## 3 Materials and Methods
### Test Results and Analysis  
A series of isotropic consolidation drained (CD) tests of RM and SG were conducted by the aforementioned triaxial apparatus. According to the results of the isotropic CD test, the relationship between the confining pressure and the volume of drained water under different diameters is shown in Figure 6a-c. It can be seen that, with the increasing confining pressure, the measured volume change showed a hyperbolic increase. The larger the diameter, the more obvious the measured volume change increases. This is because the contact area between the specimen and rubber membrane increases significantly with the diameter of specimen increasing. With the increasing confining pressure, the penetration depth of the rubber membrane around the specimen increases, thus the measured volume change increases. Under the same gradation curve conditions, the volume change of RM is much greater compared to that obtained in test SG2. This can be attributed to the different lithology of coarse-grained soil. Meanwhile, as shown in Figure 6b,c, as the particle size increases, the measured volume change of the sandy gravel increases. According to Equation (1), the relationship between \(\Delta V_{\text{T}}(P)/A_{\text{m}}\) and the diameter \(D\) can be established (as shown in Figure 7a-d). It is found that, with the increasing confining pressure, the ratio of \(\Delta V(P)/A_{\text{m}}\) increases, and there is a good linear relationship between \(\Delta V(P)/A_{\text{m}}\) and \(D\). Note that, in Figure 7, the fitted line is extended to intersect the vertical axis, and the intercept of the fitting straight line is the unit membrane penetration. Consequently, the unit membrane penetration under different confining pressures can be calculated. Figure 6: Measured volume change under different confining pressures: (**a**) RM, (**b**) SG1, (**c**) SG2. According to the calculation method of membrane penetration proposed in this paper (Equation (5)), the ratio of membrane penetration to the total volume change for rockfill materials and sandy gravel under different pressures and grain sizes are shown in Tables 2 and 3. Regarding the influence of membrane penetration of RM, it can be seen in Table 2 that the proportion changes slightly as the confining pressure increases, and has a tendency to decrease when the diameter is the same. However, under the same confining pressure, the membrane proportion decreases sharply. Compared with the specimen with a diameter of 100 mm, the proportion of membrane penetration with a diameter of 300 mm decreases from 32.1% to 13.7%, the proportion is reduced by 57.5% on average in the range of pressures from 100 kPa to 600 kPa. The results show that the diameter of the sample has a great \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**RM** & \multicolumn{5}{c}{**Diameter [mm]**} \\ \hline
**Confining Pressure (kPa)** & **100** & **150** & **200** & **250** & **300** \\ \hline
100 & 32.1 & 25.6 & 17.2 & 16.1 & 13.7 \\
200 & 39.4 & 29.4 & 21.1 & 20.5 & 15.9 \\
300 & 33.5 & 27.4 & 20.3 & 18.8 & 14.6 \\
400 & 32.1 & 25.6 & 19.8 & 17.0 & 14.0 \\
600 & 30.8 & 23.3 & 17.5 & 15.1 & 13.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Proportion of membrane penetration for RM (%). Figure 7: Membrane penetration from multiple triaxial specimens during hydrostatic loading: (a) formula fitting(RM), (b) formula fitting (SG2), (c) formula fitting(SG1), (d) comparison of unit membrane penetration. influence on the membrane penetration. It is recommended to use specimens of larger size to reduce the proportion of membrane penetration in the triaxial test. Meanwhile, the proportion of membrane penetration of SG is larger than that of RM, as can be seen in Table 3. The subsequent loading of confining pressure will lead to the rearrangement of internal particles, so that voids among large particles are filled with fine particles, and the samples are compacted. With the increase of confining pressure, the proportion of membrane penetration decreases gradually.