## 4 Discussion  
### Localization and Characteristic Length  
Localization in compression is an applied fracture mechanics problem and has been observed to happen in concrete, among other materials [65; 66; 67; 68; 69; 70]. [PERSON] and [PERSON] [67] carried out an experimental investigation on compression failure localization in normal- and high-strength concrete cylinders with H/D ratios going from 2 to 5.5, reporting that the total length of the failure zone of the longer specimens became consistent at about three times the specimen diameter. In an extensive experimental study on localized failure in concrete specimens with H/D ratios going from 2 to 8, [PERSON] et al. [34] identified three zones: (i) a failure zone (ii) a transition zone and (iii) an unloading zone. The length of the failure zone was found to be more or less constant of the order of 1.5D, whereas the lengths of the transition and the unloading zones were found to be dependent on the slenderness ratio. In their proposal for a stress-strain model for uniaxial and confined concrete under compression, [PERSON] and [PERSON] [70] carried an extensive review of previous work, identifying the shortcomings. They proposed a new model that defines a characteristic length for the development of a Compression Damage Zone (CDZ), as defined by [PERSON] and [PERSON] [66], whereby this characteristic length was estimated at about 2.5 times the width of the specimen and the cracking displacement of the concrete specimen is mainly due to deformation in the localized shear band [71]. [PERSON] et al. [42] verified the localization of failure in FRP-confined concrete cylinders, both experimentally and numerically. [PERSON] and [PERSON] [29] examined, experimentally, the localized failure in confined and unconfined concrete columns of 150 mm in diameter, with H/D going from 2 to 4.66 at six different levels of confinement. They confirmed the localization of failure and the development of a failure zone. They also observed that post peak deformation is independent of H/D for ratios greater than two and proposed a new analytical stress-strain model that accounts for localization and calculates the length of the failure zone [72]. The results presented in Figures 5-8 agree well with the published literature on experimental observations and measurements and offer a qualitative explanation for the increase in compressive strength and the effects of the stiffness of the wrap [73; 74; 75; 76; 77; 70; 5; 77; 71; 70; 5; 78; 79; 5; 7]. The results indicate the existence of a characteristic length, Lc, independent of the level of confinement that is necessary for the localization and development of an unconstrained failure mechanism or solid wedge mechanism. This characteristic length is best seen when comparing the results for H/D = 4 and H/D = 6 between Figures 7  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Cylinder** & **Number of** & \begin{tabular}{c} **Peak Axial** \\ **Normalized** \\ **Stress** \\ \end{tabular}  & \begin{tabular}{c} **Peak Axial** \\ **Strain (\%)** \\ \end{tabular}  & \begin{tabular}{c} **Average** \\ **Hoop Strain** \\ **(\%)** \\ \end{tabular}  & \ \begin{tabular}{c} **Maximum** \\ **Hoop Strain** \\ **Ratio** \\ \end{tabular}  & \begin{tabular}{c} **Hoop Strain** \\ **Ratio** \\ \end{tabular}  \\ \hline \(150\times 150\) & 1 & 1.69 & 2.14 & 1.20 & 1.52 & 0.790 \\ \(150\times 150\) & 2 & 2.19 & 2.37 & 1.24 & 1.52 & 0.815 \\ \(150\times 150\) & 4 & 3.18 & 2.78 & 1.27 & 1.52 & 0.838 \\ \(150\times 150\) & 6 & 4.16 & 3.14 & 1.27 &and 8. The total length available in the H/D = 6 specimen is sufficient to develop four successive mechanisms of length equal to the characteristic length giving Lc/D = 1.5. Depending on the length of the confined concrete cylinder, a number of fully localized failure mechanisms can develop, each one of them then witnessing solid wedge movements along a shear frictional surface, causing stress concentrations in the FRP wrap and thus precipitating its premature failure.