## 2 Experimental Setup
### Experimental Scheme  
As illustrated in Figure 2a, the granular matter in the shear box is subjected to both vertical force (normal force \(F_{N}\)) and horizontal force (shear force \(F_{S}\)). Consequently, the shear plane in the middle of the granular specimen is subjected to a normal stress \(\sigma\) and a stable shear stress \(\tau\). In the experiment, the sliding accelerations are minimal, so the inertia force on the shear box and specimen can be ignored, i.e., the force on the horizontal loading cell is equal to the shear force. During the unloading process, the shear force is kept constant by the horizontal servo system, and the applied normal force \(F_{N}\) decreases linearly with a constant rate \(a\):  
\[F_{N}=F_{N0}-at\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(d_{10}\) (mm) & \(d_{10}\) (mm) & \(d_{10}\) (mm) & \
\begin{tabular}{c} **Uniformity** \\ **Coefficient (Cu)** \\ \end{tabular} &
\begin{tabular}{c} **Coefficient of** \\ **Curvature (C\({}_{c}\))** \\ \end{tabular} \\ \hline
0.11 & 0.22 & 0.84 & 7.64 & 0.524 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Grain properties of granular matter used in experiments.  
Figure 1: Testing apparatus and experimental materials: (**a**) the DJZ-500 shear box device; (**b**) dry sands used in tests; and (**c**) grain grading curve of the sand samples.  
According to the loading scheme illustrated in Figure 2b, the test procedure includes three stages:  
* Stage I: Load the vertical force to 20 kN at a loading rate of 40 kN/min. Then, maintain this normal force for 30 s. After that, load the shear force to the predetermined value within 20 s by activating the horizontal piston.
* Stage II: Maintain the shear force and the normal force at their respective values for 60 s, where the stress state of the whole system remains unchanged.
* Stage III: Unload the normal force linearly at a predetermined rate. The gradient of the descent line in Figure 2b equals the unloading rate. When the normal force descends to a certain level, the shear box begins to slide.  
We conducted two groups of unloading direct shear tests (Group A and Group B) at room temperature, considering two variables: unloading rate and magnitude of shear force. The parameters used in the tests are shown in Table 2. Referring to a similar experiment studying rock specimens [30], the constant shear forces used in the tests are less than the ultimate shear strength under the given normal force and greater than the shear strength under zero normal force.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Tests**} & \multirow{2}{*}{**No.**} & **Unloading Rate (kN/s)** & **Shear Force (kN)** & **Initial Shear Force (kN)** & **Maximum Sliding Velocity (mm/s)** \\ \hline \hline  & A1 & 0.08 & 10 & 20 & \\  & A2 & 0.16 & 10 & 20 & \\  & A3 & 0.32 & 10 & 20 & \\ Group A & A4 & 0.4 & 10 & 20 & \\  & A5 & 0.48 & 10 & 20 & \\  & A6 & 0.56 & 10 & 20 & \\  & A7 & 0.72 & 10 & 20 & \\  & A8 & 0.8 & 10 & 20 & \\ \hline \hline  & B1 & 0.24 & 8 & 20 & \\  & B2 & 0.24 & 9 & 20 & \\ Group B & B3 & 0.24 & 11 & 20 & 3.7 \\  & B4 & 0.24 & 12 & 20 & \\  & B5 & 0.24 & 14 & 20 & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Experimental scheme under a series of unloading rate and shear force conditions. Group A: varying unloading rate, keeping constant shear force of 10 kN. Group B: varying shear force, keeping a constant unloading rate of 0.24 kN/s.  
Figure 2: Experimental configuration: (**a**) setup of direct shear test under unloading normal force and constant shear force; (**b**) normal and shear force application scheme during three-stage loading process.