## 4 Finite Element Analysis  
In this paper, ABAQUS (ABAQUS Inc., Pawtucket, RI, USA) finite element software is used for numerical simulation analysis. The steel tube and stiffener are based on an S4R shell element, and the concrete is based on a C3D8R solid element. The base is defined as a rigid body. A cubic rigid body with a 528 mm side length and a 20 mm thickness is created at the top of the steel tube column to apply a uniform vertical load to the specimen. The length of foundation is 1800 mm, width 900 mm, and height 600 mm. The height of the column is 1270 mm and the outer diameter of the tube is 508 mm. As specimen failure occurs at the column base, the top is essentially in an elastic state during the test. Therefore, the column top structure is simplified in the model. The specimen boundary conditions are as follows: the translational and rotational degrees of freedom of the base in three directions are fixed, and a 32.93 kN/m\({}^{2}\) uniform vertical load is applied to the pressure bearing plate at the top to achieve a constant resultant force of 9180 kN during the test. Cyclic horizontal displacement is applied to the column top. The displacement load history is the same as in the test. The finite element model has the same stress mechanism as the test. Steel and rebar are based on an elasticity enhancement model, as shown in Figure 14a. The stress-strain relationship of the hardening section is simplified as an oblique line. The yield load and yield strain are based on actual measurements. The test results of material properties indicated that E\({}_{s}\)\({}^{\prime}\approx\) 0.01 E\({}_{s}\). The Poisson ratio is set to 0.3, and the strengthening type is kinematic hardening. The core concrete is based on the stress-strain relational model proposed by [PERSON] [24], which considers the constraint effect coefficient, as shown in Figure 14b,c. Figure 14b shows the compression constitutive relation of circular steel tube core concrete. Figure 14c shows the tensile constitutive relation of concrete. The Poisson ratio of concrete is set to 0.2. In ABAQUS, the nominal stress \(\sigma_{\text{norm}}\) and nominal strain \(\varepsilon_{\text{norm}}\) should be converted to real stress \(\sigma_{\text{true}}\) and real strain \(\varepsilon_{\text{true}}\) via formulae \(\sigma_{\text{true}}=(1+\varepsilon_{\text{norm}})\)\(\sigma_{\text{norm}}\) and \(\varepsilon_{\text{true}}=\ln(1+\varepsilon_{\text{norm}})\)[25]. The concrete plasticity parameters are based on the concrete plastic damage model provided by ABAQUS [26]. The relevant parameters are shown in Table 7.  
Figure 14: Constitutive relationship of materials. (**a**) steel and rebar; (**b**) compression of concrete; and (**c**) tension of concrete. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dilation Angle** & **Eccentricity** & **fb0/fc0** & **K** & **Viscosity Parameter** \\ \hline
30 & 0.1 & 1.16 & 0.6667 & 0.005 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Parameters of CDP. The degradation of the elastic stiffness is characterized by two damage variables, \(d_{t}\) and \(d_{c}\), which are assumed to be functions of the plastic strains. As shown in Formulas (3) and (4):  
\[d_{t}=1-\frac{\sigma_{t}}{E_{0}(\varepsilon_{t}-\widetilde{\varepsilon}_{t}^{pl })} \tag{3}\]  
\[d_{c}=1-\frac{\sigma_{c}}{E_{0}(\varepsilon_{c}-\widetilde{\varepsilon}_{c}^{ pl})} \tag{4}\]  
where the subscripts \(t\) and \(c\) refer to tension and compression, respectively; \(\widetilde{\varepsilon}_{t}^{pl}\) and \(\widetilde{\varepsilon}_{c}^{pl}\) are the equivalent plastic strains. \(E_{0}\) is the initial modulus of the material. Stiffness degradation variable curves are shown in Figures 15a and 15b. \(\widetilde{\varepsilon}_{t}^{\backtimes k}\) is the cracking strain and \(\widetilde{\varepsilon}_{c}^{in}\) is the inelastic strain. The contact between the steel tube and concrete is defined as the surface-to-surface contact.