## 4 Axial Compression Bearing Capacity
### Bearing Capacity Calculation Model  
According to the results of the tests and extended numerical analysis, the calculation method used for the axial compression bearing capacity of concrete members strengthened involving the enlarging section method found in [24], and [PERSON]'s study on the axial compression bearing capacity of self-stressed, concrete-filled steel tube columns [28], the calculation model for the axial compression bearing capacity of specimens strengthened by IPCSAM was established. In light of the structure and working characteristics of the components strengthened by the IPCSAM, the following assumptions were made on the bearing capacity calculation model of the IPCSAM reinforcement members:  
1. The bearing capacity of the strengthened specimens was composed of three parts: the bearing capacity of the unreinforced column and the filled concrete, the bearing capacity improved by the confinement provided by the sleeve and the filled concrete, and the bearing capacity improved by self-stress;
2. The bearing capacity of the column and the filled concrete was calculated according to the calculation method of the code in [24]. In [24], the bearing capacity of strengthened components was equal to the axial compression bearing capacity of the column plus 80% of the axial compression bearing capacity of the filled concrete. In this test, the larger the filled concrete, the greater the error, so the utilization coefficient of the filled \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Name**} & **Filled Concrete** & **Longitudinal** & **Segment Concrete** & **Peak Load** \\  & **Strength** & **Stress** & **Strength** & **(kN)** \\  & **(MPa)** & **(MPa)** & **(MPa)** & **(MPa)** \\ \hline M-1 & 21.7 & 0.8 & 20.9 & 2578 \\ M-2 & 21.7 & 1 & 20.9 & 2695 \\ M-3 & 21.7 & 1.2 & 20.9 & 2802 \\ M-4 & 21.7 & 1 & 23.4 & 2810 \\ M-5 & 21.7 & 1 & 26.8 & 2876 \\ M-6 & 21.7 & 1 & 32.4 & 2992 \\ M-7 & 23.4 & 1 & 20.9 & 2771 \\ M-8 & 26.8 & 1 & 20.9 & 2859 \\ M-9 & 32.4 & 1 & 20.9 & 2955 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Material parameters of the extended models. concrete needed to be adjusted. The contribution of the LCSS on the bearing capacity of the specimens was neglected to simplify the calculation;
3. According to the calculation method in [29], the improved bearing capacity of the sleeve and filled concrete constraints was calculated. As a result, the confinement coefficient was used to consider the improvement of the bearing capacity of the axial compression;
4. According to [28], the calculation method used to improve the bearing capacity through self-stress and the relationship between the improved bearing capacity and the self-stress level (the ratio of the self-stress value to the strength of the SSAWC) involved cubic equations. According to this method, the tensile stress generated by the self-stress shall be less than the tensile bearing capacity of the sleeve concrete, so the self-stress shall not be greater than 2 MPa;
5. According to the design data for previous bridges, the concrete strength grade of the substructure mostly did not exceed C30, so it was assumed that the concrete strength grade of the columns was not greater than C30. At the same time, the substructures constructed years ago had low reinforcement ratios and there were issues related to bar exposure and corrosion. Therefore, the reinforcement of the columns was ignored. Based on assumption (1), the calculation formula for the axial compression bearing capacity of the strengthened specimens (\(N\)) was proposed as follows:  
\[N=N_{0}+N_{s}+N_{p} \tag{1}\]  
where \(N_{0}\), \(N_{s}\), and \(N_{p}\) are the bearing capacity of the column and the filled concrete, the bearing capacity improved by the confinement, and the bearing capacity improved by self-stress, respectively.