## 3 Results
### Test Results and Analyses of Large-Sized Granular Materials
#### 3.2.3 Test Results and Analyses of Large-Sized Granular Materials  
Figure 11 presents the images of fractured particles collected following the large-scale triaxial tests on glass beads. Glass beads with a diameter exceeding 10 mm exhibited varying degrees of fragmentation. A summary of fragmentation amounts for different bead diameters is provided in Table 4. By comparing the breakage of particles with different diameters, the relationship between particle interactions and material strength can be more effectively elucidated. From Table 4, it is evident that the glass beads of all sizes remained intact under a confining pressure of 100 kPa. However, under higher confining pressures, the extent of particle breakage varied significantly depending on the particle size. Particle breakage can influence the strain and strength characteristics of the materials. To quantify the particle breakage observed in shear tests of large-sized glass bead materials, the particle breakage rate (\(B_{t}\)) was employed for analysis and research, based on the concept of limit gradation proposed by [PERSON] [45]. The expression for \(B_{t}\) is given by Equation (3). \[B_{r}=\frac{B_{t}}{B_{p}} \tag{3}\]  
Figure 10: Relationship between shear strength parameters and \(d\) of each group of large-sized granular particles. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Particle Diameter (mm)**} & \multicolumn{3}{c}{**Shear Strength Parameters**} \\ \cline{2-3}  & \(\mathbf{c}\) **(kPa)** & \(\mathbf{\varphi}\) (\({}^{\circ}\)) \\ \hline
10 & 35.33 & 29.21 \\
15 & 22.54 & 30.27 \\
20 & 29.73 & 31.45 \\
25 & 39.63 & 31.35 \\
30 & 29.95 & 32.10 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The shear strength parameters of large-sized granular materials with different sizes. In the equation, \(B_{t}\) represents the area enclosed by the initial particle gradation curve before the experiment and the particle gradation curve after the experiment; \(B_{p}\) represents the area enclosed by the initial gradation curve and the limiting gradation curve. As shown in Figure 12, \(B_{t}=S_{1}-S_{0}\); \(B_{p}=S_{2}-S_{0}\). The value of \(B_{\rm r}\) varies between 0 and 1, where \(B_{r}=0\) indicates that no particle breakage occurs, and \(B_{r}=1\) indicates complete breakage of the material. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(d\) (mm) & \(\sigma_{3}\) (kPa) & \begin{tabular}{c} **Total Mass of** \\ **Design Specim** \\ **\(M_{\rm d}\) (kg)** \\ \end{tabular} & \begin{tabular}{c} **Total Mass of** \\ **Actual Specim** \\ **\(M_{\rm f}\) (kg)** \\ \end{tabular} & \
\begin{tabular}{c} **Mass of Unbroken** \\ **Particles \(M_{\rm u}\) (kg)** \\ \end{tabular} &
\begin{tabular}{c} **Mass Percent of** \\ **Crushed Particles** \\ **\(P_{\rm t}\) (\%)** \\ \end{tabular} \\ \hline \multirow{4}{*}{15} & 100 & & 63.266 & 63.266 & \multirow{4}{*}{0} \\  & 200 & 63.278 & 63.268 & 63.268 & & \\  & 300 & 63.271 & 63.271 & & \\  & 400 & & 63.272 & 61.722 & & \\ \hline \multirow{4}{*}{20} & 100 & & 62.800 & 62.800 & \multirow{4}{*}{0} \\  & 200 & 62.791 & 62.791 & 62.791 & & \\  & 300 & 62.801 & 62.801 & 61.099 & & \\  & 400 & & 62.795 & 54.029 & & \\ \hline \multirow{4}{*}{25} & 100 & & 62.412 & 62.412 & \multirow{4}{*}{0} \\  & 200 & 62.425 & 62.025 & & \\  & 300 & & 62.422 & 59.419 & & \\  & 400 & & 62.420 & 53.313 & & \\ \hline \multirow{4}{*}{30} & 100 & & 61.922 & 61.922 & \multirow{4}{*}{0} \\  & 200 & 61.920 & 61.929 & & \\ \cline{1-1}  & 300 & 300 & 61.915 & & 60.367 & \\ \cline{1-1}  & 400 & & 61.924 & & 56.673 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Particle breakage of large-sized glass bead specimens. Figure 11: Particle breakage observed in the large triaxial test (broken particles are highlighted with red circles). Figure 12: Schematic diagram illustrating the particle breakage rate \(B_{\rm r}\). The area under each grading curve can be calculated using the area integration method proposed by [PERSON] [45]. The calculation formulas are given in Equations (4) and (5). \[