Size Dependence of Strength and Fracture Properties of Brick Masonry

The test data on the size effect in the failure of masonry walls and some parts of the discussion of size effect are valuable. However, the theoretical description of the size effect is in my opinion invalid. The use of the "multifractal scaling law" proposed earlier by the senior author is unjustified, for the same reasons as it is for concrete structures. The reasons are explained in detail in Bazant (1997a,b) and Bazant and Planas (1997). Briefly, one fault, in the discusser's opinion, is that the size effect caused by the release of energy from the structure is ignored, yet it must be taking place if the crack formed before maximum load is large compared with the dimensions of the structure. The explanation is that the energy released due to fracture increases with the structure size faster than the energy is consumed and dissipated by the fracture. The second fault, which is less obvious, is that the multifractal concept, in my opinion, could apply only if the fractures that cause failures of structures of different sizes were happening on different scales of the material-in other words, if the fracture of a large structure were decided by a crack longer than several brick sizes and the fracture of a small structure were decided by a crack in the layer of mortar in one brick joint, smaller than one brick size. In that case, the representative volumes of the relevant materials on the different scales would not be the same, and their different fractal dimensions could conceivably matter. However, in the discusser's opinion, this is not the case if one deals with masonry walls (or concrete structures) per se. The authors consider the macroscopic cracks in the masonry as a whole. It has been shown mathematically (BaZant 1997a; BaZant and Chen 1997; Bazant and Planas 1997) that if there is only one and the same material, which must inevitably be characterized by one and the same representative volume, the hypothesis of multifractality reduces to monofractality. The reason is that any material volume relevant to the failure of a larger structure can be subdivided into the representative volumes of the material considered for the smaller structure (by definition, or else one would not speak of the same material, masonry in this case). Consequently, in my opinion, the only conceivable (albeit still questionable) consequence of the hypothesis of fractality of fracture (whether lacunar or invasive) would be a power law scaling, which is represented by a straight line in the loglog plot rather than a curve of declining slope. Such scaling, however, implies the absence of any characteristic length (Bazant 1997b)-obviously untrue for masonry walls, in which the brick size imposes a finite characteristic length of the material. The test data of the authors could be equally well fitted by the quasi brittle size effect law based on energy release, which was initially proposed in Bazant (1984) and was in 1987 extended to a form with a finite large-size asymptotic value of nominal strength, exhibiting at larger sizes a positive curvature in the log-log plot of nominal strength versus the size.