# Application of a Geotextile in the Treatment of Post-Subsidence in Karst Areas
## 3 Validation of the Numerical Modeling  
The numerical modeling was validated by scaled data based on similarity and the test data of the model test [31; 32] by comparing the results of the soil pressure and the tensile force for the geotextile at different anchorage ratios \(L/B\). To quantify the settlement of soil beneath the geotextile as \(S\), according to the subsidence width \(B\), the relative settlement \(d\) was proposed in Equation (2):  
\[d=S/B \tag{2}\]  
where \(d\) is relative settlement as a percentage, \(S\) is the downward movement of the soil with respect to \(d\) in m, and \(B\) is the subsidence width in m.  
Figure 4 shows the final state of the subsidence simulation for using a geotextile for the treatment of subsidence. In Figure 4a, the final state of the subsidence simulation in model test is shown, corresponding with the time that the movable bottom plate was separated from the model geotextile. The final relative settlement \(d\) for the anchorage length of the geotextile for \(L=2.0B\) was 7% in the model test. Figure 4b shows the final state of the subsidence simulation in the numerical modeling. The subsided soil in the subsidence area beneath the geotextile separated from the geotextile when its displacement was specified as 100 mm, which was considered as the final state of the subsidence simulation. The final relative settlement \(d\) for the anchorage length of \(L=2.0B\) was 6.7% in the numerical modeling, and the value was close to that of the model test. Figure 5 presents a comparison between the results of the numerical modeling and model test at the final state of subsidence for the condition that \(L=2.0B\). Figure 5a shows similar trends for the variation of soil pressure beneath the geotextile at \(L=2.0B\) for the two tests. The soil pressure rapidly increased from zero at the subsidence area to the stable area and then gradually decreased in the stable area as the horizontal distance from the subsidence area increased. Figure 5b shows a comparison of the tensile force for the geotextile at \(L=2.0B\) between the two tests. Similar trends were observed for both the numerical test and model test. The tensile force of the geotextile in the subsidence area was greater than that in the stable area, and it decreased rapidly from subsidence area to the stable area. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Variation**} & **Numerical** & **Subsidence** & **Anchorage Length of** & **Anchorage Ratio,** & **Buried Depth of** \\  & **Model** & **Width, \(B\) (mm)** & **Geotextile, \(L\) (mm)** & \(L/B\)** & **Geotextile, \(H\) (mm)** \\ \hline \multirow{4}{*}{Anchorage length of geotextile} & M1 & 1500 & 0 & 0 & N.A. \\  & M2 & 1500 & 375 & 0.25 & 5000 \\ \cline{1-1}  & M3 & 1500 & 525 & 0.35 & 5000 \\ \cline{1-1}  & M4 & 1500 & 750 & 0.50 & 5000 \\ \cline{1-1}  & M5 & 1500 & 1125 & 0.75 & 5000 \\ \cline{1-1}  & M6 & 1500 & 1500 & 1.00 & 5000 \\ \hline \multirow{4}{*}{Buried depth of geotextile} & M7 & 1500 & 850 & 0.57 & 2000 \\ \cline{1-1}  & M8 & 1500 & 850 & 0.57 & 3000 \\ \cline{1-1}  & M9 & 1500 & 850 & 0.57 & 4000 \\ \cline{1-1}  & M4 & 1500 & 850 & 0.57 & 5000 \\ \cline{1-1}  & M7 & 1500 & 850 & 0.57 & 6000 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Numerical modeling program. Figure 5c illustrates a comparison of the relative settlement \(d\) for different anchorage ratios \(L/B\) of 0, 0.25, 0.5, 1.0, and 2.0 between the numerical tests and model tests. Similar  
Figure 4: Final state of the subsidence simulation for using a geotextile for the treatment of subsidence: (**a**) model test; (**b**) numerical modeling. Figure 5: Comparison between the results of the numerical modeling and the model test at the final state of subsidence: (**a**) soil pressure beneath the geotextile at \(L=2.0B\); (**b**) tensile force for the geotextile at \(L=2.0B\); (**c**) relative settlement \(d\) for different anchorage ratios \(L/B\).