FRACTAL MODELS FOR THE FRAGMENTATION OF ROCKS AND SOILS - A REVIEW

Fragmentation, the process of breaking apart into fragments, is caused by the propagation of multiple fractures at different length scales. Such fractures can be induced by dynamic crack growth during compressi ve/tensile loading or by stress waves during impact loading. Fragmenta tion of rocks occurs in response to tectonic activity, percussive dril ling, grinding and blasting. Soil fragmentation is the result of tilla ge and planting operations. Fractal theory, which deals with the scali ng of hierarchical and irregular systems, offers new opportunities for modeling the fragmentation process. This paper reviews the literature on fractal models for the fragmentation of heterogeneous brittle eart h materials. Fractal models are available for the fragmentation of: (1 ) classical aggregates; (2) aggregates with fractal pore space; and (3 ) aggregates with fractal surfaces. In each case, the aggregates are c omposed of building blocks of finite size. Structural failure is hiera rchical in nature and takes place by multiple fracturing of the aggreg ated building blocks. The resulting number-size distribution of fragme nts depends on the probability of failure, P(1/b(i)), at each level in the hierarchy. Models for both scale-invariant and scale-dependent P( 1/b(i)) are reviewed. In the case of scale-invariant P(1/b(i))<1, theo ry predicts: D-f=3+log[P(1/b(i))]/log[b] for classical aggregates; D-f =D-m+log[P( 1/b(i))]/log[b] for aggregates with fractal pore space; an d D-f=D-s for aggregates with fractal surfaces, where b is a scaling f actor and D-f, D-m and D-s are the fragmentation, mass and surface fra ctal dimensions, respectively. The physical significance of these para meters. is discussed, methods of estimating them are reviewed, and top ics needing further research are identified. (C) 1997 Elsevier Science B.V.