Multilevel Model of Cleavage Fracture in Brittle Rocks in Compression

Abstract

This study proposes a mathematical fracture model including processes of fracture of structural bonds on micro scale (tens microns) and meso scale (millimeters and centimeters), as well as interaction of structural fragments on macro scale (fractures longer then tens centimeters). The model uses two geometrical criteria of fracture growth, connected with the structure of rocks and governing transition between structural scale. The problem on the stress–strain behavior of an elastic medium near a fracture at the change in the fracture length and in the scale of its influence is solved. The limit equilibrium of a fracture is analyzed. For a meso-scale fracture, such condition is unstable, and the fracture, therefore, develops dynamically and up to a macro scale. Sufficiently long macro fractures can grow in the mode of quasi statics due to independent advance of fracture tips.