A 3D microscale modeling method for nonlinear static analysis of stone masonry walls using mathematical programming

This study uses mathematical programming for the nonlinear static analysis of masonry walls, explicitly considering their 3D microstructure. An automated procedure is developed to convert stone masonry microstructures into rigid block models, with stones represented as polyhedrons and mortar as an assembly of tetrahedrons. Interface behaviors, such as cracking, crushing, and shear failure, are formulated as inequality constraints within a standard second-order cone programming framework, incorporating force equilibrium, failure conditions, minimization of potential and complementary energy. A unified force-based formulation is derived to support both force-controlled and displacement-controlled loading protocols for pushover analysis. The proposed method is validated through simulations of interface tests on brick–mortar samples and shear-compression tests on three single-leaf masonry walls, showing good agreement with experimental crack patterns and force–displacement curves. Finally, the correlation between mechanical properties and microstructural features of rubble stone masonry walls is investigated. The results underscore the necessity of 3D geometric feature quantification and nonlinear static analysis for accurately modeling the behavior of multi-leaf stone masonry walls. • A 3D model generation procedure is proposed for masonry walls with irregular units. • Mortar joints are modeled explicitly considering cracking, crushing, and shear failure. • A unified optimization-based formulation is established for pushover analysis. • Strength, stiffness, and crack patterns of masonry walls are accurately predicted. • The influence of 3D masonry microstructure is studied.