# Effect of the Surface Roughness on the Shear Strength of Granular Materials in Ring Shear Tests
## 3 Results
### Peak Shear Strength as a Function of Shear Velocity  
From the shear stress and shear displacement relationships, the peak and residual shear strengths could be determined. The maximum and minimum shear strengths were clearly determined from the strain-softening behaviors of materials such as dense sands or over-consolidated clays. According to [PERSON] et al. [33], there appears to be no shear rate effect for low and high plasticity clays when relatively low shear rates ranging from \(10^{-6}\) to \(10^{-3}\) mm/s are imposed on the slip surface. In this study, the strain-hardening behavior was dominant for a given drainage and shear velocity; thus, only the peak shear strength (i.e., the final shear stress) could be determined. For convenience, the value at the end of each test was selected. In this context, the ultimate shear strength and residual shear strength could not be determined. For a dense sandy soil-steel interface, [PERSON] et al. [6] demonstrated that as the roughness increases, the shear strength and friction at the peak increase, but those at the residual state essentially remain unchanged. The latter may be characterized by the thickness of the crushed grain band and the fine content in a shear zone. For gravel, the shear zone thickness can be affected by a relatively high shear speed (e.g., 300 cm/s, as tested by [PERSON] et al. [26]) and cyclic motion with surface roughness [10]. [PERSON] and [PERSON] [10] demonstrated that a large shear deformation can result in a remarkable thickness of the crushing band near the soil-structure interface for gravelly soils with a mean grain size of 7 mm. In our study, this thickness of the crushing band increased up to a maximum of 24 mm depending on the shear applied, but it reached a stable state if a large amount of shear deformation occurs.  
In general, the shear resistance increases with increasing shear velocity [34; 35]. Figure 5 shows the dependence of the peak shear strength on the shear velocity. Regardless of the drainage condition, the values were similar at the same roughness. At the lowest shear velocity, i.e., 0.1 mm/s, the difference varied from 0.3 kPa to 1.5 kPa. However, at the medium shear velocity, i.e., 0.5 mm/s, the difference varied from 11.7 kPa to 14.6 kPa. Compared to the lowest shear velocity, the change in shear resistance increased 10-fold. At the highest shear velocity, i.e., 1 mm/s, the difference varied from 5.2 kPa to 14.7 kPa. The difference in average values of shear strength (\(\Delta\)v) obtained from smooth and rough surfaces for each shear velocity were 1, 12, and 10 mm/s, for 0.1, 0.5, and 1 mm/s, respectively. The largest difference was found at the shear velocity of 0.5 mm/s, meaning that this shear velocity may induce an abrasion and fracture-dominant process not present in the 0.1 mm/s shear condition. Interestingly, in the drained condition, the shear strength at 1 mm/s was almost identical to that at 0.5 mm/s. However, in the undrained condition, the difference may have decreased by as much as 5 kPa. Hence, in the undrained condition, the water in the shear zone played an important role in shearing when measuring the torque in the ring shear test.  
Figure 5: Peak shear strength as a function of the shear velocity.