## 6 Discussion  
### Influence of the Natural Soils Internal Stability on Retention Capability  
The prediction of nonwoven geotextile filtration opening size proposed by [PERSON] [35] was used to evaluate the variation of filtration opening size of geotextile under different normal stresses:  
\[\frac{O_{f}}{d_{f}}=\frac{1}{\sqrt{1-n}}-1+\frac{\xi n}{(1-n)t_{GT}^{\prime}/d _{f}} \tag{7}\]  
where \(O_{f}\) is the geotextile filtration opening size \(O_{95}\), \(d_{f}\) is the fiber diameter, \(n\) is the geotextile porosity, \(t_{GT}^{\prime}\) is the geotextiles thickness under different normal stresses according to EN ISO 9863-1 [36], and \(\xi\) is the empirical parameter, \(\xi=10\).  
The retention ratio, \(R_{r}=O_{95}/D_{n}\), is commonly used to assess the retention capability of a given soil-geotextile system. \(D_{n}\) is the particle size of the tested soil, and \(D_{85}\) or \(D_{50}\) are the most commonly used representative particle sizes. The existing fine-grained soil retention criteria provide the upper limit of soil retention for nonwoven geotextile, i.e., \(O_{95}/D_{85}\leq 2\)-\(3\), or \(O_{95}/D_{50}\leq 18/Cu\)[37; 38; 39; 40].  
Figure 9 shows a plot of fine particles retained \(\eta\) against \(O_{95}/D_{n}\) for tests on two natural soils and geotextiles based on the above theoretical calculation of nonwoven geotextile filtration opening size. The relationship between \(\eta\) and \(O_{95}/D_{n}\) illustrates that \(R_{r}\) controls the onset of piping or erosion. The amount of fine particles retained was very sensitive to increases in the retention ratio. The results, although not as comprehensive as desired, showed no significant consistency with the existing soil retention criterion for an  
Figure 8: Relationship between fine particles retained and normal stress acting on soil–geotextile combinations.  
less than about 3.6, or an \(O_{95}/D_{50}\) less than about 16.3. They did support a relationship between filtration opening size and fine-grained soil particle size for soil retention. As the \(R_{\rm r}\) with a small variation range, the characteristic particle size \(D_{85}\) was a more sensitive indicator of retention for silty clay than \(D_{50}\), while \(D_{85}\) or \(D_{50}\) was a more sensitive indicator of retention for silt than \(D_{15}\). Furthermore, the retention ratios of silt were found to be significantly smaller than those of silty clay. Although the silt soil-geotextile combination showed a larger amount of fine particles retained inside geotextiles (Figure 9b). This indicated that internally unstable silt allowed fines to move freely through the coarse particles, resulting in a greater amount of fine particles retained.  
A \(GR\) value greater than one was obtained for both tested soils with nonwoven geotextiles (GT2, GT4) during different normal stress stages, indicating that the soil-geotextile interface was less permeable than the base soil, i.e., \(k_{\rm gg}<k_{\rm g}\) (Tables 7 and 8). Although the  
Figure 9: The amount of fine particles retained in the \(\eta\) and \(O_{95}/D_{n}\) ratios: (**a**) C-GT2/GT4 combinations; (**b**) M-GT2/GT4 combinations.  
retention ratios of GT4 were lower than those of GT2, GT4 retained more fine particles than GT2. This was due to the fact that GT4 had a smaller filtration opening size \(O_{95}\) and a larger thickness \(t_{GT}\) than GT2. Moreover, this difference in response could be attributed to the thicker GT4, which trapped fines inside the smallest constrictions in the geotextile and subsequently hampered the movement of migrating particles within the fabric.