## 3 Results and Analysis
### Shear Strength and Sliding Deceleration/Intermission  
The conventional direct shear tests (direct shear at a constant shear displacement rate with a constant normal force) are widely used to measure the frictional criteria of granular matters. In [PERSON]'s theory, as the peak shear strength increases linearly with larger normal stress, there are two frictional criteria: frictional angle (\(\varphi\)) and cohesion. Since the cohesion of the granular matter equals zero, the relationship between the ultimate shear stress and normal stress can be described as Equation (2). In Equation (2), \(\tau_{m}\) reflects the maximum shear capacity of the granular material, and the ratio of shear force to normal force (\(F_{s}/F_{N}\)) is friction coefficient (\(\mu\)), which equals the tangent of friction angle when the cohesion is zero (Equation (3)).  
\[\tau_{m}=\sigma\tan\varphi \tag{2}\]  
\[\mu=\tan\varphi=0.6897 \tag{3}\]  
To study the frictional criterion (friction angle) of the granular matter used in this study, we additionally perform a series of conventional direct shear tests (selected constant shear rate = 0.0833 mm/s) (Figure 5a,b). The obtained friction coefficient and friction angle are 0.6897 and 34.6\({}^{\circ}\), respectively, as shown in Figure 5b. As illustrated in Figure 5a, at the normal force of 30 kN, the shear resistance of the experimental granular material keeps increasing with a wide shear displacement range (from 0 to 25 mm), before reaching the potential peak strength \(\tau_{m}\) in Equation (2).  
The experimental results (Figure 5a) show that the shear resistance of the sands increases with higher normal load and larger shear displacement in a wide range. As the horizontal loading is being applied, the system is in a delicate state of equilibrium, which has a strong relationship with the accumulated sliding displacement. When the normal unloading begins, the upper restraint on the material is gradually relaxed and the balance tends to be broken, so the shear box moves forward in an attempt to find a new balance.  
From a mesoscopic point of view (Figure 5c), there are two kinds of effects in the sliding process: particle interlacing and normal relaxation. If the unloading effect is not taken into consideration (when the unloading rate is low) after horizontal displacement (\(\Delta d\)), the sheared particles are embedded. Then, the system coordination number (average contact number for a single particle) increases. This leads to shear shrinkage and enhances shear strength. On the other hand, normal unloading makes the compressed particles bounce up and reduces the contact force (the darker balls in Figure 5c) between the particles, and the  
Figure 4: Sliding velocity versus time for each test since the beginning moment of normal unloading. (**a**) Sliding velocity versus time for different unloading rates. (**b**) Sliding velocity versus time for different shear force.  
shear resistance may disappear. Within a certain unloading range, the effect of particle slip embedding may be greater than that of unloading, resulting in sliding velocity fluctuation and even sliding pause. Nevertheless, if the unloading rate or shear force is relatively high, the unloading effect will play a dominant role. In this case, there will be no obvious sliding deceleration/intermission phenomenon. The corresponding change in the normal displacement confirms our conjecture. Meanwhile, at the accelerating stage of sliding, the granular matter needs to slide rapidly to achieve the required shear force.