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It is shown that the phenomenon of strength dependence on size, for otherwise geometrically similar specimens, may be interpreted on the basis of gradient elasticity or multifractal scaling law arguments. This paper compares the predictions of these two different approaches to the scaling properties of the compressive strength in disordered materials. A detailed study for the stress concentration factor and the normalized failure stress of the borehole axisymmetric plane strain problem is presented. This problem has been already solved analytically by using a simple form of gradient elasticity theory. However the solution was not explored sufficiently to illustrate the size effect in a bilogarithmic diagram. By doing this the predictions of gradient elasticity can be related to the predictions of the multifractal scaling law. A comparison between the two mentioned approaches is presented and a common denominator is found.

Multifractal Scaling Law Versus Gradient Elasticity in the Evaluation of Disordered Materials Compressive Strength