Analysis of the Influence of the Stiffness Ratio of Rocking Walls on the Fragility of Step-Terrace Frame–Energy-Dissipation Rocking Wall Structures in Mountain Cities

A rocking wall controls the overall deformation mode of a structure and the distribution of plastic energy dissipation, and prevents failure caused by weak stories. A step-terrace frame structure has serious problems of irregular lateral stiffness, sudden changes in floor bearing capacity, and concentrated deformation of the upper grounding layer. In order to improve the yield failure mode of a step-terrace frame structure, this paper added a bottom hinged rocking wall to it to control the yield mechanism of the structure. To further reduce the seismic response of the structure and limit residual deformation, a step-terrace frame–energy-dissipation rocking wall structural system with buckling-restrained braces (BRBs) is proposed. The rationality of the model and parameters was verified by simulating low-cycle repeated loading tests of the step-terrace frame structure. A numerical model of a typical step-terrace frame–energy-dissipation rocking wall structure in a 7-degree (0.15 g) area was established. The stiffness ratio was changed by changing the cross-sectional size of the rocking wall, and incremental dynamic analysis (IDA) was used to explore the influence of stiffness ratio on the fragility of step-terrace frame–energy-dissipation rocking wall structures from the aspects of IDA quantile curve, seismic probability demand model, fragility function, failure state probability, fragility index, anticollapse reserve factor, and safety margin ratio. The results show that the rocking wall can homogenize the overall deformation of the structure, and the failure mode of the upper grounding side structure changes from the layer failure mode to the overall failure mode. BRBs improve the seismic and recoverable performance of the structure, and increasing the stiffness ratio can effectively enhance the ability of the structure to resist different degrees of damage. After comprehensive consideration, it is believed that a stiffness ratio of 10.79% for the step-terrace frame–energy-dissipating rocking wall structure is more suitable. The research results can be used to guide the control design or reinforcement and renovation engineering of the seismic failure mechanism of the step-terrace RC frame structure.