## 3 Establishment and Validation of Finite Element Model
### Constitutive Model and Parameters for Material  
The stress-strain relationship of concrete can be determined according to the Code for Design of Concrete Structures (GB50010-2010) [26]. For concrete under uniaxial compression,  
\[\sigma_{\rm c}=(1-d_{\rm c})E_{\rm c}\varepsilon_{\rm c} \tag{5}\]  
\[d_{\rm c}=\left\{ \begin{array}{l}1-\frac{\rho_{\rm c}m}{m-1+x}\ (x\leq 1)\\ 1-\frac{\rho_{\rm c}}{\varepsilon_{\rm c}(x-1)^{2}+x}\ (x>1)\end{array} \right. \tag{6}\]  
\[\rho_{\rm c}=\frac{f_{\rm c,r}}{E_{\rm c}\varepsilon_{\rm c,r}} \tag{7}\]  
\[m=\frac{E_{\rm c}\varepsilon_{\rm c,r}}{E_{0}\varepsilon_{\rm c,r}-f_{\rm c,r}} \tag{8}\]  
\[x=\frac{\varepsilon_{\rm c}}{\varepsilon_{\rm c,r}} \tag{9}\]  
where \(\sigma_{\rm c}\) is the compressive stress of the concrete; \(\varepsilon_{\rm c}\) is the compressive strain of the concrete; \(E_{\rm c}\) is the elastic modulus of the concrete; \(\alpha_{\rm c}\) is the parameter value for the descending segment of the uniaxial compressive stress-strain curve of the concrete, determined according to \(\alpha_{\rm c}=0.157f_{\rm c}^{0.785}-0.905;f_{\rm c,r}\) is the representative value of the uniaxial compressive strength of the concrete, taken as \(f_{\rm c}=38.5\) MPa; \(\varepsilon_{\rm c,r}\) is the peak strain corresponding to the representative value of uniaxial compressive strength \(f_{\rm c,r}\), determined according to \(\varepsilon_{\rm c,r}=\left(700+172\sqrt{f_{\rm c}}\right)\times 10^{-6}\); and \(d_{\rm c}\) is the damage evolution parameter for concrete under uniaxial compression. For concrete under uniaxial tension,  
\[\sigma_{\rm t}=(1-d_{\rm t})E_{\rm t}\varepsilon_{\rm t} \tag{10}\]  
\[d_{\rm t}=\left\{ \begin{array}{l}1-\rho_{\rm t}(1.2-0.2x^{5})\ (x\leq 1)\\ 1-\frac{\rho_{\rm t}}{\varepsilon_{\rm t}(x-1)^{1/2}+x}\ (x>1)\end{array} \right. \tag{11}\]  
Figure 3: Finite element fine model of the segmental joint. \[\rho_{\rm t}=\frac{f_{\rm t,r}}{E_{\rm t}\varepsilon_{\rm t,r}} \tag{12}\] \[x=\frac{\varepsilon_{\rm t}}{\varepsilon_{\rm t,r}} \tag{13}\]  
where \(\sigma_{\rm t}\) is the compressive stress of the concrete; \(\varepsilon_{\rm t}\) is the compressive strain of the concrete; \(E_{\rm t}\) is the elastic modulus of the concrete; \(\alpha_{\rm t}\) is the parameter value for the descending segment of the uniaxial compressive stress-strain curve of the concrete, determined according to \(\alpha_{\rm t}=0.312f_{\rm t,r}^{2}\); f\({}_{\rm t,r}\) is the representative value of the uniaxial compressive strength of the concrete, taken as \(f_{\rm t}=2.85\) MPa; \(\varepsilon_{\rm t,r}\) is the peak strain corresponding to the representative value of uniaxial compressive strength \(f_{\rm t,r}\), determined according to be \(\varepsilon_{\rm t,r}=f_{\rm t,r}^{0.54}\times 65\times 10^{-6}\); and \(d_{\rm t}\) is the damage evolution parameter for concrete under uniaxial tension. In this study, the mechanical behavior of concrete is represented using the Concrete Damage Plasticity (CDP) model. This model incorporates a continuum plasticity-based damage mechanism for concrete, assuming that isotropic damage and cracking occur under both compressive and tensile stresses. The strength grade of the precast segment concrete is C60. According to the Code for Design of Concrete Structures (GB50010-2010), the compressive strength of the concrete is (\(f_{\rm c}=38.5\) MPa) and the tensile strength is (\(f_{\rm t}=2.85\) MPa). The damage factors for the CDP Model are calculated using the energy equivalence principle proposed by [PERSON] [27]. Table 1 lists the parameters for the C60 concrete damage plasticity model, and Figure 4 illustrates the damage characteristics of concrete under both compression and tension. The mechanical behavior of the rebars and bolts is modeled using a bilinear elastic-plastic constitutive model, while the bolt washers are simulated with a linear elastic constitutive model. The elastic modulus and Poisson's ratio for both bolts and washers are set at 210,000 MPa and 0.22, respectively.