## 4 Validation of Proposed Empirical Model
### Discussion of Results  
Figure 10 shows the compressive strengths and strains of unconfined and confined concrete cylinders tested in the previous study [35]. The average stress-strain curves of experimental cylinders were plotted against the FEA results. The experimental results confirmed the increase in strength and ductility with the increasing number of FRP layers. It was observed that the increase of 69.42% and 87.20% occurred in axial strength of confined concrete of 12.5 MPa strength for single and double wraps of FRP, respectively and an increase of 60.82% and 103.20% occurred for 16.5 MPa concrete with single and double wraps of FRP, respectively as compared with plain concrete specimens. Similarly, the axial strain of cylinders was increased by 409.26% and 277.78% using single layer of FRP and 464.81% and 459.72% using double \begin{table}
\begin{tabular}{l c} \hline \hline
**Property** & **Value** \\ \hline \hline \
\begin{tabular}{l} Longitudinal modulus of elasticity, \(E_{1}\) (GPa) \\ Transverse modulus of elasticity, \(E_{2}\) (GPa) \\ Longitudinal-transverse Poisson’s ratio, \(v_{12}\) \\ Shear moduli \(G_{12}\), \(G_{13}\), \(G_{23}\) (MPa) \\ \end{tabular} &
\begin{tabular}{l} 230 \\ 16.583 \\ 0.3 \\ 9188.5, 12259, 5911 \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Elastic behavior of FRP. Figure 10: Stress-strain curves of (**a**) unconfined concrete cylinder and (**b–f**) confined concrete cylinders. \begin{table}
\begin{tabular}{l c} \hline \hline
**Property** & **Value** \\ \hline \hline Tensile strength in fiber dir. (MPa) & 3900 \\ Compressive strength in fiber dir. (MPa) & 3120 \\ Tensile strength in transverse dir. (MPa) & 210.6 \\ Compressive strength in transverse dir. (MPa) & 643.5 \\ Shear Strength in longitudinal dir. (MPa) & 210.6 \\ Shear Strength in transverse dir. (MPa) & 276.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Damage variables of Hashin’s Model. layer of FRP with 12.5 MPa and 16.5 MPa, respectively. This discussion shows that the confinement is effective in low strength concrete for both strength and ductility of concrete. The average percentage discrepancies between the experimental and FEA results of FRP confined concrete cylinders were 14.93% and 16.93% for axial strength and axial strain, respectively. These discrepancies may be due to the minor inaccuracies due to the difference between actual and testing and boundary conditions, assumptions made during FEA and the accuracy of the testing instruments. However, the overall experimental stress-strain curves of all the cylinders were predicted accurately by the FEA results showing that the selected constitutive FEA model can be utilized for the simulations of FRP-confined concrete. The crack patterns of some specimens obtained from FEA results are shown in Figure 11. The finite element crack patterns were represented through maximum principal plastic strains because the concrete damaged plasticity model (CDPM) assumes that the cracks in the concrete start when there is a positive value of maximum principal plastic strain. The FEA cracks in concrete can also be represented by tensile principal stresses [2; 46]. Figure 11 represents the cracking patterns of a plain concrete cylinder, a double-layered FRP cylinder with strength of 12.5 MPa and two cylinders with single and double layers of FRP sheets having the concrete strength of 16.5 MPa. It can be visualized that the FEA crack patterns are in a close agreement with the experimental cracks proving that the FEA software ABAQUS accurately predicted the behavior of FRP-wrapped concrete. The FEA cracks decrease with less expansion of concrete cylinders as the confinement thickness increases which is experimentally true. The average percentage discrepancies of the predictions of proposed empirical strain model from experimental and FEA results were 13.51% and 37.81%, respectively, which shows that the proposed model can predict the strain of FRP-confined concrete.