## 2 Theoretical Background on Pullout Resistance  
### Pullout Resistance of Reinforcement  
The internal stability of a reinforced earth wall should be evaluated on the basis of the stability of tensile failure and pullout failure. Inextensible reinforcement has significantly higher stability of tensile failure because its tensile strength is greater than that of extensible reinforcement. However, the stability of pullout failure differs from the evaluation factor of pullout resistance according to whether a transverse member is installed. Therefore, the mechanisms of the longitudinal and transverse members depend on resistance type. If transverse members do not exist, only friction resistance is considered; otherwise, friction resistance due to the longitudinal member and the bearing resistance due to the transverse member should be considered [9; 13]. Therefore, the pullout resistance of reinforcement should be evaluated from pullout test results. Over the last few years, many experimental tests and theoretical studies were carried out to follow up on the pullout mechanism of reinforcement [10; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23]. [PERSON] et al. [8] and [PERSON] [21] proposed theoretical equations on friction resistance and bearing resistance. [PERSON] et al. [9; 14; 24] and [PERSON] et al. [25; 26] evaluated the pullout behavior and bearing resistance of transverse members on a steel grid. The total pullout resistance of reinforcement (\(P_{p}\)) can be expressed as follows [13]:  
\[P_{p}=2\ L_{r}\ W_{r}\ \sigma_{v}\ f_{b}\ tan\beta, \tag{1}\]  
where \(f_{b}\) is the bond coefficient; \(\sigma_{v}\) is the effective normal stress in the soil to the reinforcement surface; \(L_{r}\) and \(W_{r}\) are the length and width of the reinforcement providing bond (i.e., being pulled out), respectively; and \(\varnothing\) is the internal friction angle of the soil.  
Total pullout resistance can be divided into friction \(P_{p(fr)}\) and bearing resistance \(P_{p(lr)}\), and these are expressed in Equations (2) and (3), respectively [13].  
\[P_{p(fr)}=2\ \alpha_{s}\ L_{r}W_{r}\ \sigma_{v}\ tan\delta, \tag{2}\]  
where \(\alpha_{s}\) is the fraction of the reinforcement plan area; \(A_{r}=\ L_{r}W_{r}\), which is solid (i.e., the plane reinforcement surface area); and \(\delta\) is the friction angle between soil and reinforcement.  
\[P_{p(br)}=\left(\frac{L_{r}}{S}\right)\ W_{r}\ \alpha_{b}\ B\ \sigma_{b}^{\prime}, \tag{3}\]  
where \(\alpha_{b}\) is the fraction of each bearing surface area \(W_{r}\ B\), available for bearing (loss of area due to connections), \(B\) is the thickness of transverse members, \(L_{r}/S\) is the number of bearing surfaces, and \(\sigma_{b}^{\prime}\) is the bearing resistance stress of the transverse member. From Equations (1)-(3), the general expression for the bond coefficient is [13].  
\[f_{b}=\alpha_{s}\left(\frac{tan\delta}{tan\varnothing}\right)+\ \left(\frac{\alpha_{b}\ B}{S}\right)\ \left(\frac{\sigma_{b}^{\prime}}{\sigma_{v}}\right)\ \frac{1}{2\tan\varnothing}. \tag{4}\]  
Generally, the inter-relation between the pullout resistance strength and maximal pullout force of reinforcement can be calculated in order to evaluate the pullout parameters as follows:  
\[\mathrm{P_{r}}=2\ \tau_{\mathrm{P}}\ \mathrm{W_{r}L_{r}}, \tag{5}\]  
where \(\mathrm{P_{r}}\) is maximal pullout force and \(\tau_{\mathrm{P}}\) is pullout strength.  
The pullout-resistance mechanism of the improved reinforcement can be explained as follows. First, the connection pin (transverse member), of which the number of transverse members ranges from 1 to 3, is inserted into the punched smooth steel strip. Second, longitudinal members have friction resistance with the existing smooth steel strip reinforcement. Bearing resistance between soil and reinforcement is also increased because the inserted transverse members have an anchor effect in the soil. Therefore, pullout-resistance characteristics should be analyzed for two resistance types.