*2.1. Bridge Main Structure Model*

This paper establishes afinite element model with ABAQUS software to carry out a structural dynamic nonlinear time-history analysis, considering the non-uniform collision response between the expansion joints of the curved continuous girder bridge and the nonlinearity of the piers, damping devices and supports.

The superstructure of the bridge is a reinforced concrete box girder. Because of the asymmetrical collision response between the expansion joints, the use of beam elements is not applicable. Considering the solid element integral model, the three-dimensional solid reduction integral element C3D8R is used to simulate the bridge deck [28]. In order to better simulate the collision response without excessive calculation workload, the bridge deck main girder uses the multi-scale method to divide the grid [29]. Refining the grid at the expansion joint, the grid size near the expansion joint is 0.18 m, and the grid size at other parts is 0.50 m. The pier adopts a separated model; the three-dimensional solid reduction integral element C3D8R is used to simulate the concrete; the two-node bar element T3D2 is used to simulate the reinforcement [28].

The concrete intensive grade is C40, and the concrete damage plasticity model is used as the constitutive model [30], which describes the stiffness degradation of concrete during an earthquake through the tensile and compressive damage factors. For C40 concrete, the modulus of elasticity is 3.25 × 10<sup>4</sup> N/mm2, the density is 2400 Kg/m3, and the Poisson's coefficient recommended is 0.2. In the plastic phase of concrete material, the stress-strain relationship and damage factor of the constitutive model are shown in Table 1. Furthermore, the characteristics of the longitudinal and transverse reinforcement bars are defined based on the bilinear elastic-plastic model shown in Figure 3. The elastic modulus of the longitudinal reinforcement and transverse reinforcement bars is 2.0 × 10<sup>5</sup> N/mm<sup>2</sup> and 2.1 × 10<sup>5</sup> N/mm2, respectively, and the yield strengths are 360 N/mm<sup>2</sup> and 270 N/mm2, respectively. The limit strain is recommended to be 0.1; the density is 7850 Kg/m3, and the Poisson's coefficientis 0.3. At the strengthening stage, the elastic modulus Eh is 1/100 of the initial elastic modulus Es.

**Table 1.** Calculation parameters of concrete damage plasticity model.


**Figure 3.** Constitutive model of reinforcement bar.
