## 1 Introduction  
Bridges are critical infrastructure and play essential roles in transportation networks. Hence, distinctive design requirements are necessary to provide their safety during earthquakes or other severe loadings. An alternative to traditional design methods is to use structural control techniques to reduce the structural vibrations produced by external forces, such as earthquakes and winds. These methods generally change the stiffness, mass, damping coefficient, and configuration of the structure. Among various control strategies, employing the base isolators is a popular tactic due to its simplicity, high potential in decreasing the seismic demand of the structure, and high energy absorption ability. Moreover, base isolators do not require any external sources to produce forces, so they are economical. Although the base isolation systems are prevalent, they have several drawbacks. The major one is the occurrence of large inelastic deformations. These deformations may lead to the collision of two adjacent parts or unseating if the minimum required distance is not provided. Additionally, the base isolation system cannot be applied anymore after inelastic deformations, and they should be replaced with new ones. To prevent these failures, researchers suggested using additional dampers in companion with the base isolators for energy dissipation ([PERSON] and [PERSON] [1], [PERSON] and [PERSON] [2], Dicleli [3]). Recently, researchers have employed intelligent materials, such as SMAs, for the aforesaid dampers. These materials are characterized by a high damping capacity, fatigue strength, erosion resistance, and a high level of super-elastic strain. Because of the exceptional characteristics, SMAs have been widely used in civil structures, and their applications include but are not limited to restraining devices, beam-column connections, special braces, reinforcement or pre-stressing bars and strips, energy dissipating elements, and base isolation systems. In the last two decades, various researchers have focused on SMAs to enhance the seismic performance of base isolators because of their outstanding properties. To improve the seismic performance of bridges, [PERSON] et al. [4] took advantage of two different systems, including rubber bearings with SMA and rubber bearings with a lead core (LRB) and lateral bracing named an NZ device. By comparing these systems, it was observed that the former system has more damping capacity in comparison with the latter one. Additionally, using SMA, this system was able to recover its deformation. However, the force applied to the base isolator with SMA was three times more than the other one. [PERSON] et al. [5] introduced a new generation of base isolation devices in which SMA wires were wrapped around an elastomeric bearing to control the instability and residual deformations. They utilized this system in a three-span continuous bridge during an earthquake and compared the results with those of the lead core bearing. The findings proved that the rubber bearing with Nitinol shape memory alloy was able to decrease the deck displacements. Also, no residual displacement was observed. Nevertheless, in extensive shear deformations (200%), the Nitinol wire experienced plastic strains, and the device was not able to work successfully anymore. [PERSON] and [PERSON] [6] numerically investigated two different configurations of SMA wires in conjunction with elastomeric bearings. They studied the effects of various parameters, such as the shear strain amplitude, SMA type, dimension ratio of the base isolation, and the level of pre-strain of the SMA wires, on the seismic behavior of base isolators. According to their results, the wire diameters should be selected based on the lateral stiffness and equivalent viscous damping to achieve high performances. [PERSON] and [PERSON] [7] proposed a constitutive model for SMA-LRBs. They used the superposition method to decouple the effect of SMA wires and LRB.