Trade-off between post-earthquake serviceability and energy dissipation capacity in RC rocking walls

The inherent limitation of self-centering structural systems in dissipating seismic energy necessitates the use of energy dissipators (ED) as sacrificial elements. While this solution enhances the energy dissipation capacity of self-centering systems, it also challenges their post-earthquake serviceability. Therefore, this study investigates the effect of the $\beta$ ratio (defined as the ratio of the moment due to EDs to the combined moments due to gravity loads and post-tensioning forces) on the response of reinforced concrete (RC) rocking walls and establishes an allowable range of $\beta$ ratios to ensure optimal post-earthquake serviceability and performance. A series of validated parametric numerical models for low- to high-rise RC rocking walls (aspect ratios (ARs) between 2.5 and 10) were developed. Multi-objective optimization was then conducted to maximize energy dissipation capacity (${\xi }_{\mathrm{eq}}$≥0.08) while minimizing $\beta$ to enhance post-earthquake serviceability. The optimization results demonstrated a trade-off: lower $\beta$ ratios improve self-centering but increase transient inter-story drift and peak floor accelerations (PFAs), particularly under the maximum considered earthquake (MCE) hazard level, risking non-structural elements damage. Conversely, higher $\beta$ ratios reduce drift and PFAs due to enhanced energy dissipation, but may increase residual drift, leading to potential permanent deformations. To determine the allowable range for $\beta$ ratios, the optimization results were post-processed for post-earthquake serviceability evaluation based on serviceability acceptance criteria, derived from snapback and nonlinear time history analyses. The study found that walls with lower aspect ratios (particularly in mid- to high-rise walls) require fewer post-tensioned (PT) tendons due to gravity-driven self-centering. In contrast, walls with higher aspect ratios necessitate adjustments in the placement and sizing of EDs and PT tendons to maintain performance. The results revealed that exceeding a threshold $\beta$ ratio leads to excessive residual drift, compromising self-centering capability. The allowable $\beta$ ratio, ranging from 0.31 to 1.45, was found to depend on the wall height, aspect ratio, and post-earthquake serviceability considerations. The range of allowable $\beta$ ratios was found to be: low-rise (AR 2.5: 0.31–1.22; AR 5: 1.05–1.45), mid-rise (AR 5: 0.30–1.30; AR 7.5: 0.63–1.35), and high-rise (AR 7.5: 0.48–1.25; AR 10: 0.83–1.15).