Fragility curves and seismic demand hazard analysis of rocking walls restrained with elasto-plastic ties

The dynamic stability of out-of-plane masonry walls can be assessed through non-linear dynamic analysis (rocking analysis), accounting for transverse walls, horizontal diaphragms and tie-rods. Steel tie-rods are widely spread in historical constructions to prevent dangerous overturning mechanisms and can be simulated by proper elasto-plastic models. Conventionally, design guidelines suggest intensity-based assessment methods, where the seismic demand distribution directly depends upon the selected intensity measure level. Fragility analysis could also be employed as a more advanced procedure able to assess the seismic vulnerability in a probabilistic manner. The boundedness of this approach is herein overcome by applying a robust stochastic seismic performance assessment to obtain seismic demand hazard curves. A sensitivity study is carried out to account for the influence of wall geometry, the minimum number of seismic inputs, and the mechanical parameters of tie-rods. Fragility analysis, prior to seismic demand hazard analysis is applied on over 6000 analyses, revealing that intensity measures are poorly correlated both for 1-D and 2-D correlation, hardly leading to the selection of the optimal intensity measure. The tie-rod ductility, followed by its axial strength and wall size, is the mechanical parameter mostly influencing the results, whereas the wall slenderness does not play a significant role in the probabilistic response.