## 4 Discussion  
### Comparison with Previous Formulas  
The semiempirical formulas for calculating the unit membrane penetration proposed by [PERSON] and [PERSON], [PERSON], [PERSON] and [PERSON] and [PERSON] et al., are shown in Equations (6)-(9), [6, 24, 25, 26]. \[\text{[PERSON] and [PERSON] : }\epsilon_{m}=0.16d_{g}\bigg{(}\frac{Pd_{g}}{E_{m}t_{m}} \bigg{)}^{\frac{1}{3}} \tag{6}\]  
\[\text{[PERSON] and [PERSON] : }\epsilon_{m}=0.125d_{g}\bigg{(}\frac{Pd_{g}}{E_{m}t_{m}} \bigg{)}^{\frac{1}{3}} \tag{7}\]  
\[\text{[PERSON] and [PERSON] : }\epsilon_{m}=0.231d_{g}\bigg{(}\frac{Pd_{g}}{E_{m}t_{m}} \bigg{)}^{\frac{1}{3}} \tag{8}\]  
\[\text{[PERSON] et al. : }\epsilon_{m}=0.66d_{g}(1+e)^{4}\bigg{(}\frac{1-\alpha}{4M} \bigg{)}^{\frac{1}{3}}\bigg{(}\frac{Pd_{g}}{E_{m}t_{m}}\bigg{)}^{\frac{1}{3}} \tag{9}\]  
where \(a=\)0.732\(d_{g}(1+e)^{\frac{1}{3}}\), \(\alpha=0.15\bigg{(}\frac{P_{g}}{E_{m}t_{m}}\bigg{)}^{\frac{1}{3}}\), and \(M=324.7\alpha^{4}+237.3\alpha^{2}-3.5\alpha+20.2\). Based on these semiempirical formulas, the relationships between the unit membrane penetration and confining pressure are shown in Figure 8a-c. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**SG**} & \multicolumn{6}{c}{**Diameter [mm]**} \\ \cline{2-6}  & \multicolumn{2}{c}{**100**} & \multicolumn{2}{c}{**200**} & \multicolumn{2}{c}{**300**} \\ \hline
**Confining Pressure [kPa]** & **SG1** & **SG2** & **SG1** & **SG2** & **SG1** & **SG2** \\ \hline
100 & 51.6 & 69.4 & 31.2 & 51.8 & 25.1 & 42.6 \\
200 & 45.1 & 68.2 & 29.7 & 51.4 & 21.6 & 41.6 \\
300 & 40.8 & 64.9 & 27.6 & 47.9 & 19.2 & 38.1 \\
400 & 40.0 & 63.8 & 27.3 & 45.7 & 18.8 & 36.7 \\
600 & 42.7 & 60.7 & 27.8 & 44.1 & 20.1 & 34.1 \\
800 & 40.5 & 57.6 & 26.5 & 41.7 & 18.8 & 31.5 \\
1000 & 40.1 & 53.5 & 25.2 & 41.2 & 18.3 & 28.9 \\
1200 & 39.1 & 52.7 & 24.6 & 39.6 & 17.7 & 28.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Proportion of membrane penetration for SG (%). For the rockfill materials, the overall trends of membrane penetration calculated by the semiempirical formulas are the same (see Figure 8a). In other words, the unit membrane penetration increases with the increasing confining pressure. Meanwhile, the calculation results of Equations (6)-(8) are smaller than the test results, and the calculation result of Equation (8) is close to that of the measured data. Figure 8b,c shows relationships between the experimental unit membrane penetration and the calculated value of SG considering the changes of confining pressure. In contrast to other methods, the results of the semiempirical formula proposed by [PERSON] and [PERSON] are close to the experimental data. In general, the prediction results of the previous semiempirical formulas of the two materials are quite different, and this may be related to different parameters used in these formulas. The theoretical formula proposed by [PERSON] et al. is related to the median particle size d\({}_{50}\), pressure, and void ratio e [26]. Equations (6)-(8) are based on the median particle size d\({}_{50}\) and pressure. For rockfill materials, the influence of sample void ratio e on membrane penetration is much greater than that of gravel materials. Therefore, the penetration calculated by the formula proposed by [PERSON] et al. is close to the experimental value. The reason is that the edge angle of rockfill particles is clear, and the bite force and friction force between particles are large based on macroscale granulometric researches [4; 5; 6]. The particles are not easy to slide and roll under certain confining pressure, so that the fine particles in the sample cannot be filled into the voids of coarse particles in time. However, the particle shape of the sandy gravel is oval or round, so that the fine particles within sandy gravel are prone to sliding and  
Figure 8: Relation curves of unit membrane penetration versus confining pressures: (**a**) RM, (**b**) SG1, (c) SG2. rolling.