A novel approach to model differential settlements and crack patterns in masonry structures

The present paper introduces a novel methodology for accurately modelling differential settlements beneath the foundations of masonry structures and the resulting crack patterns. In contrast to standard strategies, which typically impose predefined settlements at the structure's base, the proposed approach directly accounts for the soil–structure interaction by coupling the mechanical responses of masonry and soil. Specifically, the mechanical behaviour of the masonry is accurately modelled using an elastic no-tension approach, while the soil is represented as an elastic half-plane. The solution to the coupled mechanical problem, satisfying both equilibrium and compatibility conditions, is obtained through an iterative optimisation-based procedure. Several 2D numerical applications, considering different geometries and loading conditions, are provided to demonstrate the proposed procedure's effectiveness and performance and highlight its potential.