A Thermodynamic Basis for Static and Dynamic Scaling Laws in the Design of Structures in Rock

ABSTRACT: Brittle fracture is modeled as a phase change that exhibits the characteristics of a thermodynamic system at its critical point. Universality and critical scaling are shown to exist in brittle materials at incipient failure. The law of corresponding states, which applies to fluid and magnetic systems, applies to brittle fracture. Several critical exponents are calculated and compared with observation. The Griffith theory of fracture is shown to correspond exactly to Landau mean field theory for continuous phase transitions. Applied to failure of geotechnical materials, the widely used empirical Hoek-Brown type failure criterion when written in shear stress (t) versus normal stress (s) space is derived using the commonly used critical exponent of ß = 0.33.