抄録
Earthquakes are the result of fracture of the earth's material due to tectonic stress. The fracture of solids is preceded by the appearance of numerous microcracks which can propagate and coalesce. The state of the crack system is described by the size distribution function which satisfies an integro-differential kinetic equation. Under two different assumptions concerning the fusion cross-section, exponential and inverse-power solutions are deduced. The exponential form of the crack size distribution is observed in many damage experiments for metals but the inverse-power law is typical for more brittle materials like rocks. A second way of analysis of the evolution of crack populations is based on the division of all cracks into n groups, then a set of n nonlinear differential equations is obtained. This model is more handy for numerical calculations and was used for long-term evolution of the crack system.
