## 1 Introduction  
Heritage masonry constructions demonstrated over the years their extreme weakness against the dynamic loads, i.e., earthquakes. The most recent strokes, which took place in Central Italy between 2016 and 2017, highlighted the vulnerability of the masonry structures [1, 2, 3, 4, 5]. Numerous factors, including their irregular geometry, uneven evolution across time, inadequate conservation status, and noneffective box-like behavior, influence their high vulnerability [6, 7, 8]. In ordinary practice, the evaluation of masonry structures is carried out by an equivalent frame [9, 10] derived from the damage observation after very destructive earthquakes, where the vertical masonry panels make up for the piers, as the bands between the openings do for the spandrels. Both are damageable elements connected with rigid nodes, wherein the damage is not expected. The regularity of the structures, a correct distribution, an alignment of the openings, and an absence of staggering of intermediate floors represent the hypotheses underlying a correct application of the equivalent frame method. However, these assumptions fall in historical buildings due to the chaotic evolution through time [11]. Since the 1990s, scientific research has started studying increasingly effective modeling tools for analyzed heritage masonry constructions [12, 13]. In this field, there are two most popular methods, which provide a better numerical response when compared with real damage: the block-based (discontinuous) and the continuous (homogenization) models. Inthe first one, the masonry response is simulated by considering the distinct roles played by the blocks and the mortar. It includes detailed micro-modeling, where both blocks and mortar are represented [14; 15], along with simplified micro-modeling where the mortar thickness is incorporated into the blocks' dimensions [5; 10; 16; 17]. The block-based (discontinuous) approach can be modeled with both finite element (FE) and discrete element (DE) methods. In the FE one, the masonry is represented by sufficiently regular elements, interacting with each other for the interposition of interfaces [18]. The latter are, generally, governed by frictional or cohesive laws, wherein the parameters might be calibrated thanks to proper experimental tests. In the DE method, the masonry is always made of blocks that interact between themselves through the contact surfaces, where, generally, non-smooth or smooth (contact) laws are used. The main advantage of using the block-based (discontinuous) approaches is the possibility to consider the separation of the blocks as well as the possible crumbling of the multi-leaf masonry walls. This allows for studying, in a unified way, the in-plane and the out-of-plane behavior of the wall panels and their possible evolution over time. Recently, it has been possible to find a combination of the two methods [19; 20]. On the other hand, the continuous method makes no distinction between the elements composing the masonry. Typically, the walls are assumed perfectly connected to each other also in their orthogonal intersections, allowing for a detailed description of the in-plane structural response. The heterogeneity of the material is assumed as a continuous deformable body that can simulate the behavior under static and dynamic loads by means of appropriate constitutive laws [21; 22; 23; 24; 25]. These constitutive laws can be drawn either directly by the responses calibrating from standard experimental tests [26] or indirectly by considering values obtained for similar masonry [27] or by national or international regulations [28; 29]. Comparing with the first block-based (discontinuous) model, this process takes less time for the modeling and the analysis execution. In this paper, the numerical versatility of the block-based (discontinuous) approach, with the DE method, is compared to the continuous one by the classical FE method with solid elements.