# Seismic Analysis of Slender Monumental Structures: Current Strategies and Challenges
## 2 Masonry as a Complex Material with Internal Structure  
Masonry is a non-homogeneous material formed by units and joints, with or without mortar, and different bond arrangements [21]. Unlike modern masonry, which mainly consists of regularly arranged units, with or without steel reinforcement, ancient masonry is formed by rather complex three-dimensional arrangements of stone or brick units (Figure 1), usually unreinforced. Such a visible internal structure, combined with the variability of materials, unit shape and surface treatments, makes the behavior of historical masonry structures highly indeterminate and difficult to predict and assess with accuracy [22; 23; 24; 25; 26]. Due to its composite character, masonry mechanics are strongly influenced by the individual properties of its constituents as well as by the bond between them, where the latter is often the weakest link in masonry assemblages. Five basic failure mechanisms can generally occur in masonry [27]: (a) tensile cracking of the joints, (b) shear sliding along the joints, (c) direct tensile cracking of the units, (d) diagonal tensile cracking of the units and (e) compressive crushing (Figure 2). The first two modes are essentially joint mechanisms, where failure occurs at low values of normal stress due to the poor bond strength between joints and units, which is typical for strong unit-weak mortar joint combinations, widely present in ancient stone masonry. The third failure mode is a unit mechanism, which is common in masonry with low-strength units but high-strength mortar, usually with greater tensile bond strength. Instead, the last two failure modes are combined mechanisms involving both units and mortar joints. The preponderance of one failure mode over another or the combination of various failure modes is essentially related to the internal structure of masonry, including the orientation of bed joints with respect to the principal stresses. Figure 3 shows the results obtained from masonry walls with the same geometry but different units shape and arrangement, under combined vertical and cyclic horizontal in  
Figure 1: Examples of ancient masonry section with complex arrangements of units. Figure 2: Masonry failure mechanisms (adapted from [27]): (**a**) joint tensile cracking; (**b**) joint slipping; (**c**) unit direct tensile cracking; (**d**) unit diagonal tensile cracking; (**e**) masonry crushing. plane loading [21]. Three types of walls are considered, namely dry stone (without mortar), coursed masonry and rubble stone masonry (the last two with the same low-strength mortar). While the in-plane behavior of the dry masonry wall with regular large units is characterized by a rocking response with no strength degradation (no damage in the stones) and remarkable lateral displacement capacity, the response of the coursed masonry wall is predominantly flexural, with a slight strength degradation associated with the progressive spreading of flexural cracks through the joints and a considerable lateral displacement capacity, with rocking mechanisms playing a minor role. By contrast, the response of the rubble masonry wall is essentially controlled by shear, showing a significant strength degradation and a low lateral deformation capability, with consequent brittle failure after the formation of diagonal smeared shear cracks. Despite the geometry and material be the same, distinct failure modes, ultimate lateral strengths and hysteretic behaviors are found for the three walls due to aspects such as roughness of the joints, unit dimensions and interlocking. Randomly assembled masonry typically features very low friction as compared to regularly arranged units with sawn or rough surfaces [28]. The connection between leaves, in case of multi-leaf masonry, also influences the masonry behavior.