Issue 51

M. Pepe et alii, Frattura ed Integrità Strutturale, 51 (2020) 504-516; DOI: 10.3221/IGF-ESIS.51.38 509 max T being the normal interfacial strength (assumed equal to the tangential one) and max  the maximum valued attained by the effective separation parameter: 2 2 s n n nc sc s n sc , 0 , 0                                (1.6) over the entire deformation history; finally,  is the friction function, defined as: 0.5 0 max 0 max , 1 , 1 s sc                (1.7) 0  being the friction coefficient. It is worth noting that the adopted friction function is different than that appearing in [46], due to the presence of an exponent (in this work set as 0.5, in general less than 1) applied to the dimensionless mode- II separation. This novel formulation is able to account for the rapid increase of friction forces between the two sides of masonry joints during its decohesion, coherently with what suggested in [51]. The adopted TSL is versatile, meaning that it can be applied in this form for any masonry type (with dry or mortar joints), characterized by a hybrid cohesive/frictional mechanical behavior. However, for masonries characterized by a dominant frictional behavior, as in the case of dry joints analyzed in this paper, the cohesive part of the TSL (1.4) tends to vanish, so that the adoption of the friction function (1.7) allows friction forces to develop up to their maximum value from the beginning of numerical simulations, i.e. at low separations between adjacent units. Figure 2 : Mixed-mode traction-separation and contact relations in normal (a) and tangential (b) directions on a cohesive interface. N UMERICAL R ESULTS n the following a discussion about comparison of results obtained with Limit Analysis, FEM and FEM/DEM is presented. The panels analyzed by Ferris and Tin-Loi [42] are chosen as benchmark. Authors performed analysis on structures characterized by different size and geometry, providing results in terms of associate and non-associate Limit Analysis. Details of all models are: blocks with full dimension 4x1.75 and half size dimension 2x1.75 and a friction ratio tan 0.65   . Fig. 3 shows the geometries considered by the authors. Example 1 (33 blocks) and Example 2 (55 blocks) are full panels with different ratio length over height, Example 3 (46 blocks) is a panel with an opening in the central part, Example 4 (55 blocks) is a panel with two horizontal openings, I