## 4 Extended Parameter Analysis
### Finite Element Numerical Model
#### 4.1.3 Numerical Model Verification  
Two strengthened specimens, RP-0 and RP-1, were selected as the basic models to establish the corresponding numerical models, MRP-0 and MRP-1. The numerical sim  
Figure 17: Constitutive relationship curves of concrete and steel bar. (**a**) Stress-strain curve of concrete; (**b**) Stress-strain curve of steel bar.  
Figure 18: Finite element model. (**a**) Steel reinforced cage model after assembly; (**b**) Strengthened concrete pier column model after assembly; (**c**) Mesh division.  
ulation was performed according to the protocol of the cyclic displacement-control load shown in Figure 8. The accuracy and effectiveness of the finite element numerical model in Section 4.1.2 were verified by comparing the failure modes, skeleton curves, stiffness degradation curves, bearing capacity, and ductility between the test specimens and numerical models.  
The stress cloud diagrams of the numerical models MRP-0 and MRP-1 after load failure were compared with the failure phenomena that appeared in the quasi-static test as follows (Figure 19). (a) The stress distribution of the steel rebars shows that the bottom longitudinal rebars and stirrups reached their ultimate stress when the pier column was damaged, consistent with the phenomenon in which the longitudinal rebars were pulled to fracture, and the stirrups buckled at the bottom of the strengthened specimens. (b) The stress distribution of the core pier column indicated that the concrete at the bottom reached the maximum compressive stress, corresponding with the crushing and spalling of the concrete at the bottom of the strengthened specimens. (c) Similarly, as indicated by the stress distribution of the filled concrete, the maximum stress at the bottom of the filled concrete during the failure of the pier column matched the occurrence of concrete cracking and spalling at the bottom of the filling layer of the strengthened specimens. (d) As observed in the stress distribution of the segment sleeve, the maximum stress of the segment ring concrete in the middle of the sleeve was consistent with the loosening of the circumferential connection and vertical cracking of the segments in the middle of the strengthened specimens.  
Figure 19: Stress cloud diagrams of numerical models after load failure (**a,b**).  
As shown in Figures 20 and 21 and Table 6, (a) the skeleton curves of the numerical models were similar to those of the strengthened specimens. When the strengthened specimen reached the lateral bearing capacity, the downward trend of its skeleton curve was consistent with that of the numerical model, whereas the degradation rate of its bearing capacity was relatively high, and the maximum error between the skeleton curves was \(<\)15%. (b) The secant stiffness and stiffness degradation of strengthened specimens were relatively consistent with those of the numerical models, and the difference between the stiffness degradation curves was \(<\)10%. (c) The relative errors in the lateral bearing capacity and ductility coefficient between the strengthened specimens and numerical models were \(<\)5% and 10%, respectively, indicating that the specimens and models were in good agreement. Therefore, the numerical model corresponded well with the strengthened specimen, indicating that it can be used as a basic model for extended parameter analysis.  
Figure 21: Comparison of stiffness degradation curves between test specimens and numerical models. (a) Secant stiffness of RP-0 and MRP-0; (b) Secant stiffness of RP-1 and MRP-1.  
Figure 20: Comparison of skeleton curves between test specimens and numerical models. (a) Skeleton curves of RP-0 and MRP-0; (b) Skeleton curves of RP-1 and MRP-1.