## 2 Theoretical Background  
The compressive strength ratio of confined concrete to unconfined concrete derived from the experiment on concrete confined using structural steel and proposed by [PERSON] et al. is presented in Equation (1) [15]. Based on the experimental research by several researchers [9; 16; 17; 18; 19], Equation (1) has been proven to be applicable for predicting the strength of concrete confined by FRP. \[\frac{f_{cc}}{f_{co}}=1.00+k_{1}\left(\frac{f_{l}}{f_{co}}\right)\,, \tag{1}\]where, \(f_{\alpha}\) is compressive strength of confined concrete, \(f_{\alpha}\) is that of unconfined concrete, \(k_{1}\) is the confinement effective coefficient, and \(f_{\rm f}\) is the confining pressure. According to [PERSON] et al. [15], the confinement effectiveness coefficient \(k_{1}\) is 4.1 if concrete is sufficiently reinforced by the structural steel or when a tie bar is used. However, \(k_{1}\) varies according to the experimental results of different studies when concrete is confined by FRP. The confinement effectiveness coefficients proposed by various studies are summarized in Table 1.  
From Equation (1), \(k_{1}\) presented in Table 1 signifies that the correlation between the strength ratio and the confinement ratio becomes linear if expressed as constants and nonlinear if expressed as a function of the confining pressure and concrete strength. In Table 1, the coefficients proposed by [PERSON] et al. and [PERSON] et al. [17; 19] are based on the experimental results when a cylindrical FRP tube is filled with concrete, while those proposed by other researchers are based on the experimental results when a concrete column is wrapped with FRP. The axial confinement of a CFFT tube refers to the pressure generated by the confined material when a transformation occurs in the radial direction as the material expands in the direction orthogonal to the circumferential direction (radial direction) owing to a compressive load. The mechanical behavior of CFFT confinement is determined by the degree of concrete expansion and the strength and rigidity of the confining member suppressing the expansion. When the CFFT tube is under a compressive load, the stress in the radial direction and the confining stress due to the reinforcement become parallel in the ultimate state, as shown in Figure 1, thus establishing the relationship defined in Equation (2). \[{\rm f}_{\rm f}=\frac{2f_{p}\cdot t}{d}=\frac{\rho_{p}\cdot f_{p}}{2}\, \tag{2}\]  
\[\rho_{p}=\frac{\pi dt}{\frac{\pi d^{2}}{4}}=4\frac{t}{d}. \tag{3}\]  
Here, \(f_{\rm f}\) is the confining pressure, \(f_{p}\) is the tensile strength in the circumferential direction of the external reinforcement constituting the exterior, \(t\) is the reinforcement thickness, and \(\rho_{p}\) is the volume ratio of the inner concrete to external reinforcement, and \(d\) is diameter defined in Equation (3). The confining pressure (Equation (1)) is expressed as a function of the strength and thickness of the confining material, while the confining effect is influenced by the mechani \begin{table}
\begin{tabular}{c c c c c} \hline
**[PERSON] et al. [16]** & **[PERSON] et al. [17]** & **[PERSON] et al. [18]** & **[PERSON] et al. [19]** & **[PERSON] [9]** & **[PERSON] et al. [20]** \\ \hline \(2.10\ (f_{\rm f}/f_{\alpha})^{-0.12}\) & \(6.00\ f_{\rm f}^{-0.2}\) & \(2.98\) & \(2.20\ (f_{\rm f}/f_{\alpha})^{-0.16}\) & \(\begin{array}{c}3.50\\ (f_{\rm f}/f_{\alpha})^{-0.15}\end{array}\) & \(2.00\) \\ \hline \end{tabular}
\end{table} 
Table 1: Confinement effective coefficient of concrete-filled fiber-reinforced polymer tube (CFFT), \(k_{1}\). Figure 1: Confinement effect of fiber-reinforced polymer (FRP). cal properties of the confined and confining materials. The compressive behavior of CFFT is shown in Figure 2. The solid line shows the load-strain correlation of unconfined plain concrete, dotted line the load-strain curve for the axial compressive load of an FRP tube, and dashed line the combined effect of the FRP tube and plain concrete.