## 2 FE Model and Validation
### Validation of Modeling Method
#### 2.2.2 Shear Links  
The hysteretic model proposed by [PERSON] et al. [41], as shown in Figure 6, is adopted to simulate the nonlinear behavior of the shear links between the columns. The prominent features of [PERSON]'s model [40] are as follows: (1) The yielding, hardening and softening behavior are considered, as well as the pinching and strength and stiffness deterioration effects under cyclic loading; (2) different positive and negative yield strengths can be represented. Previous research [41; 42; 43] indicates that the hysteretic model can efficiently simulate the nonlinear behavior of various components, especially a successful  
Figure 4: Numerical model of self-centering pier.  
Figure 5: Comparison of the hysteretic curves of the self-centering pier.  
application in the simulation of shear links in tall buildings [42]. Consequently, the hysteretic model is adopted in this study to simulate the shear links between columns.  
The model is mainly controlled by the following parameters: (1) \(C\), a dimensionless accumulated hysteretic energy dissipation parameter that reflects the capacity of resisting strength degradation caused by the cyclic loading; (2) \(\gamma\), a parameter representing the pinching effect; (3) \(\omega\), a parameter representing the position of the end point of slip; (4) \(\alpha_{\mathrm{k}}\), a parameter defining unloading stiffness; (5) \(K_{0}\), initial stiffness; (6) \(F_{\mathrm{y}}\), yield strength; (7) \(\eta\), hardening ratio; (8) \(\eta_{\mathrm{soft}}\), softening ratio; and (9) \(\alpha\), the ratio of peak strength to yield strength. These parameters can be divided into two categories: parameters (1)-(4), namely, the backbone curve parameters, describing the force-displacement backbone curve under the cyclic lateral load; and parameters (5)-(9), namely, the hysteretic parameters, specifying the hysteretic rules. The experiment conducted by [PERSON] et al. [44] is employed to calibrate the hysteretic parameter values.  
When \(C=1500\), \(\gamma=0.9\), \(\omega=-0.01\), \(\alpha_{\mathrm{k}}=0\), the hysteretic curve of the shear link simulated using the hysteretic model [41] agrees well with the curve obtained from the experiment, which is shown in Figure 7.  
Figure 6: Hysteretic model to simulate shear links [41].  
Figure 7: Comparison of the hysteretic curves of the shear link.  
Performance of Double-Column Self-Centering Piers with Shear Links under Quasi-Static Cyclic Loading  
An FE model of the double-column self-centering piers with shear links was built based on the modeling method presented in Section 2. Each column has a height of 3.00 m with a 2.00 m \(\times\) 2.00 m cross section, and the clear distance between the columns is 3.00 m. The steel strand in each column has a total area of 15424 mm\({}^{2}\) and an initial stress of 1395 MPa. Further, a vertical concentrated load of \(3.08\times 10^{4}\) kN is applied at the bent cap to simulate the superstructure gravity. Grade C60 concrete (Chinese concrete grade, standard uniaxial unconfined compressive strength \(f_{\mathrm{c}}\) = 38.5 MPa, standard elastic modulus \(E_{\mathrm{c}}\) = \(3.6\times 10^{4}\) MPa) is adopted, while 15.2 mm diameter strands (ultimate strength \(f_{\mathrm{PT}}\) = 1860 MPa, elastic modulus \(E_{\mathrm{s}}\) = 195 GPa) are used for unbonded prestress steel strands. The initial stiffness and yield strength of the adopted shear link are 6.0\(\times\)105 kN/m and \(1.4\times 106\) kN, respectively. The responses of the piers under quasi-static cyclic loading are discussed in this section.