Issue 46

L.U. Argiento et alii, Frattura ed Integrità Strutturale, 46 (2018) 226-239; DOI: 10.3221/IGF-ESIS.46.21 237 Moreover, for the proposed macro-block model, a doubled value of the unit shape ratio m , accounted by Sets 13 and 14 (Tab. 7), involves a reduction of the load factor to about half. The values obtained, on the other hand, exactly coincide with those obtained from the micro-block model. The macro-block models of Orduña and Speranza confirm the same trend with little percentage differences with respect to the micro-block model. The model of De Buhan and de Felice, instead, is less sensible to the parameter m and its percentage variation with respect to the micro-block model is more evident. All the models, however, highlight the same trend, i.e. the load factor decreases as the unit shape ratio m increases. This trend can be explained with the reduction of the frictional resistances due to reduction of the overlapping length of the unit blocks. Thus, summarizing the mentioned results related to a single-storey wall, it arises that the proposed model together with the model of Speranza [28] are more reliable with respect to the other accounted macro-block models, since they provide limited percentage differences with respect to the micro-block model of Orduña [20], assumed as a reference. These results are also better displayed in Fig. 5. Figure 5 : Load factors provided by the literature vs. the proposed macro-block model. As previously anticipated, with reference to multi-storey walls the proposed model is comparable only with that developed by Speranza [28], since the other macro-block models do not account for this case. Thus, the results related to Sets 15, 16, 17 are reported in Tab. 9. It emerges that while the load factor of the proposed model is not influenced by the parameter p accounting for the overloading, that provided by Speranza [28] decreases with increasing p . This trend of the latter model is mainly due to the absence of the contribution F q of the frictional resistance which therefore cannot counteract the overturning moment of the increasing overloading, as is possible with the proposed model. C ONCLUSIONS n this work, the mixed rocking-sliding mechanism of multi-storey walls due to in-plane horizontal actions has been analyzed; to this aim, a macro-block model has been adopted, schematizing the geometry of the mechanism through a single crack line where the frictional resistances and the relative displacements between the macro-blocks are concentrated. Hence, the kinematic approach of limit analysis has been used to evaluate the inclination of the crack line and the position of the rotational hinge along the height of the wall, assuming that it is always located in correspondence of the floor levels. With such a purpose, a routine of minimization of the load factor related to each possible position has been implemented, comparing the results in order to choose the minimum value. The innovative aspect of the study is mainly related to the modelling of the resultant frictional resistance involved in a mixed mechanism with rocking and sliding; in fact, a criterion, based on the inclination angle of the crack line, is adopted, under the assumption of Coulomb I