an orthotropic continuum model for the analysis of masonry structures

TNO-95-NM-R0712 1995 33The explanation for the over prediction of the failure load will now be detailed. Fig. 25a shows thatthe experimental load-displacement diagram is well reproduced until a horizontal displacement dequal to 1.0 mm, which coincides with the opening of the diagonal shear crack. After this point, itseems that the behaviour of the structure is not captured by the model. The crucial question iswhether the masonry macro-model here proposed is not acceptable or the modelling strategy isinadequate. The author believes the latter to be true.Fig. 24 clearly shows an extremely localized diagonal failure type in which all inelastic phenomenaconcentrate, basically, in a single stepped crack. A complete understanding of the behaviour of thestructure is obtained by the distribution of internal forces calculated by the micro-model, see Fig.33. Fig. 33a shows that, initially, the direction of the compressive strut is determined by the geometryof the bricks and deviates from the strut direction found in the macro-analysis. The discrepancybetween the micro- and macro-model gets only larger under increasing deformation. Fig. 33bshows that in reality two independent struts occur once the diagonal crack is fully open and a welldeÞned band completely unloads, with approximately the width of a brick at the center of the specimen.This phenomenon cannot be captured by a (smeared) macro-model unless some internallength scale, that reßects the masonry micro-structure, is incorporated in the model. This problemis outside the scope of the present report and, presently, no simple solution is envisaged. It is notedthat the task is quite complex because it is not clear yet if the above length scale is a geometricalproperty dependent on the unit size or a structural property that depends on the micro-structure,geometry of the structure and loading conditions.a) d = 1.0 mm d) d = 4.0 mmFig. 33 - Minimum principal stresses for a horizontal displacement d obtained by a micro-modelLouren•o (1994)For the sake of completeness a new analysis is carried out with the macro-model formulated insuch a way that degradation of tensile strength induces degradation of compressive strength, i.e. acoupled model. Coupling is introduced via an equation of the following type: