## 1 Introduction  
Earthquake is a main threat of buildings in their lifecycle. With increasing of seismic demand, destruction of buildings, especially buildings with important functions such as hospitals, power stations and landmark buildings, is necessary to avoid. Therefore, seismic performance of structures subjected to rare and even very-rare earthquakes needs further improvement. Isolation structure is a proven resilient structure system, which can better withstand given ground motion hazards. Various isolation techniques are widely used in buildings and bridges, and among them, rubber bearing and friction pendulum bearing (FPB) are the two most used isolation techniques. Rubber bearing has small isolation stiffness and good vertical bearing capacity. When structures with rubber bearing are subjected to design earthquakes, deformation of the superstructure and the isolation layer is small. In past decades, a great deal of effort has been made to improve the isolation effect, or in other words, to isolate the seismic response of the superstructure [1; 2]. Rubber-bearing isolation with active or semi-active control are also studied to the increase isolation effect [3; 4; 5; 6] subject to design and rare earthquakes. A MR (Magneto-Rheological) damper is suitable for semi-active control in a base-isolated structure under long-period earthquakes [7]. Different damping strategies are determined by long-period earthquake ground motions or short-period ground motions [8]. Long-period earthquake ground motions include frequent earthquakes with 63% exceeding probability in 50 years, rare earthquakes with 2-3% exceeding probability in 50 years and very-rare earthquakes with 0.5% exceeding probability in 50 years [9]. The improvement of horizontal deformation capacity of the isolation layer is seldom studied, since the isolation layer will not be destroyed by design or rare earthquakes. However, isolation structures have a risk of collapse when subjected to very-rare earthquakes. Deformation of isolation bearing without an inhibiting device will exceed its deformation capability under very-rare earthquakes [10]. At the least, when the increase of deformation is stopped by an inhibiting device, the safety of the superstructure is no longer guaranteed, since the isolation layer cannot provide an isolation effect. Unfortunately, there is a contradiction between increasing deformation capacity of rubber bearing and increasing its isolation effect. Specifically, horizontal displacement of rubber bearing is limited to the length and height of the rubber: increasing length and height at the same time can guarantee economy, but meanwhile, horizontal stiffness also increases. As a result, rubber bearing is not suitable for isolation structures which need seismic performance under very-rare earthquakes. Friction pendulum bearing is another common isolation bearing. Restoring force of FPB is determined by the horizontal component of the bearing reaction. More importantly, FPB can avoid weaknesses of rubber bearing, i.e., contradiction between deformation capability and isolation effect. This is because isolation frequency is mainly determined by the radius of FPB, instead of the length of bearing as in rubber bearing. Seismic performance of structures equipped with FPB has been demonstrated by a series of experiments and engineering practice [11; 12; 13; 14; 15; 16]. Nonlinear biaxial springs are used to build the model of a friction pendulum based on the principles of the classical theory of plasticity [17]. Torsional behaviors and P-delta (P-D) effects of the structure isolated with FPB were also studied by different researchers [18; 19; 20]. Considering both isolator properties and earthquake main characteristics as random variables, seismic reliability of a base-isolated structure equipped with FPB is also evaluated [21].