*4.3. Prediction of Effective Length Considering Pullout Force*

The pullout force distribution in the geosynthetic strip occurred within a limited reinforcement length range. Therefore, it will be possible to achieve a more economical design if the effective length at which the pullout resistance is induced by the pullout force is calculated. The relationship between the pullout force and Li/L (as shown in Figure 10) can be simplified as shown in Figure 11, and it is possible to be used to reflect the experimental results. As mentioned previously, in the cases of GS50W and GS70W, the pullout forces of the reinforcement at normal stress conditions became almost similar at a length ratio (Li/L) of approximately 0.5 L. Subsequently, the induced pullout force decreased and then hardly changed after 0.75 L, at which the strain became approximately 1%. Therefore, the effective length of the geosynthetic strips used in this study was determined as follows: the effective length (LE = 0.5 L) was defined as the length at which the pullout force became almost similar, regardless of the normal stress, and the maximum effective length (LE(max) = 0.75 L) as the distance at which the pullout force hardly changed.

**Figure 11.** Prediction of effective length using the pullout force generated in reinforcement cases.

#### *4.4. Evaluation of Pullout Resistance Considering the Prediction of Effective Length*

To evaluate the effective length prediction method presented in Section 4.3, the pullout strength was evaluated according to the effective length (LE) and maximum effective length (LE(max)), respectively, based on the use of the average resistance method proposed by [23]. The pullout strength was evaluated using the total and effective area methods based on consideration of the extensibility of the geosynthetic strips, and the results are shown in Figure 12 and Table 3.

**Figure 12.** Relationship between normal stress and pullout strength: (**a**) GS50W; (**b**) GS70W.

Regarding the pullout strength of GS50W based on considerations of the maximum effective length (LE(max)), the results of the effective area method and total area method were similar at low normal stress conditions because the pullout force was transmitted to the maximum effective length (LE(max)). However, as the normal stress increased, the pullout strength gradually increased because the pullout force transmitted to the maximum effective length (LE(max)) decreased. For GS50W, the effective area method that considered the effective length (LE) yielded a higher pullout strength in normal stress conditions compared with the total and the effective area methods that considered the maximum effective length (LE(max)) because the distance from the front decreased. The same tendency was observed for GS70W.

**Table 3.** Summary of pullout parameters.


The pullout strengths of GS50W and GS70W with respect to the reinforcement width were compared. GS50W and GS70W exhibited similar pullout strengths based on the total area method. The pullout strength obtained by the effective area method, however, showed that the reinforcement width had an influence on the soil-reinforcement interface adhesion. This was more obvious when the effective length (LE) was applied.

Figure 13 shows the calculation results of the bond coefficient of the geosynthetic strips using the shear strength of the soil and the pullout strength ratio of the soil-reinforcement interface. For all evaluation methods, the bond coefficient slowly decreased and then exhibited a tendency to converge as the normal stress increased. Tatlisoz et al. [33] reported that the soil-reinforcement interface adhesion was sufficient when the bond coefficient was 1.0, and the adhesion was low when the bond coefficient was 0.5 or less. For GS50W and GS70W, the bond coefficient was the lowest when the normal stress was 150 kPa; the respective values were 0.88 and 0.80 in the case of the total area method, respectively. These values are higher than the friction coefficient of soil (0.71) and are, thus, considered stable. Therefore, for a more efficient design of geosynthetic strips, the effective length (LE) and maximum effective length (LE(max)) can be considered. However, it is reasonable to apply the effective length (LE) because there is no significant difference in the pullout force between the effective length (LE) and maximum effective length (LE(max)).

**Figure 13.** Relationship between normal stress and bond coefficient: (**a**) GS50W; (**b**) GS70W.
