## 1 Introduction  
Due to the vertical irregularity, step-terrace frame structures in mountainous regions experience abrupt changes in structural stiffness, leading to significant differences in stress and deformation characteristics compared to conventional building structures. These structures also exhibit two types of vertical irregularities, as listed in relevant codes: lateral stiffness irregularity and sudden changes in floor-bearing capacity, which are inherent and difficult to adjust [1]. Previous studies have shown that the failure of step-terrace frame structures in mountainous regions mainly occurs in the upper ground layers, where weak layers are located, often adjacent to the upper ground layers. The presence of weak layers makes the column ends of upper ground columns highly susceptible to plastic hinges, resulting in yielding and failure at the layer interfaces [2]. [PERSON] et al. [3] conducted a field survey on building damage after the Sikkim earthquake and found that the extent of damage and the collapse rate of frame structures with soft stories were significantly more severe than those of other regular frame structures on flat ground. Investigations following seismic events, such as the 12 May Wenchuan earthquake, have revealed varying degrees of damage to mountainous building structures. Figure 1 illustrates typical damage to mountainous building structures caused by the Wenchuan earthquake [4]. The distribution of plastic hinges in low-cycle repeated loading tests on step-terrace frame structures is depicted in Figure 2[5]. In the figure, circles represent sections where hinges occurred, with solid circles indicate yielding on both sides of the section (upper and lower sides for beams, left and right sides for columns), while hollow circles indicate yielding on one side only. The numbers next to the circles indicate the sequence of appearance of plastic hinges on that section. [PERSON] et al. [6] conducted comparative analyses through shake table testing on 1/8 scale step-terrace frame structures and typical frame structure models, both consisting of six stories. The seismic responses of the structures were evaluated. The experimental results indicated differences in mode shapes and slope-parallel deformations between step-terrace frame structures and typical frame structures. Moreover, the failure modes of step-terrace frame structures differ from those of typical frame structures, where the latter tend to exhibit partial floor yielding mechanisms. [PERSON] et al. [7] suggested that increasing the shear bearing capacity and ductility of the upper ground floor of soft-story frame structures can enhance the overall seismic performance of the structure. [PERSON] et al. [8] proposed that changing the support constraint method is one approach to improving the seismic performance of soft-story frame structures and recommended installing isolation or sliding bearings on the upper ground floor when there are many soft stories. [PERSON] et al. [9], from the perspective of energy dissipation and damping, recommended installing viscous dampers in soft-story frame structures. Through shaking table tests, [PERSON] [10] and [PERSON] [11] found that installing isolation bearings on both the upper and lower ground floors of hillside soft-story structures can significantly improve the seismic performance of these structures. Placing rocking walls on the upper ground side of step-terrace frame structures in mountainous regions can evenly distribute inter-story displacements, effectively improving the seismic performance of step-terrace frame structures [12; 13] and reducing the concentration of damage in the upper ground layers [14]. Energy dissipation and seismic dampening techniques involve installing energy dissipation dampers at locations with significant structural deformations to artificially increase structural damping, dissipate seismic energy, and mitigate structural damage [15].