Influence of the elasto-plastic behavior of tie-rods in the response of rocking masonry walls through seismic demand hazard curves

Rocking analysis is a powerful tool to assess the seismic vulnerability assessment of masonry walls subjected to out-of-plane modes, especially when in view of checking the efficiency of traditional retrofitting solutions, such as steel tie-rods restraining rocking blocks. The study focuses on a probabilistic approach for the seismic assessment of the out-of-plane behavior of masonry walls, mainly aiming to reliably predict fragility and seismic demand hazard curves in case steel tie rods are used as anti-seismic device. To identify the most appropriate steel tie-rod device, more than thousand multistripe analyses have been performed considering the Italian site with highest seismic hazard (Carlentini, Sicily), duly modifying ductility and strength of the tie rods themselves. The resulting fragility curves and seismic demand hazard curves are critically discussed, so allowing the definition of the most efficient and proficient intensity measures referring to five relevant limit states. As expected, remarkable changes in the response are recorded by passing from a brittle to a ductile tie-rod, but when the ultimate strain is bigger than 2%, an increased tie-rod ductility does not sensitively improve the response even for high-intensity earthquakes. The probabilistic approaches show that even low-ductility tie-rods can sensibly reduce the probability of exceedance of limited and moderate rocking limit states, up to an order of magnitude. As for the influence of the tie-rod strength, even low-medium values produce a remarkable reduction of annual exceedance rate. For instance, a severe rocking limit state occurs for the unrestrained monumental wall every 450 years and every 2000 years for the wall restrained by a tie rod of strength just fitting the minimum required design value.