Publication

A 3d Microscale Modeling Method for Nonlinear Static Analysis of Stone Masonry Walls Using Mathematical Programming

2026

Abstract

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.

Official source

https://infoscience.epfl.ch/entities/publication/aaa08f2d-28e6-452e-bd01-02ea86db712c

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2026

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/aaa08f2d-28e6-452e-bd01-02ea86db712c

About this result

Related concepts (32)

Masonry

Masonry is the craft of building a structure with brick, stone, or similar material, including mortar plastering which are often laid in, bound and pasted together by mortar; the term masonry can also refer to the building units (stone, brick, etc.) themselves. The common materials of masonry construction are bricks and building stone such as marble, granite, and limestone, cast stone, concrete blocks, glass blocks, and adobe. Masonry is generally a highly durable form of construction.

Force

In physics, a force is an influence that can cause an object to change its velocity, i.e., to accelerate, unless counterbalanced by other forces. The concept of force makes the everyday notion of pushing or pulling mathematically precise. Because the magnitude and direction of a force are both important, force is a vector quantity. It is measured in the SI unit of newton (N) and often represented by the symbol F.

Mathematical optimization

Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.