In this paper, we introduce an extension of the piecewise rigid displacement (PRD) method for addressing the stability of a generic two-dimensional masonry structure subjected to large displacements. So far, the PRD method has been applied to simulate cracks in the reference configuration considering small displacements. Here, we investigate both cracks and internal forces in the presence of large foundation displacements, also providing an approach to estimate their maximum allowable value. The proposed extension allows accounting for the evolution of both mechanism and corresponding internal stress state due to the increasing prescribed displacements.
After benchmarking the PRD analysis of a pointed arch with a physical test and results obtained through the Discrete Element Modelling software 3DEC, its strength/use is demonstrated on a complex numerical application, based on the cross-section of a Gothic cathedral. Also, in this case, the PRD results are compared with a 3DEC analysis showing good agreement in terms of cracks evolution, internal stress states and displacement capacity. This paper shows the ability of the PRD method in solving in a few seconds a critical issue in the field of masonry structures that is, the effects of large foundation displacements, both in terms of mechanisms and forces, simultaneously.