanical properties required by the prototype of the similar model were within its distribution range. Among them, the distribution range of porosity and elastic modulus of 25 groups of samples with the similar material ratios was small, and the distribution range of density and compressive strength met the requirements of the orthogonal test.  
The sensitivity analysis and significance analysis of various factors by SPSS software showed that the density and compressive strength of similar materials were most affected by the ratio of Portland cement to gypsum. The porosity was most affected by the ratio of filling material to bonding material. The proportion of silicone oil was the main factor controlling the elastic modulus.  
The multiple linear regression analysis of 25 groups of test results was carried out, and the optimized multiple linear regression equation was obtained through anomaly detection and anomaly elimination. According to the characteristics of the Shanghengshan multilayer deposit and the research conditions of the material model, the similar materials of siliceous shale, carbonaceous shale, and vanadium-bearing shale were determined. The selected similar materials had a relatively dense structure and small porosity, and their main physical and mechanical properties were similar to those of the simulated multi-layer vanadium-bearing shale. Among them, the error between the actual similarity constant and the design value of similar materials was less than 1.62%, which met the requirements of test similarity conditions and can meet the requirements of simulated shale. The selection of similar materials is feasible.  
Conceptualization, Y.Y., Y.S., and X.W.; methodology, N.H., Y.Y., and Y.S.; software, Y.S. and X.H.; validation, Y.S. and X.H.; formal analysis, N.H., Y.Y., and Y.S.; investigation, N.H. and Y.S.; resources, Y.Y. and N.H.; data curation, Y.S. and X.H.; writing--original draft preparation, Y.S., Y.Y., and N.H.; writing--review and editing, N.H., Y.S., and Y.Y.; visualization, Y.S.; supervision, N.H. and Y.Y.; project administration, Y.Y. and X.W.; funding acquisition, Y.Y. and Y.S. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Natural Science Foundation of Hubei Province (No. 2020 CFB123), Scientific Research Project of Hubei Provincial Department of Education (No. Q20201109), Key Research and Development Plan of Hubei Province (No. 2020 BCA082), and Innovation and entrepreneurship training program for college students of WUST (No. 20 ZB012).  
Not applicable.  
**Data Availability Statement:** All data are presented in this article in the form of figures and tables.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Density** & **Porosity** & **Compressive Strength** & **Elastic Modulus** \\ \hline [PERSON] & 2.1310 & 1.2180 & 2.2600 & 2.0880 \\ \hline \hline \end{tabular}
\end{table}
Table 17: Durbin Watson coefficient of multiple linear regression analysis (excluding abnormal points).