A piecewise-linear backbone model for unbonded post-tensioned concrete masonry shear walls

Unbonded post-tensioned concrete masonry (UPCM) shear walls present an effective seismic force resisting system due to their ability to mitigate expected damage risks through their self-centering capabilities. A few design procedures were proposed to predict the in-plane flexural response of UPCM walls, albeit following only basic mechanics and/or extensive iterative methods. Such procedures, however, may not be capable of capturing the complex nonlinear relationships between different parameters that affect UPCM walls’ behavior or are rather tedious to be adopted for design practice. In addition, the restricted datasets used to validate these procedures may cast doubt on their accuracy and validity for new, unseen data, further hindering their adoption by practitioners and design standards. To address these issues, an experimentally-validated nonlinear numerical model was adopted in this study and subsequently employed to simulate 95 UPCM walls with a range of different design parameters to compensate for the lack of relevant diverse experimental data in the current literature. Guided by mechanics, and employing this database, an evolutionary algorithm—multigene genetic programming (MGGP), was adopted to uncover the relationships controlling the response of UPCM walls, and subsequently develop simplified closed-form wall behavior prediction expressions. Specifically, through integrating MGGP and basic mechanics, a piecewise-linear backbone model was developed to predict the load-displacement backbone for UPCM walls up to 20% strength degradation. Compared to existing predictive procedures, the prediction accuracy of the developed model and its closed-form nature are expected to facilitate better understanding of such wall behaviors and subsequently open the gate to further incorporate other experimental and numerical results to ultimately deploy UPCM in mainstream building designs in the near future.