## 5 Conclusions  
In this study, raw materials were mixed to make sandstone-like specimens of different ratios. Based on the principle of fractal theory and NMR, the prediction model of compressive strength with the percentage of macroporous pore volume and fractal dimension of macroporce as dependent variables is established. Conclusions drawn from this study are as follows.  
(1) Internal pores of sandstone-like materials are mainly macropores, followed by mesopores, and the proportion of small pores is the smallest. The fractal dimension of pore size gradually increases with the growth of pore radius. Correlation coefficients of fractal dimension of mesopore and macropore are different from that of micropore, and pores of mesopore and macropore show obvious fractal characteristics.  
(2) The proportion of different pores volume and the fractal dimension of pore size are both linearly related to the compressive strength of materials. The fractal dimension of macroporous pore  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Specimen Numbering** & **1** & **2** & **3** & **4** & **5** & **6** & **7** \\ \hline Vmac & 2.9787 & 2.9916 & 2.9943 & 2.9946 & 2.9950 & 2.9968 & 2.9987 \\ Dmac & 0.8583 & 0.8514 & 0.8372 & 0.6983 & 0.6956 & 0.6909 & 0.6950 \\ Measured strength & 10.2068 & 13.4162 & 17.5577 & 21.5947 & 21.3907 & 28.0236 & 33.3838 \\ Forecast strength & 10.0549 & 13.287 & 17.3615 & 21.5414 & 21.5848 & 28.0728 & 33.3795 \\ error & 1.48\% & 0.96\% & 1.11\% & 0.24\% & 0.90\% & 0.17\% & 0.01\% \\ \hline \hline \end{tabular}
\end{table}
Table 11: Statistics of the strength prediction results of non-test group sandstone specimens.  
Figure 7: Regression analysis results of measured strength and predicted strength of materials.  
size and the proportion of macroporous pores have a good correlation with their respective factors and compressive strength. Therefore, the percentage of macropore and the fractal dimension of macropore pore size are selected as representative parameters of the prediction model.  
(3) The sandstone-like strength prediction model established in this study has high correlation coefficient and small MAPE. The compressive strength of non-test group specimens predicted by the strength model is close to the measured strength of the indoor test, the model has high reliability, and it could be used to predict the compressive strength of sandstone-like materials.  
In this study, some limitations still exists. The slurry-aggregate transition interface has a great influence on the macroscopic mechanical properties of sandstone-like materials. Therefore, it should be taken into account as an important internal microstructure in the subsequent research on the internal relationship between the microscopic characteristics and the macroscopic mechanical properties of sandstone.  
Conceptualization, H.D., G.T. and S.Y.; formal analysis, H.D. and G.T.; funding acquisition, G.T.; investigation, Z.J., Z.Z. and Y.Z.; methodology, H.D., G.T. and S.Y.; project administration, H.D.; writing--review and editing, S.Y. All authors have read and agreed to the published version of the manuscript.  
This work was financially supported by the National Natural Science Foundation of China under Grant number 51874352 and Graduate Research Innovation Project of Central South University under Project number 20192 zts985.  
The authors declare no conflict of interest.