## 2 Materials and Methods
### Methods  
A GDS ring shear apparatus was used in this study, modified by replacing the original rotational mold with a new mold set that allows the sand sample to interface with a continuum during the shearing test, as shown in Figure 4. The new mold set comprises two main components: the shearing mold and the interface plate. The shearing mold features a ring-shaped channel with a depth of 7.8 mm and a width of 15 mm, where the sand sample is placed. The interface plate is installed on the bottom side of the ring shear apparatus, positioned beneath the shearing mold. The continuum material is attached to the surface of the plate, interfacing with the sand sample.  
The choice of the Ring Shear Test over the Direct Shear Test is driven by several key advantages that align with the objectives of our study. The Ring Shear Test apparatus allows for continuous shearing of soil samples until a residual shear strength condition is achieved. This continuous shearing capability is crucial for investigating both peak and residual shear strengths, which are central to our study. The Direct Shear Test, with its limited travel distance, often fails to provide reliable residual shear strength measurements. Additionally, the Ring Shear Test ensures a more uniform distribution of normal and shear stresses along the shearing plane, reducing edge effects that are common in Direct Shear Tests. This uniformity leads to more accurate and representative measurements of shear  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & **\(\mathbf{R_{t}}\) (\(\mathbf{\mu}\)m)** & **HD** \\ \hline Steel & 4.2 & 112.2 \\ PVC & 0.45 & 50 \\ Stone & 82.92 & 795 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Properties of the continuous surfaces used in the study.  
Figure 3: Types of continuous surfaces used in the experiments: (**a**) steel, (**b**) PVC, and (**c**) stone.  
strength parameters. Our study requires an understanding of interface behavior under large deformations. The Ring Shear Test apparatus is designed to handle large displacements without the boundary condition limitations of the Direct Shear Test, making it more suitable for our research. Furthermore, the shearing conditions in the Ring Shear Test more closely simulate the continuous shearing experienced in many field situations, such as landslides or prolonged soil-structure interactions. This relevance to real-world conditions enhances the practical applicability of our findings.  
The testing procedure, as shown in Figure 5, involved conducting tests on normal stresses of 25, 50, and 100 kPa applied to each sand sample for each continuum, resulting in a total of 90 tests. The tests were conducted at a constant rotational rate of 0.5 mm/min.  
Figure 4: The modified ring shear apparatus.  
Figure 5: The testing procedure was used to measure the peak and residual interface shear strength at different normal stresses.  
The sand-raining method was utilized to achieve the desired initial soil density by pouring sand through a vertical pipe into the testing mold, allowing the grains to settle naturally under gravity. In this procedure, sand is dropped from a height of one meter to produce a dense sample and from zero distance to produce a loose specimen. Table 3 presents the density of used sand in both loose and dense states during the steel interface tests under 25 kPa.