Numerical study of the out-of-plane response of pre-damaged non-framed unreinforced masonry walls via an efficient block-based modeling approach with shell elements

This study examines the influence of in-plane (IP) pre-deformations and -damages on the two-way bending out-of-plane (OOP) seismic response of non-framed unreinforced masonry (URM) walls. IP and OOP behaviors of non-framed URM walls are often studied individually and their interaction, such as the effects studied here, remains insufficiently explored. Hence, current design and assessment techniques of non-framed URM walls do not consider the effects of pre-damage and pre-deformation, overestimating safety. This paper addresses this gap. First, a simplified micro-scale numerical modeling approach is developed within Finite Element framework using expanded blocks and zero-thickness interface elements. Shell elements are adopted instead of solid blocks, which are traditionally more common in such studies, to enhance computational efficiency for extensive explorations. Second, the approach is validated against wall IP and OOP experiments, showing good accuracy and reliability. Third, the effects of IP pre-damage and pre-deformation on two-way OOP bending strength and stiffness, called IP/OOP interaction effects, are investigated in a parametric study. The effects of wall openings, IP boundary conditions, vertical pre-compression, and horizontal confinement on interaction effects are investigated. OOP loading is performed at different IP performance states identified via a crack-based approach. According to the results, IP pre-damage or pre-deformation reduced OOP strength between 0% and 30% and OOP stiffness between 30% and 50% for the walls studied in this research and representative of Dutch calcium silicate masonry, emphasizing the importance of accounting for IP/OOP interactions in seismic design and assessment of URM walls. Vertical pre-compression and horizontal confinement are identified as most influential parameters due to their effect on arching mechanisms. Existing analytical models, typically developed for one-way spanning walls, significantly overestimate the loss of OOP performance due to pre-deformation or pre-damage in two-way spanning walls. The study establishes a foundation for structured future research into IP/OOP interaction.