Limit analysis and design-oriented approach for out-of-plane loaded masonry walls strengthened by grouted anchors

Masonry structures without box-like behaviour are often prone to the complete or partial out-of-plane failure of their walls under horizontal actions, i.e. mainly the seismic ones. Steel grouted anchors or tie-rods have been widely used in the past to improve connections between orthogonal walls and avoid out-of-plane mechanisms. However, reliable analytical approaches to design such strengthening systems are lacking, whereas the evaluation of their effectiveness is still a matter of ongoing research. The paper presents a force-based design approach to assess the performance of three-wall masonry systems strengthened by grouted anchors, using a frictional macro-block model and a non-standard limit analysis, previously developed for unreinforced masonry structures. The extension of this model to strengthened masonry systems, with specific reference to the use of grouted anchors, allows assessing their horizontal capacity in terms of minimum load multiplier and expected failure. The novel aspects introduced in the updated model are: (1) a simplified closed-form formulation for the calculation of the stabilising moments provided by the grouted anchors at the onset of the failure mechanism, (2) the possibility of placing the grouted anchors with variable inclinations, which may improve their stabilising contribution and optimise the intervention. The effectiveness of the simplified formulation is firstly proved by the comparison with literature results; then, several parametric analyses are carried out to highlight the influence of some variables on the capacity of both the unreinforced and the strengthened three-wall system. Finally, a literature example related to a traditional intervention with steel tie-rods is used to apply the proposed procedure and investigate the performance of different design solutions with innovative grouted anchors.