Fragility Analysis of Step-Terrace Frame-Energy Dissipating Rocking Wall Structure in Mountain Cities

Rocking walls can control the overall deformation pattern and the distribution of plastic energy dissipation in structures, suppressing the occurrence of weak layers. In the case of step-terrace frame structures, issues such as severe lateral stiffness irregularities, abrupt changes in floor-bearing capacity, and concentrated deformation in upper ground layers exist. To improve the yielding and failure modes of step-terrace frame structures in mountainous regions, this paper proposes a structural system combining step-terrace frame structures with energy dissipation rocking walls attached to their bottoms, aiming to control the yielding mechanism of the structure, further reduce the seismic response, limit residual deformation, and propose a structural system of step-terrace frame structures with buckling-restrained braces (BRBs) and energy dissipation rocking walls. Two sets of numerical models for step-terrace frame structures with different numbers of dropped layers and spans were established. Through simulating low-cycle repeated loading tests on step-terrace frame structures, the rationality of the models and parameters was verified. Incremental dynamic analysis (IDA) was employed to systematically investigate the vulnerability of step-terrace frame structures with energy dissipation rocking walls under different dropped layer and span configurations. This investigation covered aspects such as IDA curve clusters, percentile curves, seismic demand models, fragility functions, failure state probabilities, vulnerability indices, collapse resistance factors, and safety margins. The results indicated that the change in dropped layer numbers had a far greater impact on the vulnerability of step-terrace frame structures with energy dissipation rocking walls than the change in dropped span numbers. Under seismic excitations with the same peak ground acceleration (PGA), rocking walls can limit the depth of structural plasticity development, reduce the dispersion of peak responses, and lower the probability of exceeding various performance levels, thereby exhibiting good collapse resistance. The addition of buckling-restrained braces (BRBs) can further enhance the seismic performance and collapse resistance of the rocking wall frame structure. By analyzing the correlation between seismic intensity measures and peak structural responses, the validity of using peak ground acceleration as a scaling indicator for incremental dynamic analysis (IDA) has been verified.