## 3 Results and Discussion  
### Interfacial Shear Characteristics  
#### 3.1.1 The Effect of Surface Hardness on Interfacial Shear Characteristics  
The interfacial shear stress-shear displacement relationship curves for different surface hardness conditions with the same particle size are shown in Figure 5. The following results were obtained: (1) under different surface hardness conditions, the interfacial shear stress-shear displacement curve showed softening behavior where there was an obvious peak shear stress that was due to the smooth surface of the model pile in this test. The interfacial shear failure was a sliding failure along the model pile surface.  
Figure 5: \(Cont.\)  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sand Type** & **Particle Size \(d\)/mm** & **Model File** & **Surface Roughness/mm** & **Surface Hardness HV** \\ \hline \multirow{2}{*}{Fine sand} & \multirow{2}{*}{0.11} & \#45 steel pile & 0.0002 & 660 \\  & & Aluminum alloy pile & 0.0010 & 350 \\  & & Polymethyl methacrylate pile & 0.0008 & 95 \\ \hline \multirow{2}{*}{Medium sand} & \multirow{2}{*}{0.41} & \#45 steel pile & 0.0002 & 660 \\  & & Aluminum alloy pile & 0.0010 & 350 \\  & & Polymethyl methacrylate pile & 0.0008 & 95 \\ \hline \multirow{2}{*}{Coarse sand} & \multirow{2}{*}{0.69} & \#45 steel pile & 0.0002 & 660 \\  & & Aluminum alloy pile & 0.0010 & 350 \\ \cline{1-1}  & & Polymethyl methacrylate pile & 0.0008 & 95 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Test scheme.  
(2) In the case of the PMMA pile, when the interfacial shear stress reached its peak after increasing with increasing shear displacement, there were obvious fluctuations in the interfacial shear stress, and the shear stress-shear displacement curves of the coarse sand and PMMA pile showed characteristics of softening and then hardening. [PERSON] and [PERSON] [25] and [PERSON] et al. [31] argued that at normal stress, when the surface was softer, the contact area between the soil particles and the structure was larger. Thus, the surface of the structure was more susceptible to the plowing effect during the interfacial shear process, which was mainly manifest in the form of scratches and tears and increased surface roughness of the structure. Compared with the #45 steel pile and aluminum alloy pile, the surface of the PMMA pile was softer. The surface roughness of the PMMA pile increased with increasing shear displacement, which resulted in scratches and tears on the model pile surface, and the interfacial shear stress fluctuated. The plowing effect between coarse sand and PMMA pile is more significant during the interfacial shear process. Thus, the interfacial shear stress-shear displacement curve of coarse sand and the PMMA piles showed the characteristics of first softening and then hardening.  
(3) The initial slope of the interfacial shear stress-shear displacement curve (initial interfacial shear stiffness) increased with increasing surface hardness for different particle sizes. For example, in the case of fine sand, the initial shear stiffness of the interface was 626.5 kPa/mm for #45 steel piles, 219.5 kPa/mm for aluminum alloy piles, and 76.4 kPa/mm for PMMA piles.  
(4) The peak interfacial shear stress increased as the surface hardness decreased for different particle sizes. In the case of fine sand, the peak interfacial shear stress was 16.3 kPa for #45 steel, 22.2 kPa for aluminum alloy, and 45.1 kPa for the PMMA, which was due to the increase in contact area between soil particles and structure surface as the surface hardness decreased under normal stress, and the plowing effect was enhanced, which increased interfacial shear stress.