## 1 Introduction  
In recent years, basic isolation technology has been extensively applied in building construction and bridge engineering in China and overseas [1; 2; 3]. By the end of 2020, China had constructed more than 8000 seismic-isolated buildings. The rubber isolation system is currently the most widely used and mature isolation technology, among which the common isolation devices include the ordinary rubber bearing, natural rubber bearing (NRB) [4], LRB [5], HDRB [6], etc. The HDRB has plentiful advantages--such as a simple structure, stable mechanical performance, strong energy dissipation capacity, large stiffness before yielding, environmental protection, etc.--that make it an excellent choice for base-isolation structures. It is made of laminated rubber pads with multi-layer steel plates that are vulcanized and bonded at a high temperature, where the steel plate layers restrain the vertical deformation of the rubber layers from guaranteeing a certain vertical stiffness of the bearing. The rubber layers adapt the high damping material with graphite and other additives to be capable of simultaneously withstanding a vertical load and resist a large horizontal shear displacement. Compared with the ordinary rubber bearing, HDRB can achieve a higher equivalent damping ratio of more than 20% without matching dampers, which saves installation space. HDRB possesses greater stiffness before yielding, a better braking effect on the structure subjected to wind load, more minor damage caused by lead when processing, and is more applicable for those places with special requirements for environmental protection, especially in contrast with the lead-rubber bearing. When the structures are subjected to an earthquake, the HDRB will produce a large deformation and reduce the stiffness, thus achieving a better isolation effect. In recent years, many researchers have conducted studies on HDRB. [PERSON] et al. [7] conducted experimental studies on different forms of HDRB and analyzed the influence of the shape factor and steel plate forms on the performance of the bearings. [PERSON] et al. [8] took bidirectional coupling factors into consideration when testing the horizontal shear performance of HDRB. [PERSON] et al. [9] and [PERSON] et al. [10] carried out vertical compression tests along with horizontal shear tests for loading on the designed HDRB. Their results proclaimed a good energy dissipation effect. [PERSON] et al. [11] proposed a rheological model considering the nonlinear characteristics of HDRB based on the cyclic shear test, monotone relaxation test, and multi-step relaxation test. [PERSON] et al. [12] studied the influence of shear strain and vertical compressive stress on the shear performance of HDRB through the compression-shear performance test, and made an improvement to the restoring force model of the bearing with certain accuracy. [PERSON] et al. [13] applied the HDRBs to two typical r.c. framed structures and conducted the structural nonlinear incremental dynamic analyses based on the refined three-spring-two-dashpot model of the bearing. Rubber bearings, including HDRBs, are generally horizontal isolation bearings, which can reduce the horizontal seismic acceleration response of a structure by about 60%. They are incapable of decreasing or even amplifying vertical seismic effect effectively. This can be explained by the fact that ordinary rubber bearings have a vertical stiffness equivalent to thousands of times their horizontal stiffness, which means that it is likely to obtain a smaller vertical basic period of around 0.1 s and is liable to fall within the striking part of the vertical acceleration spectrum, thus resulting in poor vertical isolation. However, recent large (extra-large) earthquakes in China and abroad indicate that strong vertical ground motions that occur in high-intensity areas, especially near faults areas, may even exceed the horizontal seismic action component.