## 3 Results and Analysis  
### Displacement and Velocity During Sliding Process  
Unlike unloading slip behavior of rock joints [28; 30], the mechanical behavior of the tested dry sands during the normal unloading process is more complex. The displacement of the shear box does not change for one minute during Stage II, where the normal and shear forces remain constant. When the unloading begins, the corresponding frictional sliding does not start immediately. We define the corresponding moment when the shear box begins to move as'start time', \(t_{i}\), and the corresponding moment when the shear box reaches the maximum velocity as the 'end time', \(t_{j}\). The values of \(t_{i}\) and \(t_{j}\) recorded in the tests are shown in Table 3.  
The variation curves of normal displacement and sliding displacement versus experimental time are drawn in Figure 3, based on the original data recorded by the shear device for each test (Group A and Group B). Figure 4 illustrates the results of sliding velocity as a function of elapsed time for each test, from the beginning moment of normal unloading (i.e., the slopes of sliding displacement vs. time curve). As can be seen from the lower part of Figure 3, the sliding displacement does not increase uniformly over time. More related details can be seen in Figure 4. During the early seconds of normal unloading, the sliding velocity fluctuates (except for test B5), and in some tests the velocity value drops to zero, i.e., the sliding deceleration or intermission occur absolutely in the experiment, but the shear box accelerates persistently in the last seconds of normal unloading. Also, the slope change in sliding displacement has a strong correlation with the normal displacement.  
For our test apparatus, the maximum moving velocity of the horizontal piston is around 3.7 mm/s. Therefore, when the sliding velocity reaches 3.7 mm/s, the test will automatically be stopped, so the final vertical ordinate values of the curves in Figure 4 are the same. Note that even at the fastest sliding rate, the acceleration of the shear box is still minimal, and the unbalanced force of the shear test system (acceleration times total mass) is negligible. This is consistent with the anticipation in Section 2.2 that the shear force of the granular matter is the force on the horizontal loading cell, i.e., the constant value that we set.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Tests** & **No.** & **Start Time (s)** & **End Time (s)** \\ \hline \multirow{8}{*}{Group A} & A1 & 152.2 & 221.2 \\  & A2 & 137.4 & 194.6 \\ \cline{1-1}  & A3 & 127.5 & 160.3 \\ \cline{1-1}  & A4 & 125.6 & 151.8 \\ \cline{1-1}  & A5 & 125.1 & 147.4 \\ \cline{1-1}  & A6 & 125.1 & 143.3 \\ \cline{1-1}  & A7 & 123.1 & 139.0 \\ \cline{1-1}  & A8 & 123.3 & 139.6 \\ \cline{1-1}  & B1 & 134.0 & 191.1 \\ \cline{1-1}  & B2 & 134.9 & 183.5 \\ \cline{1-1} Group B & B3 & 132.9 & 172.0 \\ \cline{1-1}  & B4 & 131.2 & 168.2 \\ \cline{1-1}  & B5 & 127.6 & 136.4 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The timing that sliding begins (‘start time’) and ends (‘end time’).  
Figure 3: Normal force variation as function of elapsed time and experimental results of normal and sliding displacement versus time for each test. (**a**) Normal force, normal displacement, and sliding displacement versus time for different unloading rates (Group A). (**b**) Normal force, normal displacement, and sliding displacement versus time for different shear force (Group B).