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This paper describes the behavior of single rigid-block structures under dynamic loading. A comprehensive experimental investigation has been carried out to study the rocking response of four blue granite stones with different geometrical characteristics under free vibration, and harmonic and random motions of the base. In total, 275 tests on a shaking table were carried out in order to address the issues of repeatability of the results and stability of the rocking motion response. Two different tools for the numerical simulations of the rocking motion of rigid blocks are considered. The first tool is analytical and overcomes the usual limitations of the traditional piecewise equations of motion through a Lagrangian formalism. The second tool is based on the discrete element method (DEM), especially effective for the numerical modeling of rigid blocks. A new methodology is proposed for finding the parameters of the DEM by using the parameters of the classical theory. An extensive comparison between numerical and experimental data has been carried out to validate and define the limitations of the analytical tools under study. Discrete element methodDEM can be considered as a method for modeling discontinuous media. This analysis technique allows relative motion between elements, which is especially suitable for problems in which the

Masonry is a composite material made of units (brick, blocks, etc.) and mortar. For periodic arrangements of the units, the homogenisation techniques represent a powerful tool for structural analysis. The main problem pending is the errors introduced in the homogenisation process when large difference in stiffness are expected for the two components. This issue is obvious in the case of non-linear analysis, where the tangent stiffness of one component or the tangent stiffness of the two components tends to zero with increasing inelastic behaviour. The paper itself does not concentrate on the issue of non-linear homogenisation. But as the accuracy of the model is assessed for an increasing ratio between the stiffness of the two components, the benefits of adopting the proposed method for non-linear analysis are demonstrated. Therefore, the proposed model represents a major step in the application of homogenisation techniques for masonry structures. The micro-mechanical model presented has been derived from the actual deformations of the basic cell and includes additional internal deformation modes, with regard to the standard two-step homogenisation procedure. These mechanisms, which result from the staggered alignment of the units in the composite, are of capital importance for the global response. For the proposed model, it is shown that, up to a stiffness ratio of one thousand, the maximum error in the calculation of the homogenised Young's moduli is lower than five percent. It is also shown that the anisotropic failure surface obtained from the homogenised model seems to represent well experimental results available in the literature.

This paper addresses the usage of a simplified homogenization technique for the analysis of masonry subjected to out-of-plane loading. The anisotropic failure surface, based on the definition of a polynomial representation of the stress tensor components in a finite number of sub-domains, is combined with finite element triangular elements employed for the upper and lower bound limit analyses. Several comparisons between the proposed model and experimental data available in the literature are presented, for wallettes subjected to bending at different orientations and for different panels loaded out-of-plane. The limit analysis results allow to identify the distribution of internal forces at critical sections and to obtain the collapse modes, as well as the failure loads. Excellent results are found in all cases, indicating that the proposed simple tool is adequate for the safety assessment of out-of-plane loaded masonry panels. The combined usage of upper and lower bound approaches, and their respective simplifications, allow to define a narrow interval for the real collapse load.