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Non-linear static analyses are performed on samples of increasing complexity: elementary panels, structural elements (piers and spandrels) and a pilot building. The results of some tests on TRM strengthened masonry, available in the literature, are considered to assess the model reliability in terms of capacity curves and collapse mode. The model is capable of detecting the typical failure mechanism of existing masonry, namely the diagonal cracking, the in-plane bending and the out-of-plane bending and is able to detect the activation also of mixed failure modes, that often occur in actual configurations.

Given the coarse mesh size and the smear plasticization assumption, the model is not suitable for the rigorous reproduction of individual cracks but represents a good compromise between the goal to grasp the structural performances at the wide scale, including failure modes, and the analysis optimization.

A concrete-damage plasticity material model ( Cdpm2 - 33) was considered for both the masonry and the mortar of the coating, also in accordance with the assumptions of the DLM previously calibrated 22, 28 : possible materials failures for both cracking in tension and crushing in compression were, thus, considered.

Generally, the plaster parameters ( Table 2) can be set on experimental basis (characterization tests on cylinders/prisms) or, when lacking, on the values reported in the technical sheets provided by the mortar producers. However, particular attention has to be addressed to the calibration of the mortar post-cracking behavior. Practically, due to the smear-crack approach of the MLM, the mortar fracture energy needs to be fictitiously increased so to take into account for the tension stiffening effect of the mortar between cracks. In such a way, the combined effect of the plaster layer and the GFRP layer can macroscopically reproduce the typical trilinear behavior in tension of the CRM composite material, broadly analyzed and discussed when applying the DLM approach 22 .

Direct tensile tests on composite reinforced mortar (CRM) coupons: comparison in terms of ( a) capacity curves and ( b) crack pattern. Acronyms MLM and DLM stand for the multi-layer and the detailed level modelling, respectively.

In-plane tests on composite reinforced mortar (CRM) thin slabs: comparisons in terms of ( a) capacity curves and ( b) crack pattern. Acronyms MLM and DLM stand for the multi-layer and the detailed level modelling, respectively.

The application of the MLM approach to the simulation of elementary masonry specimens strengthened with CRM was at first performed, so to check its capability in detecting the main failure mechanisms of historic masonry under lateral loads, namely diagonal-cracking, in-plane bending and out-of-plane bending. The simulations concerned, respectively, diagonal-compression tests, three-point in-plane bending tests and four-point out-of-plane bending tests ( Figure 6). For each model, comparison was made with experimental tests available in the literature and carried out under loading-unloading procedures (the backbone capacity curves were considered).

The damage patterns are reported in Figure 20. The activation of the different collapse mechanisms can be clearly distinguished and are globally in agreement with the experimental damage modes. In the unstrengthened configuration, both in the shear walls (East end West) exhibited the activation of the diagonal failure in some piers at the ground floor. Also in the masonry panel above the door some shear cracking occurred. Moreover, a mixed shear-flexure collapse activated in the piers of the first floor of the East wall and the spandrels of the first floor. In the strengthened configurations, the damage mainly focused at the ground floor, with mixed shear-flexure mechanism. Moreover, horizontal cracks appeared also in the gable walls, which, due to the tensile resistance of the GFRP grid and the connection with the foundation, contributed to provide some additional resistance against the lateral action.

The article deals with the evaluation of the global effects of TRM interventions on historic masonry structures, focusing on the identification a reliable but computationally efficient numerical strategy. In particular, a multi-layer numerical modelling approach, MLM, was developed. It was based on 20-nodes brick elements composed by a sequence of through-the-thickness plies representing the masonry, the mortar coating and the fiber-based reinforcement. Nonlinear-static analyses were carried out considering the material nonlinearities (cracking and crushing, for the masonry and the mortar coating, and tensile failure of the reinforcement). The material characteristics were deduced from previous experimental evidences on individual components and on CRM coupons subjected to direct tensile tests. The simplified assumption of perfect bond among layers was considered.

The results of some tests on CRM strengthened masonry available in the literature were considered to assess the model reliability at three different scale levels, of increasing complexity: elementary specimen, structural element and building. The results were compared in terms of capacity curves (resistance vs. displacement) and collapse mode. The former level was aimed at the individual recognition of the different, typical failure modes of masonry and the MLM was confirmed capable to notice the diagonal cracking mechanism (by means of diagonal compression tests), in-plane bending mechanism (through in-plane, three point bending tests) and out-of-plane bending mechanism (by out-of-plane, four point bending tests). The intermediate level focused on the performances of actual structural elements in buildings, such as piers and spandrels, in which the MLM was proved able to detect the activation also of mixed failure modes that occurred in many cases. The latter level, at the building scale, showed the reliability of the MLM also in the global analysis, where different resistant elements are combined and interact each other to provide the structure response. The discrepancies in comparison with experimental tests were found to be acceptable at the different scale levels and were attributed to uncertainties in the materials properties (scatter in respect to the nominal values assumed numerically), possible cumulative damage (neglected in the monotonic simulations), a not precise "displacement control" in the experimental tests, the reduced numbers of experimental test available for each configuration.

Given the coarse mesh size and the smear plasticization assumption, the MLM is clearly not suitable for the rigorous reproduction of individual cracks, for which more accurate but computationally heavier models, such as the DLM, should be used. However, it represents a good compromise between the goal to grasp the structural performances at the wide scale, including failure modes, and the analysis optimization. Clearly, the simplified assumption of perfect bond among layers has to be ensured. For example, by respecting the minimum bond lengths, the limits on reinforcement ratio and the number of transversal connections. The calibration of such requirements can be achieved by experimental characterization tests ( i.e. direct tensile tests and shear-bond tests) and/or through simulations with the DLM on small samples. Alternatively, it is possible to intervene on the MLM by limiting the ultimate deformation of the reinforcement (when the debonding anticipates the reinforcement failure) and/or the compressive strength of the mortar (so to account for its buckling in the most compressed areas). 2ff7e9595c