<p>Understanding the behaviour of masonry under various loading conditions is crucial for the structural design, assessment, and preservation of masonry structures. High-fidelity computational modelling offers a powerful method for investigating the complex mechanical interactions within masonry composites, complementing and reducing the need for extensive experimental programs. To this end, this research presents a numerical framework using the discrete element method (DEM), a discontinuum-based approach, to simulate the compressive behaviour of masonry prisms. The modelling approach represents masonry (i.e., brick units and cement mortar) as rigid, irregular triangular blocks, enabling explicit simulation of cracking and damage evolution. Building on previous developments, this study provides an in-depth examination of the advantages and limitations of the proposed framework. Particular attention is given to the influence of geometrical parameters such as block size and regularity and the stochastic variations associated with the block generation process. The findings indicate that incorporating block irregularity is crucial for achieving realistic compressive responses, while variations in block size have only a minor impact on the predicted capacity within the examined range. The study also demonstrates that the stochastic nature of the tessellation process leads to some variability in predicted strength, underscoring the value of analyzing multiple realizations to obtain representative trends. Overall, the framework provides reliable predictions of behaviour and fracture patterns, supporting its use in the assessment of masonry composites under compressive loading.</p>