## 5 Conclusions  
In this paper, to explore the effect of the subsidence width on engineering problems of the geotextile treatment of a subgrade collapse, the half-symmetric model test has been established as well as numerical models. By comparing the full-section model test results with the half-symmetric model results, it proves that the half-symmetric model could represent the full-section model test. In addition, the optimized subsidence width was explored with ten different conditions conducted by numerical models to make up for the deficiencies of the model test work. The influence of the subsidence width on the soil  
Figure 13: Vertical displacement of the surface of the soil for different subsidence widths.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Anchorage Ratio, \(L/B\)**} & **Maximum Subgrade** & **Deformation Range of** & **The Ratio of the Maximum Subgrade Collapse** \\  & **Collapse, \(ds\) (mm)** & **the Payement, \(Ds\) (m)** & **to the Deformation Range of Payement, \(ds/Ds\)** \\ \hline
4.0 & 33.46 & 12.24 & 0.27\% \\
3.33 & 53.59 & 12.42 & 0.43\% \\
2.86 & 77.24 & 13.04 & 0.59\% \\
2.50 & 106.64 & 13.34 & 0.80\% \\
2.22 & 152.57 & 17.44 & 0.87\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: Settlement of the subgrade surface with the various anchorage ratios.  
pressure, the tensile force of the geotextile, and the settlement were analyzed. The main conclusions are as follows.  
The test data show a good consistency between the results obtained with the two models. The variation of the data curve for the half-symmetric model and the full-section model test are similar, which verifies the rationality of the half-symmetric model test. The numerical model results of the soil pressure, the tensile force of the geotextile and the soil displacement are consistent with the full-section model tests, which proves the validity of the numerical model.  
The subsidence width is an important parameter for the performance that geotextile does to treat a subgrade collapse. With the increase of the subsidence width, more loads of the subsidence area are transferred to the stable area through the geotextile, the vertical normal stress at the edge increases rapidly, the tensile force of the geotextile and the vertical soil displacement in the subsidence area increase sgsubstantially. It indicates that the geotextile treatment of a subgrade collapse is not suitable for projects with an anchorage ratio of \(L\leq 2.0B\). This recommendation for the geotextile control of a subgrade collapse solely based on the laboratory test, representing the minimum length for the geotextile treatment. The real area, shape, and depth of the subgrade collapse are different from the situation of a simulated subgrade collapse in the laboratory. More research needs to be conducted for the engineering practice application.  
Conceptualization and methodology, [PERSON] and J.W.; software and validation, Y.L. and J.W.; writing--original draft preparation, Y.L.; writing--review and editing, Y.Y. and D.W.; supervision, D.W. and Y.Y. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the National Natural Science Foundation of China Grant (No. 42067044) and the Natural Science Foundation of Guangxi Grant (No. 2022 GXNSFBA035569).  
Not applicable.  
The authors declare no conflict of interest.