A numerical approach for the analysis of non linear behaviour of masonry arches, reinforced by F.R.P.

The paper is concerned with a numerical procedure available for the analysis of voussoir arches, or any other masonry structure, modelled as a discrete system of rigid blocks connected by unilateral elastic contact constraints. A convenient way to define the contact device which links the blocks, through which a mortar joint could be simulated, is to consider a set of elastic links, orthogonal to the contact surface between two adjacent blocks, and an additional link, parallel to the interface, through which the shear forces can be transmitted. In accordance with the assumptions of no tensile strength in the mortar joint, only compressive forces can be transmitted from one element to another. Reasonable hypotheses can be assumed for the link parallel to the contact surface in order to calibrate both the shear behaviour and the influence of the friction between the blocks. The numerical algorithm, through the opportune use of Moore-Penrose generalized inverse, is based on the introduction of suitable distortion terms capable to generate internal coactions such as to give back the compatibility in the sign conditions where tensile stresses are not admissible. According to the Colonnetti’s theorem, the maximum number of imposed linear independent terms of distortion - that is the maximum number of the iterations in the procedure - are, at most, equal to the degree of statically indeterminacy of the structure. Through the results of the numerical procedure it is possible both to define the cracking failure pattern, highlighting the actual reacting structure within the apparent one, and to evaluate the width of the cracks located in the mortar joints. In same way it is possible to analyze a masonry arch whwn it is reinforced by a set of F.R.P. material, and so evaluate the benefit of the consolidation in relation of the collapse mechanism. The efficiency and the versatility of the procedure, besides the correctness of the results have been confirmed through the comparison with similar numerical analyses and the good agreement with experimental tests.