Seismic vulnerability of timber-reinforced earthen structures through standard and non–standard limit analysis

Earthen architecture represents one of the most widespread built heritage and shows many advantages from both the environmental and economic points of view. Disadvantages connected to low mechanical properties of earthen structures are often overcome, in historical buildings, through the employment of timber elements, which can increase a box-type behaviour enabling both in-plane and out-of-plane mechanisms, facilitating spread damage and avoiding disastrous collapses. In this study, overturning mechanisms that can activate during earthquakes are investigated employing the tools of limit analysis. Through the kinematic approach of limit analysis, geometrical and mechanical parameters most influencing the response to horizontal actions are analysed assuming different material models for masonry, i.e. finite compressive or tensile strengths, and presence of frictional strength. Within this framework, the presence of timber reinforcing elements is modelled providing a reasonable analysis method and sound results. Aiming at validation, the church of San Judas Tadeo de Malloa (Chile), built with traditional, earth-based, timber-reinforced masonries, is analysed interpreting the damage pattern suffered after the 2010 Maule earthquake (Mw 8.8). The study adapts the robust procedures of limit analysis to the peculiarities of earth-based structures, highlights the crucial role of timber elements in the response to horizontal actions, especially in areas with high seismic hazard, and proves that the beneficial effect of timber reinforcing systems can be adequately interpreted through the proposed procedure.