## 1 Introduction
FBA is the verification approach chosen by the majority of codes in most countries, and also chosen by practitioners [29]. FBA approaches analyze the equilibrium condition of a given failure mechanism at the onset of motion to find the value of the collapse load multiplier and the corresponding ground acceleration associated with its activation. For this reason, FBA is also described as linear kinematic analysis in several technical standards and scientific papers (e.g., Reference [22]). The FBA procedure works as follows: for a given masonry assemblage subjected to gravity and seismic loads, the first step is to identify all the potential collapse mechanisms likely induced by lateral loads (e.g., the overturning or vertical bending of a facade, the corner overturning etc.). Each collapse mechanism is then usually idealized into an assemblage of rigid blocks that interact with each other at their contact interfaces, under the assumption of infinite compressive strength and no-tension, frictional interfaces. Each rigid block is then subjected to vertical downward forces, which represent the permanent and variable vertical loads, and to a lateral load that is expressed as the product of the vertical forces and of the unknown collapse multiplier. The latter is calculated by analyzing the equilibrium condition of the failure mechanism, e.g., using simple analytical models which stem from the application of classic theorems of limit analysis and, in general, from the application of the virtual work principle. Collapse load multipliers are then used to evaluate the ground acceleration that activates the mechanism, as discussed in detail in Section 3. It is worth noting that a crucial aspect of FBA is the proper identification of all the potential collapse mechanisms and their individual calculation according to linear kinematic analysis. The final goal of FBA is to find the most vulnerable collapse mechanism among them all, which is the one characterized by the lowest value of ground acceleration. According to the current practices [22; 29; 33], the analyst defines a priori a set of potential collapse mechanisms according to his own expert judgement and the damage observed after seismic events of the past, as well as on the basis of the behavior of similar constructions during earthquakes (i.e., referring to a consolidated abacus of damage). Indeed, subjective judgment plays an important role in the whole evaluation process and this is a critical aspect of the current practice when analytical formulations are adopted, which might limit the application, especially in the case of non-standard construction with complex three-dimensional assets. Conversely, the approach adopted in this study relies on the automatic detection of the potential collapse mechanisms of a masonry construction. To this end, we used the in-house software code LiABlock_3D [34], which is based on the rigid block modeling approach for the linear kinematic analysis of three-dimensional masonry structures. The software was validated in previous studies [35; 36; 37], and was herein applied to an entire structural unit of a historic construction, the castle of Bussi sul Tirino (Abruzzo, Italy). The main goals were to explore to what extent numerical rigid block models can be conveniently used to identify the most important fragilities of historic masonry constructions, to evaluate the effectiveness of the structural interventions, and to provide a solid basis for the selection of the optimal retrofitting solution according to the minimum intervention principle.