Issue 46

L.U. Argiento et alii, Frattura ed Integrità Strutturale, 46 (2018) 226-239; DOI: 10.3221/IGF-ESIS.46.21 238 dry frictional contact with non-associated flow rule. This criterion, experimentally and numerically validated in previous works is now generalized to the analysis of a multi-storey masonry wall. A numerical analysis has been performed in order to test the sensitivity of the proposed model to the main geometrical parameters, as the shape ratios related to the wall and unit block and the number of rows; the overloading condition and the friction coefficient have been also taken into account. The analysis has highlighted that the overloading ratio and the number of rows are substantially irrelevant both on the load factor and the inclination angle  c of the crack line; the unit shape ratio m , instead, influences both these parameters that result decreasing with increasing values of m . Moreover, the wall shape ratio t , has a key role in the rocking-sliding mechanism of a slender multi-storey wall ( t > 1) while it is quite irrelevant for squat walls ( t <1). In the first case, in fact, increasing values of t imply increasing slenderness of the wall and decreasing load factors  . This parameter, instead, results increasing with increasing values of the friction coefficient, as expected. Lastly, the proposed model has been validated through the comparison against a micro-block and other macro-block models existing in the literature. The comparison has been performed in terms of both the load factor and the failure mode and with reference to key parameters as wall shape ratio, unit shape ratio, number of rows and overloading condition. It emerged that the proposed model provides results very close to the micro-block model, assumed as a reference, and can approach the “exact” solutions much better than the other compared macro-block models. These results can be very promising because can be obtained with lower computational effort than the micro-block modelling approaches, suggesting the possibility of using the proposed model also for extensive evaluations of the vulnerability of the ancient urban centres. A CKNOWLEDGMENTS he authors acknowledge the sponsorship of the Italian Civil Protection, through the RELUIS Project-Line: Masonry Structures (2018). R EFERENCES [1] Page, A.W. (1981). The biaxial compressive strength of brick masonry, P. I. Civil Eng. Pt. 1, 71 (2), pp. 893-906. [2] Mann, W. and Muller, H. (1982). Failure of shear-stressed masonry. An enlarged theory, tests and application to shear walls, P. Brit. Ceramic Soc., 30, pp. 223-235. [3] Dialer, C. (1991). Some remarks on the strength and deformation behaviour of shear stressed masonry panels under static monotonic loading, Proc. 9th International Brick/Block Masonry Conference, Berlin (Germany), pp. 276-283. [4] Ceradini, V. (1992). Models and experimental tests for the study of historical masonry, Ph.D. Thesis., University of Roma La Sapienza, Roma, Italy. [5] Roca, P., Cervera, M., Gariup, G. and Pelà, L. (2010). Structural Analysis of Masonry Historical Constructions. Classical and Advanced Approaches, Arch. Comput. Methods Eng., 17, pp. 299-325. DOI: 10.1007/s11831-010-9046-1. [6] Bui, T.T., Limam, A., Sarhosis, V. and Hjiaj, M. (2017). Discrete element modelling of the in plane and out of plane behaviour of dry joint masonry wall constructions, Eng. Struct., 136, pp. 277-94. DOI: 10.1016/j.engstruct.2017.01.020. [7] Cannizzaro, F., Pantò, B., Caddemi, S. and Caliò, I. (2018). A Discrete Macro-Element Method (DMEM) for the nonlinear structural assessment of masonry arches, Eng. Struct., 168, pp. 243-256. DOI: 10.1016/j.engstruct.2018.04.006. [8] Gilbert, M., Casapulla, C. and Ahmed, H.M. (2006). Limit analysis of masonry block structures with non-associative frictional joints using linear programming, Comput. Struct., 84(13-14), pp. 873-87. DOI: 10.1016/j.compstruc.2006.02.005. [9] Mousavian, E. and Mehdizadeh Saradj, F. (2018). Automated detailing and stability analysis of under-construction masonry vaults, J. Archit. Eng. ASCE 24(3), art. no. 04018014. DOI: 10.1061/(ASCE)AE.1943-5568.0000314. [10] Silva, L.C., Lourenço, P.B. and Milani, G. (2017). Nonlinear discrete homogenized model for out-of-plane loaded masonry walls, J. Struct. Eng.-ASCE, 143(9), art. no. 04017099. DOI: 10.1061/(ASCE)ST.1943-541X.0001831. T