The introduction of the "characteristic dimension" idea by Cuisiat & Haimson (1993) was an important step for the understanding of the causes of scale effects on the several rock mass properties. Subsequently Leal-Gomes (2000) introduced the idea of "hierarchy of heterogeneity". The "hierarchic organization of heterogeneity" or the "hierarchization of heterogeneity" is the gradation of heterogeneity, its arrangement and its functional disposition under the actual state of stress on the samples with reference to a given rock property. Through adequate exemplification the author shows that without hierarchic organization of heterogeneity there isn't any scale effect on rock mass properties. He analyses under this viewpoint the scale effects on the uniaxial compressive strength, on the uniaxial tensile strength, on the rock mass strength, on the deformability of rocks, on the hydraulic conductivity of joints and rock masses, on the internal stresses in rock masses and on the rock mass joint strength.
Charrua Graca (1985) has demonstrated that the scale effect in rock masses is a consequence of heterogeneity. Actually, this principle already is in Weibull's (1951) philosophy, which in the early XX century, proposed a function of statistical distribution initially intended for the study of strength of steel bars. This function shows the dependence of such strength on the tested volumes. The approach of the mechanics of fracturation pointed out the beginning of intact rock rupture at microcracks and microgaps. It was admitted in accordance with Weibull that the approach of the scale effect on strength demands the increasing of the probability of occurrence of at least one of these defects in the samples as the rock volumes increase. Therefore it was also accepted the doctrine which assets that strengths are reduced as sample dimensions grow. That is to say that the scale effects must be normal ones (represented by negative exponential regressions) and that the reverse or inverse scale effects (represented by positive exponential regressions) are due to spurious reasons which need to be understood (Figure 1). Of course the fact of the scale effects are normal or, on the contrary, reverse has enormous importance because if they are reverse the test values of small samples are on the safe side of engineering and if the scale effects are normal those test values of small samples will be on the unsafe side of engineering. However all these doctrines and deductions around Weibull's philosophy and the mechanics of fracturation only say that if there is one defect in a given volume the sample is broken, but if there aren't those defects, the sample resists. Actually, there is a hiatus between these formulations and some experimental observations, like the lack of scale effects on the tensile strength of samples tested under direct uniaxial tensile stresses (Haimson 1990), although the scale effects already be observed on tensile strength of the same rocks when these last values are obtained through brazilian tests. Besides, the reverse scale effects are much commoner than the above cited arguments suggest. Houpert (1970) and Jackson.
