The relation of nonequilibrium thermodynamics to some failure and fracture theories of rock mechanics is investigated. The basic concepts are given to connect failure to the properties of material equations describing the elastic properties. The resulted in thermodynamic conditions are proved to be compatible with classical localization and failure theories of solid materials. Compatibility with experiments and some empirical, adhoc failure criteria of rocks is also demonstrated.
In continuum physical theories the complex mechanical properties of material are described by constitutive functions. One of the basic construction methods to get reasonable constitutive functions is based on the Second Law of thermodynamics. The material equations have to be compatible with the Second Law in every system where dissipation occurs, including fracture and failure of rock materials, too. Here (of course) thermodynamics is understood not only as a theory to deal with thermal phenomena and temperature changes, but as the theory dealing with the stability of materials. In this respect Second Law is understood as a requirement of stability, restricting the possible material equations of all media.
In rock mechanics the pure mechanical properties are modeled by continuum mechanical methods, and even the violations of material stability are understood in most cases as pure mechanical phenomena using fracture mechanics as modeling tool. Fracture mechanics deals with holes (cracks) and discontinuities embedded in an ideal mechanical continuum. Several works use statistical methods to understand the interaction and interlocking of cracks in the mechanical continuum. In rocks damage processes include not only microcracking and interlocking of cracks but several other different mechanisms, therefore the applicability of this kind of statistical considerations is questionable. To understand the appearing broad range of different phenomena requires to apply different phenomenological methods and to understand, in what sense could be the different approaches unified. Some new developments in modern nonequilibrium thermodynamics give a hope to deepen our understanding of the role of the Second Law in mechanical modeling and to extend the existing models to give simple descriptions of several related phenomena. Failure and change of elastic properties are treated as independent phenomena in mechanics.
The situation is similar in the theories of plasticity, where the yield criteria is considered to be independent on elastic properties of the material (but not independent on the Second Law). Continuum damage mechanics (see e.g. Krajcinovic 1996) is a theory motivated by the need of unification of failure and nonlinear elasticity. The original idea is that growing damage can lead to failure. However, after some initial attempt the researchers in damage mechanics gave up to find a theoretical connection and nowadays the damage surfaces (critical damage) are given independently on the change of mechanic properties.
In this short paper we will show that a connection can be found, if the foundations of the underlying nonequilibrium thermodynamic theories are investigated. Failure and fracture can be considered as a kind of material instability. Moreover, we can use similar concepts and Inethods to the case of phase transitions in fluid and gaseous bodies. As particular applications we will show how the classical Griffith concept (and all the so called energy methods) includes thermodynamic instability and show, how other specific rock mechanical failure criteria can be understood as violation of thermodynamic stability. At the end a thermodynamic improvement of the empirical criteria
