Probabilistic Simulation of Crack Propagation in Masonry Walls Using a Grain-Based Energy Accumulation Model

Unreinforced masonry (URM) buildings constitute an important portion of the European building stock, where metal injection anchors are widely utilized for seismic retrofitting. While crack propagation in URM walls is extensively studied, the interaction between these cracks and structural anchors remains an underexplored area of research. This paper presents a probabilistic computational framework to serve as the foundation for investigating these crack-anchor interactions. The model simulates the progressive failure of a URM wall under diagonal compression using a two-dimensional discrete element approach implemented in MATLAB. The wall is discretised into brick and joint mortar grains, and the boundaries between them are assigned unique failure thresholds sampled from Weibull distributions specific to each pair of grain types constituting the boundary (Brick-Brick, Joint-Joint, and Joint-Brick). A novel crack propagation algorithm guides the formation of the crack pattern. A large ensemble of simulations was performed to generate a probabilistic crack map, which reveals a distinct diagonal shear band. The results quantitatively show that the failure is dominated by cracking at the joint-brick interfaces, which are shown to be the most probable locations for crack occurrence. The resulting heatmap provides a quantitative tool for identifying regions susceptible to crack occurrence, forming the basis for future investigations into anchor performance in cracked masonry.