A Macro-Distinct Element Model (M-DEM) for simulating in-plane/out-of-plane interaction and combined failure mechanisms of unreinforced masonry structures

In the seismic analysis of unreinforced masonry (URM) structures, the modeling of out-of-plane (OOP) modes and their mechanical interaction with in-plane (IP) loaded components are typically neglected when using simplified numerical methods. Although this may result in unconservative predictions, the high computational expense entailed by more refined approaches is often prohibitive for applied researchers and practitioners. To overcome these limitations, the demonstrated capabilities of a recently developed low-cost Macro-Distinct Element Model (M-DEM) to simulate IP and OOP modes are extended in this work towards the modeling of IP/OOP interaction and combined failure mechanisms of URM assemblies. In the M-DEM framework, shear and flexural damage are accounted for by zero-thickness interface spring layers, whose layout is determined a priori as a function of the masonry texture, while crushing failure is modeled through homogenized finite element macro-blocks. To adapt and validate this M-DEM scheme to model IP/OOP interaction, past experiments on full-scale C-, U-, and I-shaped URM specimens tested under quasi-static loading were simulated. The shake-table response of a full-scale C-shaped URM assembly with openings was also numerically simulated up to collapse, representing a major improvement over previous macro-element methods. After the comparison with experimental tests, a parametric investigation of the response of reference URM walls under combined IP/OOP actions was conducted, and the influence of previous IP damage on one- and two-way OOP bending capacity is quantified. This aspect, despite being widely identified as of relevant interest, has only been marginally investigated in previous research, both experimentally and numerically.