FRACTAL DAMAGE MECHANICS OF GEOMATERIALS

Recent progress in a new field of mechanics of diluted solids is reviewed -the fractal mechanics of geomaterials. It has become clear that the mechanics of geomaterials should take into consideration the influence of the fracture delocalization process on fundamental fracture characteristics such as the strength, the fractal dimension of a network of cracks, the surface energy of fracture and the elastic properties of fragmented media. The percolation model of fracture proposed by this author in 1979, in accordance with experimental data, treats the destruction process as a sequence of nucleation and coalescence of microcracks caused by their interaction. This approach enables the mathematical description of the entire process of fracturing. Many aspects of the fracture of heterogeneous solids - the magnitude-frequency distribution of seismic activity and acoustic emission, the high-surface energy of fracture in composite materials and rocks, the geometrical peculiarities of a crack network, the appearance of forerunners of mechanical collapse, and the intermittency of the fracture process in the time domain - find quantitative explanation in the percolation model. The process of determining the elasticity of fractured media, which is the object of the elastic percolation theory, also reveals some unusual features that can affect the process of geophysical interpretation. For example, the elastic modulus M and the velocity of elastic waves v become scale-dependent in the fractal regime. It is shown that the fractal dimension of the elastic modulus of a depleted solid differs significantly for 'refilled' and 'hollow' voids. Several implications of fractal mechanics for seismology are considered, namely the generalized form of the magnitude-frequency relationship, the phenomenon of anomalous tensosensitivity, the scale-dependence of the elastic moduli of massively faulted rocks and the possibility of apparent seismic boundaries.