## 1 Introduction
In addition, some special friction pendulum bearings, e.g., XY-FP isolator, double concave FPB and triple concave FPB, have been developed for preventing uplift and obtaining large restoring force and low sensitivity to the frequency content of the input [22; 23; 24; 25; 26; 27; 28; 29]. FPB with variable stiffness or variable friction coefficient is effective for a wide variety of structures and isolator properties, even when subjected to near-fault ground motions [30; 31; 32; 33; 34]. Other isolation devices such as marble-graphite slide seismic isolator [35], polymeric bearings [36] and thermal isolation made of mineral wool and polyurethane foam [37; 38] have also been proposed. These previous studies indicate the mechanical properties and isolation effect of classic or developed FPBs instead of safety of the isolation layer when subjected to rare earthquakes. However, when subjected to very-rare earthquakes, the lack of deformation capacity of FPB is more significant. It is also unfortunate that horizontal deformation of FPB is still limited by the size of bearings. Size of FPB is determined by space for placing FPB. Space of FPB is limited because classical friction pendulum bearings are mainly used at the bottom of structural columns or bridge piers, in general. As a result, it is necessary to develop an isolation technique for satisfying seismic demand of the isolation layer under very-rare earthquakes. The goal of this paper is to develop innovative FPB, namely \"super-large displacement rotation friction pendulum bearing\" (SLDRFPB) and \"super-large displacement translation friction pendulum bearing\" (SLDTFPB) to realize large deformation of the isolation layer and thus to achieve isolation safety subjected to very-rare earthquakes. Since the superstructure is completely supported by one SLDRFPB or SLDTFPB, avoiding locating them separately under the column can beat the restriction of space for placing FPB, leading to effectively achieving super-large size and super-large deformation. Large radius and small friction coefficient, which can be easily achieved in SLDRFFB and SLDTFPB, guarantee good isolation resilience. As a result, the developed SLDRFFB and SLDTFPB are suitable for important isolation structures which need to maintain sufficient safety and functionality subjected to even very-rare earthquakes. It is worth mentioning that, since damage of the isolation system is concentrated in the isolation layer, the increased cost for the implementation of the developed SLDRFPB or SLDTFPB is not too much. In addition, the two forms of developed SLDTFBs can meet the requirements of most structures. Motion state of superstructures equipped with SLDRFPB and SLDTFPB, as well as space utilization of SLDRFPB and SLDTFPB, are different. In practical implementation, the choice of SLDRFPB or SLDTFPB depends on the inclination of the superstructure and space shape of the foundation. Particularly, superstructures equipped with SLDRFPB and sliding frame in SLDTFPB will move rotationally on an arc orbit, and the rotational inertia of these components cannot be ignored. As a result, the traditional design method of friction pendulum bearing is no longer suitable. We develop a design method to accurately and conveniently evaluate seismic performance of SLDRFPB and SLDTFPB. This method is expected to be used in practical projects. The rest of the paper is organized as follows. Section 2 describes system configuration of SLDRFPB and SLDTFPB, followed by establishment of motion equations of isolation systems equipped with SLDRFPB and SLDTFPB in Section 3, and mechanical properties of the two developed bearings are illustrated. Seismic responses of superstructures and isolation layers are presented in Section 4 to demonstrate good seismic performance of SLDRFPB and SLDTFPB when subjected to rare and very-rare earthquakes.