# Interface Behavior Analysis of Different Geomembrane Liner Systems Based on PIV Techniques
## 3 Results and Discussion
### Model \(p\)-s Curve Analysis  
The \(p\)-s curves under different rib shapes, rib spacings \(d\), and rib heights \(h\) were analyzed in this section. The \(p\)-s curves of the strip and block ribbed geomembrane were similar to the variation of rib spacings and rib heights. Therefore, the following section focuses on analyzing the \(p\)-s curves of block ribbed geomembranes under different rib spacings \(d\) and rib heights \(h\). Figure 4 shows the effect of different rib shapes on the \(p\)-\(s\) curve. From Figure 4a-c, it can be seen that the ribbed geomembrane effectively reduced the settlement of the liner system model compared with the smooth geomembrane. In addition, the settlement of the strip ribbed geomembrane liner system was smaller than that of the block ribbed geomembrane liner system in each working condition. The settlement difference was maximum at \(d\) = 60 mm. On one hand, compared with block rib, strip rib had a larger friction force when sliding with the soil, as well as a more robust extrusion and occlusal effect, thus providing a more significant passive impedance force. On the other hand, the end-bearing resistance of ribs increased the overall stiffness of the surrounding soil to a greater extent and then reduced the settlement. As shown in Figure 5, when the rib spacing increased from 50 to 60 mm, the settlement of corresponding rib height \(h\) = 3 mm, 4.5 mm, and 6 mm decreased by 8.88%, 24.63%, and 8.73%, respectively. It could be seen that when the rib height was too high, the reinforcement mechanism would be weakened. The reason was the rib height made the geomembrane bond too closely with the soil above it, resulting in a shear plane at the lower edge of the geomembrane, thus increasing the settlement. When the rib spacing was further increased to 80 mm, the corresponding settlement increased by 35.8, 57.57, and 27.04%. It could be seen that when the rib spacing was too high, it also had the opposite effect, which was directly caused by weakening the stiffening mechanism. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Test Conditions**} & & & \\ \multirow{2}{*}{**Rib Shape**} & **Rib Spacing** & **Rib Height** & \multirow{2}{*}{\(S\) (mm)} & **Reduction** \\  & \(d\) (mm) & & \(h\) (mm) & \\ \hline Smooth & / & / & 5.39 & / \\ \hline \multirow{6}{*}{Strip rib} & \multirow{3}{*}{50} & 3 & 3.63 & 35.25 \\  & & 4.5 & 3.43 & 36.36 \\  & & 6 & 3.98 & 26.16 \\ \cline{2-5}  & \multirow{3}{*}{60} & 3 & 3.45 & 36.01 \\  & & 4.5 & 3.11 & 42.30 \\  & & 6 & 3.41 & 36.73 \\ \cline{2-5}  & \multirow{3}{*}{80} & 3 & 4.25 & 21.15 \\  & & 4.5 & 4.3 & 20.22 \\  & & 6 & 4.45 & 17.44 \\ \hline \multirow{6}{*}{Block rib} & \multirow{3}{*}{50} & 3 & 3.49 & 35.25 \\  & & 4.5 & 3.41 & 36.73 \\  & & 6 & 4.01 & 25.60 \\ \cline{2-5}  & \multirow{3}{*}{60} & 3 & 3.18 & 41.00 \\  & & 4.5 & 2.57 & 52.32 \\  & & 6 & 3.66 & 32.09 \\ \cline{2-5}  & \multirow{3}{*}{80} & 3 & 4.32 & 19.85 \\  & & 4.5 & 4.05 & 24.86 \\  & & 6 & 4.67 & 13.35 \\ \hline \hline \end{tabular} Note: The reduction in the model settlement of the ribbed geomembrane relative to that of the smooth geomembrane was calculated as \(\Delta=1S_{\text{Rib}}-S_{\text{Smooth}}\,1/S_{\text{Smooth}}\times 100\%\).  
\end{table} 
Table 3: Analysis of settlement under different conditions. The above test results show that the rib shapes, rib spacings \(d\), and rib heights \(h\) directly affected the reinforcing effect of the ribbed geomembrane on the sand. Within a specific range, the influence of the rib shapes was inconspicuous when the rib spacing was small, and the settlement of the strip ribbed geomembrane liner system decreased with the increase in the rib spacing. The friction and interlocking forces of the ribs on the sand increased with the increase in the rib spacing \(d\) and rib height \(h\). However, the complex formed by the ribs and the surrounding sand exceeded the limit value for the reinforcing effect of the ribs.