## 4 Extended Parameter Analysis
### Results of Extended Parameter Analysis  
The influencing parameters of the restoring force models for the strengthened specimens included the LCSS thickness, reinforcement ratio, strength, SSAWC self-stress, axial compression ratio, and length-diameter ratio of the pier column [48,49]. Considering that the influence of the length-diameter ratio on the hysteretic performance of the strengthened pier columns was studied in the quasi-static test, we established 20 numerical models based on the other five parameters for extended parameter analysis. We then investigated these five parameters' impact on the pier columns' seismic strengthening effect. Table 7 lists the main parameter settings for all numerical models. The other parameters, including the size, initial damage, and length-diameter ratio of the core pier column, filled concrete thickness, and segment sleeve reinforcement ratio, were set with reference to specimen RP-1 in Table 1. The material properties of the numerical models were set according to Table 3.  
reached their respective maximum values of 7.69 and 55.47 kN when the segment thickness was 30 and 40 mm, respectively. As the segment thickness increased from 40 to 50 mm, the peak load decreased gradually by 2.06%, whereas the ductility coefficient decreased rapidly by 11.38%. We inferred that an appropriate segment thickness could effectively improve the seismic performance indicators of the strengthened pier column. In contrast, an excessive segment thickness would cause intense sleeve stiffness, resulting in the core pier column and filling layer becoming the relatively seismically weak parts of the entire pier, failing before the sleeve, and weakening the bearing capacity and ductility of the pier column. Hence, the seismic strengthening effect is most advantageous for a pier column with a 400 mm diameter when the segment thickness is 40 mm (i.e., the thickness-diameter ratio is 1/10). (2) Influence of the SSAWC reinforcement ratio on the strengthening effect  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Model** & \(K_{0}\) **(kN/mm)** & \(F_{y}\) **(kN)** & \(\Delta_{y}\) **(mm)** & \(F_{p}\) **(kN)** & \(\Delta_{  
Table 8 shows that the initial stiffness and peak load of the pier column increased by 16.48% and 11.05%, respectively, as the reinforcement ratio of the filled concrete increased from 0.56% to 1.40%. The secant stiffness increased to a certain extent, and the stiffness degradation rates of all models were relatively similar (Figure 23). Hence, we concluded that an appropriate increase in the filled concrete's reinforcement ratio could enhance the core column's stiffness and hoop constraint, improving the pier column's overall stiffness and bearing capacity. Meanwhile, the ductility coefficient continuously decreased with an increase in the reinforcement ratio, generally decreasing by 20.08%, indicating that the decrease in the ductility of the pier column was much higher than the increase in the bearing capacity and stiffness. This might have been due to the high reinforcement ratio causing the filled concrete to crush before the internal steel wire meshes yielded, resulting in reduced pier column ductility. Moreover, while the reinforcement ratio of the filled concrete increased, the increases in the peak and ultimate loads of the pier column were relatively small and maintained at approximately 2-5%, as calculated from Table 8. Hence, under the premise of meeting the design requirements of the bearing capacity of strengthened pier columns, it is desirable to use the smallest possible reinforcement ratio of filled concrete to maintain good ductility, such as adopting the constructional reinforcement ratio. (3) Influence of SSAWC strength on the strengthening effect  
As shown in Table 8, with an increase in the strength grade of the filled concrete from C30 to C45, the initial stiffness and peak load of the pier column increased by 25.12% and 21.09%, respectively; however, the ductility coefficient generally decreased by 4.53%.